@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 s1 = @inner(@mrnd(10, 10))

matrix chol = @cholesky(s1)

matrix orig1 = chol * chol.@t

sym orig2 = @inner(chol.@t)

computes the Cholesky, and uses it to recreate the original matrix.

Inverting the Cholesky may be used to obtain the matrix inverse

sym s1inv = @inverse(s1)

matrix invchol = @inverse(chol)

matrix s2inv = invchol.@t * invchol

sym s3inv = @inner(invchol)

matrix is1 = s1inv * s1

matrix is2 = s2inv * s2

matrix is3 = s3inv * s3

uses properties of the inverse of the Cholesky to recreate the matrix inverse so that IS1, IS2, and IS3 are all different computations yielding the identity matrix.

Cross-references