chol

Cholesky factorization of a Hermitian positive-definite matrix.

Syntax

R          = chol(A)
R          = chol(A, 'lower')
[R, p]     = chol(A)
[R, p, S]  = chol(A, 'vector')   % sparse

Description

Returns the upper-triangular R such that R'*R = A, assuming A is Hermitian positive-definite. Pass 'lower' to return lower-triangular R with R*R' = A.

The optional second output p is 0 if A is positive-definite and a positive integer otherwise, indicating where the factorization failed (the leading minor of order p-1 was not positive-definite). For sparse matrices, the third output is a permutation that improves fill-in.

Examples

A = [4 12 -16; 12 37 -43; -16 -43 98];
R = chol(A)
norm(R' * R - A)         % near-zero

See also

• lu — LU decomposition (with partial pivoting).
• qr — QR decomposition.
• linsolve — Solve a linear system with optional structure hints.