CHOLSOL

The CHOLSOL function returns an n -element vector containing the solution to the set of linear equations Ax = b , where A is the positive-definite symmetric array returned by the CHOLDC procedure.

CHOLSOL is based on the routine cholsl described in section 2.9 of Numerical Recipes in C: The Art of Scientific Computing (Second Edition), published by Cambridge University Press, and is used by permission.

Calling Sequence

result = CHOLSOL( A, P, B )

Arguments

A

An n by n positive-definite symmetric array, as output by CHOLDC. Only the lower triangle of A is accessed.

P

The diagonal elements of the Cholesky factor L , as computed by CHOLDC.

B

An n -element vector containing the right-hand side of the equation.

Keywords

DOUBLE

Set this keyword to force the computation to be done in double-precision arithmetic.

Example

To solve a positive-definite symmetric system Ax = b:

A = [[ 6.0, 15.0, 55.0], $ ; Define the coefficient array.

[15.0, 55.0, 225.0], $

[55.0, 225.0, 979.0]]

B = [9.5, 50.0, 237.0] ; Define the right-hand side vector B.

CHOLDC, A, P ; Compute Cholesky decomposition of A.

PRINT, CHOLSOL(A, P, B) ; Compute and print the solution.

IDL prints:

-0.499998 -1.00000 0.500000

The exact solution vector is [-0.5, -1.0, 0.5].