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chol

Cholesky factorization

Syntax

R = chol(X)

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 — block diagonalization, generalized eigenvectors
fullrf — full rank factorization

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