Module Linalg

module Linalg: sig .. end

Linalg module

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 dsmat = Dense.dsmat

val inv : dsmat -> dsmat

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 : dsmat -> float

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

val qr : dsmat -> dsmat * dsmat

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 : dsmat -> dsmat -> dsmat

val qr_lssolve : dsmat -> dsmat -> dsmat * dsmat

val svd : dsmat -> dsmat * dsmat * dsmat

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 : dsmat -> dsmat

val is_posdef : dsmat -> bool

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

val symmtd : dsmat -> dsmat * dsmat * dsmat

val bidiag : dsmat -> dsmat * dsmat * dsmat * dsmat

val tridiag_solve : dsmat -> dsmat -> dsmat

val symm_tridiag_solve : dsmat -> dsmat -> dsmat