Math Module

rmath.linalg

Matrix decompositions and solvers powered by faer. All operations accept and return rmath.Array.

example.py

import rmath as rm

A = rm.Array([[4, 7], [2, 6]])
b = rm.Array([[1], [2]])
x = rm.linalg.solve(A, b)

Q, R = rm.linalg.qr(A)
U, S, Vt = rm.linalg.svd(A)

API Reference

Solvers

Function	Returns	Description
`solve(A, B)`	Array	Solve AX = B for X
`inv(A)`	Array	Matrix inverse via partial pivoting
`pseudo_inv(A)`	Array	Moore-Penrose pseudoinverse
`det(A)`	float	Determinant of a square matrix
`rank(A)`	int	Numerical rank

Decompositions

Function	Returns	Description
`qr(A)`	(Q, R)	QR decomposition
`svd(A)`	(U, S, Vt)	Singular value decomposition. S is a Vector.
`eigh(A)`	(eigvecs, eigvals)	Eigenvalues and eigenvectors of symmetric matrix
`cholesky(A)`	Array	Cholesky decomposition (positive definite)

Utilities

`transpose(A)`	Array	Matrix transpose
`gram_matrix(A)`	Array	AᵀA (Gram matrix)
`covariance(A)`	Array	Covariance matrix of columns