@cholesky |

Cholesky factor of matrix.

Syntax: @cholesky(s)

s: sym

Return: matrix

Returns a matrix containing the Cholesky factorization of .

The Cholesky factorization finds the lower triangular matrix such that is equal to the symmetric source matrix .

Examples

sym s = @inner(@mrnd(10, 10))

matrix chol = @cholesky(s)

matrix orig1 = chol * chol.@t

sym orig2 = @inner(chol.@t)

computes the Cholesky, and uses it to recreate the original matrix. Note that ORIG1 is a matrix object whereas ORIG2 is a sym object.

Inverting the Cholesky may be used to obtain the matrix inverse.

sym sinv1 = @inverse(s)

matrix invchol = @inverse(chol)

matrix sinv2 = invchol.@t * invchol

sym sinv3 = @inner(invchol)

matrix id1 = sinv1 * s

matrix id2 = sinv2 * s

matrix id3 = sinv3 * s

uses properties of the inverse of the Cholesky to recreate the matrix inverse so that ID1, ID2, and ID3 are all different computations yielding the identity matrix.

Cross-references