From a2d4ba6a05bb9a51da2581a33c28f05f2f298ad3 Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Mon, 1 Apr 2024 05:46:41 +0000 Subject: [PATCH] build based on cade202 --- dev/api/index.html | 2 +- dev/assets/themes/documenter-dark.css | 7699 +---------------------- dev/assets/themes/documenter-light.css | 7733 +----------------------- dev/cca/index.html | 4 +- dev/fa/index.html | 2 +- dev/ica/index.html | 2 +- dev/index.html | 2 +- dev/lda/index.html | 448 +- dev/lreg/index.html | 176 +- dev/mds/index.html | 248 +- dev/pca/index.html | 256 +- dev/search/index.html | 2 +- dev/search_index.js | 2 +- dev/whiten/index.html | 2 +- 14 files changed, 577 insertions(+), 16001 deletions(-) diff --git a/dev/api/index.html b/dev/api/index.html index bee280f..fae5295 100644 --- a/dev/api/index.html +++ b/dev/api/index.html @@ -1,2 +1,2 @@ -Development · MultivariateStats.jl
Edit on GitHub

API Reference

Current

Table of the package models and corresponding function names used by these models.

Function \ ModelCCAWHTICALDAFAPPCAPCAKPCAMDS
fitxxxxxxxxx
transformxxxxxxxxx
predictx
indimxxxxxxxx
outdimxxxxxxxxx
meanxxxxxxx?
varxx???
covx?
corx
projectionxxxxxx
reconstructxxxx
loadings??xx???
eigvals????x
eigvecs?????
length
size

Note: ? refers to a possible implementation that is missing or called differently.

New

Function \ ModelWHTCCALDAMC-LDASS-LDAICAFAPPCAPCAKPCAMDS
fitxxxxxxxxxxx
transformx-----xx---
predict+x++++++
indim----xx---
outdim-----xx---
meanxxxxxxxx
varxxx?
covxx
cor+
projection?xxxxxxxx
reconstructxxxx
loadingsxxx+
eigvals+??xxx
eigvecs??x++
length++++
size+++++x++
  • StatsBase.AbstractDataTransform
    • Whitening
      • Interface: fit, transform
      • New: length, mean, size
  • StatsBase.RegressionModel
    • Interface: fit, predict
    • LinearDiscriminant
      • Functions: coef, dof, weights, evaluate, length
    • MulticlassLDA
      • Functions: size, mean, projection, length
    • SubspaceLDA
      • Functions: size, mean, projection, length, eigvals
    • CCA
      • Functions: size, mean, projection, predict, cor
    • Subtypes:
      • AbstractDimensionalityReduction
        • Interface: projection, var, reconstruct, loadings
        • Interface: projection == weights
      • Subtypes:
        • LinearDimensionalityReduction
          • Methods: ICA, PCA
        • NonlinearDimensionalityReduction
          • Methods: KPCA, MDS
            • Functions: modelmatrix(X),
        • LatentVariableModel or LatentVariableDimensionalityReduction
          • Methods: FA, PPCA
            • Functions: cov
+Development · MultivariateStats.jl
Edit on GitHub

API Reference

Current

Table of the package models and corresponding function names used by these models.

Function \ ModelCCAWHTICALDAFAPPCAPCAKPCAMDS
fitxxxxxxxxx
transformxxxxxxxxx
predictx
indimxxxxxxxx
outdimxxxxxxxxx
meanxxxxxxx?
varxx???
covx?
corx
projectionxxxxxx
reconstructxxxx
loadings??xx???
eigvals????x
eigvecs?????
length
size

Note: ? refers to a possible implementation that is missing or called differently.

