diff --git a/.travis.yml b/.travis.yml index a8c80d9..6cd59a8 100644 --- a/.travis.yml +++ b/.travis.yml @@ -1,15 +1,21 @@ language: julia + os: - linux - osx + notifications: email: false + julia: - - 0.6 + - 0.7 + - 1.0 - nightly + matrix: allow_failures: - julia: nightly -#script: -# - if [[ -a .git/shallow ]]; then git fetch --unshallow; fi -# - julia -e 'Pkg.init(); Pkg.clone(pwd()); Pkg.test("ImplicitEquations")' + +script: + - if [[ -a .git/shallow ]]; then git fetch --unshallow; fi + - julia -e 'using Pkg; Pkg.clone(pwd()); Pkg.test("ImplicitEquations")' diff --git a/LICENSE.md b/LICENSE.md index f6b05c8..48504b9 100644 --- a/LICENSE.md +++ b/LICENSE.md @@ -1,6 +1,6 @@ The ImplicitEquations.jl package is licensed under the MIT "Expat" License: -> Copyright (c) 2014-16: jverzani. +> Copyright (c) 2014-18: jverzani. > > Permission is hereby granted, free of charge, to any person obtaining > a copy of this software and associated documentation files (the diff --git a/README.md b/README.md index e544763..4bd8332 100644 --- a/README.md +++ b/README.md @@ -1,5 +1,3 @@ -[![ImplicitEquations](http://pkg.julialang.org/badges/ImplicitEquations_0.6.svg)](http://pkg.julialang.org/?pkg=ImplicitEquations&ver=0.6) -  Linux: [![Build Status](https://travis-ci.org/jverzani/ImplicitEquations.jl.svg?branch=master)](https://travis-ci.org/jverzani/ImplicitEquations.jl)   Windows: [![Build Status](https://ci.appveyor.com/api/projects/status/github/jverzani/ImplicitEquations.jl?branch=master&svg=true)](https://ci.appveyor.com/project/jverzani/implicitequations-jl) @@ -32,5 +30,3 @@ plot(f ⩵ 0) # \Equal[tab] ``` ![DevilsCurve](http://i.imgur.com/LChTzC1.png) - - diff --git a/REQUIRE b/REQUIRE index 83bb7a9..1e8b59e 100644 --- a/REQUIRE +++ b/REQUIRE @@ -1,5 +1,3 @@ -julia 0.6 -ForwardDiff 0.3.0 -ValidatedNumerics 0.5.0 -RecipesBase 0.0.6 -Compat 0.8.6 \ No newline at end of file +julia 0.7 +IntervalArithmetic 0.15.0 +RecipesBase 0.5.0 diff --git a/appveyor.yml b/appveyor.yml index fe914b1..c34890d 100644 --- a/appveyor.yml +++ b/appveyor.yml @@ -1,13 +1,19 @@ environment: matrix: - - JULIA_URL: "https://julialang-s3.julialang.org/bin/winnt/x86/0.6/julia-0.6-latest-win32.exe" - - JULIA_URL: "https://julialang-s3.julialang.org/bin/winnt/x64/0.6/julia-0.6-latest-win64.exe" - - JULIA_URL: "https://julialangnightlies-s3.julialang.org/bin/winnt/x86/julia-latest-win32.exe" - - JULIA_URL: "https://julialangnightlies-s3.julialang.org/bin/winnt/x64/julia-latest-win64.exe" + - julia_version: 0.7 + - julia_version: 1.0 + - julia_version: latest + +platform: + - x86 # 32-bit + - x64 # 64-bit + +## uncomment the following lines to allow failures on nightly julia +## (tests will run but not make your overall status red) matrix: allow_failures: - - JULIA_URL: "https://julialangnightlies-s3.julialang.org/bin/winnt/x86/julia-latest-win32.exe" - - JULIA_URL: "https://julialangnightlies-s3.julialang.org/bin/winnt/x64/julia-latest-win64.exe" + - julia_version: latest + branches: only: @@ -21,19 +27,12 @@ notifications: on_build_status_changed: false install: - - ps: "[System.Net.ServicePointManager]::SecurityProtocol = [System.Net.SecurityProtocolType]::Tls12" -# Download most recent Julia Windows binary - - ps: (new-object net.webclient).DownloadFile( - $env:JULIA_URL, - "C:\projects\julia-binary.exe") -# Run installer silently, output to C:\projects\julia - - C:\projects\julia-binary.exe /S /D=C:\projects\julia + - ps: iex ((new-object net.webclient).DownloadString("https://raw.githubusercontent.com/JuliaCI/Appveyor.jl/version-1/bin/install.ps1")) build_script: -# Need to convert from shallow to complete for Pkg.clone to work - - IF EXIST .git\shallow (git fetch --unshallow) - - C:\projects\julia\bin\julia -e "versioninfo(); - Pkg.clone(pwd(), \"ImplicitEquations\"); Pkg.build(\"ImplicitEquations\")" + - echo "%JL_BUILD_SCRIPT%" + - C:\julia\bin\julia -e "%JL_BUILD_SCRIPT%" test_script: - - C:\projects\julia\bin\julia --check-bounds=yes -e "Pkg.test(\"ImplicitEquations\")" \ No newline at end of file + - echo "%JL_TEST_SCRIPT%" + - C:\julia\bin\julia -e "%JL_TEST_SCRIPT%" diff --git a/docs/examples.ipynb b/docs/examples.ipynb index 7c5519f..f21e7dc 100644 --- a/docs/examples.ipynb +++ b/docs/examples.ipynb @@ -4,14 +4,16 @@ {"cell_type":"markdown","source":"

