IDL Analyst Reference Guide: Linear Systems

IMSL_CHFAC

The IMSL_CHFAC procedure computes the Cholesky factor, L, of a real or complex symmetric positive definite matrix A, such that A = LL^H.

Syntax

IMSL_CHFAC, a, fac [, CONDITION=variable] [, /DOUBLE] [, INVERSE=variable]

Arguments

a

Two-dimensional matrix containing the coefficient matrix. Element A (i, j) contains the j-th coefficient of the i-th equation.

fac

A named variable that will contain a two-dimensional matrix containing the Cholesky factorization of A. Note that fac contains L in the lower triangle and L^H in the upper triangle.

Keywords

CONDITION

Named variable into which an estimate of the L₁ condition number is stored.

DOUBLE

If present and nonzero, double precision is used.

INVERSE

Named variable into which the inverse of the matrix A is stored. This keyword is not allowed if A is complex.

Discussion

The IMSL_CHFAC procedure computes the Cholesky factorization LL^H of a symmetric positive definite matrix A. When the inverse of the matrix is sought, an estimate of the L₁ condition number of A is computed using the same algorithm as in Dongarra et al. (1979). If the estimated condition number is greater than 1/e (where e is the machine precision), a warning message is issued. This indicates that very small changes in A may produce large changes in the solution x.

The IMSL_CHFAC function fails if L, the lower-triangular matrix in the factorization, has a zero diagonal element.

Example

This example computes the Cholesky factorization of a 3 x 3 matrix.

RM, a, 3, 3  
; Define the matrix A.  
row 0:  1  -3  2  
row 1: -3  10 -5  
row 2:  2  -5  6  
IMSL_CHFAC, a, fac  
; Call IMSL_CHFAC to compute the factorization.  
PM, fac, Title = 'Cholesky factor'  
Cholesky factor  
   1.00000     -3.00000      2.00000  
   -3.00000      1.00000      1.00000  
   2.00000      1.00000      1.00000