New

Function \ ModelWHTCCALDAMC-LDASS-LDAICAFAPPCAPCAKPCAMDS
fitxxxxxxxxxxx
transformx-----xx---
predict+x++++++
indim----xx---
outdim-----xx---
meanxxxxxxxx
varxxx?
covxx
cor+
projection?xxxxxxxx
reconstructxxxx
loadingsxxx+
eigvals+??xxx
eigvecs??x++
length++++
size+++++x++
  • StatsBase.AbstractDataTransform
    • Whitening
      • Interface: fit, transform
      • New: length, mean, size
  • StatsBase.RegressionModel
    • Interface: fit, predict
    • LinearDiscriminant
      • Functions: coef, dof, weights, evaluate, length
    • MulticlassLDA
      • Functions: size, mean, projection, length
    • SubspaceLDA
      • Functions: size, mean, projection, length, eigvals
    • CCA
      • Functions: size, mean, projection, predict, cor
    • Subtypes:
      • AbstractDimensionalityReduction
        • Interface: projection, var, reconstruct, loadings
        • Interface: projection == weights
      • Subtypes:
        • LinearDimensionalityReduction
          • Methods: ICA, PCA
        • NonlinearDimensionalityReduction
          • Methods: KPCA, MDS
            • Functions: modelmatrix(X),
        • LatentVariableModel or LatentVariableDimensionalityReduction
          • Methods: FA, PPCA
            • Functions: cov
diff --git a/dev/assets/themes/documenter-dark.css b/dev/assets/themes/documenter-dark.css index 0bf1af7..c94a294 100644 --- a/dev/assets/themes/documenter-dark.css +++ b/dev/assets/themes/documenter-dark.css @@ -1,7702 +1,7 @@ -@charset "UTF-8"; -/* Font Awesome 5 mixin. 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font-size: 1.25rem !important; } - .is-size-6-widescreen { - font-size: 15px !important; } - .is-size-7-widescreen { - font-size: 0.85em !important; } } - -@media screen and (min-width: 1408px) { - .is-size-1-fullhd { - font-size: 3rem !important; } - .is-size-2-fullhd { - font-size: 2.5rem !important; } - .is-size-3-fullhd { - font-size: 2rem !important; } - .is-size-4-fullhd { - font-size: 1.5rem !important; } - .is-size-5-fullhd { - font-size: 1.25rem !important; } - .is-size-6-fullhd { - font-size: 15px !important; } - .is-size-7-fullhd { - font-size: 0.85em !important; } } - -.has-text-centered { - text-align: center !important; } - -.has-text-justified { - text-align: justify !important; } - -.has-text-left { - text-align: left !important; } - -.has-text-right { - text-align: right !important; } - -@media screen and (max-width: 768px) { - .has-text-centered-mobile { - text-align: center !important; } } - -@media screen and (min-width: 769px), print { - .has-text-centered-tablet { 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background-color: #f2f2f2; } - html.theme--documenter-dark .button.is-black.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted { - background-color: white; - border-color: transparent; - box-shadow: none; - color: #0a0a0a; } - html.theme--documenter-dark .button.is-black.is-loading::after { - border-color: transparent transparent white white !important; } - html.theme--documenter-dark .button.is-black.is-outlined { - background-color: transparent; - border-color: #0a0a0a; - color: #0a0a0a; } - html.theme--documenter-dark .button.is-black.is-outlined:hover, html.theme--documenter-dark .button.is-black.is-outlined.is-hovered, html.theme--documenter-dark .button.is-black.is-outlined:focus, html.theme--documenter-dark .button.is-black.is-outlined.is-focused { - background-color: #0a0a0a; - border-color: #0a0a0a; - color: white; } - html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after { - border-color: transparent transparent #0a0a0a #0a0a0a !important; } - html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent white white !important; } - html.theme--documenter-dark .button.is-black.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined { - background-color: transparent; - border-color: #0a0a0a; - box-shadow: none; - color: #0a0a0a; } - html.theme--documenter-dark .button.is-black.is-inverted.is-outlined { - background-color: transparent; - border-color: white; - color: white; } - html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused { - background-color: white; - color: #0a0a0a; } - html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #0a0a0a #0a0a0a !important; } - html.theme--documenter-dark .button.is-black.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted.is-outlined { - background-color: transparent; - border-color: white; - box-shadow: none; - color: white; } - html.theme--documenter-dark .button.is-light { - background-color: #ecf0f1; - border-color: transparent; - color: #282f2f; } - html.theme--documenter-dark .button.is-light:hover, html.theme--documenter-dark .button.is-light.is-hovered { - background-color: #e5eaec; - border-color: transparent; - color: #282f2f; } - html.theme--documenter-dark .button.is-light:focus, html.theme--documenter-dark .button.is-light.is-focused { - border-color: transparent; - color: #282f2f; } - html.theme--documenter-dark .button.is-light:focus:not(:active), html.theme--documenter-dark .button.is-light.is-focused:not(:active) { - box-shadow: 0 0 0 0.125em rgba(236, 240, 241, 0.25); } - html.theme--documenter-dark .button.is-light:active, html.theme--documenter-dark .button.is-light.is-active { - background-color: #dde4e6; - border-color: transparent; - color: #282f2f; } - html.theme--documenter-dark .button.is-light[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-light { - background-color: #ecf0f1; - border-color: transparent; - box-shadow: none; } - html.theme--documenter-dark .button.is-light.is-inverted { - background-color: #282f2f; - color: #ecf0f1; } - html.theme--documenter-dark .button.is-light.is-inverted:hover, html.theme--documenter-dark .button.is-light.is-inverted.is-hovered { - background-color: #1d2122; } - html.theme--documenter-dark .button.is-light.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted { - background-color: #282f2f; - border-color: transparent; - box-shadow: none; - color: #ecf0f1; } - html.theme--documenter-dark .button.is-light.is-loading::after { - border-color: transparent transparent #282f2f #282f2f !important; } - html.theme--documenter-dark .button.is-light.is-outlined { - background-color: transparent; - border-color: #ecf0f1; - color: #ecf0f1; } - html.theme--documenter-dark .button.is-light.is-outlined:hover, html.theme--documenter-dark .button.is-light.is-outlined.is-hovered, html.theme--documenter-dark .button.is-light.is-outlined:focus, html.theme--documenter-dark .button.is-light.is-outlined.is-focused { - background-color: #ecf0f1; - border-color: #ecf0f1; - color: #282f2f; } - html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after { - border-color: transparent transparent #ecf0f1 #ecf0f1 !important; } - html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #282f2f #282f2f !important; } - html.theme--documenter-dark .button.is-light.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined { - background-color: transparent; - border-color: #ecf0f1; - box-shadow: none; - color: #ecf0f1; } - html.theme--documenter-dark .button.is-light.is-inverted.is-outlined { - background-color: transparent; - border-color: #282f2f; - color: #282f2f; } - html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused { - background-color: #282f2f; - color: #ecf0f1; } - html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #ecf0f1 #ecf0f1 !important; } - html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined { - background-color: transparent; - border-color: #282f2f; - box-shadow: none; - color: #282f2f; } - html.theme--documenter-dark .button.is-dark, html.theme--documenter-dark .content kbd.button { - background-color: #282f2f; - border-color: transparent; - color: #ecf0f1; } - html.theme--documenter-dark .button.is-dark:hover, html.theme--documenter-dark .content kbd.button:hover, html.theme--documenter-dark .button.is-dark.is-hovered, html.theme--documenter-dark .content kbd.button.is-hovered { - background-color: #232829; - border-color: transparent; - color: #ecf0f1; } - html.theme--documenter-dark .button.is-dark:focus, html.theme--documenter-dark .content kbd.button:focus, html.theme--documenter-dark .button.is-dark.is-focused, html.theme--documenter-dark .content kbd.button.is-focused { - border-color: transparent; - color: #ecf0f1; } - html.theme--documenter-dark .button.is-dark:focus:not(:active), html.theme--documenter-dark .content kbd.button:focus:not(:active), html.theme--documenter-dark .button.is-dark.is-focused:not(:active), html.theme--documenter-dark .content kbd.button.is-focused:not(:active) { - box-shadow: 0 0 0 0.125em rgba(40, 47, 47, 0.25); } - html.theme--documenter-dark .button.is-dark:active, html.theme--documenter-dark .content kbd.button:active, html.theme--documenter-dark .button.is-dark.is-active, html.theme--documenter-dark .content kbd.button.is-active { - background-color: #1d2122; - border-color: transparent; - color: #ecf0f1; } - html.theme--documenter-dark .button.is-dark[disabled], html.theme--documenter-dark .content kbd.button[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-dark, fieldset[disabled] html.theme--documenter-dark .content kbd.button { - background-color: #282f2f; - border-color: transparent; - box-shadow: none; } - html.theme--documenter-dark .button.is-dark.is-inverted, html.theme--documenter-dark .content kbd.button.is-inverted { - background-color: #ecf0f1; - color: #282f2f; } - html.theme--documenter-dark .button.is-dark.is-inverted:hover, html.theme--documenter-dark .content kbd.button.is-inverted:hover, html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered, html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered { - background-color: #dde4e6; } - html.theme--documenter-dark .button.is-dark.is-inverted[disabled], html.theme--documenter-dark .content kbd.button.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted, fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted { - background-color: #ecf0f1; - border-color: transparent; - box-shadow: none; - color: #282f2f; } - html.theme--documenter-dark .button.is-dark.is-loading::after, html.theme--documenter-dark .content kbd.button.is-loading::after { - border-color: transparent transparent #ecf0f1 #ecf0f1 !important; } - html.theme--documenter-dark .button.is-dark.is-outlined, html.theme--documenter-dark .content kbd.button.is-outlined { - background-color: transparent; - border-color: #282f2f; - color: #282f2f; } - html.theme--documenter-dark .button.is-dark.is-outlined:hover, html.theme--documenter-dark .content kbd.button.is-outlined:hover, html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered, html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered, html.theme--documenter-dark .button.is-dark.is-outlined:focus, html.theme--documenter-dark .content kbd.button.is-outlined:focus, html.theme--documenter-dark .button.is-dark.is-outlined.is-focused, html.theme--documenter-dark .content kbd.button.is-outlined.is-focused { - background-color: #282f2f; - border-color: #282f2f; - color: #ecf0f1; } - html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after { - border-color: transparent transparent #282f2f #282f2f !important; } - html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #ecf0f1 #ecf0f1 !important; } - html.theme--documenter-dark .button.is-dark.is-outlined[disabled], html.theme--documenter-dark .content kbd.button.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined, fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined { - background-color: transparent; - border-color: #282f2f; - box-shadow: none; - color: #282f2f; } - html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined { - background-color: transparent; - border-color: #ecf0f1; - color: #ecf0f1; } - html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused { - background-color: #ecf0f1; - color: #282f2f; } - html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #282f2f #282f2f !important; } - html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled], html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined, fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined { - background-color: transparent; - border-color: #ecf0f1; - box-shadow: none; - color: #ecf0f1; } - html.theme--documenter-dark .button.is-primary, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink { - background-color: #375a7f; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .button.is-primary:hover, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-hovered.docs-sourcelink { - background-color: #335476; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .button.is-primary:focus, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:focus, html.theme--documenter-dark .button.is-primary.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-focused.docs-sourcelink { - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .button.is-primary:focus:not(:active), html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:focus:not(:active), html.theme--documenter-dark .button.is-primary.is-focused:not(:active), html.theme--documenter-dark .docstring > section > a.button.is-focused.docs-sourcelink:not(:active) { - box-shadow: 0 0 0 0.125em rgba(55, 90, 127, 0.25); } - html.theme--documenter-dark .button.is-primary:active, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:active, html.theme--documenter-dark .button.is-primary.is-active, html.theme--documenter-dark .docstring > section > a.button.is-active.docs-sourcelink { - background-color: #2f4d6d; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .button.is-primary[disabled], html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-primary, fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink { - background-color: #375a7f; - border-color: transparent; - box-shadow: none; } - html.theme--documenter-dark .button.is-primary.is-inverted, html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink { - background-color: #fff; - color: #375a7f; } - html.theme--documenter-dark .button.is-primary.is-inverted:hover, html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-inverted.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-hovered.docs-sourcelink { - background-color: #f2f2f2; } - html.theme--documenter-dark .button.is-primary.is-inverted[disabled], html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-inverted, fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink { - background-color: #fff; - border-color: transparent; - box-shadow: none; - color: #375a7f; } - html.theme--documenter-dark .button.is-primary.is-loading::after, html.theme--documenter-dark .docstring > section > a.button.is-loading.docs-sourcelink::after { - border-color: transparent transparent #fff #fff !important; } - html.theme--documenter-dark .button.is-primary.is-outlined, html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink { - background-color: transparent; - border-color: #375a7f; - color: #375a7f; } - html.theme--documenter-dark .button.is-primary.is-outlined:hover, html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-outlined.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-hovered.docs-sourcelink, html.theme--documenter-dark .button.is-primary.is-outlined:focus, html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink:focus, html.theme--documenter-dark .button.is-primary.is-outlined.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-focused.docs-sourcelink { - background-color: #375a7f; - border-color: #375a7f; - color: #fff; } - html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink::after { - border-color: transparent transparent #375a7f #375a7f !important; } - html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:hover::after, html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after, html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:focus::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:focus::after, html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after { - border-color: transparent transparent #fff #fff !important; } - html.theme--documenter-dark .button.is-primary.is-outlined[disabled], html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-outlined, fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink { - background-color: transparent; - border-color: #375a7f; - box-shadow: none; - color: #375a7f; } - html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink { - background-color: transparent; - border-color: #fff; - color: #fff; } - html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined:hover, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-hovered.docs-sourcelink, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined:focus, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:focus, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-focused.docs-sourcelink { - background-color: #fff; - color: #375a7f; } - html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:hover::after, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-hovered.docs-sourcelink::after, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after { - border-color: transparent transparent #375a7f #375a7f !important; } - html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined[disabled], html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined, fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink { - background-color: transparent; - border-color: #fff; - box-shadow: none; - color: #fff; } - html.theme--documenter-dark .button.is-link { - background-color: #1abc9c; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .button.is-link:hover, html.theme--documenter-dark .button.is-link.is-hovered { - background-color: #18b193; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .button.is-link:focus, html.theme--documenter-dark .button.is-link.is-focused { - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .button.is-link:focus:not(:active), html.theme--documenter-dark .button.is-link.is-focused:not(:active) { - box-shadow: 0 0 0 0.125em rgba(26, 188, 156, 0.25); } - html.theme--documenter-dark .button.is-link:active, html.theme--documenter-dark .button.is-link.is-active { - background-color: #17a689; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .button.is-link[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-link { - background-color: #1abc9c; - border-color: transparent; - box-shadow: none; } - html.theme--documenter-dark .button.is-link.is-inverted { - background-color: #fff; - color: #1abc9c; } - html.theme--documenter-dark .button.is-link.is-inverted:hover, html.theme--documenter-dark .button.is-link.is-inverted.is-hovered { - background-color: #f2f2f2; } - html.theme--documenter-dark .button.is-link.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted { - background-color: #fff; - border-color: transparent; - box-shadow: none; - color: #1abc9c; } - html.theme--documenter-dark .button.is-link.is-loading::after { - border-color: transparent transparent #fff #fff !important; } - html.theme--documenter-dark .button.is-link.is-outlined { - background-color: transparent; - border-color: #1abc9c; - color: #1abc9c; } - html.theme--documenter-dark .button.is-link.is-outlined:hover, html.theme--documenter-dark .button.is-link.is-outlined.is-hovered, html.theme--documenter-dark .button.is-link.is-outlined:focus, html.theme--documenter-dark .button.is-link.is-outlined.is-focused { - background-color: #1abc9c; - border-color: #1abc9c; - color: #fff; } - html.theme--documenter-dark .button.is-link.is-outlined.is-loading::after { - border-color: transparent transparent #1abc9c #1abc9c !important; } - html.theme--documenter-dark .button.is-link.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-link.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #fff #fff !important; } - html.theme--documenter-dark .button.is-link.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-link.is-outlined { - background-color: transparent; - border-color: #1abc9c; - box-shadow: none; - color: #1abc9c; } - html.theme--documenter-dark .button.is-link.is-inverted.is-outlined { - background-color: transparent; - border-color: #fff; - color: #fff; } - html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-focused { - background-color: #fff; - color: #1abc9c; } - html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #1abc9c #1abc9c !important; } - html.theme--documenter-dark .button.is-link.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted.is-outlined { - background-color: transparent; - border-color: #fff; - box-shadow: none; - color: #fff; } - html.theme--documenter-dark .button.is-info { - background-color: #024c7d; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .button.is-info:hover, html.theme--documenter-dark .button.is-info.is-hovered { - background-color: #024470; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .button.is-info:focus, html.theme--documenter-dark .button.is-info.is-focused { - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .button.is-info:focus:not(:active), html.theme--documenter-dark .button.is-info.is-focused:not(:active) { - box-shadow: 0 0 0 0.125em rgba(2, 76, 125, 0.25); } - html.theme--documenter-dark .button.is-info:active, html.theme--documenter-dark .button.is-info.is-active { - background-color: #023d64; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .button.is-info[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-info { - background-color: #024c7d; - border-color: transparent; - box-shadow: none; } - html.theme--documenter-dark .button.is-info.is-inverted { - background-color: #fff; - color: #024c7d; } - html.theme--documenter-dark .button.is-info.is-inverted:hover, html.theme--documenter-dark .button.is-info.is-inverted.is-hovered { - background-color: #f2f2f2; } - html.theme--documenter-dark .button.is-info.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted { - background-color: #fff; - border-color: transparent; - box-shadow: none; - color: #024c7d; } - html.theme--documenter-dark .button.is-info.is-loading::after { - border-color: transparent transparent #fff #fff !important; } - html.theme--documenter-dark .button.is-info.is-outlined { - background-color: transparent; - border-color: #024c7d; - color: #024c7d; } - html.theme--documenter-dark .button.is-info.is-outlined:hover, html.theme--documenter-dark .button.is-info.is-outlined.is-hovered, html.theme--documenter-dark .button.is-info.is-outlined:focus, html.theme--documenter-dark .button.is-info.is-outlined.is-focused { - background-color: #024c7d; - border-color: #024c7d; - color: #fff; } - html.theme--documenter-dark .button.is-info.is-outlined.is-loading::after { - border-color: transparent transparent #024c7d #024c7d !important; } - html.theme--documenter-dark .button.is-info.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-info.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-info.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-info.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #fff #fff !important; } - html.theme--documenter-dark .button.is-info.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-info.is-outlined { - background-color: transparent; - border-color: #024c7d; - box-shadow: none; - color: #024c7d; } - html.theme--documenter-dark .button.is-info.is-inverted.is-outlined { - background-color: transparent; - border-color: #fff; - color: #fff; } - html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-focused { - background-color: #fff; - color: #024c7d; } - html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #024c7d #024c7d !important; } - html.theme--documenter-dark .button.is-info.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted.is-outlined { - background-color: transparent; - border-color: #fff; - box-shadow: none; - color: #fff; } - html.theme--documenter-dark .button.is-success { - background-color: #008438; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .button.is-success:hover, html.theme--documenter-dark .button.is-success.is-hovered { - background-color: #007733; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .button.is-success:focus, html.theme--documenter-dark .button.is-success.is-focused { - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .button.is-success:focus:not(:active), html.theme--documenter-dark .button.is-success.is-focused:not(:active) { - box-shadow: 0 0 0 0.125em rgba(0, 132, 56, 0.25); } - html.theme--documenter-dark .button.is-success:active, html.theme--documenter-dark .button.is-success.is-active { - background-color: #006b2d; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .button.is-success[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-success { - background-color: #008438; - border-color: transparent; - box-shadow: none; } - html.theme--documenter-dark .button.is-success.is-inverted { - background-color: #fff; - color: #008438; } - html.theme--documenter-dark .button.is-success.is-inverted:hover, html.theme--documenter-dark .button.is-success.is-inverted.is-hovered { - background-color: #f2f2f2; } - html.theme--documenter-dark .button.is-success.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted { - background-color: #fff; - border-color: transparent; - box-shadow: none; - color: #008438; } - html.theme--documenter-dark .button.is-success.is-loading::after { - border-color: transparent transparent #fff #fff !important; } - html.theme--documenter-dark .button.is-success.is-outlined { - background-color: transparent; - border-color: #008438; - color: #008438; } - html.theme--documenter-dark .button.is-success.is-outlined:hover, html.theme--documenter-dark .button.is-success.is-outlined.is-hovered, html.theme--documenter-dark .button.is-success.is-outlined:focus, html.theme--documenter-dark .button.is-success.is-outlined.is-focused { - background-color: #008438; - border-color: #008438; - color: #fff; } - html.theme--documenter-dark .button.is-success.is-outlined.is-loading::after { - border-color: transparent transparent #008438 #008438 !important; } - html.theme--documenter-dark .button.is-success.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-success.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #fff #fff !important; } - html.theme--documenter-dark .button.is-success.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-success.is-outlined { - background-color: transparent; - border-color: #008438; - box-shadow: none; - color: #008438; } - html.theme--documenter-dark .button.is-success.is-inverted.is-outlined { - background-color: transparent; - border-color: #fff; - color: #fff; } - html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-focused { - background-color: #fff; - color: #008438; } - html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #008438 #008438 !important; } - html.theme--documenter-dark .button.is-success.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted.is-outlined { - background-color: transparent; - border-color: #fff; - box-shadow: none; - color: #fff; } - html.theme--documenter-dark .button.is-warning { - background-color: #ad8100; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .button.is-warning:hover, html.theme--documenter-dark .button.is-warning.is-hovered { - background-color: #a07700; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .button.is-warning:focus, html.theme--documenter-dark .button.is-warning.is-focused { - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .button.is-warning:focus:not(:active), html.theme--documenter-dark .button.is-warning.is-focused:not(:active) { - box-shadow: 0 0 0 0.125em rgba(173, 129, 0, 0.25); } - html.theme--documenter-dark .button.is-warning:active, html.theme--documenter-dark .button.is-warning.is-active { - background-color: #946e00; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .button.is-warning[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-warning { - background-color: #ad8100; - border-color: transparent; - box-shadow: none; } - html.theme--documenter-dark .button.is-warning.is-inverted { - background-color: #fff; - color: #ad8100; } - html.theme--documenter-dark .button.is-warning.is-inverted:hover, html.theme--documenter-dark .button.is-warning.is-inverted.is-hovered { - background-color: #f2f2f2; } - html.theme--documenter-dark .button.is-warning.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted { - background-color: #fff; - border-color: transparent; - box-shadow: none; - color: #ad8100; } - html.theme--documenter-dark .button.is-warning.is-loading::after { - border-color: transparent transparent #fff #fff !important; } - html.theme--documenter-dark .button.is-warning.is-outlined { - background-color: transparent; - border-color: #ad8100; - color: #ad8100; } - html.theme--documenter-dark .button.is-warning.is-outlined:hover, html.theme--documenter-dark .button.is-warning.is-outlined.is-hovered, html.theme--documenter-dark .button.is-warning.is-outlined:focus, html.theme--documenter-dark .button.is-warning.is-outlined.is-focused { - background-color: #ad8100; - border-color: #ad8100; - color: #fff; } - html.theme--documenter-dark .button.is-warning.is-outlined.is-loading::after { - border-color: transparent transparent #ad8100 #ad8100 !important; } - html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #fff #fff !important; } - html.theme--documenter-dark .button.is-warning.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined { - background-color: transparent; - border-color: #ad8100; - box-shadow: none; - color: #ad8100; } - html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined { - background-color: transparent; - border-color: #fff; - color: #fff; } - html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused { - background-color: #fff; - color: #ad8100; } - html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #ad8100 #ad8100 !important; } - html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined { - background-color: transparent; - border-color: #fff; - box-shadow: none; - color: #fff; } - html.theme--documenter-dark .button.is-danger { - background-color: #9e1b0d; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .button.is-danger:hover, html.theme--documenter-dark .button.is-danger.is-hovered { - background-color: #92190c; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .button.is-danger:focus, html.theme--documenter-dark .button.is-danger.is-focused { - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .button.is-danger:focus:not(:active), html.theme--documenter-dark .button.is-danger.is-focused:not(:active) { - box-shadow: 0 0 0 0.125em rgba(158, 27, 13, 0.25); } - html.theme--documenter-dark .button.is-danger:active, html.theme--documenter-dark .button.is-danger.is-active { - background-color: #86170b; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .button.is-danger[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-danger { - background-color: #9e1b0d; - border-color: transparent; - box-shadow: none; } - html.theme--documenter-dark .button.is-danger.is-inverted { - background-color: #fff; - color: #9e1b0d; } - html.theme--documenter-dark .button.is-danger.is-inverted:hover, html.theme--documenter-dark .button.is-danger.is-inverted.is-hovered { - background-color: #f2f2f2; } - html.theme--documenter-dark .button.is-danger.is-inverted[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted { - background-color: #fff; - border-color: transparent; - box-shadow: none; - color: #9e1b0d; } - html.theme--documenter-dark .button.is-danger.is-loading::after { - border-color: transparent transparent #fff #fff !important; } - html.theme--documenter-dark .button.is-danger.is-outlined { - background-color: transparent; - border-color: #9e1b0d; - color: #9e1b0d; } - html.theme--documenter-dark .button.is-danger.is-outlined:hover, html.theme--documenter-dark .button.is-danger.is-outlined.is-hovered, html.theme--documenter-dark .button.is-danger.is-outlined:focus, html.theme--documenter-dark .button.is-danger.is-outlined.is-focused { - background-color: #9e1b0d; - border-color: #9e1b0d; - color: #fff; } - html.theme--documenter-dark .button.is-danger.is-outlined.is-loading::after { - border-color: transparent transparent #9e1b0d #9e1b0d !important; } - html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #fff #fff !important; } - html.theme--documenter-dark .button.is-danger.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined { - background-color: transparent; - border-color: #9e1b0d; - box-shadow: none; - color: #9e1b0d; } - html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined { - background-color: transparent; - border-color: #fff; - color: #fff; } - html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused { - background-color: #fff; - color: #9e1b0d; } - html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #9e1b0d #9e1b0d !important; } - html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled], fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined { - background-color: transparent; - border-color: #fff; - box-shadow: none; - color: #fff; } - html.theme--documenter-dark .button.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.button { - border-radius: 3px; - font-size: 0.85em; } - html.theme--documenter-dark .button.is-normal { - font-size: 15px; } - html.theme--documenter-dark .button.is-medium { - font-size: 1.25rem; } - html.theme--documenter-dark .button.is-large { - font-size: 1.5rem; } - html.theme--documenter-dark .button[disabled], fieldset[disabled] html.theme--documenter-dark .button { - background-color: #8c9b9d; - border-color: #dbdee0; - box-shadow: none; - opacity: 0.5; } - html.theme--documenter-dark .button.is-fullwidth { - display: flex; - width: 100%; } - html.theme--documenter-dark .button.is-loading { - color: transparent !important; - pointer-events: none; } - html.theme--documenter-dark .button.is-loading::after { - position: absolute; - left: calc(50% - (1em / 2)); - top: calc(50% - (1em / 2)); - position: absolute !important; } - html.theme--documenter-dark .button.is-static { - background-color: #282f2f; - border-color: #5e6d6f; - color: #dbdee0; - box-shadow: none; - pointer-events: none; } - html.theme--documenter-dark .button.is-rounded, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.button { - border-radius: 290486px; - padding-left: 1em; - padding-right: 1em; } - html.theme--documenter-dark .buttons { - align-items: center; - display: flex; - flex-wrap: wrap; - justify-content: flex-start; } - html.theme--documenter-dark .buttons .button { - margin-bottom: 0.5rem; } - html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth) { - margin-right: 0.5rem; } - html.theme--documenter-dark .buttons:last-child { - margin-bottom: -0.5rem; } - html.theme--documenter-dark .buttons:not(:last-child) { - margin-bottom: 1rem; } - html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large) { - border-radius: 3px; - font-size: 0.85em; } - html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large) { - font-size: 1.25rem; } - html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium) { - font-size: 1.5rem; } - html.theme--documenter-dark .buttons.has-addons .button:not(:first-child) { - border-bottom-left-radius: 0; - border-top-left-radius: 0; } - html.theme--documenter-dark .buttons.has-addons .button:not(:last-child) { - border-bottom-right-radius: 0; - border-top-right-radius: 0; - margin-right: -1px; } - html.theme--documenter-dark .buttons.has-addons .button:last-child { - margin-right: 0; } - html.theme--documenter-dark .buttons.has-addons .button:hover, html.theme--documenter-dark .buttons.has-addons .button.is-hovered { - z-index: 2; } - html.theme--documenter-dark .buttons.has-addons .button:focus, html.theme--documenter-dark .buttons.has-addons .button.is-focused, html.theme--documenter-dark .buttons.has-addons .button:active, html.theme--documenter-dark .buttons.has-addons .button.is-active, html.theme--documenter-dark .buttons.has-addons .button.is-selected { - z-index: 3; } - html.theme--documenter-dark .buttons.has-addons .button:focus:hover, html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover, html.theme--documenter-dark .buttons.has-addons .button:active:hover, html.theme--documenter-dark .buttons.has-addons .button.is-active:hover, html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover { - z-index: 4; } - html.theme--documenter-dark .buttons.has-addons .button.is-expanded { - flex-grow: 1; - flex-shrink: 1; } - html.theme--documenter-dark .buttons.is-centered { - justify-content: center; } - html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth) { - margin-left: 0.25rem; - margin-right: 0.25rem; } - html.theme--documenter-dark .buttons.is-right { - justify-content: flex-end; } - html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth) { - margin-left: 0.25rem; - margin-right: 0.25rem; } - html.theme--documenter-dark .container { - flex-grow: 1; - margin: 0 auto; - position: relative; - width: auto; } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark .container { - max-width: 992px; } - html.theme--documenter-dark .container.is-fluid { - margin-left: 32px; - margin-right: 32px; - max-width: none; } } - @media screen and (max-width: 1215px) { - html.theme--documenter-dark .container.is-widescreen { - max-width: 1152px; } } - @media screen and (max-width: 1407px) { - html.theme--documenter-dark .container.is-fullhd { - max-width: 1344px; } } - @media screen and (min-width: 1216px) { - html.theme--documenter-dark .container { - max-width: 1152px; } } - @media screen and (min-width: 1408px) { - html.theme--documenter-dark .container { - max-width: 1344px; } } - html.theme--documenter-dark .content li + li { - margin-top: 0.25em; } - html.theme--documenter-dark .content p:not(:last-child), - html.theme--documenter-dark .content dl:not(:last-child), - html.theme--documenter-dark .content ol:not(:last-child), - html.theme--documenter-dark .content ul:not(:last-child), - html.theme--documenter-dark .content blockquote:not(:last-child), - html.theme--documenter-dark .content pre:not(:last-child), - html.theme--documenter-dark .content table:not(:last-child) { - margin-bottom: 1em; } - html.theme--documenter-dark .content h1, - html.theme--documenter-dark .content h2, - html.theme--documenter-dark .content h3, - html.theme--documenter-dark .content h4, - html.theme--documenter-dark .content h5, - html.theme--documenter-dark .content h6 { - color: #f2f2f2; - font-weight: 600; - line-height: 1.125; } - html.theme--documenter-dark .content h1 { - font-size: 2em; - margin-bottom: 0.5em; } - html.theme--documenter-dark .content h1:not(:first-child) { - margin-top: 1em; } - html.theme--documenter-dark .content h2 { - font-size: 1.75em; - margin-bottom: 0.5714em; } - html.theme--documenter-dark .content h2:not(:first-child) { - margin-top: 1.1428em; } - html.theme--documenter-dark .content h3 { - font-size: 1.5em; - margin-bottom: 0.6666em; } - html.theme--documenter-dark .content h3:not(:first-child) { - margin-top: 1.3333em; } - html.theme--documenter-dark .content h4 { - font-size: 1.25em; - margin-bottom: 0.8em; } - html.theme--documenter-dark .content h5 { - font-size: 1.125em; - margin-bottom: 0.8888em; } - html.theme--documenter-dark .content h6 { - font-size: 1em; - margin-bottom: 1em; } - html.theme--documenter-dark .content blockquote { - background-color: #282f2f; - border-left: 5px solid #5e6d6f; - padding: 1.25em 1.5em; } - html.theme--documenter-dark .content ol { - list-style-position: outside; - margin-left: 2em; - margin-top: 1em; } - html.theme--documenter-dark .content ol:not([type]) { - list-style-type: decimal; } - html.theme--documenter-dark .content ol.is-lower-alpha:not([type]) { - list-style-type: lower-alpha; } - html.theme--documenter-dark .content ol.is-lower-roman:not([type]) { - list-style-type: lower-roman; } - html.theme--documenter-dark .content ol.is-upper-alpha:not([type]) { - list-style-type: upper-alpha; } - html.theme--documenter-dark .content ol.is-upper-roman:not([type]) { - list-style-type: upper-roman; } - html.theme--documenter-dark .content ul { - list-style: disc outside; - margin-left: 2em; - margin-top: 1em; } - html.theme--documenter-dark .content ul ul { - list-style-type: circle; - margin-top: 0.5em; } - html.theme--documenter-dark .content ul ul ul { - list-style-type: square; } - html.theme--documenter-dark .content dd { - margin-left: 2em; } - html.theme--documenter-dark .content figure { - margin-left: 2em; - margin-right: 2em; - text-align: center; } - html.theme--documenter-dark .content figure:not(:first-child) { - margin-top: 2em; } - html.theme--documenter-dark .content figure:not(:last-child) { - margin-bottom: 2em; } - html.theme--documenter-dark .content figure img { - display: inline-block; } - html.theme--documenter-dark .content figure figcaption { - font-style: italic; } - html.theme--documenter-dark .content pre { - -webkit-overflow-scrolling: touch; - overflow-x: auto; - padding: 0; - white-space: pre; - word-wrap: normal; } - html.theme--documenter-dark .content sup, - html.theme--documenter-dark .content sub { - font-size: 75%; } - html.theme--documenter-dark .content table { - width: 100%; } - html.theme--documenter-dark .content table td, - html.theme--documenter-dark .content table th { - border: 1px solid #5e6d6f; - border-width: 0 0 1px; - padding: 0.5em 0.75em; - vertical-align: top; } - html.theme--documenter-dark .content table th { - color: #f2f2f2; } - html.theme--documenter-dark .content table th:not([align]) { - text-align: left; } - html.theme--documenter-dark .content table thead td, - html.theme--documenter-dark .content table thead th { - border-width: 0 0 2px; - color: #f2f2f2; } - html.theme--documenter-dark .content table tfoot td, - html.theme--documenter-dark .content table tfoot th { - border-width: 2px 0 0; - color: #f2f2f2; } - html.theme--documenter-dark .content table tbody tr:last-child td, - html.theme--documenter-dark .content table tbody tr:last-child th { - border-bottom-width: 0; } - html.theme--documenter-dark .content .tabs li + li { - margin-top: 0; } - html.theme--documenter-dark .content.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.content { - font-size: 0.85em; } - html.theme--documenter-dark .content.is-medium { - font-size: 1.25rem; } - html.theme--documenter-dark .content.is-large { - font-size: 1.5rem; } - html.theme--documenter-dark .icon { - align-items: center; - display: inline-flex; - justify-content: center; - height: 1.5rem; - width: 1.5rem; } - html.theme--documenter-dark .icon.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.icon { - height: 1rem; - width: 1rem; } - html.theme--documenter-dark .icon.is-medium { - height: 2rem; - width: 2rem; } - html.theme--documenter-dark .icon.is-large { - height: 3rem; - width: 3rem; } - html.theme--documenter-dark .image, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img { - display: block; - position: relative; } - html.theme--documenter-dark .image img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img img { - display: block; - height: auto; - width: 100%; } - html.theme--documenter-dark .image img.is-rounded, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img img.is-rounded { - border-radius: 290486px; } - html.theme--documenter-dark .image.is-square img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square img, - html.theme--documenter-dark .image.is-square .has-ratio, - html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, html.theme--documenter-dark .image.is-1by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 img, - html.theme--documenter-dark .image.is-1by1 .has-ratio, - html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, html.theme--documenter-dark .image.is-5by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 img, - html.theme--documenter-dark .image.is-5by4 .has-ratio, - html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, html.theme--documenter-dark .image.is-4by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 img, - html.theme--documenter-dark .image.is-4by3 .has-ratio, - html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, html.theme--documenter-dark .image.is-3by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 img, - html.theme--documenter-dark .image.is-3by2 .has-ratio, - html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, html.theme--documenter-dark .image.is-5by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 img, - html.theme--documenter-dark .image.is-5by3 .has-ratio, - html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, html.theme--documenter-dark .image.is-16by9 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 img, - html.theme--documenter-dark .image.is-16by9 .has-ratio, - html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, html.theme--documenter-dark .image.is-2by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 img, - html.theme--documenter-dark .image.is-2by1 .has-ratio, - html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, html.theme--documenter-dark .image.is-3by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 img, - html.theme--documenter-dark .image.is-3by1 .has-ratio, - html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, html.theme--documenter-dark .image.is-4by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 img, - html.theme--documenter-dark .image.is-4by5 .has-ratio, - html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, html.theme--documenter-dark .image.is-3by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 img, - html.theme--documenter-dark .image.is-3by4 .has-ratio, - html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, html.theme--documenter-dark .image.is-2by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 img, - html.theme--documenter-dark .image.is-2by3 .has-ratio, - html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, html.theme--documenter-dark .image.is-3by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 img, - html.theme--documenter-dark .image.is-3by5 .has-ratio, - html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, html.theme--documenter-dark .image.is-9by16 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 img, - html.theme--documenter-dark .image.is-9by16 .has-ratio, - html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, html.theme--documenter-dark .image.is-1by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 img, - html.theme--documenter-dark .image.is-1by2 .has-ratio, - html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, html.theme--documenter-dark .image.is-1by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 img, - html.theme--documenter-dark .image.is-1by3 .has-ratio, - html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio { - height: 100%; - width: 100%; } - html.theme--documenter-dark .image.is-square, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square, html.theme--documenter-dark .image.is-1by1, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 { - padding-top: 100%; } - html.theme--documenter-dark .image.is-5by4, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 { - padding-top: 80%; } - html.theme--documenter-dark .image.is-4by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 { - padding-top: 75%; } - html.theme--documenter-dark .image.is-3by2, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 { - padding-top: 66.6666%; } - html.theme--documenter-dark .image.is-5by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 { - padding-top: 60%; } - html.theme--documenter-dark .image.is-16by9, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 { - padding-top: 56.25%; } - html.theme--documenter-dark .image.is-2by1, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 { - padding-top: 50%; } - html.theme--documenter-dark .image.is-3by1, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 { - padding-top: 33.3333%; } - html.theme--documenter-dark .image.is-4by5, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 { - padding-top: 125%; } - html.theme--documenter-dark .image.is-3by4, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 { - padding-top: 133.3333%; } - html.theme--documenter-dark .image.is-2by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 { - padding-top: 150%; } - html.theme--documenter-dark .image.is-3by5, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 { - padding-top: 166.6666%; } - html.theme--documenter-dark .image.is-9by16, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 { - padding-top: 177.7777%; } - html.theme--documenter-dark .image.is-1by2, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 { - padding-top: 200%; } - html.theme--documenter-dark .image.is-1by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 { - padding-top: 300%; } - html.theme--documenter-dark .image.is-16x16, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16x16 { - height: 16px; - width: 16px; } - html.theme--documenter-dark .image.is-24x24, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-24x24 { - height: 24px; - width: 24px; } - html.theme--documenter-dark .image.is-32x32, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-32x32 { - height: 32px; - width: 32px; } - html.theme--documenter-dark .image.is-48x48, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-48x48 { - height: 48px; - width: 48px; } - html.theme--documenter-dark .image.is-64x64, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-64x64 { - height: 64px; - width: 64px; } - html.theme--documenter-dark .image.is-96x96, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-96x96 { - height: 96px; - width: 96px; } - html.theme--documenter-dark .image.is-128x128, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-128x128 { - height: 128px; - width: 128px; } - html.theme--documenter-dark .notification { - background-color: #282f2f; - border-radius: 0.4em; - padding: 1.25rem 2.5rem 1.25rem 1.5rem; - position: relative; } - html.theme--documenter-dark .notification a:not(.button):not(.dropdown-item) { - color: currentColor; - text-decoration: underline; } - html.theme--documenter-dark .notification strong { - color: currentColor; } - html.theme--documenter-dark .notification code, - html.theme--documenter-dark .notification pre { - background: white; } - html.theme--documenter-dark .notification pre code { - background: transparent; } - html.theme--documenter-dark .notification > .delete { - position: absolute; - right: 0.5rem; - top: 0.5rem; } - html.theme--documenter-dark .notification .title, - html.theme--documenter-dark .notification .subtitle, - html.theme--documenter-dark .notification .content { - color: currentColor; } - html.theme--documenter-dark .notification.is-white { - background-color: white; - color: #0a0a0a; } - html.theme--documenter-dark .notification.is-black { - background-color: #0a0a0a; - color: white; } - html.theme--documenter-dark .notification.is-light { - background-color: #ecf0f1; - color: #282f2f; } - html.theme--documenter-dark .notification.is-dark, html.theme--documenter-dark .content kbd.notification { - background-color: #282f2f; - color: #ecf0f1; } - html.theme--documenter-dark .notification.is-primary, html.theme--documenter-dark .docstring > section > a.notification.docs-sourcelink { - background-color: #375a7f; - color: #fff; } - html.theme--documenter-dark .notification.is-link { - background-color: #1abc9c; - color: #fff; } - html.theme--documenter-dark .notification.is-info { - background-color: #024c7d; - color: #fff; } - html.theme--documenter-dark .notification.is-success { - background-color: #008438; - color: #fff; } - html.theme--documenter-dark .notification.is-warning { - background-color: #ad8100; - color: #fff; } - html.theme--documenter-dark .notification.is-danger { - background-color: #9e1b0d; - color: #fff; } - html.theme--documenter-dark .progress { - -moz-appearance: none; - -webkit-appearance: none; - border: none; - border-radius: 290486px; - display: block; - height: 15px; - overflow: hidden; - padding: 0; - width: 100%; } - html.theme--documenter-dark .progress::-webkit-progress-bar { - background-color: #5e6d6f; } - html.theme--documenter-dark .progress::-webkit-progress-value { - background-color: #dbdee0; } - html.theme--documenter-dark .progress::-moz-progress-bar { - background-color: #dbdee0; } - html.theme--documenter-dark .progress::-ms-fill { - background-color: #dbdee0; - border: none; } - html.theme--documenter-dark .progress.is-white::-webkit-progress-value { - background-color: white; } - html.theme--documenter-dark .progress.is-white::-moz-progress-bar { - background-color: white; } - html.theme--documenter-dark .progress.is-white::-ms-fill { - background-color: white; } - html.theme--documenter-dark .progress.is-white:indeterminate { - background-image: linear-gradient(to right, white 30%, #5e6d6f 30%); } - html.theme--documenter-dark .progress.is-black::-webkit-progress-value { - background-color: #0a0a0a; } - html.theme--documenter-dark .progress.is-black::-moz-progress-bar { - background-color: #0a0a0a; } - html.theme--documenter-dark .progress.is-black::-ms-fill { - background-color: #0a0a0a; } - html.theme--documenter-dark .progress.is-black:indeterminate { - background-image: linear-gradient(to right, #0a0a0a 30%, #5e6d6f 30%); } - html.theme--documenter-dark .progress.is-light::-webkit-progress-value { - background-color: #ecf0f1; } - html.theme--documenter-dark .progress.is-light::-moz-progress-bar { - background-color: #ecf0f1; } - html.theme--documenter-dark .progress.is-light::-ms-fill { - background-color: #ecf0f1; } - html.theme--documenter-dark .progress.is-light:indeterminate { - background-image: linear-gradient(to right, #ecf0f1 30%, #5e6d6f 30%); } - html.theme--documenter-dark .progress.is-dark::-webkit-progress-value, html.theme--documenter-dark .content kbd.progress::-webkit-progress-value { - background-color: #282f2f; } - html.theme--documenter-dark .progress.is-dark::-moz-progress-bar, html.theme--documenter-dark .content kbd.progress::-moz-progress-bar { - background-color: #282f2f; } - html.theme--documenter-dark .progress.is-dark::-ms-fill, html.theme--documenter-dark .content kbd.progress::-ms-fill { - background-color: #282f2f; } - html.theme--documenter-dark .progress.is-dark:indeterminate, html.theme--documenter-dark .content kbd.progress:indeterminate { - background-image: linear-gradient(to right, #282f2f 30%, #5e6d6f 30%); } - html.theme--documenter-dark .progress.is-primary::-webkit-progress-value, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink::-webkit-progress-value { - background-color: #375a7f; } - html.theme--documenter-dark .progress.is-primary::-moz-progress-bar, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink::-moz-progress-bar { - background-color: #375a7f; } - html.theme--documenter-dark .progress.is-primary::-ms-fill, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink::-ms-fill { - background-color: #375a7f; } - html.theme--documenter-dark .progress.is-primary:indeterminate, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink:indeterminate { - background-image: linear-gradient(to right, #375a7f 30%, #5e6d6f 30%); } - html.theme--documenter-dark .progress.is-link::-webkit-progress-value { - background-color: #1abc9c; } - html.theme--documenter-dark .progress.is-link::-moz-progress-bar { - background-color: #1abc9c; } - html.theme--documenter-dark .progress.is-link::-ms-fill { - background-color: #1abc9c; } - html.theme--documenter-dark .progress.is-link:indeterminate { - background-image: linear-gradient(to right, #1abc9c 30%, #5e6d6f 30%); } - html.theme--documenter-dark .progress.is-info::-webkit-progress-value { - background-color: #024c7d; } - html.theme--documenter-dark .progress.is-info::-moz-progress-bar { - background-color: #024c7d; } - html.theme--documenter-dark .progress.is-info::-ms-fill { - background-color: #024c7d; } - html.theme--documenter-dark .progress.is-info:indeterminate { - background-image: linear-gradient(to right, #024c7d 30%, #5e6d6f 30%); } - html.theme--documenter-dark .progress.is-success::-webkit-progress-value { - background-color: #008438; } - html.theme--documenter-dark .progress.is-success::-moz-progress-bar { - background-color: #008438; } - html.theme--documenter-dark .progress.is-success::-ms-fill { - background-color: #008438; } - html.theme--documenter-dark .progress.is-success:indeterminate { - background-image: linear-gradient(to right, #008438 30%, #5e6d6f 30%); } - html.theme--documenter-dark .progress.is-warning::-webkit-progress-value { - background-color: #ad8100; } - html.theme--documenter-dark .progress.is-warning::-moz-progress-bar { - background-color: #ad8100; } - html.theme--documenter-dark .progress.is-warning::-ms-fill { - background-color: #ad8100; } - html.theme--documenter-dark .progress.is-warning:indeterminate { - background-image: linear-gradient(to right, #ad8100 30%, #5e6d6f 30%); } - html.theme--documenter-dark .progress.is-danger::-webkit-progress-value { - background-color: #9e1b0d; } - html.theme--documenter-dark .progress.is-danger::-moz-progress-bar { - background-color: #9e1b0d; } - html.theme--documenter-dark .progress.is-danger::-ms-fill { - background-color: #9e1b0d; } - html.theme--documenter-dark .progress.is-danger:indeterminate { - background-image: linear-gradient(to right, #9e1b0d 30%, #5e6d6f 30%); } - html.theme--documenter-dark .progress:indeterminate { - animation-duration: 1.5s; - animation-iteration-count: infinite; - animation-name: moveIndeterminate; - animation-timing-function: linear; - background-color: #5e6d6f; - background-image: linear-gradient(to right, #fff 30%, #5e6d6f 30%); - background-position: top left; - background-repeat: no-repeat; - background-size: 150% 150%; } - html.theme--documenter-dark .progress:indeterminate::-webkit-progress-bar { - background-color: transparent; } - html.theme--documenter-dark .progress:indeterminate::-moz-progress-bar { - background-color: transparent; } - html.theme--documenter-dark .progress.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.progress { - height: 0.85em; } - html.theme--documenter-dark .progress.is-medium { - height: 1.25rem; } - html.theme--documenter-dark .progress.is-large { - height: 1.5rem; } - -@keyframes moveIndeterminate { - from { - background-position: 200% 0; } - to { - background-position: -200% 0; } } - html.theme--documenter-dark .table { - background-color: #343c3d; - color: #fff; } - html.theme--documenter-dark .table td, - html.theme--documenter-dark .table th { - border: 1px solid #5e6d6f; - border-width: 0 0 1px; - padding: 0.5em 0.75em; - vertical-align: top; } - html.theme--documenter-dark .table td.is-white, - html.theme--documenter-dark .table th.is-white { - background-color: white; - border-color: white; - color: #0a0a0a; } - html.theme--documenter-dark .table td.is-black, - html.theme--documenter-dark .table th.is-black { - background-color: #0a0a0a; - border-color: #0a0a0a; - color: white; } - html.theme--documenter-dark .table td.is-light, - html.theme--documenter-dark .table th.is-light { - background-color: #ecf0f1; - border-color: #ecf0f1; - color: #282f2f; } - html.theme--documenter-dark .table td.is-dark, - html.theme--documenter-dark .table th.is-dark { - background-color: #282f2f; - border-color: #282f2f; - color: #ecf0f1; } - html.theme--documenter-dark .table td.is-primary, - html.theme--documenter-dark .table th.is-primary { - background-color: #375a7f; - border-color: #375a7f; - color: #fff; } - html.theme--documenter-dark .table td.is-link, - html.theme--documenter-dark .table th.is-link { - background-color: #1abc9c; - border-color: #1abc9c; - color: #fff; } - html.theme--documenter-dark .table td.is-info, - html.theme--documenter-dark .table th.is-info { - background-color: #024c7d; - border-color: #024c7d; - color: #fff; } - html.theme--documenter-dark .table td.is-success, - html.theme--documenter-dark .table th.is-success { - background-color: #008438; - border-color: #008438; - color: #fff; } - html.theme--documenter-dark .table td.is-warning, - html.theme--documenter-dark .table th.is-warning { - background-color: #ad8100; - border-color: #ad8100; - color: #fff; } - html.theme--documenter-dark .table td.is-danger, - html.theme--documenter-dark .table th.is-danger { - background-color: #9e1b0d; - border-color: #9e1b0d; - color: #fff; } - html.theme--documenter-dark .table td.is-narrow, - html.theme--documenter-dark .table th.is-narrow { - white-space: nowrap; - width: 1%; } - html.theme--documenter-dark .table td.is-selected, - html.theme--documenter-dark .table th.is-selected { - background-color: #375a7f; - color: #fff; } - html.theme--documenter-dark .table td.is-selected a, - html.theme--documenter-dark .table td.is-selected strong, - html.theme--documenter-dark .table th.is-selected a, - html.theme--documenter-dark .table th.is-selected strong { - color: currentColor; } - html.theme--documenter-dark .table th { - color: #f2f2f2; } - html.theme--documenter-dark .table th:not([align]) { - text-align: left; } - html.theme--documenter-dark .table tr.is-selected { - background-color: #375a7f; - color: #fff; } - html.theme--documenter-dark .table tr.is-selected a, - html.theme--documenter-dark .table tr.is-selected strong { - color: currentColor; } - html.theme--documenter-dark .table tr.is-selected td, - html.theme--documenter-dark .table tr.is-selected th { - border-color: #fff; - color: currentColor; } - html.theme--documenter-dark .table thead { - background-color: transparent; } - html.theme--documenter-dark .table thead td, - html.theme--documenter-dark .table thead th { - border-width: 0 0 2px; - color: #f2f2f2; } - html.theme--documenter-dark .table tfoot { - background-color: transparent; } - html.theme--documenter-dark .table tfoot td, - html.theme--documenter-dark .table tfoot th { - border-width: 2px 0 0; - color: #f2f2f2; } - html.theme--documenter-dark .table tbody { - background-color: transparent; } - html.theme--documenter-dark .table tbody tr:last-child td, - html.theme--documenter-dark .table tbody tr:last-child th { - border-bottom-width: 0; } - html.theme--documenter-dark .table.is-bordered td, - html.theme--documenter-dark .table.is-bordered th { - border-width: 1px; } - html.theme--documenter-dark .table.is-bordered tr:last-child td, - html.theme--documenter-dark .table.is-bordered tr:last-child th { - border-bottom-width: 1px; } - html.theme--documenter-dark .table.is-fullwidth { - width: 100%; } - html.theme--documenter-dark .table.is-hoverable tbody tr:not(.is-selected):hover { - background-color: #282f2f; } - html.theme--documenter-dark .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover { - background-color: #282f2f; } - html.theme--documenter-dark .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover:nth-child(even) { - background-color: #2d3435; } - html.theme--documenter-dark .table.is-narrow td, - html.theme--documenter-dark .table.is-narrow th { - padding: 0.25em 0.5em; } - html.theme--documenter-dark .table.is-striped tbody tr:not(.is-selected):nth-child(even) { - background-color: #282f2f; } - html.theme--documenter-dark .table-container { - -webkit-overflow-scrolling: touch; - overflow: auto; - overflow-y: hidden; - max-width: 100%; } - html.theme--documenter-dark .tags { - align-items: center; - display: flex; - flex-wrap: wrap; - justify-content: flex-start; } - html.theme--documenter-dark .tags .tag, html.theme--documenter-dark .tags .content kbd, html.theme--documenter-dark .content .tags kbd, html.theme--documenter-dark .tags .docstring > section > a.docs-sourcelink { - margin-bottom: 0.5rem; } - html.theme--documenter-dark .tags .tag:not(:last-child), html.theme--documenter-dark .tags .content kbd:not(:last-child), html.theme--documenter-dark .content .tags kbd:not(:last-child), html.theme--documenter-dark .tags .docstring > section > a.docs-sourcelink:not(:last-child) { - margin-right: 0.5rem; } - html.theme--documenter-dark .tags:last-child { - margin-bottom: -0.5rem; } - html.theme--documenter-dark .tags:not(:last-child) { - margin-bottom: 1rem; } - html.theme--documenter-dark .tags.are-medium .tag:not(.is-normal):not(.is-large), html.theme--documenter-dark .tags.are-medium .content kbd:not(.is-normal):not(.is-large), html.theme--documenter-dark .content .tags.are-medium kbd:not(.is-normal):not(.is-large), html.theme--documenter-dark .tags.are-medium .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-large) { - font-size: 15px; } - html.theme--documenter-dark .tags.are-large .tag:not(.is-normal):not(.is-medium), html.theme--documenter-dark .tags.are-large .content kbd:not(.is-normal):not(.is-medium), html.theme--documenter-dark .content .tags.are-large kbd:not(.is-normal):not(.is-medium), html.theme--documenter-dark .tags.are-large .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-medium) { - font-size: 1.25rem; } - html.theme--documenter-dark .tags.is-centered { - justify-content: center; } - html.theme--documenter-dark .tags.is-centered .tag, html.theme--documenter-dark .tags.is-centered .content kbd, html.theme--documenter-dark .content .tags.is-centered kbd, html.theme--documenter-dark .tags.is-centered .docstring > section > a.docs-sourcelink { - margin-right: 0.25rem; - margin-left: 0.25rem; } - html.theme--documenter-dark .tags.is-right { - justify-content: flex-end; } - html.theme--documenter-dark .tags.is-right .tag:not(:first-child), html.theme--documenter-dark .tags.is-right .content kbd:not(:first-child), html.theme--documenter-dark .content .tags.is-right kbd:not(:first-child), html.theme--documenter-dark .tags.is-right .docstring > section > a.docs-sourcelink:not(:first-child) { - margin-left: 0.5rem; } - html.theme--documenter-dark .tags.is-right .tag:not(:last-child), html.theme--documenter-dark .tags.is-right .content kbd:not(:last-child), html.theme--documenter-dark .content .tags.is-right kbd:not(:last-child), html.theme--documenter-dark .tags.is-right .docstring > section > a.docs-sourcelink:not(:last-child) { - margin-right: 0; } - html.theme--documenter-dark .tags.has-addons .tag, html.theme--documenter-dark .tags.has-addons .content kbd, html.theme--documenter-dark .content .tags.has-addons kbd, html.theme--documenter-dark .tags.has-addons .docstring > section > a.docs-sourcelink { - margin-right: 0; } - html.theme--documenter-dark .tags.has-addons .tag:not(:first-child), html.theme--documenter-dark .tags.has-addons .content kbd:not(:first-child), html.theme--documenter-dark .content .tags.has-addons kbd:not(:first-child), html.theme--documenter-dark .tags.has-addons .docstring > section > a.docs-sourcelink:not(:first-child) { - margin-left: 0; - border-bottom-left-radius: 0; - border-top-left-radius: 0; } - html.theme--documenter-dark .tags.has-addons .tag:not(:last-child), html.theme--documenter-dark .tags.has-addons .content kbd:not(:last-child), html.theme--documenter-dark .content .tags.has-addons kbd:not(:last-child), html.theme--documenter-dark .tags.has-addons .docstring > section > a.docs-sourcelink:not(:last-child) { - border-bottom-right-radius: 0; - border-top-right-radius: 0; } - html.theme--documenter-dark .tag:not(body), html.theme--documenter-dark .content kbd:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) { - align-items: center; - background-color: #282f2f; - border-radius: 0.4em; - color: #fff; - display: inline-flex; - font-size: 0.85em; - height: 2em; - justify-content: center; - line-height: 1.5; - padding-left: 0.75em; - padding-right: 0.75em; - white-space: nowrap; } - html.theme--documenter-dark .tag:not(body) .delete, html.theme--documenter-dark .content kbd:not(body) .delete, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .delete { - margin-left: 0.25rem; - margin-right: -0.375rem; } - html.theme--documenter-dark .tag.is-white:not(body), html.theme--documenter-dark .content kbd.is-white:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-white:not(body) { - background-color: white; - color: #0a0a0a; } - html.theme--documenter-dark .tag.is-black:not(body), html.theme--documenter-dark .content kbd.is-black:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-black:not(body) { - background-color: #0a0a0a; - color: white; } - html.theme--documenter-dark .tag.is-light:not(body), html.theme--documenter-dark .content kbd.is-light:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-light:not(body) { - background-color: #ecf0f1; - color: #282f2f; } - html.theme--documenter-dark .tag.is-dark:not(body), html.theme--documenter-dark .content kbd:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-dark:not(body), html.theme--documenter-dark .content .docstring > section > kbd:not(body) { - background-color: #282f2f; - color: #ecf0f1; } - html.theme--documenter-dark .tag.is-primary:not(body), html.theme--documenter-dark .content kbd.is-primary:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) { - background-color: #375a7f; - color: #fff; } - html.theme--documenter-dark .tag.is-link:not(body), html.theme--documenter-dark .content kbd.is-link:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-link:not(body) { - background-color: #1abc9c; - color: #fff; } - html.theme--documenter-dark .tag.is-info:not(body), html.theme--documenter-dark .content kbd.is-info:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-info:not(body) { - background-color: #024c7d; - color: #fff; } - html.theme--documenter-dark .tag.is-success:not(body), html.theme--documenter-dark .content kbd.is-success:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-success:not(body) { - background-color: #008438; - color: #fff; } - html.theme--documenter-dark .tag.is-warning:not(body), html.theme--documenter-dark .content kbd.is-warning:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-warning:not(body) { - background-color: #ad8100; - color: #fff; } - html.theme--documenter-dark .tag.is-danger:not(body), html.theme--documenter-dark .content kbd.is-danger:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-danger:not(body) { - background-color: #9e1b0d; - color: #fff; } - html.theme--documenter-dark .tag.is-normal:not(body), html.theme--documenter-dark .content kbd.is-normal:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-normal:not(body) { - font-size: 0.85em; } - html.theme--documenter-dark .tag.is-medium:not(body), html.theme--documenter-dark .content kbd.is-medium:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-medium:not(body) { - font-size: 15px; } - html.theme--documenter-dark .tag.is-large:not(body), html.theme--documenter-dark .content kbd.is-large:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-large:not(body) { - font-size: 1.25rem; } - html.theme--documenter-dark .tag:not(body) .icon:first-child:not(:last-child), html.theme--documenter-dark .content kbd:not(body) .icon:first-child:not(:last-child), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:not(:last-child) { - margin-left: -0.375em; - margin-right: 0.1875em; } - html.theme--documenter-dark .tag:not(body) .icon:last-child:not(:first-child), html.theme--documenter-dark .content kbd:not(body) .icon:last-child:not(:first-child), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .icon:last-child:not(:first-child) { - margin-left: 0.1875em; - margin-right: -0.375em; } - html.theme--documenter-dark .tag:not(body) .icon:first-child:last-child, html.theme--documenter-dark .content kbd:not(body) .icon:first-child:last-child, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:last-child { - margin-left: -0.375em; - margin-right: -0.375em; } - html.theme--documenter-dark .tag.is-delete:not(body), html.theme--documenter-dark .content kbd.is-delete:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body) { - margin-left: 1px; - padding: 0; - position: relative; - width: 2em; } - html.theme--documenter-dark .tag.is-delete:not(body)::before, html.theme--documenter-dark .content kbd.is-delete:not(body)::before, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body)::before, html.theme--documenter-dark .tag.is-delete:not(body)::after, html.theme--documenter-dark .content kbd.is-delete:not(body)::after, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body)::after { - background-color: currentColor; - content: ""; - display: block; - left: 50%; - position: absolute; - top: 50%; - transform: translateX(-50%) translateY(-50%) rotate(45deg); - transform-origin: center center; } - html.theme--documenter-dark .tag.is-delete:not(body)::before, html.theme--documenter-dark .content kbd.is-delete:not(body)::before, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body)::before { - height: 1px; - width: 50%; } - html.theme--documenter-dark .tag.is-delete:not(body)::after, html.theme--documenter-dark .content kbd.is-delete:not(body)::after, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body)::after { - height: 50%; - width: 1px; } - html.theme--documenter-dark .tag.is-delete:not(body):hover, html.theme--documenter-dark .content kbd.is-delete:not(body):hover, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body):hover, html.theme--documenter-dark .tag.is-delete:not(body):focus, html.theme--documenter-dark .content kbd.is-delete:not(body):focus, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body):focus { - background-color: #1d2122; } - html.theme--documenter-dark .tag.is-delete:not(body):active, html.theme--documenter-dark .content kbd.is-delete:not(body):active, html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-delete:not(body):active { - background-color: #111414; } - html.theme--documenter-dark .tag.is-rounded:not(body), html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:not(body), html.theme--documenter-dark .content kbd.is-rounded:not(body), html.theme--documenter-dark #documenter .docs-sidebar .content form.docs-search > input:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink.is-rounded:not(body) { - border-radius: 290486px; } - html.theme--documenter-dark a.tag:hover, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:hover { - text-decoration: underline; } - html.theme--documenter-dark .title, - html.theme--documenter-dark .subtitle { - word-break: break-word; } - html.theme--documenter-dark .title em, - html.theme--documenter-dark .title span, - html.theme--documenter-dark .subtitle em, - html.theme--documenter-dark .subtitle span { - font-weight: inherit; } - html.theme--documenter-dark .title sub, - html.theme--documenter-dark .subtitle sub { - font-size: 0.75em; } - html.theme--documenter-dark .title sup, - html.theme--documenter-dark .subtitle sup { - font-size: 0.75em; } - html.theme--documenter-dark .title .tag, html.theme--documenter-dark .title .content kbd, html.theme--documenter-dark .content .title kbd, html.theme--documenter-dark .title .docstring > section > a.docs-sourcelink, - html.theme--documenter-dark .subtitle .tag, - html.theme--documenter-dark .subtitle .content kbd, - html.theme--documenter-dark .content .subtitle kbd, - html.theme--documenter-dark .subtitle .docstring > section > a.docs-sourcelink { - vertical-align: middle; } - html.theme--documenter-dark .title { - color: #fff; - font-size: 2rem; - font-weight: 500; - line-height: 1.125; } - html.theme--documenter-dark .title strong { - color: inherit; - font-weight: inherit; } - html.theme--documenter-dark .title + .highlight { - margin-top: -0.75rem; } - html.theme--documenter-dark .title:not(.is-spaced) + .subtitle { - margin-top: -1.25rem; } - html.theme--documenter-dark .title.is-1 { - font-size: 3rem; } - html.theme--documenter-dark .title.is-2 { - font-size: 2.5rem; } - html.theme--documenter-dark .title.is-3 { - font-size: 2rem; } - html.theme--documenter-dark .title.is-4 { - font-size: 1.5rem; } - html.theme--documenter-dark .title.is-5 { - font-size: 1.25rem; } - html.theme--documenter-dark .title.is-6 { - font-size: 15px; } - html.theme--documenter-dark .title.is-7 { - font-size: 0.85em; } - html.theme--documenter-dark .subtitle { - color: #8c9b9d; - font-size: 1.25rem; - font-weight: 400; - line-height: 1.25; } - html.theme--documenter-dark .subtitle strong { - color: #8c9b9d; - font-weight: 600; } - html.theme--documenter-dark .subtitle:not(.is-spaced) + .title { - margin-top: -1.25rem; } - html.theme--documenter-dark .subtitle.is-1 { - font-size: 3rem; } - html.theme--documenter-dark .subtitle.is-2 { - font-size: 2.5rem; } - html.theme--documenter-dark .subtitle.is-3 { - font-size: 2rem; } - html.theme--documenter-dark .subtitle.is-4 { - font-size: 1.5rem; } - html.theme--documenter-dark .subtitle.is-5 { - font-size: 1.25rem; } - html.theme--documenter-dark .subtitle.is-6 { - font-size: 15px; } - html.theme--documenter-dark .subtitle.is-7 { - font-size: 0.85em; } - html.theme--documenter-dark .heading { - display: block; - font-size: 11px; - letter-spacing: 1px; - margin-bottom: 5px; - text-transform: uppercase; } - html.theme--documenter-dark .highlight { - font-weight: 400; - max-width: 100%; - overflow: hidden; - padding: 0; } - html.theme--documenter-dark .highlight pre { - overflow: auto; - max-width: 100%; } - html.theme--documenter-dark .number { - align-items: center; - background-color: #282f2f; - border-radius: 290486px; - display: inline-flex; - font-size: 1.25rem; - height: 2em; - justify-content: center; - margin-right: 1.5rem; - min-width: 2.5em; - padding: 0.25rem 0.5rem; - text-align: center; - vertical-align: top; } - html.theme--documenter-dark .select select, html.theme--documenter-dark .textarea, html.theme--documenter-dark .input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { - background-color: #1f2424; - border-color: #5e6d6f; - border-radius: 0.4em; - color: #dbdee0; } - html.theme--documenter-dark .select select::-moz-placeholder, html.theme--documenter-dark .textarea::-moz-placeholder, html.theme--documenter-dark .input::-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-moz-placeholder { - color: rgba(219, 222, 224, 0.3); } - html.theme--documenter-dark .select select::-webkit-input-placeholder, html.theme--documenter-dark .textarea::-webkit-input-placeholder, html.theme--documenter-dark .input::-webkit-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder { - color: rgba(219, 222, 224, 0.3); } - html.theme--documenter-dark .select select:-moz-placeholder, html.theme--documenter-dark .textarea:-moz-placeholder, html.theme--documenter-dark .input:-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-moz-placeholder { - color: rgba(219, 222, 224, 0.3); } - html.theme--documenter-dark .select select:-ms-input-placeholder, html.theme--documenter-dark .textarea:-ms-input-placeholder, html.theme--documenter-dark .input:-ms-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder { - color: rgba(219, 222, 224, 0.3); } - html.theme--documenter-dark .select select:hover, html.theme--documenter-dark .textarea:hover, html.theme--documenter-dark .input:hover, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:hover, html.theme--documenter-dark .select select.is-hovered, html.theme--documenter-dark .is-hovered.textarea, html.theme--documenter-dark .is-hovered.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-hovered { - border-color: #8c9b9d; } - html.theme--documenter-dark .select select:focus, html.theme--documenter-dark .textarea:focus, html.theme--documenter-dark .input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:focus, html.theme--documenter-dark .select select.is-focused, html.theme--documenter-dark .is-focused.textarea, html.theme--documenter-dark .is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .select select:active, html.theme--documenter-dark .textarea:active, html.theme--documenter-dark .input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:active, html.theme--documenter-dark .select select.is-active, html.theme--documenter-dark .is-active.textarea, html.theme--documenter-dark .is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { - border-color: #1abc9c; - box-shadow: 0 0 0 0.125em rgba(26, 188, 156, 0.25); } - html.theme--documenter-dark .select select[disabled], html.theme--documenter-dark .textarea[disabled], html.theme--documenter-dark .input[disabled], html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled], fieldset[disabled] html.theme--documenter-dark .select select, fieldset[disabled] html.theme--documenter-dark .textarea, fieldset[disabled] html.theme--documenter-dark .input, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { - background-color: #8c9b9d; - border-color: #282f2f; - box-shadow: none; - color: white; } - html.theme--documenter-dark .select select[disabled]::-moz-placeholder, html.theme--documenter-dark .textarea[disabled]::-moz-placeholder, html.theme--documenter-dark .input[disabled]::-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]::-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .select select::-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .textarea::-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .input::-moz-placeholder, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-moz-placeholder { - color: rgba(255, 255, 255, 0.3); } - html.theme--documenter-dark .select select[disabled]::-webkit-input-placeholder, html.theme--documenter-dark .textarea[disabled]::-webkit-input-placeholder, html.theme--documenter-dark .input[disabled]::-webkit-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]::-webkit-input-placeholder, fieldset[disabled] html.theme--documenter-dark .select select::-webkit-input-placeholder, fieldset[disabled] html.theme--documenter-dark .textarea::-webkit-input-placeholder, fieldset[disabled] html.theme--documenter-dark .input::-webkit-input-placeholder, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder { - color: rgba(255, 255, 255, 0.3); } - html.theme--documenter-dark .select select[disabled]:-moz-placeholder, html.theme--documenter-dark .textarea[disabled]:-moz-placeholder, html.theme--documenter-dark .input[disabled]:-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]:-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .select select:-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .textarea:-moz-placeholder, fieldset[disabled] html.theme--documenter-dark .input:-moz-placeholder, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-moz-placeholder { - color: rgba(255, 255, 255, 0.3); } - html.theme--documenter-dark .select select[disabled]:-ms-input-placeholder, html.theme--documenter-dark .textarea[disabled]:-ms-input-placeholder, html.theme--documenter-dark .input[disabled]:-ms-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]:-ms-input-placeholder, fieldset[disabled] html.theme--documenter-dark .select select:-ms-input-placeholder, fieldset[disabled] html.theme--documenter-dark .textarea:-ms-input-placeholder, fieldset[disabled] html.theme--documenter-dark .input:-ms-input-placeholder, fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder { - color: rgba(255, 255, 255, 0.3); } - html.theme--documenter-dark .textarea, html.theme--documenter-dark .input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { - box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.1); - max-width: 100%; - width: 100%; } - html.theme--documenter-dark .textarea[readonly], html.theme--documenter-dark .input[readonly], html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[readonly] { - box-shadow: none; } - html.theme--documenter-dark .is-white.textarea, html.theme--documenter-dark .is-white.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white { - border-color: white; } - html.theme--documenter-dark .is-white.textarea:focus, html.theme--documenter-dark .is-white.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white:focus, html.theme--documenter-dark .is-white.is-focused.textarea, html.theme--documenter-dark .is-white.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-white.textarea:active, html.theme--documenter-dark .is-white.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white:active, html.theme--documenter-dark .is-white.is-active.textarea, html.theme--documenter-dark .is-white.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { - box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } - html.theme--documenter-dark .is-black.textarea, html.theme--documenter-dark .is-black.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black { - border-color: #0a0a0a; } - html.theme--documenter-dark .is-black.textarea:focus, html.theme--documenter-dark .is-black.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black:focus, html.theme--documenter-dark .is-black.is-focused.textarea, html.theme--documenter-dark .is-black.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-black.textarea:active, html.theme--documenter-dark .is-black.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black:active, html.theme--documenter-dark .is-black.is-active.textarea, html.theme--documenter-dark .is-black.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { - box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } - html.theme--documenter-dark .is-light.textarea, html.theme--documenter-dark .is-light.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light { - border-color: #ecf0f1; } - html.theme--documenter-dark .is-light.textarea:focus, html.theme--documenter-dark .is-light.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light:focus, html.theme--documenter-dark .is-light.is-focused.textarea, html.theme--documenter-dark .is-light.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-light.textarea:active, html.theme--documenter-dark .is-light.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light:active, html.theme--documenter-dark .is-light.is-active.textarea, html.theme--documenter-dark .is-light.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { - box-shadow: 0 0 0 0.125em rgba(236, 240, 241, 0.25); } - html.theme--documenter-dark .is-dark.textarea, html.theme--documenter-dark .content kbd.textarea, html.theme--documenter-dark .is-dark.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark, html.theme--documenter-dark .content kbd.input { - border-color: #282f2f; } - html.theme--documenter-dark .is-dark.textarea:focus, html.theme--documenter-dark .content kbd.textarea:focus, html.theme--documenter-dark .is-dark.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark:focus, html.theme--documenter-dark .content kbd.input:focus, html.theme--documenter-dark .is-dark.is-focused.textarea, html.theme--documenter-dark .content kbd.is-focused.textarea, html.theme--documenter-dark .is-dark.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .content kbd.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar .content form.docs-search > input.is-focused, html.theme--documenter-dark .is-dark.textarea:active, html.theme--documenter-dark .content kbd.textarea:active, html.theme--documenter-dark .is-dark.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark:active, html.theme--documenter-dark .content kbd.input:active, html.theme--documenter-dark .is-dark.is-active.textarea, html.theme--documenter-dark .content kbd.is-active.textarea, html.theme--documenter-dark .is-dark.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active, html.theme--documenter-dark .content kbd.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar .content form.docs-search > input.is-active { - box-shadow: 0 0 0 0.125em rgba(40, 47, 47, 0.25); } - html.theme--documenter-dark .is-primary.textarea, html.theme--documenter-dark .docstring > section > a.textarea.docs-sourcelink, html.theme--documenter-dark .is-primary.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary, html.theme--documenter-dark .docstring > section > a.input.docs-sourcelink { - border-color: #375a7f; } - html.theme--documenter-dark .is-primary.textarea:focus, html.theme--documenter-dark .docstring > section > a.textarea.docs-sourcelink:focus, html.theme--documenter-dark .is-primary.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary:focus, html.theme--documenter-dark .docstring > section > a.input.docs-sourcelink:focus, html.theme--documenter-dark .is-primary.is-focused.textarea, html.theme--documenter-dark .docstring > section > a.is-focused.textarea.docs-sourcelink, html.theme--documenter-dark .is-primary.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .docstring > section > a.is-focused.input.docs-sourcelink, html.theme--documenter-dark .is-primary.textarea:active, html.theme--documenter-dark .docstring > section > a.textarea.docs-sourcelink:active, html.theme--documenter-dark .is-primary.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary:active, html.theme--documenter-dark .docstring > section > a.input.docs-sourcelink:active, html.theme--documenter-dark .is-primary.is-active.textarea, html.theme--documenter-dark .docstring > section > a.is-active.textarea.docs-sourcelink, html.theme--documenter-dark .is-primary.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active, html.theme--documenter-dark .docstring > section > a.is-active.input.docs-sourcelink { - box-shadow: 0 0 0 0.125em rgba(55, 90, 127, 0.25); } - html.theme--documenter-dark .is-link.textarea, html.theme--documenter-dark .is-link.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link { - border-color: #1abc9c; } - html.theme--documenter-dark .is-link.textarea:focus, html.theme--documenter-dark .is-link.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link:focus, html.theme--documenter-dark .is-link.is-focused.textarea, html.theme--documenter-dark .is-link.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-link.textarea:active, html.theme--documenter-dark .is-link.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link:active, html.theme--documenter-dark .is-link.is-active.textarea, html.theme--documenter-dark .is-link.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { - box-shadow: 0 0 0 0.125em rgba(26, 188, 156, 0.25); } - html.theme--documenter-dark .is-info.textarea, html.theme--documenter-dark .is-info.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info { - border-color: #024c7d; } - html.theme--documenter-dark .is-info.textarea:focus, html.theme--documenter-dark .is-info.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info:focus, html.theme--documenter-dark .is-info.is-focused.textarea, html.theme--documenter-dark .is-info.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-info.textarea:active, html.theme--documenter-dark .is-info.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info:active, html.theme--documenter-dark .is-info.is-active.textarea, html.theme--documenter-dark .is-info.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { - box-shadow: 0 0 0 0.125em rgba(2, 76, 125, 0.25); } - html.theme--documenter-dark .is-success.textarea, html.theme--documenter-dark .is-success.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success { - border-color: #008438; } - html.theme--documenter-dark .is-success.textarea:focus, html.theme--documenter-dark .is-success.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success:focus, html.theme--documenter-dark .is-success.is-focused.textarea, html.theme--documenter-dark .is-success.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-success.textarea:active, html.theme--documenter-dark .is-success.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success:active, html.theme--documenter-dark .is-success.is-active.textarea, html.theme--documenter-dark .is-success.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { - box-shadow: 0 0 0 0.125em rgba(0, 132, 56, 0.25); } - html.theme--documenter-dark .is-warning.textarea, html.theme--documenter-dark .is-warning.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning { - border-color: #ad8100; } - html.theme--documenter-dark .is-warning.textarea:focus, html.theme--documenter-dark .is-warning.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning:focus, html.theme--documenter-dark .is-warning.is-focused.textarea, html.theme--documenter-dark .is-warning.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-warning.textarea:active, html.theme--documenter-dark .is-warning.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning:active, html.theme--documenter-dark .is-warning.is-active.textarea, html.theme--documenter-dark .is-warning.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { - box-shadow: 0 0 0 0.125em rgba(173, 129, 0, 0.25); } - html.theme--documenter-dark .is-danger.textarea, html.theme--documenter-dark .is-danger.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger { - border-color: #9e1b0d; } - html.theme--documenter-dark .is-danger.textarea:focus, html.theme--documenter-dark .is-danger.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger:focus, html.theme--documenter-dark .is-danger.is-focused.textarea, html.theme--documenter-dark .is-danger.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-danger.textarea:active, html.theme--documenter-dark .is-danger.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger:active, html.theme--documenter-dark .is-danger.is-active.textarea, html.theme--documenter-dark .is-danger.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active { - box-shadow: 0 0 0 0.125em rgba(158, 27, 13, 0.25); } - html.theme--documenter-dark .is-small.textarea, html.theme--documenter-dark .is-small.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { - border-radius: 3px; - font-size: 0.85em; } - html.theme--documenter-dark .is-medium.textarea, html.theme--documenter-dark .is-medium.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-medium { - font-size: 1.25rem; } - html.theme--documenter-dark .is-large.textarea, html.theme--documenter-dark .is-large.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-large { - font-size: 1.5rem; } - html.theme--documenter-dark .is-fullwidth.textarea, html.theme--documenter-dark .is-fullwidth.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-fullwidth { - display: block; - width: 100%; } - html.theme--documenter-dark .is-inline.textarea, html.theme--documenter-dark .is-inline.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-inline { - display: inline; - width: auto; } - html.theme--documenter-dark .input.is-rounded, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { - border-radius: 290486px; - padding-left: 1em; - padding-right: 1em; } - html.theme--documenter-dark .input.is-static, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-static { - background-color: transparent; - border-color: transparent; - box-shadow: none; - padding-left: 0; - padding-right: 0; } - html.theme--documenter-dark .textarea { - display: block; - max-width: 100%; - min-width: 100%; - padding: 0.625em; - resize: vertical; } - html.theme--documenter-dark .textarea:not([rows]) { - max-height: 600px; - min-height: 120px; } - html.theme--documenter-dark .textarea[rows] { - height: initial; } - html.theme--documenter-dark .textarea.has-fixed-size { - resize: none; } - html.theme--documenter-dark .radio, html.theme--documenter-dark .checkbox { - cursor: pointer; - display: inline-block; - line-height: 1.25; - position: relative; } - html.theme--documenter-dark .radio input, html.theme--documenter-dark .checkbox input { - cursor: pointer; } - html.theme--documenter-dark .radio:hover, html.theme--documenter-dark .checkbox:hover { - color: #8c9b9d; } - html.theme--documenter-dark .radio[disabled], html.theme--documenter-dark .checkbox[disabled], fieldset[disabled] html.theme--documenter-dark .radio, fieldset[disabled] html.theme--documenter-dark .checkbox { - color: white; - cursor: not-allowed; } - html.theme--documenter-dark .radio + .radio { - margin-left: 0.5em; } - html.theme--documenter-dark .select { - display: inline-block; - max-width: 100%; - position: relative; - vertical-align: top; } - html.theme--documenter-dark .select:not(.is-multiple) { - height: 2.25em; } - html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after { - border-color: #1abc9c; - right: 1.125em; - z-index: 4; } - html.theme--documenter-dark .select.is-rounded select, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.select select { - border-radius: 290486px; - padding-left: 1em; } - html.theme--documenter-dark .select select { - cursor: pointer; - display: block; - font-size: 1em; - max-width: 100%; - outline: none; } - html.theme--documenter-dark .select select::-ms-expand { - display: none; } - html.theme--documenter-dark .select select[disabled]:hover, fieldset[disabled] html.theme--documenter-dark .select select:hover { - border-color: #282f2f; } - html.theme--documenter-dark .select select:not([multiple]) { - padding-right: 2.5em; } - html.theme--documenter-dark .select select[multiple] { - height: auto; - padding: 0; } - html.theme--documenter-dark .select select[multiple] option { - padding: 0.5em 1em; } - html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading):hover::after { - border-color: #8c9b9d; } - html.theme--documenter-dark .select.is-white:not(:hover)::after { - border-color: white; } - html.theme--documenter-dark .select.is-white select { - border-color: white; } - html.theme--documenter-dark .select.is-white select:hover, html.theme--documenter-dark .select.is-white select.is-hovered { - border-color: #f2f2f2; } - html.theme--documenter-dark .select.is-white select:focus, html.theme--documenter-dark .select.is-white select.is-focused, html.theme--documenter-dark .select.is-white select:active, html.theme--documenter-dark .select.is-white select.is-active { - box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } - html.theme--documenter-dark .select.is-black:not(:hover)::after { - border-color: #0a0a0a; } - html.theme--documenter-dark .select.is-black select { - border-color: #0a0a0a; } - html.theme--documenter-dark .select.is-black select:hover, html.theme--documenter-dark .select.is-black select.is-hovered { - border-color: black; } - html.theme--documenter-dark .select.is-black select:focus, html.theme--documenter-dark .select.is-black select.is-focused, html.theme--documenter-dark .select.is-black select:active, html.theme--documenter-dark .select.is-black select.is-active { - box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } - html.theme--documenter-dark .select.is-light:not(:hover)::after { - border-color: #ecf0f1; } - html.theme--documenter-dark .select.is-light select { - border-color: #ecf0f1; } - html.theme--documenter-dark .select.is-light select:hover, html.theme--documenter-dark .select.is-light select.is-hovered { - border-color: #dde4e6; } - html.theme--documenter-dark .select.is-light select:focus, html.theme--documenter-dark .select.is-light select.is-focused, html.theme--documenter-dark .select.is-light select:active, html.theme--documenter-dark .select.is-light select.is-active { - box-shadow: 0 0 0 0.125em rgba(236, 240, 241, 0.25); } - html.theme--documenter-dark .select.is-dark:not(:hover)::after, html.theme--documenter-dark .content kbd.select:not(:hover)::after { - border-color: #282f2f; } - html.theme--documenter-dark .select.is-dark select, html.theme--documenter-dark .content kbd.select select { - border-color: #282f2f; } - html.theme--documenter-dark .select.is-dark select:hover, html.theme--documenter-dark .content kbd.select select:hover, html.theme--documenter-dark .select.is-dark select.is-hovered, html.theme--documenter-dark .content kbd.select select.is-hovered { - border-color: #1d2122; } - html.theme--documenter-dark .select.is-dark select:focus, html.theme--documenter-dark .content kbd.select select:focus, html.theme--documenter-dark .select.is-dark select.is-focused, html.theme--documenter-dark .content kbd.select select.is-focused, html.theme--documenter-dark .select.is-dark select:active, html.theme--documenter-dark .content kbd.select select:active, html.theme--documenter-dark .select.is-dark select.is-active, html.theme--documenter-dark .content kbd.select select.is-active { - box-shadow: 0 0 0 0.125em rgba(40, 47, 47, 0.25); } - html.theme--documenter-dark .select.is-primary:not(:hover)::after, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink:not(:hover)::after { - border-color: #375a7f; } - html.theme--documenter-dark .select.is-primary select, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select { - border-color: #375a7f; } - html.theme--documenter-dark .select.is-primary select:hover, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select:hover, html.theme--documenter-dark .select.is-primary select.is-hovered, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select.is-hovered { - border-color: #2f4d6d; } - html.theme--documenter-dark .select.is-primary select:focus, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select:focus, html.theme--documenter-dark .select.is-primary select.is-focused, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select.is-focused, html.theme--documenter-dark .select.is-primary select:active, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select:active, html.theme--documenter-dark .select.is-primary select.is-active, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select.is-active { - box-shadow: 0 0 0 0.125em rgba(55, 90, 127, 0.25); } - html.theme--documenter-dark .select.is-link:not(:hover)::after { - border-color: #1abc9c; } - html.theme--documenter-dark .select.is-link select { - border-color: #1abc9c; } - html.theme--documenter-dark .select.is-link select:hover, html.theme--documenter-dark .select.is-link select.is-hovered { - border-color: #17a689; } - html.theme--documenter-dark .select.is-link select:focus, html.theme--documenter-dark .select.is-link select.is-focused, html.theme--documenter-dark .select.is-link select:active, html.theme--documenter-dark .select.is-link select.is-active { - box-shadow: 0 0 0 0.125em rgba(26, 188, 156, 0.25); } - html.theme--documenter-dark .select.is-info:not(:hover)::after { - border-color: #024c7d; } - html.theme--documenter-dark .select.is-info select { - border-color: #024c7d; } - html.theme--documenter-dark .select.is-info select:hover, html.theme--documenter-dark .select.is-info select.is-hovered { - border-color: #023d64; } - html.theme--documenter-dark .select.is-info select:focus, html.theme--documenter-dark .select.is-info select.is-focused, html.theme--documenter-dark .select.is-info select:active, html.theme--documenter-dark .select.is-info select.is-active { - box-shadow: 0 0 0 0.125em rgba(2, 76, 125, 0.25); } - html.theme--documenter-dark .select.is-success:not(:hover)::after { - border-color: #008438; } - html.theme--documenter-dark .select.is-success select { - border-color: #008438; } - html.theme--documenter-dark .select.is-success select:hover, html.theme--documenter-dark .select.is-success select.is-hovered { - border-color: #006b2d; } - html.theme--documenter-dark .select.is-success select:focus, html.theme--documenter-dark .select.is-success select.is-focused, html.theme--documenter-dark .select.is-success select:active, html.theme--documenter-dark .select.is-success select.is-active { - box-shadow: 0 0 0 0.125em rgba(0, 132, 56, 0.25); } - html.theme--documenter-dark .select.is-warning:not(:hover)::after { - border-color: #ad8100; } - html.theme--documenter-dark .select.is-warning select { - border-color: #ad8100; } - html.theme--documenter-dark .select.is-warning select:hover, html.theme--documenter-dark .select.is-warning select.is-hovered { - border-color: #946e00; } - html.theme--documenter-dark .select.is-warning select:focus, html.theme--documenter-dark .select.is-warning select.is-focused, html.theme--documenter-dark .select.is-warning select:active, html.theme--documenter-dark .select.is-warning select.is-active { - box-shadow: 0 0 0 0.125em rgba(173, 129, 0, 0.25); } - html.theme--documenter-dark .select.is-danger:not(:hover)::after { - border-color: #9e1b0d; } - html.theme--documenter-dark .select.is-danger select { - border-color: #9e1b0d; } - html.theme--documenter-dark .select.is-danger select:hover, html.theme--documenter-dark .select.is-danger select.is-hovered { - border-color: #86170b; } - html.theme--documenter-dark .select.is-danger select:focus, html.theme--documenter-dark .select.is-danger select.is-focused, html.theme--documenter-dark .select.is-danger select:active, html.theme--documenter-dark .select.is-danger select.is-active { - box-shadow: 0 0 0 0.125em rgba(158, 27, 13, 0.25); } - html.theme--documenter-dark .select.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.select { - border-radius: 3px; - font-size: 0.85em; } - html.theme--documenter-dark .select.is-medium { - font-size: 1.25rem; } - html.theme--documenter-dark .select.is-large { - font-size: 1.5rem; } - html.theme--documenter-dark .select.is-disabled::after { - border-color: white; } - html.theme--documenter-dark .select.is-fullwidth { - width: 100%; } - html.theme--documenter-dark .select.is-fullwidth select { - width: 100%; } - html.theme--documenter-dark .select.is-loading::after { - margin-top: 0; - position: absolute; - right: 0.625em; - top: 0.625em; - transform: none; } - html.theme--documenter-dark .select.is-loading.is-small:after, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-loading:after { - font-size: 0.85em; } - html.theme--documenter-dark .select.is-loading.is-medium:after { - font-size: 1.25rem; } - html.theme--documenter-dark .select.is-loading.is-large:after { - font-size: 1.5rem; } - html.theme--documenter-dark .file { - align-items: stretch; - display: flex; - justify-content: flex-start; - position: relative; } - html.theme--documenter-dark .file.is-white .file-cta { - background-color: white; - border-color: transparent; - color: #0a0a0a; } - html.theme--documenter-dark .file.is-white:hover .file-cta, html.theme--documenter-dark .file.is-white.is-hovered .file-cta { - background-color: #f9f9f9; - border-color: transparent; - color: #0a0a0a; } - html.theme--documenter-dark .file.is-white:focus .file-cta, html.theme--documenter-dark .file.is-white.is-focused .file-cta { - border-color: transparent; - box-shadow: 0 0 0.5em rgba(255, 255, 255, 0.25); - color: #0a0a0a; } - html.theme--documenter-dark .file.is-white:active .file-cta, html.theme--documenter-dark .file.is-white.is-active .file-cta { - background-color: #f2f2f2; - border-color: transparent; - color: #0a0a0a; } - html.theme--documenter-dark .file.is-black .file-cta { - background-color: #0a0a0a; - border-color: transparent; - color: white; } - html.theme--documenter-dark .file.is-black:hover .file-cta, html.theme--documenter-dark .file.is-black.is-hovered .file-cta { - background-color: #040404; - border-color: transparent; - color: white; } - html.theme--documenter-dark .file.is-black:focus .file-cta, html.theme--documenter-dark .file.is-black.is-focused .file-cta { - border-color: transparent; - box-shadow: 0 0 0.5em rgba(10, 10, 10, 0.25); - color: white; } - html.theme--documenter-dark .file.is-black:active .file-cta, html.theme--documenter-dark .file.is-black.is-active .file-cta { - background-color: black; - border-color: transparent; - color: white; } - html.theme--documenter-dark .file.is-light .file-cta { - background-color: #ecf0f1; - border-color: transparent; - color: #282f2f; } - html.theme--documenter-dark .file.is-light:hover .file-cta, html.theme--documenter-dark .file.is-light.is-hovered .file-cta { - background-color: #e5eaec; - border-color: transparent; - color: #282f2f; } - html.theme--documenter-dark .file.is-light:focus .file-cta, html.theme--documenter-dark .file.is-light.is-focused .file-cta { - border-color: transparent; - box-shadow: 0 0 0.5em rgba(236, 240, 241, 0.25); - color: #282f2f; } - html.theme--documenter-dark .file.is-light:active .file-cta, html.theme--documenter-dark .file.is-light.is-active .file-cta { - background-color: #dde4e6; - border-color: transparent; - color: #282f2f; } - html.theme--documenter-dark .file.is-dark .file-cta, html.theme--documenter-dark .content kbd.file .file-cta { - background-color: #282f2f; - border-color: transparent; - color: #ecf0f1; } - html.theme--documenter-dark .file.is-dark:hover .file-cta, html.theme--documenter-dark .content kbd.file:hover .file-cta, html.theme--documenter-dark .file.is-dark.is-hovered .file-cta, html.theme--documenter-dark .content kbd.file.is-hovered .file-cta { - background-color: #232829; - border-color: transparent; - color: #ecf0f1; } - html.theme--documenter-dark .file.is-dark:focus .file-cta, html.theme--documenter-dark .content kbd.file:focus .file-cta, html.theme--documenter-dark .file.is-dark.is-focused .file-cta, html.theme--documenter-dark .content kbd.file.is-focused .file-cta { - border-color: transparent; - box-shadow: 0 0 0.5em rgba(40, 47, 47, 0.25); - color: #ecf0f1; } - html.theme--documenter-dark .file.is-dark:active .file-cta, html.theme--documenter-dark .content kbd.file:active .file-cta, html.theme--documenter-dark .file.is-dark.is-active .file-cta, html.theme--documenter-dark .content kbd.file.is-active .file-cta { - background-color: #1d2122; - border-color: transparent; - color: #ecf0f1; } - html.theme--documenter-dark .file.is-primary .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink .file-cta { - background-color: #375a7f; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .file.is-primary:hover .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink:hover .file-cta, html.theme--documenter-dark .file.is-primary.is-hovered .file-cta, html.theme--documenter-dark .docstring > section > a.file.is-hovered.docs-sourcelink .file-cta { - background-color: #335476; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .file.is-primary:focus .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink:focus .file-cta, html.theme--documenter-dark .file.is-primary.is-focused .file-cta, html.theme--documenter-dark .docstring > section > a.file.is-focused.docs-sourcelink .file-cta { - border-color: transparent; - box-shadow: 0 0 0.5em rgba(55, 90, 127, 0.25); - color: #fff; } - html.theme--documenter-dark .file.is-primary:active .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink:active .file-cta, html.theme--documenter-dark .file.is-primary.is-active .file-cta, html.theme--documenter-dark .docstring > section > a.file.is-active.docs-sourcelink .file-cta { - background-color: #2f4d6d; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .file.is-link .file-cta { - background-color: #1abc9c; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .file.is-link:hover .file-cta, html.theme--documenter-dark .file.is-link.is-hovered .file-cta { - background-color: #18b193; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .file.is-link:focus .file-cta, html.theme--documenter-dark .file.is-link.is-focused .file-cta { - border-color: transparent; - box-shadow: 0 0 0.5em rgba(26, 188, 156, 0.25); - color: #fff; } - html.theme--documenter-dark .file.is-link:active .file-cta, html.theme--documenter-dark .file.is-link.is-active .file-cta { - background-color: #17a689; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .file.is-info .file-cta { - background-color: #024c7d; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .file.is-info:hover .file-cta, html.theme--documenter-dark .file.is-info.is-hovered .file-cta { - background-color: #024470; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .file.is-info:focus .file-cta, html.theme--documenter-dark .file.is-info.is-focused .file-cta { - border-color: transparent; - box-shadow: 0 0 0.5em rgba(2, 76, 125, 0.25); - color: #fff; } - html.theme--documenter-dark .file.is-info:active .file-cta, html.theme--documenter-dark .file.is-info.is-active .file-cta { - background-color: #023d64; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .file.is-success .file-cta { - background-color: #008438; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .file.is-success:hover .file-cta, html.theme--documenter-dark .file.is-success.is-hovered .file-cta { - background-color: #007733; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .file.is-success:focus .file-cta, html.theme--documenter-dark .file.is-success.is-focused .file-cta { - border-color: transparent; - box-shadow: 0 0 0.5em rgba(0, 132, 56, 0.25); - color: #fff; } - html.theme--documenter-dark .file.is-success:active .file-cta, html.theme--documenter-dark .file.is-success.is-active .file-cta { - background-color: #006b2d; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .file.is-warning .file-cta { - background-color: #ad8100; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .file.is-warning:hover .file-cta, html.theme--documenter-dark .file.is-warning.is-hovered .file-cta { - background-color: #a07700; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .file.is-warning:focus .file-cta, html.theme--documenter-dark .file.is-warning.is-focused .file-cta { - border-color: transparent; - box-shadow: 0 0 0.5em rgba(173, 129, 0, 0.25); - color: #fff; } - html.theme--documenter-dark .file.is-warning:active .file-cta, html.theme--documenter-dark .file.is-warning.is-active .file-cta { - background-color: #946e00; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .file.is-danger .file-cta { - background-color: #9e1b0d; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .file.is-danger:hover .file-cta, html.theme--documenter-dark .file.is-danger.is-hovered .file-cta { - background-color: #92190c; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .file.is-danger:focus .file-cta, html.theme--documenter-dark .file.is-danger.is-focused .file-cta { - border-color: transparent; - box-shadow: 0 0 0.5em rgba(158, 27, 13, 0.25); - color: #fff; } - html.theme--documenter-dark .file.is-danger:active .file-cta, html.theme--documenter-dark .file.is-danger.is-active .file-cta { - background-color: #86170b; - border-color: transparent; - color: #fff; } - html.theme--documenter-dark .file.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.file { - font-size: 0.85em; } - html.theme--documenter-dark .file.is-medium { - font-size: 1.25rem; } - html.theme--documenter-dark .file.is-medium .file-icon .fa { - font-size: 21px; } - html.theme--documenter-dark .file.is-large { - font-size: 1.5rem; } - html.theme--documenter-dark .file.is-large .file-icon .fa { - font-size: 28px; } - html.theme--documenter-dark .file.has-name .file-cta { - border-bottom-right-radius: 0; - border-top-right-radius: 0; } - html.theme--documenter-dark .file.has-name .file-name { - border-bottom-left-radius: 0; - border-top-left-radius: 0; } - html.theme--documenter-dark .file.has-name.is-empty .file-cta { - border-radius: 0.4em; } - html.theme--documenter-dark .file.has-name.is-empty .file-name { - display: none; } - html.theme--documenter-dark .file.is-boxed .file-label { - flex-direction: column; } - html.theme--documenter-dark .file.is-boxed .file-cta { - flex-direction: column; - height: auto; - padding: 1em 3em; } - html.theme--documenter-dark .file.is-boxed .file-name { - border-width: 0 1px 1px; } - html.theme--documenter-dark .file.is-boxed .file-icon { - height: 1.5em; - width: 1.5em; } - html.theme--documenter-dark .file.is-boxed .file-icon .fa { - font-size: 21px; } - html.theme--documenter-dark .file.is-boxed.is-small .file-icon .fa, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-boxed .file-icon .fa { - font-size: 14px; } - html.theme--documenter-dark .file.is-boxed.is-medium .file-icon .fa { - font-size: 28px; } - html.theme--documenter-dark .file.is-boxed.is-large .file-icon .fa { - font-size: 35px; } - html.theme--documenter-dark .file.is-boxed.has-name .file-cta { - border-radius: 0.4em 0.4em 0 0; } - html.theme--documenter-dark .file.is-boxed.has-name .file-name { - border-radius: 0 0 0.4em 0.4em; - border-width: 0 1px 1px; } - html.theme--documenter-dark .file.is-centered { - justify-content: center; } - html.theme--documenter-dark .file.is-fullwidth .file-label { - width: 100%; } - html.theme--documenter-dark .file.is-fullwidth .file-name { - flex-grow: 1; - max-width: none; } - html.theme--documenter-dark .file.is-right { - justify-content: flex-end; } - html.theme--documenter-dark .file.is-right .file-cta { - border-radius: 0 0.4em 0.4em 0; } - html.theme--documenter-dark .file.is-right .file-name { - border-radius: 0.4em 0 0 0.4em; - border-width: 1px 0 1px 1px; - order: -1; } - html.theme--documenter-dark .file-label { - align-items: stretch; - display: flex; - cursor: pointer; - justify-content: flex-start; - overflow: hidden; - position: relative; } - html.theme--documenter-dark .file-label:hover .file-cta { - background-color: #e5eaec; - color: #282f2f; } - html.theme--documenter-dark .file-label:hover .file-name { - border-color: #596668; } - html.theme--documenter-dark .file-label:active .file-cta { - background-color: #dde4e6; - color: #282f2f; } - html.theme--documenter-dark .file-label:active .file-name { - border-color: #535f61; } - html.theme--documenter-dark .file-input { - height: 100%; - left: 0; - opacity: 0; - outline: none; - position: absolute; - top: 0; - width: 100%; } - html.theme--documenter-dark .file-cta, - html.theme--documenter-dark .file-name { - border-color: #5e6d6f; - border-radius: 0.4em; - font-size: 1em; - padding-left: 1em; - padding-right: 1em; - white-space: nowrap; } - html.theme--documenter-dark .file-cta { - background-color: #ecf0f1; - color: #343c3d; } - html.theme--documenter-dark .file-name { - border-color: #5e6d6f; - border-style: solid; - border-width: 1px 1px 1px 0; - display: block; - max-width: 16em; - overflow: hidden; - text-align: left; - text-overflow: ellipsis; } - html.theme--documenter-dark .file-icon { - align-items: center; - display: flex; - height: 1em; - justify-content: center; - margin-right: 0.5em; - width: 1em; } - html.theme--documenter-dark .file-icon .fa { - font-size: 14px; } - html.theme--documenter-dark .label { - color: #282f2f; - display: block; - font-size: 15px; - font-weight: 700; } - html.theme--documenter-dark .label:not(:last-child) { - margin-bottom: 0.5em; } - html.theme--documenter-dark .label.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.label { - font-size: 0.85em; } - html.theme--documenter-dark .label.is-medium { - font-size: 1.25rem; } - html.theme--documenter-dark .label.is-large { - font-size: 1.5rem; } - html.theme--documenter-dark .help { - display: block; - font-size: 0.85em; - margin-top: 0.25rem; } - html.theme--documenter-dark .help.is-white { - color: white; } - html.theme--documenter-dark .help.is-black { - color: #0a0a0a; } - html.theme--documenter-dark .help.is-light { - color: #ecf0f1; } - html.theme--documenter-dark .help.is-dark, html.theme--documenter-dark .content kbd.help { - color: #282f2f; } - html.theme--documenter-dark .help.is-primary, html.theme--documenter-dark .docstring > section > a.help.docs-sourcelink { - color: #375a7f; } - html.theme--documenter-dark .help.is-link { - color: #1abc9c; } - html.theme--documenter-dark .help.is-info { - color: #024c7d; } - html.theme--documenter-dark .help.is-success { - color: #008438; } - html.theme--documenter-dark .help.is-warning { - color: #ad8100; } - html.theme--documenter-dark .help.is-danger { - color: #9e1b0d; } - html.theme--documenter-dark .field:not(:last-child) { - margin-bottom: 0.75rem; } - html.theme--documenter-dark .field.has-addons { - display: flex; - justify-content: flex-start; } - html.theme--documenter-dark .field.has-addons .control:not(:last-child) { - margin-right: -1px; } - html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) .button, - html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) .input, - html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) #documenter .docs-sidebar form.docs-search > input, - html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control:not(:first-child):not(:last-child) form.docs-search > input, - html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) .select select { - border-radius: 0; } - html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) .button, - html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) .input, - html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input, - html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control:first-child:not(:only-child) form.docs-search > input, - html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) .select select { - border-bottom-right-radius: 0; - border-top-right-radius: 0; } - html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) .button, - html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) .input, - html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input, - html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control:last-child:not(:only-child) form.docs-search > input, - html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) .select select { - border-bottom-left-radius: 0; - border-top-left-radius: 0; } - html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):hover, html.theme--documenter-dark .field.has-addons .control .button.is-hovered:not([disabled]), - html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):hover, - html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):hover, - html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):hover, - html.theme--documenter-dark .field.has-addons .control .input.is-hovered:not([disabled]), - html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-hovered:not([disabled]), - html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-hovered:not([disabled]), - html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):hover, - html.theme--documenter-dark .field.has-addons .control .select select.is-hovered:not([disabled]) { - z-index: 2; } - html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):focus, html.theme--documenter-dark .field.has-addons .control .button.is-focused:not([disabled]), html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):active, html.theme--documenter-dark .field.has-addons .control .button.is-active:not([disabled]), - html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):focus, - html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus, - html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus, - html.theme--documenter-dark .field.has-addons .control .input.is-focused:not([disabled]), - html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-focused:not([disabled]), - html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-focused:not([disabled]), - html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):active, - html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active, - html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active, - html.theme--documenter-dark .field.has-addons .control .input.is-active:not([disabled]), - html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-active:not([disabled]), - html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-active:not([disabled]), - html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):focus, - html.theme--documenter-dark .field.has-addons .control .select select.is-focused:not([disabled]), - html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):active, - html.theme--documenter-dark .field.has-addons .control .select select.is-active:not([disabled]) { - z-index: 3; } - html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):focus:hover, html.theme--documenter-dark .field.has-addons .control .button.is-focused:not([disabled]):hover, html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):active:hover, html.theme--documenter-dark .field.has-addons .control .button.is-active:not([disabled]):hover, - html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):focus:hover, - html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus:hover, - html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus:hover, - html.theme--documenter-dark .field.has-addons .control .input.is-focused:not([disabled]):hover, - html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-focused:not([disabled]):hover, - html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-focused:not([disabled]):hover, - html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):active:hover, - html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active:hover, - html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active:hover, - html.theme--documenter-dark .field.has-addons .control .input.is-active:not([disabled]):hover, - html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-active:not([disabled]):hover, - html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-active:not([disabled]):hover, - html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):focus:hover, - html.theme--documenter-dark .field.has-addons .control .select select.is-focused:not([disabled]):hover, - html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):active:hover, - html.theme--documenter-dark .field.has-addons .control .select select.is-active:not([disabled]):hover { - z-index: 4; } - html.theme--documenter-dark .field.has-addons .control.is-expanded { - flex-grow: 1; - flex-shrink: 1; } - html.theme--documenter-dark .field.has-addons.has-addons-centered { - justify-content: center; } - html.theme--documenter-dark .field.has-addons.has-addons-right { - justify-content: flex-end; } - html.theme--documenter-dark .field.has-addons.has-addons-fullwidth .control { - flex-grow: 1; - flex-shrink: 0; } - html.theme--documenter-dark .field.is-grouped { - display: flex; - justify-content: flex-start; } - html.theme--documenter-dark .field.is-grouped > .control { - flex-shrink: 0; } - html.theme--documenter-dark .field.is-grouped > .control:not(:last-child) { - margin-bottom: 0; - margin-right: 0.75rem; } - html.theme--documenter-dark .field.is-grouped > .control.is-expanded { - flex-grow: 1; - flex-shrink: 1; } - html.theme--documenter-dark .field.is-grouped.is-grouped-centered { - justify-content: center; } - html.theme--documenter-dark .field.is-grouped.is-grouped-right { - justify-content: flex-end; } - html.theme--documenter-dark .field.is-grouped.is-grouped-multiline { - flex-wrap: wrap; } - html.theme--documenter-dark .field.is-grouped.is-grouped-multiline > .control:last-child, html.theme--documenter-dark .field.is-grouped.is-grouped-multiline > .control:not(:last-child) { - margin-bottom: 0.75rem; } - html.theme--documenter-dark .field.is-grouped.is-grouped-multiline:last-child { - margin-bottom: -0.75rem; } - html.theme--documenter-dark .field.is-grouped.is-grouped-multiline:not(:last-child) { - margin-bottom: 0; } - @media screen and (min-width: 769px), print { - html.theme--documenter-dark .field.is-horizontal { - display: flex; } } - html.theme--documenter-dark .field-label .label { - font-size: inherit; } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .field-label { - margin-bottom: 0.5rem; } } - @media screen and (min-width: 769px), print { - html.theme--documenter-dark .field-label { - flex-basis: 0; - flex-grow: 1; - flex-shrink: 0; - margin-right: 1.5rem; - text-align: right; } - html.theme--documenter-dark .field-label.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.field-label { - font-size: 0.85em; - padding-top: 0.375em; } - html.theme--documenter-dark .field-label.is-normal { - padding-top: 0.375em; } - html.theme--documenter-dark .field-label.is-medium { - font-size: 1.25rem; - padding-top: 0.375em; } - html.theme--documenter-dark .field-label.is-large { - font-size: 1.5rem; - padding-top: 0.375em; } } - html.theme--documenter-dark .field-body .field .field { - margin-bottom: 0; } - @media screen and (min-width: 769px), print { - html.theme--documenter-dark .field-body { - display: flex; - flex-basis: 0; - flex-grow: 5; - flex-shrink: 1; } - html.theme--documenter-dark .field-body .field { - margin-bottom: 0; } - html.theme--documenter-dark .field-body > .field { - flex-shrink: 1; } - html.theme--documenter-dark .field-body > .field:not(.is-narrow) { - flex-grow: 1; } - html.theme--documenter-dark .field-body > .field:not(:last-child) { - margin-right: 0.75rem; } } - html.theme--documenter-dark .control { - box-sizing: border-box; - clear: both; - font-size: 15px; - position: relative; - text-align: left; } - html.theme--documenter-dark .control.has-icons-left .input:focus ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input:focus ~ .icon, - html.theme--documenter-dark .control.has-icons-left .select:focus ~ .icon, html.theme--documenter-dark .control.has-icons-right .input:focus ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input:focus ~ .icon, - html.theme--documenter-dark .control.has-icons-right .select:focus ~ .icon { - color: #5e6d6f; } - html.theme--documenter-dark .control.has-icons-left .input.is-small ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input ~ .icon, - html.theme--documenter-dark .control.has-icons-left .select.is-small ~ .icon, html.theme--documenter-dark .control.has-icons-right .input.is-small ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input ~ .icon, - html.theme--documenter-dark .control.has-icons-right .select.is-small ~ .icon { - font-size: 0.85em; } - html.theme--documenter-dark .control.has-icons-left .input.is-medium ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-medium ~ .icon, - html.theme--documenter-dark .control.has-icons-left .select.is-medium ~ .icon, html.theme--documenter-dark .control.has-icons-right .input.is-medium ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-medium ~ .icon, - html.theme--documenter-dark .control.has-icons-right .select.is-medium ~ .icon { - font-size: 1.25rem; } - html.theme--documenter-dark .control.has-icons-left .input.is-large ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-large ~ .icon, - html.theme--documenter-dark .control.has-icons-left .select.is-large ~ .icon, html.theme--documenter-dark .control.has-icons-right .input.is-large ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-large ~ .icon, - html.theme--documenter-dark .control.has-icons-right .select.is-large ~ .icon { - font-size: 1.5rem; } - html.theme--documenter-dark .control.has-icons-left .icon, html.theme--documenter-dark .control.has-icons-right .icon { - color: #dbdee0; - height: 2.25em; - pointer-events: none; - position: absolute; - top: 0; - width: 2.25em; - z-index: 4; } - html.theme--documenter-dark .control.has-icons-left .input, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input, - html.theme--documenter-dark .control.has-icons-left .select select { - padding-left: 2.25em; } - html.theme--documenter-dark .control.has-icons-left .icon.is-left { - left: 0; } - html.theme--documenter-dark .control.has-icons-right .input, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input, - html.theme--documenter-dark .control.has-icons-right .select select { - padding-right: 2.25em; } - html.theme--documenter-dark .control.has-icons-right .icon.is-right { - right: 0; } - html.theme--documenter-dark .control.is-loading::after { - position: absolute !important; - right: 0.625em; - top: 0.625em; - z-index: 4; } - html.theme--documenter-dark .control.is-loading.is-small:after, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-loading:after { - font-size: 0.85em; } - html.theme--documenter-dark .control.is-loading.is-medium:after { - font-size: 1.25rem; } - html.theme--documenter-dark .control.is-loading.is-large:after { - font-size: 1.5rem; } - html.theme--documenter-dark .breadcrumb { - font-size: 15px; - white-space: nowrap; } - html.theme--documenter-dark .breadcrumb a { - align-items: center; - color: #1abc9c; - display: flex; - justify-content: center; - padding: 0 0.75em; } - html.theme--documenter-dark .breadcrumb a:hover { - color: #1dd2af; } - html.theme--documenter-dark .breadcrumb li { - align-items: center; - display: flex; } - html.theme--documenter-dark .breadcrumb li:first-child a { - padding-left: 0; } - html.theme--documenter-dark .breadcrumb li.is-active a { - color: #f2f2f2; - cursor: default; - pointer-events: none; } - html.theme--documenter-dark .breadcrumb li + li::before { - color: #8c9b9d; - content: "\0002f"; } - html.theme--documenter-dark .breadcrumb ul, - html.theme--documenter-dark .breadcrumb ol { - align-items: flex-start; - display: flex; - flex-wrap: wrap; - justify-content: flex-start; } - html.theme--documenter-dark .breadcrumb .icon:first-child { - margin-right: 0.5em; } - html.theme--documenter-dark .breadcrumb .icon:last-child { - margin-left: 0.5em; } - html.theme--documenter-dark .breadcrumb.is-centered ol, - html.theme--documenter-dark .breadcrumb.is-centered ul { - justify-content: center; } - html.theme--documenter-dark .breadcrumb.is-right ol, - html.theme--documenter-dark .breadcrumb.is-right ul { - justify-content: flex-end; } - html.theme--documenter-dark .breadcrumb.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.breadcrumb { - font-size: 0.85em; } - html.theme--documenter-dark .breadcrumb.is-medium { - font-size: 1.25rem; } - html.theme--documenter-dark .breadcrumb.is-large { - font-size: 1.5rem; } - html.theme--documenter-dark .breadcrumb.has-arrow-separator li + li::before { - content: "\02192"; } - html.theme--documenter-dark .breadcrumb.has-bullet-separator li + li::before { - content: "\02022"; } - html.theme--documenter-dark .breadcrumb.has-dot-separator li + li::before { - content: "\000b7"; } - html.theme--documenter-dark .breadcrumb.has-succeeds-separator li + li::before { - content: "\0227B"; } - html.theme--documenter-dark .card { - background-color: white; - box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); - color: #fff; - max-width: 100%; - position: relative; } - html.theme--documenter-dark .card-header { - background-color: transparent; - align-items: stretch; - box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1); - display: flex; } - html.theme--documenter-dark .card-header-title { - align-items: center; - color: #f2f2f2; - display: flex; - flex-grow: 1; - font-weight: 700; - padding: 0.75rem; } - html.theme--documenter-dark .card-header-title.is-centered { - justify-content: center; } - html.theme--documenter-dark .card-header-icon { - align-items: center; - cursor: pointer; - display: flex; - justify-content: center; - padding: 0.75rem; } - html.theme--documenter-dark .card-image { - display: block; - position: relative; } - html.theme--documenter-dark .card-content { - background-color: transparent; - padding: 1.5rem; } - html.theme--documenter-dark .card-footer { - background-color: transparent; - border-top: 1px solid #5e6d6f; - align-items: stretch; - display: flex; } - html.theme--documenter-dark .card-footer-item { - align-items: center; - display: flex; - flex-basis: 0; - flex-grow: 1; - flex-shrink: 0; - justify-content: center; - padding: 0.75rem; } - html.theme--documenter-dark .card-footer-item:not(:last-child) { - border-right: 1px solid #5e6d6f; } - html.theme--documenter-dark .card .media:not(:last-child) { - margin-bottom: 1.5rem; } - html.theme--documenter-dark .dropdown { - display: inline-flex; - position: relative; - vertical-align: top; } - html.theme--documenter-dark .dropdown.is-active .dropdown-menu, html.theme--documenter-dark .dropdown.is-hoverable:hover .dropdown-menu { - display: block; } - html.theme--documenter-dark .dropdown.is-right .dropdown-menu { - left: auto; - right: 0; } - html.theme--documenter-dark .dropdown.is-up .dropdown-menu { - bottom: 100%; - padding-bottom: 4px; - padding-top: initial; - top: auto; } - html.theme--documenter-dark .dropdown-menu { - display: none; - left: 0; - min-width: 12rem; - padding-top: 4px; - position: absolute; - top: 100%; - z-index: 20; } - html.theme--documenter-dark .dropdown-content { - background-color: #282f2f; - border-radius: 0.4em; - box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); - padding-bottom: 0.5rem; - padding-top: 0.5rem; } - html.theme--documenter-dark .dropdown-item { - color: #fff; - display: block; - font-size: 0.875rem; - line-height: 1.5; - padding: 0.375rem 1rem; - position: relative; } - html.theme--documenter-dark a.dropdown-item, - html.theme--documenter-dark button.dropdown-item { - padding-right: 3rem; - text-align: left; - white-space: nowrap; - width: 100%; } - html.theme--documenter-dark a.dropdown-item:hover, - html.theme--documenter-dark button.dropdown-item:hover { - background-color: #282f2f; - color: #0a0a0a; } - html.theme--documenter-dark a.dropdown-item.is-active, - html.theme--documenter-dark button.dropdown-item.is-active { - background-color: #1abc9c; - color: #fff; } - html.theme--documenter-dark .dropdown-divider { - background-color: #5e6d6f; - border: none; - display: block; - height: 1px; - margin: 0.5rem 0; } - html.theme--documenter-dark .level { - align-items: center; - justify-content: space-between; } - html.theme--documenter-dark .level code { - border-radius: 0.4em; } - html.theme--documenter-dark .level img { - display: inline-block; - vertical-align: top; } - html.theme--documenter-dark .level.is-mobile { - display: flex; } - html.theme--documenter-dark .level.is-mobile .level-left, - html.theme--documenter-dark .level.is-mobile .level-right { - display: flex; } - html.theme--documenter-dark .level.is-mobile .level-left + .level-right { - margin-top: 0; } - html.theme--documenter-dark .level.is-mobile .level-item:not(:last-child) { - margin-bottom: 0; - margin-right: 0.75rem; } - html.theme--documenter-dark .level.is-mobile .level-item:not(.is-narrow) { - flex-grow: 1; } - @media screen and (min-width: 769px), print { - html.theme--documenter-dark .level { - display: flex; } - html.theme--documenter-dark .level > .level-item:not(.is-narrow) { - flex-grow: 1; } } - html.theme--documenter-dark .level-item { - align-items: center; - display: flex; - flex-basis: auto; - flex-grow: 0; - flex-shrink: 0; - justify-content: center; } - html.theme--documenter-dark .level-item .title, - html.theme--documenter-dark .level-item .subtitle { - margin-bottom: 0; } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .level-item:not(:last-child) { - margin-bottom: 0.75rem; } } - html.theme--documenter-dark .level-left, - html.theme--documenter-dark .level-right { - flex-basis: auto; - flex-grow: 0; - flex-shrink: 0; } - html.theme--documenter-dark .level-left .level-item.is-flexible, - html.theme--documenter-dark .level-right .level-item.is-flexible { - flex-grow: 1; } - @media screen and (min-width: 769px), print { - html.theme--documenter-dark .level-left .level-item:not(:last-child), - html.theme--documenter-dark .level-right .level-item:not(:last-child) { - margin-right: 0.75rem; } } - html.theme--documenter-dark .level-left { - align-items: center; - justify-content: flex-start; } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .level-left + .level-right { - margin-top: 1.5rem; } } - @media screen and (min-width: 769px), print { - html.theme--documenter-dark .level-left { - display: flex; } } - html.theme--documenter-dark .level-right { - align-items: center; - justify-content: flex-end; } - @media screen and (min-width: 769px), print { - html.theme--documenter-dark .level-right { - display: flex; } } - html.theme--documenter-dark .list { - background-color: white; - border-radius: 0.4em; - box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); } - html.theme--documenter-dark .list-item { - display: block; - padding: 0.5em 1em; } - html.theme--documenter-dark .list-item:not(a) { - color: #fff; } - html.theme--documenter-dark .list-item:first-child { - border-top-left-radius: 0.4em; - border-top-right-radius: 0.4em; } - html.theme--documenter-dark .list-item:last-child { - border-bottom-left-radius: 0.4em; - border-bottom-right-radius: 0.4em; } - html.theme--documenter-dark .list-item:not(:last-child) { - border-bottom: 1px solid #5e6d6f; } - html.theme--documenter-dark .list-item.is-active { - background-color: #1abc9c; - color: #fff; } - html.theme--documenter-dark a.list-item { - background-color: #282f2f; - cursor: pointer; } - html.theme--documenter-dark .media { - align-items: flex-start; - display: flex; - text-align: left; } - html.theme--documenter-dark .media .content:not(:last-child) { - margin-bottom: 0.75rem; } - html.theme--documenter-dark .media .media { - border-top: 1px solid rgba(94, 109, 111, 0.5); - display: flex; - padding-top: 0.75rem; } - html.theme--documenter-dark .media .media .content:not(:last-child), - html.theme--documenter-dark .media .media .control:not(:last-child) { - margin-bottom: 0.5rem; } - html.theme--documenter-dark .media .media .media { - padding-top: 0.5rem; } - html.theme--documenter-dark .media .media .media + .media { - margin-top: 0.5rem; } - html.theme--documenter-dark .media + .media { - border-top: 1px solid rgba(94, 109, 111, 0.5); - margin-top: 1rem; - padding-top: 1rem; } - html.theme--documenter-dark .media.is-large + .media { - margin-top: 1.5rem; - padding-top: 1.5rem; } - html.theme--documenter-dark .media-left, - html.theme--documenter-dark .media-right { - flex-basis: auto; - flex-grow: 0; - flex-shrink: 0; } - html.theme--documenter-dark .media-left { - margin-right: 1rem; } - html.theme--documenter-dark .media-right { - margin-left: 1rem; } - html.theme--documenter-dark .media-content { - flex-basis: auto; - flex-grow: 1; - flex-shrink: 1; - text-align: left; } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .media-content { - overflow-x: auto; } } - html.theme--documenter-dark .menu { - font-size: 15px; } - html.theme--documenter-dark .menu.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.menu { - font-size: 0.85em; } - html.theme--documenter-dark .menu.is-medium { - font-size: 1.25rem; } - html.theme--documenter-dark .menu.is-large { - font-size: 1.5rem; } - html.theme--documenter-dark .menu-list { - line-height: 1.25; } - html.theme--documenter-dark .menu-list a { - border-radius: 3px; - color: #fff; - display: block; - padding: 0.5em 0.75em; } - html.theme--documenter-dark .menu-list a:hover { - background-color: #282f2f; - color: #f2f2f2; } - html.theme--documenter-dark .menu-list a.is-active { - background-color: #1abc9c; - color: #fff; } - html.theme--documenter-dark .menu-list li ul { - border-left: 1px solid #5e6d6f; - margin: 0.75em; - padding-left: 0.75em; } - html.theme--documenter-dark .menu-label { - color: white; - font-size: 0.75em; - letter-spacing: 0.1em; - text-transform: uppercase; } - html.theme--documenter-dark .menu-label:not(:first-child) { - margin-top: 1em; } - html.theme--documenter-dark .menu-label:not(:last-child) { - margin-bottom: 1em; } - html.theme--documenter-dark .message { - background-color: #282f2f; - border-radius: 0.4em; - font-size: 15px; } - html.theme--documenter-dark .message strong { - color: currentColor; } - html.theme--documenter-dark .message a:not(.button):not(.tag):not(.dropdown-item) { - color: currentColor; - text-decoration: underline; } - html.theme--documenter-dark .message.