This paper by Tupper details a method for graphing two-dimensional implicit equations and inequalities. This package gives an implementation of the paper's basic algorithms to allow the julia user to naturally represent and easily render graphs of implicit functions and equations.

","metadata":{}}, {"cell_type":"markdown","source":"

The basic idea is to express a equation in $x$ and $y$ variables in terms of a function of two variables as a predicate. The plot function Plots is used to plot these predicates.

","metadata":{}}, {"cell_type":"markdown","source":"

For example, the Devils curve is graphed over the default region as follows:

","metadata":{}}, 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"},"metadata":{"image/png":{"height":480,"width":600}},"execution_count":null}],"cell_type":"code","source":["using Plots, ImplicitEquations\npyplot()\n\na,b = -1,2\nf(x,y) = y^4 - x^4 + a*y^2 + b*x^2\nr = (f ⩵ 0) # \\Equal[tab]\nplot(r)"],"metadata":{},"execution_count":null}, + +{"outputs":[{"output_type":"execute_result","data":{"text/plain":"Plot(...)","image/png":"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"},"metadata":{"image/png":{"height":480,"width":600}},"execution_count":1}],"cell_type":"code","source":["using Plots, ImplicitEquations\n\na,b = -1,2\nf(x,y) = y^4 - x^4 + a*y^2 + b*x^2\nr = (f ⩵ 0) # \\Equal[tab]\nplot(r)"],"metadata":{},"execution_count":1}, {"cell_type":"markdown","source":"

The f ⩵ 0 expression above creates a Predicate that is graphed by plot. Predicates are generated using the function Lt, Le, Eq, Neq, Ge, and Gt. The infix unicode operators (\\ll[tab]), (\\leqq[tab]), (\\Equal[tab]), (\\lessgtr[tab]) or (\\gtrless[tab]), (\\geqq[tab]), (\\leqq[tab]) may also be used.

","metadata":{}}, {"cell_type":"markdown","source":"

For example, the Trident of Newton can be represented in Cartesian form as follows:

","metadata":{}}, -{"outputs":[{"output_type":"execute_result","data":{"text/plain":"Plot(...)","image/png":"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"},"metadata":{"image/png":{"height":480,"width":600}},"execution_count":null}],"cell_type":"code","source":["## trident of Newton\nc,d,e,h = 1,1,1,1\nf(x,y) = x*y\ng(x,y) = c*x^3 + d*x^2 + e*x + h\nplot(Eq(f,g)) ## aka f ⩵ g (using Unicode\\Equal)"],"metadata":{},"execution_count":null}, +{"outputs":[{"output_type":"execute_result","data":{"text/plain":"Plot(...)","image/png":"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"},"metadata":{"image/png":{"height":480,"width":600}},"execution_count":1}],"cell_type":"code","source":["## trident of Newton\nc,d,e,h = 1,1,1,1\nf(x,y) = x*y\ng(x,y) = c*x^3 + d*x^2 + e*x + h\nplot(Eq(f,g)) ## aka f ⩵ g (using Unicode\\Equal)"],"metadata":{},"execution_count":1}, {"cell_type":"markdown","source":"

Inequalities can be graphed as well

","metadata":{}}, -{"outputs":[{"output_type":"execute_result","data":{"text/plain":"Plot(...)","image/png":"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"},"metadata":{"image/png":{"height":480,"width":600}},"execution_count":null}],"cell_type":"code","source":["f(x,y) = x - y\nplot(f ≪ 0) # \\ll[tab]"],"metadata":{},"execution_count":null}, +{"outputs":[{"output_type":"execute_result","data":{"text/plain":"Plot(...)","image/png":"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"},"metadata":{"image/png":{"height":480,"width":600}},"execution_count":1}],"cell_type":"code","source":["f(x,y) = x - y\nplot(f ≪ 0) # \\ll[tab]"],"metadata":{},"execution_count":1}, {"cell_type":"markdown","source":"

This example is from Tupper's paper:

","metadata":{}}, -{"outputs":[{"output_type":"execute_result","data":{"text/plain":"Plot(...)","image/png":"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"},"metadata":{"image/png":{"height":480,"width":600}},"execution_count":null}],"cell_type":"code","source":["f(x,y) = (y-5)* cos(4sqrt((x-4)^2 +y^2))\ng(x,y) = x * sin(2*sqrt(x^2 + y^2))\n\nplot(Ge(f, g), xlims=(-10, 10), ylims=(-10, 10))"],"metadata":{},"execution_count":null}, +{"outputs":[{"output_type":"execute_result","data":{"text/plain":"Plot(...)","image/png":"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"},"metadata":{"image/png":{"height":480,"width":600}},"execution_count":1}],"cell_type":"code","source":["f(x,y) = (y-5)* cos(4sqrt((x-4)^2 +y^2))\ng(x,y) = x * sin(2*sqrt(x^2 + y^2))\n\nplot(Ge(f, g), xlims=(-10, 10), ylims=(-10, 10))"],"metadata":{},"execution_count":1}, + {"cell_type":"markdown","source":"

