NumPy for humans: a very good vectorgeometry and linearalgebra toolbelt
Project description
vg
NumPy for humans: a very good toolbelt for common tasks in vector geometry and linear algebra.
vg
makes code more readable
Normalize a stack of vectors
# ๐ฎ vs_norm = vs / np.linalg.norm(vs, axis=1)[:, np.newaxis] # ๐ vs_norm = vg.normalize(vs)
Check for zero vector
# ๐ฃ is_almost_zero = np.allclose(v, np.array([0.0, 0.0, 0.0]), rtol=0, atol=1e05) # ๐ค is_almost_zero = vg.is_almost_zero(v, atol=1e05)
Major axis of variation (first principal component)
# ๐ฉ mean = np.mean(coords, axis=0) _, _, pcs = np.linalg.svd(coords  mean) first_pc = pcs[0] # ๐ first_pc = vg.major_axis(coords)
Pairwise angles between two stacks of vectors.
# ๐ญ dot_products = np.einsum("ij,ij>i", v1s.reshape(1, 3), v2s.reshape(1, 3)) cosines = dot_products / np.linalg.norm(v1s, axis=1) / np.linalg.norm(v1s, axis=1) angles = np.arccos(np.clip(cosines, 1.0, 1.0) # ๐คฏ angles = vg.angle(v1s, v2s)
Features
See the complete API reference: http://vgpy.readthedocs.io/
All functions are optionally vectorized, meaning they accept single inputs and stacks of inputs interchangeably. They return The Right Thing โ a single result or a stack of results โ without the need to reshape inputs or outputs. With the power of NumPy, the vectorized functions are fast.
normalize
normalizes a vector.sproj
computes the scalar projection of one vector onto another.proj
computes the vector projection of one vector onto another.reject
computes the vector rejection of one vector from another.reject_axis
zeros or squashes one component of a vector.magnitude
computes the magnitude of a vector.angle
computes the unsigned angle between two vectors.signed_angle
computes the signed angle between two vectors.almost_zero
tests if a vector is almost the zero vector.almost_collinear
tests if two vectors are almost collinear.pad_with_ones
adds a column of ones.unpad
strips off a column (e.g. of ones).apply_homogeneous
applies a transformation matrix using homogeneous coordinates.principal_components
computes principal components of a set of coordinates.major_axis
returns the first one.
Installation
pip install numpy vg
Usage
import numpy as np import vg projected = vg.sproj(np.array([5.0, 3.0, 1.0]), onto=vg.basis.neg_y)
Motivation
Linear algebra is useful but it doesn't have to be dificult to use. With the power of abstractions, simple operations can be made simple, without poring through lecture slides, textbooks, inscrutable Stack Overflow answers, or dense NumPy docs. Code that uses linear algebra and geometric transformation should be readable like English, without compromising efficiency.
These common operations should be abstracted for a few reasons:

If a developer is not programming linalg every day, they might forget the underlying formula. These forms are easier to remember and more easily referenced.

These forms tend to be selfdocumenting in a way that the NumPy forms are not. If a developer is not programming linalg every day, this will again come in handy.

These implementations are more robust. They automatically inspect
ndim
on their arguments, so they work equally well if the argument is a vector or a stack of vectors. They are more careful about checking edge cases like a zero norm or zero cross product and returning a correct result or raising an appropriate error.
Acknowledgements
This collection was developed at Body Labs by Paul Melnikow and extracted
from the Body Labs codebase and opensourced as part of blmath by Alex
Weiss. blmath was subsequently forked by Paul Melnikow and later
the vx
namespace was broken out into its own package. The project was renamed
to vg
to resolve a name conflict.
License
The project is licensed under the twoclause BSD license.
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