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.message { - font-size: 0.85em; } - html.theme--documenter-dark .message.is-medium { - font-size: 1.25rem; } - html.theme--documenter-dark .message.is-large { - font-size: 1.5rem; } - html.theme--documenter-dark .message.is-white { - background-color: white; } - html.theme--documenter-dark .message.is-white .message-header { - background-color: white; - color: #0a0a0a; } - html.theme--documenter-dark .message.is-white .message-body { - border-color: white; - color: #4d4d4d; } - html.theme--documenter-dark .message.is-black { - background-color: #fafafa; } - html.theme--documenter-dark .message.is-black .message-header { - background-color: #0a0a0a; - color: white; } - html.theme--documenter-dark .message.is-black .message-body { - border-color: #0a0a0a; - color: #090909; } - html.theme--documenter-dark .message.is-light { - background-color: #f9fafb; } - html.theme--documenter-dark .message.is-light .message-header { - background-color: #ecf0f1; - color: #282f2f; } - html.theme--documenter-dark .message.is-light .message-body { - border-color: #ecf0f1; - color: #505050; } - html.theme--documenter-dark .message.is-dark, html.theme--documenter-dark .content kbd.message { - background-color: #f9fafa; } - html.theme--documenter-dark .message.is-dark .message-header, html.theme--documenter-dark .content kbd.message .message-header { - background-color: #282f2f; - color: #ecf0f1; } - html.theme--documenter-dark .message.is-dark .message-body, html.theme--documenter-dark .content kbd.message .message-body { - border-color: #282f2f; - color: #212526; } - html.theme--documenter-dark .message.is-primary, html.theme--documenter-dark .docstring > section > a.message.docs-sourcelink { - background-color: #f8fafc; } - html.theme--documenter-dark .message.is-primary .message-header, html.theme--documenter-dark .docstring > section > a.message.docs-sourcelink .message-header { - background-color: #375a7f; - color: #fff; } - html.theme--documenter-dark .message.is-primary .message-body, html.theme--documenter-dark .docstring > section > a.message.docs-sourcelink .message-body { - border-color: #375a7f; - color: #2b4159; } - html.theme--documenter-dark .message.is-link { - background-color: #f6fefc; } - html.theme--documenter-dark .message.is-link .message-header { - background-color: #1abc9c; - color: #fff; } - html.theme--documenter-dark .message.is-link .message-body { - border-color: #1abc9c; - color: #0b2f28; } - html.theme--documenter-dark .message.is-info { - background-color: #f5fbff; } - html.theme--documenter-dark .message.is-info .message-header { - background-color: #024c7d; - color: #fff; } - html.theme--documenter-dark .message.is-info .message-body { - border-color: #024c7d; - color: #033659; } - html.theme--documenter-dark .message.is-success { - background-color: #f5fff9; } - html.theme--documenter-dark .message.is-success .message-header { - background-color: #008438; - color: #fff; } - html.theme--documenter-dark .message.is-success .message-body { - border-color: #008438; - color: #023518; } - html.theme--documenter-dark .message.is-warning { - background-color: #fffcf5; } - html.theme--documenter-dark .message.is-warning .message-header { - background-color: #ad8100; - color: #fff; } - html.theme--documenter-dark .message.is-warning .message-body { - border-color: #ad8100; - color: #3d2e03; } - html.theme--documenter-dark .message.is-danger { - background-color: #fef6f6; } - html.theme--documenter-dark .message.is-danger .message-header { - background-color: #9e1b0d; - color: #fff; } - html.theme--documenter-dark .message.is-danger .message-body { - border-color: #9e1b0d; - color: #7a170c; } - html.theme--documenter-dark .message-header { - align-items: center; - background-color: #fff; - border-radius: 0.4em 0.4em 0 0; - color: rgba(0, 0, 0, 0.7); - display: flex; - font-weight: 700; - justify-content: space-between; - line-height: 1.25; - padding: 0.75em 1em; - position: relative; } - html.theme--documenter-dark .message-header .delete { - flex-grow: 0; - flex-shrink: 0; - margin-left: 0.75em; } - html.theme--documenter-dark .message-header + .message-body { - border-width: 0; - border-top-left-radius: 0; - border-top-right-radius: 0; } - html.theme--documenter-dark .message-body { - border-color: #5e6d6f; - border-radius: 0.4em; - border-style: solid; - border-width: 0 0 0 4px; - color: #fff; - padding: 1.25em 1.5em; } - html.theme--documenter-dark .message-body code, - html.theme--documenter-dark .message-body pre { - background-color: white; } - html.theme--documenter-dark .message-body pre code { - background-color: transparent; } - html.theme--documenter-dark .modal { - align-items: center; - display: none; - flex-direction: column; - justify-content: center; - overflow: hidden; - position: fixed; - z-index: 40; } - html.theme--documenter-dark .modal.is-active { - display: flex; } - html.theme--documenter-dark .modal-background { - background-color: rgba(10, 10, 10, 0.86); } - html.theme--documenter-dark .modal-content, - html.theme--documenter-dark .modal-card { - margin: 0 20px; - max-height: calc(100vh - 160px); - overflow: auto; - position: relative; - width: 100%; } - @media screen and (min-width: 769px), print { - html.theme--documenter-dark .modal-content, - html.theme--documenter-dark .modal-card { - margin: 0 auto; - max-height: calc(100vh - 40px); - width: 640px; } } - html.theme--documenter-dark .modal-close { - background: none; - height: 40px; - position: fixed; - right: 20px; - top: 20px; - width: 40px; } - html.theme--documenter-dark .modal-card { - display: flex; - flex-direction: column; - max-height: calc(100vh - 40px); - overflow: hidden; - -ms-overflow-y: visible; } - html.theme--documenter-dark .modal-card-head, - html.theme--documenter-dark .modal-card-foot { - align-items: center; - background-color: #282f2f; - display: flex; - flex-shrink: 0; - justify-content: flex-start; - padding: 20px; - position: relative; } - html.theme--documenter-dark .modal-card-head { - border-bottom: 1px solid #5e6d6f; - border-top-left-radius: 8px; - border-top-right-radius: 8px; } - html.theme--documenter-dark .modal-card-title { - color: #f2f2f2; - flex-grow: 1; - flex-shrink: 0; - font-size: 1.5rem; - line-height: 1; } - html.theme--documenter-dark .modal-card-foot { - border-bottom-left-radius: 8px; - border-bottom-right-radius: 8px; - border-top: 1px solid #5e6d6f; } - html.theme--documenter-dark .modal-card-foot .button:not(:last-child) { - margin-right: 0.5em; } - html.theme--documenter-dark .modal-card-body { - -webkit-overflow-scrolling: touch; - background-color: white; - flex-grow: 1; - flex-shrink: 1; - overflow: auto; - padding: 20px; } - html.theme--documenter-dark .navbar { - background-color: #375a7f; - min-height: 4rem; - position: relative; - z-index: 30; } - html.theme--documenter-dark .navbar.is-white { - background-color: white; - color: #0a0a0a; } - html.theme--documenter-dark .navbar.is-white .navbar-brand > .navbar-item, - html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link { - color: #0a0a0a; } - html.theme--documenter-dark .navbar.is-white .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-white .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-white .navbar-brand > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link:focus, - html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link:hover, - html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link.is-active { - background-color: #f2f2f2; - color: #0a0a0a; } - html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link::after { - border-color: #0a0a0a; } - html.theme--documenter-dark .navbar.is-white .navbar-burger { - color: #0a0a0a; } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark .navbar.is-white .navbar-start > .navbar-item, - html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link, - html.theme--documenter-dark .navbar.is-white .navbar-end > .navbar-item, - html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link { - color: #0a0a0a; } - html.theme--documenter-dark .navbar.is-white .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-white .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-white .navbar-start > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link:focus, - html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link:hover, - html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link.is-active, - html.theme--documenter-dark .navbar.is-white .navbar-end > a.navbar-item:focus, - html.theme--documenter-dark .navbar.is-white .navbar-end > a.navbar-item:hover, - html.theme--documenter-dark .navbar.is-white .navbar-end > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link:focus, - html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link:hover, - html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link.is-active { - background-color: #f2f2f2; - color: #0a0a0a; } - html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link::after, - html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link::after { - border-color: #0a0a0a; } - html.theme--documenter-dark .navbar.is-white .navbar-item.has-dropdown:focus .navbar-link, - html.theme--documenter-dark .navbar.is-white .navbar-item.has-dropdown:hover .navbar-link, - html.theme--documenter-dark .navbar.is-white .navbar-item.has-dropdown.is-active .navbar-link { - background-color: #f2f2f2; - color: #0a0a0a; } - html.theme--documenter-dark .navbar.is-white .navbar-dropdown a.navbar-item.is-active { - background-color: white; - color: #0a0a0a; } } - html.theme--documenter-dark .navbar.is-black { - background-color: #0a0a0a; - color: white; } - html.theme--documenter-dark .navbar.is-black .navbar-brand > .navbar-item, - html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link { - color: white; } - html.theme--documenter-dark .navbar.is-black .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-black .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-black .navbar-brand > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link:focus, - html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link:hover, - html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link.is-active { - background-color: black; - color: white; } - html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link::after { - border-color: white; } - html.theme--documenter-dark .navbar.is-black .navbar-burger { - color: white; } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark .navbar.is-black .navbar-start > .navbar-item, - html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link, - html.theme--documenter-dark .navbar.is-black .navbar-end > .navbar-item, - html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link { - color: white; } - html.theme--documenter-dark .navbar.is-black .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-black .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-black .navbar-start > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link:focus, - html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link:hover, - html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link.is-active, - html.theme--documenter-dark .navbar.is-black .navbar-end > a.navbar-item:focus, - html.theme--documenter-dark .navbar.is-black .navbar-end > a.navbar-item:hover, - html.theme--documenter-dark .navbar.is-black .navbar-end > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link:focus, - html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link:hover, - html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link.is-active { - background-color: black; - color: white; } - html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link::after, - html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link::after { - border-color: white; } - html.theme--documenter-dark .navbar.is-black .navbar-item.has-dropdown:focus .navbar-link, - html.theme--documenter-dark .navbar.is-black .navbar-item.has-dropdown:hover .navbar-link, - html.theme--documenter-dark .navbar.is-black .navbar-item.has-dropdown.is-active .navbar-link { - background-color: black; - color: white; } - html.theme--documenter-dark .navbar.is-black .navbar-dropdown a.navbar-item.is-active { - background-color: #0a0a0a; - color: white; } } - html.theme--documenter-dark .navbar.is-light { - background-color: #ecf0f1; - color: #282f2f; } - html.theme--documenter-dark .navbar.is-light .navbar-brand > .navbar-item, - html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link { - color: #282f2f; } - html.theme--documenter-dark .navbar.is-light .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-light .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-light .navbar-brand > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link:focus, - html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link:hover, - html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link.is-active { - background-color: #dde4e6; - color: #282f2f; } - html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link::after { - border-color: #282f2f; } - html.theme--documenter-dark .navbar.is-light .navbar-burger { - color: #282f2f; } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark .navbar.is-light .navbar-start > .navbar-item, - html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link, - html.theme--documenter-dark .navbar.is-light .navbar-end > .navbar-item, - html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link { - color: #282f2f; } - html.theme--documenter-dark .navbar.is-light .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-light .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-light .navbar-start > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link:focus, - html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link:hover, - html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link.is-active, - html.theme--documenter-dark .navbar.is-light .navbar-end > a.navbar-item:focus, - html.theme--documenter-dark .navbar.is-light .navbar-end > a.navbar-item:hover, - html.theme--documenter-dark .navbar.is-light .navbar-end > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link:focus, - html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link:hover, - html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link.is-active { - background-color: #dde4e6; - color: #282f2f; } - html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link::after, - html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link::after { - border-color: #282f2f; } - html.theme--documenter-dark .navbar.is-light .navbar-item.has-dropdown:focus .navbar-link, - html.theme--documenter-dark .navbar.is-light .navbar-item.has-dropdown:hover .navbar-link, - html.theme--documenter-dark .navbar.is-light .navbar-item.has-dropdown.is-active .navbar-link { - background-color: #dde4e6; - color: #282f2f; } - html.theme--documenter-dark .navbar.is-light .navbar-dropdown a.navbar-item.is-active { - background-color: #ecf0f1; - color: #282f2f; } } - html.theme--documenter-dark .navbar.is-dark, html.theme--documenter-dark .content kbd.navbar { - background-color: #282f2f; - color: #ecf0f1; } - html.theme--documenter-dark .navbar.is-dark .navbar-brand > .navbar-item, html.theme--documenter-dark .content kbd.navbar .navbar-brand > .navbar-item, - html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link, - html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link { - color: #ecf0f1; } - html.theme--documenter-dark .navbar.is-dark .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .content kbd.navbar .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-dark .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .content kbd.navbar .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-dark .navbar-brand > a.navbar-item.is-active, html.theme--documenter-dark .content kbd.navbar .navbar-brand > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link:focus, - html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link:focus, - html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link:hover, - html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link:hover, - html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link.is-active, - html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link.is-active { - background-color: #1d2122; - color: #ecf0f1; } - html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link::after, html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link::after { - border-color: #ecf0f1; } - html.theme--documenter-dark .navbar.is-dark .navbar-burger, html.theme--documenter-dark .content kbd.navbar .navbar-burger { - color: #ecf0f1; } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark .navbar.is-dark .navbar-start > .navbar-item, html.theme--documenter-dark .content kbd.navbar .navbar-start > .navbar-item, - html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link, - html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link, - html.theme--documenter-dark .navbar.is-dark .navbar-end > .navbar-item, - html.theme--documenter-dark .content kbd.navbar .navbar-end > .navbar-item, - html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link, - html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link { - color: #ecf0f1; } - html.theme--documenter-dark .navbar.is-dark .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .content kbd.navbar .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-dark .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .content kbd.navbar .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-dark .navbar-start > a.navbar-item.is-active, html.theme--documenter-dark .content kbd.navbar .navbar-start > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link:focus, - html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link:focus, - html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link:hover, - html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link:hover, - html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link.is-active, - html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link.is-active, - html.theme--documenter-dark .navbar.is-dark .navbar-end > a.navbar-item:focus, - html.theme--documenter-dark .content kbd.navbar .navbar-end > a.navbar-item:focus, - html.theme--documenter-dark .navbar.is-dark .navbar-end > a.navbar-item:hover, - html.theme--documenter-dark .content kbd.navbar .navbar-end > a.navbar-item:hover, - html.theme--documenter-dark .navbar.is-dark .navbar-end > a.navbar-item.is-active, - html.theme--documenter-dark .content kbd.navbar .navbar-end > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link:focus, - html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link:focus, - html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link:hover, - html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link:hover, - html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link.is-active, - html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link.is-active { - background-color: #1d2122; - color: #ecf0f1; } - html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link::after, html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link::after, - html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link::after, - html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link::after { - border-color: #ecf0f1; } - html.theme--documenter-dark .navbar.is-dark .navbar-item.has-dropdown:focus .navbar-link, html.theme--documenter-dark .content kbd.navbar .navbar-item.has-dropdown:focus .navbar-link, - html.theme--documenter-dark .navbar.is-dark .navbar-item.has-dropdown:hover .navbar-link, - html.theme--documenter-dark .content kbd.navbar .navbar-item.has-dropdown:hover .navbar-link, - html.theme--documenter-dark .navbar.is-dark .navbar-item.has-dropdown.is-active .navbar-link, - html.theme--documenter-dark .content kbd.navbar .navbar-item.has-dropdown.is-active .navbar-link { - background-color: #1d2122; - color: #ecf0f1; } - html.theme--documenter-dark .navbar.is-dark .navbar-dropdown a.navbar-item.is-active, html.theme--documenter-dark .content kbd.navbar .navbar-dropdown a.navbar-item.is-active { - background-color: #282f2f; - color: #ecf0f1; } } - html.theme--documenter-dark .navbar.is-primary, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink { - background-color: #375a7f; - color: #fff; } - html.theme--documenter-dark .navbar.is-primary .navbar-brand > .navbar-item, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > .navbar-item, - html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link, - html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link { - color: #fff; } - html.theme--documenter-dark .navbar.is-primary .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-primary .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-primary .navbar-brand > a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link:focus, - html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:focus, - html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link:hover, - html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:hover, - html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link.is-active, - html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link.is-active { - background-color: #2f4d6d; - color: #fff; } - html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link::after, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link::after { - border-color: #fff; } - html.theme--documenter-dark .navbar.is-primary .navbar-burger, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-burger { - color: #fff; } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark .navbar.is-primary .navbar-start > .navbar-item, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > .navbar-item, - html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link, - html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link, - html.theme--documenter-dark .navbar.is-primary .navbar-end > .navbar-item, - html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > .navbar-item, - html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link, - html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link { - color: #fff; } - html.theme--documenter-dark .navbar.is-primary .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-primary .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-primary .navbar-start > a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link:focus, - html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:focus, - html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link:hover, - html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:hover, - html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link.is-active, - html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link.is-active, - html.theme--documenter-dark .navbar.is-primary .navbar-end > a.navbar-item:focus, - html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:focus, - html.theme--documenter-dark .navbar.is-primary .navbar-end > a.navbar-item:hover, - html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:hover, - html.theme--documenter-dark .navbar.is-primary .navbar-end > a.navbar-item.is-active, - html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link:focus, - html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:focus, - html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link:hover, - html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:hover, - html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link.is-active, - html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link.is-active { - background-color: #2f4d6d; - color: #fff; } - html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link::after, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link::after, - html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link::after, - html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link::after { - border-color: #fff; } - html.theme--documenter-dark .navbar.is-primary .navbar-item.has-dropdown:focus .navbar-link, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:focus .navbar-link, - html.theme--documenter-dark .navbar.is-primary .navbar-item.has-dropdown:hover .navbar-link, - html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:hover .navbar-link, - html.theme--documenter-dark .navbar.is-primary .navbar-item.has-dropdown.is-active .navbar-link, - html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown.is-active .navbar-link { - background-color: #2f4d6d; - color: #fff; } - html.theme--documenter-dark .navbar.is-primary .navbar-dropdown a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-dropdown a.navbar-item.is-active { - background-color: #375a7f; - color: #fff; } } - html.theme--documenter-dark .navbar.is-link { - background-color: #1abc9c; - color: #fff; } - html.theme--documenter-dark .navbar.is-link .navbar-brand > .navbar-item, - html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link { - color: #fff; } - html.theme--documenter-dark .navbar.is-link .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-link .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-link .navbar-brand > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link:focus, - html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link:hover, - html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link.is-active { - background-color: #17a689; - color: #fff; } - html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link::after { - border-color: #fff; } - html.theme--documenter-dark .navbar.is-link .navbar-burger { - color: #fff; } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark .navbar.is-link .navbar-start > .navbar-item, - html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link, - html.theme--documenter-dark .navbar.is-link .navbar-end > .navbar-item, - html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link { - color: #fff; } - html.theme--documenter-dark .navbar.is-link .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-link .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-link .navbar-start > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link:focus, - html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link:hover, - html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link.is-active, - html.theme--documenter-dark .navbar.is-link .navbar-end > a.navbar-item:focus, - html.theme--documenter-dark .navbar.is-link .navbar-end > a.navbar-item:hover, - html.theme--documenter-dark .navbar.is-link .navbar-end > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link:focus, - html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link:hover, - html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link.is-active { - background-color: #17a689; - color: #fff; } - html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link::after, - html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link::after { - border-color: #fff; } - html.theme--documenter-dark .navbar.is-link .navbar-item.has-dropdown:focus .navbar-link, - html.theme--documenter-dark .navbar.is-link .navbar-item.has-dropdown:hover .navbar-link, - html.theme--documenter-dark .navbar.is-link .navbar-item.has-dropdown.is-active .navbar-link { - background-color: #17a689; - color: #fff; } - html.theme--documenter-dark .navbar.is-link .navbar-dropdown a.navbar-item.is-active { - background-color: #1abc9c; - color: #fff; } } - html.theme--documenter-dark .navbar.is-info { - background-color: #024c7d; - color: #fff; } - html.theme--documenter-dark .navbar.is-info .navbar-brand > .navbar-item, - html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link { - color: #fff; } - html.theme--documenter-dark .navbar.is-info .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-info .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-info .navbar-brand > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link:focus, - html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link:hover, - html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link.is-active { - background-color: #023d64; - color: #fff; } - html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link::after { - border-color: #fff; } - html.theme--documenter-dark .navbar.is-info .navbar-burger { - color: #fff; } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark .navbar.is-info .navbar-start > .navbar-item, - html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link, - html.theme--documenter-dark .navbar.is-info .navbar-end > .navbar-item, - html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link { - color: #fff; } - html.theme--documenter-dark .navbar.is-info .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-info .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-info .navbar-start > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link:focus, - html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link:hover, - html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link.is-active, - html.theme--documenter-dark .navbar.is-info .navbar-end > a.navbar-item:focus, - html.theme--documenter-dark .navbar.is-info .navbar-end > a.navbar-item:hover, - html.theme--documenter-dark .navbar.is-info .navbar-end > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link:focus, - html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link:hover, - html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link.is-active { - background-color: #023d64; - color: #fff; } - html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link::after, - html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link::after { - border-color: #fff; } - html.theme--documenter-dark .navbar.is-info .navbar-item.has-dropdown:focus .navbar-link, - html.theme--documenter-dark .navbar.is-info .navbar-item.has-dropdown:hover .navbar-link, - html.theme--documenter-dark .navbar.is-info .navbar-item.has-dropdown.is-active .navbar-link { - background-color: #023d64; - color: #fff; } - html.theme--documenter-dark .navbar.is-info .navbar-dropdown a.navbar-item.is-active { - background-color: #024c7d; - color: #fff; } } - html.theme--documenter-dark .navbar.is-success { - background-color: #008438; - color: #fff; } - html.theme--documenter-dark .navbar.is-success .navbar-brand > .navbar-item, - html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link { - color: #fff; } - html.theme--documenter-dark .navbar.is-success .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-success .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-success .navbar-brand > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link:focus, - html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link:hover, - html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link.is-active { - background-color: #006b2d; - color: #fff; } - html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link::after { - border-color: #fff; } - html.theme--documenter-dark .navbar.is-success .navbar-burger { - color: #fff; } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark .navbar.is-success .navbar-start > .navbar-item, - html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link, - html.theme--documenter-dark .navbar.is-success .navbar-end > .navbar-item, - html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link { - color: #fff; } - html.theme--documenter-dark .navbar.is-success .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-success .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-success .navbar-start > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link:focus, - html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link:hover, - html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link.is-active, - html.theme--documenter-dark .navbar.is-success .navbar-end > a.navbar-item:focus, - html.theme--documenter-dark .navbar.is-success .navbar-end > a.navbar-item:hover, - html.theme--documenter-dark .navbar.is-success .navbar-end > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link:focus, - html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link:hover, - html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link.is-active { - background-color: #006b2d; - color: #fff; } - html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link::after, - html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link::after { - border-color: #fff; } - html.theme--documenter-dark .navbar.is-success .navbar-item.has-dropdown:focus .navbar-link, - html.theme--documenter-dark .navbar.is-success .navbar-item.has-dropdown:hover .navbar-link, - html.theme--documenter-dark .navbar.is-success .navbar-item.has-dropdown.is-active .navbar-link { - background-color: #006b2d; - color: #fff; } - html.theme--documenter-dark .navbar.is-success .navbar-dropdown a.navbar-item.is-active { - background-color: #008438; - color: #fff; } } - html.theme--documenter-dark .navbar.is-warning { - background-color: #ad8100; - color: #fff; } - html.theme--documenter-dark .navbar.is-warning .navbar-brand > .navbar-item, - html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link { - color: #fff; } - html.theme--documenter-dark .navbar.is-warning .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-warning .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-warning .navbar-brand > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link:focus, - html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link:hover, - html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link.is-active { - background-color: #946e00; - color: #fff; } - html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link::after { - border-color: #fff; } - html.theme--documenter-dark .navbar.is-warning .navbar-burger { - color: #fff; } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark .navbar.is-warning .navbar-start > .navbar-item, - html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link, - html.theme--documenter-dark .navbar.is-warning .navbar-end > .navbar-item, - html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link { - color: #fff; } - html.theme--documenter-dark .navbar.is-warning .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-warning .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-warning .navbar-start > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link:focus, - html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link:hover, - html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link.is-active, - html.theme--documenter-dark .navbar.is-warning .navbar-end > a.navbar-item:focus, - html.theme--documenter-dark .navbar.is-warning .navbar-end > a.navbar-item:hover, - html.theme--documenter-dark .navbar.is-warning .navbar-end > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link:focus, - html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link:hover, - html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link.is-active { - background-color: #946e00; - color: #fff; } - html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link::after, - html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link::after { - border-color: #fff; } - html.theme--documenter-dark .navbar.is-warning .navbar-item.has-dropdown:focus .navbar-link, - html.theme--documenter-dark .navbar.is-warning .navbar-item.has-dropdown:hover .navbar-link, - html.theme--documenter-dark .navbar.is-warning .navbar-item.has-dropdown.is-active .navbar-link { - background-color: #946e00; - color: #fff; } - html.theme--documenter-dark .navbar.is-warning .navbar-dropdown a.navbar-item.is-active { - background-color: #ad8100; - color: #fff; } } - html.theme--documenter-dark .navbar.is-danger { - background-color: #9e1b0d; - color: #fff; } - html.theme--documenter-dark .navbar.is-danger .navbar-brand > .navbar-item, - html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link { - color: #fff; } - html.theme--documenter-dark .navbar.is-danger .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-danger .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-danger .navbar-brand > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link:focus, - html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link:hover, - html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link.is-active { - background-color: #86170b; - color: #fff; } - html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link::after { - border-color: #fff; } - html.theme--documenter-dark .navbar.is-danger .navbar-burger { - color: #fff; } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark .navbar.is-danger .navbar-start > .navbar-item, - html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link, - html.theme--documenter-dark .navbar.is-danger .navbar-end > .navbar-item, - html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link { - color: #fff; } - html.theme--documenter-dark .navbar.is-danger .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-danger .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-danger .navbar-start > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link:focus, - html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link:hover, - html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link.is-active, - html.theme--documenter-dark .navbar.is-danger .navbar-end > a.navbar-item:focus, - html.theme--documenter-dark .navbar.is-danger .navbar-end > a.navbar-item:hover, - html.theme--documenter-dark .navbar.is-danger .navbar-end > a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link:focus, - html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link:hover, - html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link.is-active { - background-color: #86170b; - color: #fff; } - html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link::after, - html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link::after { - border-color: #fff; } - html.theme--documenter-dark .navbar.is-danger .navbar-item.has-dropdown:focus .navbar-link, - html.theme--documenter-dark .navbar.is-danger .navbar-item.has-dropdown:hover .navbar-link, - html.theme--documenter-dark .navbar.is-danger .navbar-item.has-dropdown.is-active .navbar-link { - background-color: #86170b; - color: #fff; } - html.theme--documenter-dark .navbar.is-danger .navbar-dropdown a.navbar-item.is-active { - background-color: #9e1b0d; - color: #fff; } } - html.theme--documenter-dark .navbar > .container { - align-items: stretch; - display: flex; - min-height: 4rem; - width: 100%; } - html.theme--documenter-dark .navbar.has-shadow { - box-shadow: 0 2px 0 0 #282f2f; } - html.theme--documenter-dark .navbar.is-fixed-bottom, html.theme--documenter-dark .navbar.is-fixed-top { - left: 0; - position: fixed; - right: 0; - z-index: 30; } - html.theme--documenter-dark .navbar.is-fixed-bottom { - bottom: 0; } - html.theme--documenter-dark .navbar.is-fixed-bottom.has-shadow { - box-shadow: 0 -2px 0 0 #282f2f; } - html.theme--documenter-dark .navbar.is-fixed-top { - top: 0; } - html.theme--documenter-dark html.has-navbar-fixed-top, - html.theme--documenter-dark body.has-navbar-fixed-top { - padding-top: 4rem; } - html.theme--documenter-dark html.has-navbar-fixed-bottom, - html.theme--documenter-dark body.has-navbar-fixed-bottom { - padding-bottom: 4rem; } - html.theme--documenter-dark .navbar-brand, - html.theme--documenter-dark .navbar-tabs { - align-items: stretch; - display: flex; - flex-shrink: 0; - min-height: 4rem; } - html.theme--documenter-dark .navbar-brand a.navbar-item:focus, html.theme--documenter-dark .navbar-brand a.navbar-item:hover { - background-color: transparent; } - html.theme--documenter-dark .navbar-tabs { - -webkit-overflow-scrolling: touch; - max-width: 100vw; - overflow-x: auto; - overflow-y: hidden; } - html.theme--documenter-dark .navbar-burger { - color: #fff; - cursor: pointer; - display: block; - height: 4rem; - position: relative; - width: 4rem; - margin-left: auto; } - html.theme--documenter-dark .navbar-burger span { - background-color: currentColor; - display: block; - height: 1px; - left: calc(50% - 8px); - position: absolute; - transform-origin: center; - transition-duration: 86ms; - transition-property: background-color, opacity, transform; - transition-timing-function: ease-out; - width: 16px; } - html.theme--documenter-dark .navbar-burger span:nth-child(1) { - top: calc(50% - 6px); } - html.theme--documenter-dark .navbar-burger span:nth-child(2) { - top: calc(50% - 1px); } - html.theme--documenter-dark .navbar-burger span:nth-child(3) { - top: calc(50% + 4px); } - html.theme--documenter-dark .navbar-burger:hover { - background-color: rgba(0, 0, 0, 0.05); } - html.theme--documenter-dark .navbar-burger.is-active span:nth-child(1) { - transform: translateY(5px) rotate(45deg); } - html.theme--documenter-dark .navbar-burger.is-active span:nth-child(2) { - opacity: 0; } - html.theme--documenter-dark .navbar-burger.is-active span:nth-child(3) { - transform: translateY(-5px) rotate(-45deg); } - html.theme--documenter-dark .navbar-menu { - display: none; } - html.theme--documenter-dark .navbar-item, - html.theme--documenter-dark .navbar-link { - color: #fff; - display: block; - line-height: 1.5; - padding: 0.5rem 0.75rem; - position: relative; } - html.theme--documenter-dark .navbar-item .icon:only-child, - html.theme--documenter-dark .navbar-link .icon:only-child { - margin-left: -0.25rem; - margin-right: -0.25rem; } - html.theme--documenter-dark a.navbar-item, - html.theme--documenter-dark .navbar-link { - cursor: pointer; } - html.theme--documenter-dark a.navbar-item:focus, html.theme--documenter-dark a.navbar-item:focus-within, html.theme--documenter-dark a.navbar-item:hover, html.theme--documenter-dark a.navbar-item.is-active, - html.theme--documenter-dark .navbar-link:focus, - html.theme--documenter-dark .navbar-link:focus-within, - html.theme--documenter-dark .navbar-link:hover, - html.theme--documenter-dark .navbar-link.is-active { - background-color: transparent; - color: #1abc9c; } - html.theme--documenter-dark .navbar-item { - display: block; - flex-grow: 0; - flex-shrink: 0; } - html.theme--documenter-dark .navbar-item img { - max-height: 1.75rem; } - html.theme--documenter-dark .navbar-item.has-dropdown { - padding: 0; } - html.theme--documenter-dark .navbar-item.is-expanded { - flex-grow: 1; - flex-shrink: 1; } - html.theme--documenter-dark .navbar-item.is-tab { - border-bottom: 1px solid transparent; - min-height: 4rem; - padding-bottom: calc(0.5rem - 1px); } - html.theme--documenter-dark .navbar-item.is-tab:focus, html.theme--documenter-dark .navbar-item.is-tab:hover { - background-color: transparent; - border-bottom-color: #1abc9c; } - html.theme--documenter-dark .navbar-item.is-tab.is-active { - background-color: transparent; - border-bottom-color: #1abc9c; - border-bottom-style: solid; - border-bottom-width: 3px; - color: #1abc9c; - padding-bottom: calc(0.5rem - 3px); } - html.theme--documenter-dark .navbar-content { - flex-grow: 1; - flex-shrink: 1; } - html.theme--documenter-dark .navbar-link:not(.is-arrowless) { - padding-right: 2.5em; } - html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after { - border-color: #fff; - margin-top: -0.375em; - right: 1.125em; } - html.theme--documenter-dark .navbar-dropdown { - font-size: 0.875rem; - padding-bottom: 0.5rem; - padding-top: 0.5rem; } - html.theme--documenter-dark .navbar-dropdown .navbar-item { - padding-left: 1.5rem; - padding-right: 1.5rem; } - html.theme--documenter-dark .navbar-divider { - background-color: rgba(0, 0, 0, 0.2); - border: none; - display: none; - height: 2px; - margin: 0.5rem 0; } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark .navbar > .container { - display: block; } - html.theme--documenter-dark .navbar-brand .navbar-item, - html.theme--documenter-dark .navbar-tabs .navbar-item { - align-items: center; - display: flex; } - html.theme--documenter-dark .navbar-link::after { - display: none; } - html.theme--documenter-dark .navbar-menu { - background-color: #375a7f; - box-shadow: 0 8px 16px rgba(10, 10, 10, 0.1); - padding: 0.5rem 0; } - html.theme--documenter-dark .navbar-menu.is-active { - display: block; } - html.theme--documenter-dark .navbar.is-fixed-bottom-touch, html.theme--documenter-dark .navbar.is-fixed-top-touch { - left: 0; - position: fixed; - right: 0; - z-index: 30; } - html.theme--documenter-dark .navbar.is-fixed-bottom-touch { - bottom: 0; } - html.theme--documenter-dark .navbar.is-fixed-bottom-touch.has-shadow { - box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); } - html.theme--documenter-dark .navbar.is-fixed-top-touch { - top: 0; } - html.theme--documenter-dark .navbar.is-fixed-top .navbar-menu, html.theme--documenter-dark .navbar.is-fixed-top-touch .navbar-menu { - -webkit-overflow-scrolling: touch; - max-height: calc(100vh - 4rem); - overflow: auto; } - html.theme--documenter-dark html.has-navbar-fixed-top-touch, - html.theme--documenter-dark body.has-navbar-fixed-top-touch { - padding-top: 4rem; } - html.theme--documenter-dark html.has-navbar-fixed-bottom-touch, - html.theme--documenter-dark body.has-navbar-fixed-bottom-touch { - padding-bottom: 4rem; } } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark .navbar, - html.theme--documenter-dark .navbar-menu, - html.theme--documenter-dark .navbar-start, - html.theme--documenter-dark .navbar-end { - align-items: stretch; - display: flex; } - html.theme--documenter-dark .navbar { - min-height: 4rem; } - html.theme--documenter-dark .navbar.is-spaced { - padding: 1rem 2rem; } - html.theme--documenter-dark .navbar.is-spaced .navbar-start, - html.theme--documenter-dark .navbar.is-spaced .navbar-end { - align-items: center; } - html.theme--documenter-dark .navbar.is-spaced a.navbar-item, - html.theme--documenter-dark .navbar.is-spaced .navbar-link { - border-radius: 0.4em; } - html.theme--documenter-dark .navbar.is-transparent a.navbar-item:focus, html.theme--documenter-dark .navbar.is-transparent a.navbar-item:hover, html.theme--documenter-dark .navbar.is-transparent a.navbar-item.is-active, - html.theme--documenter-dark .navbar.is-transparent .navbar-link:focus, - html.theme--documenter-dark .navbar.is-transparent .navbar-link:hover, - html.theme--documenter-dark .navbar.is-transparent .navbar-link.is-active { - background-color: transparent !important; } - html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-active .navbar-link, html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus .navbar-link, html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus-within .navbar-link, html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:hover .navbar-link { - background-color: transparent !important; } - html.theme--documenter-dark .navbar.is-transparent .navbar-dropdown a.navbar-item:focus, html.theme--documenter-dark .navbar.is-transparent .navbar-dropdown a.navbar-item:hover { - background-color: transparent; - color: #dbdee0; } - html.theme--documenter-dark .navbar.is-transparent .navbar-dropdown a.navbar-item.is-active { - background-color: transparent; - color: #1abc9c; } - html.theme--documenter-dark .navbar-burger { - display: none; } - html.theme--documenter-dark .navbar-item, - html.theme--documenter-dark .navbar-link { - align-items: center; - display: flex; } - html.theme--documenter-dark .navbar-item { - display: flex; } - html.theme--documenter-dark .navbar-item.has-dropdown { - align-items: stretch; } - html.theme--documenter-dark .navbar-item.has-dropdown-up .navbar-link::after { - transform: rotate(135deg) translate(0.25em, -0.25em); } - html.theme--documenter-dark .navbar-item.has-dropdown-up .navbar-dropdown { - border-bottom: 1px solid rgba(0, 0, 0, 0.2); - border-radius: 8px 8px 0 0; - border-top: none; - bottom: 100%; - box-shadow: 0 -8px 8px rgba(10, 10, 10, 0.1); - top: auto; } - html.theme--documenter-dark .navbar-item.is-active .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus-within .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:hover .navbar-dropdown { - display: block; } - .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-active .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-active .navbar-dropdown.is-boxed, .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-hoverable:focus .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus .navbar-dropdown.is-boxed, .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-hoverable:focus-within .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus-within .navbar-dropdown.is-boxed, .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-hoverable:hover .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:hover .navbar-dropdown.is-boxed { - opacity: 1; - pointer-events: auto; - transform: translateY(0); } - html.theme--documenter-dark .navbar-menu { - flex-grow: 1; - flex-shrink: 0; } - html.theme--documenter-dark .navbar-start { - justify-content: flex-start; - margin-right: auto; } - html.theme--documenter-dark .navbar-end { - justify-content: flex-end; - margin-left: auto; } - html.theme--documenter-dark .navbar-dropdown { - background-color: #375a7f; - border-bottom-left-radius: 8px; - border-bottom-right-radius: 8px; - border-top: 1px solid rgba(0, 0, 0, 0.2); - box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1); - display: none; - font-size: 0.875rem; - left: 0; - min-width: 100%; - position: absolute; - top: 100%; - z-index: 20; } - html.theme--documenter-dark .navbar-dropdown .navbar-item { - padding: 0.375rem 1rem; - white-space: nowrap; } - html.theme--documenter-dark .navbar-dropdown a.navbar-item { - padding-right: 3rem; } - html.theme--documenter-dark .navbar-dropdown a.navbar-item:focus, html.theme--documenter-dark .navbar-dropdown a.navbar-item:hover { - background-color: transparent; - color: #dbdee0; } - html.theme--documenter-dark .navbar-dropdown a.navbar-item.is-active { - background-color: transparent; - color: #1abc9c; } - .navbar.is-spaced html.theme--documenter-dark .navbar-dropdown, html.theme--documenter-dark .navbar-dropdown.is-boxed { - border-radius: 8px; - border-top: none; - box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); - display: block; - opacity: 0; - pointer-events: none; - top: calc(100% + (-4px)); - transform: translateY(-5px); - transition-duration: 86ms; - transition-property: opacity, transform; } - html.theme--documenter-dark .navbar-dropdown.is-right { - left: auto; - right: 0; } - html.theme--documenter-dark .navbar-divider { - display: block; } - html.theme--documenter-dark .navbar > .container .navbar-brand, - html.theme--documenter-dark .container > .navbar .navbar-brand { - margin-left: -.75rem; } - html.theme--documenter-dark .navbar > .container .navbar-menu, - html.theme--documenter-dark .container > .navbar .navbar-menu { - margin-right: -.75rem; } - html.theme--documenter-dark .navbar.is-fixed-bottom-desktop, html.theme--documenter-dark .navbar.is-fixed-top-desktop { - left: 0; - position: fixed; - right: 0; - z-index: 30; } - html.theme--documenter-dark .navbar.is-fixed-bottom-desktop { - bottom: 0; } - html.theme--documenter-dark .navbar.is-fixed-bottom-desktop.has-shadow { - box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); } - html.theme--documenter-dark .navbar.is-fixed-top-desktop { - top: 0; } - html.theme--documenter-dark html.has-navbar-fixed-top-desktop, - html.theme--documenter-dark body.has-navbar-fixed-top-desktop { - padding-top: 4rem; } - html.theme--documenter-dark html.has-navbar-fixed-bottom-desktop, - html.theme--documenter-dark body.has-navbar-fixed-bottom-desktop { - padding-bottom: 4rem; } - html.theme--documenter-dark html.has-spaced-navbar-fixed-top, - html.theme--documenter-dark body.has-spaced-navbar-fixed-top { - padding-top: 6rem; } - html.theme--documenter-dark html.has-spaced-navbar-fixed-bottom, - html.theme--documenter-dark body.has-spaced-navbar-fixed-bottom { - padding-bottom: 6rem; } - html.theme--documenter-dark a.navbar-item.is-active, - html.theme--documenter-dark .navbar-link.is-active { - color: #1abc9c; } - html.theme--documenter-dark a.navbar-item.is-active:not(:focus):not(:hover), - html.theme--documenter-dark .navbar-link.is-active:not(:focus):not(:hover) { - background-color: transparent; } - html.theme--documenter-dark .navbar-item.has-dropdown:focus .navbar-link, html.theme--documenter-dark .navbar-item.has-dropdown:hover .navbar-link, html.theme--documenter-dark .navbar-item.has-dropdown.is-active .navbar-link { - background-color: transparent; } } - html.theme--documenter-dark .hero.is-fullheight-with-navbar { - min-height: calc(100vh - 4rem); } - html.theme--documenter-dark .pagination { - font-size: 15px; - margin: -0.25rem; } - html.theme--documenter-dark .pagination.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination { - font-size: 0.85em; } - html.theme--documenter-dark .pagination.is-medium { - font-size: 1.25rem; } - html.theme--documenter-dark .pagination.is-large { - font-size: 1.5rem; } - html.theme--documenter-dark .pagination.is-rounded .pagination-previous, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination .pagination-previous, - html.theme--documenter-dark .pagination.is-rounded .pagination-next, - html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination .pagination-next { - padding-left: 1em; - padding-right: 1em; - border-radius: 290486px; } - html.theme--documenter-dark .pagination.is-rounded .pagination-link, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination .pagination-link { - border-radius: 290486px; } - html.theme--documenter-dark .pagination, - html.theme--documenter-dark .pagination-list { - align-items: center; - display: flex; - justify-content: center; - text-align: center; } - html.theme--documenter-dark .pagination-previous, - html.theme--documenter-dark .pagination-next, - html.theme--documenter-dark .pagination-link, - html.theme--documenter-dark .pagination-ellipsis { - font-size: 1em; - justify-content: center; - margin: 0.25rem; - padding-left: 0.5em; - padding-right: 0.5em; - text-align: center; } - html.theme--documenter-dark .pagination-previous, - html.theme--documenter-dark .pagination-next, - html.theme--documenter-dark .pagination-link { - border-color: #5e6d6f; - color: #1abc9c; - min-width: 2.25em; } - html.theme--documenter-dark .pagination-previous:hover, - html.theme--documenter-dark .pagination-next:hover, - html.theme--documenter-dark .pagination-link:hover { - border-color: #8c9b9d; - color: #1dd2af; } - html.theme--documenter-dark .pagination-previous:focus, - html.theme--documenter-dark .pagination-next:focus, - html.theme--documenter-dark .pagination-link:focus { - border-color: #8c9b9d; } - html.theme--documenter-dark .pagination-previous:active, - html.theme--documenter-dark .pagination-next:active, - html.theme--documenter-dark .pagination-link:active { - box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2); } - html.theme--documenter-dark .pagination-previous[disabled], - html.theme--documenter-dark .pagination-next[disabled], - html.theme--documenter-dark .pagination-link[disabled] { - background-color: #dbdee0; - border-color: #dbdee0; - box-shadow: none; - color: #5e6d6f; - opacity: 0.5; } - html.theme--documenter-dark .pagination-previous, - html.theme--documenter-dark .pagination-next { - padding-left: 0.75em; - padding-right: 0.75em; - white-space: nowrap; } - html.theme--documenter-dark .pagination-link.is-current { - background-color: #1abc9c; - border-color: #1abc9c; - color: #fff; } - html.theme--documenter-dark .pagination-ellipsis { - color: #8c9b9d; - pointer-events: none; } - html.theme--documenter-dark .pagination-list { - flex-wrap: wrap; } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .pagination { - flex-wrap: wrap; } - html.theme--documenter-dark .pagination-previous, - html.theme--documenter-dark .pagination-next { - flex-grow: 1; - flex-shrink: 1; } - html.theme--documenter-dark .pagination-list li { - flex-grow: 1; - flex-shrink: 1; } } - @media screen and (min-width: 769px), print { - html.theme--documenter-dark .pagination-list { - flex-grow: 1; - flex-shrink: 1; - justify-content: flex-start; - order: 1; } - html.theme--documenter-dark .pagination-previous { - order: 2; } - html.theme--documenter-dark .pagination-next { - order: 3; } - html.theme--documenter-dark .pagination { - justify-content: space-between; } - html.theme--documenter-dark .pagination.is-centered .pagination-previous { - order: 1; } - html.theme--documenter-dark .pagination.is-centered .pagination-list { - justify-content: center; - order: 2; } - html.theme--documenter-dark .pagination.is-centered .pagination-next { - order: 3; } - html.theme--documenter-dark .pagination.is-right .pagination-previous { - order: 1; } - html.theme--documenter-dark .pagination.is-right .pagination-next { - order: 2; } - html.theme--documenter-dark .pagination.is-right .pagination-list { - justify-content: flex-end; - order: 3; } } - html.theme--documenter-dark .panel { - font-size: 15px; } - html.theme--documenter-dark .panel:not(:last-child) { - margin-bottom: 1.5rem; } - html.theme--documenter-dark .panel-heading, - html.theme--documenter-dark .panel-tabs, - html.theme--documenter-dark .panel-block { - border-bottom: 1px solid #5e6d6f; - border-left: 1px solid #5e6d6f; - border-right: 1px solid #5e6d6f; } - html.theme--documenter-dark .panel-heading:first-child, - html.theme--documenter-dark .panel-tabs:first-child, - html.theme--documenter-dark .panel-block:first-child { - border-top: 1px solid #5e6d6f; } - html.theme--documenter-dark .panel-heading { - background-color: #282f2f; - border-radius: 0.4em 0.4em 0 0; - color: #f2f2f2; - font-size: 1.25em; - font-weight: 300; - line-height: 1.25; - padding: 0.5em 0.75em; } - html.theme--documenter-dark .panel-tabs { - align-items: flex-end; - display: flex; - font-size: 0.875em; - justify-content: center; } - html.theme--documenter-dark .panel-tabs a { - border-bottom: 1px solid #5e6d6f; - margin-bottom: -1px; - padding: 0.5em; } - html.theme--documenter-dark .panel-tabs a.is-active { - border-bottom-color: #343c3d; - color: #17a689; } - html.theme--documenter-dark .panel-list a { - color: #fff; } - html.theme--documenter-dark .panel-list a:hover { - color: #1abc9c; } - html.theme--documenter-dark .panel-block { - align-items: center; - color: #f2f2f2; - display: flex; - justify-content: flex-start; - padding: 0.5em 0.75em; } - html.theme--documenter-dark .panel-block input[type="checkbox"] { - margin-right: 0.75em; } - html.theme--documenter-dark .panel-block > .control { - flex-grow: 1; - flex-shrink: 1; - width: 100%; } - html.theme--documenter-dark .panel-block.is-wrapped { - flex-wrap: wrap; } - html.theme--documenter-dark .panel-block.is-active { - border-left-color: #1abc9c; - color: #17a689; } - html.theme--documenter-dark .panel-block.is-active .panel-icon { - color: #1abc9c; } - html.theme--documenter-dark a.panel-block, - html.theme--documenter-dark label.panel-block { - cursor: pointer; } - html.theme--documenter-dark a.panel-block:hover, - html.theme--documenter-dark label.panel-block:hover { - background-color: #282f2f; } - html.theme--documenter-dark .panel-icon { - display: inline-block; - font-size: 14px; - height: 1em; - line-height: 1em; - text-align: center; - vertical-align: top; - width: 1em; - color: white; - margin-right: 0.75em; } - html.theme--documenter-dark .panel-icon .fa { - font-size: inherit; - line-height: inherit; } - html.theme--documenter-dark .tabs { - -webkit-overflow-scrolling: touch; - align-items: stretch; - display: flex; - font-size: 15px; - justify-content: space-between; - overflow: hidden; - overflow-x: auto; - white-space: nowrap; } - html.theme--documenter-dark .tabs a { - align-items: center; - border-bottom-color: #5e6d6f; - border-bottom-style: solid; - border-bottom-width: 1px; - color: #fff; - display: flex; - justify-content: center; - margin-bottom: -1px; - padding: 0.5em 1em; - vertical-align: top; } - html.theme--documenter-dark .tabs a:hover { - border-bottom-color: #f2f2f2; - color: #f2f2f2; } - html.theme--documenter-dark .tabs li { - display: block; } - html.theme--documenter-dark .tabs li.is-active a { - border-bottom-color: #1abc9c; - color: #1abc9c; } - html.theme--documenter-dark .tabs ul { - align-items: center; - border-bottom-color: #5e6d6f; - border-bottom-style: solid; - border-bottom-width: 1px; - display: flex; - flex-grow: 1; - flex-shrink: 0; - justify-content: flex-start; } - html.theme--documenter-dark .tabs ul.is-left { - padding-right: 0.75em; } - html.theme--documenter-dark .tabs ul.is-center { - flex: none; - justify-content: center; - padding-left: 0.75em; - padding-right: 0.75em; } - html.theme--documenter-dark .tabs ul.is-right { - justify-content: flex-end; - padding-left: 0.75em; } - html.theme--documenter-dark .tabs .icon:first-child { - margin-right: 0.5em; } - html.theme--documenter-dark .tabs .icon:last-child { - margin-left: 0.5em; } - html.theme--documenter-dark .tabs.is-centered ul { - justify-content: center; } - html.theme--documenter-dark .tabs.is-right ul { - justify-content: flex-end; } - html.theme--documenter-dark .tabs.is-boxed a { - border: 1px solid transparent; - border-radius: 0.4em 0.4em 0 0; } - html.theme--documenter-dark .tabs.is-boxed a:hover { - background-color: #282f2f; - border-bottom-color: #5e6d6f; } - html.theme--documenter-dark .tabs.is-boxed li.is-active a { - background-color: white; - border-color: #5e6d6f; - border-bottom-color: transparent !important; } - html.theme--documenter-dark .tabs.is-fullwidth li { - flex-grow: 1; - flex-shrink: 0; } - html.theme--documenter-dark .tabs.is-toggle a { - border-color: #5e6d6f; - border-style: solid; - border-width: 1px; - margin-bottom: 0; - position: relative; } - html.theme--documenter-dark .tabs.is-toggle a:hover { - background-color: #282f2f; - border-color: #8c9b9d; - z-index: 2; } - html.theme--documenter-dark .tabs.is-toggle li + li { - margin-left: -1px; } - html.theme--documenter-dark .tabs.is-toggle li:first-child a { - border-radius: 0.4em 0 0 0.4em; } - html.theme--documenter-dark .tabs.is-toggle li:last-child a { - border-radius: 0 0.4em 0.4em 0; } - html.theme--documenter-dark .tabs.is-toggle li.is-active a { - background-color: #1abc9c; - border-color: #1abc9c; - color: #fff; - z-index: 1; } - html.theme--documenter-dark .tabs.is-toggle ul { - border-bottom: none; } - html.theme--documenter-dark .tabs.is-toggle.is-toggle-rounded li:first-child a { - border-bottom-left-radius: 290486px; - border-top-left-radius: 290486px; - padding-left: 1.25em; } - html.theme--documenter-dark .tabs.is-toggle.is-toggle-rounded li:last-child a { - border-bottom-right-radius: 290486px; - border-top-right-radius: 290486px; - padding-right: 1.25em; } - html.theme--documenter-dark .tabs.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.tabs { - font-size: 0.85em; } - html.theme--documenter-dark .tabs.is-medium { - font-size: 1.25rem; } - html.theme--documenter-dark .tabs.is-large { - font-size: 1.5rem; } - html.theme--documenter-dark .column { - display: block; - flex-basis: 0; - flex-grow: 1; - flex-shrink: 1; - padding: 0.75rem; } - .columns.is-mobile > html.theme--documenter-dark .column.is-narrow { - flex: none; } - .columns.is-mobile > html.theme--documenter-dark .column.is-full { - flex: none; - width: 100%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-three-quarters { - flex: none; - width: 75%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-two-thirds { - flex: none; - width: 66.6666%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-half { - flex: none; - width: 50%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-one-third { - flex: none; - width: 33.3333%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-one-quarter { - flex: none; - width: 25%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-one-fifth { - flex: none; - width: 20%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-two-fifths { - flex: none; - width: 40%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-three-fifths { - flex: none; - width: 60%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-four-fifths { - flex: none; - width: 80%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-offset-three-quarters { - margin-left: 75%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-offset-two-thirds { - margin-left: 66.6666%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-offset-half { - margin-left: 50%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-offset-one-third { - margin-left: 33.3333%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-offset-one-quarter { - margin-left: 25%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-offset-one-fifth { - margin-left: 20%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-offset-two-fifths { - margin-left: 40%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-offset-three-fifths { - margin-left: 60%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-offset-four-fifths { - margin-left: 80%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-0 { - flex: none; - width: 0%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-offset-0 { - margin-left: 0%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-1 { - flex: none; - width: 8.3333333333%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-offset-1 { - margin-left: 8.3333333333%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-2 { - flex: none; - width: 16.6666666667%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-offset-2 { - margin-left: 16.6666666667%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-3 { - flex: none; - width: 25%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-offset-3 { - margin-left: 25%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-4 { - flex: none; - width: 33.3333333333%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-offset-4 { - margin-left: 33.3333333333%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-5 { - flex: none; - width: 41.6666666667%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-offset-5 { - margin-left: 41.6666666667%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-6 { - flex: none; - width: 50%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-offset-6 { - margin-left: 50%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-7 { - flex: none; - width: 58.3333333333%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-offset-7 { - margin-left: 58.3333333333%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-8 { - flex: none; - width: 66.6666666667%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-offset-8 { - margin-left: 66.6666666667%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-9 { - flex: none; - width: 75%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-offset-9 { - margin-left: 75%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-10 { - flex: none; - width: 83.3333333333%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-offset-10 { - margin-left: 83.3333333333%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-11 { - flex: none; - width: 91.6666666667%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-offset-11 { - margin-left: 91.6666666667%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-12 { - flex: none; - width: 100%; } - .columns.is-mobile > html.theme--documenter-dark .column.is-offset-12 { - margin-left: 100%; } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .column.is-narrow-mobile { - flex: none; } - html.theme--documenter-dark .column.is-full-mobile { - flex: none; - width: 100%; } - html.theme--documenter-dark .column.is-three-quarters-mobile { - flex: none; - width: 75%; } - html.theme--documenter-dark .column.is-two-thirds-mobile { - flex: none; - width: 66.6666%; } - html.theme--documenter-dark .column.is-half-mobile { - flex: none; - width: 50%; } - html.theme--documenter-dark .column.is-one-third-mobile { - flex: none; - width: 33.3333%; } - html.theme--documenter-dark .column.is-one-quarter-mobile { - flex: none; - width: 25%; } - html.theme--documenter-dark .column.is-one-fifth-mobile { - flex: none; - width: 20%; } - html.theme--documenter-dark .column.is-two-fifths-mobile { - flex: none; - width: 40%; } - html.theme--documenter-dark .column.is-three-fifths-mobile { - flex: none; - width: 60%; } - html.theme--documenter-dark .column.is-four-fifths-mobile { - flex: none; - width: 80%; } - html.theme--documenter-dark .column.is-offset-three-quarters-mobile { - margin-left: 75%; } - html.theme--documenter-dark .column.is-offset-two-thirds-mobile { - margin-left: 66.6666%; } - html.theme--documenter-dark .column.is-offset-half-mobile { - margin-left: 50%; } - html.theme--documenter-dark .column.is-offset-one-third-mobile { - margin-left: 33.3333%; } - html.theme--documenter-dark .column.is-offset-one-quarter-mobile { - margin-left: 25%; } - html.theme--documenter-dark .column.is-offset-one-fifth-mobile { - margin-left: 20%; } - html.theme--documenter-dark .column.is-offset-two-fifths-mobile { - margin-left: 40%; } - html.theme--documenter-dark .column.is-offset-three-fifths-mobile { - margin-left: 60%; } - html.theme--documenter-dark .column.is-offset-four-fifths-mobile { - margin-left: 80%; } - html.theme--documenter-dark .column.is-0-mobile { - flex: none; - width: 0%; } - html.theme--documenter-dark .column.is-offset-0-mobile { - margin-left: 0%; } - html.theme--documenter-dark .column.is-1-mobile { - flex: none; - width: 8.3333333333%; } - html.theme--documenter-dark .column.is-offset-1-mobile { - margin-left: 8.3333333333%; } - html.theme--documenter-dark .column.is-2-mobile { - flex: none; - width: 16.6666666667%; } - html.theme--documenter-dark .column.is-offset-2-mobile { - margin-left: 16.6666666667%; } - html.theme--documenter-dark .column.is-3-mobile { - flex: none; - width: 25%; } - html.theme--documenter-dark .column.is-offset-3-mobile { - margin-left: 25%; } - html.theme--documenter-dark .column.is-4-mobile { - flex: none; - width: 33.3333333333%; } - html.theme--documenter-dark .column.is-offset-4-mobile { - margin-left: 33.3333333333%; } - html.theme--documenter-dark .column.is-5-mobile { - flex: none; - width: 41.6666666667%; } - html.theme--documenter-dark .column.is-offset-5-mobile { - margin-left: 41.6666666667%; } - html.theme--documenter-dark .column.is-6-mobile { - flex: none; - width: 50%; } - html.theme--documenter-dark .column.is-offset-6-mobile { - margin-left: 50%; } - html.theme--documenter-dark .column.is-7-mobile { - flex: none; - width: 58.3333333333%; } - html.theme--documenter-dark .column.is-offset-7-mobile { - margin-left: 58.3333333333%; } - html.theme--documenter-dark .column.is-8-mobile { - flex: none; - width: 66.6666666667%; } - html.theme--documenter-dark .column.is-offset-8-mobile { - margin-left: 66.6666666667%; } - html.theme--documenter-dark .column.is-9-mobile { - flex: none; - width: 75%; } - html.theme--documenter-dark .column.is-offset-9-mobile { - margin-left: 75%; } - html.theme--documenter-dark .column.is-10-mobile { - flex: none; - width: 83.3333333333%; } - html.theme--documenter-dark .column.is-offset-10-mobile { - margin-left: 83.3333333333%; } - html.theme--documenter-dark .column.is-11-mobile { - flex: none; - width: 91.6666666667%; } - html.theme--documenter-dark .column.is-offset-11-mobile { - margin-left: 91.6666666667%; } - html.theme--documenter-dark .column.is-12-mobile { - flex: none; - width: 100%; } - html.theme--documenter-dark .column.is-offset-12-mobile { - margin-left: 100%; } } - @media screen and (min-width: 769px), print { - html.theme--documenter-dark .column.is-narrow, html.theme--documenter-dark .column.is-narrow-tablet { - flex: none; } - html.theme--documenter-dark .column.is-full, html.theme--documenter-dark .column.is-full-tablet { - flex: none; - width: 100%; } - html.theme--documenter-dark .column.is-three-quarters, html.theme--documenter-dark .column.is-three-quarters-tablet { - flex: none; - width: 75%; } - html.theme--documenter-dark .column.is-two-thirds, html.theme--documenter-dark .column.is-two-thirds-tablet { - flex: none; - width: 66.6666%; } - html.theme--documenter-dark .column.is-half, html.theme--documenter-dark .column.is-half-tablet { - flex: none; - width: 50%; } - html.theme--documenter-dark .column.is-one-third, html.theme--documenter-dark .column.is-one-third-tablet { - flex: none; - width: 33.3333%; } - html.theme--documenter-dark .column.is-one-quarter, html.theme--documenter-dark .column.is-one-quarter-tablet { - flex: none; - width: 25%; } - html.theme--documenter-dark .column.is-one-fifth, html.theme--documenter-dark .column.is-one-fifth-tablet { - flex: none; - width: 20%; } - html.theme--documenter-dark .column.is-two-fifths, html.theme--documenter-dark .column.is-two-fifths-tablet { - flex: none; - width: 40%; } - html.theme--documenter-dark .column.is-three-fifths, html.theme--documenter-dark .column.is-three-fifths-tablet { - flex: none; - width: 60%; } - html.theme--documenter-dark .column.is-four-fifths, html.theme--documenter-dark .column.is-four-fifths-tablet { - flex: none; - width: 80%; } - html.theme--documenter-dark .column.is-offset-three-quarters, html.theme--documenter-dark .column.is-offset-three-quarters-tablet { - margin-left: 75%; } - html.theme--documenter-dark .column.is-offset-two-thirds, html.theme--documenter-dark .column.is-offset-two-thirds-tablet { - margin-left: 66.6666%; } - html.theme--documenter-dark .column.is-offset-half, html.theme--documenter-dark .column.is-offset-half-tablet { - margin-left: 50%; } - html.theme--documenter-dark .column.is-offset-one-third, html.theme--documenter-dark .column.is-offset-one-third-tablet { - margin-left: 33.3333%; } - html.theme--documenter-dark .column.is-offset-one-quarter, html.theme--documenter-dark .column.is-offset-one-quarter-tablet { - margin-left: 25%; } - html.theme--documenter-dark .column.is-offset-one-fifth, html.theme--documenter-dark .column.is-offset-one-fifth-tablet { - margin-left: 20%; } - html.theme--documenter-dark .column.is-offset-two-fifths, html.theme--documenter-dark .column.is-offset-two-fifths-tablet { - margin-left: 40%; } - html.theme--documenter-dark .column.is-offset-three-fifths, html.theme--documenter-dark .column.is-offset-three-fifths-tablet { - margin-left: 60%; } - html.theme--documenter-dark .column.is-offset-four-fifths, html.theme--documenter-dark .column.is-offset-four-fifths-tablet { - margin-left: 80%; } - html.theme--documenter-dark .column.is-0, html.theme--documenter-dark .column.is-0-tablet { - flex: none; - width: 0%; } - html.theme--documenter-dark .column.is-offset-0, html.theme--documenter-dark .column.is-offset-0-tablet { - margin-left: 0%; } - html.theme--documenter-dark .column.is-1, html.theme--documenter-dark .column.is-1-tablet { - flex: none; - width: 8.3333333333%; } - html.theme--documenter-dark .column.is-offset-1, html.theme--documenter-dark .column.is-offset-1-tablet { - margin-left: 8.3333333333%; } - html.theme--documenter-dark .column.is-2, html.theme--documenter-dark .column.is-2-tablet { - flex: none; - width: 16.6666666667%; } - html.theme--documenter-dark .column.is-offset-2, html.theme--documenter-dark .column.is-offset-2-tablet { - margin-left: 16.6666666667%; } - html.theme--documenter-dark .column.is-3, html.theme--documenter-dark .column.is-3-tablet { - flex: none; - width: 25%; } - html.theme--documenter-dark .column.is-offset-3, html.theme--documenter-dark .column.is-offset-3-tablet { - margin-left: 25%; } - html.theme--documenter-dark .column.is-4, html.theme--documenter-dark .column.is-4-tablet { - flex: none; - width: 33.3333333333%; } - html.theme--documenter-dark .column.is-offset-4, html.theme--documenter-dark .column.is-offset-4-tablet { - margin-left: 33.3333333333%; } - html.theme--documenter-dark .column.is-5, html.theme--documenter-dark .column.is-5-tablet { - flex: none; - width: 41.6666666667%; } - html.theme--documenter-dark .column.is-offset-5, html.theme--documenter-dark .column.is-offset-5-tablet { - margin-left: 41.6666666667%; } - html.theme--documenter-dark .column.is-6, html.theme--documenter-dark .column.is-6-tablet { - flex: none; - width: 50%; } - html.theme--documenter-dark .column.is-offset-6, html.theme--documenter-dark .column.is-offset-6-tablet { - margin-left: 50%; } - html.theme--documenter-dark .column.is-7, html.theme--documenter-dark .column.is-7-tablet { - flex: none; - width: 58.3333333333%; } - html.theme--documenter-dark .column.is-offset-7, html.theme--documenter-dark .column.is-offset-7-tablet { - margin-left: 58.3333333333%; } - html.theme--documenter-dark .column.is-8, html.theme--documenter-dark .column.is-8-tablet { - flex: none; - width: 66.6666666667%; } - html.theme--documenter-dark .column.is-offset-8, html.theme--documenter-dark .column.is-offset-8-tablet { - margin-left: 66.6666666667%; } - html.theme--documenter-dark .column.is-9, html.theme--documenter-dark .column.is-9-tablet { - flex: none; - width: 75%; } - html.theme--documenter-dark .column.is-offset-9, html.theme--documenter-dark .column.is-offset-9-tablet { - margin-left: 75%; } - html.theme--documenter-dark .column.is-10, html.theme--documenter-dark .column.is-10-tablet { - flex: none; - width: 83.3333333333%; } - html.theme--documenter-dark .column.is-offset-10, html.theme--documenter-dark .column.is-offset-10-tablet { - margin-left: 83.3333333333%; } - html.theme--documenter-dark .column.is-11, html.theme--documenter-dark .column.is-11-tablet { - flex: none; - width: 91.6666666667%; } - html.theme--documenter-dark .column.is-offset-11, html.theme--documenter-dark .column.is-offset-11-tablet { - margin-left: 91.6666666667%; } - html.theme--documenter-dark .column.is-12, html.theme--documenter-dark .column.is-12-tablet { - flex: none; - width: 100%; } - html.theme--documenter-dark .column.is-offset-12, html.theme--documenter-dark .column.is-offset-12-tablet { - margin-left: 100%; } } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark .column.is-narrow-touch { - flex: none; } - html.theme--documenter-dark .column.is-full-touch { - flex: none; - width: 100%; } - html.theme--documenter-dark .column.is-three-quarters-touch { - flex: none; - width: 75%; } - html.theme--documenter-dark .column.is-two-thirds-touch { - flex: none; - width: 66.6666%; } - html.theme--documenter-dark .column.is-half-touch { - flex: none; - width: 50%; } - html.theme--documenter-dark .column.is-one-third-touch { - flex: none; - width: 33.3333%; } - html.theme--documenter-dark .column.is-one-quarter-touch { - flex: none; - width: 25%; } - html.theme--documenter-dark .column.is-one-fifth-touch { - flex: none; - width: 20%; } - html.theme--documenter-dark .column.is-two-fifths-touch { - flex: none; - width: 40%; } - html.theme--documenter-dark .column.is-three-fifths-touch { - flex: none; - width: 60%; } - html.theme--documenter-dark .column.is-four-fifths-touch { - flex: none; - width: 80%; } - html.theme--documenter-dark .column.is-offset-three-quarters-touch { - margin-left: 75%; } - html.theme--documenter-dark .column.is-offset-two-thirds-touch { - margin-left: 66.6666%; } - html.theme--documenter-dark .column.is-offset-half-touch { - margin-left: 50%; } - html.theme--documenter-dark .column.is-offset-one-third-touch { - margin-left: 33.3333%; } - html.theme--documenter-dark .column.is-offset-one-quarter-touch { - margin-left: 25%; } - html.theme--documenter-dark .column.is-offset-one-fifth-touch { - margin-left: 20%; } - html.theme--documenter-dark .column.is-offset-two-fifths-touch { - margin-left: 40%; } - html.theme--documenter-dark .column.is-offset-three-fifths-touch { - margin-left: 60%; } - html.theme--documenter-dark .column.is-offset-four-fifths-touch { - margin-left: 80%; } - html.theme--documenter-dark .column.is-0-touch { - flex: none; - width: 0%; } - html.theme--documenter-dark .column.is-offset-0-touch { - margin-left: 0%; } - html.theme--documenter-dark .column.is-1-touch { - flex: none; - width: 8.3333333333%; } - html.theme--documenter-dark .column.is-offset-1-touch { - margin-left: 8.3333333333%; } - html.theme--documenter-dark .column.is-2-touch { - flex: none; - width: 16.6666666667%; } - html.theme--documenter-dark .column.is-offset-2-touch { - margin-left: 16.6666666667%; } - html.theme--documenter-dark .column.is-3-touch { - flex: none; - width: 25%; } - html.theme--documenter-dark .column.is-offset-3-touch { - margin-left: 25%; } - html.theme--documenter-dark .column.is-4-touch { - flex: none; - width: 33.3333333333%; } - html.theme--documenter-dark .column.is-offset-4-touch { - margin-left: 33.3333333333%; } - html.theme--documenter-dark .column.is-5-touch { - flex: none; - width: 41.6666666667%; } - html.theme--documenter-dark .column.is-offset-5-touch { - margin-left: 41.6666666667%; } - html.theme--documenter-dark .column.is-6-touch { - flex: none; - width: 50%; } - html.theme--documenter-dark .column.is-offset-6-touch { - margin-left: 50%; } - html.theme--documenter-dark .column.is-7-touch { - flex: none; - width: 58.3333333333%; } - html.theme--documenter-dark .column.is-offset-7-touch { - margin-left: 58.3333333333%; } - html.theme--documenter-dark .column.is-8-touch { - flex: none; - width: 66.6666666667%; } - html.theme--documenter-dark .column.is-offset-8-touch { - margin-left: 66.6666666667%; } - html.theme--documenter-dark .column.is-9-touch { - flex: none; - width: 75%; } - html.theme--documenter-dark .column.is-offset-9-touch { - margin-left: 75%; } - html.theme--documenter-dark .column.is-10-touch { - flex: none; - width: 83.3333333333%; } - html.theme--documenter-dark .column.is-offset-10-touch { - margin-left: 83.3333333333%; } - html.theme--documenter-dark .column.is-11-touch { - flex: none; - width: 91.6666666667%; } - html.theme--documenter-dark .column.is-offset-11-touch { - margin-left: 91.6666666667%; } - html.theme--documenter-dark .column.is-12-touch { - flex: none; - width: 100%; } - html.theme--documenter-dark .column.is-offset-12-touch { - margin-left: 100%; } } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark .column.is-narrow-desktop { - flex: none; } - html.theme--documenter-dark .column.is-full-desktop { - flex: none; - width: 100%; } - html.theme--documenter-dark .column.is-three-quarters-desktop { - flex: none; - width: 75%; } - html.theme--documenter-dark .column.is-two-thirds-desktop { - flex: none; - width: 66.6666%; } - html.theme--documenter-dark .column.is-half-desktop { - flex: none; - width: 50%; } - html.theme--documenter-dark .column.is-one-third-desktop { - flex: none; - width: 33.3333%; } - html.theme--documenter-dark .column.is-one-quarter-desktop { - flex: none; - width: 25%; } - html.theme--documenter-dark .column.is-one-fifth-desktop { - flex: none; - width: 20%; } - html.theme--documenter-dark .column.is-two-fifths-desktop { - flex: none; - width: 40%; } - html.theme--documenter-dark .column.is-three-fifths-desktop { - flex: none; - width: 60%; } - html.theme--documenter-dark .column.is-four-fifths-desktop { - flex: none; - width: 80%; } - html.theme--documenter-dark .column.is-offset-three-quarters-desktop { - margin-left: 75%; } - html.theme--documenter-dark .column.is-offset-two-thirds-desktop { - margin-left: 66.6666%; } - html.theme--documenter-dark .column.is-offset-half-desktop { - margin-left: 50%; } - html.theme--documenter-dark .column.is-offset-one-third-desktop { - margin-left: 33.3333%; } - html.theme--documenter-dark .column.is-offset-one-quarter-desktop { - margin-left: 25%; } - html.theme--documenter-dark .column.is-offset-one-fifth-desktop { - margin-left: 20%; } - html.theme--documenter-dark .column.is-offset-two-fifths-desktop { - margin-left: 40%; } - html.theme--documenter-dark .column.is-offset-three-fifths-desktop { - margin-left: 60%; } - html.theme--documenter-dark .column.is-offset-four-fifths-desktop { - margin-left: 80%; } - html.theme--documenter-dark .column.is-0-desktop { - flex: none; - width: 0%; } - html.theme--documenter-dark .column.is-offset-0-desktop { - margin-left: 0%; } - html.theme--documenter-dark .column.is-1-desktop { - flex: none; - width: 8.3333333333%; } - html.theme--documenter-dark .column.is-offset-1-desktop { - margin-left: 8.3333333333%; } - html.theme--documenter-dark .column.is-2-desktop { - flex: none; - width: 16.6666666667%; } - html.theme--documenter-dark .column.is-offset-2-desktop { - margin-left: 16.6666666667%; } - html.theme--documenter-dark .column.is-3-desktop { - flex: none; - width: 25%; } - html.theme--documenter-dark .column.is-offset-3-desktop { - margin-left: 25%; } - html.theme--documenter-dark .column.is-4-desktop { - flex: none; - width: 33.3333333333%; } - html.theme--documenter-dark .column.is-offset-4-desktop { - margin-left: 33.3333333333%; } - html.theme--documenter-dark .column.is-5-desktop { - flex: none; - width: 41.6666666667%; } - html.theme--documenter-dark .column.is-offset-5-desktop { - margin-left: 41.6666666667%; } - html.theme--documenter-dark .column.is-6-desktop { - flex: none; - width: 50%; } - html.theme--documenter-dark .column.is-offset-6-desktop { - margin-left: 50%; } - html.theme--documenter-dark .column.is-7-desktop { - flex: none; - width: 58.3333333333%; } - html.theme--documenter-dark .column.is-offset-7-desktop { - margin-left: 58.3333333333%; } - html.theme--documenter-dark .column.is-8-desktop { - flex: none; - width: 66.6666666667%; } - html.theme--documenter-dark .column.is-offset-8-desktop { - margin-left: 66.6666666667%; } - html.theme--documenter-dark .column.is-9-desktop { - flex: none; - width: 75%; } - html.theme--documenter-dark .column.is-offset-9-desktop { - margin-left: 75%; } - html.theme--documenter-dark .column.is-10-desktop { - flex: none; - width: 83.3333333333%; } - html.theme--documenter-dark .column.is-offset-10-desktop { - margin-left: 83.3333333333%; } - html.theme--documenter-dark .column.is-11-desktop { - flex: none; - width: 91.6666666667%; } - html.theme--documenter-dark .column.is-offset-11-desktop { - margin-left: 91.6666666667%; } - html.theme--documenter-dark .column.is-12-desktop { - flex: none; - width: 100%; } - html.theme--documenter-dark .column.is-offset-12-desktop { - margin-left: 100%; } } - @media screen and (min-width: 1216px) { - html.theme--documenter-dark .column.is-narrow-widescreen { - flex: none; } - html.theme--documenter-dark .column.is-full-widescreen { - flex: none; - width: 100%; } - html.theme--documenter-dark .column.is-three-quarters-widescreen { - flex: none; - width: 75%; } - html.theme--documenter-dark .column.is-two-thirds-widescreen { - flex: none; - width: 66.6666%; } - html.theme--documenter-dark .column.is-half-widescreen { - flex: none; - width: 50%; } - html.theme--documenter-dark .column.is-one-third-widescreen { - flex: none; - width: 33.3333%; } - html.theme--documenter-dark .column.is-one-quarter-widescreen { - flex: none; - width: 25%; } - html.theme--documenter-dark .column.is-one-fifth-widescreen { - flex: none; - width: 20%; } - html.theme--documenter-dark .column.is-two-fifths-widescreen { - flex: none; - width: 40%; } - html.theme--documenter-dark .column.is-three-fifths-widescreen { - flex: none; - width: 60%; } - html.theme--documenter-dark .column.is-four-fifths-widescreen { - flex: none; - width: 80%; } - html.theme--documenter-dark .column.is-offset-three-quarters-widescreen { - margin-left: 75%; } - html.theme--documenter-dark .column.is-offset-two-thirds-widescreen { - margin-left: 66.6666%; } - html.theme--documenter-dark .column.is-offset-half-widescreen { - margin-left: 50%; } - html.theme--documenter-dark .column.is-offset-one-third-widescreen { - margin-left: 33.3333%; } - html.theme--documenter-dark .column.is-offset-one-quarter-widescreen { - margin-left: 25%; } - html.theme--documenter-dark .column.is-offset-one-fifth-widescreen { - margin-left: 20%; } - html.theme--documenter-dark .column.is-offset-two-fifths-widescreen { - margin-left: 40%; } - html.theme--documenter-dark .column.is-offset-three-fifths-widescreen { - margin-left: 60%; } - html.theme--documenter-dark .column.is-offset-four-fifths-widescreen { - margin-left: 80%; } - html.theme--documenter-dark .column.is-0-widescreen { - flex: none; - width: 0%; } - html.theme--documenter-dark .column.is-offset-0-widescreen { - margin-left: 0%; } - html.theme--documenter-dark .column.is-1-widescreen { - flex: none; - width: 8.3333333333%; } - html.theme--documenter-dark .column.is-offset-1-widescreen { - margin-left: 8.3333333333%; } - html.theme--documenter-dark .column.is-2-widescreen { - flex: none; - width: 16.6666666667%; } - html.theme--documenter-dark .column.is-offset-2-widescreen { - margin-left: 16.6666666667%; } - html.theme--documenter-dark .column.is-3-widescreen { - flex: none; - width: 25%; } - html.theme--documenter-dark .column.is-offset-3-widescreen { - margin-left: 25%; } - html.theme--documenter-dark .column.is-4-widescreen { - flex: none; - width: 33.3333333333%; } - html.theme--documenter-dark .column.is-offset-4-widescreen { - margin-left: 33.3333333333%; } - html.theme--documenter-dark .column.is-5-widescreen { - flex: none; - width: 41.6666666667%; } - html.theme--documenter-dark .column.is-offset-5-widescreen { - margin-left: 41.6666666667%; } - html.theme--documenter-dark .column.is-6-widescreen { - flex: none; - width: 50%; } - html.theme--documenter-dark .column.is-offset-6-widescreen { - margin-left: 50%; } - html.theme--documenter-dark .column.is-7-widescreen { - flex: none; - width: 58.3333333333%; } - html.theme--documenter-dark .column.is-offset-7-widescreen { - margin-left: 58.3333333333%; } - html.theme--documenter-dark .column.is-8-widescreen { - flex: none; - width: 66.6666666667%; } - html.theme--documenter-dark .column.is-offset-8-widescreen { - margin-left: 66.6666666667%; } - html.theme--documenter-dark .column.is-9-widescreen { - flex: none; - width: 75%; } - html.theme--documenter-dark .column.is-offset-9-widescreen { - margin-left: 75%; } - html.theme--documenter-dark .column.is-10-widescreen { - flex: none; - width: 83.3333333333%; } - html.theme--documenter-dark .column.is-offset-10-widescreen { - margin-left: 83.3333333333%; } - html.theme--documenter-dark .column.is-11-widescreen { - flex: none; - width: 91.6666666667%; } - html.theme--documenter-dark .column.is-offset-11-widescreen { - margin-left: 91.6666666667%; } - html.theme--documenter-dark .column.is-12-widescreen { - flex: none; - width: 100%; } - html.theme--documenter-dark .column.is-offset-12-widescreen { - margin-left: 100%; } } - @media screen and (min-width: 1408px) { - html.theme--documenter-dark .column.is-narrow-fullhd { - flex: none; } - html.theme--documenter-dark .column.is-full-fullhd { - flex: none; - width: 100%; } - html.theme--documenter-dark .column.is-three-quarters-fullhd { - flex: none; - width: 75%; } - html.theme--documenter-dark .column.is-two-thirds-fullhd { - flex: none; - width: 66.6666%; } - html.theme--documenter-dark .column.is-half-fullhd { - flex: none; - width: 50%; } - html.theme--documenter-dark .column.is-one-third-fullhd { - flex: none; - width: 33.3333%; } - html.theme--documenter-dark .column.is-one-quarter-fullhd { - flex: none; - width: 25%; } - html.theme--documenter-dark .column.is-one-fifth-fullhd { - flex: none; - width: 20%; } - html.theme--documenter-dark .column.is-two-fifths-fullhd { - flex: none; - width: 40%; } - html.theme--documenter-dark .column.is-three-fifths-fullhd { - flex: none; - width: 60%; } - html.theme--documenter-dark .column.is-four-fifths-fullhd { - flex: none; - width: 80%; } - html.theme--documenter-dark .column.is-offset-three-quarters-fullhd { - margin-left: 75%; } - html.theme--documenter-dark .column.is-offset-two-thirds-fullhd { - margin-left: 66.6666%; } - html.theme--documenter-dark .column.is-offset-half-fullhd { - margin-left: 50%; } - html.theme--documenter-dark .column.is-offset-one-third-fullhd { - margin-left: 33.3333%; } - html.theme--documenter-dark .column.is-offset-one-quarter-fullhd { - margin-left: 25%; } - html.theme--documenter-dark .column.is-offset-one-fifth-fullhd { - margin-left: 20%; } - html.theme--documenter-dark .column.is-offset-two-fifths-fullhd { - margin-left: 40%; } - html.theme--documenter-dark .column.is-offset-three-fifths-fullhd { - margin-left: 60%; } - html.theme--documenter-dark .column.is-offset-four-fifths-fullhd { - margin-left: 80%; } - html.theme--documenter-dark .column.is-0-fullhd { - flex: none; - width: 0%; } - html.theme--documenter-dark .column.is-offset-0-fullhd { - margin-left: 0%; } - html.theme--documenter-dark .column.is-1-fullhd { - flex: none; - width: 8.3333333333%; } - html.theme--documenter-dark .column.is-offset-1-fullhd { - margin-left: 8.3333333333%; } - html.theme--documenter-dark .column.is-2-fullhd { - flex: none; - width: 16.6666666667%; } - html.theme--documenter-dark .column.is-offset-2-fullhd { - margin-left: 16.6666666667%; } - html.theme--documenter-dark .column.is-3-fullhd { - flex: none; - width: 25%; } - html.theme--documenter-dark .column.is-offset-3-fullhd { - margin-left: 25%; } - html.theme--documenter-dark .column.is-4-fullhd { - flex: none; - width: 33.3333333333%; } - html.theme--documenter-dark .column.is-offset-4-fullhd { - margin-left: 33.3333333333%; } - html.theme--documenter-dark .column.is-5-fullhd { - flex: none; - width: 41.6666666667%; } - html.theme--documenter-dark .column.is-offset-5-fullhd { - margin-left: 41.6666666667%; } - html.theme--documenter-dark .column.is-6-fullhd { - flex: none; - width: 50%; } - html.theme--documenter-dark .column.is-offset-6-fullhd { - margin-left: 50%; } - html.theme--documenter-dark .column.is-7-fullhd { - flex: none; - width: 58.3333333333%; } - html.theme--documenter-dark .column.is-offset-7-fullhd { - margin-left: 58.3333333333%; } - html.theme--documenter-dark .column.is-8-fullhd { - flex: none; - width: 66.6666666667%; } - html.theme--documenter-dark .column.is-offset-8-fullhd { - margin-left: 66.6666666667%; } - html.theme--documenter-dark .column.is-9-fullhd { - flex: none; - width: 75%; } - html.theme--documenter-dark .column.is-offset-9-fullhd { - margin-left: 75%; } - html.theme--documenter-dark .column.is-10-fullhd { - flex: none; - width: 83.3333333333%; } - html.theme--documenter-dark .column.is-offset-10-fullhd { - margin-left: 83.3333333333%; } - html.theme--documenter-dark .column.is-11-fullhd { - flex: none; - width: 91.6666666667%; } - html.theme--documenter-dark .column.is-offset-11-fullhd { - margin-left: 91.6666666667%; } - html.theme--documenter-dark .column.is-12-fullhd { - flex: none; - width: 100%; } - html.theme--documenter-dark .column.is-offset-12-fullhd { - margin-left: 100%; } } - html.theme--documenter-dark .columns { - margin-left: -0.75rem; - margin-right: -0.75rem; - margin-top: -0.75rem; } - html.theme--documenter-dark .columns:last-child { - margin-bottom: -0.75rem; } - html.theme--documenter-dark .columns:not(:last-child) { - margin-bottom: calc(1.5rem - 0.75rem); } - html.theme--documenter-dark .columns.is-centered { - justify-content: center; } - html.theme--documenter-dark .columns.is-gapless { - margin-left: 0; - margin-right: 0; - margin-top: 0; } - html.theme--documenter-dark .columns.is-gapless > .column { - margin: 0; - padding: 0 !important; } - html.theme--documenter-dark .columns.is-gapless:not(:last-child) { - margin-bottom: 1.5rem; } - html.theme--documenter-dark .columns.is-gapless:last-child { - margin-bottom: 0; } - html.theme--documenter-dark .columns.is-mobile { - display: flex; } - html.theme--documenter-dark .columns.is-multiline { - flex-wrap: wrap; } - html.theme--documenter-dark .columns.is-vcentered { - align-items: center; } - @media screen and (min-width: 769px), print { - html.theme--documenter-dark .columns:not(.is-desktop) { - display: flex; } } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark .columns.is-desktop { - display: flex; } } - html.theme--documenter-dark .columns.is-variable { - --columnGap: 0.75rem; - margin-left: calc(-1 * var(--columnGap)); - margin-right: calc(-1 * var(--columnGap)); } - html.theme--documenter-dark .columns.is-variable .column { - padding-left: var(--columnGap); - padding-right: var(--columnGap); } - html.theme--documenter-dark .columns.is-variable.is-0 { - --columnGap: 0rem; } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .columns.is-variable.is-0-mobile { - --columnGap: 0rem; } } - @media screen and (min-width: 769px), print { - html.theme--documenter-dark .columns.is-variable.is-0-tablet { - --columnGap: 0rem; } } - @media screen and (min-width: 769px) and (max-width: 1055px) { - html.theme--documenter-dark .columns.is-variable.is-0-tablet-only { - --columnGap: 0rem; } } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark .columns.is-variable.is-0-touch { - --columnGap: 0rem; } } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark .columns.is-variable.is-0-desktop { - --columnGap: 0rem; } } - @media screen and (min-width: 1056px) and (max-width: 1215px) { - html.theme--documenter-dark .columns.is-variable.is-0-desktop-only { - --columnGap: 0rem; } } - @media screen and (min-width: 1216px) { - html.theme--documenter-dark .columns.is-variable.is-0-widescreen { - --columnGap: 0rem; } } - @media screen and (min-width: 1216px) and (max-width: 1407px) { - html.theme--documenter-dark .columns.is-variable.is-0-widescreen-only { - --columnGap: 0rem; } } - @media screen and (min-width: 1408px) { - html.theme--documenter-dark .columns.is-variable.is-0-fullhd { - --columnGap: 0rem; } } - html.theme--documenter-dark .columns.is-variable.is-1 { - --columnGap: 0.25rem; } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .columns.is-variable.is-1-mobile { - --columnGap: 0.25rem; } } - @media screen and (min-width: 769px), print { - html.theme--documenter-dark .columns.is-variable.is-1-tablet { - --columnGap: 0.25rem; } } - @media screen and (min-width: 769px) and (max-width: 1055px) { - html.theme--documenter-dark .columns.is-variable.is-1-tablet-only { - --columnGap: 0.25rem; } } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark .columns.is-variable.is-1-touch { - --columnGap: 0.25rem; } } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark .columns.is-variable.is-1-desktop { - --columnGap: 0.25rem; } } - @media screen and (min-width: 1056px) and (max-width: 1215px) { - html.theme--documenter-dark .columns.is-variable.is-1-desktop-only { - --columnGap: 0.25rem; } } - @media screen and (min-width: 1216px) { - html.theme--documenter-dark .columns.is-variable.is-1-widescreen { - --columnGap: 0.25rem; } } - @media screen and (min-width: 1216px) and (max-width: 1407px) { - html.theme--documenter-dark .columns.is-variable.is-1-widescreen-only { - --columnGap: 0.25rem; } } - @media screen and (min-width: 1408px) { - html.theme--documenter-dark .columns.is-variable.is-1-fullhd { - --columnGap: 0.25rem; } } - html.theme--documenter-dark .columns.is-variable.is-2 { - --columnGap: 0.5rem; } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .columns.is-variable.is-2-mobile { - --columnGap: 0.5rem; } } - @media screen and (min-width: 769px), print { - html.theme--documenter-dark .columns.is-variable.is-2-tablet { - --columnGap: 0.5rem; } } - @media screen and (min-width: 769px) and (max-width: 1055px) { - html.theme--documenter-dark .columns.is-variable.is-2-tablet-only { - --columnGap: 0.5rem; } } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark .columns.is-variable.is-2-touch { - --columnGap: 0.5rem; } } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark .columns.is-variable.is-2-desktop { - --columnGap: 0.5rem; } } - @media screen and (min-width: 1056px) and (max-width: 1215px) { - html.theme--documenter-dark .columns.is-variable.is-2-desktop-only { - --columnGap: 0.5rem; } } - @media screen and (min-width: 1216px) { - html.theme--documenter-dark .columns.is-variable.is-2-widescreen { - --columnGap: 0.5rem; } } - @media screen and (min-width: 1216px) and (max-width: 1407px) { - html.theme--documenter-dark .columns.is-variable.is-2-widescreen-only { - --columnGap: 0.5rem; } } - @media screen and (min-width: 1408px) { - html.theme--documenter-dark .columns.is-variable.is-2-fullhd { - --columnGap: 0.5rem; } } - html.theme--documenter-dark .columns.is-variable.is-3 { - --columnGap: 0.75rem; } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .columns.is-variable.is-3-mobile { - --columnGap: 0.75rem; } } - @media screen and (min-width: 769px), print { - html.theme--documenter-dark .columns.is-variable.is-3-tablet { - --columnGap: 0.75rem; } } - @media screen and (min-width: 769px) and (max-width: 1055px) { - html.theme--documenter-dark .columns.is-variable.is-3-tablet-only { - --columnGap: 0.75rem; } } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark .columns.is-variable.is-3-touch { - --columnGap: 0.75rem; } } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark .columns.is-variable.is-3-desktop { - --columnGap: 0.75rem; } } - @media screen and (min-width: 1056px) and (max-width: 1215px) { - html.theme--documenter-dark .columns.is-variable.is-3-desktop-only { - --columnGap: 0.75rem; } } - @media screen and (min-width: 1216px) { - html.theme--documenter-dark .columns.is-variable.is-3-widescreen { - --columnGap: 0.75rem; } } - @media screen and (min-width: 1216px) and (max-width: 1407px) { - html.theme--documenter-dark .columns.is-variable.is-3-widescreen-only { - --columnGap: 0.75rem; } } - @media screen and (min-width: 1408px) { - html.theme--documenter-dark .columns.is-variable.is-3-fullhd { - --columnGap: 0.75rem; } } - html.theme--documenter-dark .columns.is-variable.is-4 { - --columnGap: 1rem; } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .columns.is-variable.is-4-mobile { - --columnGap: 1rem; } } - @media screen and (min-width: 769px), print { - html.theme--documenter-dark .columns.is-variable.is-4-tablet { - --columnGap: 1rem; } } - @media screen and (min-width: 769px) and (max-width: 1055px) { - html.theme--documenter-dark .columns.is-variable.is-4-tablet-only { - --columnGap: 1rem; } } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark .columns.is-variable.is-4-touch { - --columnGap: 1rem; } } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark .columns.is-variable.is-4-desktop { - --columnGap: 1rem; } } - @media screen and (min-width: 1056px) and (max-width: 1215px) { - html.theme--documenter-dark .columns.is-variable.is-4-desktop-only { - --columnGap: 1rem; } } - @media screen and (min-width: 1216px) { - html.theme--documenter-dark .columns.is-variable.is-4-widescreen { - --columnGap: 1rem; } } - @media screen and (min-width: 1216px) and (max-width: 1407px) { - html.theme--documenter-dark .columns.is-variable.is-4-widescreen-only { - --columnGap: 1rem; } } - @media screen and (min-width: 1408px) { - html.theme--documenter-dark .columns.is-variable.is-4-fullhd { - --columnGap: 1rem; } } - html.theme--documenter-dark .columns.is-variable.is-5 { - --columnGap: 1.25rem; } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .columns.is-variable.is-5-mobile { - --columnGap: 1.25rem; } } - @media screen and (min-width: 769px), print { - html.theme--documenter-dark .columns.is-variable.is-5-tablet { - --columnGap: 1.25rem; } } - @media screen and (min-width: 769px) and (max-width: 1055px) { - html.theme--documenter-dark .columns.is-variable.is-5-tablet-only { - --columnGap: 1.25rem; } } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark .columns.is-variable.is-5-touch { - --columnGap: 1.25rem; } } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark .columns.is-variable.is-5-desktop { - --columnGap: 1.25rem; } } - @media screen and (min-width: 1056px) and (max-width: 1215px) { - html.theme--documenter-dark .columns.is-variable.is-5-desktop-only { - --columnGap: 1.25rem; } } - @media screen and (min-width: 1216px) { - html.theme--documenter-dark .columns.is-variable.is-5-widescreen { - --columnGap: 1.25rem; } } - @media screen and (min-width: 1216px) and (max-width: 1407px) { - html.theme--documenter-dark .columns.is-variable.is-5-widescreen-only { - --columnGap: 1.25rem; } } - @media screen and (min-width: 1408px) { - html.theme--documenter-dark .columns.is-variable.is-5-fullhd { - --columnGap: 1.25rem; } } - html.theme--documenter-dark .columns.is-variable.is-6 { - --columnGap: 1.5rem; } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .columns.is-variable.is-6-mobile { - --columnGap: 1.5rem; } } - @media screen and (min-width: 769px), print { - html.theme--documenter-dark .columns.is-variable.is-6-tablet { - --columnGap: 1.5rem; } } - @media screen and (min-width: 769px) and (max-width: 1055px) { - html.theme--documenter-dark .columns.is-variable.is-6-tablet-only { - --columnGap: 1.5rem; } } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark .columns.is-variable.is-6-touch { - --columnGap: 1.5rem; } } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark .columns.is-variable.is-6-desktop { - --columnGap: 1.5rem; } } - @media screen and (min-width: 1056px) and (max-width: 1215px) { - html.theme--documenter-dark .columns.is-variable.is-6-desktop-only { - --columnGap: 1.5rem; } } - @media screen and (min-width: 1216px) { - html.theme--documenter-dark .columns.is-variable.is-6-widescreen { - --columnGap: 1.5rem; } } - @media screen and (min-width: 1216px) and (max-width: 1407px) { - html.theme--documenter-dark .columns.is-variable.is-6-widescreen-only { - --columnGap: 1.5rem; } } - @media screen and (min-width: 1408px) { - html.theme--documenter-dark .columns.is-variable.is-6-fullhd { - --columnGap: 1.5rem; } } - html.theme--documenter-dark .columns.is-variable.is-7 { - --columnGap: 1.75rem; } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .columns.is-variable.is-7-mobile { - --columnGap: 1.75rem; } } - @media screen and (min-width: 769px), print { - html.theme--documenter-dark .columns.is-variable.is-7-tablet { - --columnGap: 1.75rem; } } - @media screen and (min-width: 769px) and (max-width: 1055px) { - html.theme--documenter-dark .columns.is-variable.is-7-tablet-only { - --columnGap: 1.75rem; } } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark .columns.is-variable.is-7-touch { - --columnGap: 1.75rem; } } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark .columns.is-variable.is-7-desktop { - --columnGap: 1.75rem; } } - @media screen and (min-width: 1056px) and (max-width: 1215px) { - html.theme--documenter-dark .columns.is-variable.is-7-desktop-only { - --columnGap: 1.75rem; } } - @media screen and (min-width: 1216px) { - html.theme--documenter-dark .columns.is-variable.is-7-widescreen { - --columnGap: 1.75rem; } } - @media screen and (min-width: 1216px) and (max-width: 1407px) { - html.theme--documenter-dark .columns.is-variable.is-7-widescreen-only { - --columnGap: 1.75rem; } } - @media screen and (min-width: 1408px) { - html.theme--documenter-dark .columns.is-variable.is-7-fullhd { - --columnGap: 1.75rem; } } - html.theme--documenter-dark .columns.is-variable.is-8 { - --columnGap: 2rem; } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .columns.is-variable.is-8-mobile { - --columnGap: 2rem; } } - @media screen and (min-width: 769px), print { - html.theme--documenter-dark .columns.is-variable.is-8-tablet { - --columnGap: 2rem; } } - @media screen and (min-width: 769px) and (max-width: 1055px) { - html.theme--documenter-dark .columns.is-variable.is-8-tablet-only { - --columnGap: 2rem; } } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark .columns.is-variable.is-8-touch { - --columnGap: 2rem; } } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark .columns.is-variable.is-8-desktop { - --columnGap: 2rem; } } - @media screen and (min-width: 1056px) and (max-width: 1215px) { - html.theme--documenter-dark .columns.is-variable.is-8-desktop-only { - --columnGap: 2rem; } } - @media screen and (min-width: 1216px) { - html.theme--documenter-dark .columns.is-variable.is-8-widescreen { - --columnGap: 2rem; } } - @media screen and (min-width: 1216px) and (max-width: 1407px) { - html.theme--documenter-dark .columns.is-variable.is-8-widescreen-only { - --columnGap: 2rem; } } - @media screen and (min-width: 1408px) { - html.theme--documenter-dark .columns.is-variable.is-8-fullhd { - --columnGap: 2rem; } } - html.theme--documenter-dark .tile { - align-items: stretch; - display: block; - flex-basis: 0; - flex-grow: 1; - flex-shrink: 1; - min-height: min-content; } - html.theme--documenter-dark .tile.is-ancestor { - margin-left: -0.75rem; - margin-right: -0.75rem; - margin-top: -0.75rem; } - html.theme--documenter-dark .tile.is-ancestor:last-child { - margin-bottom: -0.75rem; } - html.theme--documenter-dark .tile.is-ancestor:not(:last-child) { - margin-bottom: 0.75rem; } - html.theme--documenter-dark .tile.is-child { - margin: 0 !important; } - html.theme--documenter-dark .tile.is-parent { - padding: 0.75rem; } - html.theme--documenter-dark .tile.is-vertical { - flex-direction: column; } - html.theme--documenter-dark .tile.is-vertical > .tile.is-child:not(:last-child) { - margin-bottom: 1.5rem !important; } - @media screen and (min-width: 769px), print { - html.theme--documenter-dark .tile:not(.is-child) { - display: flex; } - html.theme--documenter-dark .tile.is-1 { - flex: none; - width: 8.3333333333%; } - html.theme--documenter-dark .tile.is-2 { - flex: none; - width: 16.6666666667%; } - html.theme--documenter-dark .tile.is-3 { - flex: none; - width: 25%; } - html.theme--documenter-dark .tile.is-4 { - flex: none; - width: 33.3333333333%; } - html.theme--documenter-dark .tile.is-5 { - flex: none; - width: 41.6666666667%; } - html.theme--documenter-dark .tile.is-6 { - flex: none; - width: 50%; } - html.theme--documenter-dark .tile.is-7 { - flex: none; - width: 58.3333333333%; } - html.theme--documenter-dark .tile.is-8 { - flex: none; - width: 66.6666666667%; } - html.theme--documenter-dark .tile.is-9 { - flex: none; - width: 75%; } - html.theme--documenter-dark .tile.is-10 { - flex: none; - width: 83.3333333333%; } - html.theme--documenter-dark .tile.is-11 { - flex: none; - width: 91.6666666667%; } - html.theme--documenter-dark .tile.is-12 { - flex: none; - width: 100%; } } - html.theme--documenter-dark .hero { - align-items: stretch; - display: flex; - flex-direction: column; - justify-content: space-between; } - html.theme--documenter-dark .hero .navbar { - background: none; } - html.theme--documenter-dark .hero .tabs ul { - border-bottom: none; } - html.theme--documenter-dark .hero.is-white { - background-color: white; - color: #0a0a0a; } - html.theme--documenter-dark .hero.is-white a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), - html.theme--documenter-dark .hero.is-white strong { - color: inherit; } - html.theme--documenter-dark .hero.is-white .title { - color: #0a0a0a; } - html.theme--documenter-dark .hero.is-white .subtitle { - color: rgba(10, 10, 10, 0.9); } - html.theme--documenter-dark .hero.is-white .subtitle a:not(.button), - html.theme--documenter-dark .hero.is-white .subtitle strong { - color: #0a0a0a; } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark .hero.is-white .navbar-menu { - background-color: white; } } - html.theme--documenter-dark .hero.is-white .navbar-item, - html.theme--documenter-dark .hero.is-white .navbar-link { - color: rgba(10, 10, 10, 0.7); } - html.theme--documenter-dark .hero.is-white a.navbar-item:hover, html.theme--documenter-dark .hero.is-white a.navbar-item.is-active, - html.theme--documenter-dark .hero.is-white .navbar-link:hover, - html.theme--documenter-dark .hero.is-white .navbar-link.is-active { - background-color: #f2f2f2; - color: #0a0a0a; } - html.theme--documenter-dark .hero.is-white .tabs a { - color: #0a0a0a; - opacity: 0.9; } - html.theme--documenter-dark .hero.is-white .tabs a:hover { - opacity: 1; } - html.theme--documenter-dark .hero.is-white .tabs li.is-active a { - opacity: 1; } - html.theme--documenter-dark .hero.is-white .tabs.is-boxed a, html.theme--documenter-dark .hero.is-white .tabs.is-toggle a { - color: #0a0a0a; } - html.theme--documenter-dark .hero.is-white .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-white .tabs.is-toggle a:hover { - background-color: rgba(10, 10, 10, 0.1); } - html.theme--documenter-dark .hero.is-white .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-white .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-white .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-white .tabs.is-toggle li.is-active a:hover { - background-color: #0a0a0a; - border-color: #0a0a0a; - color: white; } - html.theme--documenter-dark .hero.is-white.is-bold { - background-image: linear-gradient(141deg, #e8e3e4 0%, white 71%, white 100%); } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .hero.is-white.is-bold .navbar-menu { - background-image: linear-gradient(141deg, #e8e3e4 0%, white 71%, white 100%); } } - html.theme--documenter-dark .hero.is-black { - background-color: #0a0a0a; - color: white; } - html.theme--documenter-dark .hero.is-black a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), - html.theme--documenter-dark .hero.is-black strong { - color: inherit; } - html.theme--documenter-dark .hero.is-black .title { - color: white; } - html.theme--documenter-dark .hero.is-black .subtitle { - color: rgba(255, 255, 255, 0.9); } - html.theme--documenter-dark .hero.is-black .subtitle a:not(.button), - html.theme--documenter-dark .hero.is-black .subtitle strong { - color: white; } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark .hero.is-black .navbar-menu { - background-color: #0a0a0a; } } - html.theme--documenter-dark .hero.is-black .navbar-item, - html.theme--documenter-dark .hero.is-black .navbar-link { - color: rgba(255, 255, 255, 0.7); } - html.theme--documenter-dark .hero.is-black a.navbar-item:hover, html.theme--documenter-dark .hero.is-black a.navbar-item.is-active, - html.theme--documenter-dark .hero.is-black .navbar-link:hover, - html.theme--documenter-dark .hero.is-black .navbar-link.is-active { - background-color: black; - color: white; } - html.theme--documenter-dark .hero.is-black .tabs a { - color: white; - opacity: 0.9; } - html.theme--documenter-dark .hero.is-black .tabs a:hover { - opacity: 1; } - html.theme--documenter-dark .hero.is-black .tabs li.is-active a { - opacity: 1; } - html.theme--documenter-dark .hero.is-black .tabs.is-boxed a, html.theme--documenter-dark .hero.is-black .tabs.is-toggle a { - color: white; } - html.theme--documenter-dark .hero.is-black .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-black .tabs.is-toggle a:hover { - background-color: rgba(10, 10, 10, 0.1); } - html.theme--documenter-dark .hero.is-black .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-black .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-black .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-black .tabs.is-toggle li.is-active a:hover { - background-color: white; - border-color: white; - color: #0a0a0a; } - html.theme--documenter-dark .hero.is-black.is-bold { - background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .hero.is-black.is-bold .navbar-menu { - background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } } - html.theme--documenter-dark .hero.is-light { - background-color: #ecf0f1; - color: #282f2f; } - html.theme--documenter-dark .hero.is-light a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), - html.theme--documenter-dark .hero.is-light strong { - color: inherit; } - html.theme--documenter-dark .hero.is-light .title { - color: #282f2f; } - html.theme--documenter-dark .hero.is-light .subtitle { - color: rgba(40, 47, 47, 0.9); } - html.theme--documenter-dark .hero.is-light .subtitle a:not(.button), - html.theme--documenter-dark .hero.is-light .subtitle strong { - color: #282f2f; } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark .hero.is-light .navbar-menu { - background-color: #ecf0f1; } } - html.theme--documenter-dark .hero.is-light .navbar-item, - html.theme--documenter-dark .hero.is-light .navbar-link { - color: rgba(40, 47, 47, 0.7); } - html.theme--documenter-dark .hero.is-light a.navbar-item:hover, html.theme--documenter-dark .hero.is-light a.navbar-item.is-active, - html.theme--documenter-dark .hero.is-light .navbar-link:hover, - html.theme--documenter-dark .hero.is-light .navbar-link.is-active { - background-color: #dde4e6; - color: #282f2f; } - html.theme--documenter-dark .hero.is-light .tabs a { - color: #282f2f; - opacity: 0.9; } - html.theme--documenter-dark .hero.is-light .tabs a:hover { - opacity: 1; } - html.theme--documenter-dark .hero.is-light .tabs li.is-active a { - opacity: 1; } - html.theme--documenter-dark .hero.is-light .tabs.is-boxed a, html.theme--documenter-dark .hero.is-light .tabs.is-toggle a { - color: #282f2f; } - html.theme--documenter-dark .hero.is-light .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-light .tabs.is-toggle a:hover { - background-color: rgba(10, 10, 10, 0.1); } - html.theme--documenter-dark .hero.is-light .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-light .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-light .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-light .tabs.is-toggle li.is-active a:hover { - background-color: #282f2f; - border-color: #282f2f; - color: #ecf0f1; } - html.theme--documenter-dark .hero.is-light.is-bold { - background-image: linear-gradient(141deg, #cadfe0 0%, #ecf0f1 71%, #fafbfc 100%); } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .hero.is-light.is-bold .navbar-menu { - background-image: linear-gradient(141deg, #cadfe0 0%, #ecf0f1 71%, #fafbfc 100%); } } - html.theme--documenter-dark .hero.is-dark, html.theme--documenter-dark .content kbd.hero { - background-color: #282f2f; - color: #ecf0f1; } - html.theme--documenter-dark .hero.is-dark a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), html.theme--documenter-dark .content kbd.hero a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), - html.theme--documenter-dark .hero.is-dark strong, - html.theme--documenter-dark .content kbd.hero strong { - color: inherit; } - html.theme--documenter-dark .hero.is-dark .title, html.theme--documenter-dark .content kbd.hero .title { - color: #ecf0f1; } - html.theme--documenter-dark .hero.is-dark .subtitle, html.theme--documenter-dark .content kbd.hero .subtitle { - color: rgba(236, 240, 241, 0.9); } - html.theme--documenter-dark .hero.is-dark .subtitle a:not(.button), html.theme--documenter-dark .content kbd.hero .subtitle a:not(.button), - html.theme--documenter-dark .hero.is-dark .subtitle strong, - html.theme--documenter-dark .content kbd.hero .subtitle strong { - color: #ecf0f1; } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark .hero.is-dark .navbar-menu, html.theme--documenter-dark .content kbd.hero .navbar-menu { - background-color: #282f2f; } } - html.theme--documenter-dark .hero.is-dark .navbar-item, html.theme--documenter-dark .content kbd.hero .navbar-item, - html.theme--documenter-dark .hero.is-dark .navbar-link, - html.theme--documenter-dark .content kbd.hero .navbar-link { - color: rgba(236, 240, 241, 0.7); } - html.theme--documenter-dark .hero.is-dark a.navbar-item:hover, html.theme--documenter-dark .content kbd.hero a.navbar-item:hover, html.theme--documenter-dark .hero.is-dark a.navbar-item.is-active, html.theme--documenter-dark .content kbd.hero a.navbar-item.is-active, - html.theme--documenter-dark .hero.is-dark .navbar-link:hover, - html.theme--documenter-dark .content kbd.hero .navbar-link:hover, - html.theme--documenter-dark .hero.is-dark .navbar-link.is-active, - html.theme--documenter-dark .content kbd.hero .navbar-link.is-active { - background-color: #1d2122; - color: #ecf0f1; } - html.theme--documenter-dark .hero.is-dark .tabs a, html.theme--documenter-dark .content kbd.hero .tabs a { - color: #ecf0f1; - opacity: 0.9; } - html.theme--documenter-dark .hero.is-dark .tabs a:hover, html.theme--documenter-dark .content kbd.hero .tabs a:hover { - opacity: 1; } - html.theme--documenter-dark .hero.is-dark .tabs li.is-active a, html.theme--documenter-dark .content kbd.hero .tabs li.is-active a { - opacity: 1; } - html.theme--documenter-dark .hero.is-dark .tabs.is-boxed a, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed a, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle a, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle a { - color: #ecf0f1; } - html.theme--documenter-dark .hero.is-dark .tabs.is-boxed a:hover, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle a:hover, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle a:hover { - background-color: rgba(10, 10, 10, 0.1); } - html.theme--documenter-dark .hero.is-dark .tabs.is-boxed li.is-active a, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-dark .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle li.is-active a, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle li.is-active a:hover { - background-color: #ecf0f1; - border-color: #ecf0f1; - color: #282f2f; } - html.theme--documenter-dark .hero.is-dark.is-bold, html.theme--documenter-dark .content kbd.hero.is-bold { - background-image: linear-gradient(141deg, #0f1615 0%, #282f2f 71%, #313c40 100%); } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .hero.is-dark.is-bold .navbar-menu, html.theme--documenter-dark .content kbd.hero.is-bold .navbar-menu { - background-image: linear-gradient(141deg, #0f1615 0%, #282f2f 71%, #313c40 100%); } } - html.theme--documenter-dark .hero.is-primary, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink { - background-color: #375a7f; - color: #fff; } - html.theme--documenter-dark .hero.is-primary a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), - html.theme--documenter-dark .hero.is-primary strong, - html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink strong { - color: inherit; } - html.theme--documenter-dark .hero.is-primary .title, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .title { - color: #fff; } - html.theme--documenter-dark .hero.is-primary .subtitle, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .subtitle { - color: rgba(255, 255, 255, 0.9); } - html.theme--documenter-dark .hero.is-primary .subtitle a:not(.button), html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .subtitle a:not(.button), - html.theme--documenter-dark .hero.is-primary .subtitle strong, - html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .subtitle strong { - color: #fff; } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark .hero.is-primary .navbar-menu, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-menu { - background-color: #375a7f; } } - html.theme--documenter-dark .hero.is-primary .navbar-item, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-item, - html.theme--documenter-dark .hero.is-primary .navbar-link, - html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-link { - color: rgba(255, 255, 255, 0.7); } - html.theme--documenter-dark .hero.is-primary a.navbar-item:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink a.navbar-item:hover, html.theme--documenter-dark .hero.is-primary a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink a.navbar-item.is-active, - html.theme--documenter-dark .hero.is-primary .navbar-link:hover, - html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-link:hover, - html.theme--documenter-dark .hero.is-primary .navbar-link.is-active, - html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-link.is-active { - background-color: #2f4d6d; - color: #fff; } - html.theme--documenter-dark .hero.is-primary .tabs a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs a { - color: #fff; - opacity: 0.9; } - html.theme--documenter-dark .hero.is-primary .tabs a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs a:hover { - opacity: 1; } - html.theme--documenter-dark .hero.is-primary .tabs li.is-active a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs li.is-active a { - opacity: 1; } - html.theme--documenter-dark .hero.is-primary .tabs.is-boxed a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a { - color: #fff; } - html.theme--documenter-dark .hero.is-primary .tabs.is-boxed a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a:hover { - background-color: rgba(10, 10, 10, 0.1); } - html.theme--documenter-dark .hero.is-primary .tabs.is-boxed li.is-active a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-primary .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle li.is-active a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle li.is-active a:hover { - background-color: #fff; - border-color: #fff; - color: #375a7f; } - html.theme--documenter-dark .hero.is-primary.is-bold, html.theme--documenter-dark .docstring > section > a.hero.is-bold.docs-sourcelink { - background-image: linear-gradient(141deg, #214b62 0%, #375a7f 71%, #3a5796 100%); } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .hero.is-primary.is-bold .navbar-menu, html.theme--documenter-dark .docstring > section > a.hero.is-bold.docs-sourcelink .navbar-menu { - background-image: linear-gradient(141deg, #214b62 0%, #375a7f 71%, #3a5796 100%); } } - html.theme--documenter-dark .hero.is-link { - background-color: #1abc9c; - color: #fff; } - html.theme--documenter-dark .hero.is-link a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), - html.theme--documenter-dark .hero.is-link strong { - color: inherit; } - html.theme--documenter-dark .hero.is-link .title { - color: #fff; } - html.theme--documenter-dark .hero.is-link .subtitle { - color: rgba(255, 255, 255, 0.9); } - html.theme--documenter-dark .hero.is-link .subtitle a:not(.button), - html.theme--documenter-dark .hero.is-link .subtitle strong { - color: #fff; } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark .hero.is-link .navbar-menu { - background-color: #1abc9c; } } - html.theme--documenter-dark .hero.is-link .navbar-item, - html.theme--documenter-dark .hero.is-link .navbar-link { - color: rgba(255, 255, 255, 0.7); } - html.theme--documenter-dark .hero.is-link a.navbar-item:hover, html.theme--documenter-dark .hero.is-link a.navbar-item.is-active, - html.theme--documenter-dark .hero.is-link .navbar-link:hover, - html.theme--documenter-dark .hero.is-link .navbar-link.is-active { - background-color: #17a689; - color: #fff; } - html.theme--documenter-dark .hero.is-link .tabs a { - color: #fff; - opacity: 0.9; } - html.theme--documenter-dark .hero.is-link .tabs a:hover { - opacity: 1; } - html.theme--documenter-dark .hero.is-link .tabs li.is-active a { - opacity: 1; } - html.theme--documenter-dark .hero.is-link .tabs.is-boxed a, html.theme--documenter-dark .hero.is-link .tabs.is-toggle a { - color: #fff; } - html.theme--documenter-dark .hero.is-link .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-link .tabs.is-toggle a:hover { - background-color: rgba(10, 10, 10, 0.1); } - html.theme--documenter-dark .hero.is-link .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-link .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-link .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-link .tabs.is-toggle li.is-active a:hover { - background-color: #fff; - border-color: #fff; - color: #1abc9c; } - html.theme--documenter-dark .hero.is-link.is-bold { - background-image: linear-gradient(141deg, #0c9764 0%, #1abc9c 71%, #17d8d2 100%); } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .hero.is-link.is-bold .navbar-menu { - background-image: linear-gradient(141deg, #0c9764 0%, #1abc9c 71%, #17d8d2 100%); } } - html.theme--documenter-dark .hero.is-info { - background-color: #024c7d; - color: #fff; } - html.theme--documenter-dark .hero.is-info a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), - html.theme--documenter-dark .hero.is-info strong { - color: inherit; } - html.theme--documenter-dark .hero.is-info .title { - color: #fff; } - html.theme--documenter-dark .hero.is-info .subtitle { - color: rgba(255, 255, 255, 0.9); } - html.theme--documenter-dark .hero.is-info .subtitle a:not(.button), - html.theme--documenter-dark .hero.is-info .subtitle strong { - color: #fff; } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark .hero.is-info .navbar-menu { - background-color: #024c7d; } } - html.theme--documenter-dark .hero.is-info .navbar-item, - html.theme--documenter-dark .hero.is-info .navbar-link { - color: rgba(255, 255, 255, 0.7); } - html.theme--documenter-dark .hero.is-info a.navbar-item:hover, html.theme--documenter-dark .hero.is-info a.navbar-item.is-active, - html.theme--documenter-dark .hero.is-info .navbar-link:hover, - html.theme--documenter-dark .hero.is-info .navbar-link.is-active { - background-color: #023d64; - color: #fff; } - html.theme--documenter-dark .hero.is-info .tabs a { - color: #fff; - opacity: 0.9; } - html.theme--documenter-dark .hero.is-info .tabs a:hover { - opacity: 1; } - html.theme--documenter-dark .hero.is-info .tabs li.is-active a { - opacity: 1; } - html.theme--documenter-dark .hero.is-info .tabs.is-boxed a, html.theme--documenter-dark .hero.is-info .tabs.is-toggle a { - color: #fff; } - html.theme--documenter-dark .hero.is-info .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-info .tabs.is-toggle a:hover { - background-color: rgba(10, 10, 10, 0.1); } - html.theme--documenter-dark .hero.is-info .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-info .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-info .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-info .tabs.is-toggle li.is-active a:hover { - background-color: #fff; - border-color: #fff; - color: #024c7d; } - html.theme--documenter-dark .hero.is-info.is-bold { - background-image: linear-gradient(141deg, #003a4c 0%, #024c7d 71%, #004299 100%); } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .hero.is-info.is-bold .navbar-menu { - background-image: linear-gradient(141deg, #003a4c 0%, #024c7d 71%, #004299 100%); } } - html.theme--documenter-dark .hero.is-success { - background-color: #008438; - color: #fff; } - html.theme--documenter-dark .hero.is-success a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), - html.theme--documenter-dark .hero.is-success strong { - color: inherit; } - html.theme--documenter-dark .hero.is-success .title { - color: #fff; } - html.theme--documenter-dark .hero.is-success .subtitle { - color: rgba(255, 255, 255, 0.9); } - html.theme--documenter-dark .hero.is-success .subtitle a:not(.button), - html.theme--documenter-dark .hero.is-success .subtitle strong { - color: #fff; } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark .hero.is-success .navbar-menu { - background-color: #008438; } } - html.theme--documenter-dark .hero.is-success .navbar-item, - html.theme--documenter-dark .hero.is-success .navbar-link { - color: rgba(255, 255, 255, 0.7); } - html.theme--documenter-dark .hero.is-success a.navbar-item:hover, html.theme--documenter-dark .hero.is-success a.navbar-item.is-active, - html.theme--documenter-dark .hero.is-success .navbar-link:hover, - html.theme--documenter-dark .hero.is-success .navbar-link.is-active { - background-color: #006b2d; - color: #fff; } - html.theme--documenter-dark .hero.is-success .tabs a { - color: #fff; - opacity: 0.9; } - html.theme--documenter-dark .hero.is-success .tabs a:hover { - opacity: 1; } - html.theme--documenter-dark .hero.is-success .tabs li.is-active a { - opacity: 1; } - html.theme--documenter-dark .hero.is-success .tabs.is-boxed a, html.theme--documenter-dark .hero.is-success .tabs.is-toggle a { - color: #fff; } - html.theme--documenter-dark .hero.is-success .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-success .tabs.is-toggle a:hover { - background-color: rgba(10, 10, 10, 0.1); } - html.theme--documenter-dark .hero.is-success .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-success .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-success .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-success .tabs.is-toggle li.is-active a:hover { - background-color: #fff; - border-color: #fff; - color: #008438; } - html.theme--documenter-dark .hero.is-success.is-bold { - background-image: linear-gradient(141deg, #005115 0%, #008438 71%, #009e5d 100%); } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .hero.is-success.is-bold .navbar-menu { - background-image: linear-gradient(141deg, #005115 0%, #008438 71%, #009e5d 100%); } } - html.theme--documenter-dark .hero.is-warning { - background-color: #ad8100; - color: #fff; } - html.theme--documenter-dark .hero.is-warning a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), - html.theme--documenter-dark .hero.is-warning strong { - color: inherit; } - html.theme--documenter-dark .hero.is-warning .title { - color: #fff; } - html.theme--documenter-dark .hero.is-warning .subtitle { - color: rgba(255, 255, 255, 0.9); } - html.theme--documenter-dark .hero.is-warning .subtitle a:not(.button), - html.theme--documenter-dark .hero.is-warning .subtitle strong { - color: #fff; } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark .hero.is-warning .navbar-menu { - background-color: #ad8100; } } - html.theme--documenter-dark .hero.is-warning .navbar-item, - html.theme--documenter-dark .hero.is-warning .navbar-link { - color: rgba(255, 255, 255, 0.7); } - html.theme--documenter-dark .hero.is-warning a.navbar-item:hover, html.theme--documenter-dark .hero.is-warning a.navbar-item.is-active, - html.theme--documenter-dark .hero.is-warning .navbar-link:hover, - html.theme--documenter-dark .hero.is-warning .navbar-link.is-active { - background-color: #946e00; - color: #fff; } - html.theme--documenter-dark .hero.is-warning .tabs a { - color: #fff; - opacity: 0.9; } - html.theme--documenter-dark .hero.is-warning .tabs a:hover { - opacity: 1; } - html.theme--documenter-dark .hero.is-warning .tabs li.is-active a { - opacity: 1; } - html.theme--documenter-dark .hero.is-warning .tabs.is-boxed a, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle a { - color: #fff; } - html.theme--documenter-dark .hero.is-warning .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle a:hover { - background-color: rgba(10, 10, 10, 0.1); } - html.theme--documenter-dark .hero.is-warning .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-warning .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle li.is-active a:hover { - background-color: #fff; - border-color: #fff; - color: #ad8100; } - html.theme--documenter-dark .hero.is-warning.is-bold { - background-image: linear-gradient(141deg, #7a4700 0%, #ad8100 71%, #c7b500 100%); } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .hero.is-warning.is-bold .navbar-menu { - background-image: linear-gradient(141deg, #7a4700 0%, #ad8100 71%, #c7b500 100%); } } - html.theme--documenter-dark .hero.is-danger { - background-color: #9e1b0d; - color: #fff; } - html.theme--documenter-dark .hero.is-danger a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), - html.theme--documenter-dark .hero.is-danger strong { - color: inherit; } - html.theme--documenter-dark .hero.is-danger .title { - color: #fff; } - html.theme--documenter-dark .hero.is-danger .subtitle { - color: rgba(255, 255, 255, 0.9); } - html.theme--documenter-dark .hero.is-danger .subtitle a:not(.button), - html.theme--documenter-dark .hero.is-danger .subtitle strong { - color: #fff; } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark .hero.is-danger .navbar-menu { - background-color: #9e1b0d; } } - html.theme--documenter-dark .hero.is-danger .navbar-item, - html.theme--documenter-dark .hero.is-danger .navbar-link { - color: rgba(255, 255, 255, 0.7); } - html.theme--documenter-dark .hero.is-danger a.navbar-item:hover, html.theme--documenter-dark .hero.is-danger a.navbar-item.is-active, - html.theme--documenter-dark .hero.is-danger .navbar-link:hover, - html.theme--documenter-dark .hero.is-danger .navbar-link.is-active { - background-color: #86170b; - color: #fff; } - html.theme--documenter-dark .hero.is-danger .tabs a { - color: #fff; - opacity: 0.9; } - html.theme--documenter-dark .hero.is-danger .tabs a:hover { - opacity: 1; } - html.theme--documenter-dark .hero.is-danger .tabs li.is-active a { - opacity: 1; } - html.theme--documenter-dark .hero.is-danger .tabs.is-boxed a, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle a { - color: #fff; } - html.theme--documenter-dark .hero.is-danger .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle a:hover { - background-color: rgba(10, 10, 10, 0.1); } - html.theme--documenter-dark .hero.is-danger .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-danger .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle li.is-active a:hover { - background-color: #fff; - border-color: #fff; - color: #9e1b0d; } - html.theme--documenter-dark .hero.is-danger.is-bold { - background-image: linear-gradient(141deg, #75030b 0%, #9e1b0d 71%, #ba380a 100%); } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .hero.is-danger.is-bold .navbar-menu { - background-image: linear-gradient(141deg, #75030b 0%, #9e1b0d 71%, #ba380a 100%); } } - html.theme--documenter-dark .hero.is-small .hero-body, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.hero .hero-body { - padding-bottom: 1.5rem; - padding-top: 1.5rem; } - @media screen and (min-width: 769px), print { - html.theme--documenter-dark .hero.is-medium .hero-body { - padding-bottom: 9rem; - padding-top: 9rem; } } - @media screen and (min-width: 769px), print { - html.theme--documenter-dark .hero.is-large .hero-body { - padding-bottom: 18rem; - padding-top: 18rem; } } - html.theme--documenter-dark .hero.is-halfheight .hero-body, html.theme--documenter-dark .hero.is-fullheight .hero-body, html.theme--documenter-dark .hero.is-fullheight-with-navbar .hero-body { - align-items: center; - display: flex; } - html.theme--documenter-dark .hero.is-halfheight .hero-body > .container, html.theme--documenter-dark .hero.is-fullheight .hero-body > .container, html.theme--documenter-dark .hero.is-fullheight-with-navbar .hero-body > .container { - flex-grow: 1; - flex-shrink: 1; } - html.theme--documenter-dark .hero.is-halfheight { - min-height: 50vh; } - html.theme--documenter-dark .hero.is-fullheight { - min-height: 100vh; } - html.theme--documenter-dark .hero-video { - overflow: hidden; } - html.theme--documenter-dark .hero-video video { - left: 50%; - min-height: 100%; - min-width: 100%; - position: absolute; - top: 50%; - transform: translate3d(-50%, -50%, 0); } - html.theme--documenter-dark .hero-video.is-transparent { - opacity: 0.3; } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .hero-video { - display: none; } } - html.theme--documenter-dark .hero-buttons { - margin-top: 1.5rem; } - @media screen and (max-width: 768px) { - html.theme--documenter-dark .hero-buttons .button { - display: flex; } - html.theme--documenter-dark .hero-buttons .button:not(:last-child) { - margin-bottom: 0.75rem; } } - @media screen and (min-width: 769px), print { - html.theme--documenter-dark .hero-buttons { - display: flex; - justify-content: center; } - html.theme--documenter-dark .hero-buttons .button:not(:last-child) { - margin-right: 1.5rem; } } - html.theme--documenter-dark .hero-head, - html.theme--documenter-dark .hero-foot { - flex-grow: 0; - flex-shrink: 0; } - html.theme--documenter-dark .hero-body { - flex-grow: 1; - flex-shrink: 0; - padding: 3rem 1.5rem; } - html.theme--documenter-dark .section { - padding: 3rem 1.5rem; } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark .section.is-medium { - padding: 9rem 1.5rem; } - html.theme--documenter-dark .section.is-large { - padding: 18rem 1.5rem; } } - html.theme--documenter-dark .footer { - background-color: #282f2f; - padding: 3rem 1.5rem 6rem; } - html.theme--documenter-dark hr { - height: 1px; } - html.theme--documenter-dark h6 { - text-transform: uppercase; - letter-spacing: 0.5px; } - html.theme--documenter-dark .hero { - background-color: #343c3d; } - html.theme--documenter-dark a { - transition: all 200ms ease; } - html.theme--documenter-dark .button { - transition: all 200ms ease; - border-width: 1px; - color: white; } - html.theme--documenter-dark .button.is-active, html.theme--documenter-dark .button.is-focused, html.theme--documenter-dark .button:active, html.theme--documenter-dark .button:focus { - box-shadow: 0 0 0 2px rgba(140, 155, 157, 0.5); } - html.theme--documenter-dark .button.is-white.is-hovered, html.theme--documenter-dark .button.is-white:hover { - background-color: white; } - html.theme--documenter-dark .button.is-white.is-active, html.theme--documenter-dark .button.is-white.is-focused, html.theme--documenter-dark .button.is-white:active, html.theme--documenter-dark .button.is-white:focus { - border-color: white; - box-shadow: 0 0 0 2px rgba(255, 255, 255, 0.5); } - html.theme--documenter-dark .button.is-black.is-hovered, html.theme--documenter-dark .button.is-black:hover { - background-color: #1d1d1d; } - html.theme--documenter-dark .button.is-black.is-active, html.theme--documenter-dark .button.is-black.is-focused, html.theme--documenter-dark .button.is-black:active, html.theme--documenter-dark .button.is-black:focus { - border-color: #0a0a0a; - box-shadow: 0 0 0 2px rgba(10, 10, 10, 0.5); } - html.theme--documenter-dark .button.is-light.is-hovered, html.theme--documenter-dark .button.is-light:hover { - background-color: white; } - html.theme--documenter-dark .button.is-light.is-active, html.theme--documenter-dark .button.is-light.is-focused, html.theme--documenter-dark .button.is-light:active, html.theme--documenter-dark .button.is-light:focus { - border-color: #ecf0f1; - box-shadow: 0 0 0 2px rgba(236, 240, 241, 0.5); } - html.theme--documenter-dark .button.is-dark.is-hovered, html.theme--documenter-dark .content kbd.button.is-hovered, html.theme--documenter-dark .button.is-dark:hover, html.theme--documenter-dark .content kbd.button:hover { - background-color: #3a4344; } - html.theme--documenter-dark .button.is-dark.is-active, html.theme--documenter-dark .content kbd.button.is-active, html.theme--documenter-dark .button.is-dark.is-focused, html.theme--documenter-dark .content kbd.button.is-focused, html.theme--documenter-dark .button.is-dark:active, html.theme--documenter-dark .content kbd.button:active, html.theme--documenter-dark .button.is-dark:focus, html.theme--documenter-dark .content kbd.button:focus { - border-color: #282f2f; - box-shadow: 0 0 0 2px rgba(40, 47, 47, 0.5); } - html.theme--documenter-dark .button.is-primary.