This graph illustrates the algorithm employed to graph f ⩵ 0 where f(x,y) = y - sqrt(x):

","metadata":{}}, {"cell_type":"markdown","source":"

\"Algorithm\"

","metadata":{}}, {"cell_type":"markdown","source":"

The basic algorithm is to initially break up the graphing region into square regions. (This uses the number of pixels, which are specified by W and H above.)

","metadata":{}}, @@ -20,11 +22,13 @@ {"cell_type":"markdown","source":"

above is repeated until subdivision would be below the pixel level. At which point, the remaining \"1-by-1\" pixels are checked for possible solutions, for example for equalities where continuity is known a random sample of points is investigated with the intermediate value theorem. A region may be labeled \"black\" or \"red\" if the predicate is still ambiguous.

","metadata":{}}, {"cell_type":"markdown","source":"

The graph plots each \"black\" region as a \"pixel\". The \"red\" regions may optionally be colored, if a named color is passed through the keyword red.

","metadata":{}}, {"cell_type":"markdown","source":"

For example, the Devil's curve is a bit different with red coloring:

","metadata":{}}, -{"outputs":[{"output_type":"execute_result","data":{"text/plain":["UndefVarError(:get_l171)\n"]},"metadata":{},"execution_count":null}],"cell_type":"code","source":["a,b = -1,2\nf(x,y) = y^4 - x^4 + a*y^2 + b*x^2\nr = (f ⩵ 0)\nplot(r, red=:red) # show undecided regions in red"],"metadata":{},"execution_count":null}, + +{"outputs":[{"output_type":"execute_result","data":{"text/plain":"Plot(...)","image/png":"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"},"metadata":{"image/png":{"height":480,"width":600}},"execution_count":1}],"cell_type":"code","source":["a,b = -1,2\nf(x,y) = y^4 - x^4 + a*y^2 + b*x^2\nr = (f ⩵ 0)\nplot(r, red=:red) # show undecided regions in red"],"metadata":{},"execution_count":1}, {"cell_type":"markdown","source":"

The plot function accepts the usual keywords of Plots and also:

","metadata":{}}, {"cell_type":"markdown","source":"","metadata":{}}, {"cell_type":"markdown","source":"

This example, the Batman equation, Uses a few new things: the screen function is used to restrict ranges and logical operators to combine predicates.

","metadata":{}}, -{"outputs":[{"output_type":"execute_result","data":{"text/plain":["UndefVarError(:get_l171)\n"]},"metadata":{},"execution_count":null}],"cell_type":"code","source":["f0(x,y) = ((x/7)^2 + (y/3)^2 - 1) * screen(abs(x)>3) * screen(y > -3*sqrt(33)/7) \nf1(x,y) = ( abs(x/2)-(3 * sqrt(33)-7) * x^2/112 -3 +sqrt(1-(abs((abs(x)-2))-1)^2)-y)\nf2(x,y) = y - (9 - 8*abs(x)) * screen((abs(x)>= 3/4) & (abs(x) <= 1) )\nf3(x,y) = y - (3*abs(x) + 3/4) * I_((1/2 < abs(x)) & (abs(x) < 3/4)) # alternate name for screen\nf4(x,y) = y - 2.25 * I_(abs(x) <= 1/2) \nf5(x,y) = (6 * sqrt(10)/7 + (1.5-.5 * abs(x)) - 6 * sqrt(10)/14 * sqrt(4-(abs(x)-1)^2) -y) * screen(abs(x) >= 1)\n\nr = (f0 ⩵ 0) | (f1 ⩵ 0) | (f2 ⩵ 0) | (f3 ⩵ 0) | (f4 ⩵ 0) | (f5 ⩵ 0)\nplot(r, xlims=(-7, 7), ylims=(-4, 4), red=:black)"],"metadata":{},"execution_count":null}, +{"outputs":[{"output_type":"execute_result","data":{"text/plain":"Plot(...)","image/png":"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"},"metadata":{"image/png":{"height":480,"width":600}},"execution_count":1}],"cell_type":"code","source":["f0(x,y) = ((x/7)^2 + (y/3)^2 - 1) * screen(abs(x)>3) * screen(y > -3*sqrt(33)/7)\nf1(x,y) = ( abs(x/2)-(3 * sqrt(33)-7) * x^2/112 -3 +sqrt(1-(abs((abs(x)-2))-1)^2)-y)\nf2(x,y) = y - (9 - 8*abs(x)) * screen((abs(x)>= 3/4) & (abs(x) <= 1) )\nf3(x,y) = y - (3*abs(x) + 3/4) * I_((1/2 < abs(x)) & (abs(x) < 3/4)) # alternate name for screen\nf4(x,y) = y - 2.25 * I_(abs(x) <= 1/2)\nf5(x,y) = (6 * sqrt(10)/7 + (1.5-.5 * abs(x)) - 6 * sqrt(10)/14 * sqrt(4-(abs(x)-1)^2) -y) * screen(abs(x) >= 1)\n\nr = (f0 ⩵ 0) | (f1 ⩵ 0) | (f2 ⩵ 0) | (f3 ⩵ 0) | (f4 ⩵ 0) | (f5 ⩵ 0)\nplot(r, xlims=(-7, 7), ylims=(-4, 4), red=:black)"],"metadata":{},"execution_count":1}, + {"cell_type":"markdown","source":"

