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

# 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

```# 😮
vs_norm = vs / np.linalg.norm(vs, axis=1)[:, np.newaxis]

# 😀
vs_norm = vg.normalize(vs)
```

#### Check for zero vector

```# 😣
is_almost_zero = np.allclose(v, np.array([0.0, 0.0, 0.0]), rtol=0, atol=1e-05)

# 🤓
is_almost_zero = vg.is_almost_zero(v, atol=1e-05)
```

#### Major axis of variation (first principal component)

```# 😩
mean = np.mean(coords, axis=0)
_, _, pcs = np.linalg.svd(coords - mean)
first_pc = pcs

# 😍
first_pc = vg.major_axis(coords)
```

#### 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

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 – 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.

• `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:

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.

## Acknowledgements

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.

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