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-hovered.docs-sourcelink, html.theme--documenter-dark .button.is-primary:hover, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:hover { - background-color: #436d9a; } - html.theme--documenter-dark .button.is-primary.is-active, html.theme--documenter-dark .docstring > section > a.button.is-active.docs-sourcelink, html.theme--documenter-dark .button.is-primary.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-focused.docs-sourcelink, html.theme--documenter-dark .button.is-primary:active, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:active, html.theme--documenter-dark .button.is-primary:focus, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:focus { - border-color: #375a7f; - box-shadow: 0 0 0 2px rgba(55, 90, 127, 0.5); } - html.theme--documenter-dark .button.is-link.is-hovered, html.theme--documenter-dark .button.is-link:hover { - background-color: #1fdeb8; } - html.theme--documenter-dark .button.is-link.is-active, html.theme--documenter-dark .button.is-link.is-focused, html.theme--documenter-dark .button.is-link:active, html.theme--documenter-dark .button.is-link:focus { - border-color: #1abc9c; - box-shadow: 0 0 0 2px rgba(26, 188, 156, 0.5); } - html.theme--documenter-dark .button.is-info.is-hovered, html.theme--documenter-dark .button.is-info:hover { - background-color: #0363a3; } - html.theme--documenter-dark .button.is-info.is-active, html.theme--documenter-dark .button.is-info.is-focused, html.theme--documenter-dark .button.is-info:active, html.theme--documenter-dark .button.is-info:focus { - border-color: #024c7d; - box-shadow: 0 0 0 2px rgba(2, 76, 125, 0.5); } - html.theme--documenter-dark .button.is-success.is-hovered, html.theme--documenter-dark .button.is-success:hover { - background-color: #00aa48; } - html.theme--documenter-dark .button.is-success.is-active, html.theme--documenter-dark .button.is-success.is-focused, html.theme--documenter-dark .button.is-success:active, html.theme--documenter-dark .button.is-success:focus { - border-color: #008438; - box-shadow: 0 0 0 2px rgba(0, 132, 56, 0.5); } - html.theme--documenter-dark .button.is-warning.is-hovered, html.theme--documenter-dark .button.is-warning:hover { - background-color: #d39e00; } - html.theme--documenter-dark .button.is-warning.is-active, html.theme--documenter-dark .button.is-warning.is-focused, html.theme--documenter-dark .button.is-warning:active, html.theme--documenter-dark .button.is-warning:focus { - border-color: #ad8100; - box-shadow: 0 0 0 2px rgba(173, 129, 0, 0.5); } - html.theme--documenter-dark .button.is-danger.is-hovered, html.theme--documenter-dark .button.is-danger:hover { - background-color: #c12110; } - html.theme--documenter-dark .button.is-danger.is-active, html.theme--documenter-dark .button.is-danger.is-focused, html.theme--documenter-dark .button.is-danger:active, html.theme--documenter-dark .button.is-danger:focus { - border-color: #9e1b0d; - box-shadow: 0 0 0 2px rgba(158, 27, 13, 0.5); } - html.theme--documenter-dark .label { - color: #dbdee0; } - html.theme--documenter-dark .button, - html.theme--documenter-dark .control.has-icons-left .icon, - html.theme--documenter-dark .control.has-icons-right .icon, - html.theme--documenter-dark .input, - html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input, - html.theme--documenter-dark .pagination-ellipsis, - html.theme--documenter-dark .pagination-link, - html.theme--documenter-dark .pagination-next, - html.theme--documenter-dark .pagination-previous, - html.theme--documenter-dark .select, - html.theme--documenter-dark .select select, - html.theme--documenter-dark .textarea { - height: 2.5em; } - html.theme--documenter-dark .input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input, - html.theme--documenter-dark .textarea { - transition: all 200ms ease; - box-shadow: none; - border-width: 1px; - padding-left: 1em; - padding-right: 1em; } - html.theme--documenter-dark .select:after, - html.theme--documenter-dark .select select { - border-width: 1px; } - html.theme--documenter-dark .control.has-addons .button, - html.theme--documenter-dark .control.has-addons .input, - html.theme--documenter-dark .control.has-addons #documenter .docs-sidebar form.docs-search > input, - html.theme--documenter-dark #documenter .docs-sidebar .control.has-addons form.docs-search > input, - html.theme--documenter-dark .control.has-addons .select { - margin-right: -1px; } - html.theme--documenter-dark .notification { - background-color: #343c3d; } - html.theme--documenter-dark .card { - box-shadow: none; - border: 1px solid #343c3d; - background-color: #282f2f; - border-radius: 0.4em; } - html.theme--documenter-dark .card .card-image img { - border-radius: 0.4em 0.4em 0 0; } - html.theme--documenter-dark .card .card-header { - box-shadow: none; - background-color: rgba(18, 18, 18, 0.2); - border-radius: 0.4em 0.4em 0 0; } - html.theme--documenter-dark .card .card-footer { - background-color: rgba(18, 18, 18, 0.2); } - html.theme--documenter-dark .card .card-footer, - html.theme--documenter-dark .card .card-footer-item { - border-width: 1px; - border-color: #343c3d; } - html.theme--documenter-dark .notification.is-white a:not(.button) { - color: #0a0a0a; - text-decoration: underline; } - html.theme--documenter-dark .notification.is-black a:not(.button) { - color: white; - text-decoration: underline; } - html.theme--documenter-dark .notification.is-light a:not(.button) { - color: #282f2f; - text-decoration: underline; } - html.theme--documenter-dark .notification.is-dark a:not(.button), html.theme--documenter-dark .content kbd.notification a:not(.button) { - color: #ecf0f1; - text-decoration: underline; } - html.theme--documenter-dark .notification.is-primary a:not(.button), html.theme--documenter-dark .docstring > section > a.notification.docs-sourcelink a:not(.button) { - color: #fff; - text-decoration: underline; } - html.theme--documenter-dark .notification.is-link a:not(.button) { - color: #fff; - text-decoration: underline; } - html.theme--documenter-dark .notification.is-info a:not(.button) { - color: #fff; - text-decoration: underline; } - html.theme--documenter-dark .notification.is-success a:not(.button) { - color: #fff; - text-decoration: underline; } - html.theme--documenter-dark .notification.is-warning a:not(.button) { - color: #fff; - text-decoration: underline; } - html.theme--documenter-dark .notification.is-danger a:not(.button) { - color: #fff; - text-decoration: underline; } - html.theme--documenter-dark .tag, html.theme--documenter-dark .content kbd, html.theme--documenter-dark .docstring > section > a.docs-sourcelink { - border-radius: 0.4em; } - html.theme--documenter-dark .menu-list a { - transition: all 300ms ease; } - html.theme--documenter-dark .modal-card-body { - background-color: #282f2f; } - html.theme--documenter-dark .modal-card-foot, - html.theme--documenter-dark .modal-card-head { - border-color: #343c3d; } - html.theme--documenter-dark .message-header { - font-weight: 700; - background-color: #343c3d; - color: white; } - html.theme--documenter-dark .message-body { - border-width: 1px; - border-color: #343c3d; } - html.theme--documenter-dark .navbar { - border-radius: 0.4em; } - html.theme--documenter-dark .navbar.is-transparent { - background: none; } - html.theme--documenter-dark .navbar.is-primary .navbar-dropdown a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-dropdown a.navbar-item.is-active { - background-color: #1abc9c; } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark .navbar .navbar-menu { - background-color: #375a7f; - border-radius: 0 0 0.4em 0.4em; } } - html.theme--documenter-dark .hero .navbar, - html.theme--documenter-dark body > .navbar { - border-radius: 0; } - html.theme--documenter-dark .pagination-link, - html.theme--documenter-dark .pagination-next, - html.theme--documenter-dark .pagination-previous { - border-width: 1px; } - html.theme--documenter-dark .panel-block, - html.theme--documenter-dark .panel-heading, - html.theme--documenter-dark .panel-tabs { - border-width: 1px; } - html.theme--documenter-dark .panel-block:first-child, - html.theme--documenter-dark .panel-heading:first-child, - html.theme--documenter-dark .panel-tabs:first-child { - border-top-width: 1px; } - html.theme--documenter-dark .panel-heading { - font-weight: 700; } - html.theme--documenter-dark .panel-tabs a { - border-width: 1px; - margin-bottom: -1px; } - html.theme--documenter-dark .panel-tabs a.is-active { - border-bottom-color: #17a689; } - html.theme--documenter-dark .panel-block:hover { - color: #1dd2af; } - html.theme--documenter-dark .panel-block:hover .panel-icon { - color: #1dd2af; } - html.theme--documenter-dark .panel-block.is-active .panel-icon { - color: #17a689; } - html.theme--documenter-dark .tabs a { - border-bottom-width: 1px; - margin-bottom: -1px; } - html.theme--documenter-dark .tabs ul { - border-bottom-width: 1px; } - html.theme--documenter-dark .tabs.is-boxed a { - border-width: 1px; } - html.theme--documenter-dark .tabs.is-boxed li.is-active a { - background-color: #1f2424; } - html.theme--documenter-dark .tabs.is-toggle li a { - border-width: 1px; - margin-bottom: 0; } - html.theme--documenter-dark .tabs.is-toggle li + li { - margin-left: -1px; } - html.theme--documenter-dark .hero.is-white .navbar .navbar-dropdown .navbar-item:hover { - background-color: transparent; } - html.theme--documenter-dark .hero.is-black .navbar .navbar-dropdown .navbar-item:hover { - background-color: transparent; } - html.theme--documenter-dark .hero.is-light .navbar .navbar-dropdown .navbar-item:hover { - background-color: transparent; } - html.theme--documenter-dark .hero.is-dark .navbar .navbar-dropdown .navbar-item:hover, html.theme--documenter-dark .content kbd.hero .navbar .navbar-dropdown .navbar-item:hover { - background-color: transparent; } - html.theme--documenter-dark .hero.is-primary .navbar .navbar-dropdown .navbar-item:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar .navbar-dropdown .navbar-item:hover { - background-color: transparent; } - html.theme--documenter-dark .hero.is-link .navbar .navbar-dropdown .navbar-item:hover { - background-color: transparent; } - html.theme--documenter-dark .hero.is-info .navbar .navbar-dropdown .navbar-item:hover { - background-color: transparent; } - html.theme--documenter-dark .hero.is-success .navbar .navbar-dropdown .navbar-item:hover { - background-color: transparent; } - html.theme--documenter-dark .hero.is-warning .navbar .navbar-dropdown .navbar-item:hover { - background-color: transparent; } - html.theme--documenter-dark .hero.is-danger .navbar .navbar-dropdown .navbar-item:hover { - background-color: transparent; } - html.theme--documenter-dark h1 .docs-heading-anchor, html.theme--documenter-dark h1 .docs-heading-anchor:hover, html.theme--documenter-dark h1 .docs-heading-anchor:visited, html.theme--documenter-dark h2 .docs-heading-anchor, html.theme--documenter-dark h2 .docs-heading-anchor:hover, html.theme--documenter-dark h2 .docs-heading-anchor:visited, html.theme--documenter-dark h3 .docs-heading-anchor, html.theme--documenter-dark h3 .docs-heading-anchor:hover, html.theme--documenter-dark h3 .docs-heading-anchor:visited, html.theme--documenter-dark h4 .docs-heading-anchor, html.theme--documenter-dark h4 .docs-heading-anchor:hover, html.theme--documenter-dark h4 .docs-heading-anchor:visited, html.theme--documenter-dark h5 .docs-heading-anchor, html.theme--documenter-dark h5 .docs-heading-anchor:hover, html.theme--documenter-dark h5 .docs-heading-anchor:visited, html.theme--documenter-dark h6 .docs-heading-anchor, html.theme--documenter-dark h6 .docs-heading-anchor:hover, html.theme--documenter-dark h6 .docs-heading-anchor:visited { - color: #f2f2f2; } - html.theme--documenter-dark h1 .docs-heading-anchor-permalink, html.theme--documenter-dark h2 .docs-heading-anchor-permalink, html.theme--documenter-dark h3 .docs-heading-anchor-permalink, html.theme--documenter-dark h4 .docs-heading-anchor-permalink, html.theme--documenter-dark h5 .docs-heading-anchor-permalink, html.theme--documenter-dark h6 .docs-heading-anchor-permalink { - visibility: hidden; - vertical-align: middle; - margin-left: 0.5em; - font-size: 0.7rem; } - html.theme--documenter-dark h1 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h2 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h3 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h4 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h5 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h6 .docs-heading-anchor-permalink::before { - font-family: "Font Awesome 5 Free"; - font-weight: 900; - content: "\f0c1"; } - html.theme--documenter-dark h1:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h2:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h3:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h4:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h5:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h6:hover .docs-heading-anchor-permalink { - visibility: visible; } - html.theme--documenter-dark .docs-light-only { - display: none !important; } - html.theme--documenter-dark pre { - position: relative; - overflow: hidden; } - html.theme--documenter-dark pre code, html.theme--documenter-dark pre code.hljs { - padding: 0 0.75rem !important; - overflow: auto; - display: block; } - html.theme--documenter-dark pre code:first-of-type, html.theme--documenter-dark pre code.hljs:first-of-type { - padding-top: 0.5rem !important; } - html.theme--documenter-dark pre code:last-of-type, html.theme--documenter-dark pre code.hljs:last-of-type { - padding-bottom: 0.5rem !important; } - html.theme--documenter-dark pre .copy-button { - opacity: 0.2; - transition: opacity 0.2s; - position: absolute; - right: 0em; - top: 0em; - padding: 0.5em; - width: 2.5em; - height: 2.5em; - background: transparent; - border: none; - font-family: "Font Awesome 5 Free"; - color: #fff; - cursor: pointer; - text-align: center; } - html.theme--documenter-dark pre .copy-button:focus, html.theme--documenter-dark pre .copy-button:hover { - opacity: 1; - background: rgba(255, 255, 255, 0.1); - color: #1abc9c; } - html.theme--documenter-dark pre .copy-button.success { - color: #259a12; - opacity: 1; } - html.theme--documenter-dark pre .copy-button.error { - color: #cb3c33; - opacity: 1; } - html.theme--documenter-dark pre:hover .copy-button { - opacity: 1; } - html.theme--documenter-dark .admonition { - background-color: #282f2f; - border-style: solid; - border-width: 1px; - border-color: #5e6d6f; - border-radius: 0.4em; - font-size: 15px; } - html.theme--documenter-dark .admonition strong { - color: currentColor; } - html.theme--documenter-dark .admonition.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.admonition { - font-size: 0.85em; } - html.theme--documenter-dark .admonition.is-medium { - font-size: 1.25rem; } - html.theme--documenter-dark .admonition.is-large { - font-size: 1.5rem; } - html.theme--documenter-dark .admonition.is-default { - background-color: #282f2f; - border-color: #5e6d6f; } - html.theme--documenter-dark .admonition.is-default > .admonition-header { - background-color: #5e6d6f; } - html.theme--documenter-dark .admonition.is-info { - background-color: #282f2f; - border-color: #024c7d; } - html.theme--documenter-dark .admonition.is-info > .admonition-header { - background-color: #024c7d; } - html.theme--documenter-dark .admonition.is-success { - background-color: #282f2f; - border-color: #008438; } - html.theme--documenter-dark .admonition.is-success > .admonition-header { - background-color: #008438; } - html.theme--documenter-dark .admonition.is-warning { - background-color: #282f2f; - border-color: #ad8100; } - html.theme--documenter-dark .admonition.is-warning > .admonition-header { - background-color: #ad8100; } - html.theme--documenter-dark .admonition.is-danger { - background-color: #282f2f; - border-color: #9e1b0d; } - html.theme--documenter-dark .admonition.is-danger > .admonition-header { - background-color: #9e1b0d; } - html.theme--documenter-dark .admonition.is-compat { - background-color: #282f2f; - border-color: #137886; } - html.theme--documenter-dark .admonition.is-compat > .admonition-header { - background-color: #137886; } - html.theme--documenter-dark .admonition-header { - background-color: #5e6d6f; - align-items: center; - font-weight: 700; - justify-content: space-between; - line-height: 1.25; - padding: 0.5rem 0.75rem; - position: relative; } - html.theme--documenter-dark .admonition-header:before { - font-family: "Font Awesome 5 Free"; - font-weight: 900; - margin-right: 0.75rem; - content: "\f06a"; } - html.theme--documenter-dark .admonition-body { - color: #fff; - padding: 0.5rem 0.75rem; } - html.theme--documenter-dark .admonition-body pre { - background-color: #282f2f; } - html.theme--documenter-dark .admonition-body code { - background-color: rgba(255, 255, 255, 0.05); } - html.theme--documenter-dark .docstring { - margin-bottom: 1em; - background-color: transparent; - border: 1px solid #5e6d6f; - box-shadow: none; - max-width: 100%; } - html.theme--documenter-dark .docstring > header { - display: flex; - flex-grow: 1; - align-items: stretch; - padding: 0.5rem 0.75rem; - background-color: #282f2f; - box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1); - box-shadow: none; - border-bottom: 1px solid #5e6d6f; } - html.theme--documenter-dark .docstring > header code { - background-color: transparent; } - html.theme--documenter-dark .docstring > header .docstring-binding { - margin-right: 0.3em; } - html.theme--documenter-dark .docstring > header .docstring-category { - margin-left: 0.3em; } - html.theme--documenter-dark .docstring > section { - position: relative; - padding: 0.75rem 0.75rem; - border-bottom: 1px solid #5e6d6f; } - html.theme--documenter-dark .docstring > section:last-child { - border-bottom: none; } - html.theme--documenter-dark .docstring > section > a.docs-sourcelink { - transition: opacity 0.3s; - opacity: 0; - position: absolute; - right: 0.375rem; - bottom: 0.375rem; } - html.theme--documenter-dark .docstring > section > a.docs-sourcelink:focus { - opacity: 1 !important; } - html.theme--documenter-dark .docstring:hover > section > a.docs-sourcelink { - opacity: 0.2; } - html.theme--documenter-dark .docstring:focus-within > section > a.docs-sourcelink { - opacity: 0.2; } - html.theme--documenter-dark .docstring > section:hover a.docs-sourcelink { - opacity: 1; } - html.theme--documenter-dark .documenter-example-output { - background-color: #1f2424; } - html.theme--documenter-dark .outdated-warning-overlay { - position: fixed; - top: 0; - left: 0; - right: 0; - box-shadow: 0 0 10px rgba(0, 0, 0, 0.3); - z-index: 999; - background-color: #282f2f; - border-bottom: 3px solid #9e1b0d; - padding: 10px 35px; - text-align: center; - font-size: 15px; } - html.theme--documenter-dark .outdated-warning-overlay .outdated-warning-closer { - position: absolute; - top: calc(50% - 10px); - right: 18px; - cursor: pointer; - width: 12px; } - html.theme--documenter-dark .outdated-warning-overlay a { - color: #1abc9c; } - html.theme--documenter-dark .outdated-warning-overlay a:hover { - color: #1dd2af; } - html.theme--documenter-dark .content pre { - border: 1px solid #5e6d6f; } - html.theme--documenter-dark .content code { - font-weight: inherit; } - html.theme--documenter-dark .content a code { - color: #1abc9c; } - html.theme--documenter-dark .content h1 code, html.theme--documenter-dark .content h2 code, html.theme--documenter-dark .content h3 code, html.theme--documenter-dark .content h4 code, html.theme--documenter-dark .content h5 code, html.theme--documenter-dark .content h6 code { - color: #f2f2f2; } - html.theme--documenter-dark .content table { - display: block; - width: initial; - max-width: 100%; - overflow-x: auto; } - html.theme--documenter-dark .content blockquote > ul:first-child, html.theme--documenter-dark .content blockquote > ol:first-child, html.theme--documenter-dark .content .admonition-body > ul:first-child, html.theme--documenter-dark .content .admonition-body > ol:first-child { - margin-top: 0; } - html.theme--documenter-dark pre, html.theme--documenter-dark code { - font-variant-ligatures: no-contextual; } - html.theme--documenter-dark .breadcrumb a.is-disabled { - cursor: default; - pointer-events: none; } - html.theme--documenter-dark .breadcrumb a.is-disabled, html.theme--documenter-dark .breadcrumb a.is-disabled:hover { - color: #f2f2f2; } - html.theme--documenter-dark .hljs { - background: initial !important; } - html.theme--documenter-dark .katex .katex-mathml { - top: 0; - right: 0; } - html.theme--documenter-dark .katex-display, html.theme--documenter-dark mjx-container, html.theme--documenter-dark .MathJax_Display { - margin: 0.5em 0 !important; } - html.theme--documenter-dark html { - -moz-osx-font-smoothing: auto; - -webkit-font-smoothing: auto; } - html.theme--documenter-dark li.no-marker { - list-style: none; } - html.theme--documenter-dark #documenter .docs-main > article { - overflow-wrap: break-word; } - html.theme--documenter-dark #documenter .docs-main > article .math-container { - overflow-x: auto; - overflow-y: hidden; } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark #documenter .docs-main { - max-width: 52rem; - margin-left: 20rem; - padding-right: 1rem; } } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark #documenter .docs-main { - width: 100%; } - html.theme--documenter-dark #documenter .docs-main > article { - max-width: 52rem; - margin-left: auto; - margin-right: auto; - margin-bottom: 1rem; - padding: 0 1rem; } - html.theme--documenter-dark #documenter .docs-main > header, html.theme--documenter-dark #documenter .docs-main > nav { - max-width: 100%; - width: 100%; - margin: 0; } } - html.theme--documenter-dark #documenter .docs-main header.docs-navbar { - background-color: #1f2424; - border-bottom: 1px solid #5e6d6f; - z-index: 2; - min-height: 4rem; - margin-bottom: 1rem; - display: flex; } - html.theme--documenter-dark #documenter .docs-main header.docs-navbar .breadcrumb { - flex-grow: 1; } - html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right { - display: flex; - white-space: nowrap; } - html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-icon, html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-label, html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button { - display: inline-block; } - html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-label { - padding: 0; - margin-left: 0.3em; } - html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-settings-button { - margin: auto 0 auto 1rem; } - html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button { - font-size: 1.5rem; - margin: auto 0 auto 1rem; } - html.theme--documenter-dark #documenter .docs-main header.docs-navbar > * { - margin: auto 0; } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark #documenter .docs-main header.docs-navbar { - position: sticky; - top: 0; - padding: 0 1rem; - /* For Headroom.js */ - transition-property: top, box-shadow; - -webkit-transition-property: top, box-shadow; - /* Safari */ - transition-duration: 0.3s; - -webkit-transition-duration: 0.3s; - /* Safari */ } - html.theme--documenter-dark #documenter .docs-main header.docs-navbar.headroom--not-top { - box-shadow: 0.2rem 0rem 0.4rem #171717; - transition-duration: 0.7s; - -webkit-transition-duration: 0.7s; - /* Safari */ } - html.theme--documenter-dark #documenter .docs-main header.docs-navbar.headroom--unpinned.headroom--not-top.headroom--not-bottom { - top: -4.5rem; - transition-duration: 0.7s; - -webkit-transition-duration: 0.7s; - /* Safari */ } } - html.theme--documenter-dark #documenter .docs-main section.footnotes { - border-top: 1px solid #5e6d6f; } - html.theme--documenter-dark #documenter .docs-main section.footnotes li .tag:first-child, html.theme--documenter-dark #documenter .docs-main section.footnotes li .docstring > section > a.docs-sourcelink:first-child, html.theme--documenter-dark #documenter .docs-main section.footnotes li .content kbd:first-child, html.theme--documenter-dark .content #documenter .docs-main section.footnotes li kbd:first-child { - margin-right: 1em; - margin-bottom: 0.4em; } - html.theme--documenter-dark #documenter .docs-main .docs-footer { - display: flex; - flex-wrap: wrap; - margin-left: 0; - margin-right: 0; - border-top: 1px solid #5e6d6f; - padding-top: 1rem; - padding-bottom: 1rem; } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark #documenter .docs-main .docs-footer { - padding-left: 1rem; - padding-right: 1rem; } } - html.theme--documenter-dark #documenter .docs-main .docs-footer .docs-footer-nextpage, html.theme--documenter-dark #documenter .docs-main .docs-footer .docs-footer-prevpage { - flex-grow: 1; } - html.theme--documenter-dark #documenter .docs-main .docs-footer .docs-footer-nextpage { - text-align: right; } - html.theme--documenter-dark #documenter .docs-main .docs-footer .flexbox-break { - flex-basis: 100%; - height: 0; } - html.theme--documenter-dark #documenter .docs-main .docs-footer .footer-message { - font-size: 0.8em; - margin: 0.5em auto 0 auto; - text-align: center; } - html.theme--documenter-dark #documenter .docs-sidebar { - display: flex; - flex-direction: column; - color: #fff; - background-color: #282f2f; - border-right: 1px solid #5e6d6f; - padding: 0; - flex: 0 0 18rem; - z-index: 5; - font-size: 15px; - position: fixed; - left: -18rem; - width: 18rem; - height: 100%; - transition: left 0.3s; - /* Setting up a nicer theme style for the scrollbar */ } - html.theme--documenter-dark #documenter .docs-sidebar.visible { - left: 0; - box-shadow: 0.4rem 0rem 0.8rem #171717; } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark #documenter .docs-sidebar.visible { - box-shadow: none; } } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark #documenter .docs-sidebar { - left: 0; - top: 0; } } - html.theme--documenter-dark #documenter .docs-sidebar .docs-logo { - margin-top: 1rem; - padding: 0 1rem; } - html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img { - max-height: 6rem; - margin: auto; } - html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name { - flex-shrink: 0; - font-size: 1.5rem; - font-weight: 700; - text-align: center; - white-space: nowrap; - overflow: hidden; - padding: 0.5rem 0; } - html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name .docs-autofit { - max-width: 16.2rem; } - html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name a, html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name a:hover { - color: #fff; } - html.theme--documenter-dark #documenter .docs-sidebar .docs-version-selector { - border-top: 1px solid #5e6d6f; - display: none; - padding: 0.5rem; } - html.theme--documenter-dark #documenter .docs-sidebar .docs-version-selector.visible { - display: flex; } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu { - flex-grow: 1; - user-select: none; - border-top: 1px solid #5e6d6f; - padding-bottom: 1.5rem; - /* Managing collapsible submenus */ } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu > li > .tocitem { - font-weight: bold; } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu > li li { - font-size: 14.25px; - margin-left: 1em; - border-left: 1px solid #5e6d6f; } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu input.collapse-toggle { - display: none; } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.collapsed { - display: none; } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu input:checked ~ ul.collapsed { - display: block; } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem { - display: flex; } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-label { - flex-grow: 2; } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron { - display: inline-block; - font-style: normal; - font-variant: normal; - text-rendering: auto; - line-height: 1; - font-size: 11.25px; - margin-left: 1rem; - margin-top: auto; - margin-bottom: auto; } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron::before { - font-family: "Font Awesome 5 Free"; - font-weight: 900; - content: "\f054"; } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu input:checked ~ label.tocitem .docs-chevron::before { - content: "\f078"; } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu .tocitem { - display: block; - padding: 0.5rem 0.5rem; } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu .tocitem, html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu .tocitem:hover { - color: #fff; - background: #282f2f; } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu a.tocitem:hover, html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem:hover { - color: #fff; - background-color: #32393a; } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active { - border-top: 1px solid #5e6d6f; - border-bottom: 1px solid #5e6d6f; - background-color: #1f2424; } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem, html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem:hover { - background-color: #1f2424; - color: #fff; } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active ul.internal .tocitem:hover { - background-color: #32393a; - color: #fff; } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu > li.is-active:first-child { - border-top: none; } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal { - margin: 0 0.5rem 0.5rem; - border-top: 1px solid #5e6d6f; } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal li { - font-size: 12.75px; - border-left: none; - margin-left: 0; - margin-top: 0.5rem; } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem { - width: 100%; - padding: 0; } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem::before { - content: "⚬"; - margin-right: 0.4em; } - html.theme--documenter-dark #documenter .docs-sidebar form.docs-search { - margin: auto; - margin-top: 0.5rem; - margin-bottom: 0.5rem; } - html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input { - width: 14.4rem; } - @media screen and (min-width: 1056px) { - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu { - overflow-y: auto; - -webkit-overflow-scroll: touch; } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar { - width: .3rem; - background: none; } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb { - border-radius: 5px 0px 0px 5px; - background: #3b4445; } - html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb:hover { - background: #4e5a5c; } } - @media screen and (max-width: 1055px) { - html.theme--documenter-dark #documenter .docs-sidebar { - overflow-y: auto; - -webkit-overflow-scroll: touch; } - html.theme--documenter-dark #documenter .docs-sidebar::-webkit-scrollbar { - width: .3rem; - background: none; } - html.theme--documenter-dark #documenter .docs-sidebar::-webkit-scrollbar-thumb { - border-radius: 5px 0px 0px 5px; - background: #3b4445; } - html.theme--documenter-dark #documenter .docs-sidebar::-webkit-scrollbar-thumb:hover { - background: #4e5a5c; } } - html.theme--documenter-dark #documenter .docs-main #documenter-search-info { - margin-bottom: 1rem; } - html.theme--documenter-dark #documenter .docs-main #documenter-search-results { - list-style-type: circle; - list-style-position: outside; } - html.theme--documenter-dark #documenter .docs-main #documenter-search-results li { - margin-left: 2rem; } - html.theme--documenter-dark #documenter .docs-main #documenter-search-results .docs-highlight { - background-color: yellow; } - html.theme--documenter-dark { - background-color: #1f2424; - font-size: 16px; - min-width: 300px; - overflow-x: auto; - overflow-y: scroll; - text-rendering: optimizeLegibility; - text-size-adjust: 100%; } - html.theme--documenter-dark .ansi span.sgr1 { - font-weight: bolder; } - html.theme--documenter-dark .ansi span.sgr2 { - font-weight: lighter; } - html.theme--documenter-dark .ansi span.sgr3 { - font-style: italic; } - html.theme--documenter-dark .ansi span.sgr4 { - text-decoration: underline; } - html.theme--documenter-dark .ansi span.sgr7 { - color: #1f2424; - background-color: #fff; } - html.theme--documenter-dark .ansi span.sgr8 { - color: transparent; } - html.theme--documenter-dark .ansi span.sgr8 span { - color: transparent; } - html.theme--documenter-dark .ansi span.sgr9 { - text-decoration: line-through; } - html.theme--documenter-dark .ansi span.sgr30 { - color: #242424; } - html.theme--documenter-dark .ansi span.sgr31 { - color: #f6705f; } - html.theme--documenter-dark .ansi span.sgr32 { - color: #4fb43a; } - html.theme--documenter-dark .ansi span.sgr33 { - color: #f4c72f; } - html.theme--documenter-dark .ansi span.sgr34 { - color: #7587f0; } - html.theme--documenter-dark .ansi span.sgr35 { - color: #bc89d3; } - html.theme--documenter-dark .ansi span.sgr36 { - color: #49b6ca; } - html.theme--documenter-dark .ansi span.sgr37 { - color: #b3bdbe; } - html.theme--documenter-dark .ansi span.sgr40 { - background-color: #242424; } - html.theme--documenter-dark .ansi span.sgr41 { - background-color: #f6705f; } - html.theme--documenter-dark .ansi span.sgr42 { - background-color: #4fb43a; } - html.theme--documenter-dark .ansi span.sgr43 { - background-color: #f4c72f; } - html.theme--documenter-dark .ansi span.sgr44 { - background-color: #7587f0; } - html.theme--documenter-dark .ansi span.sgr45 { - background-color: #bc89d3; } - html.theme--documenter-dark .ansi span.sgr46 { - background-color: #49b6ca; } - html.theme--documenter-dark .ansi span.sgr47 { - background-color: #b3bdbe; } - html.theme--documenter-dark .ansi span.sgr90 { - color: #92a0a2; } - html.theme--documenter-dark .ansi span.sgr91 { - color: #ff8674; } - html.theme--documenter-dark .ansi span.sgr92 { - color: #79d462; } - html.theme--documenter-dark .ansi span.sgr93 { - color: #ffe76b; } - html.theme--documenter-dark .ansi span.sgr94 { - color: #8a98ff; } - html.theme--documenter-dark .ansi span.sgr95 { - color: #d2a4e6; } - html.theme--documenter-dark .ansi span.sgr96 { - color: #6bc8db; } - html.theme--documenter-dark .ansi span.sgr97 { - color: #ecf0f1; } - html.theme--documenter-dark .ansi span.sgr100 { - background-color: #92a0a2; } - html.theme--documenter-dark .ansi span.sgr101 { - background-color: #ff8674; } - html.theme--documenter-dark .ansi span.sgr102 { - background-color: #79d462; } - html.theme--documenter-dark .ansi span.sgr103 { - background-color: #ffe76b; } - html.theme--documenter-dark .ansi span.sgr104 { - background-color: #8a98ff; } - html.theme--documenter-dark .ansi span.sgr105 { - background-color: #d2a4e6; } - html.theme--documenter-dark .ansi span.sgr106 { - background-color: #6bc8db; } - html.theme--documenter-dark .ansi span.sgr107 { - background-color: #ecf0f1; } - html.theme--documenter-dark code.language-julia-repl > span.hljs-meta { - color: #4fb43a; - font-weight: bolder; } - html.theme--documenter-dark .hljs { - background: #2b2b2b; - color: #f8f8f2; } - html.theme--documenter-dark .hljs-comment, - html.theme--documenter-dark .hljs-quote { - color: #d4d0ab; } - html.theme--documenter-dark .hljs-variable, - html.theme--documenter-dark .hljs-template-variable, - html.theme--documenter-dark .hljs-tag, - html.theme--documenter-dark .hljs-name, - html.theme--documenter-dark .hljs-selector-id, - html.theme--documenter-dark .hljs-selector-class, - html.theme--documenter-dark .hljs-regexp, - html.theme--documenter-dark .hljs-deletion { - color: #ffa07a; } - html.theme--documenter-dark .hljs-number, - html.theme--documenter-dark .hljs-built_in, - html.theme--documenter-dark .hljs-literal, - html.theme--documenter-dark .hljs-type, - html.theme--documenter-dark .hljs-params, - html.theme--documenter-dark .hljs-meta, - html.theme--documenter-dark .hljs-link { - color: #f5ab35; } - html.theme--documenter-dark .hljs-attribute { - color: #ffd700; } - html.theme--documenter-dark .hljs-string, - html.theme--documenter-dark .hljs-symbol, - html.theme--documenter-dark .hljs-bullet, - html.theme--documenter-dark .hljs-addition { - color: #abe338; } - html.theme--documenter-dark .hljs-title, - html.theme--documenter-dark .hljs-section { - color: #00e0e0; } - html.theme--documenter-dark .hljs-keyword, - html.theme--documenter-dark .hljs-selector-tag { - color: #dcc6e0; } - html.theme--documenter-dark .hljs-emphasis { - font-style: italic; } - html.theme--documenter-dark .hljs-strong { - font-weight: bold; } - @media screen and (-ms-high-contrast: active) { - html.theme--documenter-dark .hljs-addition, - html.theme--documenter-dark .hljs-attribute, - html.theme--documenter-dark .hljs-built_in, - html.theme--documenter-dark .hljs-bullet, - html.theme--documenter-dark .hljs-comment, - html.theme--documenter-dark .hljs-link, - html.theme--documenter-dark .hljs-literal, - html.theme--documenter-dark .hljs-meta, - html.theme--documenter-dark .hljs-number, - html.theme--documenter-dark .hljs-params, - html.theme--documenter-dark .hljs-string, - html.theme--documenter-dark .hljs-symbol, - html.theme--documenter-dark .hljs-type, - html.theme--documenter-dark .hljs-quote { - color: highlight; } - html.theme--documenter-dark .hljs-keyword, - html.theme--documenter-dark .hljs-selector-tag { - font-weight: bold; } } - html.theme--documenter-dark .hljs-subst { - color: #f8f8f2; } +*/}html.theme--documenter-dark html{background-color:#1f2424;font-size:16px;-moz-osx-font-smoothing:grayscale;-webkit-font-smoothing:antialiased;min-width:300px;overflow-x:auto;overflow-y:scroll;text-rendering:optimizeLegibility;text-size-adjust:100%}html.theme--documenter-dark article,html.theme--documenter-dark aside,html.theme--documenter-dark figure,html.theme--documenter-dark footer,html.theme--documenter-dark header,html.theme--documenter-dark hgroup,html.theme--documenter-dark section{display:block}html.theme--documenter-dark body,html.theme--documenter-dark button,html.theme--documenter-dark input,html.theme--documenter-dark select,html.theme--documenter-dark textarea{font-family:"Lato Medium",-apple-system,BlinkMacSystemFont,"Segoe UI","Helvetica Neue","Helvetica","Arial",sans-serif}html.theme--documenter-dark code,html.theme--documenter-dark pre{-moz-osx-font-smoothing:auto;-webkit-font-smoothing:auto;font-family:"JuliaMono","SFMono-Regular","Menlo","Consolas","Liberation Mono","DejaVu Sans Mono",monospace}html.theme--documenter-dark body{color:#fff;font-size:1em;font-weight:400;line-height:1.5}html.theme--documenter-dark a{color:#1abc9c;cursor:pointer;text-decoration:none}html.theme--documenter-dark a strong{color:currentColor}html.theme--documenter-dark a:hover{color:#1dd2af}html.theme--documenter-dark code{background-color:rgba(255,255,255,0.05);color:#ececec;font-size:.875em;font-weight:normal;padding:.1em}html.theme--documenter-dark hr{background-color:#282f2f;border:none;display:block;height:2px;margin:1.5rem 0}html.theme--documenter-dark img{height:auto;max-width:100%}html.theme--documenter-dark input[type="checkbox"],html.theme--documenter-dark input[type="radio"]{vertical-align:baseline}html.theme--documenter-dark small{font-size:.875em}html.theme--documenter-dark span{font-style:inherit;font-weight:inherit}html.theme--documenter-dark strong{color:#f2f2f2;font-weight:700}html.theme--documenter-dark fieldset{border:none}html.theme--documenter-dark pre{-webkit-overflow-scrolling:touch;background-color:#282f2f;color:#fff;font-size:.875em;overflow-x:auto;padding:1.25rem 1.5rem;white-space:pre;word-wrap:normal}html.theme--documenter-dark pre code{background-color:transparent;color:currentColor;font-size:1em;padding:0}html.theme--documenter-dark table td,html.theme--documenter-dark table th{vertical-align:top}html.theme--documenter-dark table td:not([align]),html.theme--documenter-dark table th:not([align]){text-align:left}html.theme--documenter-dark table th{color:#f2f2f2}html.theme--documenter-dark .box{background-color:#343c3d;border-radius:8px;box-shadow:none;color:#fff;display:block;padding:1.25rem}html.theme--documenter-dark a.box:hover,html.theme--documenter-dark a.box:focus{box-shadow:0 2px 3px rgba(10,10,10,0.1),0 0 0 1px #1abc9c}html.theme--documenter-dark a.box:active{box-shadow:inset 0 1px 2px rgba(10,10,10,0.2),0 0 0 1px #1abc9c}html.theme--documenter-dark .button{background-color:#282f2f;border-color:#4c5759;border-width:1px;color:#375a7f;cursor:pointer;justify-content:center;padding-bottom:calc(0.375em - 1px);padding-left:.75em;padding-right:.75em;padding-top:calc(0.375em - 1px);text-align:center;white-space:nowrap}html.theme--documenter-dark .button strong{color:inherit}html.theme--documenter-dark .button .icon,html.theme--documenter-dark .button .icon.is-small,html.theme--documenter-dark .button #documenter .docs-sidebar form.docs-search>input.icon,html.theme--documenter-dark #documenter .docs-sidebar .button form.docs-search>input.icon,html.theme--documenter-dark .button .icon.is-medium,html.theme--documenter-dark .button .icon.is-large{height:1.5em;width:1.5em}html.theme--documenter-dark .button .icon:first-child:not(:last-child){margin-left:calc(-0.375em - 1px);margin-right:0.1875em}html.theme--documenter-dark .button .icon:last-child:not(:first-child){margin-left:0.1875em;margin-right:calc(-0.375em - 1px)}html.theme--documenter-dark .button .icon:first-child:last-child{margin-left:calc(-0.375em - 1px);margin-right:calc(-0.375em - 1px)}html.theme--documenter-dark .button:hover,html.theme--documenter-dark .button.is-hovered{border-color:#8c9b9d;color:#f2f2f2}html.theme--documenter-dark .button:focus,html.theme--documenter-dark .button.is-focused{border-color:#8c9b9d;color:#17a689}html.theme--documenter-dark .button:focus:not(:active),html.theme--documenter-dark .button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(26,188,156,0.25)}html.theme--documenter-dark .button:active,html.theme--documenter-dark .button.is-active{border-color:#343c3d;color:#f2f2f2}html.theme--documenter-dark .button.is-text{background-color:transparent;border-color:transparent;color:#fff;text-decoration:underline}html.theme--documenter-dark .button.is-text:hover,html.theme--documenter-dark .button.is-text.is-hovered,html.theme--documenter-dark .button.is-text:focus,html.theme--documenter-dark .button.is-text.is-focused{background-color:#282f2f;color:#f2f2f2}html.theme--documenter-dark .button.is-text:active,html.theme--documenter-dark .button.is-text.is-active{background-color:#1d2122;color:#f2f2f2}html.theme--documenter-dark .button.is-text[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-text{background-color:transparent;border-color:transparent;box-shadow:none}html.theme--documenter-dark .button.is-white{background-color:#fff;border-color:transparent;color:#0a0a0a}html.theme--documenter-dark .button.is-white:hover,html.theme--documenter-dark .button.is-white.is-hovered{background-color:#f9f9f9;border-color:transparent;color:#0a0a0a}html.theme--documenter-dark .button.is-white:focus,html.theme--documenter-dark .button.is-white.is-focused{border-color:transparent;color:#0a0a0a}html.theme--documenter-dark .button.is-white:focus:not(:active),html.theme--documenter-dark .button.is-white.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(255,255,255,0.25)}html.theme--documenter-dark .button.is-white:active,html.theme--documenter-dark .button.is-white.is-active{background-color:#f2f2f2;border-color:transparent;color:#0a0a0a}html.theme--documenter-dark .button.is-white[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-white{background-color:#fff;border-color:transparent;box-shadow:none}html.theme--documenter-dark 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html.theme--documenter-dark .button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:hover,html.theme--documenter-dark .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus,html.theme--documenter-dark .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black:focus:not(:active),html.theme--documenter-dark .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--documenter-dark .button.is-black:active,html.theme--documenter-dark .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-black[disabled],fieldset[disabled] 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html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:transparent;color:#ecf0f1}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#232829;border-color:transparent;color:#ecf0f1}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#ecf0f1}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content 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kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#282f2f;border-color:#282f2f;color:#ecf0f1}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark 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span.sgr105{background-color:#d2a4e6}html.theme--documenter-dark .ansi span.sgr106{background-color:#6bc8db}html.theme--documenter-dark .ansi span.sgr107{background-color:#ecf0f1}html.theme--documenter-dark code.language-julia-repl>span.hljs-meta{color:#4fb43a;font-weight:bolder}html.theme--documenter-dark .hljs{background:#2b2b2b;color:#f8f8f2}html.theme--documenter-dark .hljs-comment,html.theme--documenter-dark .hljs-quote{color:#d4d0ab}html.theme--documenter-dark .hljs-variable,html.theme--documenter-dark .hljs-template-variable,html.theme--documenter-dark .hljs-tag,html.theme--documenter-dark .hljs-name,html.theme--documenter-dark .hljs-selector-id,html.theme--documenter-dark .hljs-selector-class,html.theme--documenter-dark .hljs-regexp,html.theme--documenter-dark .hljs-deletion{color:#ffa07a}html.theme--documenter-dark .hljs-number,html.theme--documenter-dark .hljs-built_in,html.theme--documenter-dark .hljs-literal,html.theme--documenter-dark .hljs-type,html.theme--documenter-dark 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.hljs-literal,html.theme--documenter-dark .hljs-meta,html.theme--documenter-dark .hljs-number,html.theme--documenter-dark .hljs-params,html.theme--documenter-dark .hljs-string,html.theme--documenter-dark .hljs-symbol,html.theme--documenter-dark .hljs-type,html.theme--documenter-dark .hljs-quote{color:highlight}html.theme--documenter-dark .hljs-keyword,html.theme--documenter-dark .hljs-selector-tag{font-weight:bold}}html.theme--documenter-dark .hljs-subst{color:#f8f8f2} diff --git a/dev/assets/themes/documenter-light.css b/dev/assets/themes/documenter-light.css index 9595d5b..9b9a14b 100644 --- a/dev/assets/themes/documenter-light.css +++ b/dev/assets/themes/documenter-light.css @@ -1,7642 +1,4 @@ -@charset "UTF-8"; -/* Font Awesome 5 mixin. Can be included in any rule that should render Font Awesome icons. */ -@keyframes spinAround { - from { - transform: rotate(0deg); } - to { - transform: rotate(359deg); } } - -.tabs, .pagination-previous, -.pagination-next, -.pagination-link, -.pagination-ellipsis, .breadcrumb, .file, .button, .is-unselectable, .modal-close, .delete { - -webkit-touch-callout: none; - -webkit-user-select: none; - -moz-user-select: none; - -ms-user-select: none; - user-select: none; } - -.navbar-link:not(.is-arrowless)::after, .select:not(.is-multiple):not(.is-loading)::after { - border: 3px solid transparent; - border-radius: 2px; - border-right: 0; - border-top: 0; - content: " "; - display: block; - height: 0.625em; - margin-top: -0.4375em; - pointer-events: none; - position: absolute; - top: 50%; - transform: rotate(-45deg); - transform-origin: center; - width: 0.625em; } - -.admonition:not(:last-child), .tabs:not(:last-child), .message:not(:last-child), .list:not(:last-child), .level:not(:last-child), .breadcrumb:not(:last-child), .highlight:not(:last-child), .block:not(:last-child), .title:not(:last-child), -.subtitle:not(:last-child), .table-container:not(:last-child), .table:not(:last-child), .progress:not(:last-child), .notification:not(:last-child), .content:not(:last-child), .box:not(:last-child) { - margin-bottom: 1.5rem; } - -.modal-close, .delete { - -moz-appearance: none; - -webkit-appearance: none; - background-color: rgba(10, 10, 10, 0.2); - border: none; - border-radius: 290486px; - cursor: pointer; - pointer-events: auto; - display: inline-block; - flex-grow: 0; - flex-shrink: 0; - font-size: 0; - height: 20px; - max-height: 20px; - max-width: 20px; - min-height: 20px; - min-width: 20px; - outline: none; - position: relative; - vertical-align: top; - width: 20px; } - .modal-close::before, .delete::before, .modal-close::after, .delete::after { - background-color: white; - content: ""; - display: block; - left: 50%; - position: absolute; - top: 50%; - transform: translateX(-50%) translateY(-50%) rotate(45deg); - transform-origin: center center; } - .modal-close::before, .delete::before { - height: 2px; - width: 50%; } - .modal-close::after, .delete::after { - height: 50%; - width: 2px; } - .modal-close:hover, .delete:hover, .modal-close:focus, .delete:focus { - background-color: rgba(10, 10, 10, 0.3); 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} - -.is-family-monospace { - font-family: "JuliaMono", "SFMono-Regular", "Menlo", "Consolas", "Liberation Mono", "DejaVu Sans Mono", monospace !important; } - -.is-family-code { - font-family: "JuliaMono", "SFMono-Regular", "Menlo", "Consolas", "Liberation Mono", "DejaVu Sans Mono", monospace !important; } - -.is-block { - display: block !important; } - -@media screen and (max-width: 768px) { - .is-block-mobile { - display: block !important; } } - -@media screen and (min-width: 769px), print { - .is-block-tablet { - display: block !important; } } - -@media screen and (min-width: 769px) and (max-width: 1055px) { - .is-block-tablet-only { - display: block !important; } } - -@media screen and (max-width: 1055px) { - .is-block-touch { - display: block !important; } } - -@media screen and (min-width: 1056px) { - .is-block-desktop { - display: block !important; } } - -@media screen and (min-width: 1056px) and (max-width: 1215px) { - .is-block-desktop-only { - display: block !important; } } - -@media screen and (min-width: 1216px) { - .is-block-widescreen { - display: block !important; } } - -@media screen and (min-width: 1216px) and (max-width: 1407px) { - .is-block-widescreen-only { - display: block !important; } } - -@media screen and (min-width: 1408px) { - .is-block-fullhd { - display: block !important; } } - -.is-flex { - display: flex !important; } - -@media screen and (max-width: 768px) { - .is-flex-mobile { - display: flex !important; } } - -@media screen and (min-width: 769px), print { - .is-flex-tablet { - display: flex !important; } } - -@media screen and (min-width: 769px) and (max-width: 1055px) { - .is-flex-tablet-only { - display: flex !important; } } - -@media screen and (max-width: 1055px) { - .is-flex-touch { - display: flex !important; } } - -@media screen and (min-width: 1056px) { - .is-flex-desktop { - display: flex !important; } } - -@media screen and (min-width: 1056px) and (max-width: 1215px) { - .is-flex-desktop-only { - display: flex !important; } } - -@media screen and (min-width: 1216px) { - .is-flex-widescreen { - display: flex !important; } } - -@media screen and (min-width: 1216px) and (max-width: 1407px) { - .is-flex-widescreen-only { - display: flex !important; } } - -@media screen and (min-width: 1408px) { - .is-flex-fullhd { - display: flex !important; } } - -.is-inline { - display: inline !important; } - -@media screen and (max-width: 768px) { - .is-inline-mobile { - display: inline !important; } } - -@media screen and (min-width: 769px), print { - .is-inline-tablet { - display: inline !important; } } - -@media screen and (min-width: 769px) and (max-width: 1055px) { - .is-inline-tablet-only { - display: inline !important; } } - -@media screen and (max-width: 1055px) { - .is-inline-touch { - display: inline !important; } } - -@media screen and (min-width: 1056px) { - .is-inline-desktop { - display: inline !important; } } - -@media screen and (min-width: 1056px) and (max-width: 1215px) { - .is-inline-desktop-only { - display: inline !important; } } - -@media screen and (min-width: 1216px) { - .is-inline-widescreen { - display: inline !important; } } - -@media screen and (min-width: 1216px) and (max-width: 1407px) { - .is-inline-widescreen-only { - display: inline !important; } } - -@media screen and (min-width: 1408px) { - .is-inline-fullhd { - display: inline !important; } } - -.is-inline-block { - display: inline-block !important; } - -@media screen and (max-width: 768px) { - .is-inline-block-mobile { - display: inline-block !important; } } - -@media screen and (min-width: 769px), print { - .is-inline-block-tablet { - display: inline-block !important; } } - -@media screen and (min-width: 769px) and (max-width: 1055px) { - .is-inline-block-tablet-only { - display: inline-block !important; } } - -@media screen and (max-width: 1055px) { - .is-inline-block-touch { - display: inline-block !important; } } - -@media screen and (min-width: 1056px) { - .is-inline-block-desktop { - display: inline-block !important; } } - -@media screen and (min-width: 1056px) and (max-width: 1215px) { - .is-inline-block-desktop-only { - display: inline-block !important; } } - -@media screen and (min-width: 1216px) { - .is-inline-block-widescreen { - display: inline-block !important; } } - -@media screen and (min-width: 1216px) and (max-width: 1407px) { - .is-inline-block-widescreen-only { - display: inline-block !important; } } - -@media screen and (min-width: 1408px) { - .is-inline-block-fullhd { - display: inline-block !important; } } - -.is-inline-flex { - display: inline-flex !important; } - -@media screen and (max-width: 768px) { - .is-inline-flex-mobile { - display: inline-flex !important; } } - -@media screen and (min-width: 769px), print { - .is-inline-flex-tablet { - display: inline-flex !important; } } - -@media screen and (min-width: 769px) and (max-width: 1055px) { - .is-inline-flex-tablet-only { - display: inline-flex !important; } } - -@media screen and (max-width: 1055px) { - .is-inline-flex-touch { - display: inline-flex !important; } } - -@media screen and (min-width: 1056px) { - .is-inline-flex-desktop { - display: inline-flex !important; } } - -@media screen and (min-width: 1056px) and (max-width: 1215px) { - .is-inline-flex-desktop-only { - display: inline-flex !important; } } - -@media screen and (min-width: 1216px) { - .is-inline-flex-widescreen { - display: inline-flex !important; } } - -@media screen and (min-width: 1216px) and (max-width: 1407px) { - .is-inline-flex-widescreen-only { - display: inline-flex !important; } } - -@media screen and (min-width: 1408px) { - .is-inline-flex-fullhd { - display: inline-flex !important; } } - -.is-hidden { - display: none !important; } - -.is-sr-only { - border: none !important; - clip: rect(0, 0, 0, 0) !important; - height: 0.01em !important; - overflow: hidden !important; - padding: 0 !important; - position: absolute !important; - white-space: nowrap !important; - width: 0.01em !important; } - -@media screen and (max-width: 768px) { - .is-hidden-mobile { - display: none !important; } } - -@media screen and (min-width: 769px), print { - .is-hidden-tablet { - display: none !important; } } - -@media screen and (min-width: 769px) and (max-width: 1055px) { - .is-hidden-tablet-only { - display: none !important; } } - -@media screen and (max-width: 1055px) { - .is-hidden-touch { - display: none !important; } } - -@media screen and (min-width: 1056px) { - .is-hidden-desktop { - display: none !important; } } - -@media screen and (min-width: 1056px) and (max-width: 1215px) { - .is-hidden-desktop-only { - display: none !important; } } - -@media screen and (min-width: 1216px) { - .is-hidden-widescreen { - display: none !important; } } - -@media screen and (min-width: 1216px) and (max-width: 1407px) { - .is-hidden-widescreen-only { - display: none !important; } } - -@media screen and (min-width: 1408px) { - .is-hidden-fullhd { - display: none !important; } } - -.is-invisible { - visibility: hidden !important; } - -@media screen and (max-width: 768px) { - .is-invisible-mobile { - visibility: hidden !important; } } - -@media screen and (min-width: 769px), print { - .is-invisible-tablet { - visibility: hidden !important; } } - -@media screen and (min-width: 769px) and (max-width: 1055px) { - .is-invisible-tablet-only { - visibility: hidden !important; } } - -@media screen and (max-width: 1055px) { - .is-invisible-touch { - visibility: hidden !important; } } - -@media screen and (min-width: 1056px) { - .is-invisible-desktop { - visibility: hidden !important; } } - -@media screen and (min-width: 1056px) and (max-width: 1215px) { - .is-invisible-desktop-only { - visibility: hidden !important; } } - -@media screen and (min-width: 1216px) { - .is-invisible-widescreen { - visibility: hidden !important; } } - -@media screen and (min-width: 1216px) and (max-width: 1407px) { - .is-invisible-widescreen-only { - visibility: hidden !important; } } - -@media screen and (min-width: 1408px) { - .is-invisible-fullhd { - visibility: hidden !important; } } - -.is-marginless { - margin: 0 !important; } - -.is-paddingless { - padding: 0 !important; } - -.is-radiusless { - border-radius: 0 !important; } - -.is-shadowless { - box-shadow: none !important; } - -.is-relative { - position: relative !important; } - -.box { - background-color: white; - border-radius: 6px; - box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); - color: #222222; - display: block; - padding: 1.25rem; } - -a.box:hover, a.box:focus { - box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px #2e63b8; } - -a.box:active { - box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2), 0 0 0 1px #2e63b8; } - -.button { - background-color: white; - border-color: #dbdbdb; - border-width: 1px; - color: #363636; - cursor: pointer; - justify-content: center; - padding-bottom: calc(0.375em - 1px); - padding-left: 0.75em; - padding-right: 0.75em; - padding-top: calc(0.375em - 1px); - text-align: center; - white-space: nowrap; } - .button strong { - color: inherit; } - .button .icon, .button .icon.is-small, .button #documenter .docs-sidebar form.docs-search > input.icon, #documenter .docs-sidebar .button form.docs-search > input.icon, .button .icon.is-medium, .button .icon.is-large { - height: 1.5em; - width: 1.5em; } - .button .icon:first-child:not(:last-child) { - margin-left: calc(-0.375em - 1px); - margin-right: 0.1875em; } - .button .icon:last-child:not(:first-child) { - margin-left: 0.1875em; - margin-right: calc(-0.375em - 1px); } - .button .icon:first-child:last-child { - margin-left: calc(-0.375em - 1px); - margin-right: calc(-0.375em - 1px); } - .button:hover, .button.is-hovered { - border-color: #b5b5b5; - color: #363636; } - .button:focus, .button.is-focused { - border-color: #3c5dcd; - color: #363636; } - .button:focus:not(:active), .button.is-focused:not(:active) { - box-shadow: 0 0 0 0.125em rgba(46, 99, 184, 0.25); } - .button:active, .button.is-active { - border-color: #4a4a4a; - color: #363636; } - .button.is-text { - background-color: transparent; - border-color: transparent; - color: #222222; - text-decoration: underline; } - .button.is-text:hover, .button.is-text.is-hovered, .button.is-text:focus, .button.is-text.is-focused { - background-color: whitesmoke; - color: #222222; } - .button.is-text:active, .button.is-text.is-active { - background-color: #e8e8e8; - color: #222222; } - .button.is-text[disabled], fieldset[disabled] .button.is-text { - background-color: transparent; - border-color: transparent; - box-shadow: none; } - .button.is-white { - background-color: white; - border-color: transparent; - color: #0a0a0a; } - .button.is-white:hover, .button.is-white.is-hovered { - background-color: #f9f9f9; - border-color: transparent; - color: #0a0a0a; } - .button.is-white:focus, .button.is-white.is-focused { - border-color: transparent; - color: #0a0a0a; } - .button.is-white:focus:not(:active), .button.is-white.is-focused:not(:active) { - box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } - .button.is-white:active, .button.is-white.is-active { - background-color: #f2f2f2; - border-color: transparent; - color: #0a0a0a; } - .button.is-white[disabled], fieldset[disabled] .button.is-white { - background-color: white; - border-color: transparent; - box-shadow: none; } - .button.is-white.is-inverted { - background-color: #0a0a0a; - color: white; } - .button.is-white.is-inverted:hover, .button.is-white.is-inverted.is-hovered { - background-color: black; } - .button.is-white.is-inverted[disabled], fieldset[disabled] .button.is-white.is-inverted { - background-color: #0a0a0a; - border-color: transparent; - box-shadow: none; - color: white; } - .button.is-white.is-loading::after { - border-color: transparent transparent #0a0a0a #0a0a0a !important; } - .button.is-white.is-outlined { - background-color: transparent; - border-color: white; - color: white; } - .button.is-white.is-outlined:hover, .button.is-white.is-outlined.is-hovered, .button.is-white.is-outlined:focus, .button.is-white.is-outlined.is-focused { - background-color: white; - border-color: white; - color: #0a0a0a; } - .button.is-white.is-outlined.is-loading::after { - border-color: transparent transparent white white !important; } - .button.is-white.is-outlined.is-loading:hover::after, .button.is-white.is-outlined.is-loading.is-hovered::after, .button.is-white.is-outlined.is-loading:focus::after, .button.is-white.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #0a0a0a #0a0a0a !important; } - .button.is-white.is-outlined[disabled], fieldset[disabled] .button.is-white.is-outlined { - background-color: transparent; - border-color: white; - box-shadow: none; - color: white; } - .button.is-white.is-inverted.is-outlined { - background-color: transparent; - border-color: #0a0a0a; - color: #0a0a0a; } - .button.is-white.is-inverted.is-outlined:hover, .button.is-white.is-inverted.is-outlined.is-hovered, .button.is-white.is-inverted.is-outlined:focus, .button.is-white.is-inverted.is-outlined.is-focused { - background-color: #0a0a0a; - color: white; } - .button.is-white.is-inverted.is-outlined.is-loading:hover::after, .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-white.is-inverted.is-outlined.is-loading:focus::after, .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent white white !important; } - .button.is-white.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-white.is-inverted.is-outlined { - background-color: transparent; - border-color: #0a0a0a; - box-shadow: none; - color: #0a0a0a; } - .button.is-black { - background-color: #0a0a0a; - border-color: transparent; - color: white; } - .button.is-black:hover, .button.is-black.is-hovered { - background-color: #040404; - border-color: transparent; - color: white; } - .button.is-black:focus, .button.is-black.is-focused { - border-color: transparent; - color: white; } - .button.is-black:focus:not(:active), .button.is-black.is-focused:not(:active) { - box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } - .button.is-black:active, .button.is-black.is-active { - background-color: black; - border-color: transparent; - color: white; } - .button.is-black[disabled], fieldset[disabled] .button.is-black { - background-color: #0a0a0a; - border-color: transparent; - box-shadow: none; } - .button.is-black.is-inverted { - background-color: white; - color: #0a0a0a; } - .button.is-black.is-inverted:hover, .button.is-black.is-inverted.is-hovered { - background-color: #f2f2f2; } - .button.is-black.is-inverted[disabled], fieldset[disabled] .button.is-black.is-inverted { - background-color: white; - border-color: transparent; - box-shadow: none; - color: #0a0a0a; } - .button.is-black.is-loading::after { - border-color: transparent transparent white white !important; } - .button.is-black.is-outlined { - background-color: transparent; - border-color: #0a0a0a; - color: #0a0a0a; } - .button.is-black.is-outlined:hover, .button.is-black.is-outlined.is-hovered, .button.is-black.is-outlined:focus, .button.is-black.is-outlined.is-focused { - background-color: #0a0a0a; - border-color: #0a0a0a; - color: white; } - .button.is-black.is-outlined.is-loading::after { - border-color: transparent transparent #0a0a0a #0a0a0a !important; } - .button.is-black.is-outlined.is-loading:hover::after, .button.is-black.is-outlined.is-loading.is-hovered::after, .button.is-black.is-outlined.is-loading:focus::after, .button.is-black.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent white white !important; } - .button.is-black.is-outlined[disabled], fieldset[disabled] .button.is-black.is-outlined { - background-color: transparent; - border-color: #0a0a0a; - box-shadow: none; - color: #0a0a0a; } - .button.is-black.is-inverted.is-outlined { - background-color: transparent; - border-color: white; - color: white; } - .button.is-black.is-inverted.is-outlined:hover, .button.is-black.is-inverted.is-outlined.is-hovered, .button.is-black.is-inverted.is-outlined:focus, .button.is-black.is-inverted.is-outlined.is-focused { - background-color: white; - color: #0a0a0a; } - .button.is-black.is-inverted.is-outlined.is-loading:hover::after, .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-black.is-inverted.is-outlined.is-loading:focus::after, .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #0a0a0a #0a0a0a !important; } - .button.is-black.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-black.is-inverted.is-outlined { - background-color: transparent; - border-color: white; - box-shadow: none; - color: white; } - .button.is-light { - background-color: whitesmoke; - border-color: transparent; - color: #363636; } - .button.is-light:hover, .button.is-light.is-hovered { - background-color: #eeeeee; - border-color: transparent; - color: #363636; } - .button.is-light:focus, .button.is-light.is-focused { - border-color: transparent; - color: #363636; } - .button.is-light:focus:not(:active), .button.is-light.is-focused:not(:active) { - box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } - .button.is-light:active, .button.is-light.is-active { - background-color: #e8e8e8; - border-color: transparent; - color: #363636; } - .button.is-light[disabled], fieldset[disabled] .button.is-light { - background-color: whitesmoke; - border-color: transparent; - box-shadow: none; } - .button.is-light.is-inverted { - background-color: #363636; - color: whitesmoke; } - .button.is-light.is-inverted:hover, .button.is-light.is-inverted.is-hovered { - background-color: #292929; } - .button.is-light.is-inverted[disabled], fieldset[disabled] .button.is-light.is-inverted { - background-color: #363636; - border-color: transparent; - box-shadow: none; - color: whitesmoke; } - .button.is-light.is-loading::after { - border-color: transparent transparent #363636 #363636 !important; } - .button.is-light.is-outlined { - background-color: transparent; - border-color: whitesmoke; - color: whitesmoke; } - .button.is-light.is-outlined:hover, .button.is-light.is-outlined.is-hovered, .button.is-light.is-outlined:focus, .button.is-light.is-outlined.is-focused { - background-color: whitesmoke; - border-color: whitesmoke; - color: #363636; } - .button.is-light.is-outlined.is-loading::after { - border-color: transparent transparent whitesmoke whitesmoke !important; } - .button.is-light.is-outlined.is-loading:hover::after, .button.is-light.is-outlined.is-loading.is-hovered::after, .button.is-light.is-outlined.is-loading:focus::after, .button.is-light.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #363636 #363636 !important; } - .button.is-light.is-outlined[disabled], fieldset[disabled] .button.is-light.is-outlined { - background-color: transparent; - border-color: whitesmoke; - box-shadow: none; - color: whitesmoke; } - .button.is-light.is-inverted.is-outlined { - background-color: transparent; - border-color: #363636; - color: #363636; } - .button.is-light.is-inverted.is-outlined:hover, .button.is-light.is-inverted.is-outlined.is-hovered, .button.is-light.is-inverted.is-outlined:focus, .button.is-light.is-inverted.is-outlined.is-focused { - background-color: #363636; - color: whitesmoke; } - .button.is-light.is-inverted.is-outlined.is-loading:hover::after, .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-light.is-inverted.is-outlined.is-loading:focus::after, .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent whitesmoke whitesmoke !important; } - .button.is-light.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-light.is-inverted.is-outlined { - background-color: transparent; - border-color: #363636; - box-shadow: none; - color: #363636; } - .button.is-dark, .content kbd.button { - background-color: #363636; - border-color: transparent; - color: whitesmoke; } - .button.is-dark:hover, .content kbd.button:hover, .button.is-dark.is-hovered, .content kbd.button.is-hovered { - background-color: #2f2f2f; - border-color: transparent; - color: whitesmoke; } - .button.is-dark:focus, .content kbd.button:focus, .button.is-dark.is-focused, .content kbd.button.is-focused { - border-color: transparent; - color: whitesmoke; } - .button.is-dark:focus:not(:active), .content kbd.button:focus:not(:active), .button.is-dark.is-focused:not(:active), .content kbd.button.is-focused:not(:active) { - box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } - .button.is-dark:active, .content kbd.button:active, .button.is-dark.is-active, .content kbd.button.is-active { - background-color: #292929; - border-color: transparent; - color: whitesmoke; } - .button.is-dark[disabled], .content kbd.button[disabled], fieldset[disabled] .button.is-dark, fieldset[disabled] .content kbd.button, .content fieldset[disabled] kbd.button { - background-color: #363636; - border-color: transparent; - box-shadow: none; } - .button.is-dark.is-inverted, .content kbd.button.is-inverted { - background-color: whitesmoke; - color: #363636; } - .button.is-dark.is-inverted:hover, .content kbd.button.is-inverted:hover, .button.is-dark.is-inverted.is-hovered, .content kbd.button.is-inverted.is-hovered { - background-color: #e8e8e8; } - .button.is-dark.is-inverted[disabled], .content kbd.button.is-inverted[disabled], fieldset[disabled] .button.is-dark.is-inverted, fieldset[disabled] .content kbd.button.is-inverted, .content fieldset[disabled] kbd.button.is-inverted { - background-color: whitesmoke; - border-color: transparent; - box-shadow: none; - color: #363636; } - .button.is-dark.is-loading::after, .content kbd.button.is-loading::after { - border-color: transparent transparent whitesmoke whitesmoke !important; } - .button.is-dark.is-outlined, .content kbd.button.is-outlined { - background-color: transparent; - border-color: #363636; - color: #363636; } - .button.is-dark.is-outlined:hover, .content kbd.button.is-outlined:hover, .button.is-dark.is-outlined.is-hovered, .content kbd.button.is-outlined.is-hovered, .button.is-dark.is-outlined:focus, .content kbd.button.is-outlined:focus, .button.is-dark.is-outlined.is-focused, .content kbd.button.is-outlined.is-focused { - background-color: #363636; - border-color: #363636; - color: whitesmoke; } - .button.is-dark.is-outlined.is-loading::after, .content kbd.button.is-outlined.is-loading::after { - border-color: transparent transparent #363636 #363636 !important; } - .button.is-dark.is-outlined.is-loading:hover::after, .content kbd.button.is-outlined.is-loading:hover::after, .button.is-dark.is-outlined.is-loading.is-hovered::after, .content kbd.button.is-outlined.is-loading.is-hovered::after, .button.is-dark.is-outlined.is-loading:focus::after, .content kbd.button.is-outlined.is-loading:focus::after, .button.is-dark.is-outlined.is-loading.is-focused::after, .content kbd.button.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent whitesmoke whitesmoke !important; } - .button.is-dark.is-outlined[disabled], .content kbd.button.is-outlined[disabled], fieldset[disabled] .button.is-dark.is-outlined, fieldset[disabled] .content kbd.button.is-outlined, .content fieldset[disabled] kbd.button.is-outlined { - background-color: transparent; - border-color: #363636; - box-shadow: none; - color: #363636; } - .button.is-dark.is-inverted.is-outlined, .content kbd.button.is-inverted.is-outlined { - background-color: transparent; - border-color: whitesmoke; - color: whitesmoke; } - .button.is-dark.is-inverted.is-outlined:hover, .content kbd.button.is-inverted.is-outlined:hover, .button.is-dark.is-inverted.is-outlined.is-hovered, .content kbd.button.is-inverted.is-outlined.is-hovered, .button.is-dark.is-inverted.is-outlined:focus, .content kbd.button.is-inverted.is-outlined:focus, .button.is-dark.is-inverted.is-outlined.is-focused, .content kbd.button.is-inverted.is-outlined.is-focused { - background-color: whitesmoke; - color: #363636; } - .button.is-dark.is-inverted.is-outlined.is-loading:hover::after, .content kbd.button.is-inverted.is-outlined.is-loading:hover::after, .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after, .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-dark.is-inverted.is-outlined.is-loading:focus::after, .content kbd.button.is-inverted.is-outlined.is-loading:focus::after, .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after, .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #363636 #363636 !important; } - .button.is-dark.is-inverted.is-outlined[disabled], .content kbd.button.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-dark.is-inverted.is-outlined, fieldset[disabled] .content kbd.button.is-inverted.is-outlined, .content fieldset[disabled] kbd.button.is-inverted.is-outlined { - background-color: transparent; - border-color: whitesmoke; - box-shadow: none; - color: whitesmoke; } - .button.is-primary, .docstring > section > a.button.docs-sourcelink { - background-color: #4eb5de; - border-color: transparent; - color: #fff; } - .button.is-primary:hover, .docstring > section > a.button.docs-sourcelink:hover, .button.is-primary.is-hovered, .docstring > section > a.button.is-hovered.docs-sourcelink { - background-color: #43b1dc; - border-color: transparent; - color: #fff; } - .button.is-primary:focus, .docstring > section > a.button.docs-sourcelink:focus, .button.is-primary.is-focused, .docstring > section > a.button.is-focused.docs-sourcelink { - border-color: transparent; - color: #fff; } - .button.is-primary:focus:not(:active), .docstring > section > a.button.docs-sourcelink:focus:not(:active), .button.is-primary.is-focused:not(:active), .docstring > section > a.button.is-focused.docs-sourcelink:not(:active) { - box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } - .button.is-primary:active, .docstring > section > a.button.docs-sourcelink:active, .button.is-primary.is-active, .docstring > section > a.button.is-active.docs-sourcelink { - background-color: #39acda; - border-color: transparent; - color: #fff; } - .button.is-primary[disabled], .docstring > section > a.button.docs-sourcelink[disabled], fieldset[disabled] .button.is-primary, fieldset[disabled] .docstring > section > a.button.docs-sourcelink { - background-color: #4eb5de; - border-color: transparent; - box-shadow: none; } - .button.is-primary.is-inverted, .docstring > section > a.button.is-inverted.docs-sourcelink { - background-color: #fff; - color: #4eb5de; } - .button.is-primary.is-inverted:hover, .docstring > section > a.button.is-inverted.docs-sourcelink:hover, .button.is-primary.is-inverted.is-hovered, .docstring > section > a.button.is-inverted.is-hovered.docs-sourcelink { - background-color: #f2f2f2; } - .button.is-primary.is-inverted[disabled], .docstring > section > a.button.is-inverted.docs-sourcelink[disabled], fieldset[disabled] .button.is-primary.is-inverted, fieldset[disabled] .docstring > section > a.button.is-inverted.docs-sourcelink { - background-color: #fff; - border-color: transparent; - box-shadow: none; - color: #4eb5de; } - .button.is-primary.is-loading::after, .docstring > section > a.button.is-loading.docs-sourcelink::after { - border-color: transparent transparent #fff #fff !important; } - .button.is-primary.is-outlined, .docstring > section > a.button.is-outlined.docs-sourcelink { - background-color: transparent; - border-color: #4eb5de; - color: #4eb5de; } - .button.is-primary.is-outlined:hover, .docstring > section > a.button.is-outlined.docs-sourcelink:hover, .button.is-primary.is-outlined.is-hovered, .docstring > section > a.button.is-outlined.is-hovered.docs-sourcelink, .button.is-primary.is-outlined:focus, .docstring > section > a.button.is-outlined.docs-sourcelink:focus, .button.is-primary.is-outlined.is-focused, .docstring > section > a.button.is-outlined.is-focused.docs-sourcelink { - background-color: #4eb5de; - border-color: #4eb5de; - color: #fff; } - .button.is-primary.is-outlined.is-loading::after, .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink::after { - border-color: transparent transparent #4eb5de #4eb5de !important; } - .button.is-primary.is-outlined.is-loading:hover::after, .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:hover::after, .button.is-primary.is-outlined.is-loading.is-hovered::after, .docstring > section > a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after, .button.is-primary.is-outlined.is-loading:focus::after, .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:focus::after, .button.is-primary.is-outlined.is-loading.is-focused::after, .docstring > section > a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after { - border-color: transparent transparent #fff #fff !important; } - .button.is-primary.is-outlined[disabled], .docstring > section > a.button.is-outlined.docs-sourcelink[disabled], fieldset[disabled] .button.is-primary.is-outlined, fieldset[disabled] .docstring > section > a.button.is-outlined.docs-sourcelink { - background-color: transparent; - border-color: #4eb5de; - box-shadow: none; - color: #4eb5de; } - .button.is-primary.is-inverted.is-outlined, .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink { - background-color: transparent; - border-color: #fff; - color: #fff; } - .button.is-primary.is-inverted.is-outlined:hover, .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:hover, .button.is-primary.is-inverted.is-outlined.is-hovered, .docstring > section > a.button.is-inverted.is-outlined.is-hovered.docs-sourcelink, .button.is-primary.is-inverted.is-outlined:focus, .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:focus, .button.is-primary.is-inverted.is-outlined.is-focused, .docstring > section > a.button.is-inverted.is-outlined.is-focused.docs-sourcelink { - background-color: #fff; - color: #4eb5de; } - .button.is-primary.is-inverted.is-outlined.is-loading:hover::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:hover::after, .button.is-primary.is-inverted.is-outlined.is-loading.is-hovered::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-hovered.docs-sourcelink::after, .button.is-primary.is-inverted.is-outlined.is-loading:focus::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after, .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after { - border-color: transparent transparent #4eb5de #4eb5de !important; } - .button.is-primary.is-inverted.is-outlined[disabled], .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink[disabled], fieldset[disabled] .button.is-primary.is-inverted.is-outlined, fieldset[disabled] .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink { - background-color: transparent; - border-color: #fff; - box-shadow: none; - color: #fff; } - .button.is-link { - background-color: #2e63b8; - border-color: transparent; - color: #fff; } - .button.is-link:hover, .button.is-link.is-hovered { - background-color: #2b5eae; - border-color: transparent; - color: #fff; } - .button.is-link:focus, .button.is-link.is-focused { - border-color: transparent; - color: #fff; } - .button.is-link:focus:not(:active), .button.is-link.is-focused:not(:active) { - box-shadow: 0 0 0 0.125em rgba(46, 99, 184, 0.25); } - .button.is-link:active, .button.is-link.is-active { - background-color: #2958a4; - border-color: transparent; - color: #fff; } - .button.is-link[disabled], fieldset[disabled] .button.is-link { - background-color: #2e63b8; - border-color: transparent; - box-shadow: none; } - .button.is-link.is-inverted { - background-color: #fff; - color: #2e63b8; } - .button.is-link.is-inverted:hover, .button.is-link.is-inverted.is-hovered { - background-color: #f2f2f2; } - .button.is-link.is-inverted[disabled], fieldset[disabled] .button.is-link.is-inverted { - background-color: #fff; - border-color: transparent; - box-shadow: none; - color: #2e63b8; } - .button.is-link.is-loading::after { - border-color: transparent transparent #fff #fff !important; } - .button.is-link.is-outlined { - background-color: transparent; - border-color: #2e63b8; - color: #2e63b8; } - .button.is-link.is-outlined:hover, .button.is-link.is-outlined.is-hovered, .button.is-link.is-outlined:focus, .button.is-link.is-outlined.is-focused { - background-color: #2e63b8; - border-color: #2e63b8; - color: #fff; } - .button.is-link.is-outlined.is-loading::after { - border-color: transparent transparent #2e63b8 #2e63b8 !important; } - .button.is-link.is-outlined.is-loading:hover::after, .button.is-link.is-outlined.is-loading.is-hovered::after, .button.is-link.is-outlined.is-loading:focus::after, .button.is-link.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #fff #fff !important; } - .button.is-link.is-outlined[disabled], fieldset[disabled] .button.is-link.is-outlined { - background-color: transparent; - border-color: #2e63b8; - box-shadow: none; - color: #2e63b8; } - .button.is-link.is-inverted.is-outlined { - background-color: transparent; - border-color: #fff; - color: #fff; } - .button.is-link.is-inverted.is-outlined:hover, .button.is-link.is-inverted.is-outlined.is-hovered, .button.is-link.is-inverted.is-outlined:focus, .button.is-link.is-inverted.is-outlined.is-focused { - background-color: #fff; - color: #2e63b8; } - .button.is-link.is-inverted.is-outlined.is-loading:hover::after, .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-link.is-inverted.is-outlined.is-loading:focus::after, .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #2e63b8 #2e63b8 !important; } - .button.is-link.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-link.is-inverted.is-outlined { - background-color: transparent; - border-color: #fff; - box-shadow: none; - color: #fff; } - .button.is-info { - background-color: #209cee; - border-color: transparent; - color: #fff; } - .button.is-info:hover, .button.is-info.is-hovered { - background-color: #1497ed; - border-color: transparent; - color: #fff; } - .button.is-info:focus, .button.is-info.is-focused { - border-color: transparent; - color: #fff; } - .button.is-info:focus:not(:active), .button.is-info.is-focused:not(:active) { - box-shadow: 0 0 0 0.125em rgba(32, 156, 238, 0.25); } - .button.is-info:active, .button.is-info.is-active { - background-color: #1190e3; - border-color: transparent; - color: #fff; } - .button.is-info[disabled], fieldset[disabled] .button.is-info { - background-color: #209cee; - border-color: transparent; - box-shadow: none; } - .button.is-info.is-inverted { - background-color: #fff; - color: #209cee; } - .button.is-info.is-inverted:hover, .button.is-info.is-inverted.is-hovered { - background-color: #f2f2f2; } - .button.is-info.is-inverted[disabled], fieldset[disabled] .button.is-info.is-inverted { - background-color: #fff; - border-color: transparent; - box-shadow: none; - color: #209cee; } - .button.is-info.is-loading::after { - border-color: transparent transparent #fff #fff !important; } - .button.is-info.is-outlined { - background-color: transparent; - border-color: #209cee; - color: #209cee; } - .button.is-info.is-outlined:hover, .button.is-info.is-outlined.is-hovered, .button.is-info.is-outlined:focus, .button.is-info.is-outlined.is-focused { - background-color: #209cee; - border-color: #209cee; - color: #fff; } - .button.is-info.is-outlined.is-loading::after { - border-color: transparent transparent #209cee #209cee !important; } - .button.is-info.is-outlined.is-loading:hover::after, .button.is-info.is-outlined.is-loading.is-hovered::after, .button.is-info.is-outlined.is-loading:focus::after, .button.is-info.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #fff #fff !important; } - .button.is-info.is-outlined[disabled], fieldset[disabled] .button.is-info.is-outlined { - background-color: transparent; - border-color: #209cee; - box-shadow: none; - color: #209cee; } - .button.is-info.is-inverted.is-outlined { - background-color: transparent; - border-color: #fff; - color: #fff; } - .button.is-info.is-inverted.is-outlined:hover, .button.is-info.is-inverted.is-outlined.is-hovered, .button.is-info.is-inverted.is-outlined:focus, .button.is-info.is-inverted.is-outlined.is-focused { - background-color: #fff; - color: #209cee; } - .button.is-info.is-inverted.is-outlined.is-loading:hover::after, .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-info.is-inverted.is-outlined.is-loading:focus::after, .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #209cee #209cee !important; } - .button.is-info.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-info.is-inverted.is-outlined { - background-color: transparent; - border-color: #fff; - box-shadow: none; - color: #fff; } - .button.is-success { - background-color: #22c35b; - border-color: transparent; - color: #fff; } - .button.is-success:hover, .button.is-success.is-hovered { - background-color: #20b856; - border-color: transparent; - color: #fff; } - .button.is-success:focus, .button.is-success.is-focused { - border-color: transparent; - color: #fff; } - .button.is-success:focus:not(:active), .button.is-success.is-focused:not(:active) { - box-shadow: 0 0 0 0.125em rgba(34, 195, 91, 0.25); } - .button.is-success:active, .button.is-success.is-active { - background-color: #1ead51; - border-color: transparent; - color: #fff; } - .button.is-success[disabled], fieldset[disabled] .button.is-success { - background-color: #22c35b; - border-color: transparent; - box-shadow: none; } - .button.is-success.is-inverted { - background-color: #fff; - color: #22c35b; } - .button.is-success.is-inverted:hover, .button.is-success.is-inverted.is-hovered { - background-color: #f2f2f2; } - .button.is-success.is-inverted[disabled], fieldset[disabled] .button.is-success.is-inverted { - background-color: #fff; - border-color: transparent; - box-shadow: none; - color: #22c35b; } - .button.is-success.is-loading::after { - border-color: transparent transparent #fff #fff !important; } - .button.is-success.is-outlined { - background-color: transparent; - border-color: #22c35b; - color: #22c35b; } - .button.is-success.is-outlined:hover, .button.is-success.is-outlined.is-hovered, .button.is-success.is-outlined:focus, .button.is-success.is-outlined.is-focused { - background-color: #22c35b; - border-color: #22c35b; - color: #fff; } - .button.is-success.is-outlined.is-loading::after { - border-color: transparent transparent #22c35b #22c35b !important; } - .button.is-success.is-outlined.is-loading:hover::after, .button.is-success.is-outlined.is-loading.is-hovered::after, .button.is-success.is-outlined.is-loading:focus::after, .button.is-success.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #fff #fff !important; } - .button.is-success.is-outlined[disabled], fieldset[disabled] .button.is-success.is-outlined { - background-color: transparent; - border-color: #22c35b; - box-shadow: none; - color: #22c35b; } - .button.is-success.is-inverted.is-outlined { - background-color: transparent; - border-color: #fff; - color: #fff; } - .button.is-success.is-inverted.is-outlined:hover, .button.is-success.is-inverted.is-outlined.is-hovered, .button.is-success.is-inverted.is-outlined:focus, .button.is-success.is-inverted.is-outlined.is-focused { - background-color: #fff; - color: #22c35b; } - .button.is-success.is-inverted.is-outlined.is-loading:hover::after, .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-success.is-inverted.is-outlined.is-loading:focus::after, .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #22c35b #22c35b !important; } - .button.is-success.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-success.is-inverted.is-outlined { - background-color: transparent; - border-color: #fff; - box-shadow: none; - color: #fff; } - .button.is-warning { - background-color: #ffdd57; - border-color: transparent; - color: rgba(0, 0, 0, 0.7); } - .button.is-warning:hover, .button.is-warning.is-hovered { - background-color: #ffda4a; - border-color: transparent; - color: rgba(0, 0, 0, 0.7); } - .button.is-warning:focus, .button.is-warning.is-focused { - border-color: transparent; - color: rgba(0, 0, 0, 0.7); } - .button.is-warning:focus:not(:active), .button.is-warning.is-focused:not(:active) { - box-shadow: 0 0 0 0.125em rgba(255, 221, 87, 0.25); } - .button.is-warning:active, .button.is-warning.is-active { - background-color: #ffd83e; - border-color: transparent; - color: rgba(0, 0, 0, 0.7); } - .button.is-warning[disabled], fieldset[disabled] .button.is-warning { - background-color: #ffdd57; - border-color: transparent; - box-shadow: none; } - .button.is-warning.is-inverted { - background-color: rgba(0, 0, 0, 0.7); - color: #ffdd57; } - .button.is-warning.is-inverted:hover, .button.is-warning.is-inverted.is-hovered { - background-color: rgba(0, 0, 0, 0.7); } - .button.is-warning.is-inverted[disabled], fieldset[disabled] .button.is-warning.is-inverted { - background-color: rgba(0, 0, 0, 0.7); - border-color: transparent; - box-shadow: none; - color: #ffdd57; } - .button.is-warning.is-loading::after { - border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; } - .button.is-warning.is-outlined { - background-color: transparent; - border-color: #ffdd57; - color: #ffdd57; } - .button.is-warning.is-outlined:hover, .button.is-warning.is-outlined.is-hovered, .button.is-warning.is-outlined:focus, .button.is-warning.is-outlined.is-focused { - background-color: #ffdd57; - border-color: #ffdd57; - color: rgba(0, 0, 0, 0.7); } - .button.is-warning.is-outlined.is-loading::after { - border-color: transparent transparent #ffdd57 #ffdd57 !important; } - .button.is-warning.is-outlined.is-loading:hover::after, .button.is-warning.is-outlined.is-loading.is-hovered::after, .button.is-warning.is-outlined.is-loading:focus::after, .button.is-warning.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; } - .button.is-warning.is-outlined[disabled], fieldset[disabled] .button.is-warning.is-outlined { - background-color: transparent; - border-color: #ffdd57; - box-shadow: none; - color: #ffdd57; } - .button.is-warning.is-inverted.is-outlined { - background-color: transparent; - border-color: rgba(0, 0, 0, 0.7); - color: rgba(0, 0, 0, 0.7); } - .button.is-warning.is-inverted.is-outlined:hover, .button.is-warning.is-inverted.is-outlined.is-hovered, .button.is-warning.is-inverted.is-outlined:focus, .button.is-warning.is-inverted.is-outlined.is-focused { - background-color: rgba(0, 0, 0, 0.7); - color: #ffdd57; } - .button.is-warning.is-inverted.is-outlined.is-loading:hover::after, .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-warning.is-inverted.is-outlined.is-loading:focus::after, .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #ffdd57 #ffdd57 !important; } - .button.is-warning.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-warning.is-inverted.is-outlined { - background-color: transparent; - border-color: rgba(0, 0, 0, 0.7); - box-shadow: none; - color: rgba(0, 0, 0, 0.7); } - .button.is-danger { - background-color: #da0b00; - border-color: transparent; - color: #fff; } - .button.is-danger:hover, .button.is-danger.is-hovered { - background-color: #cd0a00; - border-color: transparent; - color: #fff; } - .button.is-danger:focus, .button.is-danger.is-focused { - border-color: transparent; - color: #fff; } - .button.is-danger:focus:not(:active), .button.is-danger.is-focused:not(:active) { - box-shadow: 0 0 0 0.125em rgba(218, 11, 0, 0.25); } - .button.is-danger:active, .button.is-danger.is-active { - background-color: #c10a00; - border-color: transparent; - color: #fff; } - .button.is-danger[disabled], fieldset[disabled] .button.is-danger { - background-color: #da0b00; - border-color: transparent; - box-shadow: none; } - .button.is-danger.is-inverted { - background-color: #fff; - color: #da0b00; } - .button.is-danger.is-inverted:hover, .button.is-danger.is-inverted.is-hovered { - background-color: #f2f2f2; } - .button.is-danger.is-inverted[disabled], fieldset[disabled] .button.is-danger.is-inverted { - background-color: #fff; - border-color: transparent; - box-shadow: none; - color: #da0b00; } - .button.is-danger.is-loading::after { - border-color: transparent transparent #fff #fff !important; } - .button.is-danger.is-outlined { - background-color: transparent; - border-color: #da0b00; - color: #da0b00; } - .button.is-danger.is-outlined:hover, .button.is-danger.is-outlined.is-hovered, .button.is-danger.is-outlined:focus, .button.is-danger.is-outlined.is-focused { - background-color: #da0b00; - border-color: #da0b00; - color: #fff; } - .button.is-danger.is-outlined.is-loading::after { - border-color: transparent transparent #da0b00 #da0b00 !important; } - .button.is-danger.is-outlined.is-loading:hover::after, .button.is-danger.is-outlined.is-loading.is-hovered::after, .button.is-danger.is-outlined.is-loading:focus::after, .button.is-danger.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #fff #fff !important; } - .button.is-danger.is-outlined[disabled], fieldset[disabled] .button.is-danger.is-outlined { - background-color: transparent; - border-color: #da0b00; - box-shadow: none; - color: #da0b00; } - .button.is-danger.is-inverted.is-outlined { - background-color: transparent; - border-color: #fff; - color: #fff; } - .button.is-danger.is-inverted.is-outlined:hover, .button.is-danger.is-inverted.is-outlined.is-hovered, .button.is-danger.is-inverted.is-outlined:focus, .button.is-danger.is-inverted.is-outlined.is-focused { - background-color: #fff; - color: #da0b00; } - .button.is-danger.is-inverted.is-outlined.is-loading:hover::after, .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-danger.is-inverted.is-outlined.is-loading:focus::after, .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after { - border-color: transparent transparent #da0b00 #da0b00 !important; } - .button.is-danger.is-inverted.is-outlined[disabled], fieldset[disabled] .button.is-danger.is-inverted.is-outlined { - background-color: transparent; - border-color: #fff; - box-shadow: none; - color: #fff; } - .button.is-small, #documenter .docs-sidebar form.docs-search > input.button { - border-radius: 2px; - font-size: 0.75rem; } - .button.is-normal { - font-size: 1rem; } - .button.is-medium { - font-size: 1.25rem; } - .button.is-large { - font-size: 1.5rem; } - .button[disabled], fieldset[disabled] .button { - background-color: white; - border-color: #dbdbdb; - box-shadow: none; - opacity: 0.5; } - .button.is-fullwidth { - display: flex; - width: 100%; } - .button.is-loading { - color: transparent !important; - pointer-events: none; } - .button.is-loading::after { - position: absolute; - left: calc(50% - (1em / 2)); - top: calc(50% - (1em / 2)); - position: absolute !important; } - .button.is-static { - background-color: whitesmoke; - border-color: #dbdbdb; - color: #6b6b6b; - box-shadow: none; - pointer-events: none; } - .button.is-rounded, #documenter .docs-sidebar form.docs-search > input.button { - border-radius: 290486px; - padding-left: 1em; - padding-right: 1em; } - -.buttons { - align-items: center; - display: flex; - flex-wrap: wrap; - justify-content: flex-start; } - .buttons .button { - margin-bottom: 0.5rem; } - .buttons .button:not(:last-child):not(.is-fullwidth) { - margin-right: 0.5rem; } - .buttons:last-child { - margin-bottom: -0.5rem; } - .buttons:not(:last-child) { - margin-bottom: 1rem; } - .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large) { - border-radius: 2px; - font-size: 0.75rem; } - .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large) { - font-size: 1.25rem; } - .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium) { - font-size: 1.5rem; } - .buttons.has-addons .button:not(:first-child) { - border-bottom-left-radius: 0; - border-top-left-radius: 0; } - .buttons.has-addons .button:not(:last-child) { - border-bottom-right-radius: 0; - border-top-right-radius: 0; - margin-right: -1px; } - .buttons.has-addons .button:last-child { - margin-right: 0; } - .buttons.has-addons .button:hover, .buttons.has-addons .button.is-hovered { - z-index: 2; } - .buttons.has-addons .button:focus, .buttons.has-addons .button.is-focused, .buttons.has-addons .button:active, .buttons.has-addons .button.is-active, .buttons.has-addons .button.is-selected { - z-index: 3; } - .buttons.has-addons .button:focus:hover, .buttons.has-addons .button.is-focused:hover, .buttons.has-addons .button:active:hover, .buttons.has-addons .button.is-active:hover, .buttons.has-addons .button.is-selected:hover { - z-index: 4; } - .buttons.has-addons .button.is-expanded { - flex-grow: 1; - flex-shrink: 1; } - .buttons.is-centered { - justify-content: center; } - .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth) { - margin-left: 0.25rem; - margin-right: 0.25rem; } - .buttons.is-right { - justify-content: flex-end; } - .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth) { - margin-left: 0.25rem; - margin-right: 0.25rem; } - -.container { - flex-grow: 1; - margin: 0 auto; - position: relative; - width: auto; } - @media screen and (min-width: 1056px) { - .container { - max-width: 992px; } - .container.is-fluid { - margin-left: 32px; - margin-right: 32px; - max-width: none; } } - @media screen and (max-width: 1215px) { - .container.is-widescreen { - max-width: 1152px; } } - @media screen and (max-width: 1407px) { - .container.is-fullhd { - max-width: 1344px; } } - @media screen and (min-width: 1216px) { - .container { - max-width: 1152px; } } - @media screen and (min-width: 1408px) { - .container { - max-width: 1344px; } } -.content li + li { - margin-top: 0.25em; } - -.content p:not(:last-child), -.content dl:not(:last-child), -.content ol:not(:last-child), -.content ul:not(:last-child), -.content blockquote:not(:last-child), -.content pre:not(:last-child), -.content table:not(:last-child) { - margin-bottom: 1em; } - -.content h1, -.content h2, -.content h3, -.content h4, -.content h5, -.content h6 { - color: #222222; - font-weight: 600; - line-height: 1.125; } - -.content h1 { - font-size: 2em; - margin-bottom: 0.5em; } - .content h1:not(:first-child) { - margin-top: 1em; } - -.content h2 { - font-size: 1.75em; - margin-bottom: 0.5714em; } - .content h2:not(:first-child) { - margin-top: 1.1428em; } - -.content h3 { - font-size: 1.5em; - margin-bottom: 0.6666em; } - .content h3:not(:first-child) { - margin-top: 1.3333em; } - -.content h4 { - font-size: 1.25em; - margin-bottom: 0.8em; } - -.content h5 { - font-size: 1.125em; - margin-bottom: 0.8888em; } - -.content h6 { - font-size: 1em; - margin-bottom: 1em; } - -.content blockquote { - background-color: whitesmoke; - border-left: 5px solid #dbdbdb; - padding: 1.25em 1.5em; } - -.content ol { - list-style-position: outside; - margin-left: 2em; - margin-top: 1em; } - .content ol:not([type]) { - list-style-type: decimal; } - .content ol.is-lower-alpha:not([type]) { - list-style-type: lower-alpha; } - .content ol.is-lower-roman:not([type]) { - list-style-type: lower-roman; } - .content ol.is-upper-alpha:not([type]) { - list-style-type: upper-alpha; } - .content ol.is-upper-roman:not([type]) { - list-style-type: upper-roman; } - -.content ul { - list-style: disc outside; - margin-left: 2em; - margin-top: 1em; } - .content ul ul { - list-style-type: circle; - margin-top: 0.5em; } - .content ul ul ul { - list-style-type: square; } - -.content dd { - margin-left: 2em; } - -.content figure { - margin-left: 2em; - margin-right: 2em; - text-align: center; } - .content figure:not(:first-child) { - margin-top: 2em; } - .content figure:not(:last-child) { - margin-bottom: 2em; } - .content figure img { - display: inline-block; } - .content figure figcaption { - font-style: italic; } - -.content pre { - -webkit-overflow-scrolling: touch; - overflow-x: auto; - padding: 0; - white-space: pre; - word-wrap: normal; } - -.content sup, -.content sub { - font-size: 75%; } - -.content table { - width: 100%; } - .content table td, - .content table th { - border: 1px solid #dbdbdb; - border-width: 0 0 1px; - padding: 0.5em 0.75em; - vertical-align: top; } - .content table th { - color: #222222; } - .content table th:not([align]) { - text-align: left; } - .content table thead td, - .content table thead th { - border-width: 0 0 2px; - color: #222222; } - .content table tfoot td, - .content table tfoot th { - border-width: 2px 0 0; - color: #222222; } - .content table tbody tr:last-child td, - .content table tbody tr:last-child th { - border-bottom-width: 0; } - -.content .tabs li + li { - margin-top: 0; } - -.content.is-small, #documenter .docs-sidebar form.docs-search > input.content { - font-size: 0.75rem; } - -.content.is-medium { - font-size: 1.25rem; } - -.content.is-large { - font-size: 1.5rem; } - -.icon { - align-items: center; - display: inline-flex; - justify-content: center; - height: 1.5rem; - width: 1.5rem; } - .icon.is-small, #documenter .docs-sidebar form.docs-search > input.icon { - height: 1rem; - width: 1rem; } - .icon.is-medium { - height: 2rem; - width: 2rem; } - .icon.is-large { - height: 3rem; - width: 3rem; } - -.image, #documenter .docs-sidebar .docs-logo > img { - display: block; - position: relative; } - .image img, #documenter .docs-sidebar .docs-logo > img img { - display: block; - height: auto; - width: 100%; } - .image img.is-rounded, #documenter .docs-sidebar .docs-logo > img img.is-rounded { - border-radius: 290486px; } - .image.is-square img, #documenter .docs-sidebar .docs-logo > img.is-square img, - .image.is-square .has-ratio, - #documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, .image.is-1by1 img, #documenter .docs-sidebar .docs-logo > img.is-1by1 img, - .image.is-1by1 .has-ratio, - #documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, .image.is-5by4 img, #documenter .docs-sidebar .docs-logo > img.is-5by4 img, - .image.is-5by4 .has-ratio, - #documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, .image.is-4by3 img, #documenter .docs-sidebar .docs-logo > img.is-4by3 img, - .image.is-4by3 .has-ratio, - #documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, .image.is-3by2 img, #documenter .docs-sidebar .docs-logo > img.is-3by2 img, - .image.is-3by2 .has-ratio, - #documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, .image.is-5by3 img, #documenter .docs-sidebar .docs-logo > img.is-5by3 img, - .image.is-5by3 .has-ratio, - #documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, .image.is-16by9 img, #documenter .docs-sidebar .docs-logo > img.is-16by9 img, - .image.is-16by9 .has-ratio, - #documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, .image.is-2by1 img, #documenter .docs-sidebar .docs-logo > img.is-2by1 img, - .image.is-2by1 .has-ratio, - #documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, .image.is-3by1 img, #documenter .docs-sidebar .docs-logo > img.is-3by1 img, - .image.is-3by1 .has-ratio, - #documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, .image.is-4by5 img, #documenter .docs-sidebar .docs-logo > img.is-4by5 img, - .image.is-4by5 .has-ratio, - #documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, .image.is-3by4 img, #documenter .docs-sidebar .docs-logo > img.is-3by4 img, - .image.is-3by4 .has-ratio, - #documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, .image.is-2by3 img, #documenter .docs-sidebar .docs-logo > img.is-2by3 img, - .image.is-2by3 .has-ratio, - #documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, .image.is-3by5 img, #documenter .docs-sidebar .docs-logo > img.is-3by5 img, - .image.is-3by5 .has-ratio, - #documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, .image.is-9by16 img, #documenter .docs-sidebar .docs-logo > img.is-9by16 img, - .image.is-9by16 .has-ratio, - #documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, .image.is-1by2 img, #documenter .docs-sidebar .docs-logo > img.is-1by2 img, - .image.is-1by2 .has-ratio, - #documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, .image.is-1by3 img, #documenter .docs-sidebar .docs-logo > img.is-1by3 img, - .image.is-1by3 .has-ratio, - #documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio { - height: 100%; - width: 100%; } - .image.is-square, #documenter .docs-sidebar .docs-logo > img.is-square, .image.is-1by1, #documenter .docs-sidebar .docs-logo > img.is-1by1 { - padding-top: 100%; } - .image.is-5by4, #documenter .docs-sidebar .docs-logo > img.is-5by4 { - padding-top: 80%; } - .image.is-4by3, #documenter .docs-sidebar .docs-logo > img.is-4by3 { - padding-top: 75%; } - .image.is-3by2, #documenter .docs-sidebar .docs-logo > img.is-3by2 { - padding-top: 66.6666%; } - .image.is-5by3, #documenter .docs-sidebar .docs-logo > img.is-5by3 { - padding-top: 60%; } - .image.is-16by9, #documenter .docs-sidebar .docs-logo > img.is-16by9 { - padding-top: 56.25%; } - .image.is-2by1, #documenter .docs-sidebar .docs-logo > img.is-2by1 { - padding-top: 50%; } - .image.is-3by1, #documenter .docs-sidebar .docs-logo > img.is-3by1 { - padding-top: 33.3333%; } - .image.is-4by5, #documenter .docs-sidebar .docs-logo > img.is-4by5 { - padding-top: 125%; } - .image.is-3by4, #documenter .docs-sidebar .docs-logo > img.is-3by4 { - padding-top: 133.3333%; } - .image.is-2by3, #documenter .docs-sidebar .docs-logo > img.is-2by3 { - padding-top: 150%; } - .image.is-3by5, #documenter .docs-sidebar .docs-logo > img.is-3by5 { - padding-top: 166.6666%; } - .image.is-9by16, #documenter .docs-sidebar .docs-logo > img.is-9by16 { - padding-top: 177.7777%; } - .image.is-1by2, #documenter .docs-sidebar .docs-logo > img.is-1by2 { - padding-top: 200%; } - .image.is-1by3, #documenter .docs-sidebar .docs-logo > img.is-1by3 { - padding-top: 300%; } - .image.is-16x16, #documenter .docs-sidebar .docs-logo > img.is-16x16 { - height: 16px; - width: 16px; } - .image.is-24x24, #documenter .docs-sidebar .docs-logo > img.is-24x24 { - height: 24px; - width: 24px; } - .image.is-32x32, #documenter .docs-sidebar .docs-logo > img.is-32x32 { - height: 32px; - width: 32px; } - .image.is-48x48, #documenter .docs-sidebar .docs-logo > img.is-48x48 { - height: 48px; - width: 48px; } - .image.is-64x64, #documenter .docs-sidebar .docs-logo > img.is-64x64 { - height: 64px; - width: 64px; } - .image.is-96x96, #documenter .docs-sidebar .docs-logo > img.is-96x96 { - height: 96px; - width: 96px; } - .image.is-128x128, #documenter .docs-sidebar .docs-logo > img.is-128x128 { - height: 128px; - width: 128px; } - -.notification { - background-color: whitesmoke; - border-radius: 4px; - padding: 1.25rem 2.5rem 1.25rem 1.5rem; - position: relative; } - .notification a:not(.button):not(.dropdown-item) { - color: currentColor; - text-decoration: underline; } - .notification strong { - color: currentColor; } - .notification code, - .notification pre { - background: white; } - .notification pre code { - background: transparent; } - .notification > .delete { - position: absolute; - right: 0.5rem; - top: 0.5rem; } - .notification .title, - .notification .subtitle, - .notification .content { - color: currentColor; } - .notification.is-white { - background-color: white; - color: #0a0a0a; } - .notification.is-black { - background-color: #0a0a0a; - color: white; } - .notification.is-light { - background-color: whitesmoke; - color: #363636; } - .notification.is-dark, .content kbd.notification { - background-color: #363636; - color: whitesmoke; } - .notification.is-primary, .docstring > section > a.notification.docs-sourcelink { - background-color: #4eb5de; - color: #fff; } - .notification.is-link { - background-color: #2e63b8; - color: #fff; } - .notification.is-info { - background-color: #209cee; - color: #fff; } - .notification.is-success { - background-color: #22c35b; - color: #fff; } - .notification.is-warning { - background-color: #ffdd57; - color: rgba(0, 0, 0, 0.7); } - .notification.is-danger { - background-color: #da0b00; - color: #fff; } - -.progress { - -moz-appearance: none; - -webkit-appearance: none; - border: none; - border-radius: 290486px; - display: block; - height: 1rem; - overflow: hidden; - padding: 0; - width: 100%; } - .progress::-webkit-progress-bar { - background-color: #dbdbdb; } - .progress::-webkit-progress-value { - background-color: #222222; } - .progress::-moz-progress-bar { - background-color: #222222; } - .progress::-ms-fill { - background-color: #222222; - border: none; } - .progress.is-white::-webkit-progress-value { - background-color: white; } - .progress.is-white::-moz-progress-bar { - background-color: white; } - .progress.is-white::-ms-fill { - background-color: white; } - .progress.is-white:indeterminate { - background-image: linear-gradient(to right, white 30%, #dbdbdb 30%); } - .progress.is-black::-webkit-progress-value { - background-color: #0a0a0a; } - .progress.is-black::-moz-progress-bar { - background-color: #0a0a0a; } - .progress.is-black::-ms-fill { - background-color: #0a0a0a; } - .progress.is-black:indeterminate { - background-image: linear-gradient(to right, #0a0a0a 30%, #dbdbdb 30%); } - .progress.is-light::-webkit-progress-value { - background-color: whitesmoke; } - .progress.is-light::-moz-progress-bar { - background-color: whitesmoke; } - .progress.is-light::-ms-fill { - background-color: whitesmoke; } - .progress.is-light:indeterminate { - background-image: linear-gradient(to right, whitesmoke 30%, #dbdbdb 30%); } - .progress.is-dark::-webkit-progress-value, .content kbd.progress::-webkit-progress-value { - background-color: #363636; } - .progress.is-dark::-moz-progress-bar, .content kbd.progress::-moz-progress-bar { - background-color: #363636; } - .progress.is-dark::-ms-fill, .content kbd.progress::-ms-fill { - background-color: #363636; } - .progress.is-dark:indeterminate, .content kbd.progress:indeterminate { - background-image: linear-gradient(to right, #363636 30%, #dbdbdb 30%); } - .progress.is-primary::-webkit-progress-value, .docstring > section > a.progress.docs-sourcelink::-webkit-progress-value { - background-color: #4eb5de; } - .progress.is-primary::-moz-progress-bar, .docstring > section > a.progress.docs-sourcelink::-moz-progress-bar { - background-color: #4eb5de; } - .progress.is-primary::-ms-fill, .docstring > section > a.progress.docs-sourcelink::-ms-fill { - background-color: #4eb5de; } - .progress.is-primary:indeterminate, .docstring > section > a.progress.docs-sourcelink:indeterminate { - background-image: linear-gradient(to right, #4eb5de 30%, #dbdbdb 30%); } - .progress.is-link::-webkit-progress-value { - background-color: #2e63b8; } - .progress.is-link::-moz-progress-bar { - background-color: #2e63b8; } - .progress.is-link::-ms-fill { - background-color: #2e63b8; } - .progress.is-link:indeterminate { - background-image: linear-gradient(to right, #2e63b8 30%, #dbdbdb 30%); } - .progress.is-info::-webkit-progress-value { - background-color: #209cee; } - .progress.is-info::-moz-progress-bar { - background-color: #209cee; } - .progress.is-info::-ms-fill { - background-color: #209cee; } - .progress.is-info:indeterminate { - background-image: linear-gradient(to right, #209cee 30%, #dbdbdb 30%); } - .progress.is-success::-webkit-progress-value { - background-color: #22c35b; } - .progress.is-success::-moz-progress-bar { - background-color: #22c35b; } - .progress.is-success::-ms-fill { - background-color: #22c35b; } - .progress.is-success:indeterminate { - background-image: linear-gradient(to right, #22c35b 30%, #dbdbdb 30%); } - .progress.is-warning::-webkit-progress-value { - background-color: #ffdd57; } - .progress.is-warning::-moz-progress-bar { - background-color: #ffdd57; } - .progress.is-warning::-ms-fill { - background-color: #ffdd57; } - .progress.is-warning:indeterminate { - background-image: linear-gradient(to right, #ffdd57 30%, #dbdbdb 30%); } - .progress.is-danger::-webkit-progress-value { - background-color: #da0b00; } - .progress.is-danger::-moz-progress-bar { - background-color: #da0b00; } - .progress.is-danger::-ms-fill { - background-color: #da0b00; } - .progress.is-danger:indeterminate { - background-image: linear-gradient(to right, #da0b00 30%, #dbdbdb 30%); } - .progress:indeterminate { - animation-duration: 1.5s; - animation-iteration-count: infinite; - animation-name: moveIndeterminate; - animation-timing-function: linear; - background-color: #dbdbdb; - background-image: linear-gradient(to right, #222222 30%, #dbdbdb 30%); - background-position: top left; - background-repeat: no-repeat; - background-size: 150% 150%; } - .progress:indeterminate::-webkit-progress-bar { - background-color: transparent; } - .progress:indeterminate::-moz-progress-bar { - background-color: transparent; } - .progress.is-small, #documenter .docs-sidebar form.docs-search > input.progress { - height: 0.75rem; } - .progress.is-medium { - height: 1.25rem; } - .progress.is-large { - height: 1.5rem; } - -@keyframes moveIndeterminate { - from { - background-position: 200% 0; } - to { - background-position: -200% 0; } } - -.table { - background-color: white; - color: #363636; } - .table td, - .table th { - border: 1px solid #dbdbdb; - border-width: 0 0 1px; - padding: 0.5em 0.75em; - vertical-align: top; } - .table td.is-white, - .table th.is-white { - background-color: white; - border-color: white; - color: #0a0a0a; } - .table td.is-black, - .table th.is-black { - background-color: #0a0a0a; - border-color: #0a0a0a; - color: white; } - .table td.is-light, - .table th.is-light { - background-color: whitesmoke; - border-color: whitesmoke; - color: #363636; } - .table td.is-dark, - .table th.is-dark { - background-color: #363636; - border-color: #363636; - color: whitesmoke; } - .table td.is-primary, - .table th.is-primary { - background-color: #4eb5de; - border-color: #4eb5de; - color: #fff; } - .table td.is-link, - .table th.is-link { - background-color: #2e63b8; - border-color: #2e63b8; - color: #fff; } - .table td.is-info, - .table th.is-info { - background-color: #209cee; - border-color: #209cee; - color: #fff; } - .table td.is-success, - .table th.is-success { - background-color: #22c35b; - border-color: #22c35b; - color: #fff; } - .table td.is-warning, - .table th.is-warning { - background-color: #ffdd57; - border-color: #ffdd57; - color: rgba(0, 0, 0, 0.7); } - .table td.is-danger, - .table th.is-danger { - background-color: #da0b00; - border-color: #da0b00; - color: #fff; } - .table td.is-narrow, - .table th.is-narrow { - white-space: nowrap; - width: 1%; } - .table td.is-selected, - .table th.is-selected { - background-color: #4eb5de; - color: #fff; } - .table td.is-selected a, - .table td.is-selected strong, - .table th.is-selected a, - .table th.is-selected strong { - color: currentColor; } - .table th { - color: #222222; } - .table th:not([align]) { - text-align: left; } - .table tr.is-selected { - background-color: #4eb5de; - color: #fff; } - .table tr.is-selected a, - .table tr.is-selected strong { - color: currentColor; } - .table tr.is-selected td, - .table tr.is-selected th { - border-color: #fff; - color: currentColor; } - .table thead { - background-color: transparent; } - .table thead td, - .table thead th { - border-width: 0 0 2px; - color: #222222; } - .table tfoot { - background-color: transparent; } - .table tfoot td, - .table tfoot th { - border-width: 2px 0 0; - color: #222222; } - .table tbody { - background-color: transparent; } - .table tbody tr:last-child td, - .table tbody tr:last-child th { - border-bottom-width: 0; } - .table.is-bordered td, - .table.is-bordered th { - border-width: 1px; } - .table.is-bordered tr:last-child td, - .table.is-bordered tr:last-child th { - border-bottom-width: 1px; } - .table.is-fullwidth { - width: 100%; } - .table.is-hoverable tbody tr:not(.is-selected):hover { - background-color: #fafafa; } - .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover { - background-color: #fafafa; } - .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover:nth-child(even) { - background-color: whitesmoke; } - .table.is-narrow td, - .table.is-narrow th { - padding: 0.25em 0.5em; } - .table.is-striped tbody tr:not(.is-selected):nth-child(even) { - background-color: #fafafa; } - -.table-container { - -webkit-overflow-scrolling: touch; - overflow: auto; - overflow-y: hidden; - max-width: 100%; } - -.tags { - align-items: center; - display: flex; - flex-wrap: wrap; - justify-content: flex-start; } - .tags .tag, .tags .content kbd, .content .tags kbd, .tags .docstring > section > a.docs-sourcelink { - margin-bottom: 0.5rem; } - .tags .tag:not(:last-child), .tags .content kbd:not(:last-child), .content .tags kbd:not(:last-child), .tags .docstring > section > a.docs-sourcelink:not(:last-child) { - margin-right: 0.5rem; } - .tags:last-child { - margin-bottom: -0.5rem; } - .tags:not(:last-child) { - margin-bottom: 1rem; } - .tags.are-medium .tag:not(.is-normal):not(.is-large), .tags.are-medium .content kbd:not(.is-normal):not(.is-large), .content .tags.are-medium kbd:not(.is-normal):not(.is-large), .tags.are-medium .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-large) { - font-size: 1rem; } - .tags.are-large .tag:not(.is-normal):not(.is-medium), .tags.are-large .content kbd:not(.is-normal):not(.is-medium), .content .tags.are-large kbd:not(.is-normal):not(.is-medium), .tags.are-large .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-medium) { - font-size: 1.25rem; } - .tags.is-centered { - justify-content: center; } - .tags.is-centered .tag, .tags.is-centered .content kbd, .content .tags.is-centered kbd, .tags.is-centered .docstring > section > a.docs-sourcelink { - margin-right: 0.25rem; - margin-left: 0.25rem; } - .tags.is-right { - justify-content: flex-end; } - .tags.is-right .tag:not(:first-child), .tags.is-right .content kbd:not(:first-child), .content .tags.is-right kbd:not(:first-child), .tags.is-right .docstring > section > a.docs-sourcelink:not(:first-child) { - margin-left: 0.5rem; } - .tags.is-right .tag:not(:last-child), .tags.is-right .content kbd:not(:last-child), .content .tags.is-right kbd:not(:last-child), .tags.is-right .docstring > section > a.docs-sourcelink:not(:last-child) { - margin-right: 0; } - .tags.has-addons .tag, .tags.has-addons .content kbd, .content .tags.has-addons kbd, .tags.has-addons .docstring > section > a.docs-sourcelink { - margin-right: 0; } - .tags.has-addons .tag:not(:first-child), .tags.has-addons .content kbd:not(:first-child), .content .tags.has-addons kbd:not(:first-child), .tags.has-addons .docstring > section > a.docs-sourcelink:not(:first-child) { - margin-left: 0; - border-bottom-left-radius: 0; - border-top-left-radius: 0; } - .tags.has-addons .tag:not(:last-child), .tags.has-addons .content kbd:not(:last-child), .content .tags.has-addons kbd:not(:last-child), .tags.has-addons .docstring > section > a.docs-sourcelink:not(:last-child) { - border-bottom-right-radius: 0; - border-top-right-radius: 0; } - -.tag:not(body), .content kbd:not(body), .docstring > section > a.docs-sourcelink:not(body) { - align-items: center; - background-color: whitesmoke; - border-radius: 4px; - color: #222222; - display: inline-flex; - font-size: 0.75rem; - height: 2em; - justify-content: center; - line-height: 1.5; - padding-left: 0.75em; - padding-right: 0.75em; - white-space: nowrap; } - .tag:not(body) .delete, .content kbd:not(body) .delete, .docstring > section > a.docs-sourcelink:not(body) .delete { - margin-left: 0.25rem; - margin-right: -0.375rem; } - .tag.is-white:not(body), .content kbd.is-white:not(body), .docstring > section > a.docs-sourcelink.is-white:not(body) { - background-color: white; - color: #0a0a0a; } - .tag.is-black:not(body), .content kbd.is-black:not(body), .docstring > section > a.docs-sourcelink.is-black:not(body) { - background-color: #0a0a0a; - color: white; } - .tag.is-light:not(body), .content kbd.is-light:not(body), .docstring > section > a.docs-sourcelink.is-light:not(body) { - background-color: whitesmoke; - color: #363636; } - .tag.is-dark:not(body), .content kbd:not(body), .docstring > section > a.docs-sourcelink.is-dark:not(body), .content .docstring > section > kbd:not(body) { - background-color: #363636; - color: whitesmoke; } - .tag.is-primary:not(body), .content kbd.is-primary:not(body), .docstring > section > a.docs-sourcelink:not(body) { - background-color: #4eb5de; - color: #fff; } - .tag.is-link:not(body), .content kbd.is-link:not(body), .docstring > section > a.docs-sourcelink.is-link:not(body) { - background-color: #2e63b8; - color: #fff; } - .tag.is-info:not(body), .content kbd.is-info:not(body), .docstring > section > a.docs-sourcelink.is-info:not(body) { - background-color: #209cee; - color: #fff; } - .tag.is-success:not(body), .content kbd.is-success:not(body), .docstring > section > a.docs-sourcelink.is-success:not(body) { - background-color: #22c35b; - color: #fff; } - .tag.is-warning:not(body), .content kbd.is-warning:not(body), .docstring > section > a.docs-sourcelink.is-warning:not(body) { - background-color: #ffdd57; - color: rgba(0, 0, 0, 0.7); } - .tag.is-danger:not(body), .content kbd.is-danger:not(body), .docstring > section > a.docs-sourcelink.is-danger:not(body) { - background-color: #da0b00; - color: #fff; } - .tag.is-normal:not(body), .content kbd.is-normal:not(body), .docstring > section > a.docs-sourcelink.is-normal:not(body) { - font-size: 0.75rem; } - .tag.is-medium:not(body), .content kbd.is-medium:not(body), .docstring > section > a.docs-sourcelink.is-medium:not(body) { - font-size: 1rem; } - .tag.is-large:not(body), .content kbd.is-large:not(body), .docstring > section > a.docs-sourcelink.is-large:not(body) { - font-size: 1.25rem; } - .tag:not(body) .icon:first-child:not(:last-child), .content kbd:not(body) .icon:first-child:not(:last-child), .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:not(:last-child) { - margin-left: -0.375em; - margin-right: 0.1875em; } - .tag:not(body) .icon:last-child:not(:first-child), .content kbd:not(body) .icon:last-child:not(:first-child), .docstring > section > a.docs-sourcelink:not(body) .icon:last-child:not(:first-child) { - margin-left: 0.1875em; - margin-right: -0.375em; } - .tag:not(body) .icon:first-child:last-child, .content kbd:not(body) .icon:first-child:last-child, .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:last-child { - margin-left: -0.375em; - margin-right: -0.375em; } - .tag.is-delete:not(body), .content kbd.is-delete:not(body), .docstring > section > a.docs-sourcelink.is-delete:not(body) { - margin-left: 1px; - padding: 0; - position: relative; - width: 2em; } - .tag.is-delete:not(body)::before, .content kbd.is-delete:not(body)::before, .docstring > section > a.docs-sourcelink.is-delete:not(body)::before, .tag.is-delete:not(body)::after, .content kbd.is-delete:not(body)::after, .docstring > section > a.docs-sourcelink.is-delete:not(body)::after { - background-color: currentColor; - content: ""; - display: block; - left: 50%; - position: absolute; - top: 50%; - transform: translateX(-50%) translateY(-50%) rotate(45deg); - transform-origin: center center; } - .tag.is-delete:not(body)::before, .content kbd.is-delete:not(body)::before, .docstring > section > a.docs-sourcelink.is-delete:not(body)::before { - height: 1px; - width: 50%; } - .tag.is-delete:not(body)::after, .content kbd.is-delete:not(body)::after, .docstring > section > a.docs-sourcelink.is-delete:not(body)::after { - height: 50%; - width: 1px; } - .tag.is-delete:not(body):hover, .content kbd.is-delete:not(body):hover, .docstring > section > a.docs-sourcelink.is-delete:not(body):hover, .tag.is-delete:not(body):focus, .content kbd.is-delete:not(body):focus, .docstring > section > a.docs-sourcelink.is-delete:not(body):focus { - background-color: #e8e8e8; } - .tag.is-delete:not(body):active, .content kbd.is-delete:not(body):active, .docstring > section > a.docs-sourcelink.is-delete:not(body):active { - background-color: #dbdbdb; } - .tag.is-rounded:not(body), #documenter .docs-sidebar form.docs-search > input:not(body), .content kbd.is-rounded:not(body), #documenter .docs-sidebar .content form.docs-search > input:not(body), .docstring > section > a.docs-sourcelink.is-rounded:not(body) { - border-radius: 290486px; } - -a.tag:hover, .docstring > section > a.docs-sourcelink:hover { - text-decoration: underline; } - -.title, -.subtitle { - word-break: break-word; } - .title em, - .title span, - .subtitle em, - .subtitle span { - font-weight: inherit; } - .title sub, - .subtitle sub { - font-size: 0.75em; } - .title sup, - .subtitle sup { - font-size: 0.75em; } - .title .tag, .title .content kbd, .content .title kbd, .title .docstring > section > a.docs-sourcelink, - .subtitle .tag, - .subtitle .content kbd, - .content .subtitle kbd, - .subtitle .docstring > section > a.docs-sourcelink { - vertical-align: middle; } - -.title { - color: #363636; - font-size: 2rem; - font-weight: 600; - line-height: 1.125; } - .title strong { - color: inherit; - font-weight: inherit; } - .title + .highlight { - margin-top: -0.75rem; } - .title:not(.is-spaced) + .subtitle { - margin-top: -1.25rem; } - .title.is-1 { - font-size: 3rem; } - .title.is-2 { - font-size: 2.5rem; } - .title.is-3 { - font-size: 2rem; } - .title.is-4 { - font-size: 1.5rem; } - .title.is-5 { - font-size: 1.25rem; } - .title.is-6 { - font-size: 1rem; } - .title.is-7 { - font-size: 0.75rem; } - -.subtitle { - color: #4a4a4a; - font-size: 1.25rem; - font-weight: 400; - line-height: 1.25; } - .subtitle strong { - color: #363636; - font-weight: 600; } - .subtitle:not(.is-spaced) + .title { - margin-top: -1.25rem; } - .subtitle.is-1 { - font-size: 3rem; } - .subtitle.is-2 { - font-size: 2.5rem; } - .subtitle.is-3 { - font-size: 2rem; } - .subtitle.is-4 { - font-size: 1.5rem; } - .subtitle.is-5 { - font-size: 1.25rem; } - .subtitle.is-6 { - font-size: 1rem; } - .subtitle.is-7 { - font-size: 0.75rem; } - -.heading { - display: block; - font-size: 11px; - letter-spacing: 1px; - margin-bottom: 5px; - text-transform: uppercase; } - -.highlight { - font-weight: 400; - max-width: 100%; - overflow: hidden; - padding: 0; } - .highlight pre { - overflow: auto; - max-width: 100%; } - -.number { - align-items: center; - background-color: whitesmoke; - border-radius: 290486px; - display: inline-flex; - font-size: 1.25rem; - height: 2em; - justify-content: center; - margin-right: 1.5rem; - min-width: 2.5em; - padding: 0.25rem 0.5rem; - text-align: center; - vertical-align: top; } - -.select select, .textarea, .input, #documenter .docs-sidebar form.docs-search > input { - background-color: white; - border-color: #dbdbdb; - border-radius: 4px; - color: #363636; } - .select select::-moz-placeholder, .textarea::-moz-placeholder, .input::-moz-placeholder, #documenter .docs-sidebar form.docs-search > input::-moz-placeholder { - color: rgba(54, 54, 54, 0.3); } - .select select::-webkit-input-placeholder, .textarea::-webkit-input-placeholder, .input::-webkit-input-placeholder, #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder { - color: rgba(54, 54, 54, 0.3); } - .select select:-moz-placeholder, .textarea:-moz-placeholder, .input:-moz-placeholder, #documenter .docs-sidebar form.docs-search > input:-moz-placeholder { - color: rgba(54, 54, 54, 0.3); } - .select select:-ms-input-placeholder, .textarea:-ms-input-placeholder, .input:-ms-input-placeholder, #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder { - color: rgba(54, 54, 54, 0.3); } - .select select:hover, .textarea:hover, .input:hover, #documenter .docs-sidebar form.docs-search > input:hover, .select select.is-hovered, .is-hovered.textarea, .is-hovered.input, #documenter .docs-sidebar form.docs-search > input.is-hovered { - border-color: #b5b5b5; } - .select select:focus, .textarea:focus, .input:focus, #documenter .docs-sidebar form.docs-search > input:focus, .select select.is-focused, .is-focused.textarea, .is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .select select:active, .textarea:active, .input:active, #documenter .docs-sidebar form.docs-search > input:active, .select select.is-active, .is-active.textarea, .is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { - border-color: #2e63b8; - box-shadow: 0 0 0 0.125em rgba(46, 99, 184, 0.25); } - .select select[disabled], .textarea[disabled], .input[disabled], #documenter .docs-sidebar form.docs-search > input[disabled], fieldset[disabled] .select select, .select fieldset[disabled] select, fieldset[disabled] .textarea, fieldset[disabled] .input, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input { - background-color: whitesmoke; - border-color: whitesmoke; - box-shadow: none; - color: #6b6b6b; } - .select select[disabled]::-moz-placeholder, .textarea[disabled]::-moz-placeholder, .input[disabled]::-moz-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]::-moz-placeholder, fieldset[disabled] .select select::-moz-placeholder, .select fieldset[disabled] select::-moz-placeholder, fieldset[disabled] .textarea::-moz-placeholder, fieldset[disabled] .input::-moz-placeholder, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input::-moz-placeholder, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input::-moz-placeholder { - color: rgba(107, 107, 107, 0.3); } - .select select[disabled]::-webkit-input-placeholder, .textarea[disabled]::-webkit-input-placeholder, .input[disabled]::-webkit-input-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]::-webkit-input-placeholder, fieldset[disabled] .select select::-webkit-input-placeholder, .select fieldset[disabled] select::-webkit-input-placeholder, fieldset[disabled] .textarea::-webkit-input-placeholder, fieldset[disabled] .input::-webkit-input-placeholder, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input::-webkit-input-placeholder { - color: rgba(107, 107, 107, 0.3); } - .select select[disabled]:-moz-placeholder, .textarea[disabled]:-moz-placeholder, .input[disabled]:-moz-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]:-moz-placeholder, fieldset[disabled] .select select:-moz-placeholder, .select fieldset[disabled] select:-moz-placeholder, fieldset[disabled] .textarea:-moz-placeholder, fieldset[disabled] .input:-moz-placeholder, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input:-moz-placeholder, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input:-moz-placeholder { - color: rgba(107, 107, 107, 0.3); } - .select select[disabled]:-ms-input-placeholder, .textarea[disabled]:-ms-input-placeholder, .input[disabled]:-ms-input-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]:-ms-input-placeholder, fieldset[disabled] .select select:-ms-input-placeholder, .select fieldset[disabled] select:-ms-input-placeholder, fieldset[disabled] .textarea:-ms-input-placeholder, fieldset[disabled] .input:-ms-input-placeholder, fieldset[disabled] #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder, #documenter .docs-sidebar fieldset[disabled] form.docs-search > input:-ms-input-placeholder { - color: rgba(107, 107, 107, 0.3); } - -.textarea, .input, #documenter .docs-sidebar form.docs-search > input { - box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.1); - max-width: 100%; - width: 100%; } - .textarea[readonly], .input[readonly], #documenter .docs-sidebar form.docs-search > input[readonly] { - box-shadow: none; } - .is-white.textarea, .is-white.input, #documenter .docs-sidebar form.docs-search > input.is-white { - border-color: white; } - .is-white.textarea:focus, .is-white.input:focus, #documenter .docs-sidebar form.docs-search > input.is-white:focus, .is-white.is-focused.textarea, .is-white.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-white.textarea:active, .is-white.input:active, #documenter .docs-sidebar form.docs-search > input.is-white:active, .is-white.is-active.textarea, .is-white.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { - box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } - .is-black.textarea, .is-black.input, #documenter .docs-sidebar form.docs-search > input.is-black { - border-color: #0a0a0a; } - .is-black.textarea:focus, .is-black.input:focus, #documenter .docs-sidebar form.docs-search > input.is-black:focus, .is-black.is-focused.textarea, .is-black.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-black.textarea:active, .is-black.input:active, #documenter .docs-sidebar form.docs-search > input.is-black:active, .is-black.is-active.textarea, .is-black.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { - box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } - .is-light.textarea, .is-light.input, #documenter .docs-sidebar form.docs-search > input.is-light { - border-color: whitesmoke; } - .is-light.textarea:focus, .is-light.input:focus, #documenter .docs-sidebar form.docs-search > input.is-light:focus, .is-light.is-focused.textarea, .is-light.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-light.textarea:active, .is-light.input:active, #documenter .docs-sidebar form.docs-search > input.is-light:active, .is-light.is-active.textarea, .is-light.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { - box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } - .is-dark.textarea, .content kbd.textarea, .is-dark.input, #documenter .docs-sidebar form.docs-search > input.is-dark, .content kbd.input { - border-color: #363636; } - .is-dark.textarea:focus, .content kbd.textarea:focus, .is-dark.input:focus, #documenter .docs-sidebar form.docs-search > input.is-dark:focus, .content kbd.input:focus, .is-dark.is-focused.textarea, .content kbd.is-focused.textarea, .is-dark.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .content kbd.is-focused.input, #documenter .docs-sidebar .content form.docs-search > input.is-focused, .is-dark.textarea:active, .content kbd.textarea:active, .is-dark.input:active, #documenter .docs-sidebar form.docs-search > input.is-dark:active, .content kbd.input:active, .is-dark.is-active.textarea, .content kbd.is-active.textarea, .is-dark.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active, .content kbd.is-active.input, #documenter .docs-sidebar .content form.docs-search > input.is-active { - box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } - .is-primary.textarea, .docstring > section > a.textarea.docs-sourcelink, .is-primary.input, #documenter .docs-sidebar form.docs-search > input.is-primary, .docstring > section > a.input.docs-sourcelink { - border-color: #4eb5de; } - .is-primary.textarea:focus, .docstring > section > a.textarea.docs-sourcelink:focus, .is-primary.input:focus, #documenter .docs-sidebar form.docs-search > input.is-primary:focus, .docstring > section > a.input.docs-sourcelink:focus, .is-primary.is-focused.textarea, .docstring > section > a.is-focused.textarea.docs-sourcelink, .is-primary.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .docstring > section > a.is-focused.input.docs-sourcelink, .is-primary.textarea:active, .docstring > section > a.textarea.docs-sourcelink:active, .is-primary.input:active, #documenter .docs-sidebar form.docs-search > input.is-primary:active, .docstring > section > a.input.docs-sourcelink:active, .is-primary.is-active.textarea, .docstring > section > a.is-active.textarea.docs-sourcelink, .is-primary.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active, .docstring > section > a.is-active.input.docs-sourcelink { - box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } - .is-link.textarea, .is-link.input, #documenter .docs-sidebar form.docs-search > input.is-link { - border-color: #2e63b8; } - .is-link.textarea:focus, .is-link.input:focus, #documenter .docs-sidebar form.docs-search > input.is-link:focus, .is-link.is-focused.textarea, .is-link.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-link.textarea:active, .is-link.input:active, #documenter .docs-sidebar form.docs-search > input.is-link:active, .is-link.is-active.textarea, .is-link.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { - box-shadow: 0 0 0 0.125em rgba(46, 99, 184, 0.25); } - .is-info.textarea, .is-info.input, #documenter .docs-sidebar form.docs-search > input.is-info { - border-color: #209cee; } - .is-info.textarea:focus, .is-info.input:focus, #documenter .docs-sidebar form.docs-search > input.is-info:focus, .is-info.is-focused.textarea, .is-info.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-info.textarea:active, .is-info.input:active, #documenter .docs-sidebar form.docs-search > input.is-info:active, .is-info.is-active.textarea, .is-info.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { - box-shadow: 0 0 0 0.125em rgba(32, 156, 238, 0.25); } - .is-success.textarea, .is-success.input, #documenter .docs-sidebar form.docs-search > input.is-success { - border-color: #22c35b; } - .is-success.textarea:focus, .is-success.input:focus, #documenter .docs-sidebar form.docs-search > input.is-success:focus, .is-success.is-focused.textarea, .is-success.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-success.textarea:active, .is-success.input:active, #documenter .docs-sidebar form.docs-search > input.is-success:active, .is-success.is-active.textarea, .is-success.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { - box-shadow: 0 0 0 0.125em rgba(34, 195, 91, 0.25); } - .is-warning.textarea, .is-warning.input, #documenter .docs-sidebar form.docs-search > input.is-warning { - border-color: #ffdd57; } - .is-warning.textarea:focus, .is-warning.input:focus, #documenter .docs-sidebar form.docs-search > input.is-warning:focus, .is-warning.is-focused.textarea, .is-warning.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-warning.textarea:active, .is-warning.input:active, #documenter .docs-sidebar form.docs-search > input.is-warning:active, .is-warning.is-active.textarea, .is-warning.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { - box-shadow: 0 0 0 0.125em rgba(255, 221, 87, 0.25); } - .is-danger.textarea, .is-danger.input, #documenter .docs-sidebar form.docs-search > input.is-danger { - border-color: #da0b00; } - .is-danger.textarea:focus, .is-danger.input:focus, #documenter .docs-sidebar form.docs-search > input.is-danger:focus, .is-danger.is-focused.textarea, .is-danger.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-danger.textarea:active, .is-danger.input:active, #documenter .docs-sidebar form.docs-search > input.is-danger:active, .is-danger.is-active.textarea, .is-danger.