The above example illustrates a few things:

","metadata":{}}, {"cell_type":"markdown","source":"","metadata":{}}, {"cell_type":"markdown","source":"

Maps

","metadata":{"internals":{"slide_type":"subslide","slide_helper":"subslide_end"},"slideshow":{"slide_type":"slide"},"slide_helper":"slide_end"}}, @@ -34,28 +38,32 @@ {"cell_type":"markdown","source":"

As well, the pieces plotted are polygonal approximations to the correct image. Consequently, gaps can appear.

","metadata":{}}, {"cell_type":"markdown","source":"

A \"typical\" application

","metadata":{"internals":{"slide_type":"subslide","slide_helper":"subslide_end"},"slideshow":{"slide_type":"slide"},"slide_helper":"slide_end"}}, {"cell_type":"markdown","source":"

A common calculus problem is to find the tangent line using implicit differentiation. We can plot the predicate to create the implicit graph, then add a layer with plot!:

","metadata":{}}, 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"},"metadata":{"image/png":{"height":480,"width":600}},"execution_count":null}],"cell_type":"code","source":["f(x,y) = x^2 + y^2\nplot(f ⩵ 2*3^2)\n\n## now add tangent at (3,3)\na,b = 3,3\ndydx(a,b) = -b/a # implicit differentiate to get dy/dx =-y/x\ntl(x) = b + dydx(a,b)*(x-a) \nplot!(tl, linewidth=3, -5, 5)"],"metadata":{},"execution_count":null}, + +{"outputs":[{"output_type":"execute_result","data":{"text/plain":"Plot(...)","image/png":"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"},"metadata":{"image/png":{"height":480,"width":600}},"execution_count":1}],"cell_type":"code","source":["f(x,y) = x^2 + y^2\nplot(f ⩵ 2*3^2)\n\n## now add tangent at (3,3)\na,b = 3,3\ndydx(a,b) = -b/a # implicit differentiate to get dy/dx =-y/x\ntl(x) = b + dydx(a,b)*(x-a)\nplot!(tl, linewidth=3, -5, 5)"],"metadata":{},"execution_count":1}, + {"cell_type":"markdown","source":"

Alternatives

","metadata":{"internals":{"slide_type":"subslide","slide_helper":"subslide_end"},"slideshow":{"slide_type":"slide"},"slide_helper":"slide_end"}}, {"cell_type":"markdown","source":"

Many such plots are simply a single level of a contour plot. Contour plots can be drawn with the Plots package too. A simple contour plot will be faster than this package.

","metadata":{}}, {"cell_type":"markdown","source":"

The SymPy package exposes SymPy's plot_implicit feature that will implicitly plot a symbolic expression in 2 variables including inequalities. The algorithm there also follows Tupper and uses interval arithmetic, as possible.

","metadata":{}}, -{"cell_type":"markdown","source":"

The package IntervalConstraintProgramming also allows for this type of graphing, and momre.

","metadata":{}}, +{"cell_type":"markdown","source":"

The package IntervalConstraintProgramming also allows for this type of graphing, and more.

","metadata":{}}, {"cell_type":"markdown","source":"

TODO

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LOTS:

