Linear algebra for humans: a very good vectorgeometry and linearalgebra toolbelt
Project description
vg
A very good vectorgeometry and linearalgebra toolbelt. Linear algebra for humans. Simple NumPy operations made readable, built to scale from prototyping to production.
See the complete API reference: https://vgpy.readthedocs.io/en/latest/
Examples
Normalize a stack of vectors:
# 😮 vs_norm = vs / np.linalg.norm(vs, axis=1)[:, np.newaxis] # 😀 vs_norm = vg.normalize(vs)
Check for the zero vector:
# 😣 is_almost_zero = np.allclose(v, np.array([0.0, 0.0, 0.0]), rtol=0, atol=1e05) # 🤓 is_almost_zero = vg.almost_zero(v, atol=1e05)
Find the major axis of variation (first principal component):
# 😩 mean = np.mean(coords, axis=0) _, _, pcs = np.linalg.svd(coords  mean) first_pc = pcs[0] # 😍 first_pc = vg.major_axis(coords)
Compute pairwise angles between two stacks of vectors:
# 😭 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)) # 🤯 angles = vg.angle(v1s, v2s)
Features
All functions are optionally vectorized, meaning they accept single inputs and stacks of inputs interchangeably. They return The Right Thing – a single result or a stack of results – without the need to reshape inputs or outputs. With the power of NumPy, the vectorized functions are fast.
Installation
pip install numpy vg
Usage
import numpy as np import vg projected = vg.scalar_projection( np.array([5.0, 3.0, 1.0]), onto=vg.basis.neg_y )
Design principles
Linear algebra is useful and 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.
Versioning
This library adheres to Semantic Versioning.
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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