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active { - box-shadow: 0 0 0 0.125em rgba(218, 11, 0, 0.25); } - .is-small.textarea, .is-small.input, #documenter .docs-sidebar form.docs-search > input { - border-radius: 2px; - font-size: 0.75rem; } - .is-medium.textarea, .is-medium.input, #documenter .docs-sidebar form.docs-search > input.is-medium { - font-size: 1.25rem; } - .is-large.textarea, .is-large.input, #documenter .docs-sidebar form.docs-search > input.is-large { - font-size: 1.5rem; } - .is-fullwidth.textarea, .is-fullwidth.input, #documenter .docs-sidebar form.docs-search > input.is-fullwidth { - display: block; - width: 100%; } - .is-inline.textarea, .is-inline.input, #documenter .docs-sidebar form.docs-search > input.is-inline { - display: inline; - width: auto; } - -.input.is-rounded, #documenter .docs-sidebar form.docs-search > input { - border-radius: 290486px; - padding-left: 1em; - padding-right: 1em; } - -.input.is-static, #documenter .docs-sidebar form.docs-search > input.is-static { - background-color: transparent; - border-color: transparent; - box-shadow: none; - padding-left: 0; - padding-right: 0; } - -.textarea { - display: block; - max-width: 100%; - min-width: 100%; - padding: 0.625em; - resize: vertical; } - .textarea:not([rows]) { - max-height: 600px; - min-height: 120px; } - .textarea[rows] { - height: initial; } - .textarea.has-fixed-size { - resize: none; } - -.radio, .checkbox { - cursor: pointer; - display: inline-block; - line-height: 1.25; - position: relative; } - .radio input, .checkbox input { - cursor: pointer; } - .radio:hover, .checkbox:hover { - color: #363636; } - .radio[disabled], .checkbox[disabled], fieldset[disabled] .radio, fieldset[disabled] .checkbox { - color: #6b6b6b; - cursor: not-allowed; } - -.radio + .radio { - margin-left: 0.5em; } - -.select { - display: inline-block; - max-width: 100%; - position: relative; - vertical-align: top; } - .select:not(.is-multiple) { - height: 2.25em; } - .select:not(.is-multiple):not(.is-loading)::after { - border-color: #2e63b8; - right: 1.125em; - z-index: 4; } - .select.is-rounded select, #documenter .docs-sidebar form.docs-search > input.select select { - border-radius: 290486px; - padding-left: 1em; } - .select select { - cursor: pointer; - display: block; - font-size: 1em; - max-width: 100%; - outline: none; } - .select select::-ms-expand { - display: none; } - .select select[disabled]:hover, fieldset[disabled] .select select:hover { - border-color: whitesmoke; } - .select select:not([multiple]) { - padding-right: 2.5em; } - .select select[multiple] { - height: auto; - padding: 0; } - .select select[multiple] option { - padding: 0.5em 1em; } - .select:not(.is-multiple):not(.is-loading):hover::after { - border-color: #363636; } - .select.is-white:not(:hover)::after { - border-color: white; } - .select.is-white select { - border-color: white; } - .select.is-white select:hover, .select.is-white select.is-hovered { - border-color: #f2f2f2; } - .select.is-white select:focus, .select.is-white select.is-focused, .select.is-white select:active, .select.is-white select.is-active { - box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); } - .select.is-black:not(:hover)::after { - border-color: #0a0a0a; } - .select.is-black select { - border-color: #0a0a0a; } - .select.is-black select:hover, .select.is-black select.is-hovered { - border-color: black; } - .select.is-black select:focus, .select.is-black select.is-focused, .select.is-black select:active, .select.is-black select.is-active { - box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); } - .select.is-light:not(:hover)::after { - border-color: whitesmoke; } - .select.is-light select { - border-color: whitesmoke; } - .select.is-light select:hover, .select.is-light select.is-hovered { - border-color: #e8e8e8; } - .select.is-light select:focus, .select.is-light select.is-focused, .select.is-light select:active, .select.is-light select.is-active { - box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); } - .select.is-dark:not(:hover)::after, .content kbd.select:not(:hover)::after { - border-color: #363636; } - .select.is-dark select, .content kbd.select select { - border-color: #363636; } - .select.is-dark select:hover, .content kbd.select select:hover, .select.is-dark select.is-hovered, .content kbd.select select.is-hovered { - border-color: #292929; } - .select.is-dark select:focus, .content kbd.select select:focus, .select.is-dark select.is-focused, .content kbd.select select.is-focused, .select.is-dark select:active, .content kbd.select select:active, .select.is-dark select.is-active, .content kbd.select select.is-active { - box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); } - .select.is-primary:not(:hover)::after, .docstring > section > a.select.docs-sourcelink:not(:hover)::after { - border-color: #4eb5de; } - .select.is-primary select, .docstring > section > a.select.docs-sourcelink select { - border-color: #4eb5de; } - .select.is-primary select:hover, .docstring > section > a.select.docs-sourcelink select:hover, .select.is-primary select.is-hovered, .docstring > section > a.select.docs-sourcelink select.is-hovered { - border-color: #39acda; } - .select.is-primary select:focus, .docstring > section > a.select.docs-sourcelink select:focus, .select.is-primary select.is-focused, .docstring > section > a.select.docs-sourcelink select.is-focused, .select.is-primary select:active, .docstring > section > a.select.docs-sourcelink select:active, .select.is-primary select.is-active, .docstring > section > a.select.docs-sourcelink select.is-active { - box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); } - .select.is-link:not(:hover)::after { - border-color: #2e63b8; } - .select.is-link select { - border-color: #2e63b8; } - .select.is-link select:hover, .select.is-link select.is-hovered { - border-color: #2958a4; } - .select.is-link select:focus, .select.is-link select.is-focused, .select.is-link select:active, .select.is-link select.is-active { - box-shadow: 0 0 0 0.125em rgba(46, 99, 184, 0.25); } - .select.is-info:not(:hover)::after { - border-color: #209cee; } - .select.is-info select { - border-color: #209cee; } - .select.is-info select:hover, .select.is-info select.is-hovered { - border-color: #1190e3; } - .select.is-info select:focus, .select.is-info select.is-focused, .select.is-info select:active, .select.is-info select.is-active { - box-shadow: 0 0 0 0.125em rgba(32, 156, 238, 0.25); } - .select.is-success:not(:hover)::after { - border-color: #22c35b; } - .select.is-success select { - border-color: #22c35b; } - .select.is-success select:hover, .select.is-success select.is-hovered { - border-color: #1ead51; } - .select.is-success select:focus, .select.is-success select.is-focused, .select.is-success select:active, .select.is-success select.is-active { - box-shadow: 0 0 0 0.125em rgba(34, 195, 91, 0.25); } - .select.is-warning:not(:hover)::after { - border-color: #ffdd57; } - .select.is-warning select { - border-color: #ffdd57; } - .select.is-warning select:hover, .select.is-warning select.is-hovered { - border-color: #ffd83e; } - .select.is-warning select:focus, .select.is-warning select.is-focused, .select.is-warning select:active, .select.is-warning select.is-active { - box-shadow: 0 0 0 0.125em rgba(255, 221, 87, 0.25); } - .select.is-danger:not(:hover)::after { - border-color: #da0b00; } - .select.is-danger select { - border-color: #da0b00; } - .select.is-danger select:hover, .select.is-danger select.is-hovered { - border-color: #c10a00; } - .select.is-danger select:focus, .select.is-danger select.is-focused, .select.is-danger select:active, .select.is-danger select.is-active { - box-shadow: 0 0 0 0.125em rgba(218, 11, 0, 0.25); } - .select.is-small, #documenter .docs-sidebar form.docs-search > input.select { - border-radius: 2px; - font-size: 0.75rem; } - .select.is-medium { - font-size: 1.25rem; } - .select.is-large { - font-size: 1.5rem; } - .select.is-disabled::after { - border-color: #6b6b6b; } - .select.is-fullwidth { - width: 100%; } - .select.is-fullwidth select { - width: 100%; } - .select.is-loading::after { - margin-top: 0; - position: absolute; - right: 0.625em; - top: 0.625em; - transform: none; } - .select.is-loading.is-small:after, #documenter .docs-sidebar form.docs-search > input.is-loading:after { - font-size: 0.75rem; } - .select.is-loading.is-medium:after { - font-size: 1.25rem; } - .select.is-loading.is-large:after { - font-size: 1.5rem; } - -.file { - align-items: stretch; - display: flex; - justify-content: flex-start; - position: relative; } - .file.is-white .file-cta { - background-color: white; - border-color: transparent; - color: #0a0a0a; } - .file.is-white:hover .file-cta, .file.is-white.is-hovered .file-cta { - background-color: #f9f9f9; - border-color: transparent; - color: #0a0a0a; } - .file.is-white:focus .file-cta, .file.is-white.is-focused .file-cta { - border-color: transparent; - box-shadow: 0 0 0.5em rgba(255, 255, 255, 0.25); - color: #0a0a0a; } - .file.is-white:active .file-cta, .file.is-white.is-active .file-cta { - background-color: #f2f2f2; - border-color: transparent; - color: #0a0a0a; } - .file.is-black .file-cta { - background-color: #0a0a0a; - border-color: transparent; - color: white; } - .file.is-black:hover .file-cta, .file.is-black.is-hovered .file-cta { - background-color: #040404; - border-color: transparent; - color: white; } - .file.is-black:focus .file-cta, .file.is-black.is-focused .file-cta { - border-color: transparent; - box-shadow: 0 0 0.5em rgba(10, 10, 10, 0.25); - color: white; } - .file.is-black:active .file-cta, .file.is-black.is-active .file-cta { - background-color: black; - border-color: transparent; - color: white; } - .file.is-light .file-cta { - background-color: whitesmoke; - border-color: transparent; - color: #363636; } - .file.is-light:hover .file-cta, .file.is-light.is-hovered .file-cta { - background-color: #eeeeee; - border-color: transparent; - color: #363636; } - .file.is-light:focus .file-cta, .file.is-light.is-focused .file-cta { - border-color: transparent; - box-shadow: 0 0 0.5em rgba(245, 245, 245, 0.25); - color: #363636; } - .file.is-light:active .file-cta, .file.is-light.is-active .file-cta { - background-color: #e8e8e8; - border-color: transparent; - color: #363636; } - .file.is-dark .file-cta, .content kbd.file .file-cta { - background-color: #363636; - border-color: transparent; - color: whitesmoke; } - .file.is-dark:hover .file-cta, .content kbd.file:hover .file-cta, .file.is-dark.is-hovered .file-cta, .content kbd.file.is-hovered .file-cta { - background-color: #2f2f2f; - border-color: transparent; - color: whitesmoke; } - .file.is-dark:focus .file-cta, .content kbd.file:focus .file-cta, .file.is-dark.is-focused .file-cta, .content kbd.file.is-focused .file-cta { - border-color: transparent; - box-shadow: 0 0 0.5em rgba(54, 54, 54, 0.25); - color: whitesmoke; } - .file.is-dark:active .file-cta, .content kbd.file:active .file-cta, .file.is-dark.is-active .file-cta, .content kbd.file.is-active .file-cta { - background-color: #292929; - border-color: transparent; - color: whitesmoke; } - .file.is-primary .file-cta, .docstring > section > a.file.docs-sourcelink .file-cta { - background-color: #4eb5de; - border-color: transparent; - color: #fff; } - .file.is-primary:hover .file-cta, .docstring > section > a.file.docs-sourcelink:hover .file-cta, .file.is-primary.is-hovered .file-cta, .docstring > section > a.file.is-hovered.docs-sourcelink .file-cta { - background-color: #43b1dc; - border-color: transparent; - color: #fff; } - .file.is-primary:focus .file-cta, .docstring > section > a.file.docs-sourcelink:focus .file-cta, .file.is-primary.is-focused .file-cta, .docstring > section > a.file.is-focused.docs-sourcelink .file-cta { - border-color: transparent; - box-shadow: 0 0 0.5em rgba(78, 181, 222, 0.25); - color: #fff; } - .file.is-primary:active .file-cta, .docstring > section > a.file.docs-sourcelink:active .file-cta, .file.is-primary.is-active .file-cta, .docstring > section > a.file.is-active.docs-sourcelink .file-cta { - background-color: #39acda; - border-color: transparent; - color: #fff; } - .file.is-link .file-cta { - background-color: #2e63b8; - border-color: transparent; - color: #fff; } - .file.is-link:hover .file-cta, .file.is-link.is-hovered .file-cta { - background-color: #2b5eae; - border-color: transparent; - color: #fff; } - .file.is-link:focus .file-cta, .file.is-link.is-focused .file-cta { - border-color: transparent; - box-shadow: 0 0 0.5em rgba(46, 99, 184, 0.25); - color: #fff; } - .file.is-link:active .file-cta, .file.is-link.is-active .file-cta { - background-color: #2958a4; - border-color: transparent; - color: #fff; } - .file.is-info .file-cta { - background-color: #209cee; - border-color: transparent; - color: #fff; } - .file.is-info:hover .file-cta, .file.is-info.is-hovered .file-cta { - background-color: #1497ed; - border-color: transparent; - color: #fff; } - .file.is-info:focus .file-cta, .file.is-info.is-focused .file-cta { - border-color: transparent; - box-shadow: 0 0 0.5em rgba(32, 156, 238, 0.25); - color: #fff; } - .file.is-info:active .file-cta, .file.is-info.is-active .file-cta { - background-color: #1190e3; - border-color: transparent; - color: #fff; } - .file.is-success .file-cta { - background-color: #22c35b; - border-color: transparent; - color: #fff; } - .file.is-success:hover .file-cta, .file.is-success.is-hovered .file-cta { - background-color: #20b856; - border-color: transparent; - color: #fff; } - .file.is-success:focus .file-cta, .file.is-success.is-focused .file-cta { - border-color: transparent; - box-shadow: 0 0 0.5em rgba(34, 195, 91, 0.25); - color: #fff; } - .file.is-success:active .file-cta, .file.is-success.is-active .file-cta { - background-color: #1ead51; - border-color: transparent; - color: #fff; } - .file.is-warning .file-cta { - background-color: #ffdd57; - border-color: transparent; - color: rgba(0, 0, 0, 0.7); } - .file.is-warning:hover .file-cta, .file.is-warning.is-hovered .file-cta { - background-color: #ffda4a; - border-color: transparent; - color: rgba(0, 0, 0, 0.7); } - .file.is-warning:focus .file-cta, .file.is-warning.is-focused .file-cta { - border-color: transparent; - box-shadow: 0 0 0.5em rgba(255, 221, 87, 0.25); - color: rgba(0, 0, 0, 0.7); } - .file.is-warning:active .file-cta, .file.is-warning.is-active .file-cta { - background-color: #ffd83e; - border-color: transparent; - color: rgba(0, 0, 0, 0.7); } - .file.is-danger .file-cta { - background-color: #da0b00; - border-color: transparent; - color: #fff; } - .file.is-danger:hover .file-cta, .file.is-danger.is-hovered .file-cta { - background-color: #cd0a00; - border-color: transparent; - color: #fff; } - .file.is-danger:focus .file-cta, .file.is-danger.is-focused .file-cta { - border-color: transparent; - box-shadow: 0 0 0.5em rgba(218, 11, 0, 0.25); - color: #fff; } - .file.is-danger:active .file-cta, .file.is-danger.is-active .file-cta { - background-color: #c10a00; - border-color: transparent; - color: #fff; } - .file.is-small, #documenter .docs-sidebar form.docs-search > input.file { - font-size: 0.75rem; } - .file.is-medium { - font-size: 1.25rem; } - .file.is-medium .file-icon .fa { - font-size: 21px; } - .file.is-large { - font-size: 1.5rem; } - .file.is-large .file-icon .fa { - font-size: 28px; } - .file.has-name .file-cta { - border-bottom-right-radius: 0; - border-top-right-radius: 0; } - .file.has-name .file-name { - border-bottom-left-radius: 0; - border-top-left-radius: 0; } - .file.has-name.is-empty .file-cta { - border-radius: 4px; } - .file.has-name.is-empty .file-name { - display: none; } - .file.is-boxed .file-label { - flex-direction: column; } - .file.is-boxed .file-cta { - flex-direction: column; - height: auto; - padding: 1em 3em; } - .file.is-boxed .file-name { - border-width: 0 1px 1px; } - .file.is-boxed .file-icon { - height: 1.5em; - width: 1.5em; } - .file.is-boxed .file-icon .fa { - font-size: 21px; } - .file.is-boxed.is-small .file-icon .fa, #documenter .docs-sidebar form.docs-search > input.is-boxed .file-icon .fa { - font-size: 14px; } - .file.is-boxed.is-medium .file-icon .fa { - font-size: 28px; } - .file.is-boxed.is-large .file-icon .fa { - font-size: 35px; } - .file.is-boxed.has-name .file-cta { - border-radius: 4px 4px 0 0; } - .file.is-boxed.has-name .file-name { - border-radius: 0 0 4px 4px; - border-width: 0 1px 1px; } - .file.is-centered { - justify-content: center; } - .file.is-fullwidth .file-label { - width: 100%; } - .file.is-fullwidth .file-name { - flex-grow: 1; - max-width: none; } - .file.is-right { - justify-content: flex-end; } - .file.is-right .file-cta { - border-radius: 0 4px 4px 0; } - .file.is-right .file-name { - border-radius: 4px 0 0 4px; - border-width: 1px 0 1px 1px; - order: -1; } - -.file-label { - align-items: stretch; - display: flex; - cursor: pointer; - justify-content: flex-start; - overflow: hidden; - position: relative; } - .file-label:hover .file-cta { - background-color: #eeeeee; - color: #363636; } - .file-label:hover .file-name { - border-color: #d5d5d5; } - .file-label:active .file-cta { - background-color: #e8e8e8; - color: #363636; } - .file-label:active .file-name { - border-color: #cfcfcf; } - -.file-input { - height: 100%; - left: 0; - opacity: 0; - outline: none; - position: absolute; - top: 0; - width: 100%; } - -.file-cta, -.file-name { - border-color: #dbdbdb; - border-radius: 4px; - font-size: 1em; - padding-left: 1em; - padding-right: 1em; - white-space: nowrap; } - -.file-cta { - background-color: whitesmoke; - color: #4a4a4a; } - -.file-name { - border-color: #dbdbdb; - border-style: solid; - border-width: 1px 1px 1px 0; - display: block; - max-width: 16em; - overflow: hidden; - text-align: left; - text-overflow: ellipsis; } - -.file-icon { - align-items: center; - display: flex; - height: 1em; - justify-content: center; - margin-right: 0.5em; - width: 1em; } - .file-icon .fa { - font-size: 14px; } - -.label { - color: #363636; - display: block; - font-size: 1rem; - font-weight: 700; } - .label:not(:last-child) { - margin-bottom: 0.5em; } - .label.is-small, #documenter .docs-sidebar form.docs-search > input.label { - font-size: 0.75rem; } - .label.is-medium { - font-size: 1.25rem; } - .label.is-large { - font-size: 1.5rem; } - -.help { - display: block; - font-size: 0.75rem; - margin-top: 0.25rem; } - .help.is-white { - color: white; } - .help.is-black { - color: #0a0a0a; } - .help.is-light { - color: whitesmoke; } - .help.is-dark, .content kbd.help { - color: #363636; } - .help.is-primary, .docstring > section > a.help.docs-sourcelink { - color: #4eb5de; } - .help.is-link { - color: #2e63b8; } - .help.is-info { - color: #209cee; } - .help.is-success { - color: #22c35b; } - .help.is-warning { - color: #ffdd57; } - .help.is-danger { - color: #da0b00; } - -.field:not(:last-child) { - margin-bottom: 0.75rem; } - -.field.has-addons { - display: flex; - justify-content: flex-start; } - .field.has-addons .control:not(:last-child) { - margin-right: -1px; } - .field.has-addons .control:not(:first-child):not(:last-child) .button, - .field.has-addons .control:not(:first-child):not(:last-child) .input, - .field.has-addons .control:not(:first-child):not(:last-child) #documenter .docs-sidebar form.docs-search > input, - #documenter .docs-sidebar .field.has-addons .control:not(:first-child):not(:last-child) form.docs-search > input, - .field.has-addons .control:not(:first-child):not(:last-child) .select select { - border-radius: 0; } - .field.has-addons .control:first-child:not(:only-child) .button, - .field.has-addons .control:first-child:not(:only-child) .input, - .field.has-addons .control:first-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input, - #documenter .docs-sidebar .field.has-addons .control:first-child:not(:only-child) form.docs-search > input, - .field.has-addons .control:first-child:not(:only-child) .select select { - border-bottom-right-radius: 0; - border-top-right-radius: 0; } - .field.has-addons .control:last-child:not(:only-child) .button, - .field.has-addons .control:last-child:not(:only-child) .input, - .field.has-addons .control:last-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input, - #documenter .docs-sidebar .field.has-addons .control:last-child:not(:only-child) form.docs-search > input, - .field.has-addons .control:last-child:not(:only-child) .select select { - border-bottom-left-radius: 0; - border-top-left-radius: 0; } - .field.has-addons .control .button:not([disabled]):hover, .field.has-addons .control .button.is-hovered:not([disabled]), - .field.has-addons .control .input:not([disabled]):hover, - .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):hover, - #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):hover, - .field.has-addons .control .input.is-hovered:not([disabled]), - .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-hovered:not([disabled]), - #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-hovered:not([disabled]), - .field.has-addons .control .select select:not([disabled]):hover, - .field.has-addons .control .select select.is-hovered:not([disabled]) { - z-index: 2; } - .field.has-addons .control .button:not([disabled]):focus, .field.has-addons .control .button.is-focused:not([disabled]), .field.has-addons .control .button:not([disabled]):active, .field.has-addons .control .button.is-active:not([disabled]), - .field.has-addons .control .input:not([disabled]):focus, - .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus, - #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus, - .field.has-addons .control .input.is-focused:not([disabled]), - .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-focused:not([disabled]), - #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-focused:not([disabled]), - .field.has-addons .control .input:not([disabled]):active, - .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active, - #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active, - .field.has-addons .control .input.is-active:not([disabled]), - .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-active:not([disabled]), - #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-active:not([disabled]), - .field.has-addons .control .select select:not([disabled]):focus, - .field.has-addons .control .select select.is-focused:not([disabled]), - .field.has-addons .control .select select:not([disabled]):active, - .field.has-addons .control .select select.is-active:not([disabled]) { - z-index: 3; } - .field.has-addons .control .button:not([disabled]):focus:hover, .field.has-addons .control .button.is-focused:not([disabled]):hover, .field.has-addons .control .button:not([disabled]):active:hover, .field.has-addons .control .button.is-active:not([disabled]):hover, - .field.has-addons .control .input:not([disabled]):focus:hover, - .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus:hover, - #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus:hover, - .field.has-addons .control .input.is-focused:not([disabled]):hover, - .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-focused:not([disabled]):hover, - #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-focused:not([disabled]):hover, - .field.has-addons .control .input:not([disabled]):active:hover, - .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active:hover, - #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active:hover, - .field.has-addons .control .input.is-active:not([disabled]):hover, - .field.has-addons .control #documenter .docs-sidebar form.docs-search > input.is-active:not([disabled]):hover, - #documenter .docs-sidebar .field.has-addons .control form.docs-search > input.is-active:not([disabled]):hover, - .field.has-addons .control .select select:not([disabled]):focus:hover, - .field.has-addons .control .select select.is-focused:not([disabled]):hover, - .field.has-addons .control .select select:not([disabled]):active:hover, - .field.has-addons .control .select select.is-active:not([disabled]):hover { - z-index: 4; } - .field.has-addons .control.is-expanded { - flex-grow: 1; - flex-shrink: 1; } - .field.has-addons.has-addons-centered { - justify-content: center; } - .field.has-addons.has-addons-right { - justify-content: flex-end; } - .field.has-addons.has-addons-fullwidth .control { - flex-grow: 1; - flex-shrink: 0; } - -.field.is-grouped { - display: flex; - justify-content: flex-start; } - .field.is-grouped > .control { - flex-shrink: 0; } - .field.is-grouped > .control:not(:last-child) { - margin-bottom: 0; - margin-right: 0.75rem; } - .field.is-grouped > .control.is-expanded { - flex-grow: 1; - flex-shrink: 1; } - .field.is-grouped.is-grouped-centered { - justify-content: center; } - .field.is-grouped.is-grouped-right { - justify-content: flex-end; } - .field.is-grouped.is-grouped-multiline { - flex-wrap: wrap; } - .field.is-grouped.is-grouped-multiline > .control:last-child, .field.is-grouped.is-grouped-multiline > .control:not(:last-child) { - margin-bottom: 0.75rem; } - .field.is-grouped.is-grouped-multiline:last-child { - margin-bottom: -0.75rem; } - .field.is-grouped.is-grouped-multiline:not(:last-child) { - margin-bottom: 0; } - -@media screen and (min-width: 769px), print { - .field.is-horizontal { - display: flex; } } - -.field-label .label { - font-size: inherit; } - -@media screen and (max-width: 768px) { - .field-label { - margin-bottom: 0.5rem; } } - -@media screen and (min-width: 769px), print { - .field-label { - flex-basis: 0; - flex-grow: 1; - flex-shrink: 0; - margin-right: 1.5rem; - text-align: right; } - .field-label.is-small, #documenter .docs-sidebar form.docs-search > input.field-label { - font-size: 0.75rem; - padding-top: 0.375em; } - .field-label.is-normal { - padding-top: 0.375em; } - .field-label.is-medium { - font-size: 1.25rem; - padding-top: 0.375em; } - .field-label.is-large { - font-size: 1.5rem; - padding-top: 0.375em; } } - -.field-body .field .field { - margin-bottom: 0; } - -@media screen and (min-width: 769px), print { - .field-body { - display: flex; - flex-basis: 0; - flex-grow: 5; - flex-shrink: 1; } - .field-body .field { - margin-bottom: 0; } - .field-body > .field { - flex-shrink: 1; } - .field-body > .field:not(.is-narrow) { - flex-grow: 1; } - .field-body > .field:not(:last-child) { - margin-right: 0.75rem; } } - -.control { - box-sizing: border-box; - clear: both; - font-size: 1rem; - position: relative; - text-align: left; } - .control.has-icons-left .input:focus ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input:focus ~ .icon, - .control.has-icons-left .select:focus ~ .icon, .control.has-icons-right .input:focus ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input:focus ~ .icon, - .control.has-icons-right .select:focus ~ .icon { - color: #6b6b6b; } - .control.has-icons-left .input.is-small ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input ~ .icon, - .control.has-icons-left .select.is-small ~ .icon, .control.has-icons-right .input.is-small ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input ~ .icon, - .control.has-icons-right .select.is-small ~ .icon { - font-size: 0.75rem; } - .control.has-icons-left .input.is-medium ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-medium ~ .icon, - .control.has-icons-left .select.is-medium ~ .icon, .control.has-icons-right .input.is-medium ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-medium ~ .icon, - .control.has-icons-right .select.is-medium ~ .icon { - font-size: 1.25rem; } - .control.has-icons-left .input.is-large ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-large ~ .icon, - .control.has-icons-left .select.is-large ~ .icon, .control.has-icons-right .input.is-large ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-large ~ .icon, - .control.has-icons-right .select.is-large ~ .icon { - font-size: 1.5rem; } - .control.has-icons-left .icon, .control.has-icons-right .icon { - color: #dbdbdb; - height: 2.25em; - pointer-events: none; - position: absolute; - top: 0; - width: 2.25em; - z-index: 4; } - .control.has-icons-left .input, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input, - .control.has-icons-left .select select { - padding-left: 2.25em; } - .control.has-icons-left .icon.is-left { - left: 0; } - .control.has-icons-right .input, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input, - .control.has-icons-right .select select { - padding-right: 2.25em; } - .control.has-icons-right .icon.is-right { - right: 0; } - .control.is-loading::after { - position: absolute !important; - right: 0.625em; - top: 0.625em; - z-index: 4; } - .control.is-loading.is-small:after, #documenter .docs-sidebar form.docs-search > input.is-loading:after { - font-size: 0.75rem; } - .control.is-loading.is-medium:after { - font-size: 1.25rem; } - .control.is-loading.is-large:after { - font-size: 1.5rem; } - -.breadcrumb { - font-size: 1rem; - white-space: nowrap; } - .breadcrumb a { - align-items: center; - color: #2e63b8; - display: flex; - justify-content: center; - padding: 0 0.75em; } - .breadcrumb a:hover { - color: #363636; } - .breadcrumb li { - align-items: center; - display: flex; } - .breadcrumb li:first-child a { - padding-left: 0; } - .breadcrumb li.is-active a { - color: #222222; - cursor: default; - pointer-events: none; } - .breadcrumb li + li::before { - color: #b5b5b5; - content: "\0002f"; } - .breadcrumb ul, - .breadcrumb ol { - align-items: flex-start; - display: flex; - flex-wrap: wrap; - justify-content: flex-start; } - .breadcrumb .icon:first-child { - margin-right: 0.5em; } - .breadcrumb .icon:last-child { - margin-left: 0.5em; } - .breadcrumb.is-centered ol, - .breadcrumb.is-centered ul { - justify-content: center; } - .breadcrumb.is-right ol, - .breadcrumb.is-right ul { - justify-content: flex-end; } - .breadcrumb.is-small, #documenter .docs-sidebar form.docs-search > input.breadcrumb { - font-size: 0.75rem; } - .breadcrumb.is-medium { - font-size: 1.25rem; } - .breadcrumb.is-large { - font-size: 1.5rem; } - .breadcrumb.has-arrow-separator li + li::before { - content: "\02192"; } - .breadcrumb.has-bullet-separator li + li::before { - content: "\02022"; } - .breadcrumb.has-dot-separator li + li::before { - content: "\000b7"; } - .breadcrumb.has-succeeds-separator li + li::before { - content: "\0227B"; } - -.card { - background-color: white; - box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); - color: #222222; - max-width: 100%; - position: relative; } - -.card-header { - background-color: transparent; - align-items: stretch; - box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1); - display: flex; } - -.card-header-title { - align-items: center; - color: #222222; - display: flex; - flex-grow: 1; - font-weight: 700; - padding: 0.75rem; } - .card-header-title.is-centered { - justify-content: center; } - -.card-header-icon { - align-items: center; - cursor: pointer; - display: flex; - justify-content: center; - padding: 0.75rem; } - -.card-image { - display: block; - position: relative; } - -.card-content { - background-color: transparent; - padding: 1.5rem; } - -.card-footer { - background-color: transparent; - border-top: 1px solid #dbdbdb; - align-items: stretch; - display: flex; } - -.card-footer-item { - align-items: center; - display: flex; - flex-basis: 0; - flex-grow: 1; - flex-shrink: 0; - justify-content: center; - padding: 0.75rem; } - .card-footer-item:not(:last-child) { - border-right: 1px solid #dbdbdb; } - -.card .media:not(:last-child) { - margin-bottom: 1.5rem; } - -.dropdown { - display: inline-flex; - position: relative; - vertical-align: top; } - .dropdown.is-active .dropdown-menu, .dropdown.is-hoverable:hover .dropdown-menu { - display: block; } - .dropdown.is-right .dropdown-menu { - left: auto; - right: 0; } - .dropdown.is-up .dropdown-menu { - bottom: 100%; - padding-bottom: 4px; - padding-top: initial; - top: auto; } - -.dropdown-menu { - display: none; - left: 0; - min-width: 12rem; - padding-top: 4px; - position: absolute; - top: 100%; - z-index: 20; } - -.dropdown-content { - background-color: white; - border-radius: 4px; - box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); - padding-bottom: 0.5rem; - padding-top: 0.5rem; } - -.dropdown-item { - color: #4a4a4a; - display: block; - font-size: 0.875rem; - line-height: 1.5; - padding: 0.375rem 1rem; - position: relative; } - -a.dropdown-item, -button.dropdown-item { - padding-right: 3rem; - text-align: left; - white-space: nowrap; - width: 100%; } - a.dropdown-item:hover, - button.dropdown-item:hover { - background-color: whitesmoke; - color: #0a0a0a; } - a.dropdown-item.is-active, - button.dropdown-item.is-active { - background-color: #2e63b8; - color: #fff; } - -.dropdown-divider { - background-color: #dbdbdb; - border: none; - display: block; - height: 1px; - margin: 0.5rem 0; } - -.level { - align-items: center; - justify-content: space-between; } - .level code { - border-radius: 4px; } - .level img { - display: inline-block; - vertical-align: top; } - .level.is-mobile { - display: flex; } - .level.is-mobile .level-left, - .level.is-mobile .level-right { - display: flex; } - .level.is-mobile .level-left + .level-right { - margin-top: 0; } - .level.is-mobile .level-item:not(:last-child) { - margin-bottom: 0; - margin-right: 0.75rem; } - .level.is-mobile .level-item:not(.is-narrow) { - flex-grow: 1; } - @media screen and (min-width: 769px), print { - .level { - display: flex; } - .level > .level-item:not(.is-narrow) { - flex-grow: 1; } } -.level-item { - align-items: center; - display: flex; - flex-basis: auto; - flex-grow: 0; - flex-shrink: 0; - justify-content: center; } - .level-item .title, - .level-item .subtitle { - margin-bottom: 0; } - @media screen and (max-width: 768px) { - .level-item:not(:last-child) { - margin-bottom: 0.75rem; } } -.level-left, -.level-right { - flex-basis: auto; - flex-grow: 0; - flex-shrink: 0; } - .level-left .level-item.is-flexible, - .level-right .level-item.is-flexible { - flex-grow: 1; } - @media screen and (min-width: 769px), print { - .level-left .level-item:not(:last-child), - .level-right .level-item:not(:last-child) { - margin-right: 0.75rem; } } -.level-left { - align-items: center; - justify-content: flex-start; } - @media screen and (max-width: 768px) { - .level-left + .level-right { - margin-top: 1.5rem; } } - @media screen and (min-width: 769px), print { - .level-left { - display: flex; } } -.level-right { - align-items: center; - justify-content: flex-end; } - @media screen and (min-width: 769px), print { - .level-right { - display: flex; } } -.list { - background-color: white; - border-radius: 4px; - box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); } - -.list-item { - display: block; - padding: 0.5em 1em; } - .list-item:not(a) { - color: #222222; } - .list-item:first-child { - border-top-left-radius: 4px; - border-top-right-radius: 4px; } - .list-item:last-child { - border-bottom-left-radius: 4px; - border-bottom-right-radius: 4px; } - .list-item:not(:last-child) { - border-bottom: 1px solid #dbdbdb; } - .list-item.is-active { - background-color: #2e63b8; - color: #fff; } - -a.list-item { - background-color: whitesmoke; - cursor: pointer; } - -.media { - align-items: flex-start; - display: flex; - text-align: left; } - .media .content:not(:last-child) { - margin-bottom: 0.75rem; } - .media .media { - border-top: 1px solid rgba(219, 219, 219, 0.5); - display: flex; - padding-top: 0.75rem; } - .media .media .content:not(:last-child), - .media .media .control:not(:last-child) { - margin-bottom: 0.5rem; } - .media .media .media { - padding-top: 0.5rem; } - .media .media .media + .media { - margin-top: 0.5rem; } - .media + .media { - border-top: 1px solid rgba(219, 219, 219, 0.5); - margin-top: 1rem; - padding-top: 1rem; } - .media.is-large + .media { - margin-top: 1.5rem; - padding-top: 1.5rem; } - -.media-left, -.media-right { - flex-basis: auto; - flex-grow: 0; - flex-shrink: 0; } - -.media-left { - margin-right: 1rem; } - -.media-right { - margin-left: 1rem; } - -.media-content { - flex-basis: auto; - flex-grow: 1; - flex-shrink: 1; - text-align: left; } - -@media screen and (max-width: 768px) { - .media-content { - overflow-x: auto; } } - -.menu { - font-size: 1rem; } - .menu.is-small, #documenter .docs-sidebar form.docs-search > input.menu { - font-size: 0.75rem; } - .menu.is-medium { - font-size: 1.25rem; } - .menu.is-large { - font-size: 1.5rem; } - -.menu-list { - line-height: 1.25; } - .menu-list a { - border-radius: 2px; - color: #222222; - display: block; - padding: 0.5em 0.75em; } - .menu-list a:hover { - background-color: whitesmoke; - color: #222222; } - .menu-list a.is-active { - background-color: #2e63b8; - color: #fff; } - .menu-list li ul { - border-left: 1px solid #dbdbdb; - margin: 0.75em; - padding-left: 0.75em; } - -.menu-label { - color: #6b6b6b; - font-size: 0.75em; - letter-spacing: 0.1em; - text-transform: uppercase; } - .menu-label:not(:first-child) { - margin-top: 1em; } - .menu-label:not(:last-child) { - margin-bottom: 1em; } - -.message { - background-color: whitesmoke; - border-radius: 4px; - font-size: 1rem; } - .message strong { - color: currentColor; } - .message a:not(.button):not(.tag):not(.dropdown-item) { - color: currentColor; - text-decoration: underline; } - .message.is-small, #documenter .docs-sidebar form.docs-search > input.message { - font-size: 0.75rem; } - .message.is-medium { - font-size: 1.25rem; } - .message.is-large { - font-size: 1.5rem; } - .message.is-white { - background-color: white; } - .message.is-white .message-header { - background-color: white; - color: #0a0a0a; } - .message.is-white .message-body { - border-color: white; - color: #4d4d4d; } - .message.is-black { - background-color: #fafafa; } - .message.is-black .message-header { - background-color: #0a0a0a; - color: white; } - .message.is-black .message-body { - border-color: #0a0a0a; - color: #090909; } - .message.is-light { - background-color: #fafafa; } - .message.is-light .message-header { - background-color: whitesmoke; - color: #363636; } - .message.is-light .message-body { - border-color: whitesmoke; - color: #505050; } - .message.is-dark, .content kbd.message { - background-color: #fafafa; } - .message.is-dark .message-header, .content kbd.message .message-header { - background-color: #363636; - color: whitesmoke; } - .message.is-dark .message-body, .content kbd.message .message-body { - border-color: #363636; - color: #2a2a2a; } - .message.is-primary, .docstring > section > a.message.docs-sourcelink { - background-color: #f6fbfd; } - .message.is-primary .message-header, .docstring > section > a.message.docs-sourcelink .message-header { - background-color: #4eb5de; - color: #fff; } - .message.is-primary .message-body, .docstring > section > a.message.docs-sourcelink .message-body { - border-color: #4eb5de; - color: #1f556a; } - .message.is-link { - background-color: #f7f9fd; } - .message.is-link .message-header { - background-color: #2e63b8; - color: #fff; } - .message.is-link .message-body { - border-color: #2e63b8; - color: #264981; } - .message.is-info { - background-color: #f6fbfe; } - .message.is-info .message-header { - background-color: #209cee; - color: #fff; } - .message.is-info .message-body { - border-color: #209cee; - color: #12537d; } - .message.is-success { - background-color: #f6fdf9; } - .message.is-success .message-header { - background-color: #22c35b; - color: #fff; } - .message.is-success .message-body { - border-color: #22c35b; - color: #0f361d; } - .message.is-warning { - background-color: #fffdf5; } - .message.is-warning .message-header { - background-color: #ffdd57; - color: rgba(0, 0, 0, 0.7); } - .message.is-warning .message-body { - border-color: #ffdd57; - color: #3c3108; } - .message.is-danger { - background-color: #fff5f5; } - .message.is-danger .message-header { - background-color: #da0b00; - color: #fff; } - .message.is-danger .message-body { - border-color: #da0b00; - color: #9b0c04; } - -.message-header { - align-items: center; - background-color: #222222; - border-radius: 4px 4px 0 0; - color: #fff; - display: flex; - font-weight: 700; - justify-content: space-between; - line-height: 1.25; - padding: 0.75em 1em; - position: relative; } - .message-header .delete { - flex-grow: 0; - flex-shrink: 0; - margin-left: 0.75em; } - .message-header + .message-body { - border-width: 0; - border-top-left-radius: 0; - border-top-right-radius: 0; } - -.message-body { - border-color: #dbdbdb; - border-radius: 4px; - border-style: solid; - border-width: 0 0 0 4px; - color: #222222; - padding: 1.25em 1.5em; } - .message-body code, - .message-body pre { - background-color: white; } - .message-body pre code { - background-color: transparent; } - -.modal { - align-items: center; - display: none; - flex-direction: column; - justify-content: center; - overflow: hidden; - position: fixed; - z-index: 40; } - .modal.is-active { - display: flex; } - -.modal-background { - background-color: rgba(10, 10, 10, 0.86); } - -.modal-content, -.modal-card { - margin: 0 20px; - max-height: calc(100vh - 160px); - overflow: auto; - position: relative; - width: 100%; } - @media screen and (min-width: 769px), print { - .modal-content, - .modal-card { - margin: 0 auto; - max-height: calc(100vh - 40px); - width: 640px; } } -.modal-close { - background: none; - height: 40px; - position: fixed; - right: 20px; - top: 20px; - width: 40px; } - -.modal-card { - display: flex; - flex-direction: column; - max-height: calc(100vh - 40px); - overflow: hidden; - -ms-overflow-y: visible; } - -.modal-card-head, -.modal-card-foot { - align-items: center; - background-color: whitesmoke; - display: flex; - flex-shrink: 0; - justify-content: flex-start; - padding: 20px; - position: relative; } - -.modal-card-head { - border-bottom: 1px solid #dbdbdb; - border-top-left-radius: 6px; - border-top-right-radius: 6px; } - -.modal-card-title { - color: #222222; - flex-grow: 1; - flex-shrink: 0; - font-size: 1.5rem; - line-height: 1; } - -.modal-card-foot { - border-bottom-left-radius: 6px; - border-bottom-right-radius: 6px; - border-top: 1px solid #dbdbdb; } - .modal-card-foot .button:not(:last-child) { - margin-right: 0.5em; } - -.modal-card-body { - -webkit-overflow-scrolling: touch; - background-color: white; - flex-grow: 1; - flex-shrink: 1; - overflow: auto; - padding: 20px; } - -.navbar { - background-color: white; - min-height: 3.25rem; - position: relative; - z-index: 30; } - .navbar.is-white { - background-color: white; - color: #0a0a0a; } - .navbar.is-white .navbar-brand > .navbar-item, - .navbar.is-white .navbar-brand .navbar-link { - color: #0a0a0a; } - .navbar.is-white .navbar-brand > a.navbar-item:focus, .navbar.is-white .navbar-brand > a.navbar-item:hover, .navbar.is-white .navbar-brand > a.navbar-item.is-active, - .navbar.is-white .navbar-brand .navbar-link:focus, - .navbar.is-white .navbar-brand .navbar-link:hover, - .navbar.is-white .navbar-brand .navbar-link.is-active { - background-color: #f2f2f2; - color: #0a0a0a; } - .navbar.is-white .navbar-brand .navbar-link::after { - border-color: #0a0a0a; } - .navbar.is-white .navbar-burger { - color: #0a0a0a; } - @media screen and (min-width: 1056px) { - .navbar.is-white .navbar-start > .navbar-item, - .navbar.is-white .navbar-start .navbar-link, - .navbar.is-white .navbar-end > .navbar-item, - .navbar.is-white .navbar-end .navbar-link { - color: #0a0a0a; } - .navbar.is-white .navbar-start > a.navbar-item:focus, .navbar.is-white .navbar-start > a.navbar-item:hover, .navbar.is-white .navbar-start > a.navbar-item.is-active, - .navbar.is-white .navbar-start .navbar-link:focus, - .navbar.is-white .navbar-start .navbar-link:hover, - .navbar.is-white .navbar-start .navbar-link.is-active, - .navbar.is-white .navbar-end > a.navbar-item:focus, - .navbar.is-white .navbar-end > a.navbar-item:hover, - .navbar.is-white .navbar-end > a.navbar-item.is-active, - .navbar.is-white .navbar-end .navbar-link:focus, - .navbar.is-white .navbar-end .navbar-link:hover, - .navbar.is-white .navbar-end .navbar-link.is-active { - background-color: #f2f2f2; - color: #0a0a0a; } - .navbar.is-white .navbar-start .navbar-link::after, - .navbar.is-white .navbar-end .navbar-link::after { - border-color: #0a0a0a; } - .navbar.is-white .navbar-item.has-dropdown:focus .navbar-link, - .navbar.is-white .navbar-item.has-dropdown:hover .navbar-link, - .navbar.is-white .navbar-item.has-dropdown.is-active .navbar-link { - background-color: #f2f2f2; - color: #0a0a0a; } - .navbar.is-white .navbar-dropdown a.navbar-item.is-active { - background-color: white; - color: #0a0a0a; } } - .navbar.is-black { - background-color: #0a0a0a; - color: white; } - .navbar.is-black .navbar-brand > .navbar-item, - .navbar.is-black .navbar-brand .navbar-link { - color: white; } - .navbar.is-black .navbar-brand > a.navbar-item:focus, .navbar.is-black .navbar-brand > a.navbar-item:hover, .navbar.is-black .navbar-brand > a.navbar-item.is-active, - .navbar.is-black .navbar-brand .navbar-link:focus, - .navbar.is-black .navbar-brand .navbar-link:hover, - .navbar.is-black .navbar-brand .navbar-link.is-active { - background-color: black; - color: white; } - .navbar.is-black .navbar-brand .navbar-link::after { - border-color: white; } - .navbar.is-black .navbar-burger { - color: white; } - @media screen and (min-width: 1056px) { - .navbar.is-black .navbar-start > .navbar-item, - .navbar.is-black .navbar-start .navbar-link, - .navbar.is-black .navbar-end > .navbar-item, - .navbar.is-black .navbar-end .navbar-link { - color: white; } - .navbar.is-black .navbar-start > a.navbar-item:focus, .navbar.is-black .navbar-start > a.navbar-item:hover, .navbar.is-black .navbar-start > a.navbar-item.is-active, - .navbar.is-black .navbar-start .navbar-link:focus, - .navbar.is-black .navbar-start .navbar-link:hover, - .navbar.is-black .navbar-start .navbar-link.is-active, - .navbar.is-black .navbar-end > a.navbar-item:focus, - .navbar.is-black .navbar-end > a.navbar-item:hover, - .navbar.is-black .navbar-end > a.navbar-item.is-active, - .navbar.is-black .navbar-end .navbar-link:focus, - .navbar.is-black .navbar-end .navbar-link:hover, - .navbar.is-black .navbar-end .navbar-link.is-active { - background-color: black; - color: white; } - .navbar.is-black .navbar-start .navbar-link::after, - .navbar.is-black .navbar-end .navbar-link::after { - border-color: white; } - .navbar.is-black .navbar-item.has-dropdown:focus .navbar-link, - .navbar.is-black .navbar-item.has-dropdown:hover .navbar-link, - .navbar.is-black .navbar-item.has-dropdown.is-active .navbar-link { - background-color: black; - color: white; } - .navbar.is-black .navbar-dropdown a.navbar-item.is-active { - background-color: #0a0a0a; - color: white; } } - .navbar.is-light { - background-color: whitesmoke; - color: #363636; } - .navbar.is-light .navbar-brand > .navbar-item, - .navbar.is-light .navbar-brand .navbar-link { - color: #363636; } - .navbar.is-light .navbar-brand > a.navbar-item:focus, .navbar.is-light .navbar-brand > a.navbar-item:hover, .navbar.is-light .navbar-brand > a.navbar-item.is-active, - .navbar.is-light .navbar-brand .navbar-link:focus, - .navbar.is-light .navbar-brand .navbar-link:hover, - .navbar.is-light .navbar-brand .navbar-link.is-active { - background-color: #e8e8e8; - color: #363636; } - .navbar.is-light .navbar-brand .navbar-link::after { - border-color: #363636; } - .navbar.is-light .navbar-burger { - color: #363636; } - @media screen and (min-width: 1056px) { - .navbar.is-light .navbar-start > .navbar-item, - .navbar.is-light .navbar-start .navbar-link, - .navbar.is-light .navbar-end > .navbar-item, - .navbar.is-light .navbar-end .navbar-link { - color: #363636; } - .navbar.is-light .navbar-start > a.navbar-item:focus, .navbar.is-light .navbar-start > a.navbar-item:hover, .navbar.is-light .navbar-start > a.navbar-item.is-active, - .navbar.is-light .navbar-start .navbar-link:focus, - .navbar.is-light .navbar-start .navbar-link:hover, - .navbar.is-light .navbar-start .navbar-link.is-active, - .navbar.is-light .navbar-end > a.navbar-item:focus, - .navbar.is-light .navbar-end > a.navbar-item:hover, - .navbar.is-light .navbar-end > a.navbar-item.is-active, - .navbar.is-light .navbar-end .navbar-link:focus, - .navbar.is-light .navbar-end .navbar-link:hover, - .navbar.is-light .navbar-end .navbar-link.is-active { - background-color: #e8e8e8; - color: #363636; } - .navbar.is-light .navbar-start .navbar-link::after, - .navbar.is-light .navbar-end .navbar-link::after { - border-color: #363636; } - .navbar.is-light .navbar-item.has-dropdown:focus .navbar-link, - .navbar.is-light .navbar-item.has-dropdown:hover .navbar-link, - .navbar.is-light .navbar-item.has-dropdown.is-active .navbar-link { - background-color: #e8e8e8; - color: #363636; } - .navbar.is-light .navbar-dropdown a.navbar-item.is-active { - background-color: whitesmoke; - color: #363636; } } - .navbar.is-dark, .content kbd.navbar { - background-color: #363636; - color: whitesmoke; } - .navbar.is-dark .navbar-brand > .navbar-item, .content kbd.navbar .navbar-brand > .navbar-item, - .navbar.is-dark .navbar-brand .navbar-link, - .content kbd.navbar .navbar-brand .navbar-link { - color: whitesmoke; } - .navbar.is-dark .navbar-brand > a.navbar-item:focus, .content kbd.navbar .navbar-brand > a.navbar-item:focus, .navbar.is-dark .navbar-brand > a.navbar-item:hover, .content kbd.navbar .navbar-brand > a.navbar-item:hover, .navbar.is-dark .navbar-brand > a.navbar-item.is-active, .content kbd.navbar .navbar-brand > a.navbar-item.is-active, - .navbar.is-dark .navbar-brand .navbar-link:focus, - .content kbd.navbar .navbar-brand .navbar-link:focus, - .navbar.is-dark .navbar-brand .navbar-link:hover, - .content kbd.navbar .navbar-brand .navbar-link:hover, - .navbar.is-dark .navbar-brand .navbar-link.is-active, - .content kbd.navbar .navbar-brand .navbar-link.is-active { - background-color: #292929; - color: whitesmoke; } - .navbar.is-dark .navbar-brand .navbar-link::after, .content kbd.navbar .navbar-brand .navbar-link::after { - border-color: whitesmoke; } - .navbar.is-dark .navbar-burger, .content kbd.navbar .navbar-burger { - color: whitesmoke; } - @media screen and (min-width: 1056px) { - .navbar.is-dark .navbar-start > .navbar-item, .content kbd.navbar .navbar-start > .navbar-item, - .navbar.is-dark .navbar-start .navbar-link, - .content kbd.navbar .navbar-start .navbar-link, - .navbar.is-dark .navbar-end > .navbar-item, - .content kbd.navbar .navbar-end > .navbar-item, - .navbar.is-dark .navbar-end .navbar-link, - .content kbd.navbar .navbar-end .navbar-link { - color: whitesmoke; } - .navbar.is-dark .navbar-start > a.navbar-item:focus, .content kbd.navbar .navbar-start > a.navbar-item:focus, .navbar.is-dark .navbar-start > a.navbar-item:hover, .content kbd.navbar .navbar-start > a.navbar-item:hover, .navbar.is-dark .navbar-start > a.navbar-item.is-active, .content kbd.navbar .navbar-start > a.navbar-item.is-active, - .navbar.is-dark .navbar-start .navbar-link:focus, - .content kbd.navbar .navbar-start .navbar-link:focus, - .navbar.is-dark .navbar-start .navbar-link:hover, - .content kbd.navbar .navbar-start .navbar-link:hover, - .navbar.is-dark .navbar-start .navbar-link.is-active, - .content kbd.navbar .navbar-start .navbar-link.is-active, - .navbar.is-dark .navbar-end > a.navbar-item:focus, - .content kbd.navbar .navbar-end > a.navbar-item:focus, - .navbar.is-dark .navbar-end > a.navbar-item:hover, - .content kbd.navbar .navbar-end > a.navbar-item:hover, - .navbar.is-dark .navbar-end > a.navbar-item.is-active, - .content kbd.navbar .navbar-end > a.navbar-item.is-active, - .navbar.is-dark .navbar-end .navbar-link:focus, - .content kbd.navbar .navbar-end .navbar-link:focus, - .navbar.is-dark .navbar-end .navbar-link:hover, - .content kbd.navbar .navbar-end .navbar-link:hover, - .navbar.is-dark .navbar-end .navbar-link.is-active, - .content kbd.navbar .navbar-end .navbar-link.is-active { - background-color: #292929; - color: whitesmoke; } - .navbar.is-dark .navbar-start .navbar-link::after, .content kbd.navbar .navbar-start .navbar-link::after, - .navbar.is-dark .navbar-end .navbar-link::after, - .content kbd.navbar .navbar-end .navbar-link::after { - border-color: whitesmoke; } - .navbar.is-dark .navbar-item.has-dropdown:focus .navbar-link, .content kbd.navbar .navbar-item.has-dropdown:focus .navbar-link, - .navbar.is-dark .navbar-item.has-dropdown:hover .navbar-link, - .content kbd.navbar .navbar-item.has-dropdown:hover .navbar-link, - .navbar.is-dark .navbar-item.has-dropdown.is-active .navbar-link, - .content kbd.navbar .navbar-item.has-dropdown.is-active .navbar-link { - background-color: #292929; - color: whitesmoke; } - .navbar.is-dark .navbar-dropdown a.navbar-item.is-active, .content kbd.navbar .navbar-dropdown a.navbar-item.is-active { - background-color: #363636; - color: whitesmoke; } } - .navbar.is-primary, .docstring > section > a.navbar.docs-sourcelink { - background-color: #4eb5de; - color: #fff; } - .navbar.is-primary .navbar-brand > .navbar-item, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > .navbar-item, - .navbar.is-primary .navbar-brand .navbar-link, - .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link { - color: #fff; } - .navbar.is-primary .navbar-brand > a.navbar-item:focus, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:focus, .navbar.is-primary .navbar-brand > a.navbar-item:hover, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:hover, .navbar.is-primary .navbar-brand > a.navbar-item.is-active, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item.is-active, - .navbar.is-primary .navbar-brand .navbar-link:focus, - .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:focus, - .navbar.is-primary .navbar-brand .navbar-link:hover, - .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:hover, - .navbar.is-primary .navbar-brand .navbar-link.is-active, - .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link.is-active { - background-color: #39acda; - color: #fff; } - .navbar.is-primary .navbar-brand .navbar-link::after, .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link::after { - border-color: #fff; } - .navbar.is-primary .navbar-burger, .docstring > section > a.navbar.docs-sourcelink .navbar-burger { - color: #fff; } - @media screen and (min-width: 1056px) { - .navbar.is-primary .navbar-start > .navbar-item, .docstring > section > a.navbar.docs-sourcelink .navbar-start > .navbar-item, - .navbar.is-primary .navbar-start .navbar-link, - .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link, - .navbar.is-primary .navbar-end > .navbar-item, - .docstring > section > a.navbar.docs-sourcelink .navbar-end > .navbar-item, - .navbar.is-primary .navbar-end .navbar-link, - .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link { - color: #fff; } - .navbar.is-primary .navbar-start > a.navbar-item:focus, .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:focus, .navbar.is-primary .navbar-start > a.navbar-item:hover, .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:hover, .navbar.is-primary .navbar-start > a.navbar-item.is-active, .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item.is-active, - .navbar.is-primary .navbar-start .navbar-link:focus, - .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:focus, - .navbar.is-primary .navbar-start .navbar-link:hover, - .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:hover, - .navbar.is-primary .navbar-start .navbar-link.is-active, - .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link.is-active, - .navbar.is-primary .navbar-end > a.navbar-item:focus, - .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:focus, - .navbar.is-primary .navbar-end > a.navbar-item:hover, - .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:hover, - .navbar.is-primary .navbar-end > a.navbar-item.is-active, - .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item.is-active, - .navbar.is-primary .navbar-end .navbar-link:focus, - .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:focus, - .navbar.is-primary .navbar-end .navbar-link:hover, - .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:hover, - .navbar.is-primary .navbar-end .navbar-link.is-active, - .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link.is-active { - background-color: #39acda; - color: #fff; } - .navbar.is-primary .navbar-start .navbar-link::after, .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link::after, - .navbar.is-primary .navbar-end .navbar-link::after, - .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link::after { - border-color: #fff; } - .navbar.is-primary .navbar-item.has-dropdown:focus .navbar-link, .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:focus .navbar-link, - .navbar.is-primary .navbar-item.has-dropdown:hover .navbar-link, - .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:hover .navbar-link, - .navbar.is-primary .navbar-item.has-dropdown.is-active .navbar-link, - .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown.is-active .navbar-link { - background-color: #39acda; - color: #fff; } - .navbar.is-primary .navbar-dropdown a.navbar-item.is-active, .docstring > section > a.navbar.docs-sourcelink .navbar-dropdown a.navbar-item.is-active { - background-color: #4eb5de; - color: #fff; } } - .navbar.is-link { - background-color: #2e63b8; - color: #fff; } - .navbar.is-link .navbar-brand > .navbar-item, - .navbar.is-link .navbar-brand .navbar-link { - color: #fff; } - .navbar.is-link .navbar-brand > a.navbar-item:focus, .navbar.is-link .navbar-brand > a.navbar-item:hover, .navbar.is-link .navbar-brand > a.navbar-item.is-active, - .navbar.is-link .navbar-brand .navbar-link:focus, - .navbar.is-link .navbar-brand .navbar-link:hover, - .navbar.is-link .navbar-brand .navbar-link.is-active { - background-color: #2958a4; - color: #fff; } - .navbar.is-link .navbar-brand .navbar-link::after { - border-color: #fff; } - .navbar.is-link .navbar-burger { - color: #fff; } - @media screen and (min-width: 1056px) { - .navbar.is-link .navbar-start > .navbar-item, - .navbar.is-link .navbar-start .navbar-link, - .navbar.is-link .navbar-end > .navbar-item, - .navbar.is-link .navbar-end .navbar-link { - color: #fff; } - .navbar.is-link .navbar-start > a.navbar-item:focus, .navbar.is-link .navbar-start > a.navbar-item:hover, .navbar.is-link .navbar-start > a.navbar-item.is-active, - .navbar.is-link .navbar-start .navbar-link:focus, - .navbar.is-link .navbar-start .navbar-link:hover, - .navbar.is-link .navbar-start .navbar-link.is-active, - .navbar.is-link .navbar-end > a.navbar-item:focus, - .navbar.is-link .navbar-end > a.navbar-item:hover, - .navbar.is-link .navbar-end > a.navbar-item.is-active, - .navbar.is-link .navbar-end .navbar-link:focus, - .navbar.is-link .navbar-end .navbar-link:hover, - .navbar.is-link .navbar-end .navbar-link.is-active { - background-color: #2958a4; - color: #fff; } - .navbar.is-link .navbar-start .navbar-link::after, - .navbar.is-link .navbar-end .navbar-link::after { - border-color: #fff; } - .navbar.is-link .navbar-item.has-dropdown:focus .navbar-link, - .navbar.is-link .navbar-item.has-dropdown:hover .navbar-link, - .navbar.is-link .navbar-item.has-dropdown.is-active .navbar-link { - background-color: #2958a4; - color: #fff; } - .navbar.is-link .navbar-dropdown a.navbar-item.is-active { - background-color: #2e63b8; - color: #fff; } } - .navbar.is-info { - background-color: #209cee; - color: #fff; } - .navbar.is-info .navbar-brand > .navbar-item, - .navbar.is-info .navbar-brand .navbar-link { - color: #fff; } - .navbar.is-info .navbar-brand > a.navbar-item:focus, .navbar.is-info .navbar-brand > a.navbar-item:hover, .navbar.is-info .navbar-brand > a.navbar-item.is-active, - .navbar.is-info .navbar-brand .navbar-link:focus, - .navbar.is-info .navbar-brand .navbar-link:hover, - .navbar.is-info .navbar-brand .navbar-link.is-active { - background-color: #1190e3; - color: #fff; } - .navbar.is-info .navbar-brand .navbar-link::after { - border-color: #fff; } - .navbar.is-info .navbar-burger { - color: #fff; } - @media screen and (min-width: 1056px) { - .navbar.is-info .navbar-start > .navbar-item, - .navbar.is-info .navbar-start .navbar-link, - .navbar.is-info .navbar-end > .navbar-item, - .navbar.is-info .navbar-end .navbar-link { - color: #fff; } - .navbar.is-info .navbar-start > a.navbar-item:focus, .navbar.is-info .navbar-start > a.navbar-item:hover, .navbar.is-info .navbar-start > a.navbar-item.is-active, - .navbar.is-info .navbar-start .navbar-link:focus, - .navbar.is-info .navbar-start .navbar-link:hover, - .navbar.is-info .navbar-start .navbar-link.is-active, - .navbar.is-info .navbar-end > a.navbar-item:focus, - .navbar.is-info .navbar-end > a.navbar-item:hover, - .navbar.is-info .navbar-end > a.navbar-item.is-active, - .navbar.is-info .navbar-end .navbar-link:focus, - .navbar.is-info .navbar-end .navbar-link:hover, - .navbar.is-info .navbar-end .navbar-link.is-active { - background-color: #1190e3; - color: #fff; } - .navbar.is-info .navbar-start .navbar-link::after, - .navbar.is-info .navbar-end .navbar-link::after { - border-color: #fff; } - .navbar.is-info .navbar-item.has-dropdown:focus .navbar-link, - .navbar.is-info .navbar-item.has-dropdown:hover .navbar-link, - .navbar.is-info .navbar-item.has-dropdown.is-active .navbar-link { - background-color: #1190e3; - color: #fff; } - .navbar.is-info .navbar-dropdown a.navbar-item.is-active { - background-color: #209cee; - color: #fff; } } - .navbar.is-success { - background-color: #22c35b; - color: #fff; } - .navbar.is-success .navbar-brand > .navbar-item, - .navbar.is-success .navbar-brand .navbar-link { - color: #fff; } - .navbar.is-success .navbar-brand > a.navbar-item:focus, .navbar.is-success .navbar-brand > a.navbar-item:hover, .navbar.is-success .navbar-brand > a.navbar-item.is-active, - .navbar.is-success .navbar-brand .navbar-link:focus, - .navbar.is-success .navbar-brand .navbar-link:hover, - .navbar.is-success .navbar-brand .navbar-link.is-active { - background-color: #1ead51; - color: #fff; } - .navbar.is-success .navbar-brand .navbar-link::after { - border-color: #fff; } - .navbar.is-success .navbar-burger { - color: #fff; } - @media screen and (min-width: 1056px) { - .navbar.is-success .navbar-start > .navbar-item, - .navbar.is-success .navbar-start .navbar-link, - .navbar.is-success .navbar-end > .navbar-item, - .navbar.is-success .navbar-end .navbar-link { - color: #fff; } - .navbar.is-success .navbar-start > a.navbar-item:focus, .navbar.is-success .navbar-start > a.navbar-item:hover, .navbar.is-success .navbar-start > a.navbar-item.is-active, - .navbar.is-success .navbar-start .navbar-link:focus, - .navbar.is-success .navbar-start .navbar-link:hover, - .navbar.is-success .navbar-start .navbar-link.is-active, - .navbar.is-success .navbar-end > a.navbar-item:focus, - .navbar.is-success .navbar-end > a.navbar-item:hover, - .navbar.is-success .navbar-end > a.navbar-item.is-active, - .navbar.is-success .navbar-end .navbar-link:focus, - .navbar.is-success .navbar-end .navbar-link:hover, - .navbar.is-success .navbar-end .navbar-link.is-active { - background-color: #1ead51; - color: #fff; } - .navbar.is-success .navbar-start .navbar-link::after, - .navbar.is-success .navbar-end .navbar-link::after { - border-color: #fff; } - .navbar.is-success .navbar-item.has-dropdown:focus .navbar-link, - .navbar.is-success .navbar-item.has-dropdown:hover .navbar-link, - .navbar.is-success .navbar-item.has-dropdown.is-active .navbar-link { - background-color: #1ead51; - color: #fff; } - .navbar.is-success .navbar-dropdown a.navbar-item.is-active { - background-color: #22c35b; - color: #fff; } } - .navbar.is-warning { - background-color: #ffdd57; - color: rgba(0, 0, 0, 0.7); } - .navbar.is-warning .navbar-brand > .navbar-item, - .navbar.is-warning .navbar-brand .navbar-link { - color: rgba(0, 0, 0, 0.7); } - .navbar.is-warning .navbar-brand > a.navbar-item:focus, .navbar.is-warning .navbar-brand > a.navbar-item:hover, .navbar.is-warning .navbar-brand > a.navbar-item.is-active, - .navbar.is-warning .navbar-brand .navbar-link:focus, - .navbar.is-warning .navbar-brand .navbar-link:hover, - .navbar.is-warning .navbar-brand .navbar-link.is-active { - background-color: #ffd83e; - color: rgba(0, 0, 0, 0.7); } - .navbar.is-warning .navbar-brand .navbar-link::after { - border-color: rgba(0, 0, 0, 0.7); } - .navbar.is-warning .navbar-burger { - color: rgba(0, 0, 0, 0.7); } - @media screen and (min-width: 1056px) { - .navbar.is-warning .navbar-start > .navbar-item, - .navbar.is-warning .navbar-start .navbar-link, - .navbar.is-warning .navbar-end > .navbar-item, - .navbar.is-warning .navbar-end .navbar-link { - color: rgba(0, 0, 0, 0.7); } - .navbar.is-warning .navbar-start > a.navbar-item:focus, .navbar.is-warning .navbar-start > a.navbar-item:hover, .navbar.is-warning .navbar-start > a.navbar-item.is-active, - .navbar.is-warning .navbar-start .navbar-link:focus, - .navbar.is-warning .navbar-start .navbar-link:hover, - .navbar.is-warning .navbar-start .navbar-link.is-active, - .navbar.is-warning .navbar-end > a.navbar-item:focus, - .navbar.is-warning .navbar-end > a.navbar-item:hover, - .navbar.is-warning .navbar-end > a.navbar-item.is-active, - .navbar.is-warning .navbar-end .navbar-link:focus, - .navbar.is-warning .navbar-end .navbar-link:hover, - .navbar.is-warning .navbar-end .navbar-link.is-active { - background-color: #ffd83e; - color: rgba(0, 0, 0, 0.7); } - .navbar.is-warning .navbar-start .navbar-link::after, - .navbar.is-warning .navbar-end .navbar-link::after { - border-color: rgba(0, 0, 0, 0.7); } - .navbar.is-warning .navbar-item.has-dropdown:focus .navbar-link, - .navbar.is-warning .navbar-item.has-dropdown:hover .navbar-link, - .navbar.is-warning .navbar-item.has-dropdown.is-active .navbar-link { - background-color: #ffd83e; - color: rgba(0, 0, 0, 0.7); } - .navbar.is-warning .navbar-dropdown a.navbar-item.is-active { - background-color: #ffdd57; - color: rgba(0, 0, 0, 0.7); } } - .navbar.is-danger { - background-color: #da0b00; - color: #fff; } - .navbar.is-danger .navbar-brand > .navbar-item, - .navbar.is-danger .navbar-brand .navbar-link { - color: #fff; } - .navbar.is-danger .navbar-brand > a.navbar-item:focus, .navbar.is-danger .navbar-brand > a.navbar-item:hover, .navbar.is-danger .navbar-brand > a.navbar-item.is-active, - .navbar.is-danger .navbar-brand .navbar-link:focus, - .navbar.is-danger .navbar-brand .navbar-link:hover, - .navbar.is-danger .navbar-brand .navbar-link.is-active { - background-color: #c10a00; - color: #fff; } - .navbar.is-danger .navbar-brand .navbar-link::after { - border-color: #fff; } - .navbar.is-danger .navbar-burger { - color: #fff; } - @media screen and (min-width: 1056px) { - .navbar.is-danger .navbar-start > .navbar-item, - .navbar.is-danger .navbar-start .navbar-link, - .navbar.is-danger .navbar-end > .navbar-item, - .navbar.is-danger .navbar-end .navbar-link { - color: #fff; } - .navbar.is-danger .navbar-start > a.navbar-item:focus, .navbar.is-danger .navbar-start > a.navbar-item:hover, .navbar.is-danger .navbar-start > a.navbar-item.is-active, - .navbar.is-danger .navbar-start .navbar-link:focus, - .navbar.is-danger .navbar-start .navbar-link:hover, - .navbar.is-danger .navbar-start .navbar-link.is-active, - .navbar.is-danger .navbar-end > a.navbar-item:focus, - .navbar.is-danger .navbar-end > a.navbar-item:hover, - .navbar.is-danger .navbar-end > a.navbar-item.is-active, - .navbar.is-danger .navbar-end .navbar-link:focus, - .navbar.is-danger .navbar-end .navbar-link:hover, - .navbar.is-danger .navbar-end .navbar-link.is-active { - background-color: #c10a00; - color: #fff; } - .navbar.is-danger .navbar-start .navbar-link::after, - .navbar.is-danger .navbar-end .navbar-link::after { - border-color: #fff; } - .navbar.is-danger .navbar-item.has-dropdown:focus .navbar-link, - .navbar.is-danger .navbar-item.has-dropdown:hover .navbar-link, - .navbar.is-danger .navbar-item.has-dropdown.is-active .navbar-link { - background-color: #c10a00; - color: #fff; } - .navbar.is-danger .navbar-dropdown a.navbar-item.is-active { - background-color: #da0b00; - color: #fff; } } - .navbar > .container { - align-items: stretch; - display: flex; - min-height: 3.25rem; - width: 100%; } - .navbar.has-shadow { - box-shadow: 0 2px 0 0 whitesmoke; } - .navbar.is-fixed-bottom, .navbar.is-fixed-top { - left: 0; - position: fixed; - right: 0; - z-index: 30; } - .navbar.is-fixed-bottom { - bottom: 0; } - .navbar.is-fixed-bottom.has-shadow { - box-shadow: 0 -2px 0 0 whitesmoke; } - .navbar.is-fixed-top { - top: 0; } - -html.has-navbar-fixed-top, -body.has-navbar-fixed-top { - padding-top: 3.25rem; } - -html.has-navbar-fixed-bottom, -body.has-navbar-fixed-bottom { - padding-bottom: 3.25rem; } - -.navbar-brand, -.navbar-tabs { - align-items: stretch; - display: flex; - flex-shrink: 0; - min-height: 3.25rem; } - -.navbar-brand a.navbar-item:focus, .navbar-brand a.navbar-item:hover { - background-color: transparent; } - -.navbar-tabs { - -webkit-overflow-scrolling: touch; - max-width: 100vw; - overflow-x: auto; - overflow-y: hidden; } - -.navbar-burger { - color: #4a4a4a; - cursor: pointer; - display: block; - height: 3.25rem; - position: relative; - width: 3.25rem; - margin-left: auto; } - .navbar-burger span { - background-color: currentColor; - display: block; - height: 1px; - left: calc(50% - 8px); - position: absolute; - transform-origin: center; - transition-duration: 86ms; - transition-property: background-color, opacity, transform; - transition-timing-function: ease-out; - width: 16px; } - .navbar-burger span:nth-child(1) { - top: calc(50% - 6px); } - .navbar-burger span:nth-child(2) { - top: calc(50% - 1px); } - .navbar-burger span:nth-child(3) { - top: calc(50% + 4px); } - .navbar-burger:hover { - background-color: rgba(0, 0, 0, 0.05); } - .navbar-burger.is-active span:nth-child(1) { - transform: translateY(5px) rotate(45deg); } - .navbar-burger.is-active span:nth-child(2) { - opacity: 0; } - .navbar-burger.is-active span:nth-child(3) { - transform: translateY(-5px) rotate(-45deg); } - -.navbar-menu { - display: none; } - -.navbar-item, -.navbar-link { - color: #4a4a4a; - display: block; - line-height: 1.5; - padding: 0.5rem 0.75rem; - position: relative; } - .navbar-item .icon:only-child, - .navbar-link .icon:only-child { - margin-left: -0.25rem; - margin-right: -0.25rem; } - -a.navbar-item, -.navbar-link { - cursor: pointer; } - a.navbar-item:focus, a.navbar-item:focus-within, a.navbar-item:hover, a.navbar-item.is-active, - .navbar-link:focus, - .navbar-link:focus-within, - .navbar-link:hover, - .navbar-link.is-active { - background-color: #fafafa; - color: #2e63b8; } - -.navbar-item { - display: block; - flex-grow: 0; - flex-shrink: 0; } - .navbar-item img { - max-height: 1.75rem; } - .navbar-item.has-dropdown { - padding: 0; } - .navbar-item.is-expanded { - flex-grow: 1; - flex-shrink: 1; } - .navbar-item.is-tab { - border-bottom: 1px solid transparent; - min-height: 3.25rem; - padding-bottom: calc(0.5rem - 1px); } - .navbar-item.is-tab:focus, .navbar-item.is-tab:hover { - background-color: transparent; - border-bottom-color: #2e63b8; } - .navbar-item.is-tab.is-active { - background-color: transparent; - border-bottom-color: #2e63b8; - border-bottom-style: solid; - border-bottom-width: 3px; - color: #2e63b8; - padding-bottom: calc(0.5rem - 3px); } - -.navbar-content { - flex-grow: 1; - flex-shrink: 1; } - -.navbar-link:not(.is-arrowless) { - padding-right: 2.5em; } - .navbar-link:not(.is-arrowless)::after { - border-color: #2e63b8; - margin-top: -0.375em; - right: 1.125em; } - -.navbar-dropdown { - font-size: 0.875rem; - padding-bottom: 0.5rem; - padding-top: 0.5rem; } - .navbar-dropdown .navbar-item { - padding-left: 1.5rem; - padding-right: 1.5rem; } - -.navbar-divider { - background-color: whitesmoke; - border: none; - display: none; - height: 2px; - margin: 0.5rem 0; } - -@media screen and (max-width: 1055px) { - .navbar > .container { - display: block; } - .navbar-brand .navbar-item, - .navbar-tabs .navbar-item { - align-items: center; - display: flex; } - .navbar-link::after { - display: none; } - .navbar-menu { - background-color: white; - box-shadow: 0 8px 16px rgba(10, 10, 10, 0.1); - padding: 0.5rem 0; } - .navbar-menu.is-active { - display: block; } - .navbar.is-fixed-bottom-touch, .navbar.is-fixed-top-touch { - left: 0; - position: fixed; - right: 0; - z-index: 30; } - .navbar.is-fixed-bottom-touch { - bottom: 0; } - .navbar.is-fixed-bottom-touch.has-shadow { - box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); } - .navbar.is-fixed-top-touch { - top: 0; } - .navbar.is-fixed-top .navbar-menu, .navbar.is-fixed-top-touch .navbar-menu { - -webkit-overflow-scrolling: touch; - max-height: calc(100vh - 3.25rem); - overflow: auto; } - html.has-navbar-fixed-top-touch, - body.has-navbar-fixed-top-touch { - padding-top: 3.25rem; } - html.has-navbar-fixed-bottom-touch, - body.has-navbar-fixed-bottom-touch { - padding-bottom: 3.25rem; } } - -@media screen and (min-width: 1056px) { - .navbar, - .navbar-menu, - .navbar-start, - .navbar-end { - align-items: stretch; - display: flex; } - .navbar { - min-height: 3.25rem; } - .navbar.is-spaced { - padding: 1rem 2rem; } - .navbar.is-spaced .navbar-start, - .navbar.is-spaced .navbar-end { - align-items: center; } - .navbar.is-spaced a.navbar-item, - .navbar.is-spaced .navbar-link { - border-radius: 4px; } - .navbar.is-transparent a.navbar-item:focus, .navbar.is-transparent a.navbar-item:hover, .navbar.is-transparent a.navbar-item.is-active, - .navbar.is-transparent .navbar-link:focus, - .navbar.is-transparent .navbar-link:hover, - .navbar.is-transparent .navbar-link.is-active { - background-color: transparent !important; } - .navbar.is-transparent .navbar-item.has-dropdown.is-active .navbar-link, .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus .navbar-link, .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus-within .navbar-link, .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:hover .navbar-link { - background-color: transparent !important; } - .navbar.is-transparent .navbar-dropdown a.navbar-item:focus, .navbar.is-transparent .navbar-dropdown a.navbar-item:hover { - background-color: whitesmoke; - color: #0a0a0a; } - .navbar.is-transparent .navbar-dropdown a.navbar-item.is-active { - background-color: whitesmoke; - color: #2e63b8; } - .navbar-burger { - display: none; } - .navbar-item, - .navbar-link { - align-items: center; - display: flex; } - .navbar-item { - display: flex; } - .navbar-item.has-dropdown { - align-items: stretch; } - .navbar-item.has-dropdown-up .navbar-link::after { - transform: rotate(135deg) translate(0.25em, -0.25em); } - .navbar-item.has-dropdown-up .navbar-dropdown { - border-bottom: 2px solid #dbdbdb; - border-radius: 6px 6px 0 0; - border-top: none; - bottom: 100%; - box-shadow: 0 -8px 8px rgba(10, 10, 10, 0.1); - top: auto; } - .navbar-item.is-active .navbar-dropdown, .navbar-item.is-hoverable:focus .navbar-dropdown, .navbar-item.is-hoverable:focus-within .navbar-dropdown, .navbar-item.is-hoverable:hover .navbar-dropdown { - display: block; } - .navbar.is-spaced .navbar-item.is-active .navbar-dropdown, .navbar-item.is-active .navbar-dropdown.is-boxed, .navbar.is-spaced .navbar-item.is-hoverable:focus .navbar-dropdown, .navbar-item.is-hoverable:focus .navbar-dropdown.is-boxed, .navbar.is-spaced .navbar-item.is-hoverable:focus-within .navbar-dropdown, .navbar-item.is-hoverable:focus-within .navbar-dropdown.is-boxed, .navbar.is-spaced .navbar-item.is-hoverable:hover .navbar-dropdown, .navbar-item.is-hoverable:hover .navbar-dropdown.is-boxed { - opacity: 1; - pointer-events: auto; - transform: translateY(0); } - .navbar-menu { - flex-grow: 1; - flex-shrink: 0; } - .navbar-start { - justify-content: flex-start; - margin-right: auto; } - .navbar-end { - justify-content: flex-end; - margin-left: auto; } - .navbar-dropdown { - background-color: white; - border-bottom-left-radius: 6px; - border-bottom-right-radius: 6px; - border-top: 2px solid #dbdbdb; - box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1); - display: none; - font-size: 0.875rem; - left: 0; - min-width: 100%; - position: absolute; - top: 100%; - z-index: 20; } - .navbar-dropdown .navbar-item { - padding: 0.375rem 1rem; - white-space: nowrap; } - .navbar-dropdown a.navbar-item { - padding-right: 3rem; } - .navbar-dropdown a.navbar-item:focus, .navbar-dropdown a.navbar-item:hover { - background-color: whitesmoke; - color: #0a0a0a; } - .navbar-dropdown a.navbar-item.is-active { - background-color: whitesmoke; - color: #2e63b8; } - .navbar.is-spaced .navbar-dropdown, .navbar-dropdown.is-boxed { - border-radius: 6px; - border-top: none; - box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); - display: block; - opacity: 0; - pointer-events: none; - top: calc(100% + (-4px)); - transform: translateY(-5px); - transition-duration: 86ms; - transition-property: opacity, transform; } - .navbar-dropdown.is-right { - left: auto; - right: 0; } - .navbar-divider { - display: block; } - .navbar > .container .navbar-brand, - .container > .navbar .navbar-brand { - margin-left: -.75rem; } - .navbar > .container .navbar-menu, - .container > .navbar .navbar-menu { - margin-right: -.75rem; } - .navbar.is-fixed-bottom-desktop, .navbar.is-fixed-top-desktop { - left: 0; - position: fixed; - right: 0; - z-index: 30; } - .navbar.is-fixed-bottom-desktop { - bottom: 0; } - .navbar.is-fixed-bottom-desktop.has-shadow { - box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); } - .navbar.is-fixed-top-desktop { - top: 0; } - html.has-navbar-fixed-top-desktop, - body.has-navbar-fixed-top-desktop { - padding-top: 3.25rem; } - html.has-navbar-fixed-bottom-desktop, - body.has-navbar-fixed-bottom-desktop { - padding-bottom: 3.25rem; } - html.has-spaced-navbar-fixed-top, - body.has-spaced-navbar-fixed-top { - padding-top: 5.25rem; } - html.has-spaced-navbar-fixed-bottom, - body.has-spaced-navbar-fixed-bottom { - padding-bottom: 5.25rem; } - a.navbar-item.is-active, - .navbar-link.is-active { - color: #0a0a0a; } - a.navbar-item.is-active:not(:focus):not(:hover), - .navbar-link.is-active:not(:focus):not(:hover) { - background-color: transparent; } - .navbar-item.has-dropdown:focus .navbar-link, .navbar-item.has-dropdown:hover .navbar-link, .navbar-item.has-dropdown.is-active .navbar-link { - background-color: #fafafa; } } - -.hero.is-fullheight-with-navbar { - min-height: calc(100vh - 3.25rem); } - -.pagination { - font-size: 1rem; - margin: -0.25rem; } - .pagination.is-small, #documenter .docs-sidebar form.docs-search > input.pagination { - font-size: 0.75rem; } - .pagination.is-medium { - font-size: 1.25rem; } - .pagination.is-large { - font-size: 1.5rem; } - .pagination.is-rounded .pagination-previous, #documenter .docs-sidebar form.docs-search > input.pagination .pagination-previous, - .pagination.is-rounded .pagination-next, - #documenter .docs-sidebar form.docs-search > input.pagination .pagination-next { - padding-left: 1em; - padding-right: 1em; - border-radius: 290486px; } - .pagination.is-rounded .pagination-link, #documenter .docs-sidebar form.docs-search > input.pagination .pagination-link { - border-radius: 290486px; } - -.pagination, -.pagination-list { - align-items: center; - display: flex; - justify-content: center; - text-align: center; } - -.pagination-previous, -.pagination-next, -.pagination-link, -.pagination-ellipsis { - font-size: 1em; - justify-content: center; - margin: 0.25rem; - padding-left: 0.5em; - padding-right: 0.5em; - text-align: center; } - -.pagination-previous, -.pagination-next, -.pagination-link { - border-color: #dbdbdb; - color: #363636; - min-width: 2.25em; } - .pagination-previous:hover, - .pagination-next:hover, - .pagination-link:hover { - border-color: #b5b5b5; - color: #363636; } - .pagination-previous:focus, - .pagination-next:focus, - .pagination-link:focus { - border-color: #3c5dcd; } - .pagination-previous:active, - .pagination-next:active, - .pagination-link:active { - box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2); } - .pagination-previous[disabled], - .pagination-next[disabled], - .pagination-link[disabled] { - background-color: #dbdbdb; - border-color: #dbdbdb; - box-shadow: none; - color: #6b6b6b; - opacity: 0.5; } - -.pagination-previous, -.pagination-next { - padding-left: 0.75em; - padding-right: 0.75em; - white-space: nowrap; } - -.pagination-link.is-current { - background-color: #2e63b8; - border-color: #2e63b8; - color: #fff; } - -.pagination-ellipsis { - color: #b5b5b5; - pointer-events: none; } - -.pagination-list { - flex-wrap: wrap; } - -@media screen and (max-width: 768px) { - .pagination { - flex-wrap: wrap; } - .pagination-previous, - .pagination-next { - flex-grow: 1; - flex-shrink: 1; } - .pagination-list li { - flex-grow: 1; - flex-shrink: 1; } } - -@media screen and (min-width: 769px), print { - .pagination-list { - flex-grow: 1; - flex-shrink: 1; - justify-content: flex-start; - order: 1; } - .pagination-previous { - order: 2; } - .pagination-next { - order: 3; } - .pagination { - justify-content: space-between; } - .pagination.is-centered .pagination-previous { - order: 1; } - .pagination.is-centered .pagination-list { - justify-content: center; - order: 2; } - .pagination.is-centered .pagination-next { - order: 3; } - .pagination.is-right .pagination-previous { - order: 1; } - .pagination.is-right .pagination-next { - order: 2; } - .pagination.is-right .pagination-list { - justify-content: flex-end; - order: 3; } } - -.panel { - font-size: 1rem; } - .panel:not(:last-child) { - margin-bottom: 1.5rem; } - -.panel-heading, -.panel-tabs, -.panel-block { - border-bottom: 1px solid #dbdbdb; - border-left: 1px solid #dbdbdb; - border-right: 1px solid #dbdbdb; } - .panel-heading:first-child, - .panel-tabs:first-child, - .panel-block:first-child { - border-top: 1px solid #dbdbdb; } - -.panel-heading { - background-color: whitesmoke; - border-radius: 4px 4px 0 0; - color: #222222; - font-size: 1.25em; - font-weight: 300; - line-height: 1.25; - padding: 0.5em 0.75em; } - -.panel-tabs { - align-items: flex-end; - display: flex; - font-size: 0.875em; - justify-content: center; } - .panel-tabs a { - border-bottom: 1px solid #dbdbdb; - margin-bottom: -1px; - padding: 0.5em; } - .panel-tabs a.is-active { - border-bottom-color: #4a4a4a; - color: #363636; } - -.panel-list a { - color: #222222; } - .panel-list a:hover { - color: #2e63b8; } - -.panel-block { - align-items: center; - color: #222222; - display: flex; - justify-content: flex-start; - padding: 0.5em 0.75em; } - .panel-block input[type="checkbox"] { - margin-right: 0.75em; } - .panel-block > .control { - flex-grow: 1; - flex-shrink: 1; - width: 100%; } - .panel-block.is-wrapped { - flex-wrap: wrap; } - .panel-block.is-active { - border-left-color: #2e63b8; - color: #363636; } - .panel-block.is-active .panel-icon { - color: #2e63b8; } - -a.panel-block, -label.panel-block { - cursor: pointer; } - a.panel-block:hover, - label.panel-block:hover { - background-color: whitesmoke; } - -.panel-icon { - display: inline-block; - font-size: 14px; - height: 1em; - line-height: 1em; - text-align: center; - vertical-align: top; - width: 1em; - color: #6b6b6b; - margin-right: 0.75em; } - .panel-icon .fa { - font-size: inherit; - line-height: inherit; } - -.tabs { - -webkit-overflow-scrolling: touch; - align-items: stretch; - display: flex; - font-size: 1rem; - justify-content: space-between; - overflow: hidden; - overflow-x: auto; - white-space: nowrap; } - .tabs a { - align-items: center; - border-bottom-color: #dbdbdb; - border-bottom-style: solid; - border-bottom-width: 1px; - color: #222222; - display: flex; - justify-content: center; - margin-bottom: -1px; - padding: 0.5em 1em; - vertical-align: top; } - .tabs a:hover { - border-bottom-color: #222222; - color: #222222; } - .tabs li { - display: block; } - .tabs li.is-active a { - border-bottom-color: #2e63b8; - color: #2e63b8; } - .tabs ul { - align-items: center; - border-bottom-color: #dbdbdb; - border-bottom-style: solid; - border-bottom-width: 1px; - display: flex; - flex-grow: 1; - flex-shrink: 0; - justify-content: flex-start; } - .tabs ul.is-left { - padding-right: 0.75em; } - .tabs ul.is-center { - flex: none; - justify-content: center; - padding-left: 0.75em; - padding-right: 0.75em; } - .tabs ul.is-right { - justify-content: flex-end; - padding-left: 0.75em; } - .tabs .icon:first-child { - margin-right: 0.5em; } - .tabs .icon:last-child { - margin-left: 0.5em; } - .tabs.is-centered ul { - justify-content: center; } - .tabs.is-right ul { - justify-content: flex-end; } - .tabs.is-boxed a { - border: 1px solid transparent; - border-radius: 4px 4px 0 0; } - .tabs.is-boxed a:hover { - background-color: whitesmoke; - border-bottom-color: #dbdbdb; } - .tabs.is-boxed li.is-active a { - background-color: white; - border-color: #dbdbdb; - border-bottom-color: transparent !important; } - .tabs.is-fullwidth li { - flex-grow: 1; - flex-shrink: 0; } - .tabs.is-toggle a { - border-color: #dbdbdb; - border-style: solid; - border-width: 1px; - margin-bottom: 0; - position: relative; } - .tabs.is-toggle a:hover { - background-color: whitesmoke; - border-color: #b5b5b5; - z-index: 2; } - .tabs.is-toggle li + li { - margin-left: -1px; } - .tabs.is-toggle li:first-child a { - border-radius: 4px 0 0 4px; } - .tabs.is-toggle li:last-child a { - border-radius: 0 4px 4px 0; } - .tabs.is-toggle li.is-active a { - background-color: #2e63b8; - border-color: #2e63b8; - color: #fff; - z-index: 1; } - .tabs.is-toggle ul { - border-bottom: none; } - .tabs.is-toggle.is-toggle-rounded li:first-child a { - border-bottom-left-radius: 290486px; - border-top-left-radius: 290486px; - padding-left: 1.25em; } - .tabs.is-toggle.is-toggle-rounded li:last-child a { - border-bottom-right-radius: 290486px; - border-top-right-radius: 290486px; - padding-right: 1.25em; } - .tabs.is-small, #documenter .docs-sidebar form.docs-search > input.tabs { - font-size: 0.75rem; } - .tabs.is-medium { - font-size: 1.25rem; } - .tabs.is-large { - font-size: 1.5rem; } - -.column { - display: block; - flex-basis: 0; - flex-grow: 1; - flex-shrink: 1; - padding: 0.75rem; } - .columns.is-mobile > .column.is-narrow { - flex: none; } - .columns.is-mobile > .column.is-full { - flex: none; - width: 100%; } - .columns.is-mobile > .column.is-three-quarters { - flex: none; - width: 75%; } - .columns.is-mobile > .column.is-two-thirds { - flex: none; - width: 66.6666%; } - .columns.is-mobile > .column.is-half { - flex: none; - width: 50%; } - .columns.is-mobile > .column.is-one-third { - flex: none; - width: 33.3333%; } - .columns.is-mobile > .column.is-one-quarter { - flex: none; - width: 25%; } - .columns.is-mobile > .column.is-one-fifth { - flex: none; - width: 20%; } - .columns.is-mobile > .column.is-two-fifths { - flex: none; - width: 40%; } - .columns.is-mobile > .column.is-three-fifths { - flex: none; - width: 60%; } - .columns.is-mobile > .column.is-four-fifths { - flex: none; - width: 80%; } - .columns.is-mobile > .column.is-offset-three-quarters { - margin-left: 75%; } - .columns.is-mobile > .column.is-offset-two-thirds { - margin-left: 66.6666%; } - .columns.is-mobile > .column.is-offset-half { - margin-left: 50%; } - .columns.is-mobile > .column.is-offset-one-third { - margin-left: 33.3333%; } - .columns.is-mobile > .column.is-offset-one-quarter { - margin-left: 25%; } - .columns.is-mobile > .column.is-offset-one-fifth { - margin-left: 20%; } - .columns.is-mobile > .column.is-offset-two-fifths { - margin-left: 40%; } - .columns.is-mobile > .column.is-offset-three-fifths { - margin-left: 60%; } - .columns.is-mobile > .column.is-offset-four-fifths { - margin-left: 80%; } - .columns.is-mobile > .column.is-0 { - flex: none; - width: 0%; } - .columns.is-mobile > .column.is-offset-0 { - margin-left: 0%; } - .columns.is-mobile > .column.is-1 { - flex: none; - width: 8.3333333333%; } - .columns.is-mobile > .column.is-offset-1 { - margin-left: 8.3333333333%; } - .columns.is-mobile > .column.is-2 { - flex: none; - width: 16.6666666667%; } - .columns.is-mobile > .column.is-offset-2 { - margin-left: 16.6666666667%; } - .columns.is-mobile > .column.is-3 { - flex: none; - width: 25%; } - .columns.is-mobile > .column.is-offset-3 { - margin-left: 25%; } - .columns.is-mobile > .column.is-4 { - flex: none; - width: 33.3333333333%; } - .columns.is-mobile > .column.is-offset-4 { - margin-left: 33.3333333333%; } - .columns.is-mobile > .column.is-5 { - flex: none; - width: 41.6666666667%; } - .columns.is-mobile > .column.is-offset-5 { - margin-left: 41.6666666667%; } - .columns.is-mobile > .column.is-6 { - flex: none; - width: 50%; } - .columns.is-mobile > .column.is-offset-6 { - margin-left: 50%; } - .columns.is-mobile > .column.is-7 { - flex: none; - width: 58.3333333333%; } - .columns.is-mobile > .column.is-offset-7 { - margin-left: 58.3333333333%; } - .columns.is-mobile > .column.is-8 { - flex: none; - width: 66.6666666667%; } - .columns.is-mobile > .column.is-offset-8 { - margin-left: 66.6666666667%; } - .columns.is-mobile > .column.is-9 { - flex: none; - width: 75%; } - .columns.is-mobile > .column.is-offset-9 { - margin-left: 75%; } - .columns.is-mobile > .column.is-10 { - flex: none; - width: 83.3333333333%; } - .columns.is-mobile > .column.is-offset-10 { - margin-left: 83.3333333333%; } - .columns.is-mobile > .column.is-11 { - flex: none; - width: 91.6666666667%; } - .columns.is-mobile > .column.is-offset-11 { - margin-left: 91.6666666667%; } - .columns.is-mobile > .column.is-12 { - flex: none; - width: 100%; } - .columns.is-mobile > .column.is-offset-12 { - margin-left: 100%; } - @media screen and (max-width: 768px) { - .column.is-narrow-mobile { - flex: none; } - .column.is-full-mobile { - flex: none; - width: 100%; } - .column.is-three-quarters-mobile { - flex: none; - width: 75%; } - .column.is-two-thirds-mobile { - flex: none; - width: 66.6666%; } - .column.is-half-mobile { - flex: none; - width: 50%; } - .column.is-one-third-mobile { - flex: none; - width: 33.3333%; } - .column.is-one-quarter-mobile { - flex: none; - width: 25%; } - .column.is-one-fifth-mobile { - flex: none; - width: 20%; } - .column.is-two-fifths-mobile { - flex: none; - width: 40%; } - .column.is-three-fifths-mobile { - flex: none; - width: 60%; } - .column.is-four-fifths-mobile { - flex: none; - width: 80%; } - .column.is-offset-three-quarters-mobile { - margin-left: 75%; } - .column.is-offset-two-thirds-mobile { - margin-left: 66.6666%; } - .column.is-offset-half-mobile { - margin-left: 50%; } - .column.is-offset-one-third-mobile { - margin-left: 33.3333%; } - .column.is-offset-one-quarter-mobile { - margin-left: 25%; } - .column.is-offset-one-fifth-mobile { - margin-left: 20%; } - .column.is-offset-two-fifths-mobile { - margin-left: 40%; } - .column.is-offset-three-fifths-mobile { - margin-left: 60%; } - .column.is-offset-four-fifths-mobile { - margin-left: 80%; } - .column.is-0-mobile { - flex: none; - width: 0%; } - .column.is-offset-0-mobile { - margin-left: 0%; } - .column.is-1-mobile { - flex: none; - width: 8.3333333333%; } - .column.is-offset-1-mobile { - margin-left: 8.3333333333%; } - .column.is-2-mobile { - flex: none; - width: 16.6666666667%; } - .column.is-offset-2-mobile { - margin-left: 16.6666666667%; } - .column.is-3-mobile { - flex: none; - width: 25%; } - .column.is-offset-3-mobile { - margin-left: 25%; } - .column.is-4-mobile { - flex: none; - width: 33.3333333333%; } - .column.is-offset-4-mobile { - margin-left: 33.3333333333%; } - .column.is-5-mobile { - flex: none; - width: 41.6666666667%; } - .column.is-offset-5-mobile { - margin-left: 41.6666666667%; } - .column.is-6-mobile { - flex: none; - width: 50%; } - .column.is-offset-6-mobile { - margin-left: 50%; } - .column.is-7-mobile { - flex: none; - width: 58.3333333333%; } - .column.is-offset-7-mobile { - margin-left: 58.3333333333%; } - .column.is-8-mobile { - flex: none; - width: 66.6666666667%; } - .column.is-offset-8-mobile { - margin-left: 66.6666666667%; } - .column.is-9-mobile { - flex: none; - width: 75%; } - .column.is-offset-9-mobile { - margin-left: 75%; } - .column.is-10-mobile { - flex: none; - width: 83.3333333333%; } - .column.is-offset-10-mobile { - margin-left: 83.3333333333%; } - .column.is-11-mobile { - flex: none; - width: 91.6666666667%; } - .column.is-offset-11-mobile { - margin-left: 91.6666666667%; } - .column.is-12-mobile { - flex: none; - width: 100%; } - .column.is-offset-12-mobile { - margin-left: 100%; } } - @media screen and (min-width: 769px), print { - .column.is-narrow, .column.is-narrow-tablet { - flex: none; } - .column.is-full, .column.is-full-tablet { - flex: none; - width: 100%; } - .column.is-three-quarters, .column.is-three-quarters-tablet { - flex: none; - width: 75%; } - .column.is-two-thirds, .column.is-two-thirds-tablet { - flex: none; - width: 66.6666%; } - .column.is-half, .column.is-half-tablet { - flex: none; - width: 50%; } - .column.is-one-third, .column.is-one-third-tablet { - flex: none; - width: 33.3333%; } - .column.is-one-quarter, .column.is-one-quarter-tablet { - flex: none; - width: 25%; } - .column.is-one-fifth, .column.is-one-fifth-tablet { - flex: none; - width: 20%; } - .column.is-two-fifths, .column.is-two-fifths-tablet { - flex: none; - width: 40%; } - .column.is-three-fifths, .column.is-three-fifths-tablet { - flex: none; - width: 60%; } - .column.is-four-fifths, .column.is-four-fifths-tablet { - flex: none; - width: 80%; } - .column.is-offset-three-quarters, .column.is-offset-three-quarters-tablet { - margin-left: 75%; } - .column.is-offset-two-thirds, .column.is-offset-two-thirds-tablet { - margin-left: 66.6666%; } - .column.is-offset-half, .column.is-offset-half-tablet { - margin-left: 50%; } - .column.is-offset-one-third, .column.is-offset-one-third-tablet { - margin-left: 33.3333%; } - .column.is-offset-one-quarter, .column.is-offset-one-quarter-tablet { - margin-left: 25%; } - .column.is-offset-one-fifth, .column.is-offset-one-fifth-tablet { - margin-left: 20%; } - .column.is-offset-two-fifths, .column.is-offset-two-fifths-tablet { - margin-left: 40%; } - .column.is-offset-three-fifths, .column.is-offset-three-fifths-tablet { - margin-left: 60%; } - .column.is-offset-four-fifths, .column.is-offset-four-fifths-tablet { - margin-left: 80%; } - .column.is-0, .column.is-0-tablet { - flex: none; - width: 0%; } - .column.is-offset-0, .column.is-offset-0-tablet { - margin-left: 0%; } - .column.is-1, .column.is-1-tablet { - flex: none; - width: 8.3333333333%; } - .column.is-offset-1, .column.is-offset-1-tablet { - margin-left: 8.3333333333%; } - .column.is-2, .column.is-2-tablet { - flex: none; - width: 16.6666666667%; } - .column.is-offset-2, .column.is-offset-2-tablet { - margin-left: 16.6666666667%; } - .column.is-3, .column.is-3-tablet { - flex: none; - width: 25%; } - .column.is-offset-3, .column.is-offset-3-tablet { - margin-left: 25%; } - .column.is-4, .column.is-4-tablet { - flex: none; - width: 33.3333333333%; } - .column.is-offset-4, .column.is-offset-4-tablet { - margin-left: 33.3333333333%; } - .column.is-5, .column.is-5-tablet { - flex: none; - width: 41.6666666667%; } - .column.is-offset-5, .column.is-offset-5-tablet { - margin-left: 41.6666666667%; } - .column.is-6, .column.is-6-tablet { - flex: none; - width: 50%; } - .column.is-offset-6, .column.is-offset-6-tablet { - margin-left: 50%; } - .column.is-7, .column.is-7-tablet { - flex: none; - width: 58.3333333333%; } - .column.is-offset-7, .column.is-offset-7-tablet { - margin-left: 58.3333333333%; } - .column.is-8, .column.is-8-tablet { - flex: none; - width: 66.6666666667%; } - .column.is-offset-8, .column.is-offset-8-tablet { - margin-left: 66.6666666667%; } - .column.is-9, .column.is-9-tablet { - flex: none; - width: 75%; } - .column.is-offset-9, .column.is-offset-9-tablet { - margin-left: 75%; } - .column.is-10, .column.is-10-tablet { - flex: none; - width: 83.3333333333%; } - .column.is-offset-10, .column.is-offset-10-tablet { - margin-left: 83.3333333333%; } - .column.is-11, .column.is-11-tablet { - flex: none; - width: 91.6666666667%; } - .column.is-offset-11, .column.is-offset-11-tablet { - margin-left: 91.6666666667%; } - .column.is-12, .column.is-12-tablet { - flex: none; - width: 100%; } - .column.is-offset-12, .column.is-offset-12-tablet { - margin-left: 100%; } } - @media screen and (max-width: 1055px) { - .column.is-narrow-touch { - flex: none; } - .column.is-full-touch { - flex: none; - width: 100%; } - .column.is-three-quarters-touch { - flex: none; - width: 75%; } - .column.is-two-thirds-touch { - flex: none; - width: 66.6666%; } - .column.is-half-touch { - flex: none; - width: 50%; } - .column.is-one-third-touch { - flex: none; - width: 33.3333%; } - .column.is-one-quarter-touch { - flex: none; - width: 25%; } - .column.is-one-fifth-touch { - flex: none; - width: 20%; } - .column.is-two-fifths-touch { - flex: none; - width: 40%; } - .column.is-three-fifths-touch { - flex: none; - width: 60%; } - .column.is-four-fifths-touch { - flex: none; - width: 80%; } - .column.is-offset-three-quarters-touch { - margin-left: 75%; } - .column.is-offset-two-thirds-touch { - margin-left: 66.6666%; } - .column.is-offset-half-touch { - margin-left: 50%; } - .column.is-offset-one-third-touch { - margin-left: 33.3333%; } - .column.is-offset-one-quarter-touch { - margin-left: 25%; } - .column.is-offset-one-fifth-touch { - margin-left: 20%; } - .column.is-offset-two-fifths-touch { - margin-left: 40%; } - .column.is-offset-three-fifths-touch { - margin-left: 60%; } - .column.is-offset-four-fifths-touch { - margin-left: 80%; } - .column.is-0-touch { - flex: none; - width: 0%; } - .column.is-offset-0-touch { - margin-left: 0%; } - .column.is-1-touch { - flex: none; - width: 8.3333333333%; } - .column.is-offset-1-touch { - margin-left: 8.3333333333%; } - .column.is-2-touch { - flex: none; - width: 16.6666666667%; } - .column.is-offset-2-touch { - margin-left: 16.6666666667%; } - .column.is-3-touch { - flex: none; - width: 25%; } - .column.is-offset-3-touch { - margin-left: 25%; } - .column.is-4-touch { - flex: none; - width: 33.3333333333%; } - .column.is-offset-4-touch { - margin-left: 33.3333333333%; } - .column.is-5-touch { - flex: none; - width: 41.6666666667%; } - .column.is-offset-5-touch { - margin-left: 41.6666666667%; } - .column.is-6-touch { - flex: none; - width: 50%; } - .column.is-offset-6-touch { - margin-left: 50%; } - .column.is-7-touch { - flex: none; - width: 58.3333333333%; } - .column.is-offset-7-touch { - margin-left: 58.3333333333%; } - .column.is-8-touch { - flex: none; - width: 66.6666666667%; } - .column.is-offset-8-touch { - margin-left: 66.6666666667%; } - .column.is-9-touch { - flex: none; - width: 75%; } - .column.is-offset-9-touch { - margin-left: 75%; } - .column.is-10-touch { - flex: none; - width: 83.3333333333%; } - .column.is-offset-10-touch { - margin-left: 83.3333333333%; } - .column.is-11-touch { - flex: none; - width: 91.6666666667%; } - .column.is-offset-11-touch { - margin-left: 91.6666666667%; } - .column.is-12-touch { - flex: none; - width: 100%; } - .column.is-offset-12-touch { - margin-left: 100%; } } - @media screen and (min-width: 1056px) { - .column.is-narrow-desktop { - flex: none; } - .column.is-full-desktop { - flex: none; - width: 100%; } - .column.is-three-quarters-desktop { - flex: none; - width: 75%; } - .column.is-two-thirds-desktop { - flex: none; - width: 66.6666%; } - .column.is-half-desktop { - flex: none; - width: 50%; } - .column.is-one-third-desktop { - flex: none; - width: 33.3333%; } - .column.is-one-quarter-desktop { - flex: none; - width: 25%; } - .column.is-one-fifth-desktop { - flex: none; - width: 20%; } - .column.is-two-fifths-desktop { - flex: none; - width: 40%; } - .column.is-three-fifths-desktop { - flex: none; - width: 60%; } - .column.is-four-fifths-desktop { - flex: none; - width: 80%; } - .column.is-offset-three-quarters-desktop { - margin-left: 75%; } - .column.is-offset-two-thirds-desktop { - margin-left: 66.6666%; } - .column.is-offset-half-desktop { - margin-left: 50%; } - .column.is-offset-one-third-desktop { - margin-left: 33.3333%; } - .column.is-offset-one-quarter-desktop { - margin-left: 25%; } - .column.is-offset-one-fifth-desktop { - margin-left: 20%; } - .column.is-offset-two-fifths-desktop { - margin-left: 40%; } - .column.is-offset-three-fifths-desktop { - margin-left: 60%; } - .column.is-offset-four-fifths-desktop { - margin-left: 80%; } - .column.is-0-desktop { - flex: none; - width: 0%; } - .column.is-offset-0-desktop { - margin-left: 0%; } - .column.is-1-desktop { - flex: none; - width: 8.3333333333%; } - .column.is-offset-1-desktop { - margin-left: 8.3333333333%; } - .column.is-2-desktop { - flex: none; - width: 16.6666666667%; } - .column.is-offset-2-desktop { - margin-left: 16.6666666667%; } - .column.is-3-desktop { - flex: none; - width: 25%; } - .column.is-offset-3-desktop { - margin-left: 25%; } - .column.is-4-desktop { - flex: none; - width: 33.3333333333%; } - .column.is-offset-4-desktop { - margin-left: 33.3333333333%; } - .column.is-5-desktop { - flex: none; - width: 41.6666666667%; } - .column.is-offset-5-desktop { - margin-left: 41.6666666667%; } - .column.is-6-desktop { - flex: none; - width: 50%; } - .column.is-offset-6-desktop { - margin-left: 50%; } - .column.is-7-desktop { - flex: none; - width: 58.3333333333%; } - .column.is-offset-7-desktop { - margin-left: 58.3333333333%; } - .column.is-8-desktop { - flex: none; - width: 66.6666666667%; } - .column.is-offset-8-desktop { - margin-left: 66.6666666667%; } - .column.is-9-desktop { - flex: none; - width: 75%; } - .column.is-offset-9-desktop { - margin-left: 75%; } - .column.is-10-desktop { - flex: none; - width: 83.3333333333%; } - .column.is-offset-10-desktop { - margin-left: 83.3333333333%; } - .column.is-11-desktop { - flex: none; - width: 91.6666666667%; } - .column.is-offset-11-desktop { - margin-left: 91.6666666667%; } - .column.is-12-desktop { - flex: none; - width: 100%; } - .column.is-offset-12-desktop { - margin-left: 100%; } } - @media screen and (min-width: 1216px) { - .column.is-narrow-widescreen { - flex: none; } - .column.is-full-widescreen { - flex: none; - width: 100%; } - .column.is-three-quarters-widescreen { - flex: none; - width: 75%; } - .column.is-two-thirds-widescreen { - flex: none; - width: 66.6666%; } - .column.is-half-widescreen { - flex: none; - width: 50%; } - .column.is-one-third-widescreen { - flex: none; - width: 33.3333%; } - .column.is-one-quarter-widescreen { - flex: none; - width: 25%; } - .column.is-one-fifth-widescreen { - flex: none; - width: 20%; } - .column.is-two-fifths-widescreen { - flex: none; - width: 40%; } - .column.is-three-fifths-widescreen { - flex: none; - width: 60%; } - .column.is-four-fifths-widescreen { - flex: none; - width: 80%; } - .column.is-offset-three-quarters-widescreen { - margin-left: 75%; } - .column.is-offset-two-thirds-widescreen { - margin-left: 66.6666%; } - .column.is-offset-half-widescreen { - margin-left: 50%; } - .column.is-offset-one-third-widescreen { - margin-left: 33.3333%; } - .column.is-offset-one-quarter-widescreen { - margin-left: 25%; } - .column.is-offset-one-fifth-widescreen { - margin-left: 20%; } - .column.is-offset-two-fifths-widescreen { - margin-left: 40%; } - .column.is-offset-three-fifths-widescreen { - margin-left: 60%; } - .column.is-offset-four-fifths-widescreen { - margin-left: 80%; } - .column.is-0-widescreen { - flex: none; - width: 0%; } - .column.is-offset-0-widescreen { - margin-left: 0%; } - .column.is-1-widescreen { - flex: none; - width: 8.3333333333%; } - .column.is-offset-1-widescreen { - margin-left: 8.3333333333%; } - .column.is-2-widescreen { - flex: none; - width: 16.6666666667%; } - .column.is-offset-2-widescreen { - margin-left: 16.6666666667%; } - .column.is-3-widescreen { - flex: none; - width: 25%; } - .column.is-offset-3-widescreen { - margin-left: 25%; } - .column.is-4-widescreen { - flex: none; - width: 33.3333333333%; } - .column.is-offset-4-widescreen { - margin-left: 33.3333333333%; } - .column.is-5-widescreen { - flex: none; - width: 41.6666666667%; } - .column.is-offset-5-widescreen { - margin-left: 41.6666666667%; } - .column.is-6-widescreen { - flex: none; - width: 50%; } - .column.is-offset-6-widescreen { - margin-left: 50%; } - .column.is-7-widescreen { - flex: none; - width: 58.3333333333%; } - .column.is-offset-7-widescreen { - margin-left: 58.3333333333%; } - .column.is-8-widescreen { - flex: none; - width: 66.6666666667%; } - .column.is-offset-8-widescreen { - margin-left: 66.6666666667%; } - .column.is-9-widescreen { - flex: none; - width: 75%; } - .column.is-offset-9-widescreen { - margin-left: 75%; } - .column.is-10-widescreen { - flex: none; - width: 83.3333333333%; } - .column.is-offset-10-widescreen { - margin-left: 83.3333333333%; } - .column.is-11-widescreen { - flex: none; - width: 91.6666666667%; } - .column.is-offset-11-widescreen { - margin-left: 91.6666666667%; } - .column.is-12-widescreen { - flex: none; - width: 100%; } - .column.is-offset-12-widescreen { - margin-left: 100%; } } - @media screen and (min-width: 1408px) { - .column.is-narrow-fullhd { - flex: none; } - .column.is-full-fullhd { - flex: none; - width: 100%; } - .column.is-three-quarters-fullhd { - flex: none; - width: 75%; } - .column.is-two-thirds-fullhd { - flex: none; - width: 66.6666%; } - .column.is-half-fullhd { - flex: none; - width: 50%; } - .column.is-one-third-fullhd { - flex: none; - width: 33.3333%; } - .column.is-one-quarter-fullhd { - flex: none; - width: 25%; } - .column.is-one-fifth-fullhd { - flex: none; - width: 20%; } - .column.is-two-fifths-fullhd { - flex: none; - width: 40%; } - .column.is-three-fifths-fullhd { - flex: none; - width: 60%; } - .column.is-four-fifths-fullhd { - flex: none; - width: 80%; } - .column.is-offset-three-quarters-fullhd { - margin-left: 75%; } - .column.is-offset-two-thirds-fullhd { - margin-left: 66.6666%; } - .column.is-offset-half-fullhd { - margin-left: 50%; } - .column.is-offset-one-third-fullhd { - margin-left: 33.3333%; } - .column.is-offset-one-quarter-fullhd { - margin-left: 25%; } - .column.is-offset-one-fifth-fullhd { - margin-left: 20%; } - .column.is-offset-two-fifths-fullhd { - margin-left: 40%; } - .column.is-offset-three-fifths-fullhd { - margin-left: 60%; } - .column.is-offset-four-fifths-fullhd { - margin-left: 80%; } - .column.is-0-fullhd { - flex: none; - width: 0%; } - .column.is-offset-0-fullhd { - margin-left: 0%; } - .column.is-1-fullhd { - flex: none; - width: 8.3333333333%; } - .column.is-offset-1-fullhd { - margin-left: 8.3333333333%; } - .column.is-2-fullhd { - flex: none; - width: 16.6666666667%; } - .column.is-offset-2-fullhd { - margin-left: 16.6666666667%; } - .column.is-3-fullhd { - flex: none; - width: 25%; } - .column.is-offset-3-fullhd { - margin-left: 25%; } - .column.is-4-fullhd { - flex: none; - width: 33.3333333333%; } - .column.is-offset-4-fullhd { - margin-left: 33.3333333333%; } - .column.is-5-fullhd { - flex: none; - width: 41.6666666667%; } - .column.is-offset-5-fullhd { - margin-left: 41.6666666667%; } - .column.is-6-fullhd { - flex: none; - width: 50%; } - .column.is-offset-6-fullhd { - margin-left: 50%; } - .column.is-7-fullhd { - flex: none; - width: 58.3333333333%; } - .column.is-offset-7-fullhd { - margin-left: 58.3333333333%; } - .column.is-8-fullhd { - flex: none; - width: 66.6666666667%; } - .column.is-offset-8-fullhd { - margin-left: 66.6666666667%; } - .column.is-9-fullhd { - flex: none; - width: 75%; } - .column.is-offset-9-fullhd { - margin-left: 75%; } - .column.is-10-fullhd { - flex: none; - width: 83.3333333333%; } - .column.is-offset-10-fullhd { - margin-left: 83.3333333333%; } - .column.is-11-fullhd { - flex: none; - width: 91.6666666667%; } - .column.is-offset-11-fullhd { - margin-left: 91.6666666667%; } - .column.is-12-fullhd { - flex: none; - width: 100%; } - .column.is-offset-12-fullhd { - margin-left: 100%; } } -.columns { - margin-left: -0.75rem; - margin-right: -0.75rem; - margin-top: -0.75rem; } - .columns:last-child { - margin-bottom: -0.75rem; } - .columns:not(:last-child) { - margin-bottom: calc(1.5rem - 0.75rem); } - .columns.is-centered { - justify-content: center; } - .columns.is-gapless { - margin-left: 0; - margin-right: 0; - margin-top: 0; } - .columns.is-gapless > .column { - margin: 0; - padding: 0 !important; } - .columns.is-gapless:not(:last-child) { - margin-bottom: 1.5rem; } - .columns.is-gapless:last-child { - margin-bottom: 0; } - .columns.is-mobile { - display: flex; } - .columns.is-multiline { - flex-wrap: wrap; } - .columns.is-vcentered { - align-items: center; } - @media screen and (min-width: 769px), print { - .columns:not(.is-desktop) { - display: flex; } } - @media screen and (min-width: 1056px) { - .columns.is-desktop { - display: flex; } } -.columns.is-variable { - --columnGap: 0.75rem; - margin-left: calc(-1 * var(--columnGap)); - margin-right: calc(-1 * var(--columnGap)); } - .columns.is-variable .column { - padding-left: var(--columnGap); - padding-right: var(--columnGap); } - .columns.is-variable.is-0 { - --columnGap: 0rem; } - @media screen and (max-width: 768px) { - .columns.is-variable.is-0-mobile { - --columnGap: 0rem; } } - @media screen and (min-width: 769px), print { - .columns.is-variable.is-0-tablet { - --columnGap: 0rem; } } - @media screen and (min-width: 769px) and (max-width: 1055px) { - .columns.is-variable.is-0-tablet-only { - --columnGap: 0rem; } } - @media screen and (max-width: 1055px) { - .columns.is-variable.is-0-touch { - --columnGap: 0rem; } } - @media screen and (min-width: 1056px) { - .columns.is-variable.is-0-desktop { - --columnGap: 0rem; } } - @media screen and (min-width: 1056px) and (max-width: 1215px) { - .columns.is-variable.is-0-desktop-only { - --columnGap: 0rem; } } - @media screen and (min-width: 1216px) { - .columns.is-variable.is-0-widescreen { - --columnGap: 0rem; } } - @media screen and (min-width: 1216px) and (max-width: 1407px) { - .columns.is-variable.is-0-widescreen-only { - --columnGap: 0rem; } } - @media screen and (min-width: 1408px) { - .columns.is-variable.is-0-fullhd { - --columnGap: 0rem; } } - .columns.is-variable.is-1 { - --columnGap: 0.25rem; } - @media screen and (max-width: 768px) { - .columns.is-variable.is-1-mobile { - --columnGap: 0.25rem; } } - @media screen and (min-width: 769px), print { - .columns.is-variable.is-1-tablet { - --columnGap: 0.25rem; } } - @media screen and (min-width: 769px) and (max-width: 1055px) { - .columns.is-variable.is-1-tablet-only { - --columnGap: 0.25rem; } } - @media screen and (max-width: 1055px) { - .columns.is-variable.is-1-touch { - --columnGap: 0.25rem; } } - @media screen and (min-width: 1056px) { - .columns.is-variable.is-1-desktop { - --columnGap: 0.25rem; } } - @media screen and (min-width: 1056px) and (max-width: 1215px) { - .columns.is-variable.is-1-desktop-only { - --columnGap: 0.25rem; } } - @media screen and (min-width: 1216px) { - .columns.is-variable.is-1-widescreen { - --columnGap: 0.25rem; } } - @media screen and (min-width: 1216px) and (max-width: 1407px) { - .columns.is-variable.is-1-widescreen-only { - --columnGap: 0.25rem; } } - @media screen and (min-width: 1408px) { - .columns.is-variable.is-1-fullhd { - --columnGap: 0.25rem; } } - .columns.is-variable.is-2 { - --columnGap: 0.5rem; } - @media screen and (max-width: 768px) { - .columns.is-variable.is-2-mobile { - --columnGap: 0.5rem; } } - @media screen and (min-width: 769px), print { - .columns.is-variable.is-2-tablet { - --columnGap: 0.5rem; } } - @media screen and (min-width: 769px) and (max-width: 1055px) { - .columns.is-variable.is-2-tablet-only { - --columnGap: 0.5rem; } } - @media screen and (max-width: 1055px) { - .columns.is-variable.is-2-touch { - --columnGap: 0.5rem; } } - @media screen and (min-width: 1056px) { - .columns.is-variable.is-2-desktop { - --columnGap: 0.5rem; } } - @media screen and (min-width: 1056px) and (max-width: 1215px) { - .columns.is-variable.is-2-desktop-only { - --columnGap: 0.5rem; } } - @media screen and (min-width: 1216px) { - .columns.is-variable.is-2-widescreen { - --columnGap: 0.5rem; } } - @media screen and (min-width: 1216px) and (max-width: 1407px) { - .columns.is-variable.is-2-widescreen-only { - --columnGap: 0.5rem; } } - @media screen and (min-width: 1408px) { - .columns.is-variable.is-2-fullhd { - --columnGap: 0.5rem; } } - .columns.is-variable.is-3 { - --columnGap: 0.75rem; } - @media screen and (max-width: 768px) { - .columns.is-variable.is-3-mobile { - --columnGap: 0.75rem; } } - @media screen and (min-width: 769px), print { - .columns.is-variable.is-3-tablet { - --columnGap: 0.75rem; } } - @media screen and (min-width: 769px) and (max-width: 1055px) { - .columns.is-variable.is-3-tablet-only { - --columnGap: 0.75rem; } } - @media screen and (max-width: 1055px) { - .columns.is-variable.is-3-touch { - --columnGap: 0.75rem; } } - @media screen and (min-width: 1056px) { - .columns.is-variable.is-3-desktop { - --columnGap: 0.75rem; } } - @media screen and (min-width: 1056px) and (max-width: 1215px) { - .columns.is-variable.is-3-desktop-only { - --columnGap: 0.75rem; } } - @media screen and (min-width: 1216px) { - .columns.is-variable.is-3-widescreen { - --columnGap: 0.75rem; } } - @media screen and (min-width: 1216px) and (max-width: 1407px) { - .columns.is-variable.is-3-widescreen-only { - --columnGap: 0.75rem; } } - @media screen and (min-width: 1408px) { - .columns.is-variable.is-3-fullhd { - --columnGap: 0.75rem; } } - .columns.is-variable.is-4 { - --columnGap: 1rem; } - @media screen and (max-width: 768px) { - .columns.is-variable.is-4-mobile { - --columnGap: 1rem; } } - @media screen and (min-width: 769px), print { - .columns.is-variable.is-4-tablet { - --columnGap: 1rem; } } - @media screen and (min-width: 769px) and (max-width: 1055px) { - .columns.is-variable.is-4-tablet-only { - --columnGap: 1rem; } } - @media screen and (max-width: 1055px) { - .columns.is-variable.is-4-touch { - --columnGap: 1rem; } } - @media screen and (min-width: 1056px) { - .columns.is-variable.is-4-desktop { - --columnGap: 1rem; } } - @media screen and (min-width: 1056px) and (max-width: 1215px) { - .columns.is-variable.is-4-desktop-only { - --columnGap: 1rem; } } - @media screen and (min-width: 1216px) { - .columns.is-variable.is-4-widescreen { - --columnGap: 1rem; } } - @media screen and (min-width: 1216px) and (max-width: 1407px) { - .columns.is-variable.is-4-widescreen-only { - --columnGap: 1rem; } } - @media screen and (min-width: 1408px) { - .columns.is-variable.is-4-fullhd { - --columnGap: 1rem; } } - .columns.is-variable.is-5 { - --columnGap: 1.25rem; } - @media screen and (max-width: 768px) { - .columns.is-variable.is-5-mobile { - --columnGap: 1.25rem; } } - @media screen and (min-width: 769px), print { - .columns.is-variable.is-5-tablet { - --columnGap: 1.25rem; } } - @media screen and (min-width: 769px) and (max-width: 1055px) { - .columns.is-variable.is-5-tablet-only { - --columnGap: 1.25rem; } } - @media screen and (max-width: 1055px) { - .columns.is-variable.is-5-touch { - --columnGap: 1.25rem; } } - @media screen and (min-width: 1056px) { - .columns.is-variable.is-5-desktop { - --columnGap: 1.25rem; } } - @media screen and (min-width: 1056px) and (max-width: 1215px) { - .columns.is-variable.is-5-desktop-only { - --columnGap: 1.25rem; } } - @media screen and (min-width: 1216px) { - .columns.is-variable.is-5-widescreen { - --columnGap: 1.25rem; } } - @media screen and (min-width: 1216px) and (max-width: 1407px) { - .columns.is-variable.is-5-widescreen-only { - --columnGap: 1.25rem; } } - @media screen and (min-width: 1408px) { - .columns.is-variable.is-5-fullhd { - --columnGap: 1.25rem; } } - .columns.is-variable.is-6 { - --columnGap: 1.5rem; } - @media screen and (max-width: 768px) { - .columns.is-variable.is-6-mobile { - --columnGap: 1.5rem; } } - @media screen and (min-width: 769px), print { - .columns.is-variable.is-6-tablet { - --columnGap: 1.5rem; } } - @media screen and (min-width: 769px) and (max-width: 1055px) { - .columns.is-variable.is-6-tablet-only { - --columnGap: 1.5rem; } } - @media screen and (max-width: 1055px) { - .columns.is-variable.is-6-touch { - --columnGap: 1.5rem; } } - @media screen and (min-width: 1056px) { - .columns.is-variable.is-6-desktop { - --columnGap: 1.5rem; } } - @media screen and (min-width: 1056px) and (max-width: 1215px) { - .columns.is-variable.is-6-desktop-only { - --columnGap: 1.5rem; } } - @media screen and (min-width: 1216px) { - .columns.is-variable.is-6-widescreen { - --columnGap: 1.5rem; } } - @media screen and (min-width: 1216px) and (max-width: 1407px) { - .columns.is-variable.is-6-widescreen-only { - --columnGap: 1.5rem; } } - @media screen and (min-width: 1408px) { - .columns.is-variable.is-6-fullhd { - --columnGap: 1.5rem; } } - .columns.is-variable.is-7 { - --columnGap: 1.75rem; } - @media screen and (max-width: 768px) { - .columns.is-variable.is-7-mobile { - --columnGap: 1.75rem; } } - @media screen and (min-width: 769px), print { - .columns.is-variable.is-7-tablet { - --columnGap: 1.75rem; } } - @media screen and (min-width: 769px) and (max-width: 1055px) { - .columns.is-variable.is-7-tablet-only { - --columnGap: 1.75rem; } } - @media screen and (max-width: 1055px) { - .columns.is-variable.is-7-touch { - --columnGap: 1.75rem; } } - @media screen and (min-width: 1056px) { - .columns.is-variable.is-7-desktop { - --columnGap: 1.75rem; } } - @media screen and (min-width: 1056px) and (max-width: 1215px) { - .columns.is-variable.is-7-desktop-only { - --columnGap: 1.75rem; } } - @media screen and (min-width: 1216px) { - .columns.is-variable.is-7-widescreen { - --columnGap: 1.75rem; } } - @media screen and (min-width: 1216px) and (max-width: 1407px) { - .columns.is-variable.is-7-widescreen-only { - --columnGap: 1.75rem; } } - @media screen and (min-width: 1408px) { - .columns.is-variable.is-7-fullhd { - --columnGap: 1.75rem; } } - .columns.is-variable.is-8 { - --columnGap: 2rem; } - @media screen and (max-width: 768px) { - .columns.is-variable.is-8-mobile { - --columnGap: 2rem; } } - @media screen and (min-width: 769px), print { - .columns.is-variable.is-8-tablet { - --columnGap: 2rem; } } - @media screen and (min-width: 769px) and (max-width: 1055px) { - .columns.is-variable.is-8-tablet-only { - --columnGap: 2rem; } } - @media screen and (max-width: 1055px) { - .columns.is-variable.is-8-touch { - --columnGap: 2rem; } } - @media screen and (min-width: 1056px) { - .columns.is-variable.is-8-desktop { - --columnGap: 2rem; } } - @media screen and (min-width: 1056px) and (max-width: 1215px) { - .columns.is-variable.is-8-desktop-only { - --columnGap: 2rem; } } - @media screen and (min-width: 1216px) { - .columns.is-variable.is-8-widescreen { - --columnGap: 2rem; } } - @media screen and (min-width: 1216px) and (max-width: 1407px) { - .columns.is-variable.is-8-widescreen-only { - --columnGap: 2rem; } } - @media screen and (min-width: 1408px) { - .columns.is-variable.is-8-fullhd { - --columnGap: 2rem; } } -.tile { - align-items: stretch; - display: block; - flex-basis: 0; - flex-grow: 1; - flex-shrink: 1; - min-height: min-content; } - .tile.is-ancestor { - margin-left: -0.75rem; - margin-right: -0.75rem; - margin-top: -0.75rem; } - .tile.is-ancestor:last-child { - margin-bottom: -0.75rem; } - .tile.is-ancestor:not(:last-child) { - margin-bottom: 0.75rem; } - .tile.is-child { - margin: 0 !important; } - .tile.is-parent { - padding: 0.75rem; } - .tile.is-vertical { - flex-direction: column; } - .tile.is-vertical > .tile.is-child:not(:last-child) { - margin-bottom: 1.5rem !important; } - @media screen and (min-width: 769px), print { - .tile:not(.is-child) { - display: flex; } - .tile.is-1 { - flex: none; - width: 8.3333333333%; } - .tile.is-2 { - flex: none; - width: 16.6666666667%; } - .tile.is-3 { - flex: none; - width: 25%; } - .tile.is-4 { - flex: none; - width: 33.3333333333%; } - .tile.is-5 { - flex: none; - width: 41.6666666667%; } - .tile.is-6 { - flex: none; - width: 50%; } - .tile.is-7 { - flex: none; - width: 58.3333333333%; } - .tile.is-8 { - flex: none; - width: 66.6666666667%; } - .tile.is-9 { - flex: none; - width: 75%; } - .tile.is-10 { - flex: none; - width: 83.3333333333%; } - .tile.is-11 { - flex: none; - width: 91.6666666667%; } - .tile.is-12 { - flex: none; - width: 100%; } } -.hero { - align-items: stretch; - display: flex; - flex-direction: column; - justify-content: space-between; } - .hero .navbar { - background: none; } - .hero .tabs ul { - border-bottom: none; } - .hero.is-white { - background-color: white; - color: #0a0a0a; } - .hero.is-white a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), - .hero.is-white strong { - color: inherit; } - .hero.is-white .title { - color: #0a0a0a; } - .hero.is-white .subtitle { - color: rgba(10, 10, 10, 0.9); } - .hero.is-white .subtitle a:not(.button), - .hero.is-white .subtitle strong { - color: #0a0a0a; } - @media screen and (max-width: 1055px) { - .hero.is-white .navbar-menu { - background-color: white; } } - .hero.is-white .navbar-item, - .hero.is-white .navbar-link { - color: rgba(10, 10, 10, 0.7); } - .hero.is-white a.navbar-item:hover, .hero.is-white a.navbar-item.is-active, - .hero.is-white .navbar-link:hover, - .hero.is-white .navbar-link.is-active { - background-color: #f2f2f2; - color: #0a0a0a; } - .hero.is-white .tabs a { - color: #0a0a0a; - opacity: 0.9; } - .hero.is-white .tabs a:hover { - opacity: 1; } - .hero.is-white .tabs li.is-active a { - opacity: 1; } - .hero.is-white .tabs.is-boxed a, .hero.is-white .tabs.is-toggle a { - color: #0a0a0a; } - .hero.is-white .tabs.is-boxed a:hover, .hero.is-white .tabs.is-toggle a:hover { - background-color: rgba(10, 10, 10, 0.1); } - .hero.is-white .tabs.is-boxed li.is-active a, .hero.is-white .tabs.is-boxed li.is-active a:hover, .hero.is-white .tabs.is-toggle li.is-active a, .hero.is-white .tabs.is-toggle li.is-active a:hover { - background-color: #0a0a0a; - border-color: #0a0a0a; - color: white; } - .hero.is-white.is-bold { - background-image: linear-gradient(141deg, #e8e3e4 0%, white 71%, white 100%); } - @media screen and (max-width: 768px) { - .hero.is-white.is-bold .navbar-menu { - background-image: linear-gradient(141deg, #e8e3e4 0%, white 71%, white 100%); } } - .hero.is-black { - background-color: #0a0a0a; - color: white; } - .hero.is-black a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), - .hero.is-black strong { - color: inherit; } - .hero.is-black .title { - color: white; } - .hero.is-black .subtitle { - color: rgba(255, 255, 255, 0.9); } - .hero.is-black .subtitle a:not(.button), - .hero.is-black .subtitle strong { - color: white; } - @media screen and (max-width: 1055px) { - .hero.is-black .navbar-menu { - background-color: #0a0a0a; } } - .hero.is-black .navbar-item, - .hero.is-black .navbar-link { - color: rgba(255, 255, 255, 0.7); } - .hero.is-black a.navbar-item:hover, .hero.is-black a.navbar-item.is-active, - .hero.is-black .navbar-link:hover, - .hero.is-black .navbar-link.is-active { - background-color: black; - color: white; } - .hero.is-black .tabs a { - color: white; - opacity: 0.9; } - .hero.is-black .tabs a:hover { - opacity: 1; } - .hero.is-black .tabs li.is-active a { - opacity: 1; } - .hero.is-black .tabs.is-boxed a, .hero.is-black .tabs.is-toggle a { - color: white; } - .hero.is-black .tabs.is-boxed a:hover, .hero.is-black .tabs.is-toggle a:hover { - background-color: rgba(10, 10, 10, 0.1); } - .hero.is-black .tabs.is-boxed li.is-active a, .hero.is-black .tabs.is-boxed li.is-active a:hover, .hero.is-black .tabs.is-toggle li.is-active a, .hero.is-black .tabs.is-toggle li.is-active a:hover { - background-color: white; - border-color: white; - color: #0a0a0a; } - .hero.is-black.is-bold { - background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } - @media screen and (max-width: 768px) { - .hero.is-black.is-bold .navbar-menu { - background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } } - .hero.is-light { - background-color: whitesmoke; - color: #363636; } - .hero.is-light a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), - .hero.is-light strong { - color: inherit; } - .hero.is-light .title { - color: #363636; } - .hero.is-light .subtitle { - color: rgba(54, 54, 54, 0.9); } - .hero.is-light .subtitle a:not(.button), - .hero.is-light .subtitle strong { - color: #363636; } - @media screen and (max-width: 1055px) { - .hero.is-light .navbar-menu { - background-color: whitesmoke; } } - .hero.is-light .navbar-item, - .hero.is-light .navbar-link { - color: rgba(54, 54, 54, 0.7); } - .hero.is-light a.navbar-item:hover, .hero.is-light a.navbar-item.is-active, - .hero.is-light .navbar-link:hover, - .hero.is-light .navbar-link.is-active { - background-color: #e8e8e8; - color: #363636; } - .hero.is-light .tabs a { - color: #363636; - opacity: 0.9; } - .hero.is-light .tabs a:hover { - opacity: 1; } - .hero.is-light .tabs li.is-active a { - opacity: 1; } - .hero.is-light .tabs.is-boxed a, .hero.is-light .tabs.is-toggle a { - color: #363636; } - .hero.is-light .tabs.is-boxed a:hover, .hero.is-light .tabs.is-toggle a:hover { - background-color: rgba(10, 10, 10, 0.1); } - .hero.is-light .tabs.is-boxed li.is-active a, .hero.is-light .tabs.is-boxed li.is-active a:hover, .hero.is-light .tabs.is-toggle li.is-active a, .hero.is-light .tabs.is-toggle li.is-active a:hover { - background-color: #363636; - border-color: #363636; - color: whitesmoke; } - .hero.is-light.is-bold { - background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); } - @media screen and (max-width: 768px) { - .hero.is-light.is-bold .navbar-menu { - background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); } } - .hero.is-dark, .content kbd.hero { - background-color: #363636; - color: whitesmoke; } - .hero.is-dark a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), .content kbd.hero a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), - .hero.is-dark strong, - .content kbd.hero strong { - color: inherit; } - .hero.is-dark .title, .content kbd.hero .title { - color: whitesmoke; } - .hero.is-dark .subtitle, .content kbd.hero .subtitle { - color: rgba(245, 245, 245, 0.9); } - .hero.is-dark .subtitle a:not(.button), .content kbd.hero .subtitle a:not(.button), - .hero.is-dark .subtitle strong, - .content kbd.hero .subtitle strong { - color: whitesmoke; } - @media screen and (max-width: 1055px) { - .hero.is-dark .navbar-menu, .content kbd.hero .navbar-menu { - background-color: #363636; } } - .hero.is-dark .navbar-item, .content kbd.hero .navbar-item, - .hero.is-dark .navbar-link, - .content kbd.hero .navbar-link { - color: rgba(245, 245, 245, 0.7); } - .hero.is-dark a.navbar-item:hover, .content kbd.hero a.navbar-item:hover, .hero.is-dark a.navbar-item.is-active, .content kbd.hero a.navbar-item.is-active, - .hero.is-dark .navbar-link:hover, - .content kbd.hero .navbar-link:hover, - .hero.is-dark .navbar-link.is-active, - .content kbd.hero .navbar-link.is-active { - background-color: #292929; - color: whitesmoke; } - .hero.is-dark .tabs a, .content kbd.hero .tabs a { - color: whitesmoke; - opacity: 0.9; } - .hero.is-dark .tabs a:hover, .content kbd.hero .tabs a:hover { - opacity: 1; } - .hero.is-dark .tabs li.is-active a, .content kbd.hero .tabs li.is-active a { - opacity: 1; } - .hero.is-dark .tabs.is-boxed a, .content kbd.hero .tabs.is-boxed a, .hero.is-dark .tabs.is-toggle a, .content kbd.hero .tabs.is-toggle a { - color: whitesmoke; } - .hero.is-dark .tabs.is-boxed a:hover, .content kbd.hero .tabs.is-boxed a:hover, .hero.is-dark .tabs.is-toggle a:hover, .content kbd.hero .tabs.is-toggle a:hover { - background-color: rgba(10, 10, 10, 0.1); } - .hero.is-dark .tabs.is-boxed li.is-active a, .content kbd.hero .tabs.is-boxed li.is-active a, .hero.is-dark .tabs.is-boxed li.is-active a:hover, .hero.is-dark .tabs.is-toggle li.is-active a, .content kbd.hero .tabs.is-toggle li.is-active a, .hero.is-dark .tabs.is-toggle li.is-active a:hover { - background-color: whitesmoke; - border-color: whitesmoke; - color: #363636; } - .hero.is-dark.is-bold, .content kbd.hero.is-bold { - background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); } - @media screen and (max-width: 768px) { - .hero.is-dark.is-bold .navbar-menu, .content kbd.hero.is-bold .navbar-menu { - background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); } } - .hero.is-primary, .docstring > section > a.hero.docs-sourcelink { - background-color: #4eb5de; - color: #fff; } - .hero.is-primary a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), .docstring > section > a.hero.docs-sourcelink a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), - .hero.is-primary strong, - .docstring > section > a.hero.docs-sourcelink strong { - color: inherit; } - .hero.is-primary .title, .docstring > section > a.hero.docs-sourcelink .title { - color: #fff; } - .hero.is-primary .subtitle, .docstring > section > a.hero.docs-sourcelink .subtitle { - color: rgba(255, 255, 255, 0.9); } - .hero.is-primary .subtitle a:not(.button), .docstring > section > a.hero.docs-sourcelink .subtitle a:not(.button), - .hero.is-primary .subtitle strong, - .docstring > section > a.hero.docs-sourcelink .subtitle strong { - color: #fff; } - @media screen and (max-width: 1055px) { - .hero.is-primary .navbar-menu, .docstring > section > a.hero.docs-sourcelink .navbar-menu { - background-color: #4eb5de; } } - .hero.is-primary .navbar-item, .docstring > section > a.hero.docs-sourcelink .navbar-item, - .hero.is-primary .navbar-link, - .docstring > section > a.hero.docs-sourcelink .navbar-link { - color: rgba(255, 255, 255, 0.7); } - .hero.is-primary a.navbar-item:hover, .docstring > section > a.hero.docs-sourcelink a.navbar-item:hover, .hero.is-primary a.navbar-item.is-active, .docstring > section > a.hero.docs-sourcelink a.navbar-item.is-active, - .hero.is-primary .navbar-link:hover, - .docstring > section > a.hero.docs-sourcelink .navbar-link:hover, - .hero.is-primary .navbar-link.is-active, - .docstring > section > a.hero.docs-sourcelink .navbar-link.is-active { - background-color: #39acda; - color: #fff; } - .hero.is-primary .tabs a, .docstring > section > a.hero.docs-sourcelink .tabs a { - color: #fff; - opacity: 0.9; } - .hero.is-primary .tabs a:hover, .docstring > section > a.hero.docs-sourcelink .tabs a:hover { - opacity: 1; } - .hero.is-primary .tabs li.is-active a, .docstring > section > a.hero.docs-sourcelink .tabs li.is-active a { - opacity: 1; } - .hero.is-primary .tabs.is-boxed a, .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a, .hero.is-primary .tabs.is-toggle a, .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a { - color: #fff; } - .hero.is-primary .tabs.is-boxed a:hover, .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a:hover, .hero.is-primary .tabs.is-toggle a:hover, .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a:hover { - background-color: rgba(10, 10, 10, 0.1); } - .hero.is-primary .tabs.is-boxed li.is-active a, .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed li.is-active a, .hero.is-primary .tabs.is-boxed li.is-active a:hover, .hero.is-primary .tabs.is-toggle li.is-active a, .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle li.is-active a, .hero.is-primary .tabs.is-toggle li.is-active a:hover { - background-color: #fff; - border-color: #fff; - color: #4eb5de; } - .hero.is-primary.is-bold, .docstring > section > a.hero.is-bold.docs-sourcelink { - background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); } - @media screen and (max-width: 768px) { - .hero.is-primary.is-bold .navbar-menu, .docstring > section > a.hero.is-bold.docs-sourcelink .navbar-menu { - background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); } } - .hero.is-link { - background-color: #2e63b8; - color: #fff; } - .hero.is-link a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), - .hero.is-link strong { - color: inherit; } - .hero.is-link .title { - color: #fff; } - .hero.is-link .subtitle { - color: rgba(255, 255, 255, 0.9); } - .hero.is-link .subtitle a:not(.button), - .hero.is-link .subtitle strong { - color: #fff; } - @media screen and (max-width: 1055px) { - .hero.is-link .navbar-menu { - background-color: #2e63b8; } } - .hero.is-link .navbar-item, - .hero.is-link .navbar-link { - color: rgba(255, 255, 255, 0.7); } - .hero.is-link a.navbar-item:hover, .hero.is-link a.navbar-item.is-active, - .hero.is-link .navbar-link:hover, - .hero.is-link .navbar-link.is-active { - background-color: #2958a4; - color: #fff; } - .hero.is-link .tabs a { - color: #fff; - opacity: 0.9; } - .hero.is-link .tabs a:hover { - opacity: 1; } - .hero.is-link .tabs li.is-active a { - opacity: 1; } - .hero.is-link .tabs.is-boxed a, .hero.is-link .tabs.is-toggle a { - color: #fff; } - .hero.is-link .tabs.is-boxed a:hover, .hero.is-link .tabs.is-toggle a:hover { - background-color: rgba(10, 10, 10, 0.1); } - .hero.is-link .tabs.is-boxed li.is-active a, .hero.is-link .tabs.is-boxed li.is-active a:hover, .hero.is-link .tabs.is-toggle li.is-active a, .hero.is-link .tabs.is-toggle li.is-active a:hover { - background-color: #fff; - border-color: #fff; - color: #2e63b8; } - .hero.is-link.is-bold { - background-image: linear-gradient(141deg, #1b6098 0%, #2e63b8 71%, #2d51d2 100%); } - @media screen and (max-width: 768px) { - .hero.is-link.is-bold .navbar-menu { - background-image: linear-gradient(141deg, #1b6098 0%, #2e63b8 71%, #2d51d2 100%); } } - .hero.is-info { - background-color: #209cee; - color: #fff; } - .hero.is-info a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), - .hero.is-info strong { - color: inherit; } - .hero.is-info .title { - color: #fff; } - .hero.is-info .subtitle { - color: rgba(255, 255, 255, 0.9); } - .hero.is-info .subtitle a:not(.button), - .hero.is-info .subtitle strong { - color: #fff; } - @media screen and (max-width: 1055px) { - .hero.is-info .navbar-menu { - background-color: #209cee; } } - .hero.is-info .navbar-item, - .hero.is-info .navbar-link { - color: rgba(255, 255, 255, 0.7); } - .hero.is-info a.navbar-item:hover, .hero.is-info a.navbar-item.is-active, - .hero.is-info .navbar-link:hover, - .hero.is-info .navbar-link.is-active { - background-color: #1190e3; - color: #fff; } - .hero.is-info .tabs a { - color: #fff; - opacity: 0.9; } - .hero.is-info .tabs a:hover { - opacity: 1; } - .hero.is-info .tabs li.is-active a { - opacity: 1; } - .hero.is-info .tabs.is-boxed a, .hero.is-info .tabs.is-toggle a { - color: #fff; } - .hero.is-info .tabs.is-boxed a:hover, .hero.is-info .tabs.is-toggle a:hover { - background-color: rgba(10, 10, 10, 0.1); } - .hero.is-info .tabs.is-boxed li.is-active a, .hero.is-info .tabs.is-boxed li.is-active a:hover, .hero.is-info .tabs.is-toggle li.is-active a, .hero.is-info .tabs.is-toggle li.is-active a:hover { - background-color: #fff; - border-color: #fff; - color: #209cee; } - .hero.is-info.is-bold { - background-image: linear-gradient(141deg, #05a6d6 0%, #209cee 71%, #3287f5 100%); } - @media screen and (max-width: 768px) { - .hero.is-info.is-bold .navbar-menu { - background-image: linear-gradient(141deg, #05a6d6 0%, #209cee 71%, #3287f5 100%); } } - .hero.is-success { - background-color: #22c35b; - color: #fff; } - .hero.is-success a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), - .hero.is-success strong { - color: inherit; } - .hero.is-success .title { - color: #fff; } - .hero.is-success .subtitle { - color: rgba(255, 255, 255, 0.9); } - .hero.is-success .subtitle a:not(.button), - .hero.is-success .subtitle strong { - color: #fff; } - @media screen and (max-width: 1055px) { - .hero.is-success .navbar-menu { - background-color: #22c35b; } } - .hero.is-success .navbar-item, - .hero.is-success .navbar-link { - color: rgba(255, 255, 255, 0.7); } - .hero.is-success a.navbar-item:hover, .hero.is-success a.navbar-item.is-active, - .hero.is-success .navbar-link:hover, - .hero.is-success .navbar-link.is-active { - background-color: #1ead51; - color: #fff; } - .hero.is-success .tabs a { - color: #fff; - opacity: 0.9; } - .hero.is-success .tabs a:hover { - opacity: 1; } - .hero.is-success .tabs li.is-active a { - opacity: 1; } - .hero.is-success .tabs.is-boxed a, .hero.is-success .tabs.is-toggle a { - color: #fff; } - .hero.is-success .tabs.is-boxed a:hover, .hero.is-success .tabs.is-toggle a:hover { - background-color: rgba(10, 10, 10, 0.1); } - .hero.is-success .tabs.is-boxed li.is-active a, .hero.is-success .tabs.is-boxed li.is-active a:hover, .hero.is-success .tabs.is-toggle li.is-active a, .hero.is-success .tabs.is-toggle li.is-active a:hover { - background-color: #fff; - border-color: #fff; - color: #22c35b; } - .hero.is-success.is-bold { - background-image: linear-gradient(141deg, #12a02c 0%, #22c35b 71%, #1fdf83 100%); } - @media screen and (max-width: 768px) { - .hero.is-success.is-bold .navbar-menu { - background-image: linear-gradient(141deg, #12a02c 0%, #22c35b 71%, #1fdf83 100%); } } - .hero.is-warning { - background-color: #ffdd57; - color: rgba(0, 0, 0, 0.7); } - .hero.is-warning a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), - .hero.is-warning strong { - color: inherit; } - .hero.is-warning .title { - color: rgba(0, 0, 0, 0.7); } - .hero.is-warning .subtitle { - color: rgba(0, 0, 0, 0.9); } - .hero.is-warning .subtitle a:not(.button), - .hero.is-warning .subtitle strong { - color: rgba(0, 0, 0, 0.7); } - @media screen and (max-width: 1055px) { - .hero.is-warning .navbar-menu { - background-color: #ffdd57; } } - .hero.is-warning .navbar-item, - .hero.is-warning .navbar-link { - color: rgba(0, 0, 0, 0.7); } - .hero.is-warning a.navbar-item:hover, .hero.is-warning a.navbar-item.is-active, - .hero.is-warning .navbar-link:hover, - .hero.is-warning .navbar-link.is-active { - background-color: #ffd83e; - color: rgba(0, 0, 0, 0.7); } - .hero.is-warning .tabs a { - color: rgba(0, 0, 0, 0.7); - opacity: 0.9; } - .hero.is-warning .tabs a:hover { - opacity: 1; } - .hero.is-warning .tabs li.is-active a { - opacity: 1; } - .hero.is-warning .tabs.is-boxed a, .hero.is-warning .tabs.is-toggle a { - color: rgba(0, 0, 0, 0.7); } - .hero.is-warning .tabs.is-boxed a:hover, .hero.is-warning .tabs.is-toggle a:hover { - background-color: rgba(10, 10, 10, 0.1); } - .hero.is-warning .tabs.is-boxed li.is-active a, .hero.is-warning .tabs.is-boxed li.is-active a:hover, .hero.is-warning .tabs.is-toggle li.is-active a, .hero.is-warning .tabs.is-toggle li.is-active a:hover { - background-color: rgba(0, 0, 0, 0.7); - border-color: rgba(0, 0, 0, 0.7); - color: #ffdd57; } - .hero.is-warning.is-bold { - background-image: linear-gradient(141deg, #ffae24 0%, #ffdd57 71%, #fffa71 100%); } - @media screen and (max-width: 768px) { - .hero.is-warning.is-bold .navbar-menu { - background-image: linear-gradient(141deg, #ffae24 0%, #ffdd57 71%, #fffa71 100%); } } - .hero.is-danger { - background-color: #da0b00; - color: #fff; } - .hero.is-danger a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), - .hero.is-danger strong { - color: inherit; } - .hero.is-danger .title { - color: #fff; } - .hero.is-danger .subtitle { - color: rgba(255, 255, 255, 0.9); } - .hero.is-danger .subtitle a:not(.button), - .hero.is-danger .subtitle strong { - color: #fff; } - @media screen and (max-width: 1055px) { - .hero.is-danger .navbar-menu { - background-color: #da0b00; } } - .hero.is-danger .navbar-item, - .hero.is-danger .navbar-link { - color: rgba(255, 255, 255, 0.7); } - .hero.is-danger a.navbar-item:hover, .hero.is-danger a.navbar-item.is-active, - .hero.is-danger .navbar-link:hover, - .hero.is-danger .navbar-link.is-active { - background-color: #c10a00; - color: #fff; } - .hero.is-danger .tabs a { - color: #fff; - opacity: 0.9; } - .hero.is-danger .tabs a:hover { - opacity: 1; } - .hero.is-danger .tabs li.is-active a { - opacity: 1; } - .hero.is-danger .tabs.is-boxed a, .hero.is-danger .tabs.is-toggle a { - color: #fff; } - .hero.is-danger .tabs.is-boxed a:hover, .hero.is-danger .tabs.is-toggle a:hover { - background-color: rgba(10, 10, 10, 0.1); } - .hero.is-danger .tabs.is-boxed li.is-active a, .hero.is-danger .tabs.is-boxed li.is-active a:hover, .hero.is-danger .tabs.is-toggle li.is-active a, .hero.is-danger .tabs.is-toggle li.is-active a:hover { - background-color: #fff; - border-color: #fff; - color: #da0b00; } - .hero.is-danger.is-bold { - background-image: linear-gradient(141deg, #a70013 0%, #da0b00 71%, #f43500 100%); } - @media screen and (max-width: 768px) { - .hero.is-danger.is-bold .navbar-menu { - background-image: linear-gradient(141deg, #a70013 0%, #da0b00 71%, #f43500 100%); } } - .hero.is-small .hero-body, #documenter .docs-sidebar form.docs-search > input.hero .hero-body { - padding-bottom: 1.5rem; - padding-top: 1.5rem; } - @media screen and (min-width: 769px), print { - .hero.is-medium .hero-body { - padding-bottom: 9rem; - padding-top: 9rem; } } - @media screen and (min-width: 769px), print { - .hero.is-large .hero-body { - padding-bottom: 18rem; - padding-top: 18rem; } } - .hero.is-halfheight .hero-body, .hero.is-fullheight .hero-body, .hero.is-fullheight-with-navbar .hero-body { - align-items: center; - display: flex; } - .hero.is-halfheight .hero-body > .container, .hero.is-fullheight .hero-body > .container, .hero.is-fullheight-with-navbar .hero-body > .container { - flex-grow: 1; - flex-shrink: 1; } - .hero.is-halfheight { - min-height: 50vh; } - .hero.is-fullheight { - min-height: 100vh; } - -.hero-video { - overflow: hidden; } - .hero-video video { - left: 50%; - min-height: 100%; - min-width: 100%; - position: absolute; - top: 50%; - transform: translate3d(-50%, -50%, 0); } - .hero-video.is-transparent { - opacity: 0.3; } - @media screen and (max-width: 768px) { - .hero-video { - display: none; } } -.hero-buttons { - margin-top: 1.5rem; } - @media screen and (max-width: 768px) { - .hero-buttons .button { - display: flex; } - .hero-buttons .button:not(:last-child) { - margin-bottom: 0.75rem; } } - @media screen and (min-width: 769px), print { - .hero-buttons { - display: flex; - justify-content: center; } - .hero-buttons .button:not(:last-child) { - margin-right: 1.5rem; } } -.hero-head, -.hero-foot { - flex-grow: 0; - flex-shrink: 0; } - -.hero-body { - flex-grow: 1; - flex-shrink: 0; - padding: 3rem 1.5rem; } - -.section { - padding: 3rem 1.5rem; } - @media screen and (min-width: 1056px) { - .section.is-medium { - padding: 9rem 1.5rem; } - .section.is-large { - padding: 18rem 1.5rem; } } -.footer { - background-color: #fafafa; - padding: 3rem 1.5rem 6rem; } - -h1 .docs-heading-anchor, h1 .docs-heading-anchor:hover, h1 .docs-heading-anchor:visited, h2 .docs-heading-anchor, h2 .docs-heading-anchor:hover, h2 .docs-heading-anchor:visited, h3 .docs-heading-anchor, h3 .docs-heading-anchor:hover, h3 .docs-heading-anchor:visited, h4 .docs-heading-anchor, h4 .docs-heading-anchor:hover, h4 .docs-heading-anchor:visited, h5 .docs-heading-anchor, h5 .docs-heading-anchor:hover, h5 .docs-heading-anchor:visited, h6 .docs-heading-anchor, h6 .docs-heading-anchor:hover, h6 .docs-heading-anchor:visited { - color: #222222; 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0.3s; - -webkit-transition-duration: 0.3s; - /* Safari */ } - #documenter .docs-main header.docs-navbar.headroom--not-top { - box-shadow: 0.2rem 0rem 0.4rem #bbb; - transition-duration: 0.7s; - -webkit-transition-duration: 0.7s; - /* Safari */ } - #documenter .docs-main header.docs-navbar.headroom--unpinned.headroom--not-top.headroom--not-bottom { - top: -4.5rem; - transition-duration: 0.7s; - -webkit-transition-duration: 0.7s; - /* Safari */ } } -#documenter .docs-main section.footnotes { - border-top: 1px solid #dbdbdb; } - #documenter .docs-main section.footnotes li .tag:first-child, #documenter .docs-main section.footnotes li .docstring > section > a.docs-sourcelink:first-child, #documenter .docs-main section.footnotes li .content kbd:first-child, .content #documenter .docs-main section.footnotes li kbd:first-child { - margin-right: 1em; - margin-bottom: 0.4em; } - -#documenter .docs-main .docs-footer { - display: flex; - flex-wrap: wrap; - margin-left: 0; - margin-right: 0; - 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Theme: Default Description: Original highlight.js style Author: (c) Ivan Sagalaev @@ -7644,95 +6,4 @@ code.language-julia-repl > span.hljs-meta { Website: https://highlightjs.org/ License: see project LICENSE Touched: 2021 -*/ -/* -This is left on purpose making default.css the single file that can be lifted -as-is from the repository directly without the need for a build step - -Typically this "required" baseline CSS is added by `makestuff.js` during build. -*/ -pre code.hljs { - display: block; - overflow-x: auto; } - -code.hljs { - padding: 3px 5px; } - -/* end baseline CSS */ -.hljs { - background: #F0F0F0; - color: #444; } - -/* Base color: saturation 0; */ -.hljs-subst { - /* default */ } - -/* purposely ignored */ -.hljs-comment { - color: #888888; } - -.hljs-tag, -.hljs-punctuation { - color: #444a; } - -.hljs-tag .hljs-name, -.hljs-tag .hljs-attr { - color: #444; } - -.hljs-keyword, -.hljs-attribute, -.hljs-selector-tag, -.hljs-meta .hljs-keyword, -.hljs-doctag, -.hljs-name { - font-weight: bold; } - -/* User color: hue: 0 */ -.hljs-type, -.hljs-string, -.hljs-number, -.hljs-selector-id, -.hljs-selector-class, -.hljs-quote, -.hljs-template-tag, -.hljs-deletion { - color: #880000; } - -.hljs-title, -.hljs-section { - color: #880000; - font-weight: bold; } - -.hljs-regexp, -.hljs-symbol, -.hljs-variable, -.hljs-template-variable, -.hljs-link, -.hljs-selector-attr, -.hljs-operator, -.hljs-selector-pseudo { - color: #BC6060; } - -/* Language color: hue: 90; */ -.hljs-literal { - color: #78A960; } - -.hljs-built_in, -.hljs-bullet, -.hljs-code, -.hljs-addition { - color: #397300; } - -/* Meta color: hue: 200 */ -.hljs-meta { - color: #1f7199; } - -.hljs-meta .hljs-string { - color: #4d99bf; } - -/* Misc effects */ -.hljs-emphasis { - font-style: italic; } - -.hljs-strong { - font-weight: bold; } +*/pre code.hljs{display:block;overflow-x:auto}code.hljs{padding:3px 5px}.hljs{background:#F0F0F0;color:#444}.hljs-comment{color:#888888}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#BC6060}.hljs-literal{color:#78A960}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#4d99bf}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold} diff --git a/dev/cca/index.html b/dev/cca/index.html index 3ac9524..54f47da 100644 --- a/dev/cca/index.html +++ b/dev/cca/index.html @@ -1,3 +1,3 @@ -Canonical Correlation Analysis · MultivariateStats.jl
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Canonical Correlation Analysis

