blmath

A collection of math related utilities used by many bits of BodyLabs' code.

Requirements

On macOS:

brew install homebrew/science/suite-sparse
brew install homebrew/science/opencv --without-numpy

On Linux:

sudo apt-get install python-opencv libsuitesparse-dev

On windows:

TODO: Windows install instructions

blmath.numerics

Functions for manipulating numeric arrays, numbers, and linear algebra.

The most commonly used of these are directly imported into blmath.numerics.

• blmath.numerics.vx is a namespace of common linear algebra operations. These are easily expressed in numpy, but abstracted for readability purposes.
• blmath.numerics.coercion contains a validation function as_numeric_array, which produces useful error messages up front on bad inputs, in place of cryptic messages like "cannot broadcast..." later on.
• blmath.numerics.operations contains basic numerical operations such as zero_safe_divide.
• blmath.numerics.predicates contains functions like isnumeric.
• blmath.numerics.rounding contains functions including "round to nearest" and roundedlist.
• blmath.numerics.numpy_ext contains numpy utility functions.
• blmath.numerics.matlab contains some matlab shortcuts which have no numpy equivalent. At MPI the fitting code was originally written in Matlab before it was ported to Python.

blmath.numerics.linalg contains linear algebra operations.

• blmath.numerics.linalg.sparse_cg contains a faster matrix solve optimized for sparse Jacobians.
• blmath.numerics.linalg.lchol contains a Cythonized implementation of Cholesky factorization.
• blmath.numerics.linalg.isomorphism computes the isomorphism between two bases.
• blmath.numerics.linalg.gram_schmidt provides a function for orthonormalization.

blmath.geometry

Geometric operations, transforms, and primitives, in 2D and 3D.

The most commonly used of these are directly imported into blmath.geometry.

• blmath.geometry.Box represents an axis-aligned cuboid.
• blmath.geometry.Plane represents a 2-D plane in 3-space (not a hyperplane).
• blmath.geometry.Polyline represents an unconstrained polygonal chain in 3-space.

blmath.geometry.transform includes code for 3D transforms.

• blmath.geometry.transform.CompositeTransform represents a composite transform using homogeneous coordinates. (Thanks avd!)
• blmath.geometry.transform.CoordinateManager provides a convenient interface for named reference frames within a stack of transforms and projecting points from one reference frame to another.
• blmath.geometry.transform.find_rigid_transform finds a rotation and translation that closely transforms one set of points to another. Its cousin find_rigid_rotation does the same, but only allows rotation, not translation.
• blmath.geometry.transform.rotation.rotation_from_up_and_look produces a rotation matrix that gets a mesh into the canonical reference frame from "up" and "look" vectors.

Other modules:

• blmath.geometry.apex provides functions for finding the most extreme point.
• blmath.geometry.barycentric provides a function for projecting a point to a triangle using barycentric coordinates.
• blmath.geometry.convexify provides a function for producing a convex hull from a mostly-planar curve.
• blmath.geometry.segment provides functions for working with line segments in n-space.

blmath.value

Class for wrapping and manipulating value/units pairs.

blmath.units

TODO write something here

blmath.console

• blmath.console.input_float reads and returns a float from console.
• blmath.console.input_value combines units with a float input from console and returns Value object.

Development

pip install -r requirements_dev.txt
pip install -e .  # builds the native extension
rake unittest
rake lint

Contribute

• Issue Tracker: github.com/bodylabs/blmath/issues
• Source Code: github.com/bodylabs/blmath

Pull requests welcome!

Support

If you are having issues, please let us know.

License

The project is licensed under the two-clause BSD license.