LUSOL

The LUSOL function is used in conjunction with the LUDC procedure to solve a set of n linear equations in n unknowns Ax = b. The parameter A is input not as the original array, but as its LU decomposition, created by the routine LUDC.

LUSOL is based on the routine lubksb described in section 2.3 of Numerical Recipes in C: The Art of Scientific Computing (Second Edition), published by Cambridge University Press, and is used by permission.

Note
If you are working with complex inputs, use the LA_LUSOL function instead.

Syntax

Result = LUSOL(A, Index, B [, /COLUMN] [, /DOUBLE])

Return Value

The result is an n-element vector whose type is identical to A.

Arguments

A

The n by n LU decomposition of an array created by the LUDC procedure.

Note
If LUSOL is complex then only the real part is used for the computation.

Index

An input vector, created by the LUDC procedure, containing a record of the row permutations which occurred as a result of partial pivoting.

B

An n-element vector containing the right-hand side of the linear system Ax = b.

Keywords

COLUMN

Set this keyword if the input array A is in column-major format (composed of column vectors) rather than in row-major format (composed of row vectors).

DOUBLE

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

Examples

This example solves the linear system Ax = b using LU decomposition and back substitution:

; Define array A:
A = [[ 2.0, 1.0, 1.0], $
[ 4.0, -6.0, 0.0], $
[-2.0, 7.0, 2.0]]

; Define right-hand side vector B:
B = [3.0, -8.0, 10.0]

; Decompose A:
LUDC, A, INDEX

; Compute the solution using back substitution:
result = LUSOL(A, INDEX, B)

; Print the result:
PRINT, result

IDL prints:

  1.00000   2.00000   -1.00000

This is the exact solution vector.

Version History


Pre 4.0	Introduced