Canonical Correlation Analysis(CCA) is a statistical analysis technique to identify correlations between two sets of variables. Given two vector variables $X$ and $Y$, it finds two projections, one for each, to transform them to a common space with maximum correlations.

The package defines a CCA type to represent a CCA model, and provides a set of methods to access the properties.

Let M be an instance of CCA, dx be the dimension of X, dy the dimension of Y, and p the output dimension (i.e the dimension of the common space).

StatsAPI.fit — Method
fit(CCA, X, Y; ...)

Perform CCA over the data given in matrices X and Y. Each column of X and Y is an observation.

X and Y should have the same number of columns (denoted by n below).

This method returns an instance of CCA.

Keyword arguments:

  • method: The choice of methods:
    • :cov: based on covariance matrices
    • :svd: based on SVD of the input data (default)
  • outdim: The output dimension, i.e dimension of the common space (default: min(dx, dy, n))
  • mean: The mean vector, which can be either of:
    • 0: the input data has already been centralized
    • nothing: this function will compute the mean (default)
    • a pre-computed mean vector

Notes: This function calls ccacov or ccasvd internally, depending on the choice of method.

source
Base.size — Method
size(M:CCA)

Return a tuple with the dimension of X, Y, and the output dimension.

source
Statistics.mean — Method
mean(M::CCA, c::Symbol)

Get the mean vector for the component c of the model M. The component parameter can be :x or :y.

source
MultivariateStats.projection — Method
projection(M::CCA, c::Symbol)

Get the projection matrix for the component c of the model M. The component parameter can be :x or :y.

source
Statistics.cor — Method
cor(M::CCA)

The correlations of the projected components (a vector of length p).

source
StatsAPI.predict — Method
predict(M::CCA, Z::AbstractVecOrMat{<:Real}, c::Symbol)

Given a CCA model, one can transform observations into both spaces into a common space, as

\[\mathbf{z}_x = \mathbf{P}_x^T (\mathbf{x} - \boldsymbol{\mu}_x) \\ -\mathbf{z}_y = \mathbf{P}_y^T (\mathbf{y} - \boldsymbol{\mu}_y)\]

Here, $\mathbf{P}_x$ and $\mathbf{P}_y$ are projection matrices for $X$ and $Y$; $\boldsymbol{\mu}_x$ and $\boldsymbol{\mu}_y$ are mean vectors.

Parameter Z can be either a vector of length dx, dy, or a matrix where each column is an observation. The component parameter c can be :x or :y.

source

Auxiliary functions:

MultivariateStats.ccacov — Function
ccacov(Cxx, Cyy, Cxy, xmean, ymean, p)

Compute CCA based on analysis of the given covariance matrices, using generalized eigenvalue decomposition, and return CCA model.

Parameters:

  • Cxx: The covariance matrix of X.
  • Cyy: The covariance matrix of Y.
  • Cxy: The covariance matrix between X and Y.
  • xmean: The mean vector of the original samples of X, which can be

a vector of length dx, or an empty vector indicating a zero mean.

  • ymean: The mean vector of the original samples of Y, which can be

a vector of length dy, or an empty vector indicating a zero mean.

  • p: The output dimension, i.e the dimension of the common space.
source
MultivariateStats.ccasvd — Function
ccasvd(Zx, Zy, xmean, ymean, p)

Compute CCA based on singular value decomposition of centralized sample matrices Zx and Zy, and return CCA model[1].

Parameters:

  • Zx: The centralized sample matrix for X.
  • Zy: The centralized sample matrix for Y.
  • xmean: The mean vector of the original samples of X, which can be

a vector of length dx, or an empty vector indicating a zero mean.

  • ymean: The mean vector of the original samples of Y, which can be

a vector of length dy, or an empty vector indicating a zero mean.

  • p: The output dimension, i.e the dimension of the common space.
source

References

  • 1David Weenink, Canonical Correlation Analysis, Institute of Phonetic Sciences, Univ. of Amsterdam, Proceedings 25, 81-99, 2003.
+Canonical Correlation Analysis · MultivariateStats.jl
Edit on GitHub

Canonical Correlation Analysis

Canonical Correlation Analysis(CCA) is a statistical analysis technique to identify correlations between two sets of variables. Given two vector variables $X$ and $Y$, it finds two projections, one for each, to transform them to a common space with maximum correlations.

The package defines a CCA type to represent a CCA model, and provides a set of methods to access the properties.

Let M be an instance of CCA, dx be the dimension of X, dy the dimension of Y, and p the output dimension (i.e the dimension of the common space).

StatsAPI.fit — Method
fit(CCA, X, Y; ...)

Perform CCA over the data given in matrices X and Y. Each column of X and Y is an observation.

X and Y should have the same number of columns (denoted by n below).

This method returns an instance of CCA.

Keyword arguments:

  • method: The choice of methods:
    • :cov: based on covariance matrices
    • :svd: based on SVD of the input data (default)
  • outdim: The output dimension, i.e dimension of the common space (default: min(dx, dy, n))
  • mean: The mean vector, which can be either of:
    • 0: the input data has already been centralized
    • nothing: this function will compute the mean (default)
    • a pre-computed mean vector

Notes: This function calls ccacov or ccasvd internally, depending on the choice of method.

source
Base.size — Method
size(M:CCA)

Return a tuple with the dimension of X, Y, and the output dimension.

source
Statistics.mean — Method
mean(M::CCA, c::Symbol)

Get the mean vector for the component c of the model M. The component parameter can be :x or :y.

source
MultivariateStats.projection — Method
projection(M::CCA, c::Symbol)

Get the projection matrix for the component c of the model M. The component parameter can be :x or :y.

source
Statistics.cor — Method
cor(M::CCA)

The correlations of the projected components (a vector of length p).

source
StatsAPI.predict — Method
predict(M::CCA, Z::AbstractVecOrMat{<:Real}, c::Symbol)

Given a CCA model, one can transform observations into both spaces into a common space, as

\[\mathbf{z}_x = \mathbf{P}_x^T (\mathbf{x} - \boldsymbol{\mu}_x) \\ +\mathbf{z}_y = \mathbf{P}_y^T (\mathbf{y} - \boldsymbol{\mu}_y)\]

Here, $\mathbf{P}_x$ and $\mathbf{P}_y$ are projection matrices for $X$ and $Y$; $\boldsymbol{\mu}_x$ and $\boldsymbol{\mu}_y$ are mean vectors.

Parameter Z can be either a vector of length dx, dy, or a matrix where each column is an observation. The component parameter c can be :x or :y.

source

Auxiliary functions:

MultivariateStats.ccacov — Function
ccacov(Cxx, Cyy, Cxy, xmean, ymean, p)

Compute CCA based on analysis of the given covariance matrices, using generalized eigenvalue decomposition, and return CCA model.

Parameters:

  • Cxx: The covariance matrix of X.
  • Cyy: The covariance matrix of Y.
  • Cxy: The covariance matrix between X and Y.
  • xmean: The mean vector of the original samples of X, which can be

a vector of length dx, or an empty vector indicating a zero mean.

  • ymean: The mean vector of the original samples of Y, which can be

a vector of length dy, or an empty vector indicating a zero mean.

  • p: The output dimension, i.e the dimension of the common space.
source
MultivariateStats.ccasvd — Function
ccasvd(Zx, Zy, xmean, ymean, p)

Compute CCA based on singular value decomposition of centralized sample matrices Zx and Zy, and return CCA model[1].

Parameters:

  • Zx: The centralized sample matrix for X.
  • Zy: The centralized sample matrix for Y.
  • xmean: The mean vector of the original samples of X, which can be

a vector of length dx, or an empty vector indicating a zero mean.

  • ymean: The mean vector of the original samples of Y, which can be

a vector of length dy, or an empty vector indicating a zero mean.

  • p: The output dimension, i.e the dimension of the common space.
source

References

  • 1David Weenink, Canonical Correlation Analysis, Institute of Phonetic Sciences, Univ. of Amsterdam, Proceedings 25, 81-99, 2003.
diff --git a/dev/fa/index.html b/dev/fa/index.html index ea980f6..47e2b6b 100644 --- a/dev/fa/index.html +++ b/dev/fa/index.html @@ -1,2 +1,2 @@ -Factor Analysis · MultivariateStats.jl
Edit on GitHub

Factor Analysis

Factor Analysis (FA) is a linear-Gaussian latent variable model that is closely related to probabilistic PCA. In contrast to the probabilistic PCA model, the covariance of conditional distribution of the observed variable given the latent variable is diagonal rather than isotropic[1].

This package defines a FactorAnalysis type to represent a factor analysis model, and provides a set of methods to access the properties.

The package provides a set of methods to access the properties of the factor analysis model. Let $M$ be an instance of FactorAnalysis, $d$ be the dimension of observations, and $p$ be the output dimension (i.e the dimension of the principal subspace).

StatsAPI.fit — Method
fit(FactorAnalysis, X; ...)

Perform factor analysis over the data given in a matrix X. Each column of X is an observation. This method returns an instance of FactorAnalysis.

Keyword arguments:

Let (d, n) = size(X) be respectively the input dimension and the number of observations:

  • method: The choice of methods:
    • :em: use EM version of factor analysis
    • :cm: use CM version of factor analysis (default)
  • maxoutdim: Maximum output dimension (default d-1)
  • mean: The mean vector, which can be either of:
    • 0: the input data has already been centralized
    • nothing: this function will compute the mean (default)
    • a pre-computed mean vector
  • tol: Convergence tolerance (default 1.0e-6)
  • maxiter: Maximum number of iterations (default 1000)
  • η: Variance low bound (default 1.0e-6)

Notes: This function calls facm or faem internally, depending on the choice of method.

source
Base.size — Method
size(M::PPCA)

Returns a tuple with values of the input dimension $d$, i.e the dimension of the observation space, and the output dimension $p$, i.e the dimension of the principal subspace.

source

Given a factor analysis model $M$, one can use it to transform observations into latent variables, as

\mathbf{z} =  \mathbf{W}^T \mathbf{\Sigma}^{-1} (\mathbf{x} - \boldsymbol{\mu})

or use it to reconstruct (approximately) the observations from latent variables, as

\tilde{\mathbf{x}} = \mathbf{\Sigma} \mathbf{W} (\mathbf{W}^T \mathbf{W})^{-1} \mathbf{z} + \boldsymbol{\mu}

Here, $\mathbf{W}$ is the factor loadings or weight matrix, $\mathbf{\Sigma} = \mathbf{\Psi} + \mathbf{W}^T \mathbf{W}$ is the covariance matrix.

The package provides methods to do so:

StatsAPI.predict — Method
predict(M::FactorAnalysis, x)

Transform observations x into latent variables. Here, x can be either a vector of length d or a matrix where each column is an observation.

source
MultivariateStats.reconstruct — Method
reconstruct(M::FactorAnalysis, z)

Approximately reconstruct observations from the latent variable given in z. Here, z can be either a vector of length $p$ or a matrix where each column gives the latent variables for an observation.

source

Auxiliary functions:

MultivariateStats.faem — Function
faem(S, mean, n; ...)

Performs factor analysis using an expectation-maximization algorithm for a given sample covariance matrix S[2].

Parameters

  • S: The sample covariance matrix.
  • mean: The mean vector of original samples, which can be a vector of length $d$,

or an empty vector indicating a zero mean.

  • n: The number of observations.

Returns the resultant FactorAnalysis model.

Note: This function accepts two keyword arguments: maxoutdim,tol, and maxiter.

source
MultivariateStats.facm — Function
facm(S, mean, n; ...)

Performs factor analysis using a fast conditional maximization algorithm for a given sample covariance matrix S[3].

Parameters

  • S: The sample covariance matrix.
  • mean: The mean vector of original samples, which can be a vector of length $d$,

or an empty vector indicating a zero mean.

  • n: The number of observations.

Returns the resultant FactorAnalysis model.

Note: This function accepts two keyword arguments: maxoutdim,tol, maxiter, and η.

source

References

  • 1Bishop, C. M. Pattern Recognition and Machine Learning, 2006.
  • 2Rubin, Donald B., and Dorothy T. Thayer. EM algorithms for ML factor analysis. Psychometrika 47.1, 69-76, 1982.
  • 3Zhao, J-H., Philip LH Yu, and Qibao Jiang. ML estimation for factor analysis: EM or non-EM?. Statistics and computing 18.2, 109-123, 2008.
+Factor Analysis · MultivariateStats.jl
Edit on GitHub

Factor Analysis

Factor Analysis (FA) is a linear-Gaussian latent variable model that is closely related to probabilistic PCA. In contrast to the probabilistic PCA model, the covariance of conditional distribution of the observed variable given the latent variable is diagonal rather than isotropic[1].

This package defines a FactorAnalysis type to represent a factor analysis model, and provides a set of methods to access the properties.

The package provides a set of methods to access the properties of the factor analysis model. Let $M$ be an instance of FactorAnalysis, $d$ be the dimension of observations, and $p$ be the output dimension (i.e the dimension of the principal subspace).

StatsAPI.fit — Method
fit(FactorAnalysis, X; ...)

Perform factor analysis over the data given in a matrix X. Each column of X is an observation. This method returns an instance of FactorAnalysis.

Keyword arguments:

Let (d, n) = size(X) be respectively the input dimension and the number of observations:

  • method: The choice of methods:
    • :em: use EM version of factor analysis
    • :cm: use CM version of factor analysis (default)
  • maxoutdim: Maximum output dimension (default d-1)
  • mean: The mean vector, which can be either of:
    • 0: the input data has already been centralized
    • nothing: this function will compute the mean (default)
    • a pre-computed mean vector
  • tol: Convergence tolerance (default 1.0e-6)
  • maxiter: Maximum number of iterations (default 1000)
  • η: Variance low bound (default 1.0e-6)

Notes: This function calls facm or faem internally, depending on the choice of method.

source
Base.size — Method
size(M::PPCA)

Returns a tuple with values of the input dimension $d$, i.e the dimension of the observation space, and the output dimension $p$, i.e the dimension of the principal subspace.

source

Given a factor analysis model $M$, one can use it to transform observations into latent variables, as

\mathbf{z} =  \mathbf{W}^T \mathbf{\Sigma}^{-1} (\mathbf{x} - \boldsymbol{\mu})

or use it to reconstruct (approximately) the observations from latent variables, as

\tilde{\mathbf{x}} = \mathbf{\Sigma} \mathbf{W} (\mathbf{W}^T \mathbf{W})^{-1} \mathbf{z} + \boldsymbol{\mu}

Here, $\mathbf{W}$ is the factor loadings or weight matrix, $\mathbf{\Sigma} = \mathbf{\Psi} + \mathbf{W}^T \mathbf{W}$ is the covariance matrix.

The package provides methods to do so:

StatsAPI.predict — Method
predict(M::FactorAnalysis, x)

Transform observations x into latent variables. Here, x can be either a vector of length d or a matrix where each column is an observation.

source
MultivariateStats.reconstruct — Method
reconstruct(M::FactorAnalysis, z)

Approximately reconstruct observations from the latent variable given in z. Here, z can be either a vector of length $p$ or a matrix where each column gives the latent variables for an observation.

source

Auxiliary functions:

MultivariateStats.faem — Function
faem(S, mean, n; ...)

Performs factor analysis using an expectation-maximization algorithm for a given sample covariance matrix S[2].

Parameters

  • S: The sample covariance matrix.
  • mean: The mean vector of original samples, which can be a vector of length $d$,

or an empty vector indicating a zero mean.

  • n: The number of observations.

Returns the resultant FactorAnalysis model.

Note: This function accepts two keyword arguments: maxoutdim,tol, and maxiter.

source
MultivariateStats.facm — Function
facm(S, mean, n; ...)

Performs factor analysis using a fast conditional maximization algorithm for a given sample covariance matrix S[3].

Parameters

  • S: The sample covariance matrix.
  • mean: The mean vector of original samples, which can be a vector of length $d$,

or an empty vector indicating a zero mean.

  • n: The number of observations.

Returns the resultant FactorAnalysis model.

Note: This function accepts two keyword arguments: maxoutdim,tol, maxiter, and η.

source

References

  • 1Bishop, C. M. Pattern Recognition and Machine Learning, 2006.
  • 2Rubin, Donald B., and Dorothy T. Thayer. EM algorithms for ML factor analysis. Psychometrika 47.1, 69-76, 1982.
  • 3Zhao, J-H., Philip LH Yu, and Qibao Jiang. ML estimation for factor analysis: EM or non-EM?. Statistics and computing 18.2, 109-123, 2008.
diff --git a/dev/ica/index.html b/dev/ica/index.html index 761ba9b..a0b3e4b 100644 --- a/dev/ica/index.html +++ b/dev/ica/index.html @@ -1,2 +1,2 @@ -Independent Component Analysis · MultivariateStats.jl
Edit on GitHub

Independent Component Analysis

Independent Component Analysis (ICA) is a computational technique for separating a multivariate signal into additive subcomponents, with the assumption that the subcomponents are non-Gaussian and independent from each other.

There are multiple algorithms for ICA. Currently, this package implements the Fast ICA algorithm.

FastICA

This package implements the FastICA algorithm[1]. The package uses the ICA type to define a FastICA model:

MultivariateStats.ICA — Type

This type contains ICA model parameters: mean and component matrix $W$.

Note: Each column of the component matrix $W$ corresponds to an independent component.

source

Several methods are provided to work with ICA. Let $M$ be an instance of ICA:

StatsAPI.fit — Method
fit(ICA, X, k; ...)

Perform ICA over the data set given in X.

Parameters: -X: The data matrix, of size $(m, n)$. Each row corresponds to a mixed signal, while each column corresponds to an observation (e.g all signal value at a particular time step). -k: The number of independent components to recover.

Keyword Arguments:

  • alg: The choice of algorithm (default :fastica)
  • fun: The approx neg-entropy functor (default Tanh)
  • do_whiten: Whether to perform pre-whitening (default true)
  • maxiter: Maximum number of iterations (default 100)
  • tol: Tolerable change of $W$ at convergence (default 1.0e-6)
  • mean: The mean vector, which can be either of:
    • 0: the input data has already been centralized
    • nothing: this function will compute the mean (default)
    • a pre-computed mean vector
  • winit: Initial guess of $W$, which should be either of:
    • empty matrix: the function will perform random initialization (default)
    • a matrix of size $(k, k)$ (when do_whiten)
    • a matrix of size $(m, k)$ (when !do_whiten)

Returns the resultant ICA model, an instance of type ICA.

Note: If do_whiten is true, the return W satisfies $\mathbf{W}^T \mathbf{C} \mathbf{W} = \mathbf{I}$, otherwise $W$ is orthonormal, i.e $\mathbf{W}^T \mathbf{W} = \mathbf{I}$.

source
Base.size — Method
size(M::ICA)

Returns a tuple with the input dimension, i.e the number of observed mixtures, and the output dimension, i.e the number of independent components.

source
StatsAPI.predict — Method
predict(M::ICA, x)

Transform x to the output space to extract independent components, as $\mathbf{W}^T (\mathbf{x} - \boldsymbol{\mu})$, given the model M.

source

The package also exports functions of the core algorithms. Sometimes, it can be more efficient to directly invoke them instead of going through the fit interface.

MultivariateStats.fastica! — Function
fastica!(W, X, fun, maxiter, tol, verbose)

Invoke the Fast ICA algorithm[1].

Parameters:

  • W: The initial un-mixing matrix, of size $(m, k)$. The function updates this matrix inplace.
  • X: The data matrix, of size $(m, n)$. This matrix is input only, and won't be modified.
  • fun: The approximate neg-entropy functor of type ICAGDeriv.
  • maxiter: Maximum number of iterations.
  • tol: Tolerable change of W at convergence.

Returns the updated W.

Note: The number of components is inferred from W as size(W, 2).

source

The FastICA method requires a first derivative of a functor $g$ to approximate negative entropy. The package implements an following interface for defining derivative value estimation:

MultivariateStats.ICAGDeriv — Type

The abstract type for all g (derivative) functions.

Let g be an instance of such type, then update!(g, U, E) given

  • U = w'x

returns updated in-place U and E, s.t.

  • g(w'x) --> U and E{g'(w'x)} --> E
source

References

  • 1Aapo Hyvarinen and Erkki Oja, Independent Component Analysis: Algorithms and Applications. Neural Network 13(4-5), 2000.
+Independent Component Analysis · MultivariateStats.jl
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Independent Component Analysis

Independent Component Analysis (ICA) is a computational technique for separating a multivariate signal into additive subcomponents, with the assumption that the subcomponents are non-Gaussian and independent from each other.

There are multiple algorithms for ICA. Currently, this package implements the Fast ICA algorithm.

FastICA

This package implements the FastICA algorithm[1]. The package uses the ICA type to define a FastICA model:

MultivariateStats.ICA — Type

This type contains ICA model parameters: mean and component matrix $W$.

Note: Each column of the component matrix $W$ corresponds to an independent component.

source

Several methods are provided to work with ICA. Let $M$ be an instance of ICA:

StatsAPI.fit — Method
fit(ICA, X, k; ...)

Perform ICA over the data set given in X.

Parameters: -X: The data matrix, of size $(m, n)$. Each row corresponds to a mixed signal, while each column corresponds to an observation (e.g all signal value at a particular time step). -k: The number of independent components to recover.

Keyword Arguments:

  • alg: The choice of algorithm (default :fastica)
  • fun: The approx neg-entropy functor (default Tanh)
  • do_whiten: Whether to perform pre-whitening (default true)
  • maxiter: Maximum number of iterations (default 100)
  • tol: Tolerable change of $W$ at convergence (default 1.0e-6)
  • mean: The mean vector, which can be either of:
    • 0: the input data has already been centralized
    • nothing: this function will compute the mean (default)
    • a pre-computed mean vector
  • winit: Initial guess of $W$, which should be either of:
    • empty matrix: the function will perform random initialization (default)
    • a matrix of size $(k, k)$ (when do_whiten)
    • a matrix of size $(m, k)$ (when !do_whiten)

Returns the resultant ICA model, an instance of type ICA.

Note: If do_whiten is true, the return W satisfies $\mathbf{W}^T \mathbf{C} \mathbf{W} = \mathbf{I}$, otherwise $W$ is orthonormal, i.e $\mathbf{W}^T \mathbf{W} = \mathbf{I}$.

source
Base.size — Method
size(M::ICA)

Returns a tuple with the input dimension, i.e the number of observed mixtures, and the output dimension, i.e the number of independent components.

source
StatsAPI.predict — Method
predict(M::ICA, x)

Transform x to the output space to extract independent components, as $\mathbf{W}^T (\mathbf{x} - \boldsymbol{\mu})$, given the model M.

source

The package also exports functions of the core algorithms. Sometimes, it can be more efficient to directly invoke them instead of going through the fit interface.

MultivariateStats.fastica! — Function
fastica!(W, X, fun, maxiter, tol, verbose)

Invoke the Fast ICA algorithm[1].

Parameters:

  • W: The initial un-mixing matrix, of size $(m, k)$. The function updates this matrix inplace.
  • X: The data matrix, of size $(m, n)$. This matrix is input only, and won't be modified.
  • fun: The approximate neg-entropy functor of type ICAGDeriv.
  • maxiter: Maximum number of iterations.
  • tol: Tolerable change of W at convergence.

Returns the updated W.

Note: The number of components is inferred from W as size(W, 2).

source

The FastICA method requires a first derivative of a functor $g$ to approximate negative entropy. The package implements an following interface for defining derivative value estimation:

MultivariateStats.ICAGDeriv — Type

The abstract type for all g (derivative) functions.

Let g be an instance of such type, then update!(g, U, E) given

  • U = w'x

returns updated in-place U and E, s.t.

  • g(w'x) --> U and E{g'(w'x)} --> E
source

References

  • 1Aapo Hyvarinen and Erkki Oja, Independent Component Analysis: Algorithms and Applications. Neural Network 13(4-5), 2000.
diff --git a/dev/index.html b/dev/index.html index 60f33d3..452dded 100644 --- a/dev/index.html +++ b/dev/index.html @@ -1,2 +1,2 @@ -Home · MultivariateStats.jl
Edit on GitHub

MultivariateStats.jl Documentation

MultivariateStats.jl is a Julia package for multivariate statistical analysis. It provides a rich set of useful analysis techniques, such as PCA, CCA, LDA, ICA, etc.

Notes: All methods implemented in this package adopt the column-major convention of JuliaStats: in a data matrix, each column corresponds to a sample/observation, while each row corresponds to a feature (variable or attribute).

+Home · MultivariateStats.jl
Edit on GitHub

MultivariateStats.jl Documentation

MultivariateStats.jl is a Julia package for multivariate statistical analysis. It provides a rich set of useful analysis techniques, such as PCA, CCA, LDA, ICA, etc.

Notes: All methods implemented in this package adopt the column-major convention of JuliaStats: in a data matrix, each column corresponds to a sample/observation, while each row corresponds to a feature (variable or attribute).

diff --git a/dev/lda/index.html b/dev/lda/index.html index 3b6d14e..024d83a 100644 --- a/dev/lda/index.html +++ b/dev/lda/index.html @@ -24,240 +24,240 @@ plot!(p[2], title="LDA") - + - + - + - + - - + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - - + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Two-class Linear Discriminant Analysis

This package uses the LinearDiscriminant type to capture a linear discriminant functional:

MultivariateStats.LinearDiscriminant — Type

A linear discriminant functional can be written as

\[ f(\mathbf{x}) = \mathbf{w}^T \mathbf{x} + b\]

Here, $w$ is the coefficient vector, and $b$ is the bias constant.

source

This type comes with several methods where $f$ be an instance of LinearDiscriminant.

StatsAPI.fit — Method
fit(LinearDiscriminant, Xp, Xn; covestimator = SimpleCovariance())

Performs LDA given both positive and negative samples. The function accepts following parameters:

Parameters

  • Xp: The sample matrix of the positive class.
  • Xn: The sample matrix of the negative class.

Keyword arguments:

  • covestimator: Custom covariance estimator for between-class covariance. The covariance matrix will be calculated as cov(covestimator_between, #=data=#; dims=2, mean=zeros(#=...=#). Custom covariance estimators, available in other packages, may result in more robust discriminants for data with more features than observations.
source
MultivariateStats.evaluate — Method
evaluate(f, X::AbstractMatrix)

Evaluate the linear discriminant value, i.e $w'x + b$, for each sample in columns of X. The function returns a vector of length size(X, 2).

source
StatsAPI.predict — Method
predict(f, x::AbstractVector)

Make prediction for the vector x. It returns true iff evaluate(f, x) is positive.

source
StatsAPI.coef — Method
coef(f::LinearDiscriminant)

Return the coefficients of the linear discriminant model.

source
StatsAPI.dof — Method
dof(f::LinearDiscriminant)

Return the number of degrees of freedom in the linear discriminant model.

source
StatsAPI.weights — Method
weights(f::LinearDiscriminant)

Return the linear discriminant model coefficient vector.

source

Additional functionality:

MultivariateStats.ldacov — Function
ldacov(C, μp, μn)

Performs LDA given a covariance matrix C and both mean vectors μp & μn. Returns a linear discriminant functional of type LinearDiscriminant.

Parameters

  • C: The pooled covariance matrix (i.e $(Cp + Cn)/2$)
  • μp: The mean vector of the positive class.
  • μn: The mean vector of the negative class.
source
ldacov(Cp, Cn, μp, μn)

Performs LDA given covariances and mean vectors. Returns a linear discriminant functional of type LinearDiscriminant.

Parameters

  • Cp: The covariance matrix of the positive class.
  • Cn: The covariance matrix of the negative class.
  • μp: The mean vector of the positive class.
  • μn: The mean vector of the negative class.

Note: The coefficient vector is scaled such that $w'μp + b = 1$ and $w'μn + b = -1$.

source

Multi-class Linear Discriminant Analysis

Multi-class LDA is a generalization of standard two-class LDA that can handle arbitrary number of classes.

Overview

Multi-class LDA is based on the analysis of two scatter matrices: within-class scatter matrix and between-class scatter matrix.

Given a set of samples $\mathbf{x}_1, \ldots, \mathbf{x}_n$, and their class labels $y_1, \ldots, y_n$:

  • The within-class scatter matrix is defined as:

\[\mathbf{S}_w = \sum_{i=1}^n (\mathbf{x}_i - \boldsymbol{\mu}_{y_i}) (\mathbf{x}_i - \boldsymbol{\mu}_{y_i})^T\]

Here, $\boldsymbol{\mu}_k$ is the sample mean of the $k$-th class.

  • The between-class scatter matrix is defined as:

\[\mathbf{S}_b = \sum_{k=1}^m n_k (\boldsymbol{\mu}_k - \boldsymbol{\mu}) (\boldsymbol{\mu}_k - \boldsymbol{\mu})^T\]

Here, $m$ is the number of classes, $\boldsymbol{\mu}$ is the overall sample mean, and $n_k$ is the number of samples in the $k$-th class.

Then, multi-class LDA can be formulated as an optimization problem to find a set of linear combinations (with coefficients $\mathbf{w}$) that maximizes the ratio of the between-class scattering to the within-class scattering, as

\[\hat{\mathbf{w}} = \mathop{\mathrm{argmax}}_{\mathbf{w}} - \frac{\mathbf{w}^T \mathbf{S}_b \mathbf{w}}{\mathbf{w}^T \mathbf{S}_w \mathbf{w}}\]

The solution is given by the following generalized eigenvalue problem:

\[\mathbf{S}_b \mathbf{w} = \lambda \mathbf{S}_w \mathbf{w}\]

Generally, at most $m - 1$ generalized eigenvectors are useful to discriminate between $m$ classes.

When the dimensionality is high, it may not be feasible to construct the scatter matrices explicitly. In such cases, see SubspaceLDA below.

Normalization by number of observations

An alternative definition of the within- and between-class scatter matrices normalizes for the number of observations in each group:

\[\mathbf{S}_w^* = n \sum_{k=1}^m \frac{1}{n_k} \sum_{i \mid y_i=k} (\mathbf{x}_i - \boldsymbol{\mu}_{k}) (\mathbf{x}_i - \boldsymbol{\mu}_{k})^T\]

\[\mathbf{S}_b^* = n \sum_{k=1}^m (\boldsymbol{\mu}_k - \boldsymbol{\mu}^*) (\boldsymbol{\mu}_k - \boldsymbol{\mu}^*)^T\]

where

\[\boldsymbol{\mu}^* = \frac{1}{k} \sum_{k=1}^m \boldsymbol{\mu}_k.\]

This definition can sometimes be more useful when looking for directions which discriminate among clusters containing widely-varying numbers of observations.

Multi-class LDA

The package defines a MulticlassLDA type to represent a multi-class LDA model, as:

MultivariateStats.MulticlassLDA — Type

A multi-class linear discriminant model type has following fields:

  • proj is the projection matrix
  • pmeans is the projected means of all classes
  • stats is an instance of MulticlassLDAStats type that captures all statistics computed to train the model (which we will discuss later).
source

Several methods are provided to access properties of the LDA model. Let M be an instance of MulticlassLDA:

StatsAPI.fit — Method
fit(MulticlassLDA, X, y; ...)

Perform multi-class LDA over a given data set X with corresponding labels y with nc number of classes.

This function returns the resultant multi-class LDA model as an instance of MulticlassLDA.

Parameters

  • X: the matrix of input samples, of size (d, n). Each column in X is an observation.
  • y: the vector of class labels, of length n.

Keyword arguments

  • method: The choice of methods:
    • :gevd: based on generalized eigenvalue decomposition (default).
    • :whiten: first derive a whitening transform from Sw and then solve the problem based on eigenvalue
    decomposition of the whiten Sb.
  • outdim: The output dimension, i.e. dimension of the transformed space min(d, nc-1)
  • regcoef: The regularization coefficient (default: 1.0e-6). A positive value regcoef * eigmax(Sw) is added to the diagonal of Sw to improve numerical stability.
  • covestimator_between: Custom covariance estimator for between-class covariance (default: SimpleCovariance()). The covariance matrix will be calculated as cov(covestimator_between, #=data=#; dims=2, mean=zeros(#=...=#)). Custom covariance estimators, available in other packages, may result in more robust discriminants for data with more features than observations.
  • covestimator_within: Custom covariance estimator for within-class covariance (default: SimpleCovariance()). The covariance matrix will be calculated as cov(covestimator_within, #=data=#; dims=2, mean=zeros(nc)). Custom covariance estimators, available in other packages, may result in more robust discriminants for data with more features than observations.

Notes:

The resultant projection matrix $P$ satisfies:

\[\mathbf{P}^T (\mathbf{S}_w + \kappa \mathbf{I}) \mathbf{P} = \mathbf{I}\]

Here, $\kappa$ equals regcoef * eigmax(Sw). The columns of $P$ are arranged in descending order of the corresponding generalized eigenvalues.

Note that MulticlassLDA does not currently support the normalized version using $\mathbf{S}_w^*$ and $\mathbf{S}_b^*$ (see SubspaceLDA).

source
StatsAPI.predict — Method
predict(M::MulticlassLDA, x)

Transform input sample(s) in x to the output space of MC-LDA model M. Here, x can be either a sample vector or a matrix comprised of samples in columns.

source
Base.size — Method
size(M::MulticlassLDA)

Get the input (i.e the dimension of the observation space) and output (i.e the dimension of the transformed features) dimensions of the model M.

source
MultivariateStats.classweights — Method
classweights(M)

Get the weights of individual classes (a vector of length $m$). If the samples are not weighted, the weight equals the number of samples of each class.

source

Subspace Linear Discriminant Analysis

The package also defines a SubspaceLDA type to represent a multi-class LDA model for high-dimensional spaces. MulticlassLDA, because it stores the scatter matrices, is not well-suited for high-dimensional data. For example, if you are performing LDA on images, and each image has $10^6$ pixels, then the scatter matrices would contain $10^12$ elements, far too many to store directly. SubspaceLDA calculates the projection direction without the intermediary of the scatter matrices, by focusing on the subspace that lies within the span of the within-class scatter. This also serves to regularize the computation.

SubspaceLDA supports all the same methods as MulticlassLDA, with the exception of the functions that return a scatter matrix. The overall projection is represented as a factorization $P*L$, where $P'*x$ projects data points to the subspace spanned by the within-class scatter, and $L$ is the LDA projection in the subspace. The projection directions $w$ (the columns of $projection(M)$) satisfy the equation

\[ \mathbf{P}^T \mathbf{S}_b \mathbf{w} = \lambda \mathbf{P}^T \mathbf{S}_w \mathbf{w}.\]

When $P$ is of full rank (e.g., if there are more data points than dimensions), then this equation guarantees that $\mathbf{S}_b \mathbf{w} = \lambda \mathbf{S}_w \mathbf{w}$ will also hold.

The package defines a SubspaceLDA type to represent a multi-class LDA model, as:

MultivariateStats.SubspaceLDA — Type

Subspace LDA model type has following fields:

  • projw: the projection matrix of the subspace spanned by the between-class scatter
  • projLDA: the projection matrix of the subspace spanned by the within-class scatter
  • λ: the projection eigenvalues
  • cmeans: the class centroids
  • cweights: the class weights
source

Several methods are provided to access properties of the LDA model. Let M be an instance of SubspaceLDA:

StatsAPI.fit — Method
fit(SubspaceLDA, X, y; normalize=true)

Fit an subspace projection of LDA model over a given data set X with corresponding labels y using the equivalent of $\mathbf{S}_w^*$ and $\mathbf{S}_b^*$`.

Note: Subspace LDA also supports the normalized version of LDA via the normalize keyword.

source
StatsAPI.predict — Method
predict(M::SubspaceLDA, x)

Transform input sample(s) in x to the output space of LDA model M. Here, x can be either a sample vector or a matrix comprised of samples in columns.

source
Base.size — Method
size(M)

Get the input (i.e the dimension of the observation space) and output (i.e the dimension of the subspace projection) dimensions of the model M.

source
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Two-class Linear Discriminant Analysis

This package uses the LinearDiscriminant type to capture a linear discriminant functional:

MultivariateStats.LinearDiscriminant — Type

A linear discriminant functional can be written as

\[ f(\mathbf{x}) = \mathbf{w}^T \mathbf{x} + b\]

Here, $w$ is the coefficient vector, and $b$ is the bias constant.

source

This type comes with several methods where $f$ be an instance of LinearDiscriminant.

StatsAPI.fit — Method
fit(LinearDiscriminant, Xp, Xn; covestimator = SimpleCovariance())

Performs LDA given both positive and negative samples. The function accepts following parameters:

Parameters

  • Xp: The sample matrix of the positive class.
  • Xn: The sample matrix of the negative class.

Keyword arguments:

  • covestimator: Custom covariance estimator for between-class covariance. The covariance matrix will be calculated as cov(covestimator_between, #=data=#; dims=2, mean=zeros(#=...=#). Custom covariance estimators, available in other packages, may result in more robust discriminants for data with more features than observations.
source
MultivariateStats.evaluate — Method
evaluate(f, X::AbstractMatrix)

Evaluate the linear discriminant value, i.e $w'x + b$, for each sample in columns of X. The function returns a vector of length size(X, 2).

source
StatsAPI.predict — Method
predict(f, x::AbstractVector)

Make prediction for the vector x. It returns true iff evaluate(f, x) is positive.

source
StatsAPI.coef — Method
coef(f::LinearDiscriminant)

Return the coefficients of the linear discriminant model.

source
StatsAPI.dof — Method
dof(f::LinearDiscriminant)

Return the number of degrees of freedom in the linear discriminant model.

source
StatsAPI.weights — Method
weights(f::LinearDiscriminant)

Return the linear discriminant model coefficient vector.

source
Base.length — Method
length(f::LinearDiscriminant)

Get the length of the coefficient vector.

source

Additional functionality:

MultivariateStats.ldacov — Function
ldacov(C, μp, μn)

Performs LDA given a covariance matrix C and both mean vectors μp & μn. Returns a linear discriminant functional of type LinearDiscriminant.

Parameters

  • C: The pooled covariance matrix (i.e $(Cp + Cn)/2$)
  • μp: The mean vector of the positive class.
  • μn: The mean vector of the negative class.
source
ldacov(Cp, Cn, μp, μn)

Performs LDA given covariances and mean vectors. Returns a linear discriminant functional of type LinearDiscriminant.

Parameters

  • Cp: The covariance matrix of the positive class.
  • Cn: The covariance matrix of the negative class.
  • μp: The mean vector of the positive class.
  • μn: The mean vector of the negative class.

Note: The coefficient vector is scaled such that $w'μp + b = 1$ and $w'μn + b = -1$.

source

Multi-class Linear Discriminant Analysis

Multi-class LDA is a generalization of standard two-class LDA that can handle arbitrary number of classes.

Overview

Multi-class LDA is based on the analysis of two scatter matrices: within-class scatter matrix and between-class scatter matrix.

Given a set of samples $\mathbf{x}_1, \ldots, \mathbf{x}_n$, and their class labels $y_1, \ldots, y_n$:

  • The within-class scatter matrix is defined as:

\[\mathbf{S}_w = \sum_{i=1}^n (\mathbf{x}_i - \boldsymbol{\mu}_{y_i}) (\mathbf{x}_i - \boldsymbol{\mu}_{y_i})^T\]

Here, $\boldsymbol{\mu}_k$ is the sample mean of the $k$-th class.

  • The between-class scatter matrix is defined as:

\[\mathbf{S}_b = \sum_{k=1}^m n_k (\boldsymbol{\mu}_k - \boldsymbol{\mu}) (\boldsymbol{\mu}_k - \boldsymbol{\mu})^T\]

Here, $m$ is the number of classes, $\boldsymbol{\mu}$ is the overall sample mean, and $n_k$ is the number of samples in the $k$-th class.

Then, multi-class LDA can be formulated as an optimization problem to find a set of linear combinations (with coefficients $\mathbf{w}$) that maximizes the ratio of the between-class scattering to the within-class scattering, as

\[\hat{\mathbf{w}} = \mathop{\mathrm{argmax}}_{\mathbf{w}} + \frac{\mathbf{w}^T \mathbf{S}_b \mathbf{w}}{\mathbf{w}^T \mathbf{S}_w \mathbf{w}}\]

The solution is given by the following generalized eigenvalue problem:

\[\mathbf{S}_b \mathbf{w} = \lambda \mathbf{S}_w \mathbf{w}\]

Generally, at most $m - 1$ generalized eigenvectors are useful to discriminate between $m$ classes.

When the dimensionality is high, it may not be feasible to construct the scatter matrices explicitly. In such cases, see SubspaceLDA below.

Normalization by number of observations

An alternative definition of the within- and between-class scatter matrices normalizes for the number of observations in each group:

\[\mathbf{S}_w^* = n \sum_{k=1}^m \frac{1}{n_k} \sum_{i \mid y_i=k} (\mathbf{x}_i - \boldsymbol{\mu}_{k}) (\mathbf{x}_i - \boldsymbol{\mu}_{k})^T\]

\[\mathbf{S}_b^* = n \sum_{k=1}^m (\boldsymbol{\mu}_k - \boldsymbol{\mu}^*) (\boldsymbol{\mu}_k - \boldsymbol{\mu}^*)^T\]

where

\[\boldsymbol{\mu}^* = \frac{1}{k} \sum_{k=1}^m \boldsymbol{\mu}_k.\]

This definition can sometimes be more useful when looking for directions which discriminate among clusters containing widely-varying numbers of observations.

Multi-class LDA

The package defines a MulticlassLDA type to represent a multi-class LDA model, as:

MultivariateStats.MulticlassLDA — Type

A multi-class linear discriminant model type has following fields:

  • proj is the projection matrix
  • pmeans is the projected means of all classes
  • stats is an instance of MulticlassLDAStats type that captures all statistics computed to train the model (which we will discuss later).
source

Several methods are provided to access properties of the LDA model. Let M be an instance of MulticlassLDA:

StatsAPI.fit — Method
fit(MulticlassLDA, X, y; ...)

Perform multi-class LDA over a given data set X with corresponding labels y with nc number of classes.

This function returns the resultant multi-class LDA model as an instance of MulticlassLDA.

Parameters

  • X: the matrix of input samples, of size (d, n). Each column in X is an observation.
  • y: the vector of class labels, of length n.

Keyword arguments

  • method: The choice of methods:
    • :gevd: based on generalized eigenvalue decomposition (default).
    • :whiten: first derive a whitening transform from Sw and then solve the problem based on eigenvalue
    decomposition of the whiten Sb.
  • outdim: The output dimension, i.e. dimension of the transformed space min(d, nc-1)
  • regcoef: The regularization coefficient (default: 1.0e-6). A positive value regcoef * eigmax(Sw) is added to the diagonal of Sw to improve numerical stability.
  • covestimator_between: Custom covariance estimator for between-class covariance (default: SimpleCovariance()). The covariance matrix will be calculated as cov(covestimator_between, #=data=#; dims=2, mean=zeros(#=...=#)). Custom covariance estimators, available in other packages, may result in more robust discriminants for data with more features than observations.
  • covestimator_within: Custom covariance estimator for within-class covariance (default: SimpleCovariance()). The covariance matrix will be calculated as cov(covestimator_within, #=data=#; dims=2, mean=zeros(nc)). Custom covariance estimators, available in other packages, may result in more robust discriminants for data with more features than observations.

Notes:

The resultant projection matrix $P$ satisfies:

\[\mathbf{P}^T (\mathbf{S}_w + \kappa \mathbf{I}) \mathbf{P} = \mathbf{I}\]

Here, $\kappa$ equals regcoef * eigmax(Sw). The columns of $P$ are arranged in descending order of the corresponding generalized eigenvalues.

Note that MulticlassLDA does not currently support the normalized version using $\mathbf{S}_w^*$ and $\mathbf{S}_b^*$ (see SubspaceLDA).

source
StatsAPI.predict — Method
predict(M::MulticlassLDA, x)

Transform input sample(s) in x to the output space of MC-LDA model M. Here, x can be either a sample vector or a matrix comprised of samples in columns.

source
Base.size — Method
size(M::MulticlassLDA)

Get the input (i.e the dimension of the observation space) and output (i.e the dimension of the transformed features) dimensions of the model M.

source
MultivariateStats.classweights — Method
classweights(M)

Get the weights of individual classes (a vector of length $m$). If the samples are not weighted, the weight equals the number of samples of each class.

source

Subspace Linear Discriminant Analysis

The package also defines a SubspaceLDA type to represent a multi-class LDA model for high-dimensional spaces. MulticlassLDA, because it stores the scatter matrices, is not well-suited for high-dimensional data. For example, if you are performing LDA on images, and each image has $10^6$ pixels, then the scatter matrices would contain $10^12$ elements, far too many to store directly. SubspaceLDA calculates the projection direction without the intermediary of the scatter matrices, by focusing on the subspace that lies within the span of the within-class scatter. This also serves to regularize the computation.

SubspaceLDA supports all the same methods as MulticlassLDA, with the exception of the functions that return a scatter matrix. The overall projection is represented as a factorization $P*L$, where $P'*x$ projects data points to the subspace spanned by the within-class scatter, and $L$ is the LDA projection in the subspace. The projection directions $w$ (the columns of $projection(M)$) satisfy the equation

\[ \mathbf{P}^T \mathbf{S}_b \mathbf{w} = \lambda \mathbf{P}^T \mathbf{S}_w \mathbf{w}.\]

When $P$ is of full rank (e.g., if there are more data points than dimensions), then this equation guarantees that $\mathbf{S}_b \mathbf{w} = \lambda \mathbf{S}_w \mathbf{w}$ will also hold.

The package defines a SubspaceLDA type to represent a multi-class LDA model, as:

MultivariateStats.SubspaceLDA — Type

Subspace LDA model type has following fields:

  • projw: the projection matrix of the subspace spanned by the between-class scatter
  • projLDA: the projection matrix of the subspace spanned by the within-class scatter
  • λ: the projection eigenvalues
  • cmeans: the class centroids
  • cweights: the class weights
source

Several methods are provided to access properties of the LDA model. Let M be an instance of SubspaceLDA:

StatsAPI.fit — Method
fit(SubspaceLDA, X, y; normalize=true)

Fit an subspace projection of LDA model over a given data set X with corresponding labels y using the equivalent of $\mathbf{S}_w^*$ and $\mathbf{S}_b^*$`.

Note: Subspace LDA also supports the normalized version of LDA via the normalize keyword.

source
StatsAPI.predict — Method
predict(M::SubspaceLDA, x)

Transform input sample(s) in x to the output space of LDA model M. Here, x can be either a sample vector or a matrix comprised of samples in columns.

source
Base.size — Method
size(M)

Get the input (i.e the dimension of the observation space) and output (i.e the dimension of the subspace projection) dimensions of the model M.

source
diff --git a/dev/lreg/index.html b/dev/lreg/index.html index f9cf862..34fbfe6 100644 --- a/dev/lreg/index.html +++ b/dev/lreg/index.html @@ -17,102 +17,102 @@ end - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

For a single response vector y (without using bias):

# prepare data
 X = rand(1000, 3)               # feature matrix
 a0 = rand(3)                    # ground truths
@@ -152,10 +152,10 @@
 # do prediction
 Yp = X'*A .+ b'

Linear Least Square

Linear Least Square is to find linear combination(s) of given variables to fit the responses by minimizing the squared error between them. This can be formulated as an optimization as follows:

\[\mathop{\mathrm{minimize}}_{(\mathbf{a}, b)} \ \frac{1}{2} \|\mathbf{y} - (\mathbf{X} \mathbf{a} + b)\|^2\]

Sometimes, the coefficient matrix is given in a transposed form, in which case, the optimization is modified as:

\[\mathop{\mathrm{minimize}}_{(\mathbf{a}, b)} \ - \frac{1}{2} \|\mathbf{y} - (\mathbf{X}^T \mathbf{a} + b)\|^2\]

The package provides following functions to solve the above problems:

MultivariateStats.llsq — Function
llsq(X, y; ...)

Solve the linear least square problem.

Here, y can be either a vector, or a matrix where each column is a response vector.

This function accepts two keyword arguments:

  • dims: whether input observations are stored as rows (1) or columns (2). (default is 1)
  • bias: whether to include the bias term b. (default is true)

The function results the solution a. In particular, when y is a vector (matrix), a is also a vector (matrix). If bias is true, then the returned array is augmented as [a; b].

source

Ridge Regression

Compared to linear least square, Ridge Regression uses an additional quadratic term to regularize the problem:

\[\mathop{\mathrm{minimize}}_{(\mathbf{a}, b)} \ + \frac{1}{2} \|\mathbf{y} - (\mathbf{X}^T \mathbf{a} + b)\|^2\]

The package provides following functions to solve the above problems:

MultivariateStats.llsq — Function
llsq(X, y; ...)

Solve the linear least square problem.

Here, y can be either a vector, or a matrix where each column is a response vector.

This function accepts two keyword arguments:

  • dims: whether input observations are stored as rows (1) or columns (2). (default is 1)
  • bias: whether to include the bias term b. (default is true)

The function results the solution a. In particular, when y is a vector (matrix), a is also a vector (matrix). If bias is true, then the returned array is augmented as [a; b].

source

Ridge Regression

Compared to linear least square, Ridge Regression uses an additional quadratic term to regularize the problem:

\[\mathop{\mathrm{minimize}}_{(\mathbf{a}, b)} \ \frac{1}{2} \|\mathbf{y} - (\mathbf{X} \mathbf{a} + b)\|^2 + \frac{1}{2} \mathbf{a}^T \mathbf{Q} \mathbf{a}\]

The transposed form:

\[ \mathop{\mathrm{minimize}}_{(\mathbf{a}, b)} \ \frac{1}{2} \|\mathbf{y} - (\mathbf{X}^T \mathbf{a} + b)\|^2 + - \frac{1}{2} \mathbf{a}^T \mathbf{Q} \mathbf{a}\]

The package provides following functions to solve the above problems:

MultivariateStats.ridge — Function
ridge(X, y, r; ...)

Solve the ridge regression problem.

Here, $y$ can be either a vector, or a matrix where each column is a response vector.

The argument r gives the quadratic regularization matrix $Q$, which can be in either of the following forms:

  • r is a real scalar, then $Q$ is considered to be r * eye(n), where n is the dimension of a.
  • r is a real vector, then $Q$ is considered to be diagm(r).
  • r is a real symmetric matrix, then $Q$ is simply considered to be r.

This function accepts two keyword arguments:

  • dims: whether input observations are stored as rows (1) or columns (2). (default is 1)
  • bias: whether to include the bias term b. (default is true)

The function results the solution a. In particular, when y is a vector (matrix), a is also a vector (matrix). If bias is true, then the returned array is augmented as [a; b].

source

Isotonic Regression

Isotonic regression or monotonic regression fits a sequence of observations into a fitted line that is non-decreasing (or non-increasing) everywhere. The problem defined as a weighted least-squares fit ${\hat {y}}_{i} \approx y_{i}$ for all $i$, subject to the constraint that ${\hat {y}}_{i} \leq {\hat {y}}_{j}$ whenever $x_{i} \leq x_{j}$. This gives the following quadratic program:

\[\min \sum_{i=1}^{n} w_{i}({\hat {y}}_{i}-y_{i})^{2} + \frac{1}{2} \mathbf{a}^T \mathbf{Q} \mathbf{a}\]

The package provides following functions to solve the above problems:

MultivariateStats.ridge — Function
ridge(X, y, r; ...)

Solve the ridge regression problem.

Here, $y$ can be either a vector, or a matrix where each column is a response vector.

The argument r gives the quadratic regularization matrix $Q$, which can be in either of the following forms:

  • r is a real scalar, then $Q$ is considered to be r * eye(n), where n is the dimension of a.
  • r is a real vector, then $Q$ is considered to be diagm(r).
  • r is a real symmetric matrix, then $Q$ is simply considered to be r.

This function accepts two keyword arguments:

  • dims: whether input observations are stored as rows (1) or columns (2). (default is 1)
  • bias: whether to include the bias term b. (default is true)

The function results the solution a. In particular, when y is a vector (matrix), a is also a vector (matrix). If bias is true, then the returned array is augmented as [a; b].

source

Isotonic Regression

Isotonic regression or monotonic regression fits a sequence of observations into a fitted line that is non-decreasing (or non-increasing) everywhere. The problem defined as a weighted least-squares fit ${\hat {y}}_{i} \approx y_{i}$ for all $i$, subject to the constraint that ${\hat {y}}_{i} \leq {\hat {y}}_{j}$ whenever $x_{i} \leq x_{j}$. This gives the following quadratic program:

\[\min \sum_{i=1}^{n} w_{i}({\hat {y}}_{i}-y_{i})^{2} \text{ subject to } {\hat {y}}_{i} \leq {\hat {y}}_{j} -\text{ for all } (i,j) \in E\]

where $E=\{(i,j):x_{i}\leq x_{j}\}$ specifies the partial ordering of the observed inputs $x_{i}$.

The package provides following functions to solve the above problems:

MultivariateStats.isotonic — Function
isotonic(x, y[, w])

Solve the isotonic regression problem using the pool adjacent violators algorithm[1].

Here x is the regressor vector, y is response vector, and w is an optional weights vector.

The function returns a prediction vector of the same size as the regressor vector x.

source

References

  • 1Best, M.J., Chakravarti, N. Active set algorithms for isotonic regression; A unifying framework. Mathematical Programming 47, 425–439 (1990).
+\text{ for all } (i,j) \in E\]

where $E=\{(i,j):x_{i}\leq x_{j}\}$ specifies the partial ordering of the observed inputs $x_{i}$.

The package provides following functions to solve the above problems:

MultivariateStats.isotonic — Function
isotonic(x, y[, w])

Solve the isotonic regression problem using the pool adjacent violators algorithm[1].

Here x is the regressor vector, y is response vector, and w is an optional weights vector.

The function returns a prediction vector of the same size as the regressor vector x.

source

References

  • 1Best, M.J., Chakravarti, N. Active set algorithms for isotonic regression; A unifying framework. Mathematical Programming 47, 425–439 (1990).
diff --git a/dev/mds/index.html b/dev/mds/index.html index 8b4d5c5..763290a 100644 --- a/dev/mds/index.html +++ b/dev/mds/index.html @@ -18,138 +18,138 @@ scatter!(virginica[1,:],virginica[2,:],virginica[3,:],marker=:circle,linewidth=0) - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Classical Multidimensional Scaling

This package defines a MDS type to represent a classical MDS model[1], and provides a set of methods to access the properties.

MultivariateStats.MDS — Type

Classical Multidimensional Scaling (MDS), also known as Principal Coordinates Analysis (PCoA), is a specific technique in this family that accomplishes the embedding in two steps:

  1. Convert the distance matrix to a Gram matrix. This conversion is based on

the following relations between a distance matrix $D$ and a Gram matrix $G$:

\[\mathrm{sqr}(\mathbf{D}) = \mathbf{g} \mathbf{1}^T + \mathbf{1} \mathbf{g}^T - 2 \mathbf{G}\]

Here, $\mathrm{sqr}(\mathbf{D})$ indicates the element-wise square of $\mathbf{D}$, and $\mathbf{g}$ is the diagonal elements of $\mathbf{G}$. This relation is itself based on the following decomposition of squared Euclidean distance:

\[\| \mathbf{x} - \mathbf{y} \|^2 = \| \mathbf{x} \|^2 + \| \mathbf{y} \|^2 - 2 \mathbf{x}^T \mathbf{y}\]

  1. Perform eigenvalue decomposition of the Gram matrix to derive the coordinates.

Note: The Gramian derived from $D$ may have non-positive or degenerate eigenvalues. The subspace of non-positive eigenvalues is projected out of the MDS solution so that the strain function is minimized in a least-squares sense. If the smallest remaining eigenvalue that is used for the MDS is degenerate, then the solution is not unique, as any linear combination of degenerate eigenvectors will also yield a MDS solution with the same strain value.

source

The MDS method type comes with several methods where $M$ be an instance of MDS, $d$ be the dimension of observations, and $p$ be the output dimension, i.e. the embedding dimension, and $n$ is the number of the observations.

StatsAPI.fit — Method
fit(MDS, X; kwargs...)

Compute an embedding of X points by classical multidimensional scaling (MDS). There are two calling options, specified via the required keyword argument distances:

mds = fit(MDS, X; distances=false, maxoutdim=size(X,1)-1)

where X is the data matrix. Distances between pairs of columns of X are computed using the Euclidean norm. This is equivalent to performing PCA on X.

mds = fit(MDS, D; distances=true, maxoutdim=size(D,1)-1)

where D is a symmetric matrix D of distances between points.

source
StatsAPI.predict — Method
predict(M)

Returns a coordinate matrix of size $(p, n)$ for the MDS model M, where each column is the coordinates for an observation in the embedding space.

source
StatsAPI.predict — Method
predict(M, x::AbstractVector)

Calculate the out-of-sample transformation of the observation x for the MDS model M. Here, x is a vector of length d.

source
Base.size — Method
size(M::MDS)

Returns tuple where the first value is the MDS model M input dimension, i.e the dimension of the observation space, and the second value is the output dimension, i.e the dimension of the embedding.

source
MultivariateStats.projection — Method
projection(M::MDS)

Get the MDS model M eigenvectors matrix (of size $(n, p)$) of the embedding space. The eigenvectors are arranged in descending order of the corresponding eigenvalues.

source

This package provides following functions related to classical MDS.

Metric Multidimensional Scaling

This package defines a MetricMDS type to represent a (non)metric MDS model[1], and provides a set of methods to access the properties.

MultivariateStats.MetricMDS — Type

(Non)Metric Multidimensional Scaling

Use this class to perform (non)metric multidimensional scaling.

There are two calling options, specified via the required keyword argument distances:

mds = fit(MDS, X; distances=false, maxoutdim=size(X,1)-1)

where X is the data matrix. Distances between pairs of columns of X are computed using the Euclidean norm. This is equivalent to performing PCA on X.

mds = fit(MDS, D; distances=true, maxoutdim=size(D,1)-1)

where D is a symmetric matrix D of distances between points.

In addition, the metric parameter specifies type of MDS, By default, it is assigned with nothing value which results in performing metric MDS with dissimilarities calculated as Euclidean distances.

An arbitrary transformation function can be provided to metric parameter to perform metric MDS with transformed proximities. The function has to accept two parameters, a vector of proximities and a vector of distances, corresponding to the proximities, to calculate disparities required for stress calculation. Internally, the proximity and distance vectors are obtained from compact triangular matrix representation of proximity and distance matrices.

For ratio MDS, a following ratio transformation function can be used

mds = fit(MDS, D; distances=true, metric=((p,d)->2 .* p))

For order MDS, use isotonic regression function in the metric parameter:

mds = fit(MDS, D; distances=true, metric=isotonic)
source

The metric MDS type comes with several methods where $M$ be an instance of MetricMDS, $d$ be the dimension of observations, and $p$ be the output dimension, i.e. the embedding dimension, and $n$ is the number of the observations.

StatsAPI.fit — Method
fit(MetricMDS, X; kwargs...)

Compute an embedding of X points by (non)metric multidimensional scaling (MDS).

Keyword arguments:

Let (d, n) = size(X) be respectively the input dimension and the number of observations:

  • distances: The choice of input (required):
    • false: use X to calculate dissimilarity matrix using Euclidean distance
    • true: use X input as precomputed dissimilarity symmetric matrix (distances)
  • maxoutdim: Maximum output dimension (default d-1)
  • metric : a function for calculation of disparity values
    • nothing: use dissimilarity values as the disparities to perform the metric MDS (default)
    • isotonic: converts dissimilarity values to ordinal disparities to perform non-metric MDS
    • any two parameter disparity transformation function, where the first parameter is a vector of proximities (i.e. dissimilarities) and the second parameter is a vector of distances, e.g. (p,d)->b*p for some b is a transformation function for ratio MDS.
  • tol: Convergence tolerance (default 1.0e-3)
  • maxiter: Maximum number of iterations (default 300)
  • initial: an initial reduced space point configuration
    • nothing: then an initial configuration is randomly generated (default)
    • pre-defined matrix
  • weights: a weight matrix
    • nothing: then weights are set to one, $w_{ij} = 1$ (default)
    • pre-defined matrix

Note: if the algorithm is unable to converge then ConvergenceException is thrown.

source
StatsAPI.predict — Method
predict(M::MetricMDS)

Returns a coordinate matrix of size $(p, n)$ for the MDS model M, where each column is the coordinates for an observation in the embedding space.

source
Base.size — Method
size(M::MetricMDS)

Returns tuple where the first value is the MDS model M input dimension, i.e the dimension of the observation space, and the second value is the output dimension, i.e the dimension of the embedding.

source

References

  • 1Ingwer Borg and Patrick J. F. Groenen, "Modern Multidimensional Scaling: Theory and Applications", Springer, pp. 201–268, 2005.
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

Classical Multidimensional Scaling

This package defines a MDS type to represent a classical MDS model[1], and provides a set of methods to access the properties.

MultivariateStats.MDS — Type

Classical Multidimensional Scaling (MDS), also known as Principal Coordinates Analysis (PCoA), is a specific technique in this family that accomplishes the embedding in two steps:

  1. Convert the distance matrix to a Gram matrix. This conversion is based on

the following relations between a distance matrix $D$ and a Gram matrix $G$:

\[\mathrm{sqr}(\mathbf{D}) = \mathbf{g} \mathbf{1}^T + \mathbf{1} \mathbf{g}^T - 2 \mathbf{G}\]

Here, $\mathrm{sqr}(\mathbf{D})$ indicates the element-wise square of $\mathbf{D}$, and $\mathbf{g}$ is the diagonal elements of $\mathbf{G}$. This relation is itself based on the following decomposition of squared Euclidean distance:

\[\| \mathbf{x} - \mathbf{y} \|^2 = \| \mathbf{x} \|^2 + \| \mathbf{y} \|^2 - 2 \mathbf{x}^T \mathbf{y}\]

  1. Perform eigenvalue decomposition of the Gram matrix to derive the coordinates.

Note: The Gramian derived from $D$ may have non-positive or degenerate eigenvalues. The subspace of non-positive eigenvalues is projected out of the MDS solution so that the strain function is minimized in a least-squares sense. If the smallest remaining eigenvalue that is used for the MDS is degenerate, then the solution is not unique, as any linear combination of degenerate eigenvectors will also yield a MDS solution with the same strain value.

source

The MDS method type comes with several methods where $M$ be an instance of MDS, $d$ be the dimension of observations, and $p$ be the output dimension, i.e. the embedding dimension, and $n$ is the number of the observations.

StatsAPI.fit — Method
fit(MDS, X; kwargs...)

Compute an embedding of X points by classical multidimensional scaling (MDS). There are two calling options, specified via the required keyword argument distances:

mds = fit(MDS, X; distances=false, maxoutdim=size(X,1)-1)

where X is the data matrix. Distances between pairs of columns of X are computed using the Euclidean norm. This is equivalent to performing PCA on X.

mds = fit(MDS, D; distances=true, maxoutdim=size(D,1)-1)

where D is a symmetric matrix D of distances between points.

source
StatsAPI.predict — Method
predict(M)

Returns a coordinate matrix of size $(p, n)$ for the MDS model M, where each column is the coordinates for an observation in the embedding space.

source
StatsAPI.predict — Method
predict(M, x::AbstractVector)

Calculate the out-of-sample transformation of the observation x for the MDS model M. Here, x is a vector of length d.

source
Base.size — Method
size(M::MDS)

Returns tuple where the first value is the MDS model M input dimension, i.e the dimension of the observation space, and the second value is the output dimension, i.e the dimension of the embedding.

source
MultivariateStats.projection — Method
projection(M::MDS)

Get the MDS model M eigenvectors matrix (of size $(n, p)$) of the embedding space. The eigenvectors are arranged in descending order of the corresponding eigenvalues.

source

This package provides following functions related to classical MDS.

Metric Multidimensional Scaling

This package defines a MetricMDS type to represent a (non)metric MDS model[1], and provides a set of methods to access the properties.

MultivariateStats.MetricMDS — Type

(Non)Metric Multidimensional Scaling

Use this class to perform (non)metric multidimensional scaling.

There are two calling options, specified via the required keyword argument distances:

mds = fit(MDS, X; distances=false, maxoutdim=size(X,1)-1)

where X is the data matrix. Distances between pairs of columns of X are computed using the Euclidean norm. This is equivalent to performing PCA on X.

mds = fit(MDS, D; distances=true, maxoutdim=size(D,1)-1)

where D is a symmetric matrix D of distances between points.

In addition, the metric parameter specifies type of MDS, By default, it is assigned with nothing value which results in performing metric MDS with dissimilarities calculated as Euclidean distances.

An arbitrary transformation function can be provided to metric parameter to perform metric MDS with transformed proximities. The function has to accept two parameters, a vector of proximities and a vector of distances, corresponding to the proximities, to calculate disparities required for stress calculation. Internally, the proximity and distance vectors are obtained from compact triangular matrix representation of proximity and distance matrices.

For ratio MDS, a following ratio transformation function can be used

mds = fit(MDS, D; distances=true, metric=((p,d)->2 .* p))

For order MDS, use isotonic regression function in the metric parameter:

mds = fit(MDS, D; distances=true, metric=isotonic)
source

The metric MDS type comes with several methods where $M$ be an instance of MetricMDS, $d$ be the dimension of observations, and $p$ be the output dimension, i.e. the embedding dimension, and $n$ is the number of the observations.

StatsAPI.fit — Method
fit(MetricMDS, X; kwargs...)

Compute an embedding of X points by (non)metric multidimensional scaling (MDS).

Keyword arguments:

Let (d, n) = size(X) be respectively the input dimension and the number of observations:

  • distances: The choice of input (required):
    • false: use X to calculate dissimilarity matrix using Euclidean distance
    • true: use X input as precomputed dissimilarity symmetric matrix (distances)
  • maxoutdim: Maximum output dimension (default d-1)
  • metric : a function for calculation of disparity values
    • nothing: use dissimilarity values as the disparities to perform the metric MDS (default)
    • isotonic: converts dissimilarity values to ordinal disparities to perform non-metric MDS
    • any two parameter disparity transformation function, where the first parameter is a vector of proximities (i.e. dissimilarities) and the second parameter is a vector of distances, e.g. (p,d)->b*p for some b is a transformation function for ratio MDS.
  • tol: Convergence tolerance (default 1.0e-3)
  • maxiter: Maximum number of iterations (default 300)
  • initial: an initial reduced space point configuration
    • nothing: then an initial configuration is randomly generated (default)
    • pre-defined matrix
  • weights: a weight matrix
    • nothing: then weights are set to one, $w_{ij} = 1$ (default)
    • pre-defined matrix

Note: if the algorithm is unable to converge then ConvergenceException is thrown.

source
StatsAPI.predict — Method
predict(M::MetricMDS)

Returns a coordinate matrix of size $(p, n)$ for the MDS model M, where each column is the coordinates for an observation in the embedding space.

source
Base.size — Method
size(M::MetricMDS)

Returns tuple where the first value is the MDS model M input dimension, i.e the dimension of the observation space, and the second value is the output dimension, i.e the dimension of the embedding.

source

References

  • 1Ingwer Borg and Patrick J. F. Groenen, "Modern Multidimensional Scaling: Theory and Applications", Springer, pp. 201–268, 2005.
diff --git a/dev/pca/index.html b/dev/pca/index.html index f3a4a24..54aa659 100644 --- a/dev/pca/index.html +++ b/dev/pca/index.html @@ -10,7 +10,7 @@ # split other half to testing set Xte = Matrix(iris[2:2:end,1:4])' -Xte_labels = Vector(iris[2:2:end,5])

Suppose Xtr and Xte are training and testing data matrix, with each observation in a column. We train a PCA model, allowing up to 3 dimensions:

M = fit(PCA, Xtr; maxoutdim=3)
PCA(indim = 4, outdim = 3, principalratio = 0.9957325846529409)
+Xte_labels = Vector(iris[2:2:end,5])

Suppose Xtr and Xte are training and testing data matrix, with each observation in a column. We train a PCA model, allowing up to 3 dimensions:

M = fit(PCA, Xtr; maxoutdim=3)
PCA(indim = 4, outdim = 3, principalratio = 0.9957325846529407)
 
 Pattern matrix (unstandardized loadings):
 ────────────────────────────────────
@@ -48,141 +48,141 @@
 plot!(p,xlabel="PC1",ylabel="PC2",zlabel="PC3")
- + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Linear Principal Component Analysis

This package uses the PCA type to define a linear PCA model:

This type comes with several methods where $M$ be an instance of PCA, $d$ be the dimension of observations, and $p$ be the output dimension (i.e the dimension of the principal subspace).

StatsAPI.fit — Method
fit(PCA, X; ...)

Perform PCA over the data given in a matrix X. Each column of X is an observation.

Keyword arguments

  • method: The choice of methods:
    • :auto: use :cov when d < n or :svd otherwise (default).
    • :cov: based on covariance matrix decomposition.
    • :svd: based on SVD of the input data.
  • maxoutdim: The output dimension, i.e. dimension of the transformed space (min(d, nc-1))
  • pratio: The ratio of variances preserved in the principal subspace (0.99)
  • mean: The mean vector, which can be either of
    • 0: the input data has already been centralized
    • nothing: this function will compute the mean (default)
    • a pre-computed mean vector

Notes:

  • The output dimension p depends on both maxoutdim and pratio, as follows. Suppose the first k principal components preserve at least pratio of the total variance, while the first k-1 preserves less than pratio, then the actual output dimension will be $\min(k, maxoutdim)$.

  • This function calls pcacov or pcasvd internally, depending on the choice of method.

source
StatsAPI.predict — Method
predict(M::PCA, x::AbstractVecOrMat{<:Real})

Given a PCA model M, transform observations x into principal components space, as

\[\mathbf{y} = \mathbf{P}^T (\mathbf{x} - \boldsymbol{\mu})\]

Here, x can be either a vector of length d or a matrix where each column is an observation, and \mathbf{P} is the projection matrix.

source
MultivariateStats.reconstruct — Method
reconstruct(M::PCA, y::AbstractVecOrMat{<:Real})

Given a PCA model M, returns a (approximately) reconstructed observations from principal components space, as

\[\tilde{\mathbf{x}} = \mathbf{P} \mathbf{y} + \boldsymbol{\mu}\]

Here, y can be either a vector of length p or a matrix where each column gives the principal components for an observation, and $\mathbf{P}$ is the projection matrix.

source
Base.size — Method
size(M)

Returns a tuple with the dimensions of input (the dimension of the observation space) and output (the dimension of the principal subspace).

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MultivariateStats.projection — Method
projection(M::PCA)

Returns the projection matrix (of size (d, p)). Each column of the projection matrix corresponds to a principal component. The principal components are arranged in descending order of the corresponding variances.

source
Statistics.var — Method
var(M::PCA)

Returns the total observation variance, which is equal to tprincipalvar(M) + tresidualvar(M).

source
StatsAPI.r2 — Method
r2(M::PCA)
-principalratio(M::PCA)

Returns the ratio of variance preserved in the principal subspace, which is equal to tprincipalvar(M) / var(M).

source
MultivariateStats.loadings — Method
loadings(M::PCA)

Returns model loadings, i.e. the weights for each original variable when calculating the principal component.

source

Auxiliary functions:

MultivariateStats.pcacov — Function
pcacov(C, mean; ...)

Compute and return a PCA model based on eigenvalue decomposition of a given covariance matrix C.

Parameters:

  • C: The covariance matrix of the samples.
  • mean: The mean vector of original samples, which can be a vector of length d, or an empty vector Float64[] indicating a zero mean.

Note: This function accepts two keyword arguments: maxoutdim and pratio.

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MultivariateStats.pcasvd — Function
pcasvd(Z, mean, tw; ...)

Compute and return a PCA model based on singular value decomposition of a centralized sample matrix Z.

Parameters:

  • Z: a matrix of centralized samples.
  • mean: The mean vector of the original samples, which can be a vector of length d, or an empty vector Float64[] indicating a zero mean.
  • n: a number of samples.

Note: This function accepts two keyword arguments: maxoutdim and pratio.

source

Kernel Principal Component Analysis

Kernel Principal Component Analysis (kernel PCA) is an extension of principal component analysis (PCA) using techniques of kernel methods. Using a kernel, the originally linear operations of PCA are performed in a reproducing kernel Hilbert space.

This package defines a KernelPCA type to represent a kernel PCA model.

The package provides a set of methods to access the properties of the kernel PCA model. Let $M$ be an instance of KernelPCA, $d$ be the dimension of observations, and $p$ be the output dimension (i.e the dimension of the principal subspace).

StatsAPI.fit — Method
fit(KernelPCA, X; ...)

Perform kernel PCA over the data given in a matrix X. Each column of X is an observation.

This method returns an instance of KernelPCA.

Keyword arguments:

Let (d, n) = size(X) be respectively the input dimension and the number of observations:

  • kernel: The kernel function. This functions accepts two vector arguments x and y,

and returns a scalar value (default: (x,y)->x'y). If set to nothing, the matrix X is the pre-computed symmetric kernel (Gram) matrix.

  • solver: The choice of solver:
    • :eig: uses LinearAlgebra.eigen (default)
    • :eigs: uses Arpack.eigs (always used for sparse data)
  • maxoutdim: Maximum output dimension (default min(d, n))
  • inverse: Whether to perform calculation for inverse transform for non-precomputed kernels (default false)
  • β: Hyperparameter of the ridge regression that learns the inverse transform (default 1 when inverse is true).
  • tol: Convergence tolerance for eigs solver (default 0.0)
  • maxiter: Maximum number of iterations for eigs solver (default 300)
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StatsAPI.predict — Method
predict(M::KernelPCA)

Transform the data fitted to the model M to a kernel space of the model.

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StatsAPI.predict — Method
predict(M::KernelPCA, x)

Transform out-of-sample transformation of x into a kernel space of the model M.

Here, x can be either a vector of length d or a matrix where each column is an observation.

source
MultivariateStats.reconstruct — Method
reconstruct(M::KernelPCA, y)

Approximately reconstruct observations, given in y, to the original space using the kernel PCA model M.

Here, y can be either a vector of length p or a matrix where each column gives the principal components for an observation.

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Base.size — Method
size(M::KernelPCA)

Returns a tuple with the input dimension $d$, i.e the dimension of the observation space, and the output dimension $p$, i.e the dimension of the principal subspace.

source
MultivariateStats.projection — Method
projection(M::KernelPCA)

Return the projection matrix (of size $n \times p$). Each column of the projection matrix corresponds to an eigenvector, and $n$ is a number of observations.

The principal components are arranged in descending order of the corresponding eigenvalues.

source

Kernels

List of the commonly used kernels:

functiondescription
(x,y)->x'yLinear
(x,y)->(x'y+c)^dPolynomial
(x,y)->exp(-γ*norm(x-y)^2.0)Radial basis function (RBF)

This package has a separate interface for adjusting kernel matrices.

Probabilistic Principal Component Analysis

Probabilistic Principal Component Analysis (PPCA) represents a constrained form of the Gaussian distribution in which the number of free parameters can be restricted while still allowing the model to capture the dominant correlations in a data set. It is expressed as the maximum likelihood solution of a probabilistic latent variable model[1].

This package defines a PPCA type to represent a probabilistic PCA model, and provides a set of methods to access the properties.

Let $M$ be an instance of PPCA, $d$ be the dimension of observations, and $p$ be the output dimension (i.e the dimension of the principal subspace).

StatsAPI.fit — Function
fit(Whitening, X::AbstractMatrix{T}; kwargs...)

Estimate a whitening transform from the data given in X.

This function returns an instance of Whitening

Keyword Arguments:

  • regcoef: The regularization coefficient. The covariance will be regularized as follows when regcoef is positive C + (eigmax(C) * regcoef) * eye(d). Default values is zero(T).

  • dims: if 1 the transformation calculated from the row samples. fit standardization parameters in column-wise fashion; if 2 the transformation calculated from the column samples. The default is nothing, which is equivalent to dims=2 with a deprecation warning.

  • mean: The mean vector, which can be either of:

    • 0: the input data has already been centralized
    • nothing: this function will compute the mean (default)
    • a pre-computed mean vector

Note: This function internally relies on cov_whitening to derive the transformation W.

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fit(PCA, X; ...)

Perform PCA over the data given in a matrix X. Each column of X is an observation.

Keyword arguments

  • method: The choice of methods:
    • :auto: use :cov when d < n or :svd otherwise (default).
    • :cov: based on covariance matrix decomposition.
    • :svd: based on SVD of the input data.
  • maxoutdim: The output dimension, i.e. dimension of the transformed space (min(d, nc-1))
  • pratio: The ratio of variances preserved in the principal subspace (0.99)
  • mean: The mean vector, which can be either of
    • 0: the input data has already been centralized
    • nothing: this function will compute the mean (default)
    • a pre-computed mean vector

Notes:

  • The output dimension p depends on both maxoutdim and pratio, as follows. Suppose the first k principal components preserve at least pratio of the total variance, while the first k-1 preserves less than pratio, then the actual output dimension will be $\min(k, maxoutdim)$.

  • This function calls pcacov or pcasvd internally, depending on the choice of method.

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fit(PPCA, X; ...)

Perform probabilistic PCA over the data given in a matrix X. Each column of X is an observation. This method returns an instance of PPCA.

Keyword arguments:

Let (d, n) = size(X) be respectively the input dimension and the number of observations:

  • method: The choice of methods:
    • :ml: use maximum likelihood version of probabilistic PCA (default)
    • :em: use EM version of probabilistic PCA
    • :bayes: use Bayesian PCA
  • maxoutdim: Maximum output dimension (default d-1)
  • mean: The mean vector, which can be either of:
    • 0: the input data has already been centralized
    • nothing: this function will compute the mean (default)
    • a pre-computed mean vector
  • tol: Convergence tolerance (default 1.0e-6)
  • maxiter: Maximum number of iterations (default 1000)

Notes: This function calls ppcaml, ppcaem or bayespca internally, depending on the choice of method.

source

Fit KernelCenter object

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fit(KernelPCA, X; ...)

Perform kernel PCA over the data given in a matrix X. Each column of X is an observation.

This method returns an instance of KernelPCA.

Keyword arguments:

Let (d, n) = size(X) be respectively the input dimension and the number of observations:

  • kernel: The kernel function. This functions accepts two vector arguments x and y,

and returns a scalar value (default: (x,y)->x'y). If set to nothing, the matrix X is the pre-computed symmetric kernel (Gram) matrix.

  • solver: The choice of solver:
    • :eig: uses LinearAlgebra.eigen (default)
    • :eigs: uses Arpack.eigs (always used for sparse data)
  • maxoutdim: Maximum output dimension (default min(d, n))
  • inverse: Whether to perform calculation for inverse transform for non-precomputed kernels (default false)
  • β: Hyperparameter of the ridge regression that learns the inverse transform (default 1 when inverse is true).
  • tol: Convergence tolerance for eigs solver (default 0.0)
  • maxiter: Maximum number of iterations for eigs solver (default 300)
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fit(CCA, X, Y; ...)

Perform CCA over the data given in matrices X and Y. Each column of X and Y is an observation.

X and Y should have the same number of columns (denoted by n below).

This method returns an instance of CCA.

Keyword arguments:

  • method: The choice of methods:
    • :cov: based on covariance matrices
    • :svd: based on SVD of the input data (default)
  • outdim: The output dimension, i.e dimension of the common space (default: min(dx, dy, n))
  • mean: The mean vector, which can be either of:
    • 0: the input data has already been centralized
    • nothing: this function will compute the mean (default)
    • a pre-computed mean vector

Notes: This function calls ccacov or ccasvd internally, depending on the choice of method.

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fit(MDS, X; kwargs...)

Compute an embedding of X points by classical multidimensional scaling (MDS). There are two calling options, specified via the required keyword argument distances:

mds = fit(MDS, X; distances=false, maxoutdim=size(X,1)-1)

where X is the data matrix. Distances between pairs of columns of X are computed using the Euclidean norm. This is equivalent to performing PCA on X.

mds = fit(MDS, D; distances=true, maxoutdim=size(D,1)-1)

where D is a symmetric matrix D of distances between points.

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fit(MetricMDS, X; kwargs...)

Compute an embedding of X points by (non)metric multidimensional scaling (MDS).

Keyword arguments:

Let (d, n) = size(X) be respectively the input dimension and the number of observations:

  • distances: The choice of input (required):
    • false: use X to calculate dissimilarity matrix using Euclidean distance
    • true: use X input as precomputed dissimilarity symmetric matrix (distances)
  • maxoutdim: Maximum output dimension (default d-1)
  • metric : a function for calculation of disparity values
    • nothing: use dissimilarity values as the disparities to perform the metric MDS (default)
    • isotonic: converts dissimilarity values to ordinal disparities to perform non-metric MDS
    • any two parameter disparity transformation function, where the first parameter is a vector of proximities (i.e. dissimilarities) and the second parameter is a vector of distances, e.g. (p,d)->b*p for some b is a transformation function for ratio MDS.
  • tol: Convergence tolerance (default 1.0e-3)
  • maxiter: Maximum number of iterations (default 300)
  • initial: an initial reduced space point configuration
    • nothing: then an initial configuration is randomly generated (default)
    • pre-defined matrix
  • weights: a weight matrix
    • nothing: then weights are set to one, $w_{ij} = 1$ (default)
    • pre-defined matrix

Note: if the algorithm is unable to converge then ConvergenceException is thrown.

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fit(LinearDiscriminant, Xp, Xn; covestimator = SimpleCovariance())

Performs LDA given both positive and negative samples. The function accepts following parameters:

Parameters

  • Xp: The sample matrix of the positive class.
  • Xn: The sample matrix of the negative class.

Keyword arguments:

  • covestimator: Custom covariance estimator for between-class covariance. The covariance matrix will be calculated as cov(covestimator_between, #=data=#; dims=2, mean=zeros(#=...=#). Custom covariance estimators, available in other packages, may result in more robust discriminants for data with more features than observations.
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fit(MulticlassLDA, X, y; ...)

Perform multi-class LDA over a given data set X with corresponding labels y with nc number of classes.

This function returns the resultant multi-class LDA model as an instance of MulticlassLDA.

Parameters

  • X: the matrix of input samples, of size (d, n). Each column in X is an observation.
  • y: the vector of class labels, of length n.

Keyword arguments

  • method: The choice of methods:
    • :gevd: based on generalized eigenvalue decomposition (default).
    • :whiten: first derive a whitening transform from Sw and then solve the problem based on eigenvalue
    decomposition of the whiten Sb.
  • outdim: The output dimension, i.e. dimension of the transformed space min(d, nc-1)
  • regcoef: The regularization coefficient (default: 1.0e-6). A positive value regcoef * eigmax(Sw) is added to the diagonal of Sw to improve numerical stability.
  • covestimator_between: Custom covariance estimator for between-class covariance (default: SimpleCovariance()). The covariance matrix will be calculated as cov(covestimator_between, #=data=#; dims=2, mean=zeros(#=...=#)). Custom covariance estimators, available in other packages, may result in more robust discriminants for data with more features than observations.
  • covestimator_within: Custom covariance estimator for within-class covariance (default: SimpleCovariance()). The covariance matrix will be calculated as cov(covestimator_within, #=data=#; dims=2, mean=zeros(nc)). Custom covariance estimators, available in other packages, may result in more robust discriminants for data with more features than observations.

Notes:

The resultant projection matrix $P$ satisfies:

\[\mathbf{P}^T (\mathbf{S}_w + \kappa \mathbf{I}) \mathbf{P} = \mathbf{I}\]

Here, $\kappa$ equals regcoef * eigmax(Sw). The columns of $P$ are arranged in descending order of the corresponding generalized eigenvalues.

Note that MulticlassLDA does not currently support the normalized version using $\mathbf{S}_w^*$ and $\mathbf{S}_b^*$ (see SubspaceLDA).

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fit(SubspaceLDA, X, y; normalize=true)

Fit an subspace projection of LDA model over a given data set X with corresponding labels y using the equivalent of $\mathbf{S}_w^*$ and $\mathbf{S}_b^*$`.

Note: Subspace LDA also supports the normalized version of LDA via the normalize keyword.

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fit(ICA, X, k; ...)

Perform ICA over the data set given in X.

Parameters: -X: The data matrix, of size $(m, n)$. Each row corresponds to a mixed signal, while each column corresponds to an observation (e.g all signal value at a particular time step). -k: The number of independent components to recover.

Keyword Arguments:

  • alg: The choice of algorithm (default :fastica)
  • fun: The approx neg-entropy functor (default Tanh)
  • do_whiten: Whether to perform pre-whitening (default true)
  • maxiter: Maximum number of iterations (default 100)
  • tol: Tolerable change of $W$ at convergence (default 1.0e-6)
  • mean: The mean vector, which can be either of:
    • 0: the input data has already been centralized
    • nothing: this function will compute the mean (default)
    • a pre-computed mean vector
  • winit: Initial guess of $W$, which should be either of:
    • empty matrix: the function will perform random initialization (default)
    • a matrix of size $(k, k)$ (when do_whiten)
    • a matrix of size $(m, k)$ (when !do_whiten)

Returns the resultant ICA model, an instance of type ICA.

Note: If do_whiten is true, the return W satisfies $\mathbf{W}^T \mathbf{C} \mathbf{W} = \mathbf{I}$, otherwise $W$ is orthonormal, i.e $\mathbf{W}^T \mathbf{W} = \mathbf{I}$.

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fit(FactorAnalysis, X; ...)

Perform factor analysis over the data given in a matrix X. Each column of X is an observation. This method returns an instance of FactorAnalysis.

Keyword arguments:

Let (d, n) = size(X) be respectively the input dimension and the number of observations:

  • method: The choice of methods:
    • :em: use EM version of factor analysis
    • :cm: use CM version of factor analysis (default)
  • maxoutdim: Maximum output dimension (default d-1)
  • mean: The mean vector, which can be either of:
    • 0: the input data has already been centralized
    • nothing: this function will compute the mean (default)
    • a pre-computed mean vector
  • tol: Convergence tolerance (default 1.0e-6)
  • maxiter: Maximum number of iterations (default 1000)
  • η: Variance low bound (default 1.0e-6)

Notes: This function calls facm or faem internally, depending on the choice of method.

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Base.size — Method
size(M::PPCA)

Returns a tuple with values of the input dimension $d$, i.e the dimension of the observation space, and the output dimension $p$, i.e the dimension of the principal subspace.

source
MultivariateStats.projection — Method
projection(M::PPCA)

Returns the projection matrix (of size $(d, p)$). Each column of the projection matrix corresponds to a principal component.

The principal components are arranged in descending order of the corresponding variances.

source

Given a probabilistic PCA model $M$, one can use it to transform observations into latent variables, as

\mathbf{z} = (\mathbf{W}^T \mathbf{W} + \sigma^2 \mathbf{I}) \mathbf{W}^T (\mathbf{x} - \boldsymbol{\mu})

or use it to reconstruct (approximately) the observations from latent variables, as

\tilde{\mathbf{x}} = \mathbf{W} \mathbb{E}[\mathbf{z}] + \boldsymbol{\mu}

Here, $\mathbf{W}$ is the factor loadings or weight matrix.

StatsAPI.predict — Method
predict(M::PPCA, x)

Transform observations x into latent variables. Here, x can be either a vector of length d or a matrix where each column is an observation.

source
MultivariateStats.reconstruct — Method
reconstruct(M::PPCA, z)

Approximately reconstruct observations from the latent variable given in z. Here, z can be either a vector of length p or a matrix where each column gives the latent variables for an observation.

source

Auxiliary functions:

MultivariateStats.ppcaml — Function
ppcaml(Z, mean; ...)

Compute probabilistic PCA using on maximum likelihood formulation for a centralized sample matrix Z.

Parameters:

  • Z: a centralized samples matrix
  • mean: The mean vector of the original samples, which can be a vector of

length d, or an empty vector indicating a zero mean.

Returns the resultant PPCA model.

Note: This function accepts two keyword arguments: maxoutdim and tol.

source
MultivariateStats.ppcaem — Function
ppcaem(S, mean, n; ...)

Compute probabilistic PCA based on expectation-maximization algorithm for a given sample covariance matrix S.

Parameters:

  • S: The sample covariance matrix.
  • mean: The mean vector of original samples, which can be a vector of length d,

or an empty vector indicating a zero mean.

  • n: The number of observations.

Returns the resultant PPCA model.

Note: This function accepts three keyword arguments: maxoutdim, tol, and maxiter.

source
MultivariateStats.bayespca — Function
bayespca(S, mean, n; ...)

Compute probabilistic PCA using a Bayesian algorithm for a given sample covariance matrix S.

Parameters:

  • S: The sample covariance matrix.
  • mean: The mean vector of original samples, which can be a vector of length d,

or an empty vector indicating a zero mean.

  • n: The number of observations.

Returns the resultant PPCA model.

Notes:

  • This function accepts three keyword arguments: maxoutdim, tol, and maxiter.
  • Function uses the maxoutdim parameter as an upper boundary when it automatically

determines the latent space dimensionality.

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References

  • 1Bishop, C. M. Pattern Recognition and Machine Learning, 2006.
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

Linear Principal Component Analysis

This package uses the PCA type to define a linear PCA model:

This type comes with several methods where $M$ be an instance of PCA, $d$ be the dimension of observations, and $p$ be the output dimension (i.e the dimension of the principal subspace).

StatsAPI.fit — Method
fit(PCA, X; ...)

Perform PCA over the data given in a matrix X. Each column of X is an observation.

Keyword arguments

  • method: The choice of methods:
    • :auto: use :cov when d < n or :svd otherwise (default).
    • :cov: based on covariance matrix decomposition.
    • :svd: based on SVD of the input data.
  • maxoutdim: The output dimension, i.e. dimension of the transformed space (min(d, nc-1))
  • pratio: The ratio of variances preserved in the principal subspace (0.99)
  • mean: The mean vector, which can be either of
    • 0: the input data has already been centralized
    • nothing: this function will compute the mean (default)
    • a pre-computed mean vector

Notes:

  • The output dimension p depends on both maxoutdim and pratio, as follows. Suppose the first k principal components preserve at least pratio of the total variance, while the first k-1 preserves less than pratio, then the actual output dimension will be $\min(k, maxoutdim)$.

  • This function calls pcacov or pcasvd internally, depending on the choice of method.

source
StatsAPI.predict — Method
predict(M::PCA, x::AbstractVecOrMat{<:Real})

Given a PCA model M, transform observations x into principal components space, as

\[\mathbf{y} = \mathbf{P}^T (\mathbf{x} - \boldsymbol{\mu})\]

Here, x can be either a vector of length d or a matrix where each column is an observation, and \mathbf{P} is the projection matrix.

source
MultivariateStats.reconstruct — Method
reconstruct(M::PCA, y::AbstractVecOrMat{<:Real})

Given a PCA model M, returns a (approximately) reconstructed observations from principal components space, as

\[\tilde{\mathbf{x}} = \mathbf{P} \mathbf{y} + \boldsymbol{\mu}\]

Here, y can be either a vector of length p or a matrix where each column gives the principal components for an observation, and $\mathbf{P}$ is the projection matrix.

source
Base.size — Method
size(M)

Returns a tuple with the dimensions of input (the dimension of the observation space) and output (the dimension of the principal subspace).

source
MultivariateStats.projection — Method
projection(M::PCA)

Returns the projection matrix (of size (d, p)). Each column of the projection matrix corresponds to a principal component. The principal components are arranged in descending order of the corresponding variances.

source
Statistics.var — Method
var(M::PCA)

Returns the total observation variance, which is equal to tprincipalvar(M) + tresidualvar(M).

source
StatsAPI.r2 — Method
r2(M::PCA)
+principalratio(M::PCA)

Returns the ratio of variance preserved in the principal subspace, which is equal to tprincipalvar(M) / var(M).

source
MultivariateStats.loadings — Method
loadings(M::PCA)

Returns model loadings, i.e. the weights for each original variable when calculating the principal component.

source

Auxiliary functions:

MultivariateStats.pcacov — Function
pcacov(C, mean; ...)

Compute and return a PCA model based on eigenvalue decomposition of a given covariance matrix C.

Parameters:

  • C: The covariance matrix of the samples.
  • mean: The mean vector of original samples, which can be a vector of length d, or an empty vector Float64[] indicating a zero mean.

Note: This function accepts two keyword arguments: maxoutdim and pratio.

source
MultivariateStats.pcasvd — Function
pcasvd(Z, mean, tw; ...)

Compute and return a PCA model based on singular value decomposition of a centralized sample matrix Z.

Parameters:

  • Z: a matrix of centralized samples.
  • mean: The mean vector of the original samples, which can be a vector of length d, or an empty vector Float64[] indicating a zero mean.
  • n: a number of samples.

Note: This function accepts two keyword arguments: maxoutdim and pratio.

source

Kernel Principal Component Analysis

Kernel Principal Component Analysis (kernel PCA) is an extension of principal component analysis (PCA) using techniques of kernel methods. Using a kernel, the originally linear operations of PCA are performed in a reproducing kernel Hilbert space.

This package defines a KernelPCA type to represent a kernel PCA model.

The package provides a set of methods to access the properties of the kernel PCA model. Let $M$ be an instance of KernelPCA, $d$ be the dimension of observations, and $p$ be the output dimension (i.e the dimension of the principal subspace).

StatsAPI.fit — Method
fit(KernelPCA, X; ...)

Perform kernel PCA over the data given in a matrix X. Each column of X is an observation.

This method returns an instance of KernelPCA.

Keyword arguments:

Let (d, n) = size(X) be respectively the input dimension and the number of observations:

  • kernel: The kernel function. This functions accepts two vector arguments x and y,

and returns a scalar value (default: (x,y)->x'y). If set to nothing, the matrix X is the pre-computed symmetric kernel (Gram) matrix.

  • solver: The choice of solver:
    • :eig: uses LinearAlgebra.eigen (default)
    • :eigs: uses Arpack.eigs (always used for sparse data)
  • maxoutdim: Maximum output dimension (default min(d, n))
  • inverse: Whether to perform calculation for inverse transform for non-precomputed kernels (default false)
  • β: Hyperparameter of the ridge regression that learns the inverse transform (default 1 when inverse is true).
  • tol: Convergence tolerance for eigs solver (default 0.0)
  • maxiter: Maximum number of iterations for eigs solver (default 300)
source
StatsAPI.predict — Method
predict(M::KernelPCA)

Transform the data fitted to the model M to a kernel space of the model.

source
StatsAPI.predict — Method
predict(M::KernelPCA, x)

Transform out-of-sample transformation of x into a kernel space of the model M.

Here, x can be either a vector of length d or a matrix where each column is an observation.

source
MultivariateStats.reconstruct — Method
reconstruct(M::KernelPCA, y)

Approximately reconstruct observations, given in y, to the original space using the kernel PCA model M.

Here, y can be either a vector of length p or a matrix where each column gives the principal components for an observation.

source
Base.size — Method
size(M::KernelPCA)

Returns a tuple with the input dimension $d$, i.e the dimension of the observation space, and the output dimension $p$, i.e the dimension of the principal subspace.

source
MultivariateStats.projection — Method
projection(M::KernelPCA)

Return the projection matrix (of size $n \times p$). Each column of the projection matrix corresponds to an eigenvector, and $n$ is a number of observations.

The principal components are arranged in descending order of the corresponding eigenvalues.

source

Kernels

List of the commonly used kernels:

functiondescription
(x,y)->x'yLinear
(x,y)->(x'y+c)^dPolynomial
(x,y)->exp(-γ*norm(x-y)^2.0)Radial basis function (RBF)

This package has a separate interface for adjusting kernel matrices.

Probabilistic Principal Component Analysis

Probabilistic Principal Component Analysis (PPCA) represents a constrained form of the Gaussian distribution in which the number of free parameters can be restricted while still allowing the model to capture the dominant correlations in a data set. It is expressed as the maximum likelihood solution of a probabilistic latent variable model[1].

This package defines a PPCA type to represent a probabilistic PCA model, and provides a set of methods to access the properties.

Let $M$ be an instance of PPCA, $d$ be the dimension of observations, and $p$ be the output dimension (i.e the dimension of the principal subspace).

StatsAPI.fit — Function
fit(Whitening, X::AbstractMatrix{T}; kwargs...)

Estimate a whitening transform from the data given in X.

This function returns an instance of Whitening

Keyword Arguments:

  • regcoef: The regularization coefficient. The covariance will be regularized as follows when regcoef is positive C + (eigmax(C) * regcoef) * eye(d). Default values is zero(T).

  • dims: if 1 the transformation calculated from the row samples. fit standardization parameters in column-wise fashion; if 2 the transformation calculated from the column samples. The default is nothing, which is equivalent to dims=2 with a deprecation warning.

  • mean: The mean vector, which can be either of:

    • 0: the input data has already been centralized
    • nothing: this function will compute the mean (default)
    • a pre-computed mean vector

Note: This function internally relies on cov_whitening to derive the transformation W.

source
fit(PCA, X; ...)

Perform PCA over the data given in a matrix X. Each column of X is an observation.

Keyword arguments

  • method: The choice of methods:
    • :auto: use :cov when d < n or :svd otherwise (default).
    • :cov: based on covariance matrix decomposition.
    • :svd: based on SVD of the input data.
  • maxoutdim: The output dimension, i.e. dimension of the transformed space (min(d, nc-1))
  • pratio: The ratio of variances preserved in the principal subspace (0.99)
  • mean: The mean vector, which can be either of
    • 0: the input data has already been centralized
    • nothing: this function will compute the mean (default)
    • a pre-computed mean vector

Notes:

  • The output dimension p depends on both maxoutdim and pratio, as follows. Suppose the first k principal components preserve at least pratio of the total variance, while the first k-1 preserves less than pratio, then the actual output dimension will be $\min(k, maxoutdim)$.

  • This function calls pcacov or pcasvd internally, depending on the choice of method.

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fit(PPCA, X; ...)

Perform probabilistic PCA over the data given in a matrix X. Each column of X is an observation. This method returns an instance of PPCA.

Keyword arguments:

Let (d, n) = size(X) be respectively the input dimension and the number of observations:

  • method: The choice of methods:
    • :ml: use maximum likelihood version of probabilistic PCA (default)
    • :em: use EM version of probabilistic PCA
    • :bayes: use Bayesian PCA
  • maxoutdim: Maximum output dimension (default d-1)
  • mean: The mean vector, which can be either of:
    • 0: the input data has already been centralized
    • nothing: this function will compute the mean (default)
    • a pre-computed mean vector
  • tol: Convergence tolerance (default 1.0e-6)
  • maxiter: Maximum number of iterations (default 1000)

Notes: This function calls ppcaml, ppcaem or bayespca internally, depending on the choice of method.

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Fit KernelCenter object

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fit(KernelPCA, X; ...)

Perform kernel PCA over the data given in a matrix X. Each column of X is an observation.

This method returns an instance of KernelPCA.

Keyword arguments:

Let (d, n) = size(X) be respectively the input dimension and the number of observations:

  • kernel: The kernel function. This functions accepts two vector arguments x and y,

and returns a scalar value (default: (x,y)->x'y). If set to nothing, the matrix X is the pre-computed symmetric kernel (Gram) matrix.

  • solver: The choice of solver:
    • :eig: uses LinearAlgebra.eigen (default)
    • :eigs: uses Arpack.eigs (always used for sparse data)
  • maxoutdim: Maximum output dimension (default min(d, n))
  • inverse: Whether to perform calculation for inverse transform for non-precomputed kernels (default false)
  • β: Hyperparameter of the ridge regression that learns the inverse transform (default 1 when inverse is true).
  • tol: Convergence tolerance for eigs solver (default 0.0)
  • maxiter: Maximum number of iterations for eigs solver (default 300)
source
fit(CCA, X, Y; ...)

Perform CCA over the data given in matrices X and Y. Each column of X and Y is an observation.

X and Y should have the same number of columns (denoted by n below).

This method returns an instance of CCA.

Keyword arguments:

  • method: The choice of methods:
    • :cov: based on covariance matrices
    • :svd: based on SVD of the input data (default)
  • outdim: The output dimension, i.e dimension of the common space (default: min(dx, dy, n))
  • mean: The mean vector, which can be either of:
    • 0: the input data has already been centralized
    • nothing: this function will compute the mean (default)
    • a pre-computed mean vector

Notes: This function calls ccacov or ccasvd internally, depending on the choice of method.

source
fit(MDS, X; kwargs...)

Compute an embedding of X points by classical multidimensional scaling (MDS). There are two calling options, specified via the required keyword argument distances:

mds = fit(MDS, X; distances=false, maxoutdim=size(X,1)-1)

where X is the data matrix. Distances between pairs of columns of X are computed using the Euclidean norm. This is equivalent to performing PCA on X.

mds = fit(MDS, D; distances=true, maxoutdim=size(D,1)-1)

where D is a symmetric matrix D of distances between points.

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fit(MetricMDS, X; kwargs...)

Compute an embedding of X points by (non)metric multidimensional scaling (MDS).

Keyword arguments:

Let (d, n) = size(X) be respectively the input dimension and the number of observations:

  • distances: The choice of input (required):
    • false: use X to calculate dissimilarity matrix using Euclidean distance
    • true: use X input as precomputed dissimilarity symmetric matrix (distances)
  • maxoutdim: Maximum output dimension (default d-1)
  • metric : a function for calculation of disparity values
    • nothing: use dissimilarity values as the disparities to perform the metric MDS (default)
    • isotonic: converts dissimilarity values to ordinal disparities to perform non-metric MDS
    • any two parameter disparity transformation function, where the first parameter is a vector of proximities (i.e. dissimilarities) and the second parameter is a vector of distances, e.g. (p,d)->b*p for some b is a transformation function for ratio MDS.
  • tol: Convergence tolerance (default 1.0e-3)
  • maxiter: Maximum number of iterations (default 300)
  • initial: an initial reduced space point configuration
    • nothing: then an initial configuration is randomly generated (default)
    • pre-defined matrix
  • weights: a weight matrix
    • nothing: then weights are set to one, $w_{ij} = 1$ (default)
    • pre-defined matrix

Note: if the algorithm is unable to converge then ConvergenceException is thrown.

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fit(LinearDiscriminant, Xp, Xn; covestimator = SimpleCovariance())

Performs LDA given both positive and negative samples. The function accepts following parameters:

Parameters

  • Xp: The sample matrix of the positive class.
  • Xn: The sample matrix of the negative class.

Keyword arguments:

  • covestimator: Custom covariance estimator for between-class covariance. The covariance matrix will be calculated as cov(covestimator_between, #=data=#; dims=2, mean=zeros(#=...=#). Custom covariance estimators, available in other packages, may result in more robust discriminants for data with more features than observations.
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fit(MulticlassLDA, X, y; ...)

Perform multi-class LDA over a given data set X with corresponding labels y with nc number of classes.

This function returns the resultant multi-class LDA model as an instance of MulticlassLDA.

Parameters

  • X: the matrix of input samples, of size (d, n). Each column in X is an observation.
  • y: the vector of class labels, of length n.

Keyword arguments

  • method: The choice of methods:
    • :gevd: based on generalized eigenvalue decomposition (default).
    • :whiten: first derive a whitening transform from Sw and then solve the problem based on eigenvalue
    decomposition of the whiten Sb.
  • outdim: The output dimension, i.e. dimension of the transformed space min(d, nc-1)
  • regcoef: The regularization coefficient (default: 1.0e-6). A positive value regcoef * eigmax(Sw) is added to the diagonal of Sw to improve numerical stability.
  • covestimator_between: Custom covariance estimator for between-class covariance (default: SimpleCovariance()). The covariance matrix will be calculated as cov(covestimator_between, #=data=#; dims=2, mean=zeros(#=...=#)). Custom covariance estimators, available in other packages, may result in more robust discriminants for data with more features than observations.
  • covestimator_within: Custom covariance estimator for within-class covariance (default: SimpleCovariance()). The covariance matrix will be calculated as cov(covestimator_within, #=data=#; dims=2, mean=zeros(nc)). Custom covariance estimators, available in other packages, may result in more robust discriminants for data with more features than observations.

Notes:

The resultant projection matrix $P$ satisfies:

\[\mathbf{P}^T (\mathbf{S}_w + \kappa \mathbf{I}) \mathbf{P} = \mathbf{I}\]

Here, $\kappa$ equals regcoef * eigmax(Sw). The columns of $P$ are arranged in descending order of the corresponding generalized eigenvalues.

Note that MulticlassLDA does not currently support the normalized version using $\mathbf{S}_w^*$ and $\mathbf{S}_b^*$ (see SubspaceLDA).

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fit(SubspaceLDA, X, y; normalize=true)

Fit an subspace projection of LDA model over a given data set X with corresponding labels y using the equivalent of $\mathbf{S}_w^*$ and $\mathbf{S}_b^*$`.

Note: Subspace LDA also supports the normalized version of LDA via the normalize keyword.

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fit(ICA, X, k; ...)

Perform ICA over the data set given in X.

Parameters: -X: The data matrix, of size $(m, n)$. Each row corresponds to a mixed signal, while each column corresponds to an observation (e.g all signal value at a particular time step). -k: The number of independent components to recover.

Keyword Arguments:

  • alg: The choice of algorithm (default :fastica)
  • fun: The approx neg-entropy functor (default Tanh)
  • do_whiten: Whether to perform pre-whitening (default true)
  • maxiter: Maximum number of iterations (default 100)
  • tol: Tolerable change of $W$ at convergence (default 1.0e-6)
  • mean: The mean vector, which can be either of:
    • 0: the input data has already been centralized
    • nothing: this function will compute the mean (default)
    • a pre-computed mean vector
  • winit: Initial guess of $W$, which should be either of:
    • empty matrix: the function will perform random initialization (default)
    • a matrix of size $(k, k)$ (when do_whiten)
    • a matrix of size $(m, k)$ (when !do_whiten)

Returns the resultant ICA model, an instance of type ICA.