","metadata":{}}, {"cell_type":"markdown","source":"","metadata":{}} ], "metadata": { "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", "name": "julia", - "version": "0.4" + "version": "0.6" }, "kernelspec": { - "display_name": "Julia 0.4.0", + "display_name": "Julia 0.6.0", "language": "julia", - "name": "julia-0.4" + "name": "julia-0.6" } }, "nbformat": 4, - "nbformat_minor": 0 + "nbformat_minor": 2 } diff --git a/docs/examples.md b/docs/examples.md index d77e937..543f5fb 100644 --- a/docs/examples.md +++ b/docs/examples.md @@ -22,7 +22,6 @@ is graphed over the default region as follows: ``` using Plots, ImplicitEquations -pyplot() a,b = -1,2 f(x,y) = y^4 - x^4 + a*y^2 + b*x^2 @@ -121,11 +120,11 @@ Uses a few new things: the `screen` function is used to restrict ranges and logical operators to combine predicates. ``` -f0(x,y) = ((x/7)^2 + (y/3)^2 - 1) * screen(abs(x)>3) * screen(y > -3*sqrt(33)/7) +f0(x,y) = ((x/7)^2 + (y/3)^2 - 1) * screen(abs(x)>3) * screen(y > -3*sqrt(33)/7) f1(x,y) = ( abs(x/2)-(3 * sqrt(33)-7) * x^2/112 -3 +sqrt(1-(abs((abs(x)-2))-1)^2)-y) f2(x,y) = y - (9 - 8*abs(x)) * screen((abs(x)>= 3/4) & (abs(x) <= 1) ) f3(x,y) = y - (3*abs(x) + 3/4) * I_((1/2 < abs(x)) & (abs(x) < 3/4)) # alternate name for screen -f4(x,y) = y - 2.25 * I_(abs(x) <= 1/2) +f4(x,y) = y - 2.25 * I_(abs(x) <= 1/2) f5(x,y) = (6 * sqrt(10)/7 + (1.5-.5 * abs(x)) - 6 * sqrt(10)/14 * sqrt(4-(abs(x)-1)^2) -y) * screen(abs(x) >= 1) r = (f0 ⩵ 0) | (f1 ⩵ 0) | (f2 ⩵ 0) | (f3 ⩵ 0) | (f4 ⩵ 0) | (f5 ⩵ 0) @@ -186,7 +185,7 @@ plot(f ⩵ 2*3^2) ## now add tangent at (3,3) a,b = 3,3 dydx(a,b) = -b/a # implicit differentiate to get dy/dx =-y/x -tl(x) = b + dydx(a,b)*(x-a) +tl(x) = b + dydx(a,b)*(x-a) plot!(tl, linewidth=3, -5, 5) ``` @@ -204,7 +203,7 @@ interval arithmetic, as possible. The package [IntervalConstraintProgramming ](https://github.com/dpsanders/IntervalConstraintProgramming.jl) -also allows for this type of graphing, and momre. +also allows for this type of graphing, and more. ## TODO @@ -221,4 +220,3 @@ also allows for this type of graphing, and momre. * Tupper sketches out how to be more rigorous with computing whether a region is black or white. * increase speed (could color 1-pixel regions better if so, perhaps; division checks; type stability). - diff --git a/src/ImplicitEquations.jl b/src/ImplicitEquations.jl index 478a7ac..afa5eed 100644 --- a/src/ImplicitEquations.jl +++ b/src/ImplicitEquations.jl @@ -1,12 +1,8 @@ -__precompile__(true) - module ImplicitEquations -using ForwardDiff -import ValidatedNumerics: Interval, diam, isempty +import IntervalArithmetic: Interval, diam, isempty using RecipesBase -using Compat include("predicates.jl") include("intervals.jl") diff --git a/src/intervals.jl b/src/intervals.jl index f7cab2e..33ad7ad 100644 --- a/src/intervals.jl +++ b/src/intervals.jl @@ -4,7 +4,7 @@ import Base: <, <=, ==, !==, >=, >, +, -, *, /, ^ ## a few definitionsn for ValidatedNumerics that don't fit in there: -## Validated numerics doesn't define these, as the order ins't a total order +## Validated numerics doesn't define these, as the order ins't a total order Base.isless(i::Interval{T}, j::Interval{S}) where {T<:Real, S<:Real} = isless(i.hi, j.lo) #<=(i::Interval{T}, j::Interval{S}) where {T<:Real, S<:Real} = <=(i.hi, j.lo) @@ -14,7 +14,7 @@ Base.isless(i::Interval{T}, j::Interval{S}) where {T<:Real, S<:Real} = isless(i. ## BInterval represents TRUE (true, true), FALSE (false, false) and MAYBE (false, true) -immutable BInterval <: Integer +struct BInterval <: Integer lo :: Bool hi :: Bool @@ -50,13 +50,13 @@ function negate_op(op) end ## OIinterval includes interval, if defined on interval and if continuous on interval -immutable OInterval <: Real +struct OInterval <: Real val::Interval def::BInterval cont::BInterval OInterval(val, def, cont) = new(val, def, cont) end - +(O::OInterval)(o::OInterval) = o Base.show(io::IO, o::OInterval) = print(io, "OInterval: ", o.val, " def=", o.def, " cont=",o.cont) ## some outer constructors... @@ -66,22 +66,16 @@ OInterval(a) = OInterval(a,a) # thin one... OInterval(i::Interval) = OInterval(i.lo, i.hi) Base.convert(::Type{OInterval}, i::Interval) = OInterval(i.lo, i.hi) -Base.convert(::Type{OInterval}, x::S) where {S<:Real}= OInterval(x) -Base.promote_rule(::Type{OInterval}, ::Type{ForwardDiff.Dual{N,B}}) where {N,B<:Real} = warn("defined to remove ambiguity") + Base.promote_rule(::Type{OInterval}, ::Type{A}) where {A<:Real} = OInterval ## A region is two OIntervals. -immutable Region +struct Region x::OInterval y::OInterval end -## not good for v0.5+ -#call(f::Function, u::Region) = f(u.x, u.y) - - -#ValidatedNumerics.diam(x::OInterval) = diam(x.val) -diam(x::OInterval) = diam(x.val) +ImplicitEquations.diam(x::OInterval) = diam(x.val) ## extend functions for OInterval ## Notice these return BIntervals -- not Bools @@ -116,7 +110,7 @@ rather a `BInterval` which allows for a "MAYBE" state. As such, a simple ternary operator, like `x > 0 ? 1 : NaN` won't work, to screen values. """ -screen(ex) = (ex == FALSE) ? NaN : 1 +screen(ex) = (ex == FALSE) ? NaN : 1 const I_ = screen # indicator function like! ## Functions which are continuous everywhere @@ -159,7 +153,7 @@ Base.tanh(x::OInterval) = sinh(x)/cosh(x) Base.coth(x::OInterval) = 1/tanh(x) function Base.asin(x::OInterval) - if x.val.hi < -1.0 || x.val.lo > 1.0 + if x.val.hi < -1.0 || x.val.lo > 1.0 OInterval(x.val, FALSE, FALSE) elseif (x.val.lo < -1.0) & (x.val.hi > 1.0) OInterval(Interval(-pi/2, pi/2), x.def & MAYBE, x.cont) @@ -208,7 +202,7 @@ Base.exp(x::OInterval) = OInterval(exp(x.val), x.def, x.cont) ## / ## division is slow function /(x::OInterval, y::OInterval) - ## 0 is the issue. + ## 0 is the issue. if 0.0 ∈ y.val ## maybe defined, maybe continuous OInterval(x.val/y.val, x.def & MAYBE, x.cont & MAYBE) @@ -218,7 +212,7 @@ function /(x::OInterval, y::OInterval) end ## log -function Base.log(x::OInterval) +function Base.log(x::OInterval) if x.val.hi <= 0 OInterval(x.val, FALSE, FALSE) elseif x.val.lo <= 0 @@ -254,7 +248,6 @@ function ^(x::OInterval, q::Rational) OInterval(val, x.def, x.cont) end -^(x::OInterval, r::ForwardDiff.Dual) = warn("defined to resolve ambiguity") function ^(x::OInterval, r::Real) r < 0 && return(1/x^(-r)) if x.val.hi < 0 @@ -287,7 +280,7 @@ end Base.max(x::OInterval, y::OInterval) = OInterval(max(x.val, y.val), x.def & y.def, x.cont & y.cont) Base.min(x::OInterval, y::OInterval) = OInterval(min(x.val, y.val), x.def & y.def, x.cont & y.cont) - + ## others sign, mod, ... function Base.sign(x::OInterval) @@ -304,7 +297,7 @@ function xy_region(u, L, R, B, T, W, H) c = B + py.lo * (T - B) / H d = B + (py.hi) * (T - B) / H delta = sqrt(eps()) - + x, y = OInterval(a+(u.x.cont==TRUE)*delta,b-delta), OInterval(c+0*delta,d-delta) x, y end @@ -324,7 +317,7 @@ function compute(p::Pred, u::Region, L, R, B, T, W, H) (fxy.def == FALSE) && return (FALSE) isempty(fxy.val) && return (FALSE & fxy.def) - + if p.op === == return((p.val ∈ fxy.val) ? MAYBE : FALSE) elseif negate_op(p.op) === == @@ -340,7 +333,7 @@ end ## build up answer function compute(ps::Preds, u::Region, L, R, B, T, W, H) vals = [compute(p, u, L, R, B, T, W, H) for p in ps.ps] - val = shift!(vals) + val = popfirst!(vals) for i in 1:length(ps.ops) val = ps.ops[i](val, vals[i]) end @@ -351,14 +344,14 @@ end Does this function have a zero crossing? Heuristic check. -We return `TRUE` or `MAYBE`. However, that +We return `TRUE` or `MAYBE`. However, that leaves some functions showing too much red in the case where there is no zero. """ function cross_zero(r::Pred, u::Region, L, R, B, T, W, H) x, y = xy_region(u, L, R, B, T, W, H) dx, dy = diam(x), diam(y) - + n = 20 # number of random points chosen λ1s, λ2s = [0.0; 1.0;rand(n)], [0.0; 1.0; rand(n)] β1s, β2s = [1.0; 0.0; rand(n)], [1.0; 0.0; rand(n)] @@ -370,7 +363,7 @@ function