chol

Arguments

X

a square positive definite real symmetric or complex hermitian matrix.

Description

If X is positive definite, then R = chol(X) produces an upper triangular matrix R such that R'*R = X.

chol(X) uses only the diagonal and upper triangle of X. The lower triangular is assumed to be the (complex conjugate) transpose of the upper.

The Cholesky decomposition is based on the Lapack routines DPOTRF for real matrices and ZPOTRF for the complex case.

Examples

W = rand(5,5) + %i*rand(5,5);
X = W*W';
R = chol(X)
norm(R'*R-X)

See also

• spchol — sparse cholesky factorization
• qr — QR decomposition
• svd — singular value decomposition
• bdiag — блоковая диагонализация, обобщённые собственные векторы
• fullrf — full rank factorization