Note: If do_whiten is true, the return W satisfies $\mathbf{W}^T \mathbf{C} \mathbf{W} = \mathbf{I}$, otherwise $W$ is orthonormal, i.e $\mathbf{W}^T \mathbf{W} = \mathbf{I}$.

source
fit(FactorAnalysis, X; ...)

Perform factor analysis over the data given in a matrix X. Each column of X is an observation. This method returns an instance of FactorAnalysis.

Keyword arguments:

Let (d, n) = size(X) be respectively the input dimension and the number of observations:

  • method: The choice of methods:
    • :em: use EM version of factor analysis
    • :cm: use CM version of factor analysis (default)
  • maxoutdim: Maximum output dimension (default d-1)
  • mean: The mean vector, which can be either of:
    • 0: the input data has already been centralized
    • nothing: this function will compute the mean (default)
    • a pre-computed mean vector
  • tol: Convergence tolerance (default 1.0e-6)
  • maxiter: Maximum number of iterations (default 1000)
  • η: Variance low bound (default 1.0e-6)

Notes: This function calls facm or faem internally, depending on the choice of method.

source
Base.size — Method
size(M::PPCA)

Returns a tuple with values of the input dimension $d$, i.e the dimension of the observation space, and the output dimension $p$, i.e the dimension of the principal subspace.

source
MultivariateStats.projection — Method
projection(M::PPCA)

Returns the projection matrix (of size $(d, p)$). Each column of the projection matrix corresponds to a principal component.

The principal components are arranged in descending order of the corresponding variances.

source

Given a probabilistic PCA model $M$, one can use it to transform observations into latent variables, as

\mathbf{z} = (\mathbf{W}^T \mathbf{W} + \sigma^2 \mathbf{I}) \mathbf{W}^T (\mathbf{x} - \boldsymbol{\mu})

or use it to reconstruct (approximately) the observations from latent variables, as

\tilde{\mathbf{x}} = \mathbf{W} \mathbb{E}[\mathbf{z}] + \boldsymbol{\mu}

Here, $\mathbf{W}$ is the factor loadings or weight matrix.

StatsAPI.predict — Method
predict(M::PPCA, x)

Transform observations x into latent variables. Here, x can be either a vector of length d or a matrix where each column is an observation.

source
MultivariateStats.reconstruct — Method
reconstruct(M::PPCA, z)

Approximately reconstruct observations from the latent variable given in z. Here, z can be either a vector of length p or a matrix where each column gives the latent variables for an observation.

source

Auxiliary functions:

MultivariateStats.ppcaml — Function
ppcaml(Z, mean; ...)

Compute probabilistic PCA using on maximum likelihood formulation for a centralized sample matrix Z.

Parameters:

  • Z: a centralized samples matrix
  • mean: The mean vector of the original samples, which can be a vector of

length d, or an empty vector indicating a zero mean.

Returns the resultant PPCA model.

Note: This function accepts two keyword arguments: maxoutdim and tol.

source
MultivariateStats.ppcaem — Function
ppcaem(S, mean, n; ...)

Compute probabilistic PCA based on expectation-maximization algorithm for a given sample covariance matrix S.

Parameters:

  • S: The sample covariance matrix.
  • mean: The mean vector of original samples, which can be a vector of length d,

or an empty vector indicating a zero mean.

  • n: The number of observations.

Returns the resultant PPCA model.

Note: This function accepts three keyword arguments: maxoutdim, tol, and maxiter.

source
MultivariateStats.bayespca — Function
bayespca(S, mean, n; ...)

Compute probabilistic PCA using a Bayesian algorithm for a given sample covariance matrix S.

Parameters:

  • S: The sample covariance matrix.
  • mean: The mean vector of original samples, which can be a vector of length d,

or an empty vector indicating a zero mean.

  • n: The number of observations.

Returns the resultant PPCA model.

Notes:

  • This function accepts three keyword arguments: maxoutdim, tol, and maxiter.
  • Function uses the maxoutdim parameter as an upper boundary when it automatically

determines the latent space dimensionality.

source

References

  • 1Bishop, C. M. Pattern Recognition and Machine Learning, 2006.
diff --git a/dev/search/index.html b/dev/search/index.html index 1b41244..ba83e58 100644 --- a/dev/search/index.html +++ b/dev/search/index.html @@ -1,2 +1,2 @@ -Search · MultivariateStats.jl +Search · MultivariateStats.jl

Loading search...

    diff --git a/dev/search_index.js b/dev/search_index.js index e134438..d77a09a 100644 --- a/dev/search_index.js +++ b/dev/search_index.js @@ -1,3 +1,3 @@ var documenterSearchIndex = {"docs": -[{"location":"pca/#Principal-Component-Analysis","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"","category":"section"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"Principal Component Analysis (PCA) derives an orthogonal projection to convert a given set of observations to linearly uncorrelated variables, called principal components.","category":"page"},{"location":"pca/#Example","page":"Principal Component Analysis","title":"Example","text":"","category":"section"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"using Plots\ngr(fmt=:svg)","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"Performing PCA on Iris data set:","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"using MultivariateStats, RDatasets, Plots\n\n# load iris dataset\niris = dataset(\"datasets\", \"iris\")\n\n# split half to training set\nXtr = Matrix(iris[1:2:end,1:4])'\nXtr_labels = Vector(iris[1:2:end,5])\n\n# split other half to testing set\nXte = Matrix(iris[2:2:end,1:4])'\nXte_labels = Vector(iris[2:2:end,5])\nnothing # hide","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"Suppose Xtr and Xte are training and testing data matrix, with each observation in a column. 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Each column of X is an observation.\n\nKeyword arguments\n\nmethod: The choice of methods:\n:auto: use :cov when d < n or :svd otherwise (default).\n:cov: based on covariance matrix decomposition.\n:svd: based on SVD of the input data.\nmaxoutdim: The output dimension, i.e. dimension of the transformed space (min(d, nc-1))\npratio: The ratio of variances preserved in the principal subspace (0.99)\nmean: The mean vector, which can be either of\n0: the input data has already been centralized\nnothing: this function will compute the mean (default)\na pre-computed mean vector\n\nNotes:\n\nThe output dimension p depends on both maxoutdim and pratio, as follows. 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Let M be an instance of KernelPCA, d be the dimension of observations, and p be the output dimension (i.e the dimension of the principal subspace).","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"fit(::Type{KernelPCA}, ::AbstractMatrix{T}; kwargs...) where {T<:Real}\npredict(::KernelPCA)\npredict(::KernelPCA, ::AbstractVecOrMat{T}) where {T<:Real}\nreconstruct(::KernelPCA, ::AbstractVecOrMat{T}) where {T<:Real}\nsize(::KernelPCA)\nprojection(::KernelPCA)\neigvals(::KernelPCA)\neigvecs(::KernelPCA)","category":"page"},{"location":"pca/#StatsAPI.fit-Union{Tuple{T}, Tuple{Type{KernelPCA}, AbstractMatrix{T}}} where T<:Real","page":"Principal Component Analysis","title":"StatsAPI.fit","text":"fit(KernelPCA, X; ...)\n\nPerform kernel PCA over the data given in a matrix X. Each column of X is an observation.\n\nThis method returns an instance of KernelPCA.\n\nKeyword arguments:\n\nLet (d, n) = size(X) be respectively the input dimension and the number of observations:\n\nkernel: The kernel function. This functions accepts two vector arguments x and y,\n\nand returns a scalar value (default: (x,y)->x'y). If set to nothing, the matrix X is the pre-computed symmetric kernel (Gram) matrix.\n\nsolver: The choice of solver:\n:eig: uses LinearAlgebra.eigen (default)\n:eigs: uses Arpack.eigs (always used for sparse data)\nmaxoutdim: Maximum output dimension (default min(d, n))\ninverse: Whether to perform calculation for inverse transform for non-precomputed kernels (default false)\nβ: Hyperparameter of the ridge regression that learns the inverse transform (default 1 when inverse is true).\ntol: Convergence tolerance for eigs solver (default 0.0)\nmaxiter: Maximum number of iterations for eigs solver (default 300)\n\n\n\n\n\n","category":"method"},{"location":"pca/#StatsAPI.predict-Tuple{KernelPCA}","page":"Principal Component Analysis","title":"StatsAPI.predict","text":"predict(M::KernelPCA)\n\nTransform the data fitted to the model M to a kernel space of the model.\n\n\n\n\n\n","category":"method"},{"location":"pca/#StatsAPI.predict-Union{Tuple{T}, Tuple{KernelPCA, AbstractVecOrMat{T}}} where T<:Real","page":"Principal Component Analysis","title":"StatsAPI.predict","text":"predict(M::KernelPCA, x)\n\nTransform out-of-sample transformation of x into a kernel space of the model M.\n\nHere, x can be either a vector of length d or a matrix where each column is an observation.\n\n\n\n\n\n","category":"method"},{"location":"pca/#MultivariateStats.reconstruct-Union{Tuple{T}, Tuple{KernelPCA, AbstractVecOrMat{T}}} where T<:Real","page":"Principal Component Analysis","title":"MultivariateStats.reconstruct","text":"reconstruct(M::KernelPCA, y)\n\nApproximately reconstruct observations, given in y, to the original space using the kernel PCA model M.\n\nHere, y can be either a vector of length p or a matrix where each column gives the principal components for an observation.\n\n\n\n\n\n","category":"method"},{"location":"pca/#Base.size-Tuple{KernelPCA}","page":"Principal Component Analysis","title":"Base.size","text":"size(M::KernelPCA)\n\nReturns a tuple with the input dimension d, i.e the dimension of the observation space, and the output dimension p, i.e the dimension of the principal subspace.\n\n\n\n\n\n","category":"method"},{"location":"pca/#MultivariateStats.projection-Tuple{KernelPCA}","page":"Principal Component Analysis","title":"MultivariateStats.projection","text":"projection(M::KernelPCA)\n\nReturn the projection matrix (of size n times p). Each column of the projection matrix corresponds to an eigenvector, and n is a number of observations.\n\nThe principal components are arranged in descending order of the corresponding eigenvalues.\n\n\n\n\n\n","category":"method"},{"location":"pca/#LinearAlgebra.eigvals-Tuple{KernelPCA}","page":"Principal Component Analysis","title":"LinearAlgebra.eigvals","text":"eigvals(M::KernelPCA)\n\nReturn eigenvalues of the kernel matrix of the model M.\n\n\n\n\n\n","category":"method"},{"location":"pca/#LinearAlgebra.eigvecs-Tuple{KernelPCA}","page":"Principal Component Analysis","title":"LinearAlgebra.eigvecs","text":"eigvecs(M::KernelPCA)\n\nReturn eigenvectors of the kernel matrix of the model M.\n\n\n\n\n\n","category":"method"},{"location":"pca/#Kernels","page":"Principal Component Analysis","title":"Kernels","text":"","category":"section"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"List of the commonly used kernels:","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"function description\n(x,y)->x'y Linear\n(x,y)->(x'y+c)^d Polynomial\n(x,y)->exp(-γ*norm(x-y)^2.0) Radial basis function (RBF)","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"This package has a separate interface for adjusting kernel matrices.","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"MultivariateStats.KernelCenter\nfit(::Type{MultivariateStats.KernelCenter}, ::AbstractMatrix{<:Real})\nMultivariateStats.transform!(::MultivariateStats.KernelCenter, ::AbstractMatrix{<:Real})","category":"page"},{"location":"pca/#MultivariateStats.KernelCenter","page":"Principal Component Analysis","title":"MultivariateStats.KernelCenter","text":"Center a kernel matrix\n\n\n\n\n\n","category":"type"},{"location":"pca/#StatsAPI.fit-Tuple{Type{MultivariateStats.KernelCenter}, AbstractMatrix{<:Real}}","page":"Principal Component Analysis","title":"StatsAPI.fit","text":"Fit KernelCenter object\n\n\n\n\n\n","category":"method"},{"location":"pca/#MultivariateStats.transform!-Tuple{MultivariateStats.KernelCenter, AbstractMatrix{<:Real}}","page":"Principal Component Analysis","title":"MultivariateStats.transform!","text":"Center kernel matrix.\n\n\n\n\n\n","category":"method"},{"location":"pca/#Probabilistic-Principal-Component-Analysis","page":"Principal Component Analysis","title":"Probabilistic Principal Component Analysis","text":"","category":"section"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"Probabilistic Principal Component Analysis (PPCA) represents a constrained form of the Gaussian distribution in which the number of free parameters can be restricted while still allowing the model to capture the dominant correlations in a data set. It is expressed as the maximum likelihood solution of a probabilistic latent variable model[1].","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"This package defines a PPCA type to represent a probabilistic PCA model, and provides a set of methods to access the properties.","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"PPCA","category":"page"},{"location":"pca/#MultivariateStats.PPCA","page":"Principal Component Analysis","title":"MultivariateStats.PPCA","text":"This type contains probabilistic PCA model parameters.\n\n\n\n\n\n","category":"type"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"Let M be an instance of PPCA, d be the dimension of observations, and p be the output dimension (i.e the dimension of the principal subspace).","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"fit\nsize(::PPCA)\nmean(::PPCA)\nvar(::PPCA)\ncov(::PPCA)\nprojection(::PPCA)\nloadings(::PPCA)","category":"page"},{"location":"pca/#StatsAPI.fit","page":"Principal Component Analysis","title":"StatsAPI.fit","text":"fit(Whitening, X::AbstractMatrix{T}; kwargs...)\n\nEstimate a whitening transform from the data given in X.\n\nThis function returns an instance of Whitening\n\nKeyword Arguments:\n\nregcoef: The regularization coefficient. The covariance will be regularized as follows when regcoef is positive C + (eigmax(C) * regcoef) * eye(d). Default values is zero(T).\ndims: if 1 the transformation calculated from the row samples. fit standardization parameters in column-wise fashion; if 2 the transformation calculated from the column samples. The default is nothing, which is equivalent to dims=2 with a deprecation warning.\nmean: The mean vector, which can be either of:\n0: the input data has already been centralized\nnothing: this function will compute the mean (default)\na pre-computed mean vector\n\nNote: This function internally relies on cov_whitening to derive the transformation W.\n\n\n\n\n\nfit(PCA, X; ...)\n\nPerform PCA over the data given in a matrix X. Each column of X is an observation.\n\nKeyword arguments\n\nmethod: The choice of methods:\n:auto: use :cov when d < n or :svd otherwise (default).\n:cov: based on covariance matrix decomposition.\n:svd: based on SVD of the input data.\nmaxoutdim: The output dimension, i.e. dimension of the transformed space (min(d, nc-1))\npratio: The ratio of variances preserved in the principal subspace (0.99)\nmean: The mean vector, which can be either of\n0: the input data has already been centralized\nnothing: this function will compute the mean (default)\na pre-computed mean vector\n\nNotes:\n\nThe output dimension p depends on both maxoutdim and pratio, as follows. Suppose the first k principal components preserve at least pratio of the total variance, while the first k-1 preserves less than pratio, then the actual output dimension will be min(k maxoutdim).\nThis function calls pcacov or pcasvd internally, depending on the choice of method.\n\n\n\n\n\nfit(PPCA, X; ...)\n\nPerform probabilistic PCA over the data given in a matrix X. Each column of X is an observation. This method returns an instance of PPCA.\n\nKeyword arguments:\n\nLet (d, n) = size(X) be respectively the input dimension and the number of observations:\n\nmethod: The choice of methods:\n:ml: use maximum likelihood version of probabilistic PCA (default)\n:em: use EM version of probabilistic PCA\n:bayes: use Bayesian PCA\nmaxoutdim: Maximum output dimension (default d-1)\nmean: The mean vector, which can be either of:\n0: the input data has already been centralized\nnothing: this function will compute the mean (default)\na pre-computed mean vector\ntol: Convergence tolerance (default 1.0e-6)\nmaxiter: Maximum number of iterations (default 1000)\n\nNotes: This function calls ppcaml, ppcaem or bayespca internally, depending on the choice of method.\n\n\n\n\n\nFit KernelCenter object\n\n\n\n\n\nfit(KernelPCA, X; ...)\n\nPerform kernel PCA over the data given in a matrix X. Each column of X is an observation.\n\nThis method returns an instance of KernelPCA.\n\nKeyword arguments:\n\nLet (d, n) = size(X) be respectively the input dimension and the number of observations:\n\nkernel: The kernel function. This functions accepts two vector arguments x and y,\n\nand returns a scalar value (default: (x,y)->x'y). If set to nothing, the matrix X is the pre-computed symmetric kernel (Gram) matrix.\n\nsolver: The choice of solver:\n:eig: uses LinearAlgebra.eigen (default)\n:eigs: uses Arpack.eigs (always used for sparse data)\nmaxoutdim: Maximum output dimension (default min(d, n))\ninverse: Whether to perform calculation for inverse transform for non-precomputed kernels (default false)\nβ: Hyperparameter of the ridge regression that learns the inverse transform (default 1 when inverse is true).\ntol: Convergence tolerance for eigs solver (default 0.0)\nmaxiter: Maximum number of iterations for eigs solver (default 300)\n\n\n\n\n\nfit(CCA, X, Y; ...)\n\nPerform CCA over the data given in matrices X and Y. Each column of X and Y is an observation.\n\nX and Y should have the same number of columns (denoted by n below).\n\nThis method returns an instance of CCA.\n\nKeyword arguments:\n\nmethod: The choice of methods:\n:cov: based on covariance matrices\n:svd: based on SVD of the input data (default)\noutdim: The output dimension, i.e dimension of the common space (default: min(dx, dy, n))\nmean: The mean vector, which can be either of:\n0: the input data has already been centralized\nnothing: this function will compute the mean (default)\na pre-computed mean vector\n\nNotes: This function calls ccacov or ccasvd internally, depending on the choice of method.\n\n\n\n\n\nfit(MDS, X; kwargs...)\n\nCompute an embedding of X points by classical multidimensional scaling (MDS). There are two calling options, specified via the required keyword argument distances:\n\nmds = fit(MDS, X; distances=false, maxoutdim=size(X,1)-1)\n\nwhere X is the data matrix. Distances between pairs of columns of X are computed using the Euclidean norm. This is equivalent to performing PCA on X.\n\nmds = fit(MDS, D; distances=true, maxoutdim=size(D,1)-1)\n\nwhere D is a symmetric matrix D of distances between points.\n\n\n\n\n\nfit(MetricMDS, X; kwargs...)\n\nCompute an embedding of X points by (non)metric multidimensional scaling (MDS).\n\nKeyword arguments:\n\nLet (d, n) = size(X) be respectively the input dimension and the number of observations:\n\ndistances: The choice of input (required):\nfalse: use X to calculate dissimilarity matrix using Euclidean distance\ntrue: use X input as precomputed dissimilarity symmetric matrix (distances)\nmaxoutdim: Maximum output dimension (default d-1)\nmetric : a function for calculation of disparity values\nnothing: use dissimilarity values as the disparities to perform the metric MDS (default)\nisotonic: converts dissimilarity values to ordinal disparities to perform non-metric MDS\nany two parameter disparity transformation function, where the first parameter is a vector of proximities (i.e. dissimilarities) and the second parameter is a vector of distances, e.g. (p,d)->b*p for some b is a transformation function for ratio MDS.\ntol: Convergence tolerance (default 1.0e-3)\nmaxiter: Maximum number of iterations (default 300)\ninitial: an initial reduced space point configuration\nnothing: then an initial configuration is randomly generated (default)\npre-defined matrix\nweights: a weight matrix\nnothing: then weights are set to one, w_ij = 1 (default)\npre-defined matrix\n\nNote: if the algorithm is unable to converge then ConvergenceException is thrown.\n\n\n\n\n\nfit(LinearDiscriminant, Xp, Xn; covestimator = SimpleCovariance())\n\nPerforms LDA given both positive and negative samples. The function accepts following parameters:\n\nParameters\n\nXp: The sample matrix of the positive class.\nXn: The sample matrix of the negative class.\n\nKeyword arguments:\n\ncovestimator: Custom covariance estimator for between-class covariance. The covariance matrix will be calculated as cov(covestimator_between, #=data=#; dims=2, mean=zeros(#=...=#). Custom covariance estimators, available in other packages, may result in more robust discriminants for data with more features than observations.\n\n\n\n\n\nfit(MulticlassLDA, X, y; ...)\n\nPerform multi-class LDA over a given data set X with corresponding labels y with nc number of classes.\n\nThis function returns the resultant multi-class LDA model as an instance of MulticlassLDA.\n\nParameters\n\nX: the matrix of input samples, of size (d, n). Each column in X is an observation.\ny: the vector of class labels, of length n.\n\nKeyword arguments\n\nmethod: The choice of methods:\n:gevd: based on generalized eigenvalue decomposition (default).\n:whiten: first derive a whitening transform from Sw and then solve the problem based on eigenvalue\ndecomposition of the whiten Sb.\noutdim: The output dimension, i.e. dimension of the transformed space min(d, nc-1)\nregcoef: The regularization coefficient (default: 1.0e-6). A positive value regcoef * eigmax(Sw) is added to the diagonal of Sw to improve numerical stability.\ncovestimator_between: Custom covariance estimator for between-class covariance (default: SimpleCovariance()). The covariance matrix will be calculated as cov(covestimator_between, #=data=#; dims=2, mean=zeros(#=...=#)). Custom covariance estimators, available in other packages, may result in more robust discriminants for data with more features than observations.\ncovestimator_within: Custom covariance estimator for within-class covariance (default: SimpleCovariance()). The covariance matrix will be calculated as cov(covestimator_within, #=data=#; dims=2, mean=zeros(nc)). Custom covariance estimators, available in other packages, may result in more robust discriminants for data with more features than observations.\n\nNotes:\n\nThe resultant projection matrix P satisfies:\n\nmathbfP^T (mathbfS_w + kappa mathbfI) mathbfP = mathbfI\n\nHere, kappa equals regcoef * eigmax(Sw). The columns of P are arranged in descending order of the corresponding generalized eigenvalues.\n\nNote that MulticlassLDA does not currently support the normalized version using mathbfS_w^* and mathbfS_b^* (see SubspaceLDA).\n\n\n\n\n\nfit(SubspaceLDA, X, y; normalize=true)\n\nFit an subspace projection of LDA model over a given data set X with corresponding labels y using the equivalent of mathbfS_w^* and mathbfS_b^*`.\n\nNote: Subspace LDA also supports the normalized version of LDA via the normalize keyword.\n\n\n\n\n\nfit(ICA, X, k; ...)\n\nPerform ICA over the data set given in X.\n\nParameters: -X: The data matrix, of size (m n). Each row corresponds to a mixed signal, while each column corresponds to an observation (e.g all signal value at a particular time step). -k: The number of independent components to recover.\n\nKeyword Arguments:\n\nalg: The choice of algorithm (default :fastica)\nfun: The approx neg-entropy functor (default Tanh)\ndo_whiten: Whether to perform pre-whitening (default true)\nmaxiter: Maximum number of iterations (default 100)\ntol: Tolerable change of W at convergence (default 1.0e-6)\nmean: The mean vector, which can be either of:\n0: the input data has already been centralized\nnothing: this function will compute the mean (default)\na pre-computed mean vector\nwinit: Initial guess of W, which should be either of:\nempty matrix: the function will perform random initialization (default)\na matrix of size (k k) (when do_whiten)\na matrix of size (m k) (when !do_whiten)\n\nReturns the resultant ICA model, an instance of type ICA.\n\nNote: If do_whiten is true, the return W satisfies mathbfW^T mathbfC mathbfW = mathbfI, otherwise W is orthonormal, i.e mathbfW^T mathbfW = mathbfI.\n\n\n\n\n\nfit(FactorAnalysis, X; ...)\n\nPerform factor analysis over the data given in a matrix X. Each column of X is an observation. This method returns an instance of FactorAnalysis.\n\nKeyword arguments:\n\nLet (d, n) = size(X) be respectively the input dimension and the number of observations:\n\nmethod: The choice of methods:\n:em: use EM version of factor analysis\n:cm: use CM version of factor analysis (default)\nmaxoutdim: Maximum output dimension (default d-1)\nmean: The mean vector, which can be either of:\n0: the input data has already been centralized\nnothing: this function will compute the mean (default)\na pre-computed mean vector\ntol: Convergence tolerance (default 1.0e-6)\nmaxiter: Maximum number of iterations (default 1000)\nη: Variance low bound (default 1.0e-6)\n\nNotes: This function calls facm or faem internally, depending on the choice of method.\n\n\n\n\n\n","category":"function"},{"location":"pca/#Base.size-Tuple{PPCA}","page":"Principal Component Analysis","title":"Base.size","text":"size(M::PPCA)\n\nReturns a tuple with values of the input dimension d, i.e the dimension of the observation space, and the output dimension p, i.e the dimension of the principal subspace.\n\n\n\n\n\n","category":"method"},{"location":"pca/#Statistics.mean-Tuple{PPCA}","page":"Principal Component Analysis","title":"Statistics.mean","text":"mean(M::PPCA)\n\nGet the mean vector (of length d).\n\n\n\n\n\n","category":"method"},{"location":"pca/#Statistics.var-Tuple{PPCA}","page":"Principal Component Analysis","title":"Statistics.var","text":"var(M::PPCA)\n\nReturns the total residual variance of the model M.\n\n\n\n\n\n","category":"method"},{"location":"pca/#Statistics.cov-Tuple{PPCA}","page":"Principal Component Analysis","title":"Statistics.cov","text":"cov(M::PPCA)\n\nReturns the covariance of the model M.\n\n\n\n\n\n","category":"method"},{"location":"pca/#MultivariateStats.projection-Tuple{PPCA}","page":"Principal Component Analysis","title":"MultivariateStats.projection","text":"projection(M::PPCA)\n\nReturns the projection matrix (of size (d p)). Each column of the projection matrix corresponds to a principal component.\n\nThe principal components are arranged in descending order of the corresponding variances.\n\n\n\n\n\n","category":"method"},{"location":"pca/#MultivariateStats.loadings-Tuple{PPCA}","page":"Principal Component Analysis","title":"MultivariateStats.loadings","text":"loadings(M::PPCA)\n\nReturns the factor loadings matrix (of size (d p)) of the model M.\n\n\n\n\n\n","category":"method"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"Given a probabilistic PCA model M, one can use it to transform observations into latent variables, as","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"\\mathbf{z} = (\\mathbf{W}^T \\mathbf{W} + \\sigma^2 \\mathbf{I}) \\mathbf{W}^T (\\mathbf{x} - \\boldsymbol{\\mu})","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"or use it to reconstruct (approximately) the observations from latent variables, as","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"\\tilde{\\mathbf{x}} = \\mathbf{W} \\mathbb{E}[\\mathbf{z}] + \\boldsymbol{\\mu}","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"Here, mathbfW is the factor loadings or weight matrix.","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"predict(::PPCA, ::AbstractVecOrMat{T}) where {T<:Real}\nreconstruct(::PPCA, ::AbstractVecOrMat{T}) where {T<:Real}","category":"page"},{"location":"pca/#StatsAPI.predict-Union{Tuple{T}, Tuple{PPCA, AbstractVecOrMat{T}}} where T<:Real","page":"Principal Component Analysis","title":"StatsAPI.predict","text":"predict(M::PPCA, x)\n\nTransform observations x into latent variables. Here, x can be either a vector of length d or a matrix where each column is an observation.\n\n\n\n\n\n","category":"method"},{"location":"pca/#MultivariateStats.reconstruct-Union{Tuple{T}, Tuple{PPCA, AbstractVecOrMat{T}}} where T<:Real","page":"Principal Component Analysis","title":"MultivariateStats.reconstruct","text":"reconstruct(M::PPCA, z)\n\nApproximately reconstruct observations from the latent variable given in z. Here, z can be either a vector of length p or a matrix where each column gives the latent variables for an observation.\n\n\n\n\n\n","category":"method"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"Auxiliary functions:","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"ppcaml\nppcaem\nbayespca","category":"page"},{"location":"pca/#MultivariateStats.ppcaml","page":"Principal Component Analysis","title":"MultivariateStats.ppcaml","text":"ppcaml(Z, mean; ...)\n\nCompute probabilistic PCA using on maximum likelihood formulation for a centralized sample matrix Z.\n\nParameters:\n\nZ: a centralized samples matrix\nmean: The mean vector of the original samples, which can be a vector of\n\nlength d, or an empty vector indicating a zero mean.\n\nReturns the resultant PPCA model.\n\nNote: This function accepts two keyword arguments: maxoutdim and tol.\n\n\n\n\n\n","category":"function"},{"location":"pca/#MultivariateStats.ppcaem","page":"Principal Component Analysis","title":"MultivariateStats.ppcaem","text":"ppcaem(S, mean, n; ...)\n\nCompute probabilistic PCA based on expectation-maximization algorithm for a given sample covariance matrix S.\n\nParameters:\n\nS: The sample covariance matrix.\nmean: The mean vector of original samples, which can be a vector of length d,\n\nor an empty vector indicating a zero mean.\n\nn: The number of observations.\n\nReturns the resultant PPCA model.\n\nNote: This function accepts three keyword arguments: maxoutdim, tol, and maxiter.\n\n\n\n\n\n","category":"function"},{"location":"pca/#MultivariateStats.bayespca","page":"Principal Component Analysis","title":"MultivariateStats.bayespca","text":"bayespca(S, mean, n; ...)\n\nCompute probabilistic PCA using a Bayesian algorithm for a given sample covariance matrix S.\n\nParameters:\n\nS: The sample covariance matrix.\nmean: The mean vector of original samples, which can be a vector of length d,\n\nor an empty vector indicating a zero mean.\n\nn: The number of observations.\n\nReturns the resultant PPCA model.\n\nNotes:\n\nThis function accepts three keyword arguments: maxoutdim, tol, and maxiter.\nFunction uses the maxoutdim parameter as an upper boundary when it automatically\n\ndetermines the latent space dimensionality.\n\n\n\n\n\n","category":"function"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"","category":"page"},{"location":"pca/#References","page":"Principal Component Analysis","title":"References","text":"","category":"section"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"[1]: Bishop, C. M. Pattern Recognition and Machine Learning, 2006.","category":"page"},{"location":"fa/#Factor-Analysis","page":"Factor Analysis","title":"Factor Analysis","text":"","category":"section"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"Factor Analysis (FA) is a linear-Gaussian latent variable model that is closely related to probabilistic PCA. In contrast to the probabilistic PCA model, the covariance of conditional distribution of the observed variable given the latent variable is diagonal rather than isotropic[1].","category":"page"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"This package defines a FactorAnalysis type to represent a factor analysis model, and provides a set of methods to access the properties.","category":"page"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"FactorAnalysis","category":"page"},{"location":"fa/#MultivariateStats.FactorAnalysis","page":"Factor Analysis","title":"MultivariateStats.FactorAnalysis","text":"This type contains factor analysis model parameters.\n\n\n\n\n\n","category":"type"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"The package provides a set of methods to access the properties of the factor analysis model. Let M be an instance of FactorAnalysis, d be the dimension of observations, and p be the output dimension (i.e the dimension of the principal subspace).","category":"page"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"fit(::Type{FactorAnalysis}, ::AbstractMatrix{T}) where {T<:Real}\nsize(::FactorAnalysis)\nmean(::FactorAnalysis)\nvar(::FactorAnalysis)\ncov(::FactorAnalysis)\nprojection(::FactorAnalysis)\nloadings(::FactorAnalysis)","category":"page"},{"location":"fa/#StatsAPI.fit-Union{Tuple{T}, Tuple{Type{FactorAnalysis}, AbstractMatrix{T}}} where T<:Real","page":"Factor Analysis","title":"StatsAPI.fit","text":"fit(FactorAnalysis, X; ...)\n\nPerform factor analysis over the data given in a matrix X. Each column of X is an observation. This method returns an instance of FactorAnalysis.\n\nKeyword arguments:\n\nLet (d, n) = size(X) be respectively the input dimension and the number of observations:\n\nmethod: The choice of methods:\n:em: use EM version of factor analysis\n:cm: use CM version of factor analysis (default)\nmaxoutdim: Maximum output dimension (default d-1)\nmean: The mean vector, which can be either of:\n0: the input data has already been centralized\nnothing: this function will compute the mean (default)\na pre-computed mean vector\ntol: Convergence tolerance (default 1.0e-6)\nmaxiter: Maximum number of iterations (default 1000)\nη: Variance low bound (default 1.0e-6)\n\nNotes: This function calls facm or faem internally, depending on the choice of method.\n\n\n\n\n\n","category":"method"},{"location":"fa/#Base.size-Tuple{FactorAnalysis}","page":"Factor Analysis","title":"Base.size","text":"size(M::PPCA)\n\nReturns a tuple with values of the input dimension d, i.e the dimension of the observation space, and the output dimension p, i.e the dimension of the principal subspace.\n\n\n\n\n\n","category":"method"},{"location":"fa/#Statistics.mean-Tuple{FactorAnalysis}","page":"Factor Analysis","title":"Statistics.mean","text":"mean(M::PPCA)\n\nGet the mean vector (of length d).\n\n\n\n\n\n","category":"method"},{"location":"fa/#Statistics.var-Tuple{FactorAnalysis}","page":"Factor Analysis","title":"Statistics.var","text":"var(M::FactorAnalysis)\n\nReturns the variance of the model M.\n\n\n\n\n\n","category":"method"},{"location":"fa/#Statistics.cov-Tuple{FactorAnalysis}","page":"Factor Analysis","title":"Statistics.cov","text":"cov(M::FactorAnalysis)\n\nReturns the covariance of the model M.\n\n\n\n\n\n","category":"method"},{"location":"fa/#MultivariateStats.projection-Tuple{FactorAnalysis}","page":"Factor Analysis","title":"MultivariateStats.projection","text":"projection(M::FactorAnalysis)\n\nRecovers principle components from the weight matrix of the model M.\n\n\n\n\n\n","category":"method"},{"location":"fa/#MultivariateStats.loadings-Tuple{FactorAnalysis}","page":"Factor Analysis","title":"MultivariateStats.loadings","text":"loadings(M::FactorAnalysis)\n\nReturns the factor loadings matrix of the model M.\n\n\n\n\n\n","category":"method"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"Given a factor analysis model M, one can use it to transform observations into latent variables, as","category":"page"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"\\mathbf{z} = \\mathbf{W}^T \\mathbf{\\Sigma}^{-1} (\\mathbf{x} - \\boldsymbol{\\mu})","category":"page"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"or use it to reconstruct (approximately) the observations from latent variables, as","category":"page"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"\\tilde{\\mathbf{x}} = \\mathbf{\\Sigma} \\mathbf{W} (\\mathbf{W}^T \\mathbf{W})^{-1} \\mathbf{z} + \\boldsymbol{\\mu}","category":"page"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"Here, mathbfW is the factor loadings or weight matrix, mathbfSigma = mathbfPsi + mathbfW^T mathbfW is the covariance matrix.","category":"page"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"The package provides methods to do so:","category":"page"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"predict(::FactorAnalysis, ::AbstractVecOrMat{T}) where {T<:Real}\nreconstruct(::FactorAnalysis, ::AbstractVecOrMat{T}) where {T<:Real}","category":"page"},{"location":"fa/#StatsAPI.predict-Union{Tuple{T}, Tuple{FactorAnalysis, AbstractVecOrMat{T}}} where T<:Real","page":"Factor Analysis","title":"StatsAPI.predict","text":"predict(M::FactorAnalysis, x)\n\nTransform observations x into latent variables. Here, x can be either a vector of length d or a matrix where each column is an observation.\n\n\n\n\n\n","category":"method"},{"location":"fa/#MultivariateStats.reconstruct-Union{Tuple{T}, Tuple{FactorAnalysis, AbstractVecOrMat{T}}} where T<:Real","page":"Factor Analysis","title":"MultivariateStats.reconstruct","text":"reconstruct(M::FactorAnalysis, z)\n\nApproximately reconstruct observations from the latent variable given in z. Here, z can be either a vector of length p or a matrix where each column gives the latent variables for an observation.\n\n\n\n\n\n","category":"method"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"Auxiliary functions:","category":"page"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"faem\nfacm","category":"page"},{"location":"fa/#MultivariateStats.faem","page":"Factor Analysis","title":"MultivariateStats.faem","text":"faem(S, mean, n; ...)\n\nPerforms factor analysis using an expectation-maximization algorithm for a given sample covariance matrix S[2].\n\nParameters\n\nS: The sample covariance matrix.\nmean: The mean vector of original samples, which can be a vector of length d,\n\nor an empty vector indicating a zero mean.\n\nn: The number of observations.\n\nReturns the resultant FactorAnalysis model.\n\nNote: This function accepts two keyword arguments: maxoutdim,tol, and maxiter.\n\n\n\n\n\n","category":"function"},{"location":"fa/#MultivariateStats.facm","page":"Factor Analysis","title":"MultivariateStats.facm","text":"facm(S, mean, n; ...)\n\nPerforms factor analysis using a fast conditional maximization algorithm for a given sample covariance matrix S[3].\n\nParameters\n\nS: The sample covariance matrix.\nmean: The mean vector of original samples, which can be a vector of length d,\n\nor an empty vector indicating a zero mean.\n\nn: The number of observations.\n\nReturns the resultant FactorAnalysis model.\n\nNote: This function accepts two keyword arguments: maxoutdim,tol, maxiter, and η.\n\n\n\n\n\n","category":"function"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"","category":"page"},{"location":"fa/#References","page":"Factor Analysis","title":"References","text":"","category":"section"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"[1]: Bishop, C. M. Pattern Recognition and Machine Learning, 2006.","category":"page"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"[2]: Rubin, Donald B., and Dorothy T. Thayer. EM algorithms for ML factor analysis. Psychometrika 47.1, 69-76, 1982.","category":"page"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"[3]: Zhao, J-H., Philip LH Yu, and Qibao Jiang. ML estimation for factor analysis: EM or non-EM?. Statistics and computing 18.2, 109-123, 2008.","category":"page"},{"location":"api/#API-Reference","page":"Development","title":"API Reference","text":"","category":"section"},{"location":"api/#Current","page":"Development","title":"Current","text":"","category":"section"},{"location":"api/","page":"Development","title":"Development","text":"Table of the package models and corresponding function names used by these models.","category":"page"},{"location":"api/","page":"Development","title":"Development","text":"Function \\ Model CCA WHT ICA LDA FA PPCA PCA KPCA MDS\nfit x x x x x x x x x\ntransform x x x x x x x x x\npredict x \nindim x x x x x x x x\noutdim x x x x x x x x x\nmean x x x x x x x ? \nvar x x ? ? ?\ncov x ? \ncor x \nprojection x x x x x x\nreconstruct x x x x \nloadings ? ? x x ? ? ?\neigvals ? ? ? ? x\neigvecs ? ? ? ? ?\nlength \nsize ","category":"page"},{"location":"api/","page":"Development","title":"Development","text":"Note: ? refers to a possible implementation that is missing or called differently.","category":"page"},{"location":"api/#New","page":"Development","title":"New","text":"","category":"section"},{"location":"api/","page":"Development","title":"Development","text":"Function \\ Model WHT CCA LDA MC-LDA SS-LDA ICA FA PPCA PCA KPCA MDS\nfit x x x x x x x x x x x\ntransform x - - - - - x x - - -\npredict + x + + + + + +\nindim - - - - x x - - -\noutdim - - - - - x x - - -\nmean x x x x x x x x \nvar x x x ?\ncov x x \ncor + \nprojection ? x x x x x x x x\nreconstruct x x x x \nloadings x x x +\neigvals + ? ? x x x\neigvecs ? ? x + +\nlength + + + + \nsize + + + + + x + +\n ","category":"page"},{"location":"api/","page":"Development","title":"Development","text":"StatsBase.AbstractDataTransform\nWhitening\nInterface: fit, transform\nNew: length, mean, size\nStatsBase.RegressionModel\nInterface: fit, predict\nLinearDiscriminant\nFunctions: coef, dof, weights, evaluate, length\nMulticlassLDA\nFunctions: size, mean, projection, length\nSubspaceLDA\nFunctions: size, mean, projection, length, eigvals\nCCA\nFunctions: size, mean, projection, predict, cor\nSubtypes:\nAbstractDimensionalityReduction\nInterface: projection, var, reconstruct, loadings\nInterface: projection == weights\nSubtypes:\nLinearDimensionalityReduction\nMethods: ICA, PCA\nNonlinearDimensionalityReduction\nMethods: KPCA, MDS\nFunctions: modelmatrix(X),\nLatentVariableModel or LatentVariableDimensionalityReduction\nMethods: FA, PPCA\nFunctions: cov","category":"page"},{"location":"lda/#Linear-Discriminant-Analysis","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"","category":"section"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Linear Discriminant Analysis (LDA) are statistical analysis methods to find a linear combination of features for separating observations in two classes.","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Note: Please refer to MulticlassLDA for methods that can discriminate between multiple classes.","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Suppose the samples in the positive and negative classes respectively with means: boldsymbolmu_p and boldsymbolmu_n, and covariances mathbfC_p and mathbfC_n. Then based on Fisher's Linear Discriminant Criteria, the optimal projection direction can be expressed as:","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"mathbfw = alpha cdot (mathbfC_p + mathbfC_n)^-1 (boldsymbolmu_p - boldsymbolmu_n)","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Here alpha is an arbitrary non-negative coefficient.","category":"page"},{"location":"lda/#Example","page":"Linear Discriminant Analysis","title":"Example","text":"","category":"section"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"using Plots\ngr(fmt=:svg)","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Let's compare LDA and PCA 2D projection of Iris dataset. Principal Component Analysis identifies the directions that explain the most variance in the data. ","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"using MultivariateStats, RDatasets\n\niris = dataset(\"datasets\", \"iris\")\n\nX = Matrix(iris[1:2:end,1:4])'\nX_labels = Vector(iris[1:2:end,5])\n\npca = fit(PCA, X; maxoutdim=2)\nYpca = predict(pca, X)\nnothing # hide","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"In contrast, Linear Discriminant Analysis attempts to identify the attributes that account for the most variance between classes. Therefore, with LDA, you must use known class labels.","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"lda = fit(MulticlassLDA, X, X_labels; outdim=2)\nYlda = predict(lda, X)\n\np = plot(layout=(1,2), size=(800,300))\n\nfor s in [\"setosa\", \"versicolor\", \"virginica\"]\n\n points = Ypca[:,X_labels.==s]\n scatter!(p[1], points[1,:],points[2,:], label=s, legend=:bottomleft)\n points = Ylda[:,X_labels.==s]\n scatter!(p[2], points[1,:],points[2,:], label=s, legend=:bottomleft)\n\nend\nplot!(p[1], title=\"PCA\")\nplot!(p[2], title=\"LDA\")","category":"page"},{"location":"lda/#Two-class-Linear-Discriminant-Analysis","page":"Linear Discriminant Analysis","title":"Two-class Linear Discriminant Analysis","text":"","category":"section"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"This package uses the LinearDiscriminant type to capture a linear discriminant functional:","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"LinearDiscriminant","category":"page"},{"location":"lda/#MultivariateStats.LinearDiscriminant","page":"Linear Discriminant Analysis","title":"MultivariateStats.LinearDiscriminant","text":"A linear discriminant functional can be written as\n\n f(mathbfx) = mathbfw^T mathbfx + b\n\nHere, w is the coefficient vector, and b is the bias constant.\n\n\n\n\n\n","category":"type"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"This type comes with several methods where f be an instance of LinearDiscriminant.","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"fit(::Type{LinearDiscriminant}, Xp::DenseMatrix{T}, Xn::DenseMatrix{T}; kwargs) where T<:Real\nevaluate(::LinearDiscriminant, ::AbstractVector)\nevaluate(::LinearDiscriminant, ::AbstractMatrix)\npredict(::LinearDiscriminant, ::AbstractVector)\npredict(::LinearDiscriminant, ::AbstractMatrix)\ncoef(::LinearDiscriminant)\ndof(::LinearDiscriminant)\nweights(::LinearDiscriminant)\nlength(::LinearDiscriminant)","category":"page"},{"location":"lda/#StatsAPI.fit-Union{Tuple{T}, Tuple{Type{LinearDiscriminant}, DenseMatrix{T}, DenseMatrix{T}}} where T<:Real","page":"Linear Discriminant Analysis","title":"StatsAPI.fit","text":"fit(LinearDiscriminant, Xp, Xn; covestimator = SimpleCovariance())\n\nPerforms LDA given both positive and negative samples. The function accepts following parameters:\n\nParameters\n\nXp: The sample matrix of the positive class.\nXn: The sample matrix of the negative class.\n\nKeyword arguments:\n\ncovestimator: Custom covariance estimator for between-class covariance. The covariance matrix will be calculated as cov(covestimator_between, #=data=#; dims=2, mean=zeros(#=...=#). Custom covariance estimators, available in other packages, may result in more robust discriminants for data with more features than observations.\n\n\n\n\n\n","category":"method"},{"location":"lda/#MultivariateStats.evaluate-Tuple{LinearDiscriminant, AbstractVector}","page":"Linear Discriminant Analysis","title":"MultivariateStats.evaluate","text":"evaluate(f, x::AbstractVector)\n\nEvaluate the linear discriminant value, i.e wx + b, it returns a real value.\n\n\n\n\n\n","category":"method"},{"location":"lda/#MultivariateStats.evaluate-Tuple{LinearDiscriminant, AbstractMatrix}","page":"Linear Discriminant Analysis","title":"MultivariateStats.evaluate","text":"evaluate(f, X::AbstractMatrix)\n\nEvaluate the linear discriminant value, i.e wx + b, for each sample in columns of X. The function returns a vector of length size(X, 2).\n\n\n\n\n\n","category":"method"},{"location":"lda/#StatsAPI.predict-Tuple{LinearDiscriminant, AbstractVector}","page":"Linear Discriminant Analysis","title":"StatsAPI.predict","text":"predict(f, x::AbstractVector)\n\nMake prediction for the vector x. It returns true iff evaluate(f, x) is positive.\n\n\n\n\n\n","category":"method"},{"location":"lda/#StatsAPI.predict-Tuple{LinearDiscriminant, AbstractMatrix}","page":"Linear Discriminant Analysis","title":"StatsAPI.predict","text":"predict(f, X::AbstractMatrix)\n\nMake predictions for the matrix X.\n\n\n\n\n\n","category":"method"},{"location":"lda/#StatsAPI.coef-Tuple{LinearDiscriminant}","page":"Linear Discriminant Analysis","title":"StatsAPI.coef","text":"coef(f::LinearDiscriminant)\n\nReturn the coefficients of the linear discriminant model.\n\n\n\n\n\n","category":"method"},{"location":"lda/#StatsAPI.dof-Tuple{LinearDiscriminant}","page":"Linear Discriminant Analysis","title":"StatsAPI.dof","text":"dof(f::LinearDiscriminant)\n\nReturn the number of degrees of freedom in the linear discriminant model.\n\n\n\n\n\n","category":"method"},{"location":"lda/#StatsAPI.weights-Tuple{LinearDiscriminant}","page":"Linear Discriminant Analysis","title":"StatsAPI.weights","text":"weights(f::LinearDiscriminant)\n\nReturn the linear discriminant model coefficient vector.\n\n\n\n\n\n","category":"method"},{"location":"lda/#Base.length-Tuple{LinearDiscriminant}","page":"Linear Discriminant Analysis","title":"Base.length","text":"Get the length of the coefficient vector.\n\n\n\n\n\n","category":"method"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Additional functionality:","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"ldacov","category":"page"},{"location":"lda/#MultivariateStats.ldacov","page":"Linear Discriminant Analysis","title":"MultivariateStats.ldacov","text":"ldacov(C, μp, μn)\n\nPerforms LDA given a covariance matrix C and both mean vectors μp & μn. Returns a linear discriminant functional of type LinearDiscriminant.\n\nParameters\n\nC: The pooled covariance matrix (i.e (Cp + Cn)2)\nμp: The mean vector of the positive class.\nμn: The mean vector of the negative class.\n\n\n\n\n\nldacov(Cp, Cn, μp, μn)\n\nPerforms LDA given covariances and mean vectors. Returns a linear discriminant functional of type LinearDiscriminant.\n\nParameters\n\nCp: The covariance matrix of the positive class.\nCn: The covariance matrix of the negative class.\nμp: The mean vector of the positive class.\nμn: The mean vector of the negative class.\n\nNote: The coefficient vector is scaled such that wμp + b = 1 and wμn + b = -1.\n\n\n\n\n\n","category":"function"},{"location":"lda/#Multi-class-Linear-Discriminant-Analysis","page":"Linear Discriminant Analysis","title":"Multi-class Linear Discriminant Analysis","text":"","category":"section"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Multi-class LDA is a generalization of standard two-class LDA that can handle arbitrary number of classes.","category":"page"},{"location":"lda/#Overview","page":"Linear Discriminant Analysis","title":"Overview","text":"","category":"section"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Multi-class LDA is based on the analysis of two scatter matrices: within-class scatter matrix and between-class scatter matrix.","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Given a set of samples mathbfx_1 ldots mathbfx_n, and their class labels y_1 ldots y_n:","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"The within-class scatter matrix is defined as:","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"mathbfS_w = sum_i=1^n (mathbfx_i - boldsymbolmu_y_i) (mathbfx_i - boldsymbolmu_y_i)^T","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Here, boldsymbolmu_k is the sample mean of the k-th class.","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"The between-class scatter matrix is defined as:","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"mathbfS_b = sum_k=1^m n_k (boldsymbolmu_k - boldsymbolmu) (boldsymbolmu_k - boldsymbolmu)^T","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Here, m is the number of classes, boldsymbolmu is the overall sample mean, and n_k is the number of samples in the k-th class.","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Then, multi-class LDA can be formulated as an optimization problem to find a set of linear combinations (with coefficients mathbfw) that maximizes the ratio of the between-class scattering to the within-class scattering, as","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"hatmathbfw = mathopmathrmargmax_mathbfw\n fracmathbfw^T mathbfS_b mathbfwmathbfw^T mathbfS_w mathbfw","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"The solution is given by the following generalized eigenvalue problem:","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"mathbfS_b mathbfw = lambda mathbfS_w mathbfw","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Generally, at most m - 1 generalized eigenvectors are useful to discriminate between m classes.","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"When the dimensionality is high, it may not be feasible to construct the scatter matrices explicitly. In such cases, see SubspaceLDA below.","category":"page"},{"location":"lda/#Normalization-by-number-of-observations","page":"Linear Discriminant Analysis","title":"Normalization by number of observations","text":"","category":"section"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"An alternative definition of the within- and between-class scatter matrices normalizes for the number of observations in each group:","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"mathbfS_w^* = n sum_k=1^m frac1n_k sum_i mid y_i=k (mathbfx_i - boldsymbolmu_k) (mathbfx_i - boldsymbolmu_k)^T","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"mathbfS_b^* = n sum_k=1^m (boldsymbolmu_k - boldsymbolmu^*) (boldsymbolmu_k - boldsymbolmu^*)^T","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"where","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"boldsymbolmu^* = frac1k sum_k=1^m boldsymbolmu_k","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"This definition can sometimes be more useful when looking for directions which discriminate among clusters containing widely-varying numbers of observations.","category":"page"},{"location":"lda/#Multi-class-LDA","page":"Linear Discriminant Analysis","title":"Multi-class LDA","text":"","category":"section"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"The package defines a MulticlassLDA type to represent a multi-class LDA model, as:","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"MulticlassLDA\nMulticlassLDAStats","category":"page"},{"location":"lda/#MultivariateStats.MulticlassLDA","page":"Linear Discriminant Analysis","title":"MultivariateStats.MulticlassLDA","text":"A multi-class linear discriminant model type has following fields:\n\nproj is the projection matrix\npmeans is the projected means of all classes\nstats is an instance of MulticlassLDAStats type that captures all statistics computed to train the model (which we will discuss later).\n\n\n\n\n\n","category":"type"},{"location":"lda/#MultivariateStats.MulticlassLDAStats","page":"Linear Discriminant Analysis","title":"MultivariateStats.MulticlassLDAStats","text":"Resulting statistics of the multi-class LDA evaluation.\n\n\n\n\n\n","category":"type"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Several methods are provided to access properties of the LDA model. Let M be an instance of MulticlassLDA:","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"fit(::Type{MulticlassLDA}, ::AbstractMatrix{T}, ::AbstractVector; kwargs...) where T<:Real\npredict(::MulticlassLDA, ::AbstractVecOrMat{T}) where {T<:Real}\nmean(::MulticlassLDA)\nsize(::MulticlassLDA)\nlength(::MulticlassLDA)\nclassmeans(::MulticlassLDA)\nclassweights(::MulticlassLDA)\nwithclass_scatter(::MulticlassLDA)\nbetweenclass_scatter(::MulticlassLDA)\nprojection(::MulticlassLDA)","category":"page"},{"location":"lda/#StatsAPI.fit-Union{Tuple{T}, Tuple{Type{MulticlassLDA}, AbstractMatrix{T}, AbstractVector}} where T<:Real","page":"Linear Discriminant Analysis","title":"StatsAPI.fit","text":"fit(MulticlassLDA, X, y; ...)\n\nPerform multi-class LDA over a given data set X with corresponding labels y with nc number of classes.\n\nThis function returns the resultant multi-class LDA model as an instance of MulticlassLDA.\n\nParameters\n\nX: the matrix of input samples, of size (d, n). Each column in X is an observation.\ny: the vector of class labels, of length n.\n\nKeyword arguments\n\nmethod: The choice of methods:\n:gevd: based on generalized eigenvalue decomposition (default).\n:whiten: first derive a whitening transform from Sw and then solve the problem based on eigenvalue\ndecomposition of the whiten Sb.\noutdim: The output dimension, i.e. dimension of the transformed space min(d, nc-1)\nregcoef: The regularization coefficient (default: 1.0e-6). A positive value regcoef * eigmax(Sw) is added to the diagonal of Sw to improve numerical stability.\ncovestimator_between: Custom covariance estimator for between-class covariance (default: SimpleCovariance()). The covariance matrix will be calculated as cov(covestimator_between, #=data=#; dims=2, mean=zeros(#=...=#)). Custom covariance estimators, available in other packages, may result in more robust discriminants for data with more features than observations.\ncovestimator_within: Custom covariance estimator for within-class covariance (default: SimpleCovariance()). The covariance matrix will be calculated as cov(covestimator_within, #=data=#; dims=2, mean=zeros(nc)). Custom covariance estimators, available in other packages, may result in more robust discriminants for data with more features than observations.\n\nNotes:\n\nThe resultant projection matrix P satisfies:\n\nmathbfP^T (mathbfS_w + kappa mathbfI) mathbfP = mathbfI\n\nHere, kappa equals regcoef * eigmax(Sw). The columns of P are arranged in descending order of the corresponding generalized eigenvalues.\n\nNote that MulticlassLDA does not currently support the normalized version using mathbfS_w^* and mathbfS_b^* (see SubspaceLDA).\n\n\n\n\n\n","category":"method"},{"location":"lda/#StatsAPI.predict-Union{Tuple{T}, Tuple{MulticlassLDA, AbstractVecOrMat{T}}} where T<:Real","page":"Linear Discriminant Analysis","title":"StatsAPI.predict","text":"predict(M::MulticlassLDA, x)\n\nTransform input sample(s) in x to the output space of MC-LDA model M. Here, x can be either a sample vector or a matrix comprised of samples in columns.\n\n\n\n\n\n","category":"method"},{"location":"lda/#Statistics.mean-Tuple{MulticlassLDA}","page":"Linear Discriminant Analysis","title":"Statistics.mean","text":"mean(M::MulticlassLDA)\n\nGet the overall sample mean vector (of length d).\n\n\n\n\n\n","category":"method"},{"location":"lda/#Base.size-Tuple{MulticlassLDA}","page":"Linear Discriminant Analysis","title":"Base.size","text":"size(M::MulticlassLDA)\n\nGet the input (i.e the dimension of the observation space) and output (i.e the dimension of the transformed features) dimensions of the model M.\n\n\n\n\n\n","category":"method"},{"location":"lda/#Base.length-Tuple{MulticlassLDA}","page":"Linear Discriminant Analysis","title":"Base.length","text":"length(M::MulticlassLDA)\n\nGet the sample dimensions.\n\n\n\n\n\n","category":"method"},{"location":"lda/#MultivariateStats.classmeans-Tuple{MulticlassLDA}","page":"Linear Discriminant Analysis","title":"MultivariateStats.classmeans","text":"classmeans(M)\n\nGet the matrix comprised of class-specific means as columns (of size (d m)).\n\n\n\n\n\n","category":"method"},{"location":"lda/#MultivariateStats.classweights-Tuple{MulticlassLDA}","page":"Linear Discriminant Analysis","title":"MultivariateStats.classweights","text":"classweights(M)\n\nGet the weights of individual classes (a vector of length m). If the samples are not weighted, the weight equals the number of samples of each class.\n\n\n\n\n\n","category":"method"},{"location":"lda/#MultivariateStats.withclass_scatter-Tuple{MulticlassLDA}","page":"Linear Discriminant Analysis","title":"MultivariateStats.withclass_scatter","text":"withinclass_scatter(M)\n\nGet the within-class scatter matrix (of size ``(d, d)``).\n\n\n\n\n\n","category":"method"},{"location":"lda/#MultivariateStats.betweenclass_scatter-Tuple{MulticlassLDA}","page":"Linear Discriminant Analysis","title":"MultivariateStats.betweenclass_scatter","text":"betweenclass_scatter(M)\n\nGet the between-class scatter matrix (of size ``(d, d)``).\n\n\n\n\n\n","category":"method"},{"location":"lda/#MultivariateStats.projection-Tuple{MulticlassLDA}","page":"Linear Discriminant Analysis","title":"MultivariateStats.projection","text":"projection(M::MulticlassLDA)\n\nGet the projection matrix (of size d x p).\n\n\n\n\n\n","category":"method"},{"location":"lda/#Subspace-Linear-Discriminant-Analysis","page":"Linear Discriminant Analysis","title":"Subspace Linear Discriminant Analysis","text":"","category":"section"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"The package also defines a SubspaceLDA type to represent a multi-class LDA model for high-dimensional spaces. MulticlassLDA, because it stores the scatter matrices, is not well-suited for high-dimensional data. For example, if you are performing LDA on images, and each image has 10^6 pixels, then the scatter matrices would contain 10^12 elements, far too many to store directly. SubspaceLDA calculates the projection direction without the intermediary of the scatter matrices, by focusing on the subspace that lies within the span of the within-class scatter. This also serves to regularize the computation.","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"SubspaceLDA supports all the same methods as MulticlassLDA, with the exception of the functions that return a scatter matrix. The overall projection is represented as a factorization P*L, where P*x projects data points to the subspace spanned by the within-class scatter, and L is the LDA projection in the subspace. The projection directions w (the columns of projection(M)) satisfy the equation","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":" mathbfP^T mathbfS_b mathbfw = lambda mathbfP^T mathbfS_w mathbfw","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"When P is of full rank (e.g., if there are more data points than dimensions), then this equation guarantees that mathbfS_b mathbfw = lambda mathbfS_w mathbfw will also hold.","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"The package defines a SubspaceLDA type to represent a multi-class LDA model, as:","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"SubspaceLDA","category":"page"},{"location":"lda/#MultivariateStats.SubspaceLDA","page":"Linear Discriminant Analysis","title":"MultivariateStats.SubspaceLDA","text":"Subspace LDA model type has following fields:\n\nprojw: the projection matrix of the subspace spanned by the between-class scatter\nprojLDA: the projection matrix of the subspace spanned by the within-class scatter\nλ: the projection eigenvalues\ncmeans: the class centroids\ncweights: the class weights\n\n\n\n\n\n","category":"type"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Several methods are provided to access properties of the LDA model. Let M be an instance of SubspaceLDA:","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"fit(::Type{SubspaceLDA}, ::AbstractMatrix{T}, ::AbstractVector; kwargs...) where T<:Real\npredict(::SubspaceLDA, ::AbstractVecOrMat{T}) where {T<:Real}\nmean(::SubspaceLDA)\nprojection(::SubspaceLDA)\nsize(::SubspaceLDA)\nlength(::SubspaceLDA)\neigvals(::SubspaceLDA)","category":"page"},{"location":"lda/#StatsAPI.fit-Union{Tuple{T}, Tuple{Type{SubspaceLDA}, AbstractMatrix{T}, AbstractVector}} where T<:Real","page":"Linear Discriminant Analysis","title":"StatsAPI.fit","text":"fit(SubspaceLDA, X, y; normalize=true)\n\nFit an subspace projection of LDA model over a given data set X with corresponding labels y using the equivalent of mathbfS_w^* and mathbfS_b^*`.\n\nNote: Subspace LDA also supports the normalized version of LDA via the normalize keyword.\n\n\n\n\n\n","category":"method"},{"location":"lda/#StatsAPI.predict-Union{Tuple{T}, Tuple{SubspaceLDA, AbstractVecOrMat{T}}} where T<:Real","page":"Linear Discriminant Analysis","title":"StatsAPI.predict","text":"predict(M::SubspaceLDA, x)\n\nTransform input sample(s) in x to the output space of LDA model M. Here, x can be either a sample vector or a matrix comprised of samples in columns.\n\n\n\n\n\n","category":"method"},{"location":"lda/#Statistics.mean-Tuple{SubspaceLDA}","page":"Linear Discriminant Analysis","title":"Statistics.mean","text":"mean(M::SubspaceLDA)\n\nReturns the mean vector of the subspace LDA model M.\n\n\n\n\n\n","category":"method"},{"location":"lda/#MultivariateStats.projection-Tuple{SubspaceLDA}","page":"Linear Discriminant Analysis","title":"MultivariateStats.projection","text":"projection(M)\n\nGet the projection matrix.\n\n\n\n\n\n","category":"method"},{"location":"lda/#Base.size-Tuple{SubspaceLDA}","page":"Linear Discriminant Analysis","title":"Base.size","text":"size(M)\n\nGet the input (i.e the dimension of the observation space) and output (i.e the dimension of the subspace projection) dimensions of the model M.\n\n\n\n\n\n","category":"method"},{"location":"lda/#Base.length-Tuple{SubspaceLDA}","page":"Linear Discriminant Analysis","title":"Base.length","text":"length(M)\n\nGet dimension of the LDA model.\n\n\n\n\n\n","category":"method"},{"location":"lda/#LinearAlgebra.eigvals-Tuple{SubspaceLDA}","page":"Linear Discriminant Analysis","title":"LinearAlgebra.eigvals","text":"eigvals(M::SubspaceLDA)\n\nGet the eigenvalues of the subspace LDA model M.\n\n\n\n\n\n","category":"method"},{"location":"cca/#Canonical-Correlation-Analysis","page":"Canonical Correlation Analysis","title":"Canonical Correlation Analysis","text":"","category":"section"},{"location":"cca/","page":"Canonical Correlation Analysis","title":"Canonical Correlation Analysis","text":"Canonical Correlation Analysis(CCA) is a statistical analysis technique to identify correlations between two sets of variables. Given two vector variables X and Y, it finds two projections, one for each, to transform them to a common space with maximum correlations.","category":"page"},{"location":"cca/","page":"Canonical Correlation Analysis","title":"Canonical Correlation Analysis","text":"The package defines a CCA type to represent a CCA model, and provides a set of methods to access the properties.","category":"page"},{"location":"cca/","page":"Canonical Correlation Analysis","title":"Canonical Correlation Analysis","text":"CCA","category":"page"},{"location":"cca/#MultivariateStats.CCA","page":"Canonical Correlation Analysis","title":"MultivariateStats.CCA","text":"Canonical Correlation Analysis Model\n\n\n\n\n\n","category":"type"},{"location":"cca/","page":"Canonical Correlation Analysis","title":"Canonical Correlation Analysis","text":"Let M be an instance of CCA, dx be the dimension of X, dy the dimension of Y, and p the output dimension (i.e the dimension of the common space).","category":"page"},{"location":"cca/","page":"Canonical Correlation Analysis","title":"Canonical Correlation Analysis","text":"fit(::Type{CCA}, ::AbstractMatrix{T}, ::AbstractMatrix{T}) where {T<:Real}\nsize(::CCA)\nmean(::CCA, ::Symbol)\nprojection(::CCA, ::Symbol)\ncor(::CCA)\npredict(::CCA, ::AbstractVecOrMat{<:Real}, ::Symbol)","category":"page"},{"location":"cca/#StatsAPI.fit-Union{Tuple{T}, Tuple{Type{CCA}, AbstractMatrix{T}, AbstractMatrix{T}}} where T<:Real","page":"Canonical Correlation Analysis","title":"StatsAPI.fit","text":"fit(CCA, X, Y; ...)\n\nPerform CCA over the data given in matrices X and Y. Each column of X and Y is an observation.\n\nX and Y should have the same number of columns (denoted by n below).\n\nThis method returns an instance of CCA.\n\nKeyword arguments:\n\nmethod: The choice of methods:\n:cov: based on covariance matrices\n:svd: based on SVD of the input data (default)\noutdim: The output dimension, i.e dimension of the common space (default: min(dx, dy, n))\nmean: The mean vector, which can be either of:\n0: the input data has already been centralized\nnothing: this function will compute the mean (default)\na pre-computed mean vector\n\nNotes: This function calls ccacov or ccasvd internally, depending on the choice of method.\n\n\n\n\n\n","category":"method"},{"location":"cca/#Base.size-Tuple{CCA}","page":"Canonical Correlation Analysis","title":"Base.size","text":"size(M:CCA)\n\nReturn a tuple with the dimension of X, Y, and the output dimension.\n\n\n\n\n\n","category":"method"},{"location":"cca/#Statistics.mean-Tuple{CCA, Symbol}","page":"Canonical Correlation Analysis","title":"Statistics.mean","text":"mean(M::CCA, c::Symbol)\n\nGet the mean vector for the component c of the model M. The component parameter can be :x or :y.\n\n\n\n\n\n","category":"method"},{"location":"cca/#MultivariateStats.projection-Tuple{CCA, Symbol}","page":"Canonical Correlation Analysis","title":"MultivariateStats.projection","text":"projection(M::CCA, c::Symbol)\n\nGet the projection matrix for the component c of the model M. The component parameter can be :x or :y.\n\n\n\n\n\n","category":"method"},{"location":"cca/#Statistics.cor-Tuple{CCA}","page":"Canonical Correlation Analysis","title":"Statistics.cor","text":"cor(M::CCA)\n\nThe correlations of the projected components (a vector of length p).\n\n\n\n\n\n","category":"method"},{"location":"cca/#StatsAPI.predict-Tuple{CCA, AbstractVecOrMat{<:Real}, Symbol}","page":"Canonical Correlation Analysis","title":"StatsAPI.predict","text":"predict(M::CCA, Z::AbstractVecOrMat{<:Real}, c::Symbol)\n\nGiven a CCA model, one can transform observations into both spaces into a common space, as\n\nmathbfz_x = mathbfP_x^T (mathbfx - boldsymbolmu_x) \nmathbfz_y = mathbfP_y^T (mathbfy - boldsymbolmu_y)\n\nHere, mathbfP_x and mathbfP_y are projection matrices for X and Y; boldsymbolmu_x and boldsymbolmu_y are mean vectors.\n\nParameter Z can be either a vector of length dx, dy, or a matrix where each column is an observation. The component parameter c can be :x or :y.\n\n\n\n\n\n","category":"method"},{"location":"cca/","page":"Canonical Correlation Analysis","title":"Canonical Correlation Analysis","text":"Auxiliary functions:","category":"page"},{"location":"cca/","page":"Canonical Correlation Analysis","title":"Canonical Correlation Analysis","text":"ccacov\nccasvd","category":"page"},{"location":"cca/#MultivariateStats.ccacov","page":"Canonical Correlation Analysis","title":"MultivariateStats.ccacov","text":"ccacov(Cxx, Cyy, Cxy, xmean, ymean, p)\n\nCompute CCA based on analysis of the given covariance matrices, using generalized eigenvalue decomposition, and return CCA model.\n\nParameters:\n\nCxx: The covariance matrix of X.\nCyy: The covariance matrix of Y.\nCxy: The covariance matrix between X and Y.\nxmean: The mean vector of the original samples of X, which can be\n\na vector of length dx, or an empty vector indicating a zero mean.\n\nymean: The mean vector of the original samples of Y, which can be\n\na vector of length dy, or an empty vector indicating a zero mean.\n\np: The output dimension, i.e the dimension of the common space.\n\n\n\n\n\n","category":"function"},{"location":"cca/#MultivariateStats.ccasvd","page":"Canonical Correlation Analysis","title":"MultivariateStats.ccasvd","text":"ccasvd(Zx, Zy, xmean, ymean, p)\n\nCompute CCA based on singular value decomposition of centralized sample matrices Zx and Zy, and return CCA model[1].\n\nParameters:\n\nZx: The centralized sample matrix for X.\nZy: The centralized sample matrix for Y.\nxmean: The mean vector of the original samples of X, which can be\n\na vector of length dx, or an empty vector indicating a zero mean.\n\nymean: The mean vector of the original samples of Y, which can be\n\na vector of length dy, or an empty vector indicating a zero mean.\n\np: The output dimension, i.e the dimension of the common space.\n\n\n\n\n\n","category":"function"},{"location":"cca/","page":"Canonical Correlation Analysis","title":"Canonical Correlation Analysis","text":"","category":"page"},{"location":"cca/#References","page":"Canonical Correlation Analysis","title":"References","text":"","category":"section"},{"location":"cca/","page":"Canonical Correlation Analysis","title":"Canonical Correlation Analysis","text":"[1]: David Weenink, Canonical Correlation Analysis, Institute of Phonetic Sciences, Univ. of Amsterdam, Proceedings 25, 81-99, 2003.","category":"page"},{"location":"ica/#Independent-Component-Analysis","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"","category":"section"},{"location":"ica/","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"Independent Component Analysis (ICA) is a computational technique for separating a multivariate signal into additive subcomponents, with the assumption that the subcomponents are non-Gaussian and independent from each other.","category":"page"},{"location":"ica/","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"There are multiple algorithms for ICA. Currently, this package implements the Fast ICA algorithm.","category":"page"},{"location":"ica/#FastICA","page":"Independent Component Analysis","title":"FastICA","text":"","category":"section"},{"location":"ica/","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"This package implements the FastICA algorithm[1]. The package uses the ICA type to define a FastICA model:","category":"page"},{"location":"ica/","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"ICA","category":"page"},{"location":"ica/#MultivariateStats.ICA","page":"Independent Component Analysis","title":"MultivariateStats.ICA","text":"This type contains ICA model parameters: mean and component matrix W.\n\nNote: Each column of the component matrix W corresponds to an independent component.\n\n\n\n\n\n","category":"type"},{"location":"ica/","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"Several methods are provided to work with ICA. Let M be an instance of ICA:","category":"page"},{"location":"ica/","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"fit(::Type{ICA}, ::AbstractMatrix{T}, ::Int) where {T<:Real}\nsize(::ICA)\nmean(::ICA)\npredict(::ICA, ::AbstractVecOrMat{<:Real})","category":"page"},{"location":"ica/#StatsAPI.fit-Union{Tuple{T}, Tuple{Type{ICA}, AbstractMatrix{T}, Int64}} where T<:Real","page":"Independent Component Analysis","title":"StatsAPI.fit","text":"fit(ICA, X, k; ...)\n\nPerform ICA over the data set given in X.\n\nParameters: -X: The data matrix, of size (m n). Each row corresponds to a mixed signal, while each column corresponds to an observation (e.g all signal value at a particular time step). -k: The number of independent components to recover.\n\nKeyword Arguments:\n\nalg: The choice of algorithm (default :fastica)\nfun: The approx neg-entropy functor (default Tanh)\ndo_whiten: Whether to perform pre-whitening (default true)\nmaxiter: Maximum number of iterations (default 100)\ntol: Tolerable change of W at convergence (default 1.0e-6)\nmean: The mean vector, which can be either of:\n0: the input data has already been centralized\nnothing: this function will compute the mean (default)\na pre-computed mean vector\nwinit: Initial guess of W, which should be either of:\nempty matrix: the function will perform random initialization (default)\na matrix of size (k k) (when do_whiten)\na matrix of size (m k) (when !do_whiten)\n\nReturns the resultant ICA model, an instance of type ICA.\n\nNote: If do_whiten is true, the return W satisfies mathbfW^T mathbfC mathbfW = mathbfI, otherwise W is orthonormal, i.e mathbfW^T mathbfW = mathbfI.\n\n\n\n\n\n","category":"method"},{"location":"ica/#Base.size-Tuple{ICA}","page":"Independent Component Analysis","title":"Base.size","text":"size(M::ICA)\n\nReturns a tuple with the input dimension, i.e the number of observed mixtures, and the output dimension, i.e the number of independent components.\n\n\n\n\n\n","category":"method"},{"location":"ica/#Statistics.mean-Tuple{ICA}","page":"Independent Component Analysis","title":"Statistics.mean","text":"mean(M::ICA)\n\nReturns the mean vector.\n\n\n\n\n\n","category":"method"},{"location":"ica/#StatsAPI.predict-Tuple{ICA, AbstractVecOrMat{<:Real}}","page":"Independent Component Analysis","title":"StatsAPI.predict","text":"predict(M::ICA, x)\n\nTransform x to the output space to extract independent components, as mathbfW^T (mathbfx - boldsymbolmu), given the model M.\n\n\n\n\n\n","category":"method"},{"location":"ica/","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"The package also exports functions of the core algorithms. Sometimes, it can be more efficient to directly invoke them instead of going through the fit interface.","category":"page"},{"location":"ica/","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"fastica!","category":"page"},{"location":"ica/#MultivariateStats.fastica!","page":"Independent Component Analysis","title":"MultivariateStats.fastica!","text":"fastica!(W, X, fun, maxiter, tol, verbose)\n\nInvoke the Fast ICA algorithm[1].\n\nParameters:\n\nW: The initial un-mixing matrix, of size (m k). The function updates this matrix inplace.\nX: The data matrix, of size (m n). This matrix is input only, and won't be modified.\nfun: The approximate neg-entropy functor of type ICAGDeriv.\nmaxiter: Maximum number of iterations.\ntol: Tolerable change of W at convergence.\n\nReturns the updated W.\n\nNote: The number of components is inferred from W as size(W, 2).\n\n\n\n\n\n","category":"function"},{"location":"ica/","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"The FastICA method requires a first derivative of a functor g to approximate negative entropy. The package implements an following interface for defining derivative value estimation:","category":"page"},{"location":"ica/","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"MultivariateStats.ICAGDeriv\nMultivariateStats.Tanh\nMultivariateStats.Gaus","category":"page"},{"location":"ica/#MultivariateStats.ICAGDeriv","page":"Independent Component Analysis","title":"MultivariateStats.ICAGDeriv","text":"The abstract type for all g (derivative) functions.\n\nLet g be an instance of such type, then update!(g, U, E) given\n\nU = w'x\n\nreturns updated in-place U and E, s.t.\n\ng(w'x) --> U and E{g'(w'x)} --> E\n\n\n\n\n\n","category":"type"},{"location":"ica/#MultivariateStats.Tanh","page":"Independent Component Analysis","title":"MultivariateStats.Tanh","text":"Derivative for (1a_1)logcosh a_1 u\n\n\n\n\n\n","category":"type"},{"location":"ica/#MultivariateStats.Gaus","page":"Independent Component Analysis","title":"MultivariateStats.Gaus","text":"Derivative for -e^frac-u^22\n\n\n\n\n\n","category":"type"},{"location":"ica/","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"","category":"page"},{"location":"ica/#References","page":"Independent Component Analysis","title":"References","text":"","category":"section"},{"location":"ica/","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"[1]: Aapo Hyvarinen and Erkki Oja, Independent Component Analysis: Algorithms and Applications. Neural Network 13(4-5), 2000.","category":"page"},{"location":"whiten/#Data-Transformation","page":"Data Transformation","title":"Data Transformation","text":"","category":"section"},{"location":"whiten/#Whitening","page":"Data Transformation","title":"Whitening","text":"","category":"section"},{"location":"whiten/","page":"Data Transformation","title":"Data Transformation","text":"A whitening transformation is a decorrelation transformation that transforms a set of random variables into a set of new random variables with identity covariance (uncorrelated with unit variances).","category":"page"},{"location":"whiten/","page":"Data Transformation","title":"Data Transformation","text":"In particular, suppose a random vector has covariance mathbfC, then a whitening transform mathbfW is one that satisfy:","category":"page"},{"location":"whiten/","page":"Data Transformation","title":"Data Transformation","text":" mathbfW^T mathbfC mathbfW = mathbfI","category":"page"},{"location":"whiten/","page":"Data Transformation","title":"Data Transformation","text":"Note that mathbfW is generally not unique. In particular, if mathbfW is a whitening transform, so is any of its rotation mathbfW mathbfR with mathbfR^T mathbfR = mathbfI.","category":"page"},{"location":"whiten/","page":"Data Transformation","title":"Data Transformation","text":"The package uses Whitening to represent a whitening transform.","category":"page"},{"location":"whiten/","page":"Data Transformation","title":"Data Transformation","text":"Whitening","category":"page"},{"location":"whiten/#MultivariateStats.Whitening","page":"Data Transformation","title":"MultivariateStats.Whitening","text":"A whitening transform representation.\n\n\n\n\n\n","category":"type"},{"location":"whiten/","page":"Data Transformation","title":"Data Transformation","text":"Whitening transformation can be fitted to data using the fit method.","category":"page"},{"location":"whiten/","page":"Data Transformation","title":"Data Transformation","text":"fit(::Type{Whitening}, X::AbstractMatrix{T}; kwargs...) where {T<:Real}\nMultivariateStats.transform(::Whitening, ::AbstractVecOrMat{<:Real})\nlength(::Whitening)\nmean(::Whitening)\nsize(::Whitening)","category":"page"},{"location":"whiten/#StatsAPI.fit-Union{Tuple{T}, Tuple{Type{Whitening}, AbstractMatrix{T}}} where T<:Real","page":"Data Transformation","title":"StatsAPI.fit","text":"fit(Whitening, X::AbstractMatrix{T}; kwargs...)\n\nEstimate a whitening transform from the data given in X.\n\nThis function returns an instance of Whitening\n\nKeyword Arguments:\n\nregcoef: The regularization coefficient. The covariance will be regularized as follows when regcoef is positive C + (eigmax(C) * regcoef) * eye(d). Default values is zero(T).\ndims: if 1 the transformation calculated from the row samples. fit standardization parameters in column-wise fashion; if 2 the transformation calculated from the column samples. The default is nothing, which is equivalent to dims=2 with a deprecation warning.\nmean: The mean vector, which can be either of:\n0: the input data has already been centralized\nnothing: this function will compute the mean (default)\na pre-computed mean vector\n\nNote: This function internally relies on cov_whitening to derive the transformation W.\n\n\n\n\n\n","category":"method"},{"location":"whiten/#MultivariateStats.transform-Tuple{Whitening, AbstractVecOrMat{<:Real}}","page":"Data Transformation","title":"MultivariateStats.transform","text":"transform(f, x)\n\nApply the whitening transform f to a vector or a matrix x with samples in columns, as mathbfW^T (mathbfx - boldsymbolmu).\n\n\n\n\n\n","category":"method"},{"location":"whiten/#Base.length-Tuple{Whitening}","page":"Data Transformation","title":"Base.length","text":"length(f)\n\nGet the dimension of the whitening transform f.\n\n\n\n\n\n","category":"method"},{"location":"whiten/#Statistics.mean-Tuple{Whitening}","page":"Data Transformation","title":"Statistics.mean","text":"mean(f)\n\nGet the mean vector of the whitening transformation f.\n\nNote: if mean is empty, this function returns a zero vector of length(f).\n\n\n\n\n\n","category":"method"},{"location":"whiten/#Base.size-Tuple{Whitening}","page":"Data Transformation","title":"Base.size","text":"size(f)\n\nDimensions of the coefficient matrix of the whitening transform f.\n\n\n\n\n\n","category":"method"},{"location":"whiten/","page":"Data Transformation","title":"Data Transformation","text":"Additional methods","category":"page"},{"location":"whiten/","page":"Data Transformation","title":"Data Transformation","text":"cov_whitening\ncov_whitening!","category":"page"},{"location":"whiten/#MultivariateStats.cov_whitening","page":"Data Transformation","title":"MultivariateStats.cov_whitening","text":"cov_whitening(C)\n\nDerive the whitening transform coefficient matrix W given the covariance matrix C. Here, C can be either a square matrix, or an instance of Cholesky.\n\nInternally, this function solves the whitening transform using Cholesky factorization. The rationale is as follows: let mathbfC = mathbfU^T mathbfU and mathbfW = mathbfU^-1, then mathbfW^T mathbfC mathbfW = mathbfI.\n\nNote: The return matrix W is an upper triangular matrix.\n\n\n\n\n\ncov_whitening(C, regcoef)\n\nDerive a whitening transform based on a regularized covariance, as C + (eigmax(C) * regcoef) * eye(d).\n\n\n\n\n\n","category":"function"},{"location":"whiten/#MultivariateStats.cov_whitening!","page":"Data Transformation","title":"MultivariateStats.cov_whitening!","text":"cov_whitening!(C)\n\nIn-place version of cov_whitening(C), in which the input matrix C will be overwritten during computation. This can be more efficient when C is no longer used.\n\n\n\n\n\ncov_whitening!(C, regcoef)\n\nIn-place version of cov_whitening(C, regcoef), in which the input matrix C will be overwritten during computation. This can be more efficient when C is no longer used.\n\n\n\n\n\n","category":"function"},{"location":"#MultivariateStats.jl-Documentation","page":"Home","title":"MultivariateStats.jl Documentation","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"CurrentModule = MultivariateStats\nDocTestSetup = quote\n using Statistics\n using Random\nend","category":"page"},{"location":"","page":"Home","title":"Home","text":"MultivariateStats.jl is a Julia package for multivariate statistical analysis. It provides a rich set of useful analysis techniques, such as PCA, CCA, LDA, ICA, etc.","category":"page"},{"location":"","page":"Home","title":"Home","text":"Pages = [\"whiten.md\", \"lreg.md\", \"lda.md\", \"pca.md\", \"ica.md\", \"cca.md\", \"fa.md\", \"mds.md\", \"api.md\"]\nDepth = 2","category":"page"},{"location":"","page":"Home","title":"Home","text":"Notes: All methods implemented in this package adopt the column-major convention of JuliaStats: in a data matrix, each column corresponds to a sample/observation, while each row corresponds to a feature (variable or attribute).","category":"page"},{"location":"lreg/#Regression","page":"Regression","title":"Regression","text":"","category":"section"},{"location":"lreg/","page":"Regression","title":"Regression","text":"The package provides functions to perform Linear Least Square, Ridge, and Isotonic Regression.","category":"page"},{"location":"lreg/#Examples","page":"Regression","title":"Examples","text":"","category":"section"},{"location":"lreg/","page":"Regression","title":"Regression","text":"using Plots\ngr(fmt=:svg)","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"Performing llsq regression on cars data set:","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"using MultivariateStats, RDatasets, Plots\n\n# load cars dataset\ncars = dataset(\"datasets\", \"cars\")\n\n# calculate regression models\na = llsq(cars[!,:Speed], cars[!, :Dist])\nb = isotonic(cars[!,:Speed], cars[!, :Dist])\n\n# plot results\np = scatter(cars[!,:Speed], cars[!,:Dist], xlab=\"Speed\", ylab=\"Distance\",\n leg=:topleft, lab=\"data\")\nlet xs = cars[!,:Speed]\n plot!(p, xs, map(x->a[1]*x+a[2], xs), lab=\"llsq\")\n plot!(p, xs, b, lab=\"isotonic\")\nend","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"For a single response vector y (without using bias):","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"# prepare data\nX = rand(1000, 3) # feature matrix\na0 = rand(3) # ground truths\ny = X * a0 + 0.1 * randn(1000) # generate response\n\n# solve using llsq\na = llsq(X, y; bias=false)\n\n# do prediction\nyp = X * a\n\n# measure the error\nrmse = sqrt(mean(abs2.(y - yp)))\nprint(\"rmse = $rmse\")","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"For a single response vector y (using bias):","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"# prepare data\nX = rand(1000, 3)\na0, b0 = rand(3), rand()\ny = X * a0 .+ b0 .+ 0.1 * randn(1000)\n\n# solve using llsq\nsol = llsq(X, y)\n\n# extract results\na, b = sol[1:end-1], sol[end]\n\n# do prediction\nyp = X * a .+ b'","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"For a matrix of column-stored regressors X and a matrix comprised of multiple columns of dependent variables Y:","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"# prepare data\nX = rand(3, 1000)\nA0, b0 = rand(3, 5), rand(1, 5)\nY = (X' * A0 .+ b0) + 0.1 * randn(1000, 5)\n\n# solve using llsq\nsol = llsq(X, Y, dims=2)\n\n# extract results\nA, b = sol[1:end-1,:], sol[end,:]\n\n# do prediction\nYp = X'*A .+ b'","category":"page"},{"location":"lreg/#Linear-Least-Square","page":"Regression","title":"Linear Least Square","text":"","category":"section"},{"location":"lreg/","page":"Regression","title":"Regression","text":"Linear Least Square is to find linear combination(s) of given variables to fit the responses by minimizing the squared error between them. This can be formulated as an optimization as follows:","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"mathopmathrmminimize_(mathbfa b) \n frac12 mathbfy - (mathbfX mathbfa + b)^2","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"Sometimes, the coefficient matrix is given in a transposed form, in which case, the optimization is modified as:","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"mathopmathrmminimize_(mathbfa b) \n frac12 mathbfy - (mathbfX^T mathbfa + b)^2","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"The package provides following functions to solve the above problems:","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"llsq","category":"page"},{"location":"lreg/#MultivariateStats.llsq","page":"Regression","title":"MultivariateStats.llsq","text":"llsq(X, y; ...)\n\nSolve the linear least square problem.\n\nHere, y can be either a vector, or a matrix where each column is a response vector.\n\nThis function accepts two keyword arguments:\n\ndims: whether input observations are stored as rows (1) or columns (2). (default is 1)\nbias: whether to include the bias term b. (default is true)\n\nThe function results the solution a. In particular, when y is a vector (matrix), a is also a vector (matrix). If bias is true, then the returned array is augmented as [a; b].\n\n\n\n\n\n","category":"function"},{"location":"lreg/#Ridge-Regression","page":"Regression","title":"Ridge Regression","text":"","category":"section"},{"location":"lreg/","page":"Regression","title":"Regression","text":"Compared to linear least square, Ridge Regression uses an additional quadratic term to regularize the problem:","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"mathopmathrmminimize_(mathbfa b) \n frac12 mathbfy - (mathbfX mathbfa + b)^2 +\n frac12 mathbfa^T mathbfQ mathbfa","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"The transposed form:","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":" mathopmathrmminimize_(mathbfa b) \n frac12 mathbfy - (mathbfX^T mathbfa + b)^2 +\n frac12 mathbfa^T mathbfQ mathbfa","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"The package provides following functions to solve the above problems:","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"ridge","category":"page"},{"location":"lreg/#MultivariateStats.ridge","page":"Regression","title":"MultivariateStats.ridge","text":"ridge(X, y, r; ...)\n\nSolve the ridge regression problem.\n\nHere, y can be either a vector, or a matrix where each column is a response vector.\n\nThe argument r gives the quadratic regularization matrix Q, which can be in either of the following forms:\n\nr is a real scalar, then Q is considered to be r * eye(n), where n is the dimension of a.\nr is a real vector, then Q is considered to be diagm(r).\nr is a real symmetric matrix, then Q is simply considered to be r.\n\nThis function accepts two keyword arguments:\n\ndims: whether input observations are stored as rows (1) or columns (2). (default is 1)\nbias: whether to include the bias term b. (default is true)\n\nThe function results the solution a. In particular, when y is a vector (matrix), a is also a vector (matrix). If bias is true, then the returned array is augmented as [a; b].\n\n\n\n\n\n","category":"function"},{"location":"lreg/#Isotonic-Regression","page":"Regression","title":"Isotonic Regression","text":"","category":"section"},{"location":"lreg/","page":"Regression","title":"Regression","text":"Isotonic regression or monotonic regression fits a sequence of observations into a fitted line that is non-decreasing (or non-increasing) everywhere. The problem defined as a weighted least-squares fit hat y_i approx y_i for all i, subject to the constraint that hat y_i leq hat y_j whenever x_i leq x_j. This gives the following quadratic program:","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"min sum_i=1^n w_i(hat y_i-y_i)^2\ntext subject to hat y_i leq hat y_j\ntext for all (ij) in E","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"where E=(ij)x_ileq x_j specifies the partial ordering of the observed inputs x_i.","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"The package provides following functions to solve the above problems:","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"isotonic","category":"page"},{"location":"lreg/#MultivariateStats.isotonic","page":"Regression","title":"MultivariateStats.isotonic","text":"isotonic(x, y[, w])\n\nSolve the isotonic regression problem using the pool adjacent violators algorithm[1].\n\nHere x is the regressor vector, y is response vector, and w is an optional weights vector.\n\nThe function returns a prediction vector of the same size as the regressor vector x.\n\n\n\n\n\n","category":"function"},{"location":"lreg/","page":"Regression","title":"Regression","text":"","category":"page"},{"location":"lreg/#References","page":"Regression","title":"References","text":"","category":"section"},{"location":"lreg/","page":"Regression","title":"Regression","text":"[1]: Best, M.J., Chakravarti, N. Active set algorithms for isotonic regression; A unifying framework. Mathematical Programming 47, 425–439 (1990).","category":"page"},{"location":"mds/#Multidimensional-Scaling","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"","category":"section"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"In general, Multidimensional Scaling (MDS) refers to techniques that transforms samples into lower dimensional space while preserving the inter-sample distances as well as possible.","category":"page"},{"location":"mds/#Example","page":"Multidimensional Scaling","title":"Example","text":"","category":"section"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"using Plots\ngr(fmt=:svg)","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"Performing MDS on Iris data set:","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"using MultivariateStats, RDatasets, Plots\n\n# load iris dataset\niris = dataset(\"datasets\", \"iris\")\n\n# take half of the dataset\nX = Matrix(iris[1:2:end,1:4])'\nX_labels = Vector(iris[1:2:end,5])\nnothing # hide","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"Suppose X is our data matrix, with each observation in a column. We train a MDS model, allowing up to 3 dimensions:","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"M = fit(MDS, X; maxoutdim=3, distances=false)","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"Then, apply MDS model to get an embedding of our data in 3D space:","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"Y = predict(M)","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"Now, we group results by testing set labels for color coding and visualize first 3 principal components in 3D interactive plot","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"setosa = Y[:,X_labels.==\"setosa\"]\nversicolor = Y[:,X_labels.==\"versicolor\"]\nvirginica = Y[:,X_labels.==\"virginica\"]\n\np = scatter(setosa[1,:],setosa[2,:],setosa[3,:],marker=:circle,linewidth=0)\nscatter!(versicolor[1,:],versicolor[2,:],versicolor[3,:],marker=:circle,linewidth=0)\nscatter!(virginica[1,:],virginica[2,:],virginica[3,:],marker=:circle,linewidth=0)","category":"page"},{"location":"mds/#Classical-Multidimensional-Scaling","page":"Multidimensional Scaling","title":"Classical Multidimensional Scaling","text":"","category":"section"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"This package defines a MDS type to represent a classical MDS model[1], and provides a set of methods to access the properties.","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"MDS","category":"page"},{"location":"mds/#MultivariateStats.MDS","page":"Multidimensional Scaling","title":"MultivariateStats.MDS","text":"Classical Multidimensional Scaling (MDS), also known as Principal Coordinates Analysis (PCoA), is a specific technique in this family that accomplishes the embedding in two steps:\n\nConvert the distance matrix to a Gram matrix. This conversion is based on\n\nthe following relations between a distance matrix D and a Gram matrix G:\n\nmathrmsqr(mathbfD) = mathbfg mathbf1^T + mathbf1 mathbfg^T - 2 mathbfG\n\nHere, mathrmsqr(mathbfD) indicates the element-wise square of mathbfD, and mathbfg is the diagonal elements of mathbfG. This relation is itself based on the following decomposition of squared Euclidean distance:\n\n mathbfx - mathbfy ^2 = mathbfx ^2 + mathbfy ^2 - 2 mathbfx^T mathbfy\n\nPerform eigenvalue decomposition of the Gram matrix to derive the coordinates.\n\nNote: The Gramian derived from D may have non-positive or degenerate eigenvalues. The subspace of non-positive eigenvalues is projected out of the MDS solution so that the strain function is minimized in a least-squares sense. If the smallest remaining eigenvalue that is used for the MDS is degenerate, then the solution is not unique, as any linear combination of degenerate eigenvectors will also yield a MDS solution with the same strain value.\n\n\n\n\n\n","category":"type"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"The MDS method type comes with several methods where M be an instance of MDS, d be the dimension of observations, and p be the output dimension, i.e. the embedding dimension, and n is the number of the observations.","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"fit(::Type{MDS}, ::AbstractMatrix{T}; kwargs) where {T<:Real}\npredict(::MDS{T}) where {T<:Real}\npredict(::MDS, ::AbstractVector{<:Real})\nsize(::MDS)\nprojection(M::MDS)\nloadings(M::MDS)\neigvals(M::MDS)\neigvecs(M::MDS)\nstress","category":"page"},{"location":"mds/#StatsAPI.fit-Union{Tuple{T}, Tuple{Type{MDS}, AbstractMatrix{T}}} where T<:Real","page":"Multidimensional Scaling","title":"StatsAPI.fit","text":"fit(MDS, X; kwargs...)\n\nCompute an embedding of X points by classical multidimensional scaling (MDS). There are two calling options, specified via the required keyword argument distances:\n\nmds = fit(MDS, X; distances=false, maxoutdim=size(X,1)-1)\n\nwhere X is the data matrix. Distances between pairs of columns of X are computed using the Euclidean norm. This is equivalent to performing PCA on X.\n\nmds = fit(MDS, D; distances=true, maxoutdim=size(D,1)-1)\n\nwhere D is a symmetric matrix D of distances between points.\n\n\n\n\n\n","category":"method"},{"location":"mds/#StatsAPI.predict-Union{Tuple{MDS{T}}, Tuple{T}} where T<:Real","page":"Multidimensional Scaling","title":"StatsAPI.predict","text":"predict(M)\n\nReturns a coordinate matrix of size (p n) for the MDS model M, where each column is the coordinates for an observation in the embedding space.\n\n\n\n\n\n","category":"method"},{"location":"mds/#StatsAPI.predict-Tuple{MDS, AbstractVector{<:Real}}","page":"Multidimensional Scaling","title":"StatsAPI.predict","text":"predict(M, x::AbstractVector)\n\nCalculate the out-of-sample transformation of the observation x for the MDS model M. Here, x is a vector of length d.\n\n\n\n\n\n","category":"method"},{"location":"mds/#Base.size-Tuple{MDS}","page":"Multidimensional Scaling","title":"Base.size","text":"size(M::MDS)\n\nReturns tuple where the first value is the MDS model M input dimension, i.e the dimension of the observation space, and the second value is the output dimension, i.e the dimension of the embedding.\n\n\n\n\n\n","category":"method"},{"location":"mds/#MultivariateStats.projection-Tuple{MDS}","page":"Multidimensional Scaling","title":"MultivariateStats.projection","text":"projection(M::MDS)\n\nGet the MDS model M eigenvectors matrix (of size (n p)) of the embedding space. The eigenvectors are arranged in descending order of the corresponding eigenvalues.\n\n\n\n\n\n","category":"method"},{"location":"mds/#MultivariateStats.loadings-Tuple{MDS}","page":"Multidimensional Scaling","title":"MultivariateStats.loadings","text":"loadings(M::MDS)\n\nGet the loading of the MDS model M.\n\n\n\n\n\n","category":"method"},{"location":"mds/#LinearAlgebra.eigvals-Tuple{MDS}","page":"Multidimensional Scaling","title":"LinearAlgebra.eigvals","text":"eigvals(M::MDS)\n\nGet the eigenvalues of the MDS model M.\n\n\n\n\n\n","category":"method"},{"location":"mds/#LinearAlgebra.eigvecs-Tuple{MDS}","page":"Multidimensional Scaling","title":"LinearAlgebra.eigvecs","text":"eigvecs(M::MDS)\n\nGet the MDS model M eigenvectors matrix. \n\n\n\n\n\n","category":"method"},{"location":"mds/#MultivariateStats.stress","page":"Multidimensional Scaling","title":"MultivariateStats.stress","text":"stress(M::MDS)\n\nGet the stress of the MDS mode M.\n\n\n\n\n\nstress(M::MetricMDS)\n\nGet the stress of the MDS model M.\n\n\n\n\n\n","category":"function"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"This package provides following functions related to classical MDS.","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"gram2dmat\ngram2dmat!\ndmat2gram\ndmat2gram!","category":"page"},{"location":"mds/#MultivariateStats.gram2dmat","page":"Multidimensional Scaling","title":"MultivariateStats.gram2dmat","text":"gram2dmat(G)\n\nConvert a Gram matrix G to a distance matrix.\n\n\n\n\n\n","category":"function"},{"location":"mds/#MultivariateStats.gram2dmat!","page":"Multidimensional Scaling","title":"MultivariateStats.gram2dmat!","text":"gram2dmat!(D, G)\n\nConvert a Gram matrix G to a distance matrix, and write the results to D.\n\n\n\n\n\n","category":"function"},{"location":"mds/#MultivariateStats.dmat2gram","page":"Multidimensional Scaling","title":"MultivariateStats.dmat2gram","text":"dmat2gram(D)\n\nConvert a distance matrix D to a Gram matrix.\n\n\n\n\n\n","category":"function"},{"location":"mds/#MultivariateStats.dmat2gram!","page":"Multidimensional Scaling","title":"MultivariateStats.dmat2gram!","text":"dmat2gram!(G, D)\n\nConvert a distance matrix D to a Gram matrix, and write the results to G.\n\n\n\n\n\n","category":"function"},{"location":"mds/#Metric-Multidimensional-Scaling","page":"Multidimensional Scaling","title":"Metric Multidimensional Scaling","text":"","category":"section"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"This package defines a MetricMDS type to represent a (non)metric MDS model[1], and provides a set of methods to access the properties.","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"MetricMDS","category":"page"},{"location":"mds/#MultivariateStats.MetricMDS","page":"Multidimensional Scaling","title":"MultivariateStats.MetricMDS","text":"(Non)Metric Multidimensional Scaling\n\nUse this class to perform (non)metric multidimensional scaling.\n\nThere are two calling options, specified via the required keyword argument distances:\n\nmds = fit(MDS, X; distances=false, maxoutdim=size(X,1)-1)\n\nwhere X is the data matrix. Distances between pairs of columns of X are computed using the Euclidean norm. This is equivalent to performing PCA on X.\n\nmds = fit(MDS, D; distances=true, maxoutdim=size(D,1)-1)\n\nwhere D is a symmetric matrix D of distances between points.\n\nIn addition, the metric parameter specifies type of MDS, By default, it is assigned with nothing value which results in performing metric MDS with dissimilarities calculated as Euclidean distances.\n\nAn arbitrary transformation function can be provided to metric parameter to perform metric MDS with transformed proximities. The function has to accept two parameters, a vector of proximities and a vector of distances, corresponding to the proximities, to calculate disparities required for stress calculation. Internally, the proximity and distance vectors are obtained from compact triangular matrix representation of proximity and distance matrices.\n\nFor ratio MDS, a following ratio transformation function can be used\n\nmds = fit(MDS, D; distances=true, metric=((p,d)->2 .* p))\n\nFor order MDS, use isotonic regression function in the metric parameter:\n\nmds = fit(MDS, D; distances=true, metric=isotonic)\n\n\n\n\n\n","category":"type"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"The metric MDS type comes with several methods where M be an instance of MetricMDS, d be the dimension of observations, and p be the output dimension, i.e. the embedding dimension, and n is the number of the observations.","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"fit(::Type{MetricMDS}, ::AbstractMatrix{T}; kwargs) where {T<:Real}\npredict(::MetricMDS)\nsize(::MetricMDS)\nstress(::MetricMDS)","category":"page"},{"location":"mds/#StatsAPI.fit-Union{Tuple{T}, Tuple{Type{MetricMDS}, AbstractMatrix{T}}} where T<:Real","page":"Multidimensional Scaling","title":"StatsAPI.fit","text":"fit(MetricMDS, X; kwargs...)\n\nCompute an embedding of X points by (non)metric multidimensional scaling (MDS).\n\nKeyword arguments:\n\nLet (d, n) = size(X) be respectively the input dimension and the number of observations:\n\ndistances: The choice of input (required):\nfalse: use X to calculate dissimilarity matrix using Euclidean distance\ntrue: use X input as precomputed dissimilarity symmetric matrix (distances)\nmaxoutdim: Maximum output dimension (default d-1)\nmetric : a function for calculation of disparity values\nnothing: use dissimilarity values as the disparities to perform the metric MDS (default)\nisotonic: converts dissimilarity values to ordinal disparities to perform non-metric MDS\nany two parameter disparity transformation function, where the first parameter is a vector of proximities (i.e. dissimilarities) and the second parameter is a vector of distances, e.g. (p,d)->b*p for some b is a transformation function for ratio MDS.\ntol: Convergence tolerance (default 1.0e-3)\nmaxiter: Maximum number of iterations (default 300)\ninitial: an initial reduced space point configuration\nnothing: then an initial configuration is randomly generated (default)\npre-defined matrix\nweights: a weight matrix\nnothing: then weights are set to one, w_ij = 1 (default)\npre-defined matrix\n\nNote: if the algorithm is unable to converge then ConvergenceException is thrown.\n\n\n\n\n\n","category":"method"},{"location":"mds/#StatsAPI.predict-Tuple{MetricMDS}","page":"Multidimensional Scaling","title":"StatsAPI.predict","text":"predict(M::MetricMDS)\n\nReturns a coordinate matrix of size (p n) for the MDS model M, where each column is the coordinates for an observation in the embedding space.\n\n\n\n\n\n","category":"method"},{"location":"mds/#Base.size-Tuple{MetricMDS}","page":"Multidimensional Scaling","title":"Base.size","text":"size(M::MetricMDS)\n\nReturns tuple where the first value is the MDS model M input dimension, i.e the dimension of the observation space, and the second value is the output dimension, i.e the dimension of the embedding.\n\n\n\n\n\n","category":"method"},{"location":"mds/#MultivariateStats.stress-Tuple{MetricMDS}","page":"Multidimensional Scaling","title":"MultivariateStats.stress","text":"stress(M::MetricMDS)\n\nGet the stress of the MDS model M.\n\n\n\n\n\n","category":"method"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"","category":"page"},{"location":"mds/#References","page":"Multidimensional Scaling","title":"References","text":"","category":"section"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"[1]: Ingwer Borg and Patrick J. F. Groenen, \"Modern Multidimensional Scaling: Theory and Applications\", Springer, pp. 201–268, 2005.","category":"page"}] +[{"location":"pca/#Principal-Component-Analysis","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"","category":"section"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"Principal Component Analysis (PCA) derives an orthogonal projection to convert a given set of observations to linearly uncorrelated variables, called principal components.","category":"page"},{"location":"pca/#Example","page":"Principal Component Analysis","title":"Example","text":"","category":"section"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"using Plots\ngr(fmt=:svg)","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"Performing PCA on Iris data set:","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"using MultivariateStats, RDatasets, Plots\n\n# load iris dataset\niris = dataset(\"datasets\", \"iris\")\n\n# split half to training set\nXtr = Matrix(iris[1:2:end,1:4])'\nXtr_labels = Vector(iris[1:2:end,5])\n\n# split other half to testing set\nXte = Matrix(iris[2:2:end,1:4])'\nXte_labels = Vector(iris[2:2:end,5])\nnothing # hide","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"Suppose Xtr and Xte are training and testing data matrix, with each observation in a column. We train a PCA model, allowing up to 3 dimensions:","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"M = fit(PCA, Xtr; maxoutdim=3)","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"Then, apply PCA model to the testing set","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"Yte = predict(M, Xte)","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"And, reconstruct testing observations (approximately) to the original space","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"Xr = reconstruct(M, Yte)","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"Now, we group results by testing set labels for color coding and visualize first 3 principal components in 3D plot","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"setosa = Yte[:,Xte_labels.==\"setosa\"]\nversicolor = Yte[:,Xte_labels.==\"versicolor\"]\nvirginica = Yte[:,Xte_labels.==\"virginica\"]\n\np = scatter(setosa[1,:],setosa[2,:],setosa[3,:],marker=:circle,linewidth=0)\nscatter!(versicolor[1,:],versicolor[2,:],versicolor[3,:],marker=:circle,linewidth=0)\nscatter!(virginica[1,:],virginica[2,:],virginica[3,:],marker=:circle,linewidth=0)\nplot!(p,xlabel=\"PC1\",ylabel=\"PC2\",zlabel=\"PC3\")","category":"page"},{"location":"pca/#Linear-Principal-Component-Analysis","page":"Principal Component Analysis","title":"Linear Principal Component Analysis","text":"","category":"section"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"This package uses the PCA type to define a linear PCA model:","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"PCA","category":"page"},{"location":"pca/#MultivariateStats.PCA","page":"Principal Component Analysis","title":"MultivariateStats.PCA","text":"Linear Principal Component Analysis\n\n\n\n\n\n","category":"type"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"This type comes with several methods where M be an instance of PCA, d be the dimension of observations, and p be the output dimension (i.e the dimension of the principal subspace).","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"fit(::Type{PCA}, ::AbstractMatrix{T}; kwargs) where {T<:Real}\npredict(::PCA, ::AbstractVecOrMat{T}) where {T<:Real}\nreconstruct(::PCA, ::AbstractVecOrMat{T}) where {T<:Real}\nsize(::PCA)\nmean(::PCA)\nprojection(::PCA)\nvar(::PCA)\nprincipalvars(::PCA)\ntprincipalvar(::PCA)\ntresidualvar(::PCA)\nr2(::PCA)\nloadings(::PCA)\neigvals(::PCA)\neigvecs(::PCA)","category":"page"},{"location":"pca/#StatsAPI.fit-Union{Tuple{T}, Tuple{Type{PCA}, AbstractMatrix{T}}} where T<:Real","page":"Principal Component Analysis","title":"StatsAPI.fit","text":"fit(PCA, X; ...)\n\nPerform PCA over the data given in a matrix X. Each column of X is an observation.\n\nKeyword arguments\n\nmethod: The choice of methods:\n:auto: use :cov when d < n or :svd otherwise (default).\n:cov: based on covariance matrix decomposition.\n:svd: based on SVD of the input data.\nmaxoutdim: The output dimension, i.e. dimension of the transformed space (min(d, nc-1))\npratio: The ratio of variances preserved in the principal subspace (0.99)\nmean: The mean vector, which can be either of\n0: the input data has already been centralized\nnothing: this function will compute the mean (default)\na pre-computed mean vector\n\nNotes:\n\nThe output dimension p depends on both maxoutdim and pratio, as follows. Suppose the first k principal components preserve at least pratio of the total variance, while the first k-1 preserves less than pratio, then the actual output dimension will be min(k maxoutdim).\nThis function calls pcacov or pcasvd internally, depending on the choice of method.\n\n\n\n\n\n","category":"method"},{"location":"pca/#StatsAPI.predict-Union{Tuple{T}, Tuple{PCA, AbstractVecOrMat{T}}} where T<:Real","page":"Principal Component Analysis","title":"StatsAPI.predict","text":"predict(M::PCA, x::AbstractVecOrMat{<:Real})\n\nGiven a PCA model M, transform observations x into principal components space, as\n\nmathbfy = mathbfP^T (mathbfx - boldsymbolmu)\n\nHere, x can be either a vector of length d or a matrix where each column is an observation, and \\mathbf{P} is the projection matrix.\n\n\n\n\n\n","category":"method"},{"location":"pca/#MultivariateStats.reconstruct-Union{Tuple{T}, Tuple{PCA, AbstractVecOrMat{T}}} where T<:Real","page":"Principal Component Analysis","title":"MultivariateStats.reconstruct","text":"reconstruct(M::PCA, y::AbstractVecOrMat{<:Real})\n\nGiven a PCA model M, returns a (approximately) reconstructed observations from principal components space, as\n\ntildemathbfx = mathbfP mathbfy + boldsymbolmu\n\nHere, y can be either a vector of length p or a matrix where each column gives the principal components for an observation, and mathbfP is the projection matrix.\n\n\n\n\n\n","category":"method"},{"location":"pca/#Base.size-Tuple{PCA}","page":"Principal Component Analysis","title":"Base.size","text":"size(M)\n\nReturns a tuple with the dimensions of input (the dimension of the observation space) and output (the dimension of the principal subspace).\n\n\n\n\n\n","category":"method"},{"location":"pca/#Statistics.mean-Tuple{PCA}","page":"Principal Component Analysis","title":"Statistics.mean","text":"mean(M::PCA)\n\nReturns the mean vector (of length d).\n\n\n\n\n\n","category":"method"},{"location":"pca/#MultivariateStats.projection-Tuple{PCA}","page":"Principal Component Analysis","title":"MultivariateStats.projection","text":"projection(M::PCA)\n\nReturns the projection matrix (of size (d, p)). Each column of the projection matrix corresponds to a principal component. The principal components are arranged in descending order of the corresponding variances.\n\n\n\n\n\n","category":"method"},{"location":"pca/#Statistics.var-Tuple{PCA}","page":"Principal Component Analysis","title":"Statistics.var","text":"var(M::PCA)\n\nReturns the total observation variance, which is equal to tprincipalvar(M) + tresidualvar(M).\n\n\n\n\n\n","category":"method"},{"location":"pca/#MultivariateStats.principalvars-Tuple{PCA}","page":"Principal Component Analysis","title":"MultivariateStats.principalvars","text":"principalvars(M::PCA)\n\nReturns the variances of principal components.\n\n\n\n\n\n","category":"method"},{"location":"pca/#MultivariateStats.tprincipalvar-Tuple{PCA}","page":"Principal Component Analysis","title":"MultivariateStats.tprincipalvar","text":"tprincipalvar(M::PCA)\n\nReturns the total variance of principal components, which is equal to sum(principalvars(M)).\n\n\n\n\n\n","category":"method"},{"location":"pca/#MultivariateStats.tresidualvar-Tuple{PCA}","page":"Principal Component Analysis","title":"MultivariateStats.tresidualvar","text":"tresidualvar(M::PCA)\n\nReturns the total residual variance.\n\n\n\n\n\n","category":"method"},{"location":"pca/#StatsAPI.r2-Tuple{PCA}","page":"Principal Component Analysis","title":"StatsAPI.r2","text":"r2(M::PCA)\nprincipalratio(M::PCA)\n\nReturns the ratio of variance preserved in the principal subspace, which is equal to tprincipalvar(M) / var(M).\n\n\n\n\n\n","category":"method"},{"location":"pca/#MultivariateStats.loadings-Tuple{PCA}","page":"Principal Component Analysis","title":"MultivariateStats.loadings","text":"loadings(M::PCA)\n\nReturns model loadings, i.e. the weights for each original variable when calculating the principal component.\n\n\n\n\n\n","category":"method"},{"location":"pca/#LinearAlgebra.eigvals-Tuple{PCA}","page":"Principal Component Analysis","title":"LinearAlgebra.eigvals","text":"eigvals(M::PCA)\n\nGet the eigenvalues of the PCA model M.\n\n\n\n\n\n","category":"method"},{"location":"pca/#LinearAlgebra.eigvecs-Tuple{PCA}","page":"Principal Component Analysis","title":"LinearAlgebra.eigvecs","text":"eigvecs(M::PCA)\n\nGet the eigenvalues of the PCA model M.\n\n\n\n\n\n","category":"method"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"Auxiliary functions:","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"pcacov\npcasvd","category":"page"},{"location":"pca/#MultivariateStats.pcacov","page":"Principal Component Analysis","title":"MultivariateStats.pcacov","text":"pcacov(C, mean; ...)\n\nCompute and return a PCA model based on eigenvalue decomposition of a given covariance matrix C.\n\nParameters:\n\nC: The covariance matrix of the samples.\nmean: The mean vector of original samples, which can be a vector of length d, or an empty vector Float64[] indicating a zero mean.\n\nNote: This function accepts two keyword arguments: maxoutdim and pratio.\n\n\n\n\n\n","category":"function"},{"location":"pca/#MultivariateStats.pcasvd","page":"Principal Component Analysis","title":"MultivariateStats.pcasvd","text":"pcasvd(Z, mean, tw; ...)\n\nCompute and return a PCA model based on singular value decomposition of a centralized sample matrix Z.\n\nParameters:\n\nZ: a matrix of centralized samples.\nmean: The mean vector of the original samples, which can be a vector of length d, or an empty vector Float64[] indicating a zero mean.\nn: a number of samples.\n\nNote: This function accepts two keyword arguments: maxoutdim and pratio.\n\n\n\n\n\n","category":"function"},{"location":"pca/#Kernel-Principal-Component-Analysis","page":"Principal Component Analysis","title":"Kernel Principal Component Analysis","text":"","category":"section"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"Kernel Principal Component Analysis (kernel PCA) is an extension of principal component analysis (PCA) using techniques of kernel methods. Using a kernel, the originally linear operations of PCA are performed in a reproducing kernel Hilbert space.","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"This package defines a KernelPCA type to represent a kernel PCA model.","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"KernelPCA","category":"page"},{"location":"pca/#MultivariateStats.KernelPCA","page":"Principal Component Analysis","title":"MultivariateStats.KernelPCA","text":"This type contains kernel PCA model parameters.\n\n\n\n\n\n","category":"type"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"The package provides a set of methods to access the properties of the kernel PCA model. Let M be an instance of KernelPCA, d be the dimension of observations, and p be the output dimension (i.e the dimension of the principal subspace).","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"fit(::Type{KernelPCA}, ::AbstractMatrix{T}; kwargs...) where {T<:Real}\npredict(::KernelPCA)\npredict(::KernelPCA, ::AbstractVecOrMat{T}) where {T<:Real}\nreconstruct(::KernelPCA, ::AbstractVecOrMat{T}) where {T<:Real}\nsize(::KernelPCA)\nprojection(::KernelPCA)\neigvals(::KernelPCA)\neigvecs(::KernelPCA)","category":"page"},{"location":"pca/#StatsAPI.fit-Union{Tuple{T}, Tuple{Type{KernelPCA}, AbstractMatrix{T}}} where T<:Real","page":"Principal Component Analysis","title":"StatsAPI.fit","text":"fit(KernelPCA, X; ...)\n\nPerform kernel PCA over the data given in a matrix X. Each column of X is an observation.\n\nThis method returns an instance of KernelPCA.\n\nKeyword arguments:\n\nLet (d, n) = size(X) be respectively the input dimension and the number of observations:\n\nkernel: The kernel function. This functions accepts two vector arguments x and y,\n\nand returns a scalar value (default: (x,y)->x'y). If set to nothing, the matrix X is the pre-computed symmetric kernel (Gram) matrix.\n\nsolver: The choice of solver:\n:eig: uses LinearAlgebra.eigen (default)\n:eigs: uses Arpack.eigs (always used for sparse data)\nmaxoutdim: Maximum output dimension (default min(d, n))\ninverse: Whether to perform calculation for inverse transform for non-precomputed kernels (default false)\nβ: Hyperparameter of the ridge regression that learns the inverse transform (default 1 when inverse is true).\ntol: Convergence tolerance for eigs solver (default 0.0)\nmaxiter: Maximum number of iterations for eigs solver (default 300)\n\n\n\n\n\n","category":"method"},{"location":"pca/#StatsAPI.predict-Tuple{KernelPCA}","page":"Principal Component Analysis","title":"StatsAPI.predict","text":"predict(M::KernelPCA)\n\nTransform the data fitted to the model M to a kernel space of the model.\n\n\n\n\n\n","category":"method"},{"location":"pca/#StatsAPI.predict-Union{Tuple{T}, Tuple{KernelPCA, AbstractVecOrMat{T}}} where T<:Real","page":"Principal Component Analysis","title":"StatsAPI.predict","text":"predict(M::KernelPCA, x)\n\nTransform out-of-sample transformation of x into a kernel space of the model M.\n\nHere, x can be either a vector of length d or a matrix where each column is an observation.\n\n\n\n\n\n","category":"method"},{"location":"pca/#MultivariateStats.reconstruct-Union{Tuple{T}, Tuple{KernelPCA, AbstractVecOrMat{T}}} where T<:Real","page":"Principal Component Analysis","title":"MultivariateStats.reconstruct","text":"reconstruct(M::KernelPCA, y)\n\nApproximately reconstruct observations, given in y, to the original space using the kernel PCA model M.\n\nHere, y can be either a vector of length p or a matrix where each column gives the principal components for an observation.\n\n\n\n\n\n","category":"method"},{"location":"pca/#Base.size-Tuple{KernelPCA}","page":"Principal Component Analysis","title":"Base.size","text":"size(M::KernelPCA)\n\nReturns a tuple with the input dimension d, i.e the dimension of the observation space, and the output dimension p, i.e the dimension of the principal subspace.\n\n\n\n\n\n","category":"method"},{"location":"pca/#MultivariateStats.projection-Tuple{KernelPCA}","page":"Principal Component Analysis","title":"MultivariateStats.projection","text":"projection(M::KernelPCA)\n\nReturn the projection matrix (of size n times p). Each column of the projection matrix corresponds to an eigenvector, and n is a number of observations.\n\nThe principal components are arranged in descending order of the corresponding eigenvalues.\n\n\n\n\n\n","category":"method"},{"location":"pca/#LinearAlgebra.eigvals-Tuple{KernelPCA}","page":"Principal Component Analysis","title":"LinearAlgebra.eigvals","text":"eigvals(M::KernelPCA)\n\nReturn eigenvalues of the kernel matrix of the model M.\n\n\n\n\n\n","category":"method"},{"location":"pca/#LinearAlgebra.eigvecs-Tuple{KernelPCA}","page":"Principal Component Analysis","title":"LinearAlgebra.eigvecs","text":"eigvecs(M::KernelPCA)\n\nReturn eigenvectors of the kernel matrix of the model M.\n\n\n\n\n\n","category":"method"},{"location":"pca/#Kernels","page":"Principal Component Analysis","title":"Kernels","text":"","category":"section"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"List of the commonly used kernels:","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"function description\n(x,y)->x'y Linear\n(x,y)->(x'y+c)^d Polynomial\n(x,y)->exp(-γ*norm(x-y)^2.0) Radial basis function (RBF)","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"This package has a separate interface for adjusting kernel matrices.","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"MultivariateStats.KernelCenter\nfit(::Type{MultivariateStats.KernelCenter}, ::AbstractMatrix{<:Real})\nMultivariateStats.transform!(::MultivariateStats.KernelCenter, ::AbstractMatrix{<:Real})","category":"page"},{"location":"pca/#MultivariateStats.KernelCenter","page":"Principal Component Analysis","title":"MultivariateStats.KernelCenter","text":"Center a kernel matrix\n\n\n\n\n\n","category":"type"},{"location":"pca/#StatsAPI.fit-Tuple{Type{MultivariateStats.KernelCenter}, AbstractMatrix{<:Real}}","page":"Principal Component Analysis","title":"StatsAPI.fit","text":"Fit KernelCenter object\n\n\n\n\n\n","category":"method"},{"location":"pca/#MultivariateStats.transform!-Tuple{MultivariateStats.KernelCenter, AbstractMatrix{<:Real}}","page":"Principal Component Analysis","title":"MultivariateStats.transform!","text":"Center kernel matrix.\n\n\n\n\n\n","category":"method"},{"location":"pca/#Probabilistic-Principal-Component-Analysis","page":"Principal Component Analysis","title":"Probabilistic Principal Component Analysis","text":"","category":"section"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"Probabilistic Principal Component Analysis (PPCA) represents a constrained form of the Gaussian distribution in which the number of free parameters can be restricted while still allowing the model to capture the dominant correlations in a data set. It is expressed as the maximum likelihood solution of a probabilistic latent variable model[1].","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"This package defines a PPCA type to represent a probabilistic PCA model, and provides a set of methods to access the properties.","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"PPCA","category":"page"},{"location":"pca/#MultivariateStats.PPCA","page":"Principal Component Analysis","title":"MultivariateStats.PPCA","text":"This type contains probabilistic PCA model parameters.\n\n\n\n\n\n","category":"type"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"Let M be an instance of PPCA, d be the dimension of observations, and p be the output dimension (i.e the dimension of the principal subspace).","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"fit\nsize(::PPCA)\nmean(::PPCA)\nvar(::PPCA)\ncov(::PPCA)\nprojection(::PPCA)\nloadings(::PPCA)","category":"page"},{"location":"pca/#StatsAPI.fit","page":"Principal Component Analysis","title":"StatsAPI.fit","text":"fit(Whitening, X::AbstractMatrix{T}; kwargs...)\n\nEstimate a whitening transform from the data given in X.\n\nThis function returns an instance of Whitening\n\nKeyword Arguments:\n\nregcoef: The regularization coefficient. The covariance will be regularized as follows when regcoef is positive C + (eigmax(C) * regcoef) * eye(d). Default values is zero(T).\ndims: if 1 the transformation calculated from the row samples. fit standardization parameters in column-wise fashion; if 2 the transformation calculated from the column samples. The default is nothing, which is equivalent to dims=2 with a deprecation warning.\nmean: The mean vector, which can be either of:\n0: the input data has already been centralized\nnothing: this function will compute the mean (default)\na pre-computed mean vector\n\nNote: This function internally relies on cov_whitening to derive the transformation W.\n\n\n\n\n\nfit(PCA, X; ...)\n\nPerform PCA over the data given in a matrix X. Each column of X is an observation.\n\nKeyword arguments\n\nmethod: The choice of methods:\n:auto: use :cov when d < n or :svd otherwise (default).\n:cov: based on covariance matrix decomposition.\n:svd: based on SVD of the input data.\nmaxoutdim: The output dimension, i.e. dimension of the transformed space (min(d, nc-1))\npratio: The ratio of variances preserved in the principal subspace (0.99)\nmean: The mean vector, which can be either of\n0: the input data has already been centralized\nnothing: this function will compute the mean (default)\na pre-computed mean vector\n\nNotes:\n\nThe output dimension p depends on both maxoutdim and pratio, as follows. Suppose the first k principal components preserve at least pratio of the total variance, while the first k-1 preserves less than pratio, then the actual output dimension will be min(k maxoutdim).\nThis function calls pcacov or pcasvd internally, depending on the choice of method.\n\n\n\n\n\nfit(PPCA, X; ...)\n\nPerform probabilistic PCA over the data given in a matrix X. Each column of X is an observation. This method returns an instance of PPCA.\n\nKeyword arguments:\n\nLet (d, n) = size(X) be respectively the input dimension and the number of observations:\n\nmethod: The choice of methods:\n:ml: use maximum likelihood version of probabilistic PCA (default)\n:em: use EM version of probabilistic PCA\n:bayes: use Bayesian PCA\nmaxoutdim: Maximum output dimension (default d-1)\nmean: The mean vector, which can be either of:\n0: the input data has already been centralized\nnothing: this function will compute the mean (default)\na pre-computed mean vector\ntol: Convergence tolerance (default 1.0e-6)\nmaxiter: Maximum number of iterations (default 1000)\n\nNotes: This function calls ppcaml, ppcaem or bayespca internally, depending on the choice of method.\n\n\n\n\n\nFit KernelCenter object\n\n\n\n\n\nfit(KernelPCA, X; ...)\n\nPerform kernel PCA over the data given in a matrix X. Each column of X is an observation.\n\nThis method returns an instance of KernelPCA.\n\nKeyword arguments:\n\nLet (d, n) = size(X) be respectively the input dimension and the number of observations:\n\nkernel: The kernel function. This functions accepts two vector arguments x and y,\n\nand returns a scalar value (default: (x,y)->x'y). If set to nothing, the matrix X is the pre-computed symmetric kernel (Gram) matrix.\n\nsolver: The choice of solver:\n:eig: uses LinearAlgebra.eigen (default)\n:eigs: uses Arpack.eigs (always used for sparse data)\nmaxoutdim: Maximum output dimension (default min(d, n))\ninverse: Whether to perform calculation for inverse transform for non-precomputed kernels (default false)\nβ: Hyperparameter of the ridge regression that learns the inverse transform (default 1 when inverse is true).\ntol: Convergence tolerance for eigs solver (default 0.0)\nmaxiter: Maximum number of iterations for eigs solver (default 300)\n\n\n\n\n\nfit(CCA, X, Y; ...)\n\nPerform CCA over the data given in matrices X and Y. Each column of X and Y is an observation.\n\nX and Y should have the same number of columns (denoted by n below).\n\nThis method returns an instance of CCA.\n\nKeyword arguments:\n\nmethod: The choice of methods:\n:cov: based on covariance matrices\n:svd: based on SVD of the input data (default)\noutdim: The output dimension, i.e dimension of the common space (default: min(dx, dy, n))\nmean: The mean vector, which can be either of:\n0: the input data has already been centralized\nnothing: this function will compute the mean (default)\na pre-computed mean vector\n\nNotes: This function calls ccacov or ccasvd internally, depending on the choice of method.\n\n\n\n\n\nfit(MDS, X; kwargs...)\n\nCompute an embedding of X points by classical multidimensional scaling (MDS). There are two calling options, specified via the required keyword argument distances:\n\nmds = fit(MDS, X; distances=false, maxoutdim=size(X,1)-1)\n\nwhere X is the data matrix. Distances between pairs of columns of X are computed using the Euclidean norm. This is equivalent to performing PCA on X.\n\nmds = fit(MDS, D; distances=true, maxoutdim=size(D,1)-1)\n\nwhere D is a symmetric matrix D of distances between points.\n\n\n\n\n\nfit(MetricMDS, X; kwargs...)\n\nCompute an embedding of X points by (non)metric multidimensional scaling (MDS).\n\nKeyword arguments:\n\nLet (d, n) = size(X) be respectively the input dimension and the number of observations:\n\ndistances: The choice of input (required):\nfalse: use X to calculate dissimilarity matrix using Euclidean distance\ntrue: use X input as precomputed dissimilarity symmetric matrix (distances)\nmaxoutdim: Maximum output dimension (default d-1)\nmetric : a function for calculation of disparity values\nnothing: use dissimilarity values as the disparities to perform the metric MDS (default)\nisotonic: converts dissimilarity values to ordinal disparities to perform non-metric MDS\nany two parameter disparity transformation function, where the first parameter is a vector of proximities (i.e. dissimilarities) and the second parameter is a vector of distances, e.g. (p,d)->b*p for some b is a transformation function for ratio MDS.\ntol: Convergence tolerance (default 1.0e-3)\nmaxiter: Maximum number of iterations (default 300)\ninitial: an initial reduced space point configuration\nnothing: then an initial configuration is randomly generated (default)\npre-defined matrix\nweights: a weight matrix\nnothing: then weights are set to one, w_ij = 1 (default)\npre-defined matrix\n\nNote: if the algorithm is unable to converge then ConvergenceException is thrown.\n\n\n\n\n\nfit(LinearDiscriminant, Xp, Xn; covestimator = SimpleCovariance())\n\nPerforms LDA given both positive and negative samples. The function accepts following parameters:\n\nParameters\n\nXp: The sample matrix of the positive class.\nXn: The sample matrix of the negative class.\n\nKeyword arguments:\n\ncovestimator: Custom covariance estimator for between-class covariance. The covariance matrix will be calculated as cov(covestimator_between, #=data=#; dims=2, mean=zeros(#=...=#). Custom covariance estimators, available in other packages, may result in more robust discriminants for data with more features than observations.\n\n\n\n\n\nfit(MulticlassLDA, X, y; ...)\n\nPerform multi-class LDA over a given data set X with corresponding labels y with nc number of classes.\n\nThis function returns the resultant multi-class LDA model as an instance of MulticlassLDA.\n\nParameters\n\nX: the matrix of input samples, of size (d, n). Each column in X is an observation.\ny: the vector of class labels, of length n.\n\nKeyword arguments\n\nmethod: The choice of methods:\n:gevd: based on generalized eigenvalue decomposition (default).\n:whiten: first derive a whitening transform from Sw and then solve the problem based on eigenvalue\ndecomposition of the whiten Sb.\noutdim: The output dimension, i.e. dimension of the transformed space min(d, nc-1)\nregcoef: The regularization coefficient (default: 1.0e-6). A positive value regcoef * eigmax(Sw) is added to the diagonal of Sw to improve numerical stability.\ncovestimator_between: Custom covariance estimator for between-class covariance (default: SimpleCovariance()). The covariance matrix will be calculated as cov(covestimator_between, #=data=#; dims=2, mean=zeros(#=...=#)). Custom covariance estimators, available in other packages, may result in more robust discriminants for data with more features than observations.\ncovestimator_within: Custom covariance estimator for within-class covariance (default: SimpleCovariance()). The covariance matrix will be calculated as cov(covestimator_within, #=data=#; dims=2, mean=zeros(nc)). Custom covariance estimators, available in other packages, may result in more robust discriminants for data with more features than observations.\n\nNotes:\n\nThe resultant projection matrix P satisfies:\n\nmathbfP^T (mathbfS_w + kappa mathbfI) mathbfP = mathbfI\n\nHere, kappa equals regcoef * eigmax(Sw). The columns of P are arranged in descending order of the corresponding generalized eigenvalues.\n\nNote that MulticlassLDA does not currently support the normalized version using mathbfS_w^* and mathbfS_b^* (see SubspaceLDA).\n\n\n\n\n\nfit(SubspaceLDA, X, y; normalize=true)\n\nFit an subspace projection of LDA model over a given data set X with corresponding labels y using the equivalent of mathbfS_w^* and mathbfS_b^*`.\n\nNote: Subspace LDA also supports the normalized version of LDA via the normalize keyword.\n\n\n\n\n\nfit(ICA, X, k; ...)\n\nPerform ICA over the data set given in X.\n\nParameters: -X: The data matrix, of size (m n). Each row corresponds to a mixed signal, while each column corresponds to an observation (e.g all signal value at a particular time step). -k: The number of independent components to recover.\n\nKeyword Arguments:\n\nalg: The choice of algorithm (default :fastica)\nfun: The approx neg-entropy functor (default Tanh)\ndo_whiten: Whether to perform pre-whitening (default true)\nmaxiter: Maximum number of iterations (default 100)\ntol: Tolerable change of W at convergence (default 1.0e-6)\nmean: The mean vector, which can be either of:\n0: the input data has already been centralized\nnothing: this function will compute the mean (default)\na pre-computed mean vector\nwinit: Initial guess of W, which should be either of:\nempty matrix: the function will perform random initialization (default)\na matrix of size (k k) (when do_whiten)\na matrix of size (m k) (when !do_whiten)\n\nReturns the resultant ICA model, an instance of type ICA.\n\nNote: If do_whiten is true, the return W satisfies mathbfW^T mathbfC mathbfW = mathbfI, otherwise W is orthonormal, i.e mathbfW^T mathbfW = mathbfI.\n\n\n\n\n\nfit(FactorAnalysis, X; ...)\n\nPerform factor analysis over the data given in a matrix X. Each column of X is an observation. This method returns an instance of FactorAnalysis.\n\nKeyword arguments:\n\nLet (d, n) = size(X) be respectively the input dimension and the number of observations:\n\nmethod: The choice of methods:\n:em: use EM version of factor analysis\n:cm: use CM version of factor analysis (default)\nmaxoutdim: Maximum output dimension (default d-1)\nmean: The mean vector, which can be either of:\n0: the input data has already been centralized\nnothing: this function will compute the mean (default)\na pre-computed mean vector\ntol: Convergence tolerance (default 1.0e-6)\nmaxiter: Maximum number of iterations (default 1000)\nη: Variance low bound (default 1.0e-6)\n\nNotes: This function calls facm or faem internally, depending on the choice of method.\n\n\n\n\n\n","category":"function"},{"location":"pca/#Base.size-Tuple{PPCA}","page":"Principal Component Analysis","title":"Base.size","text":"size(M::PPCA)\n\nReturns a tuple with values of the input dimension d, i.e the dimension of the observation space, and the output dimension p, i.e the dimension of the principal subspace.\n\n\n\n\n\n","category":"method"},{"location":"pca/#Statistics.mean-Tuple{PPCA}","page":"Principal Component Analysis","title":"Statistics.mean","text":"mean(M::PPCA)\n\nGet the mean vector (of length d).\n\n\n\n\n\n","category":"method"},{"location":"pca/#Statistics.var-Tuple{PPCA}","page":"Principal Component Analysis","title":"Statistics.var","text":"var(M::PPCA)\n\nReturns the total residual variance of the model M.\n\n\n\n\n\n","category":"method"},{"location":"pca/#Statistics.cov-Tuple{PPCA}","page":"Principal Component Analysis","title":"Statistics.cov","text":"cov(M::PPCA)\n\nReturns the covariance of the model M.\n\n\n\n\n\n","category":"method"},{"location":"pca/#MultivariateStats.projection-Tuple{PPCA}","page":"Principal Component Analysis","title":"MultivariateStats.projection","text":"projection(M::PPCA)\n\nReturns the projection matrix (of size (d p)). Each column of the projection matrix corresponds to a principal component.\n\nThe principal components are arranged in descending order of the corresponding variances.\n\n\n\n\n\n","category":"method"},{"location":"pca/#MultivariateStats.loadings-Tuple{PPCA}","page":"Principal Component Analysis","title":"MultivariateStats.loadings","text":"loadings(M::PPCA)\n\nReturns the factor loadings matrix (of size (d p)) of the model M.\n\n\n\n\n\n","category":"method"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"Given a probabilistic PCA model M, one can use it to transform observations into latent variables, as","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"\\mathbf{z} = (\\mathbf{W}^T \\mathbf{W} + \\sigma^2 \\mathbf{I}) \\mathbf{W}^T (\\mathbf{x} - \\boldsymbol{\\mu})","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"or use it to reconstruct (approximately) the observations from latent variables, as","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"\\tilde{\\mathbf{x}} = \\mathbf{W} \\mathbb{E}[\\mathbf{z}] + \\boldsymbol{\\mu}","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"Here, mathbfW is the factor loadings or weight matrix.","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"predict(::PPCA, ::AbstractVecOrMat{T}) where {T<:Real}\nreconstruct(::PPCA, ::AbstractVecOrMat{T}) where {T<:Real}","category":"page"},{"location":"pca/#StatsAPI.predict-Union{Tuple{T}, Tuple{PPCA, AbstractVecOrMat{T}}} where T<:Real","page":"Principal Component Analysis","title":"StatsAPI.predict","text":"predict(M::PPCA, x)\n\nTransform observations x into latent variables. Here, x can be either a vector of length d or a matrix where each column is an observation.\n\n\n\n\n\n","category":"method"},{"location":"pca/#MultivariateStats.reconstruct-Union{Tuple{T}, Tuple{PPCA, AbstractVecOrMat{T}}} where T<:Real","page":"Principal Component Analysis","title":"MultivariateStats.reconstruct","text":"reconstruct(M::PPCA, z)\n\nApproximately reconstruct observations from the latent variable given in z. Here, z can be either a vector of length p or a matrix where each column gives the latent variables for an observation.\n\n\n\n\n\n","category":"method"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"Auxiliary functions:","category":"page"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"ppcaml\nppcaem\nbayespca","category":"page"},{"location":"pca/#MultivariateStats.ppcaml","page":"Principal Component Analysis","title":"MultivariateStats.ppcaml","text":"ppcaml(Z, mean; ...)\n\nCompute probabilistic PCA using on maximum likelihood formulation for a centralized sample matrix Z.\n\nParameters:\n\nZ: a centralized samples matrix\nmean: The mean vector of the original samples, which can be a vector of\n\nlength d, or an empty vector indicating a zero mean.\n\nReturns the resultant PPCA model.\n\nNote: This function accepts two keyword arguments: maxoutdim and tol.\n\n\n\n\n\n","category":"function"},{"location":"pca/#MultivariateStats.ppcaem","page":"Principal Component Analysis","title":"MultivariateStats.ppcaem","text":"ppcaem(S, mean, n; ...)\n\nCompute probabilistic PCA based on expectation-maximization algorithm for a given sample covariance matrix S.\n\nParameters:\n\nS: The sample covariance matrix.\nmean: The mean vector of original samples, which can be a vector of length d,\n\nor an empty vector indicating a zero mean.\n\nn: The number of observations.\n\nReturns the resultant PPCA model.\n\nNote: This function accepts three keyword arguments: maxoutdim, tol, and maxiter.\n\n\n\n\n\n","category":"function"},{"location":"pca/#MultivariateStats.bayespca","page":"Principal Component Analysis","title":"MultivariateStats.bayespca","text":"bayespca(S, mean, n; ...)\n\nCompute probabilistic PCA using a Bayesian algorithm for a given sample covariance matrix S.\n\nParameters:\n\nS: The sample covariance matrix.\nmean: The mean vector of original samples, which can be a vector of length d,\n\nor an empty vector indicating a zero mean.\n\nn: The number of observations.\n\nReturns the resultant PPCA model.\n\nNotes:\n\nThis function accepts three keyword arguments: maxoutdim, tol, and maxiter.\nFunction uses the maxoutdim parameter as an upper boundary when it automatically\n\ndetermines the latent space dimensionality.\n\n\n\n\n\n","category":"function"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"","category":"page"},{"location":"pca/#References","page":"Principal Component Analysis","title":"References","text":"","category":"section"},{"location":"pca/","page":"Principal Component Analysis","title":"Principal Component Analysis","text":"[1]: Bishop, C. M. Pattern Recognition and Machine Learning, 2006.","category":"page"},{"location":"fa/#Factor-Analysis","page":"Factor Analysis","title":"Factor Analysis","text":"","category":"section"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"Factor Analysis (FA) is a linear-Gaussian latent variable model that is closely related to probabilistic PCA. In contrast to the probabilistic PCA model, the covariance of conditional distribution of the observed variable given the latent variable is diagonal rather than isotropic[1].","category":"page"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"This package defines a FactorAnalysis type to represent a factor analysis model, and provides a set of methods to access the properties.","category":"page"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"FactorAnalysis","category":"page"},{"location":"fa/#MultivariateStats.FactorAnalysis","page":"Factor Analysis","title":"MultivariateStats.FactorAnalysis","text":"This type contains factor analysis model parameters.\n\n\n\n\n\n","category":"type"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"The package provides a set of methods to access the properties of the factor analysis model. Let M be an instance of FactorAnalysis, d be the dimension of observations, and p be the output dimension (i.e the dimension of the principal subspace).","category":"page"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"fit(::Type{FactorAnalysis}, ::AbstractMatrix{T}) where {T<:Real}\nsize(::FactorAnalysis)\nmean(::FactorAnalysis)\nvar(::FactorAnalysis)\ncov(::FactorAnalysis)\nprojection(::FactorAnalysis)\nloadings(::FactorAnalysis)","category":"page"},{"location":"fa/#StatsAPI.fit-Union{Tuple{T}, Tuple{Type{FactorAnalysis}, AbstractMatrix{T}}} where T<:Real","page":"Factor Analysis","title":"StatsAPI.fit","text":"fit(FactorAnalysis, X; ...)\n\nPerform factor analysis over the data given in a matrix X. Each column of X is an observation. This method returns an instance of FactorAnalysis.\n\nKeyword arguments:\n\nLet (d, n) = size(X) be respectively the input dimension and the number of observations:\n\nmethod: The choice of methods:\n:em: use EM version of factor analysis\n:cm: use CM version of factor analysis (default)\nmaxoutdim: Maximum output dimension (default d-1)\nmean: The mean vector, which can be either of:\n0: the input data has already been centralized\nnothing: this function will compute the mean (default)\na pre-computed mean vector\ntol: Convergence tolerance (default 1.0e-6)\nmaxiter: Maximum number of iterations (default 1000)\nη: Variance low bound (default 1.0e-6)\n\nNotes: This function calls facm or faem internally, depending on the choice of method.\n\n\n\n\n\n","category":"method"},{"location":"fa/#Base.size-Tuple{FactorAnalysis}","page":"Factor Analysis","title":"Base.size","text":"size(M::PPCA)\n\nReturns a tuple with values of the input dimension d, i.e the dimension of the observation space, and the output dimension p, i.e the dimension of the principal subspace.\n\n\n\n\n\n","category":"method"},{"location":"fa/#Statistics.mean-Tuple{FactorAnalysis}","page":"Factor Analysis","title":"Statistics.mean","text":"mean(M::PPCA)\n\nGet the mean vector (of length d).\n\n\n\n\n\n","category":"method"},{"location":"fa/#Statistics.var-Tuple{FactorAnalysis}","page":"Factor Analysis","title":"Statistics.var","text":"var(M::FactorAnalysis)\n\nReturns the variance of the model M.\n\n\n\n\n\n","category":"method"},{"location":"fa/#Statistics.cov-Tuple{FactorAnalysis}","page":"Factor Analysis","title":"Statistics.cov","text":"cov(M::FactorAnalysis)\n\nReturns the covariance of the model M.\n\n\n\n\n\n","category":"method"},{"location":"fa/#MultivariateStats.projection-Tuple{FactorAnalysis}","page":"Factor Analysis","title":"MultivariateStats.projection","text":"projection(M::FactorAnalysis)\n\nRecovers principle components from the weight matrix of the model M.\n\n\n\n\n\n","category":"method"},{"location":"fa/#MultivariateStats.loadings-Tuple{FactorAnalysis}","page":"Factor Analysis","title":"MultivariateStats.loadings","text":"loadings(M::FactorAnalysis)\n\nReturns the factor loadings matrix of the model M.\n\n\n\n\n\n","category":"method"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"Given a factor analysis model M, one can use it to transform observations into latent variables, as","category":"page"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"\\mathbf{z} = \\mathbf{W}^T \\mathbf{\\Sigma}^{-1} (\\mathbf{x} - \\boldsymbol{\\mu})","category":"page"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"or use it to reconstruct (approximately) the observations from latent variables, as","category":"page"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"\\tilde{\\mathbf{x}} = \\mathbf{\\Sigma} \\mathbf{W} (\\mathbf{W}^T \\mathbf{W})^{-1} \\mathbf{z} + \\boldsymbol{\\mu}","category":"page"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"Here, mathbfW is the factor loadings or weight matrix, mathbfSigma = mathbfPsi + mathbfW^T mathbfW is the covariance matrix.","category":"page"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"The package provides methods to do so:","category":"page"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"predict(::FactorAnalysis, ::AbstractVecOrMat{T}) where {T<:Real}\nreconstruct(::FactorAnalysis, ::AbstractVecOrMat{T}) where {T<:Real}","category":"page"},{"location":"fa/#StatsAPI.predict-Union{Tuple{T}, Tuple{FactorAnalysis, AbstractVecOrMat{T}}} where T<:Real","page":"Factor Analysis","title":"StatsAPI.predict","text":"predict(M::FactorAnalysis, x)\n\nTransform observations x into latent variables. Here, x can be either a vector of length d or a matrix where each column is an observation.\n\n\n\n\n\n","category":"method"},{"location":"fa/#MultivariateStats.reconstruct-Union{Tuple{T}, Tuple{FactorAnalysis, AbstractVecOrMat{T}}} where T<:Real","page":"Factor Analysis","title":"MultivariateStats.reconstruct","text":"reconstruct(M::FactorAnalysis, z)\n\nApproximately reconstruct observations from the latent variable given in z. Here, z can be either a vector of length p or a matrix where each column gives the latent variables for an observation.\n\n\n\n\n\n","category":"method"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"Auxiliary functions:","category":"page"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"faem\nfacm","category":"page"},{"location":"fa/#MultivariateStats.faem","page":"Factor Analysis","title":"MultivariateStats.faem","text":"faem(S, mean, n; ...)\n\nPerforms factor analysis using an expectation-maximization algorithm for a given sample covariance matrix S[2].\n\nParameters\n\nS: The sample covariance matrix.\nmean: The mean vector of original samples, which can be a vector of length d,\n\nor an empty vector indicating a zero mean.\n\nn: The number of observations.\n\nReturns the resultant FactorAnalysis model.\n\nNote: This function accepts two keyword arguments: maxoutdim,tol, and maxiter.\n\n\n\n\n\n","category":"function"},{"location":"fa/#MultivariateStats.facm","page":"Factor Analysis","title":"MultivariateStats.facm","text":"facm(S, mean, n; ...)\n\nPerforms factor analysis using a fast conditional maximization algorithm for a given sample covariance matrix S[3].\n\nParameters\n\nS: The sample covariance matrix.\nmean: The mean vector of original samples, which can be a vector of length d,\n\nor an empty vector indicating a zero mean.\n\nn: The number of observations.\n\nReturns the resultant FactorAnalysis model.\n\nNote: This function accepts two keyword arguments: maxoutdim,tol, maxiter, and η.\n\n\n\n\n\n","category":"function"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"","category":"page"},{"location":"fa/#References","page":"Factor Analysis","title":"References","text":"","category":"section"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"[1]: Bishop, C. M. Pattern Recognition and Machine Learning, 2006.","category":"page"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"[2]: Rubin, Donald B., and Dorothy T. Thayer. EM algorithms for ML factor analysis. Psychometrika 47.1, 69-76, 1982.","category":"page"},{"location":"fa/","page":"Factor Analysis","title":"Factor Analysis","text":"[3]: Zhao, J-H., Philip LH Yu, and Qibao Jiang. ML estimation for factor analysis: EM or non-EM?. Statistics and computing 18.2, 109-123, 2008.","category":"page"},{"location":"api/#API-Reference","page":"Development","title":"API Reference","text":"","category":"section"},{"location":"api/#Current","page":"Development","title":"Current","text":"","category":"section"},{"location":"api/","page":"Development","title":"Development","text":"Table of the package models and corresponding function names used by these models.","category":"page"},{"location":"api/","page":"Development","title":"Development","text":"Function \\ Model CCA WHT ICA LDA FA PPCA PCA KPCA MDS\nfit x x x x x x x x x\ntransform x x x x x x x x x\npredict x \nindim x x x x x x x x\noutdim x x x x x x x x x\nmean x x x x x x x ? \nvar x x ? ? ?\ncov x ? \ncor x \nprojection x x x x x x\nreconstruct x x x x \nloadings ? ? x x ? ? ?\neigvals ? ? ? ? x\neigvecs ? ? ? ? ?\nlength \nsize ","category":"page"},{"location":"api/","page":"Development","title":"Development","text":"Note: ? refers to a possible implementation that is missing or called differently.","category":"page"},{"location":"api/#New","page":"Development","title":"New","text":"","category":"section"},{"location":"api/","page":"Development","title":"Development","text":"Function \\ Model WHT CCA LDA MC-LDA SS-LDA ICA FA PPCA PCA KPCA MDS\nfit x x x x x x x x x x x\ntransform x - - - - - x x - - -\npredict + x + + + + + +\nindim - - - - x x - - -\noutdim - - - - - x x - - -\nmean x x x x x x x x \nvar x x x ?\ncov x x \ncor + \nprojection ? x x x x x x x x\nreconstruct x x x x \nloadings x x x +\neigvals + ? ? x x x\neigvecs ? ? x + +\nlength + + + + \nsize + + + + + x + +\n ","category":"page"},{"location":"api/","page":"Development","title":"Development","text":"StatsBase.AbstractDataTransform\nWhitening\nInterface: fit, transform\nNew: length, mean, size\nStatsBase.RegressionModel\nInterface: fit, predict\nLinearDiscriminant\nFunctions: coef, dof, weights, evaluate, length\nMulticlassLDA\nFunctions: size, mean, projection, length\nSubspaceLDA\nFunctions: size, mean, projection, length, eigvals\nCCA\nFunctions: size, mean, projection, predict, cor\nSubtypes:\nAbstractDimensionalityReduction\nInterface: projection, var, reconstruct, loadings\nInterface: projection == weights\nSubtypes:\nLinearDimensionalityReduction\nMethods: ICA, PCA\nNonlinearDimensionalityReduction\nMethods: KPCA, MDS\nFunctions: modelmatrix(X),\nLatentVariableModel or LatentVariableDimensionalityReduction\nMethods: FA, PPCA\nFunctions: cov","category":"page"},{"location":"lda/#Linear-Discriminant-Analysis","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"","category":"section"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Linear Discriminant Analysis (LDA) are statistical analysis methods to find a linear combination of features for separating observations in two classes.","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Note: Please refer to MulticlassLDA for methods that can discriminate between multiple classes.","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Suppose the samples in the positive and negative classes respectively with means: boldsymbolmu_p and boldsymbolmu_n, and covariances mathbfC_p and mathbfC_n. Then based on Fisher's Linear Discriminant Criteria, the optimal projection direction can be expressed as:","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"mathbfw = alpha cdot (mathbfC_p + mathbfC_n)^-1 (boldsymbolmu_p - boldsymbolmu_n)","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Here alpha is an arbitrary non-negative coefficient.","category":"page"},{"location":"lda/#Example","page":"Linear Discriminant Analysis","title":"Example","text":"","category":"section"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"using Plots\ngr(fmt=:svg)","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Let's compare LDA and PCA 2D projection of Iris dataset. Principal Component Analysis identifies the directions that explain the most variance in the data. ","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"using MultivariateStats, RDatasets\n\niris = dataset(\"datasets\", \"iris\")\n\nX = Matrix(iris[1:2:end,1:4])'\nX_labels = Vector(iris[1:2:end,5])\n\npca = fit(PCA, X; maxoutdim=2)\nYpca = predict(pca, X)\nnothing # hide","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"In contrast, Linear Discriminant Analysis attempts to identify the attributes that account for the most variance between classes. Therefore, with LDA, you must use known class labels.","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"lda = fit(MulticlassLDA, X, X_labels; outdim=2)\nYlda = predict(lda, X)\n\np = plot(layout=(1,2), size=(800,300))\n\nfor s in [\"setosa\", \"versicolor\", \"virginica\"]\n\n points = Ypca[:,X_labels.==s]\n scatter!(p[1], points[1,:],points[2,:], label=s, legend=:bottomleft)\n points = Ylda[:,X_labels.==s]\n scatter!(p[2], points[1,:],points[2,:], label=s, legend=:bottomleft)\n\nend\nplot!(p[1], title=\"PCA\")\nplot!(p[2], title=\"LDA\")","category":"page"},{"location":"lda/#Two-class-Linear-Discriminant-Analysis","page":"Linear Discriminant Analysis","title":"Two-class Linear Discriminant Analysis","text":"","category":"section"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"This package uses the LinearDiscriminant type to capture a linear discriminant functional:","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"LinearDiscriminant","category":"page"},{"location":"lda/#MultivariateStats.LinearDiscriminant","page":"Linear Discriminant Analysis","title":"MultivariateStats.LinearDiscriminant","text":"A linear discriminant functional can be written as\n\n f(mathbfx) = mathbfw^T mathbfx + b\n\nHere, w is the coefficient vector, and b is the bias constant.\n\n\n\n\n\n","category":"type"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"This type comes with several methods where f be an instance of LinearDiscriminant.","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"fit(::Type{LinearDiscriminant}, Xp::DenseMatrix{T}, Xn::DenseMatrix{T}; kwargs) where T<:Real\nevaluate(::LinearDiscriminant, ::AbstractVector)\nevaluate(::LinearDiscriminant, ::AbstractMatrix)\npredict(::LinearDiscriminant, ::AbstractVector)\npredict(::LinearDiscriminant, ::AbstractMatrix)\ncoef(::LinearDiscriminant)\ndof(::LinearDiscriminant)\nweights(::LinearDiscriminant)\nlength(::LinearDiscriminant)","category":"page"},{"location":"lda/#StatsAPI.fit-Union{Tuple{T}, Tuple{Type{LinearDiscriminant}, DenseMatrix{T}, DenseMatrix{T}}} where T<:Real","page":"Linear Discriminant Analysis","title":"StatsAPI.fit","text":"fit(LinearDiscriminant, Xp, Xn; covestimator = SimpleCovariance())\n\nPerforms LDA given both positive and negative samples. The function accepts following parameters:\n\nParameters\n\nXp: The sample matrix of the positive class.\nXn: The sample matrix of the negative class.\n\nKeyword arguments:\n\ncovestimator: Custom covariance estimator for between-class covariance. The covariance matrix will be calculated as cov(covestimator_between, #=data=#; dims=2, mean=zeros(#=...=#). Custom covariance estimators, available in other packages, may result in more robust discriminants for data with more features than observations.\n\n\n\n\n\n","category":"method"},{"location":"lda/#MultivariateStats.evaluate-Tuple{LinearDiscriminant, AbstractVector}","page":"Linear Discriminant Analysis","title":"MultivariateStats.evaluate","text":"evaluate(f, x::AbstractVector)\n\nEvaluate the linear discriminant value, i.e wx + b, it returns a real value.\n\n\n\n\n\n","category":"method"},{"location":"lda/#MultivariateStats.evaluate-Tuple{LinearDiscriminant, AbstractMatrix}","page":"Linear Discriminant Analysis","title":"MultivariateStats.evaluate","text":"evaluate(f, X::AbstractMatrix)\n\nEvaluate the linear discriminant value, i.e wx + b, for each sample in columns of X. The function returns a vector of length size(X, 2).\n\n\n\n\n\n","category":"method"},{"location":"lda/#StatsAPI.predict-Tuple{LinearDiscriminant, AbstractVector}","page":"Linear Discriminant Analysis","title":"StatsAPI.predict","text":"predict(f, x::AbstractVector)\n\nMake prediction for the vector x. It returns true iff evaluate(f, x) is positive.\n\n\n\n\n\n","category":"method"},{"location":"lda/#StatsAPI.predict-Tuple{LinearDiscriminant, AbstractMatrix}","page":"Linear Discriminant Analysis","title":"StatsAPI.predict","text":"predict(f, X::AbstractMatrix)\n\nMake predictions for the matrix X.\n\n\n\n\n\n","category":"method"},{"location":"lda/#StatsAPI.coef-Tuple{LinearDiscriminant}","page":"Linear Discriminant Analysis","title":"StatsAPI.coef","text":"coef(f::LinearDiscriminant)\n\nReturn the coefficients of the linear discriminant model.\n\n\n\n\n\n","category":"method"},{"location":"lda/#StatsAPI.dof-Tuple{LinearDiscriminant}","page":"Linear Discriminant Analysis","title":"StatsAPI.dof","text":"dof(f::LinearDiscriminant)\n\nReturn the number of degrees of freedom in the linear discriminant model.\n\n\n\n\n\n","category":"method"},{"location":"lda/#StatsAPI.weights-Tuple{LinearDiscriminant}","page":"Linear Discriminant Analysis","title":"StatsAPI.weights","text":"weights(f::LinearDiscriminant)\n\nReturn the linear discriminant model coefficient vector.\n\n\n\n\n\n","category":"method"},{"location":"lda/#Base.length-Tuple{LinearDiscriminant}","page":"Linear Discriminant Analysis","title":"Base.length","text":"length(f::LinearDiscriminant)\n\nGet the length of the coefficient vector.\n\n\n\n\n\n","category":"method"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Additional functionality:","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"ldacov","category":"page"},{"location":"lda/#MultivariateStats.ldacov","page":"Linear Discriminant Analysis","title":"MultivariateStats.ldacov","text":"ldacov(C, μp, μn)\n\nPerforms LDA given a covariance matrix C and both mean vectors μp & μn. Returns a linear discriminant functional of type LinearDiscriminant.\n\nParameters\n\nC: The pooled covariance matrix (i.e (Cp + Cn)2)\nμp: The mean vector of the positive class.\nμn: The mean vector of the negative class.\n\n\n\n\n\nldacov(Cp, Cn, μp, μn)\n\nPerforms LDA given covariances and mean vectors. Returns a linear discriminant functional of type LinearDiscriminant.\n\nParameters\n\nCp: The covariance matrix of the positive class.\nCn: The covariance matrix of the negative class.\nμp: The mean vector of the positive class.\nμn: The mean vector of the negative class.\n\nNote: The coefficient vector is scaled such that wμp + b = 1 and wμn + b = -1.\n\n\n\n\n\n","category":"function"},{"location":"lda/#Multi-class-Linear-Discriminant-Analysis","page":"Linear Discriminant Analysis","title":"Multi-class Linear Discriminant Analysis","text":"","category":"section"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Multi-class LDA is a generalization of standard two-class LDA that can handle arbitrary number of classes.","category":"page"},{"location":"lda/#Overview","page":"Linear Discriminant Analysis","title":"Overview","text":"","category":"section"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Multi-class LDA is based on the analysis of two scatter matrices: within-class scatter matrix and between-class scatter matrix.","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Given a set of samples mathbfx_1 ldots mathbfx_n, and their class labels y_1 ldots y_n:","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"The within-class scatter matrix is defined as:","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"mathbfS_w = sum_i=1^n (mathbfx_i - boldsymbolmu_y_i) (mathbfx_i - boldsymbolmu_y_i)^T","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Here, boldsymbolmu_k is the sample mean of the k-th class.","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"The between-class scatter matrix is defined as:","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"mathbfS_b = sum_k=1^m n_k (boldsymbolmu_k - boldsymbolmu) (boldsymbolmu_k - boldsymbolmu)^T","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Here, m is the number of classes, boldsymbolmu is the overall sample mean, and n_k is the number of samples in the k-th class.","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Then, multi-class LDA can be formulated as an optimization problem to find a set of linear combinations (with coefficients mathbfw) that maximizes the ratio of the between-class scattering to the within-class scattering, as","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"hatmathbfw = mathopmathrmargmax_mathbfw\n fracmathbfw^T mathbfS_b mathbfwmathbfw^T mathbfS_w mathbfw","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"The solution is given by the following generalized eigenvalue problem:","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"mathbfS_b mathbfw = lambda mathbfS_w mathbfw","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Generally, at most m - 1 generalized eigenvectors are useful to discriminate between m classes.","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"When the dimensionality is high, it may not be feasible to construct the scatter matrices explicitly. In such cases, see SubspaceLDA below.","category":"page"},{"location":"lda/#Normalization-by-number-of-observations","page":"Linear Discriminant Analysis","title":"Normalization by number of observations","text":"","category":"section"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"An alternative definition of the within- and between-class scatter matrices normalizes for the number of observations in each group:","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"mathbfS_w^* = n sum_k=1^m frac1n_k sum_i mid y_i=k (mathbfx_i - boldsymbolmu_k) (mathbfx_i - boldsymbolmu_k)^T","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"mathbfS_b^* = n sum_k=1^m (boldsymbolmu_k - boldsymbolmu^*) (boldsymbolmu_k - boldsymbolmu^*)^T","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"where","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"boldsymbolmu^* = frac1k sum_k=1^m boldsymbolmu_k","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"This definition can sometimes be more useful when looking for directions which discriminate among clusters containing widely-varying numbers of observations.","category":"page"},{"location":"lda/#Multi-class-LDA","page":"Linear Discriminant Analysis","title":"Multi-class LDA","text":"","category":"section"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"The package defines a MulticlassLDA type to represent a multi-class LDA model, as:","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"MulticlassLDA\nMulticlassLDAStats","category":"page"},{"location":"lda/#MultivariateStats.MulticlassLDA","page":"Linear Discriminant Analysis","title":"MultivariateStats.MulticlassLDA","text":"A multi-class linear discriminant model type has following fields:\n\nproj is the projection matrix\npmeans is the projected means of all classes\nstats is an instance of MulticlassLDAStats type that captures all statistics computed to train the model (which we will discuss later).\n\n\n\n\n\n","category":"type"},{"location":"lda/#MultivariateStats.MulticlassLDAStats","page":"Linear Discriminant Analysis","title":"MultivariateStats.MulticlassLDAStats","text":"Resulting statistics of the multi-class LDA evaluation.\n\n\n\n\n\n","category":"type"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Several methods are provided to access properties of the LDA model. Let M be an instance of MulticlassLDA:","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"fit(::Type{MulticlassLDA}, ::AbstractMatrix{T}, ::AbstractVector; kwargs...) where T<:Real\npredict(::MulticlassLDA, ::AbstractVecOrMat{T}) where {T<:Real}\nmean(::MulticlassLDA)\nsize(::MulticlassLDA)\nlength(::MulticlassLDA)\nclassmeans(::MulticlassLDA)\nclassweights(::MulticlassLDA)\nwithclass_scatter(::MulticlassLDA)\nbetweenclass_scatter(::MulticlassLDA)\nprojection(::MulticlassLDA)","category":"page"},{"location":"lda/#StatsAPI.fit-Union{Tuple{T}, Tuple{Type{MulticlassLDA}, AbstractMatrix{T}, AbstractVector}} where T<:Real","page":"Linear Discriminant Analysis","title":"StatsAPI.fit","text":"fit(MulticlassLDA, X, y; ...)\n\nPerform multi-class LDA over a given data set X with corresponding labels y with nc number of classes.\n\nThis function returns the resultant multi-class LDA model as an instance of MulticlassLDA.\n\nParameters\n\nX: the matrix of input samples, of size (d, n). Each column in X is an observation.\ny: the vector of class labels, of length n.\n\nKeyword arguments\n\nmethod: The choice of methods:\n:gevd: based on generalized eigenvalue decomposition (default).\n:whiten: first derive a whitening transform from Sw and then solve the problem based on eigenvalue\ndecomposition of the whiten Sb.\noutdim: The output dimension, i.e. dimension of the transformed space min(d, nc-1)\nregcoef: The regularization coefficient (default: 1.0e-6). A positive value regcoef * eigmax(Sw) is added to the diagonal of Sw to improve numerical stability.\ncovestimator_between: Custom covariance estimator for between-class covariance (default: SimpleCovariance()). The covariance matrix will be calculated as cov(covestimator_between, #=data=#; dims=2, mean=zeros(#=...=#)). Custom covariance estimators, available in other packages, may result in more robust discriminants for data with more features than observations.\ncovestimator_within: Custom covariance estimator for within-class covariance (default: SimpleCovariance()). The covariance matrix will be calculated as cov(covestimator_within, #=data=#; dims=2, mean=zeros(nc)). Custom covariance estimators, available in other packages, may result in more robust discriminants for data with more features than observations.\n\nNotes:\n\nThe resultant projection matrix P satisfies:\n\nmathbfP^T (mathbfS_w + kappa mathbfI) mathbfP = mathbfI\n\nHere, kappa equals regcoef * eigmax(Sw). The columns of P are arranged in descending order of the corresponding generalized eigenvalues.\n\nNote that MulticlassLDA does not currently support the normalized version using mathbfS_w^* and mathbfS_b^* (see SubspaceLDA).\n\n\n\n\n\n","category":"method"},{"location":"lda/#StatsAPI.predict-Union{Tuple{T}, Tuple{MulticlassLDA, AbstractVecOrMat{T}}} where T<:Real","page":"Linear Discriminant Analysis","title":"StatsAPI.predict","text":"predict(M::MulticlassLDA, x)\n\nTransform input sample(s) in x to the output space of MC-LDA model M. Here, x can be either a sample vector or a matrix comprised of samples in columns.\n\n\n\n\n\n","category":"method"},{"location":"lda/#Statistics.mean-Tuple{MulticlassLDA}","page":"Linear Discriminant Analysis","title":"Statistics.mean","text":"mean(M::MulticlassLDA)\n\nGet the overall sample mean vector (of length d).\n\n\n\n\n\n","category":"method"},{"location":"lda/#Base.size-Tuple{MulticlassLDA}","page":"Linear Discriminant Analysis","title":"Base.size","text":"size(M::MulticlassLDA)\n\nGet the input (i.e the dimension of the observation space) and output (i.e the dimension of the transformed features) dimensions of the model M.\n\n\n\n\n\n","category":"method"},{"location":"lda/#Base.length-Tuple{MulticlassLDA}","page":"Linear Discriminant Analysis","title":"Base.length","text":"length(M::MulticlassLDA)\n\nGet the sample dimensions.\n\n\n\n\n\n","category":"method"},{"location":"lda/#MultivariateStats.classmeans-Tuple{MulticlassLDA}","page":"Linear Discriminant Analysis","title":"MultivariateStats.classmeans","text":"classmeans(M)\n\nGet the matrix comprised of class-specific means as columns (of size (d m)).\n\n\n\n\n\n","category":"method"},{"location":"lda/#MultivariateStats.classweights-Tuple{MulticlassLDA}","page":"Linear Discriminant Analysis","title":"MultivariateStats.classweights","text":"classweights(M)\n\nGet the weights of individual classes (a vector of length m). If the samples are not weighted, the weight equals the number of samples of each class.\n\n\n\n\n\n","category":"method"},{"location":"lda/#MultivariateStats.withclass_scatter-Tuple{MulticlassLDA}","page":"Linear Discriminant Analysis","title":"MultivariateStats.withclass_scatter","text":"withinclass_scatter(M)\n\nGet the within-class scatter matrix (of size (d d)).\n\n\n\n\n\n","category":"method"},{"location":"lda/#MultivariateStats.betweenclass_scatter-Tuple{MulticlassLDA}","page":"Linear Discriminant Analysis","title":"MultivariateStats.betweenclass_scatter","text":"betweenclass_scatter(M)\n\nGet the between-class scatter matrix (of size (d d)).\n\n\n\n\n\n","category":"method"},{"location":"lda/#MultivariateStats.projection-Tuple{MulticlassLDA}","page":"Linear Discriminant Analysis","title":"MultivariateStats.projection","text":"projection(M::MulticlassLDA)\n\nGet the projection matrix (of size d x p).\n\n\n\n\n\n","category":"method"},{"location":"lda/#Subspace-Linear-Discriminant-Analysis","page":"Linear Discriminant Analysis","title":"Subspace Linear Discriminant Analysis","text":"","category":"section"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"The package also defines a SubspaceLDA type to represent a multi-class LDA model for high-dimensional spaces. MulticlassLDA, because it stores the scatter matrices, is not well-suited for high-dimensional data. For example, if you are performing LDA on images, and each image has 10^6 pixels, then the scatter matrices would contain 10^12 elements, far too many to store directly. SubspaceLDA calculates the projection direction without the intermediary of the scatter matrices, by focusing on the subspace that lies within the span of the within-class scatter. This also serves to regularize the computation.","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"SubspaceLDA supports all the same methods as MulticlassLDA, with the exception of the functions that return a scatter matrix. The overall projection is represented as a factorization P*L, where P*x projects data points to the subspace spanned by the within-class scatter, and L is the LDA projection in the subspace. The projection directions w (the columns of projection(M)) satisfy the equation","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":" mathbfP^T mathbfS_b mathbfw = lambda mathbfP^T mathbfS_w mathbfw","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"When P is of full rank (e.g., if there are more data points than dimensions), then this equation guarantees that mathbfS_b mathbfw = lambda mathbfS_w mathbfw will also hold.","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"The package defines a SubspaceLDA type to represent a multi-class LDA model, as:","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"SubspaceLDA","category":"page"},{"location":"lda/#MultivariateStats.SubspaceLDA","page":"Linear Discriminant Analysis","title":"MultivariateStats.SubspaceLDA","text":"Subspace LDA model type has following fields:\n\nprojw: the projection matrix of the subspace spanned by the between-class scatter\nprojLDA: the projection matrix of the subspace spanned by the within-class scatter\nλ: the projection eigenvalues\ncmeans: the class centroids\ncweights: the class weights\n\n\n\n\n\n","category":"type"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"Several methods are provided to access properties of the LDA model. Let M be an instance of SubspaceLDA:","category":"page"},{"location":"lda/","page":"Linear Discriminant Analysis","title":"Linear Discriminant Analysis","text":"fit(::Type{SubspaceLDA}, ::AbstractMatrix{T}, ::AbstractVector; kwargs...) where T<:Real\npredict(::SubspaceLDA, ::AbstractVecOrMat{T}) where {T<:Real}\nmean(::SubspaceLDA)\nprojection(::SubspaceLDA)\nsize(::SubspaceLDA)\nlength(::SubspaceLDA)\neigvals(::SubspaceLDA)","category":"page"},{"location":"lda/#StatsAPI.fit-Union{Tuple{T}, Tuple{Type{SubspaceLDA}, AbstractMatrix{T}, AbstractVector}} where T<:Real","page":"Linear Discriminant Analysis","title":"StatsAPI.fit","text":"fit(SubspaceLDA, X, y; normalize=true)\n\nFit an subspace projection of LDA model over a given data set X with corresponding labels y using the equivalent of mathbfS_w^* and mathbfS_b^*`.\n\nNote: Subspace LDA also supports the normalized version of LDA via the normalize keyword.\n\n\n\n\n\n","category":"method"},{"location":"lda/#StatsAPI.predict-Union{Tuple{T}, Tuple{SubspaceLDA, AbstractVecOrMat{T}}} where T<:Real","page":"Linear Discriminant Analysis","title":"StatsAPI.predict","text":"predict(M::SubspaceLDA, x)\n\nTransform input sample(s) in x to the output space of LDA model M. Here, x can be either a sample vector or a matrix comprised of samples in columns.\n\n\n\n\n\n","category":"method"},{"location":"lda/#Statistics.mean-Tuple{SubspaceLDA}","page":"Linear Discriminant Analysis","title":"Statistics.mean","text":"mean(M::SubspaceLDA)\n\nReturns the mean vector of the subspace LDA model M.\n\n\n\n\n\n","category":"method"},{"location":"lda/#MultivariateStats.projection-Tuple{SubspaceLDA}","page":"Linear Discriminant Analysis","title":"MultivariateStats.projection","text":"projection(M)\n\nGet the projection matrix.\n\n\n\n\n\n","category":"method"},{"location":"lda/#Base.size-Tuple{SubspaceLDA}","page":"Linear Discriminant Analysis","title":"Base.size","text":"size(M)\n\nGet the input (i.e the dimension of the observation space) and output (i.e the dimension of the subspace projection) dimensions of the model M.\n\n\n\n\n\n","category":"method"},{"location":"lda/#Base.length-Tuple{SubspaceLDA}","page":"Linear Discriminant Analysis","title":"Base.length","text":"length(M)\n\nGet dimension of the LDA model.\n\n\n\n\n\n","category":"method"},{"location":"lda/#LinearAlgebra.eigvals-Tuple{SubspaceLDA}","page":"Linear Discriminant Analysis","title":"LinearAlgebra.eigvals","text":"eigvals(M::SubspaceLDA)\n\nGet the eigenvalues of the subspace LDA model M.\n\n\n\n\n\n","category":"method"},{"location":"cca/#Canonical-Correlation-Analysis","page":"Canonical Correlation Analysis","title":"Canonical Correlation Analysis","text":"","category":"section"},{"location":"cca/","page":"Canonical Correlation Analysis","title":"Canonical Correlation Analysis","text":"Canonical Correlation Analysis(CCA) is a statistical analysis technique to identify correlations between two sets of variables. Given two vector variables X and Y, it finds two projections, one for each, to transform them to a common space with maximum correlations.","category":"page"},{"location":"cca/","page":"Canonical Correlation Analysis","title":"Canonical Correlation Analysis","text":"The package defines a CCA type to represent a CCA model, and provides a set of methods to access the properties.","category":"page"},{"location":"cca/","page":"Canonical Correlation Analysis","title":"Canonical Correlation Analysis","text":"CCA","category":"page"},{"location":"cca/#MultivariateStats.CCA","page":"Canonical Correlation Analysis","title":"MultivariateStats.CCA","text":"Canonical Correlation Analysis Model\n\n\n\n\n\n","category":"type"},{"location":"cca/","page":"Canonical Correlation Analysis","title":"Canonical Correlation Analysis","text":"Let M be an instance of CCA, dx be the dimension of X, dy the dimension of Y, and p the output dimension (i.e the dimension of the common space).","category":"page"},{"location":"cca/","page":"Canonical Correlation Analysis","title":"Canonical Correlation Analysis","text":"fit(::Type{CCA}, ::AbstractMatrix{T}, ::AbstractMatrix{T}) where {T<:Real}\nsize(::CCA)\nmean(::CCA, ::Symbol)\nprojection(::CCA, ::Symbol)\ncor(::CCA)\npredict(::CCA, ::AbstractVecOrMat{<:Real}, ::Symbol)","category":"page"},{"location":"cca/#StatsAPI.fit-Union{Tuple{T}, Tuple{Type{CCA}, AbstractMatrix{T}, AbstractMatrix{T}}} where T<:Real","page":"Canonical Correlation Analysis","title":"StatsAPI.fit","text":"fit(CCA, X, Y; ...)\n\nPerform CCA over the data given in matrices X and Y. Each column of X and Y is an observation.\n\nX and Y should have the same number of columns (denoted by n below).\n\nThis method returns an instance of CCA.\n\nKeyword arguments:\n\nmethod: The choice of methods:\n:cov: based on covariance matrices\n:svd: based on SVD of the input data (default)\noutdim: The output dimension, i.e dimension of the common space (default: min(dx, dy, n))\nmean: The mean vector, which can be either of:\n0: the input data has already been centralized\nnothing: this function will compute the mean (default)\na pre-computed mean vector\n\nNotes: This function calls ccacov or ccasvd internally, depending on the choice of method.\n\n\n\n\n\n","category":"method"},{"location":"cca/#Base.size-Tuple{CCA}","page":"Canonical Correlation Analysis","title":"Base.size","text":"size(M:CCA)\n\nReturn a tuple with the dimension of X, Y, and the output dimension.\n\n\n\n\n\n","category":"method"},{"location":"cca/#Statistics.mean-Tuple{CCA, Symbol}","page":"Canonical Correlation Analysis","title":"Statistics.mean","text":"mean(M::CCA, c::Symbol)\n\nGet the mean vector for the component c of the model M. The component parameter can be :x or :y.\n\n\n\n\n\n","category":"method"},{"location":"cca/#MultivariateStats.projection-Tuple{CCA, Symbol}","page":"Canonical Correlation Analysis","title":"MultivariateStats.projection","text":"projection(M::CCA, c::Symbol)\n\nGet the projection matrix for the component c of the model M. The component parameter can be :x or :y.\n\n\n\n\n\n","category":"method"},{"location":"cca/#Statistics.cor-Tuple{CCA}","page":"Canonical Correlation Analysis","title":"Statistics.cor","text":"cor(M::CCA)\n\nThe correlations of the projected components (a vector of length p).\n\n\n\n\n\n","category":"method"},{"location":"cca/#StatsAPI.predict-Tuple{CCA, AbstractVecOrMat{<:Real}, Symbol}","page":"Canonical Correlation Analysis","title":"StatsAPI.predict","text":"predict(M::CCA, Z::AbstractVecOrMat{<:Real}, c::Symbol)\n\nGiven a CCA model, one can transform observations into both spaces into a common space, as\n\nmathbfz_x = mathbfP_x^T (mathbfx - boldsymbolmu_x) \nmathbfz_y = mathbfP_y^T (mathbfy - boldsymbolmu_y)\n\nHere, mathbfP_x and mathbfP_y are projection matrices for X and Y; boldsymbolmu_x and boldsymbolmu_y are mean vectors.\n\nParameter Z can be either a vector of length dx, dy, or a matrix where each column is an observation. The component parameter c can be :x or :y.\n\n\n\n\n\n","category":"method"},{"location":"cca/","page":"Canonical Correlation Analysis","title":"Canonical Correlation Analysis","text":"Auxiliary functions:","category":"page"},{"location":"cca/","page":"Canonical Correlation Analysis","title":"Canonical Correlation Analysis","text":"ccacov\nccasvd","category":"page"},{"location":"cca/#MultivariateStats.ccacov","page":"Canonical Correlation Analysis","title":"MultivariateStats.ccacov","text":"ccacov(Cxx, Cyy, Cxy, xmean, ymean, p)\n\nCompute CCA based on analysis of the given covariance matrices, using generalized eigenvalue decomposition, and return CCA model.\n\nParameters:\n\nCxx: The covariance matrix of X.\nCyy: The covariance matrix of Y.\nCxy: The covariance matrix between X and Y.\nxmean: The mean vector of the original samples of X, which can be\n\na vector of length dx, or an empty vector indicating a zero mean.\n\nymean: The mean vector of the original samples of Y, which can be\n\na vector of length dy, or an empty vector indicating a zero mean.\n\np: The output dimension, i.e the dimension of the common space.\n\n\n\n\n\n","category":"function"},{"location":"cca/#MultivariateStats.ccasvd","page":"Canonical Correlation Analysis","title":"MultivariateStats.ccasvd","text":"ccasvd(Zx, Zy, xmean, ymean, p)\n\nCompute CCA based on singular value decomposition of centralized sample matrices Zx and Zy, and return CCA model[1].\n\nParameters:\n\nZx: The centralized sample matrix for X.\nZy: The centralized sample matrix for Y.\nxmean: The mean vector of the original samples of X, which can be\n\na vector of length dx, or an empty vector indicating a zero mean.\n\nymean: The mean vector of the original samples of Y, which can be\n\na vector of length dy, or an empty vector indicating a zero mean.\n\np: The output dimension, i.e the dimension of the common space.\n\n\n\n\n\n","category":"function"},{"location":"cca/","page":"Canonical Correlation Analysis","title":"Canonical Correlation Analysis","text":"","category":"page"},{"location":"cca/#References","page":"Canonical Correlation Analysis","title":"References","text":"","category":"section"},{"location":"cca/","page":"Canonical Correlation Analysis","title":"Canonical Correlation Analysis","text":"[1]: David Weenink, Canonical Correlation Analysis, Institute of Phonetic Sciences, Univ. of Amsterdam, Proceedings 25, 81-99, 2003.","category":"page"},{"location":"ica/#Independent-Component-Analysis","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"","category":"section"},{"location":"ica/","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"Independent Component Analysis (ICA) is a computational technique for separating a multivariate signal into additive subcomponents, with the assumption that the subcomponents are non-Gaussian and independent from each other.","category":"page"},{"location":"ica/","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"There are multiple algorithms for ICA. Currently, this package implements the Fast ICA algorithm.","category":"page"},{"location":"ica/#FastICA","page":"Independent Component Analysis","title":"FastICA","text":"","category":"section"},{"location":"ica/","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"This package implements the FastICA algorithm[1]. The package uses the ICA type to define a FastICA model:","category":"page"},{"location":"ica/","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"ICA","category":"page"},{"location":"ica/#MultivariateStats.ICA","page":"Independent Component Analysis","title":"MultivariateStats.ICA","text":"This type contains ICA model parameters: mean and component matrix W.\n\nNote: Each column of the component matrix W corresponds to an independent component.\n\n\n\n\n\n","category":"type"},{"location":"ica/","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"Several methods are provided to work with ICA. Let M be an instance of ICA:","category":"page"},{"location":"ica/","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"fit(::Type{ICA}, ::AbstractMatrix{T}, ::Int) where {T<:Real}\nsize(::ICA)\nmean(::ICA)\npredict(::ICA, ::AbstractVecOrMat{<:Real})","category":"page"},{"location":"ica/#StatsAPI.fit-Union{Tuple{T}, Tuple{Type{ICA}, AbstractMatrix{T}, Int64}} where T<:Real","page":"Independent Component Analysis","title":"StatsAPI.fit","text":"fit(ICA, X, k; ...)\n\nPerform ICA over the data set given in X.\n\nParameters: -X: The data matrix, of size (m n). Each row corresponds to a mixed signal, while each column corresponds to an observation (e.g all signal value at a particular time step). -k: The number of independent components to recover.\n\nKeyword Arguments:\n\nalg: The choice of algorithm (default :fastica)\nfun: The approx neg-entropy functor (default Tanh)\ndo_whiten: Whether to perform pre-whitening (default true)\nmaxiter: Maximum number of iterations (default 100)\ntol: Tolerable change of W at convergence (default 1.0e-6)\nmean: The mean vector, which can be either of:\n0: the input data has already been centralized\nnothing: this function will compute the mean (default)\na pre-computed mean vector\nwinit: Initial guess of W, which should be either of:\nempty matrix: the function will perform random initialization (default)\na matrix of size (k k) (when do_whiten)\na matrix of size (m k) (when !do_whiten)\n\nReturns the resultant ICA model, an instance of type ICA.\n\nNote: If do_whiten is true, the return W satisfies mathbfW^T mathbfC mathbfW = mathbfI, otherwise W is orthonormal, i.e mathbfW^T mathbfW = mathbfI.\n\n\n\n\n\n","category":"method"},{"location":"ica/#Base.size-Tuple{ICA}","page":"Independent Component Analysis","title":"Base.size","text":"size(M::ICA)\n\nReturns a tuple with the input dimension, i.e the number of observed mixtures, and the output dimension, i.e the number of independent components.\n\n\n\n\n\n","category":"method"},{"location":"ica/#Statistics.mean-Tuple{ICA}","page":"Independent Component Analysis","title":"Statistics.mean","text":"mean(M::ICA)\n\nReturns the mean vector.\n\n\n\n\n\n","category":"method"},{"location":"ica/#StatsAPI.predict-Tuple{ICA, AbstractVecOrMat{<:Real}}","page":"Independent Component Analysis","title":"StatsAPI.predict","text":"predict(M::ICA, x)\n\nTransform x to the output space to extract independent components, as mathbfW^T (mathbfx - boldsymbolmu), given the model M.\n\n\n\n\n\n","category":"method"},{"location":"ica/","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"The package also exports functions of the core algorithms. Sometimes, it can be more efficient to directly invoke them instead of going through the fit interface.","category":"page"},{"location":"ica/","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"fastica!","category":"page"},{"location":"ica/#MultivariateStats.fastica!","page":"Independent Component Analysis","title":"MultivariateStats.fastica!","text":"fastica!(W, X, fun, maxiter, tol, verbose)\n\nInvoke the Fast ICA algorithm[1].\n\nParameters:\n\nW: The initial un-mixing matrix, of size (m k). The function updates this matrix inplace.\nX: The data matrix, of size (m n). This matrix is input only, and won't be modified.\nfun: The approximate neg-entropy functor of type ICAGDeriv.\nmaxiter: Maximum number of iterations.\ntol: Tolerable change of W at convergence.\n\nReturns the updated W.\n\nNote: The number of components is inferred from W as size(W, 2).\n\n\n\n\n\n","category":"function"},{"location":"ica/","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"The FastICA method requires a first derivative of a functor g to approximate negative entropy. The package implements an following interface for defining derivative value estimation:","category":"page"},{"location":"ica/","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"MultivariateStats.ICAGDeriv\nMultivariateStats.Tanh\nMultivariateStats.Gaus","category":"page"},{"location":"ica/#MultivariateStats.ICAGDeriv","page":"Independent Component Analysis","title":"MultivariateStats.ICAGDeriv","text":"The abstract type for all g (derivative) functions.\n\nLet g be an instance of such type, then update!(g, U, E) given\n\nU = w'x\n\nreturns updated in-place U and E, s.t.\n\ng(w'x) --> U and E{g'(w'x)} --> E\n\n\n\n\n\n","category":"type"},{"location":"ica/#MultivariateStats.Tanh","page":"Independent Component Analysis","title":"MultivariateStats.Tanh","text":"Derivative for (1a_1)logcosh a_1 u\n\n\n\n\n\n","category":"type"},{"location":"ica/#MultivariateStats.Gaus","page":"Independent Component Analysis","title":"MultivariateStats.Gaus","text":"Derivative for -e^frac-u^22\n\n\n\n\n\n","category":"type"},{"location":"ica/","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"","category":"page"},{"location":"ica/#References","page":"Independent Component Analysis","title":"References","text":"","category":"section"},{"location":"ica/","page":"Independent Component Analysis","title":"Independent Component Analysis","text":"[1]: Aapo Hyvarinen and Erkki Oja, Independent Component Analysis: Algorithms and Applications. Neural Network 13(4-5), 2000.","category":"page"},{"location":"whiten/#Data-Transformation","page":"Data Transformation","title":"Data Transformation","text":"","category":"section"},{"location":"whiten/#Whitening","page":"Data Transformation","title":"Whitening","text":"","category":"section"},{"location":"whiten/","page":"Data Transformation","title":"Data Transformation","text":"A whitening transformation is a decorrelation transformation that transforms a set of random variables into a set of new random variables with identity covariance (uncorrelated with unit variances).","category":"page"},{"location":"whiten/","page":"Data Transformation","title":"Data Transformation","text":"In particular, suppose a random vector has covariance mathbfC, then a whitening transform mathbfW is one that satisfy:","category":"page"},{"location":"whiten/","page":"Data Transformation","title":"Data Transformation","text":" mathbfW^T mathbfC mathbfW = mathbfI","category":"page"},{"location":"whiten/","page":"Data Transformation","title":"Data Transformation","text":"Note that mathbfW is generally not unique. In particular, if mathbfW is a whitening transform, so is any of its rotation mathbfW mathbfR with mathbfR^T mathbfR = mathbfI.","category":"page"},{"location":"whiten/","page":"Data Transformation","title":"Data Transformation","text":"The package uses Whitening to represent a whitening transform.","category":"page"},{"location":"whiten/","page":"Data Transformation","title":"Data Transformation","text":"Whitening","category":"page"},{"location":"whiten/#MultivariateStats.Whitening","page":"Data Transformation","title":"MultivariateStats.Whitening","text":"A whitening transform representation.\n\n\n\n\n\n","category":"type"},{"location":"whiten/","page":"Data Transformation","title":"Data Transformation","text":"Whitening transformation can be fitted to data using the fit method.","category":"page"},{"location":"whiten/","page":"Data Transformation","title":"Data Transformation","text":"fit(::Type{Whitening}, X::AbstractMatrix{T}; kwargs...) where {T<:Real}\nMultivariateStats.transform(::Whitening, ::AbstractVecOrMat{<:Real})\nlength(::Whitening)\nmean(::Whitening)\nsize(::Whitening)","category":"page"},{"location":"whiten/#StatsAPI.fit-Union{Tuple{T}, Tuple{Type{Whitening}, AbstractMatrix{T}}} where T<:Real","page":"Data Transformation","title":"StatsAPI.fit","text":"fit(Whitening, X::AbstractMatrix{T}; kwargs...)\n\nEstimate a whitening transform from the data given in X.\n\nThis function returns an instance of Whitening\n\nKeyword Arguments:\n\nregcoef: The regularization coefficient. The covariance will be regularized as follows when regcoef is positive C + (eigmax(C) * regcoef) * eye(d). Default values is zero(T).\ndims: if 1 the transformation calculated from the row samples. fit standardization parameters in column-wise fashion; if 2 the transformation calculated from the column samples. The default is nothing, which is equivalent to dims=2 with a deprecation warning.\nmean: The mean vector, which can be either of:\n0: the input data has already been centralized\nnothing: this function will compute the mean (default)\na pre-computed mean vector\n\nNote: This function internally relies on cov_whitening to derive the transformation W.\n\n\n\n\n\n","category":"method"},{"location":"whiten/#MultivariateStats.transform-Tuple{Whitening, AbstractVecOrMat{<:Real}}","page":"Data Transformation","title":"MultivariateStats.transform","text":"transform(f, x)\n\nApply the whitening transform f to a vector or a matrix x with samples in columns, as mathbfW^T (mathbfx - boldsymbolmu).\n\n\n\n\n\n","category":"method"},{"location":"whiten/#Base.length-Tuple{Whitening}","page":"Data Transformation","title":"Base.length","text":"length(f)\n\nGet the dimension of the whitening transform f.\n\n\n\n\n\n","category":"method"},{"location":"whiten/#Statistics.mean-Tuple{Whitening}","page":"Data Transformation","title":"Statistics.mean","text":"mean(f)\n\nGet the mean vector of the whitening transformation f.\n\nNote: if mean is empty, this function returns a zero vector of length(f).\n\n\n\n\n\n","category":"method"},{"location":"whiten/#Base.size-Tuple{Whitening}","page":"Data Transformation","title":"Base.size","text":"size(f)\n\nDimensions of the coefficient matrix of the whitening transform f.\n\n\n\n\n\n","category":"method"},{"location":"whiten/","page":"Data Transformation","title":"Data Transformation","text":"Additional methods","category":"page"},{"location":"whiten/","page":"Data Transformation","title":"Data Transformation","text":"cov_whitening\ncov_whitening!","category":"page"},{"location":"whiten/#MultivariateStats.cov_whitening","page":"Data Transformation","title":"MultivariateStats.cov_whitening","text":"cov_whitening(C)\n\nDerive the whitening transform coefficient matrix W given the covariance matrix C. Here, C can be either a square matrix, or an instance of Cholesky.\n\nInternally, this function solves the whitening transform using Cholesky factorization. The rationale is as follows: let mathbfC = mathbfU^T mathbfU and mathbfW = mathbfU^-1, then mathbfW^T mathbfC mathbfW = mathbfI.\n\nNote: The return matrix W is an upper triangular matrix.\n\n\n\n\n\ncov_whitening(C, regcoef)\n\nDerive a whitening transform based on a regularized covariance, as C + (eigmax(C) * regcoef) * eye(d).\n\n\n\n\n\n","category":"function"},{"location":"whiten/#MultivariateStats.cov_whitening!","page":"Data Transformation","title":"MultivariateStats.cov_whitening!","text":"cov_whitening!(C)\n\nIn-place version of cov_whitening(C), in which the input matrix C will be overwritten during computation. This can be more efficient when C is no longer used.\n\n\n\n\n\ncov_whitening!(C, regcoef)\n\nIn-place version of cov_whitening(C, regcoef), in which the input matrix C will be overwritten during computation. This can be more efficient when C is no longer used.\n\n\n\n\n\n","category":"function"},{"location":"#MultivariateStats.jl-Documentation","page":"Home","title":"MultivariateStats.jl Documentation","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"CurrentModule = MultivariateStats\nDocTestSetup = quote\n using Statistics\n using Random\nend","category":"page"},{"location":"","page":"Home","title":"Home","text":"MultivariateStats.jl is a Julia package for multivariate statistical analysis. It provides a rich set of useful analysis techniques, such as PCA, CCA, LDA, ICA, etc.","category":"page"},{"location":"","page":"Home","title":"Home","text":"Pages = [\"whiten.md\", \"lreg.md\", \"lda.md\", \"pca.md\", \"ica.md\", \"cca.md\", \"fa.md\", \"mds.md\", \"api.md\"]\nDepth = 2","category":"page"},{"location":"","page":"Home","title":"Home","text":"Notes: All methods implemented in this package adopt the column-major convention of JuliaStats: in a data matrix, each column corresponds to a sample/observation, while each row corresponds to a feature (variable or attribute).","category":"page"},{"location":"lreg/#Regression","page":"Regression","title":"Regression","text":"","category":"section"},{"location":"lreg/","page":"Regression","title":"Regression","text":"The package provides functions to perform Linear Least Square, Ridge, and Isotonic Regression.","category":"page"},{"location":"lreg/#Examples","page":"Regression","title":"Examples","text":"","category":"section"},{"location":"lreg/","page":"Regression","title":"Regression","text":"using Plots\ngr(fmt=:svg)","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"Performing llsq regression on cars data set:","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"using MultivariateStats, RDatasets, Plots\n\n# load cars dataset\ncars = dataset(\"datasets\", \"cars\")\n\n# calculate regression models\na = llsq(cars[!,:Speed], cars[!, :Dist])\nb = isotonic(cars[!,:Speed], cars[!, :Dist])\n\n# plot results\np = scatter(cars[!,:Speed], cars[!,:Dist], xlab=\"Speed\", ylab=\"Distance\",\n leg=:topleft, lab=\"data\")\nlet xs = cars[!,:Speed]\n plot!(p, xs, map(x->a[1]*x+a[2], xs), lab=\"llsq\")\n plot!(p, xs, b, lab=\"isotonic\")\nend","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"For a single response vector y (without using bias):","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"# prepare data\nX = rand(1000, 3) # feature matrix\na0 = rand(3) # ground truths\ny = X * a0 + 0.1 * randn(1000) # generate response\n\n# solve using llsq\na = llsq(X, y; bias=false)\n\n# do prediction\nyp = X * a\n\n# measure the error\nrmse = sqrt(mean(abs2.(y - yp)))\nprint(\"rmse = $rmse\")","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"For a single response vector y (using bias):","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"# prepare data\nX = rand(1000, 3)\na0, b0 = rand(3), rand()\ny = X * a0 .+ b0 .+ 0.1 * randn(1000)\n\n# solve using llsq\nsol = llsq(X, y)\n\n# extract results\na, b = sol[1:end-1], sol[end]\n\n# do prediction\nyp = X * a .+ b'","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"For a matrix of column-stored regressors X and a matrix comprised of multiple columns of dependent variables Y:","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"# prepare data\nX = rand(3, 1000)\nA0, b0 = rand(3, 5), rand(1, 5)\nY = (X' * A0 .+ b0) + 0.1 * randn(1000, 5)\n\n# solve using llsq\nsol = llsq(X, Y, dims=2)\n\n# extract results\nA, b = sol[1:end-1,:], sol[end,:]\n\n# do prediction\nYp = X'*A .+ b'","category":"page"},{"location":"lreg/#Linear-Least-Square","page":"Regression","title":"Linear Least Square","text":"","category":"section"},{"location":"lreg/","page":"Regression","title":"Regression","text":"Linear Least Square is to find linear combination(s) of given variables to fit the responses by minimizing the squared error between them. This can be formulated as an optimization as follows:","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"mathopmathrmminimize_(mathbfa b) \n frac12 mathbfy - (mathbfX mathbfa + b)^2","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"Sometimes, the coefficient matrix is given in a transposed form, in which case, the optimization is modified as:","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"mathopmathrmminimize_(mathbfa b) \n frac12 mathbfy - (mathbfX^T mathbfa + b)^2","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"The package provides following functions to solve the above problems:","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"llsq","category":"page"},{"location":"lreg/#MultivariateStats.llsq","page":"Regression","title":"MultivariateStats.llsq","text":"llsq(X, y; ...)\n\nSolve the linear least square problem.\n\nHere, y can be either a vector, or a matrix where each column is a response vector.\n\nThis function accepts two keyword arguments:\n\ndims: whether input observations are stored as rows (1) or columns (2). (default is 1)\nbias: whether to include the bias term b. (default is true)\n\nThe function results the solution a. In particular, when y is a vector (matrix), a is also a vector (matrix). If bias is true, then the returned array is augmented as [a; b].\n\n\n\n\n\n","category":"function"},{"location":"lreg/#Ridge-Regression","page":"Regression","title":"Ridge Regression","text":"","category":"section"},{"location":"lreg/","page":"Regression","title":"Regression","text":"Compared to linear least square, Ridge Regression uses an additional quadratic term to regularize the problem:","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"mathopmathrmminimize_(mathbfa b) \n frac12 mathbfy - (mathbfX mathbfa + b)^2 +\n frac12 mathbfa^T mathbfQ mathbfa","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"The transposed form:","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":" mathopmathrmminimize_(mathbfa b) \n frac12 mathbfy - (mathbfX^T mathbfa + b)^2 +\n frac12 mathbfa^T mathbfQ mathbfa","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"The package provides following functions to solve the above problems:","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"ridge","category":"page"},{"location":"lreg/#MultivariateStats.ridge","page":"Regression","title":"MultivariateStats.ridge","text":"ridge(X, y, r; ...)\n\nSolve the ridge regression problem.\n\nHere, y can be either a vector, or a matrix where each column is a response vector.\n\nThe argument r gives the quadratic regularization matrix Q, which can be in either of the following forms:\n\nr is a real scalar, then Q is considered to be r * eye(n), where n is the dimension of a.\nr is a real vector, then Q is considered to be diagm(r).\nr is a real symmetric matrix, then Q is simply considered to be r.\n\nThis function accepts two keyword arguments:\n\ndims: whether input observations are stored as rows (1) or columns (2). (default is 1)\nbias: whether to include the bias term b. (default is true)\n\nThe function results the solution a. In particular, when y is a vector (matrix), a is also a vector (matrix). If bias is true, then the returned array is augmented as [a; b].\n\n\n\n\n\n","category":"function"},{"location":"lreg/#Isotonic-Regression","page":"Regression","title":"Isotonic Regression","text":"","category":"section"},{"location":"lreg/","page":"Regression","title":"Regression","text":"Isotonic regression or monotonic regression fits a sequence of observations into a fitted line that is non-decreasing (or non-increasing) everywhere. The problem defined as a weighted least-squares fit hat y_i approx y_i for all i, subject to the constraint that hat y_i leq hat y_j whenever x_i leq x_j. This gives the following quadratic program:","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"min sum_i=1^n w_i(hat y_i-y_i)^2\ntext subject to hat y_i leq hat y_j\ntext for all (ij) in E","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"where E=(ij)x_ileq x_j specifies the partial ordering of the observed inputs x_i.","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"The package provides following functions to solve the above problems:","category":"page"},{"location":"lreg/","page":"Regression","title":"Regression","text":"isotonic","category":"page"},{"location":"lreg/#MultivariateStats.isotonic","page":"Regression","title":"MultivariateStats.isotonic","text":"isotonic(x, y[, w])\n\nSolve the isotonic regression problem using the pool adjacent violators algorithm[1].\n\nHere x is the regressor vector, y is response vector, and w is an optional weights vector.\n\nThe function returns a prediction vector of the same size as the regressor vector x.\n\n\n\n\n\n","category":"function"},{"location":"lreg/","page":"Regression","title":"Regression","text":"","category":"page"},{"location":"lreg/#References","page":"Regression","title":"References","text":"","category":"section"},{"location":"lreg/","page":"Regression","title":"Regression","text":"[1]: Best, M.J., Chakravarti, N. Active set algorithms for isotonic regression; A unifying framework. Mathematical Programming 47, 425–439 (1990).","category":"page"},{"location":"mds/#Multidimensional-Scaling","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"","category":"section"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"In general, Multidimensional Scaling (MDS) refers to techniques that transforms samples into lower dimensional space while preserving the inter-sample distances as well as possible.","category":"page"},{"location":"mds/#Example","page":"Multidimensional Scaling","title":"Example","text":"","category":"section"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"using Plots\ngr(fmt=:svg)","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"Performing MDS on Iris data set:","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"using MultivariateStats, RDatasets, Plots\n\n# load iris dataset\niris = dataset(\"datasets\", \"iris\")\n\n# take half of the dataset\nX = Matrix(iris[1:2:end,1:4])'\nX_labels = Vector(iris[1:2:end,5])\nnothing # hide","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"Suppose X is our data matrix, with each observation in a column. We train a MDS model, allowing up to 3 dimensions:","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"M = fit(MDS, X; maxoutdim=3, distances=false)","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"Then, apply MDS model to get an embedding of our data in 3D space:","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"Y = predict(M)","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"Now, we group results by testing set labels for color coding and visualize first 3 principal components in 3D interactive plot","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"setosa = Y[:,X_labels.==\"setosa\"]\nversicolor = Y[:,X_labels.==\"versicolor\"]\nvirginica = Y[:,X_labels.==\"virginica\"]\n\np = scatter(setosa[1,:],setosa[2,:],setosa[3,:],marker=:circle,linewidth=0)\nscatter!(versicolor[1,:],versicolor[2,:],versicolor[3,:],marker=:circle,linewidth=0)\nscatter!(virginica[1,:],virginica[2,:],virginica[3,:],marker=:circle,linewidth=0)","category":"page"},{"location":"mds/#Classical-Multidimensional-Scaling","page":"Multidimensional Scaling","title":"Classical Multidimensional Scaling","text":"","category":"section"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"This package defines a MDS type to represent a classical MDS model[1], and provides a set of methods to access the properties.","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"MDS","category":"page"},{"location":"mds/#MultivariateStats.MDS","page":"Multidimensional Scaling","title":"MultivariateStats.MDS","text":"Classical Multidimensional Scaling (MDS), also known as Principal Coordinates Analysis (PCoA), is a specific technique in this family that accomplishes the embedding in two steps:\n\nConvert the distance matrix to a Gram matrix. This conversion is based on\n\nthe following relations between a distance matrix D and a Gram matrix G:\n\nmathrmsqr(mathbfD) = mathbfg mathbf1^T + mathbf1 mathbfg^T - 2 mathbfG\n\nHere, mathrmsqr(mathbfD) indicates the element-wise square of mathbfD, and mathbfg is the diagonal elements of mathbfG. This relation is itself based on the following decomposition of squared Euclidean distance:\n\n mathbfx - mathbfy ^2 = mathbfx ^2 + mathbfy ^2 - 2 mathbfx^T mathbfy\n\nPerform eigenvalue decomposition of the Gram matrix to derive the coordinates.\n\nNote: The Gramian derived from D may have non-positive or degenerate eigenvalues. The subspace of non-positive eigenvalues is projected out of the MDS solution so that the strain function is minimized in a least-squares sense. If the smallest remaining eigenvalue that is used for the MDS is degenerate, then the solution is not unique, as any linear combination of degenerate eigenvectors will also yield a MDS solution with the same strain value.\n\n\n\n\n\n","category":"type"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"The MDS method type comes with several methods where M be an instance of MDS, d be the dimension of observations, and p be the output dimension, i.e. the embedding dimension, and n is the number of the observations.","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"fit(::Type{MDS}, ::AbstractMatrix{T}; kwargs) where {T<:Real}\npredict(::MDS{T}) where {T<:Real}\npredict(::MDS, ::AbstractVector{<:Real})\nsize(::MDS)\nprojection(M::MDS)\nloadings(M::MDS)\neigvals(M::MDS)\neigvecs(M::MDS)\nstress","category":"page"},{"location":"mds/#StatsAPI.fit-Union{Tuple{T}, Tuple{Type{MDS}, AbstractMatrix{T}}} where T<:Real","page":"Multidimensional Scaling","title":"StatsAPI.fit","text":"fit(MDS, X; kwargs...)\n\nCompute an embedding of X points by classical multidimensional scaling (MDS). There are two calling options, specified via the required keyword argument distances:\n\nmds = fit(MDS, X; distances=false, maxoutdim=size(X,1)-1)\n\nwhere X is the data matrix. Distances between pairs of columns of X are computed using the Euclidean norm. This is equivalent to performing PCA on X.\n\nmds = fit(MDS, D; distances=true, maxoutdim=size(D,1)-1)\n\nwhere D is a symmetric matrix D of distances between points.\n\n\n\n\n\n","category":"method"},{"location":"mds/#StatsAPI.predict-Union{Tuple{MDS{T}}, Tuple{T}} where T<:Real","page":"Multidimensional Scaling","title":"StatsAPI.predict","text":"predict(M)\n\nReturns a coordinate matrix of size (p n) for the MDS model M, where each column is the coordinates for an observation in the embedding space.\n\n\n\n\n\n","category":"method"},{"location":"mds/#StatsAPI.predict-Tuple{MDS, AbstractVector{<:Real}}","page":"Multidimensional Scaling","title":"StatsAPI.predict","text":"predict(M, x::AbstractVector)\n\nCalculate the out-of-sample transformation of the observation x for the MDS model M. Here, x is a vector of length d.\n\n\n\n\n\n","category":"method"},{"location":"mds/#Base.size-Tuple{MDS}","page":"Multidimensional Scaling","title":"Base.size","text":"size(M::MDS)\n\nReturns tuple where the first value is the MDS model M input dimension, i.e the dimension of the observation space, and the second value is the output dimension, i.e the dimension of the embedding.\n\n\n\n\n\n","category":"method"},{"location":"mds/#MultivariateStats.projection-Tuple{MDS}","page":"Multidimensional Scaling","title":"MultivariateStats.projection","text":"projection(M::MDS)\n\nGet the MDS model M eigenvectors matrix (of size (n p)) of the embedding space. The eigenvectors are arranged in descending order of the corresponding eigenvalues.\n\n\n\n\n\n","category":"method"},{"location":"mds/#MultivariateStats.loadings-Tuple{MDS}","page":"Multidimensional Scaling","title":"MultivariateStats.loadings","text":"loadings(M::MDS)\n\nGet the loading of the MDS model M.\n\n\n\n\n\n","category":"method"},{"location":"mds/#LinearAlgebra.eigvals-Tuple{MDS}","page":"Multidimensional Scaling","title":"LinearAlgebra.eigvals","text":"eigvals(M::MDS)\n\nGet the eigenvalues of the MDS model M.\n\n\n\n\n\n","category":"method"},{"location":"mds/#LinearAlgebra.eigvecs-Tuple{MDS}","page":"Multidimensional Scaling","title":"LinearAlgebra.eigvecs","text":"eigvecs(M::MDS)\n\nGet the MDS model M eigenvectors matrix. \n\n\n\n\n\n","category":"method"},{"location":"mds/#MultivariateStats.stress","page":"Multidimensional Scaling","title":"MultivariateStats.stress","text":"stress(M::MDS)\n\nGet the stress of the MDS mode M.\n\n\n\n\n\nstress(M::MetricMDS)\n\nGet the stress of the MDS model M.\n\n\n\n\n\n","category":"function"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"This package provides following functions related to classical MDS.","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"gram2dmat\ngram2dmat!\ndmat2gram\ndmat2gram!","category":"page"},{"location":"mds/#MultivariateStats.gram2dmat","page":"Multidimensional Scaling","title":"MultivariateStats.gram2dmat","text":"gram2dmat(G)\n\nConvert a Gram matrix G to a distance matrix.\n\n\n\n\n\n","category":"function"},{"location":"mds/#MultivariateStats.gram2dmat!","page":"Multidimensional Scaling","title":"MultivariateStats.gram2dmat!","text":"gram2dmat!(D, G)\n\nConvert a Gram matrix G to a distance matrix, and write the results to D.\n\n\n\n\n\n","category":"function"},{"location":"mds/#MultivariateStats.dmat2gram","page":"Multidimensional Scaling","title":"MultivariateStats.dmat2gram","text":"dmat2gram(D)\n\nConvert a distance matrix D to a Gram matrix.\n\n\n\n\n\n","category":"function"},{"location":"mds/#MultivariateStats.dmat2gram!","page":"Multidimensional Scaling","title":"MultivariateStats.dmat2gram!","text":"dmat2gram!(G, D)\n\nConvert a distance matrix D to a Gram matrix, and write the results to G.\n\n\n\n\n\n","category":"function"},{"location":"mds/#Metric-Multidimensional-Scaling","page":"Multidimensional Scaling","title":"Metric Multidimensional Scaling","text":"","category":"section"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"This package defines a MetricMDS type to represent a (non)metric MDS model[1], and provides a set of methods to access the properties.","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"MetricMDS","category":"page"},{"location":"mds/#MultivariateStats.MetricMDS","page":"Multidimensional Scaling","title":"MultivariateStats.MetricMDS","text":"(Non)Metric Multidimensional Scaling\n\nUse this class to perform (non)metric multidimensional scaling.\n\nThere are two calling options, specified via the required keyword argument distances:\n\nmds = fit(MDS, X; distances=false, maxoutdim=size(X,1)-1)\n\nwhere X is the data matrix. Distances between pairs of columns of X are computed using the Euclidean norm. This is equivalent to performing PCA on X.\n\nmds = fit(MDS, D; distances=true, maxoutdim=size(D,1)-1)\n\nwhere D is a symmetric matrix D of distances between points.\n\nIn addition, the metric parameter specifies type of MDS, By default, it is assigned with nothing value which results in performing metric MDS with dissimilarities calculated as Euclidean distances.\n\nAn arbitrary transformation function can be provided to metric parameter to perform metric MDS with transformed proximities. The function has to accept two parameters, a vector of proximities and a vector of distances, corresponding to the proximities, to calculate disparities required for stress calculation. Internally, the proximity and distance vectors are obtained from compact triangular matrix representation of proximity and distance matrices.\n\nFor ratio MDS, a following ratio transformation function can be used\n\nmds = fit(MDS, D; distances=true, metric=((p,d)->2 .* p))\n\nFor order MDS, use isotonic regression function in the metric parameter:\n\nmds = fit(MDS, D; distances=true, metric=isotonic)\n\n\n\n\n\n","category":"type"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"The metric MDS type comes with several methods where M be an instance of MetricMDS, d be the dimension of observations, and p be the output dimension, i.e. the embedding dimension, and n is the number of the observations.","category":"page"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"fit(::Type{MetricMDS}, ::AbstractMatrix{T}; kwargs) where {T<:Real}\npredict(::MetricMDS)\nsize(::MetricMDS)\nstress(::MetricMDS)","category":"page"},{"location":"mds/#StatsAPI.fit-Union{Tuple{T}, Tuple{Type{MetricMDS}, AbstractMatrix{T}}} where T<:Real","page":"Multidimensional Scaling","title":"StatsAPI.fit","text":"fit(MetricMDS, X; kwargs...)\n\nCompute an embedding of X points by (non)metric multidimensional scaling (MDS).\n\nKeyword arguments:\n\nLet (d, n) = size(X) be respectively the input dimension and the number of observations:\n\ndistances: The choice of input (required):\nfalse: use X to calculate dissimilarity matrix using Euclidean distance\ntrue: use X input as precomputed dissimilarity symmetric matrix (distances)\nmaxoutdim: Maximum output dimension (default d-1)\nmetric : a function for calculation of disparity values\nnothing: use dissimilarity values as the disparities to perform the metric MDS (default)\nisotonic: converts dissimilarity values to ordinal disparities to perform non-metric MDS\nany two parameter disparity transformation function, where the first parameter is a vector of proximities (i.e. dissimilarities) and the second parameter is a vector of distances, e.g. (p,d)->b*p for some b is a transformation function for ratio MDS.\ntol: Convergence tolerance (default 1.0e-3)\nmaxiter: Maximum number of iterations (default 300)\ninitial: an initial reduced space point configuration\nnothing: then an initial configuration is randomly generated (default)\npre-defined matrix\nweights: a weight matrix\nnothing: then weights are set to one, w_ij = 1 (default)\npre-defined matrix\n\nNote: if the algorithm is unable to converge then ConvergenceException is thrown.\n\n\n\n\n\n","category":"method"},{"location":"mds/#StatsAPI.predict-Tuple{MetricMDS}","page":"Multidimensional Scaling","title":"StatsAPI.predict","text":"predict(M::MetricMDS)\n\nReturns a coordinate matrix of size (p n) for the MDS model M, where each column is the coordinates for an observation in the embedding space.\n\n\n\n\n\n","category":"method"},{"location":"mds/#Base.size-Tuple{MetricMDS}","page":"Multidimensional Scaling","title":"Base.size","text":"size(M::MetricMDS)\n\nReturns tuple where the first value is the MDS model M input dimension, i.e the dimension of the observation space, and the second value is the output dimension, i.e the dimension of the embedding.\n\n\n\n\n\n","category":"method"},{"location":"mds/#MultivariateStats.stress-Tuple{MetricMDS}","page":"Multidimensional Scaling","title":"MultivariateStats.stress","text":"stress(M::MetricMDS)\n\nGet the stress of the MDS model M.\n\n\n\n\n\n","category":"method"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"","category":"page"},{"location":"mds/#References","page":"Multidimensional Scaling","title":"References","text":"","category":"section"},{"location":"mds/","page":"Multidimensional Scaling","title":"Multidimensional Scaling","text":"[1]: Ingwer Borg and Patrick J. F. Groenen, \"Modern Multidimensional Scaling: Theory and Applications\", Springer, pp. 201–268, 2005.","category":"page"}] } diff --git a/dev/whiten/index.html b/dev/whiten/index.html index de956a4..b182064 100644 --- a/dev/whiten/index.html +++ b/dev/whiten/index.html @@ -1,2 +1,2 @@ -Data Transformation · MultivariateStats.jl
    Edit on GitHub