cross_zero(r::Pred, u::Region, L, R, B, T, W, H) val = (r.f(ll...) - r.val) * (r.f(ur...) - r.val) ((val <= 0)==TRUE) && return(TRUE) end - return(MAYBE) + return(MAYBE) end diff --git a/src/plot_recipe.jl b/src/plot_recipe.jl index 3326c9c..3f40a57 100644 --- a/src/plot_recipe.jl +++ b/src/plot_recipe.jl @@ -38,7 +38,7 @@ plot(f == 0) c,d,e,h = 1,1,1,1 f(x,y) = x*y g(x,y) =c*x^3 + d*x^2 + e*x + h -plot(eq(f,g), title="Trident of Newton") ## aka f ⩵ g (using Unicode\Equal[tab]) +plot(eq(f,g), title="Trident of Newton") ## aka f ⩵ g (using Unicode\\Equal[tab]) ## inequality f(x,y)= (y-5)*cos(4*sqrt((x-4)^2 + y^2)) @@ -49,7 +49,7 @@ plot(r, (-10, 10), (-10, 10), N=9, M=9) # (xmin, xmax), (ymin, ymax), """ plot_implicit = nothing -## Helpers to convert +## Helpers to convert linterp(A,B,a,b,W) = (a + A/W*(b-a),a + B/W*(b-a)) function xyrange(u, L, R, B, T, W, H; offset=0) @@ -58,7 +58,7 @@ function xyrange(u, L, R, B, T, W, H; offset=0) end -function get_xs_ys(map::Void, rs, L, R, B, T, W, H) +function get_xs_ys(map::Nothing, rs, L, R, B, T, W, H) xs = Float64[] ys = Float64[] for u in rs @@ -134,14 +134,14 @@ end M=8, # oddly m as keyword fails. 9/8 too slow red=nothing, # or :red ... black=:black, - map=nothing # union(Void, Function...) + map=nothing # union(Nothing, Function...) ) - + # L, R = extrema(x) # B, T = extrema(y) - xlims = get(d,:xlims, (-5,5)) - ylims = get(d, :ylims, (-5,5)) + xlims = get(plotattributes,:xlims, (-5,5)) + ylims = get(plotattributes, :ylims, (-5,5)) L, R = extrema(xlims) B, T = extrema(ylims) @@ -154,15 +154,16 @@ end ## add red as a series if length(r) > 0 && red != nothing @series begin - xs, ys = get_l171 - get_xs_ys(map, r, L, R, B, T, W, H) - + + xs, ys = get_xs_ys(r, L, R, B, T, W, H) + + seriestype := :shape fillcolor := red linewidth := 0 x := xs y := ys - + () end end @@ -179,9 +180,7 @@ end xs, ys = get_xs_ys(map, b, L, R, B, T, W, H) x --> xs y --> ys - - () - -end + () +end diff --git a/src/predicates.jl b/src/predicates.jl index 2dfe153..1738fd5 100644 --- a/src/predicates.jl +++ b/src/predicates.jl @@ -14,12 +14,12 @@ inquality, and either another function or a real number. They are conveniently created by the functions `Lt`, `Le`, `Eq`, `Neq`, `Ge`, and `Gt`. The equivalent unicode operators: -* `≪` (`\ll[tab]`), -* `≦` (`\leqq[tab]`), -* `⩵` (`\Equal[tab]`), -* `≶` (`\lessgtr[tab]`) or `≷` (`\gtrless[tab]`), -* `≧` (`\geqq[tab]`), -* `≫` (`\leqq[tab]`) may also be used. +* `≪` (`\\ll[tab]`), +* `≦` (`\\leqq[tab]`), +* `⩵` (`\\Equal[tab]`), +* `≶` (`\\lessgtr[tab]`) or `≷` (`\\gtrless[tab]`), +* `≧` (`\\geqq[tab]`), +* `≫` (`\\leqq[tab]`) may also be used. The use of Julia's usual comparison operators is no longer supported. @@ -28,7 +28,7 @@ To combine predicates, `&` and `|` can be used. To negate a predicate, `!` is used. """ -type Pred <: Predicate +mutable struct Pred <: Predicate f::Function op val @@ -46,11 +46,6 @@ preds = [(:Lt, :≪, :<), # \ll for (fn, uop, op) in preds fnname = string(fn) @eval begin - @doc """ - `$($fnname)`: Create predicate for plotting. -The operators are `Lt` (≪, \ll[tab]), `Le` (≦ \leqq[tab]), `Ge` (≧ \geqq[tab]), `Gt` (≫ \gg[tab]), -`Eq` (⩵ \Equal[tab]), or `Neq` (≷ \gtrless[tab] or ≶ \lessgtr[tab]). -""" -> ($fn)(f::Function, x::Real) = Pred(f, $op, x) ($uop)(f::Function, x::Real) = ($fn)(f, x) ($fn)(f::Function, g::Function) = $(fn)((x,y) -> f(x,y) - g(x,y), 0) @@ -60,22 +55,6 @@ The operators are `Lt` (≪, \ll[tab]), `Le` (≦ \leqq[tab]), `Ge` (≧ \geqq[t eval(Expr(:export, uop)) end -# <(f::Function, x::Real) = Pred(f, < , x) -# <(f::Function, g::Function) = Pred((x,y) -> f(x,y) - g(x,y), < , 0) - - - -# <=(f::Function, x::Real) = Pred(f, <= , x) -# <=(f::Function, g::Function) = Pred((x,y) -> f(x,y) - g(x,y), <= , 0) - -# ==(f::Function, x::Real) = Pred(f, == , x) -# ## ==(f::Function, g::Function) this crosses up Gadfly and others so... -# eq(f::Function, g::Function) = Pred((x,y) -> f(x,y) - g(x,y), == , 0) -# ## unicode variants -# ⩵(f::Function, x::Real) = f == x -# ⩵(f::Function, g::Function) = eq(f,g) - - Neq(f::Function, x::Real) = Pred(f, !