Module Owl_linalg

module Owl_linalg: sig .. end

Linear algebra module including high-level functions to solve linear systems, factorisation, and etc.

The module includes a set of advanced linear algebra operations such as singular value decomposition, and etc.

Currently, Linalg module only supports dense matrix. The support for sparse matrices will be provided very soon.

type mat_d = Owl_dense_matrix_d.mat

type mat_z = Owl_dense_matrix_z.mat

type ('a, 'b) t = ('a, 'b) Owl_dense_matrix_generic.t

val inv : mat_d -> mat_d

A general square matrix A has an LU decomposition into upper and lower triangular matrices, P A = L U where P is a permutation matrix, L is unit lower triangular matrix and U is upper triangular matrix. For square matrices this decomposition can be used to convert the linear system A x = b into a pair of triangular systems (L y = P b, U x = y), which can be solved by forward and back-substitution. Note that the LU decomposition is valid for singular matrices.

val det : mat_d -> float

det x computes the determinant of a matrix x from its LU decomposition.

val qr : mat_d -> mat_d * mat_d

qr x calculates QR decomposition for an m by n matrix x as x = Q R. Q is an m by m square matrix (where Q^T Q = I) and R is an m by n right-triangular matrix.

val qr_sqsolve : mat_d -> mat_d -> mat_d

val qr_lssolve : mat_d -> mat_d -> mat_d * mat_d

val svd : mat_d -> mat_d * mat_d * mat_d

svd x calculates the singular value decomposition of x, and returns a tuple (u,s,v). u is an m by n orthogonal matrix, s an n by 1 matrix of singular values, and v is the transpose of an n by n orthogonal square matrix.

val cholesky : mat_d -> mat_d

val is_posdef : mat_d -> bool

is_posdef x checks whether x is a positive semi-definite matrix.

val symmtd : mat_d -> mat_d * mat_d * mat_d

val bidiag : mat_d ->
       mat_d * mat_d * mat_d * mat_d

val tridiag_solve : mat_d -> mat_d -> mat_d

val symm_tridiag_solve : mat_d -> mat_d -> mat_d

Solve Eigen systems

val eigen_symm : mat_d -> mat_d

val eigen_symmv : mat_d -> mat_d * mat_d

val eigen_nonsymm : mat_d -> mat_z

val eigen_nonsymmv : mat_d -> mat_z * mat_z

val eigen_herm : mat_z -> mat_d

val eigen_hermv : mat_z -> mat_d * mat_z