    Data Transformation

    Whitening

    A whitening transformation is a decorrelation transformation that transforms a set of random variables into a set of new random variables with identity covariance (uncorrelated with unit variances).

    In particular, suppose a random vector has covariance $\mathbf{C}$, then a whitening transform $\mathbf{W}$ is one that satisfy:

    \[ \mathbf{W}^T \mathbf{C} \mathbf{W} = \mathbf{I}\]

    Note that $\mathbf{W}$ is generally not unique. In particular, if $\mathbf{W}$ is a whitening transform, so is any of its rotation $\mathbf{W} \mathbf{R}$ with $\mathbf{R}^T \mathbf{R} = \mathbf{I}$.

    The package uses Whitening to represent a whitening transform.

    Whitening transformation can be fitted to data using the fit method.

    StatsAPI.fit — Method
    fit(Whitening, X::AbstractMatrix{T}; kwargs...)

    Estimate a whitening transform from the data given in X.

    This function returns an instance of Whitening

    Keyword Arguments:

    • regcoef: The regularization coefficient. The covariance will be regularized as follows when regcoef is positive C + (eigmax(C) * regcoef) * eye(d). Default values is zero(T).

    • dims: if 1 the transformation calculated from the row samples. fit standardization parameters in column-wise fashion; if 2 the transformation calculated from the column samples. The default is nothing, which is equivalent to dims=2 with a deprecation warning.

    • mean: The mean vector, which can be either of:

      • 0: the input data has already been centralized
      • nothing: this function will compute the mean (default)
      • a pre-computed mean vector

    Note: This function internally relies on cov_whitening to derive the transformation W.

    source
    MultivariateStats.transform — Method
    transform(f, x)

    Apply the whitening transform f to a vector or a matrix x with samples in columns, as $\mathbf{W}^T (\mathbf{x} - \boldsymbol{\mu})$.

    source
    Statistics.mean — Method
    mean(f)

    Get the mean vector of the whitening transformation f.

    Note: if mean is empty, this function returns a zero vector of length(f).

    source
    Base.size — Method
    size(f)

    Dimensions of the coefficient matrix of the whitening transform f.

    source

    Additional methods

    MultivariateStats.cov_whitening — Function
    cov_whitening(C)

    Derive the whitening transform coefficient matrix W given the covariance matrix C. Here, C can be either a square matrix, or an instance of Cholesky.

    Internally, this function solves the whitening transform using Cholesky factorization. The rationale is as follows: let $\mathbf{C} = \mathbf{U}^T \mathbf{U}$ and $\mathbf{W} = \mathbf{U}^{-1}$, then $\mathbf{W}^T \mathbf{C} \mathbf{W} = \mathbf{I}$.

    Note: The return matrix W is an upper triangular matrix.

    source
    cov_whitening(C, regcoef)

    Derive a whitening transform based on a regularized covariance, as C + (eigmax(C) * regcoef) * eye(d).

    source
    MultivariateStats.cov_whitening! — Function
    cov_whitening!(C)

    In-place version of cov_whitening(C), in which the input matrix C will be overwritten during computation. This can be more efficient when C is no longer used.

    source
    cov_whitening!(C, regcoef)

    In-place version of cov_whitening(C, regcoef), in which the input matrix C will be overwritten during computation. This can be more efficient when C is no longer used.

    source
    +Data Transformation · MultivariateStats.jl
    Edit on GitHub

    Data Transformation

    Whitening

    A whitening transformation is a decorrelation transformation that transforms a set of random variables into a set of new random variables with identity covariance (uncorrelated with unit variances).

    In particular, suppose a random vector has covariance $\mathbf{C}$, then a whitening transform $\mathbf{W}$ is one that satisfy:

    \[ \mathbf{W}^T \mathbf{C} \mathbf{W} = \mathbf{I}\]

    Note that $\mathbf{W}$ is generally not unique. In particular, if $\mathbf{W}$ is a whitening transform, so is any of its rotation $\mathbf{W} \mathbf{R}$ with $\mathbf{R}^T \mathbf{R} = \mathbf{I}$.

    The package uses Whitening to represent a whitening transform.

    Whitening transformation can be fitted to data using the fit method.

    StatsAPI.fit — Method
    fit(Whitening, X::AbstractMatrix{T}; kwargs...)

    Estimate a whitening transform from the data given in X.

    This function returns an instance of Whitening

    Keyword Arguments:

    • regcoef: The regularization coefficient. The covariance will be regularized as follows when regcoef is positive C + (eigmax(C) * regcoef) * eye(d). Default values is zero(T).

    • dims: if 1 the transformation calculated from the row samples. fit standardization parameters in column-wise fashion; if 2 the transformation calculated from the column samples. The default is nothing, which is equivalent to dims=2 with a deprecation warning.

    • mean: The mean vector, which can be either of:

      • 0: the input data has already been centralized
      • nothing: this function will compute the mean (default)
      • a pre-computed mean vector

    Note: This function internally relies on cov_whitening to derive the transformation W.

    source
    MultivariateStats.transform — Method
    transform(f, x)

    Apply the whitening transform f to a vector or a matrix x with samples in columns, as $\mathbf{W}^T (\mathbf{x} - \boldsymbol{\mu})$.

    source
    Statistics.mean — Method
    mean(f)

    Get the mean vector of the whitening transformation f.

    Note: if mean is empty, this function returns a zero vector of length(f).

    source
    Base.size — Method
    size(f)

    Dimensions of the coefficient matrix of the whitening transform f.

    source

    Additional methods

    MultivariateStats.cov_whitening — Function
    cov_whitening(C)

    Derive the whitening transform coefficient matrix W given the covariance matrix C. Here, C can be either a square matrix, or an instance of Cholesky.

    Internally, this function solves the whitening transform using Cholesky factorization. The rationale is as follows: let $\mathbf{C} = \mathbf{U}^T \mathbf{U}$ and $\mathbf{W} = \mathbf{U}^{-1}$, then $\mathbf{W}^T \mathbf{C} \mathbf{W} = \mathbf{I}$.

    Note: The return matrix W is an upper triangular matrix.

    source
    cov_whitening(C, regcoef)

    Derive a whitening transform based on a regularized covariance, as C + (eigmax(C) * regcoef) * eye(d).

    source
    MultivariateStats.cov_whitening! — Function
    cov_whitening!(C)

    In-place version of cov_whitening(C), in which the input matrix C will be overwritten during computation. This can be more efficient when C is no longer used.

    source
    cov_whitening!(C, regcoef)

    In-place version of cov_whitening(C, regcoef), in which the input matrix C will be overwritten during computation. This can be more efficient when C is no longer used.

    source