== , x) Neq(f::Function, g::Function) = Neq((x,y) -> f(x,y) - g(x,y), 0) @@ -91,17 +70,6 @@ Neq(f::Function, g::Function) = Neq((x,y) -> f(x,y) - g(x,y), 0) - -#>=(f::Function, x::Real) = Pred(f, >= , x) -#>=(f::Function, g::Function) = Pred((x,y) -> f(x,y) - g(x,y), >= , 0) - -#>(f::Function, x::Real) = Pred(f, > , x) -#>(f::Function, g::Function) = Pred((x,y) -> f(x,y) - g(x,y), > , 0) - -#Base.isless(x::Real, f::Function) = Ge(F, x) #(f >= x) -#Base.isless(f::Function, x::Real) = Lt(f, x) #(f < x) - - """ Predicates can be joined together with either `&` or `|`. Individual @@ -109,7 +77,7 @@ predicates can be negated with `!`. The parsing rules require the individual predicates to be enclosed with parentheses, as in `(f==0) | (g==0)`. """ -type Preds <: Predicate +mutable struct Preds <: Predicate ps ops end @@ -122,5 +90,3 @@ end (&)(r1::Pred, ps::Preds) = ps & r1 (|)(ps::Preds, r1::Pred) = Preds(vcat(ps.ps, r1), vcat(ps.ops, |)) (|)(r1::Pred, ps::Preds) = ps | r1 - - diff --git a/src/tupper.jl b/src/tupper.jl index 6baa58b..c6708b5 100644 --- a/src/tupper.jl +++ b/src/tupper.jl @@ -55,12 +55,12 @@ Return red, black and white vectors of Regions. """ function GRAPH(r, L, R, B, T, W, H) rects = break_into_squares(W, H) - + k = min(floor(Integer,log2(W)), floor(Integer,log2(H))) # largest square is size 2^k x 2^k reds = [Region(OInterval(u[1], u[2]), OInterval(u[3], u[4])) for u in rects] sizehint!(reds, W) - + red = Region[] # 1-pixel red, can't decide via check_continuity black = Region[] white = Region[] @@ -69,7 +69,7 @@ function GRAPH(r, L, R, B, T, W, H) reds = RefinePixels(r, reds, L, R, B, T, W, H, black, white, red) k = k - 1 end - red, black, white + red, black, white end ## Refine the region @@ -89,7 +89,7 @@ function RefinePixels(r, U_k, L, R, B, T, W, H, black, white, red) if (dx > 1) & (dy > 1) hx = div(dx,2); hy = div(dy,2) for i in 0:1, j in 0:1 - uij = Region(OInterval(x.lo + i*hx, x.lo + (i+1)*hx), + uij = Region(OInterval(x.lo + i*hx, x.lo + (i+1)*hx), OInterval(y.lo + j*hy, y.lo + (j+1)*hy)) push!(Uk_1, uij) end @@ -112,7 +112,7 @@ end ## for 1-pixel squares, check NaN and continuity ## Return TRUE (Black), FALSE (white) or MAYBE (red) function check_continuity(r::Pred, u, L, R, B, T, W, H) - + fxy = compute_fxy(r, u, L, R, B, T, W, H) ## check for NaN @@ -122,13 +122,13 @@ function check_continuity(r::Pred, u, L, R, B, T, W, H) if (fxy.def == FALSE) || (fxy.def == MAYBE) return(FALSE) end - + ## now check continuity, val = FALSE if (fxy.cont == TRUE) && ((r.op === ==) || (r.op === <=) || (r.op === >=)) ## use intermediate value theorem here val = val | cross_zero(r, u, L, R, B, T, W, H) - + end ## Now check for inequalities @@ -150,7 +150,7 @@ end ## Return TRUE, FALSE or MAYBE for predicates function check_continuity(rs::Preds, u, L, R, B, T, W, H) vals = map(r -> check_continuity(r, u, L, R, B, T, W, H), rs.ps) - val = shift!(vals) + val = popfirst!(vals) for i in 1:length(rs.ops) val = rs.ops[i](val, vals[i]) end diff --git a/test/runtests.jl b/test/runtests.jl index 3ce987c..cdd0762 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -1,5 +1,5 @@ using ImplicitEquations -using Base.Test +using Test f(x,y) = y-x diff --git a/travis.yml b/travis.yml deleted file mode 100644 index 0a1fe4e..0000000 --- a/travis.yml +++ /dev/null @@ -1,13 +0,0 @@ -language: julia -os: - - osx - - linux -julia: - - release - - nightly -notifications: - email: false -script: - - if [[ -a .git/shallow ]]; then git fetch --unshallow; fi - - julia -e 'Pkg.clone(pwd()); Pkg.build("ImplicitEquations"); Pkg.test("ImplicitEquations"; coverage=true)'; - - julia -e 'cd(Pkg.dir("ImplicitEquations")); Pkg.add("Coverage"); using Coverage; Coveralls.submit(Coveralls.process_folder())';