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NumPy for humans: a very good vector-geometry and linear-algebra toolbelt

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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

# ๐Ÿ˜ฎ
vs_norm = vs / np.linalg.norm(vs, axis=1)[:, np.newaxis]

# ๐Ÿ˜€
vs_norm = vg.normalize(vs)

Check for zero vector

# ๐Ÿ˜ฃ
is_almost_zero = np.allclose(v, np.array([0.0, 0.0, 0.0]), rtol=0, atol=1e-05)

# ๐Ÿค“
is_almost_zero = vg.is_almost_zero(v, atol=1e-05)

Major axis of variation (first principal component)

# ๐Ÿ˜ฉ
mean = np.mean(coords, axis=0)
_, _, pcs = np.linalg.svd(coords - mean)
first_pc = pcs[0]

# ๐Ÿ˜
first_pc = vg.major_axis(coords)

Pairwise angles between two stacks of vectors.

# ๐Ÿ˜ญ
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)

# ๐Ÿคฏ
angles = vg.angle(v1s, v2s)


See the complete API reference:

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.


pip install numpy vg


import numpy as np
import vg

projected = vg.sproj(np.array([5.0, -3.0, 1.0]), onto=vg.basis.neg_y)


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:

  1. 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.

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

  3. 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.


This collection was developed at Body Labs by Paul Melnikow and extracted from the Body Labs codebase and open-sourced 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.


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

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