Utility functions that involve numerical linear algebra.


inner_product(v, w[, A])

Inner product \(\langle v, w \rangle_A := v^T A w\).

induced_norm(v[, A, axis])

Induced norm \(\lVert v \rVert_A := \sqrt{v^T A v}\).

cholesky_update(S1[, S2])

Compute Cholesky update/factorization \(L\) such that \(L L^\top = S_1 S_1^\top + S_2 S_2^\top\) holds.


Orthogonally transform a lower-triangular matrix into a lower-triangular matrix with positive diagonal.

gram_schmidt(v, orthogonal_basis[, ...])

Orthogonalize a vector with respect to an orthogonal basis and inner product.

modified_gram_schmidt(v, orthogonal_basis[, ...])

Stabilized Gram-Schmidt process.

double_gram_schmidt(v, orthogonal_basis[, ...])

Perform the (modified) Gram-Schmidt process twice.