IDL Reference Guide: Procedures and Functions

LA_LUSOL

The LA_LUSOL function is used in conjunction with the LA_LUDC procedure to solve a set of n linear equations in n unknowns, AX = B. The parameter A is not the original array, but its LU decomposition, created by the routine LA_LUDC.

The LA_LUSOL function may also be used to solve for multiple systems of linear equations, with each column of B representing a different set of equations. In this case, the result is a k-by-n array where each of the k columns represents the solution vector for that set of equations.

LA_LUSOL is based on the following LAPACK routines:

For details see Anderson et al., LAPACK Users' Guide, 3rd ed., SIAM, 1999.

Syntax

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

Return Value

The result is an n-element vector or k-by-n array.

Arguments

A

The n-by-n LU decomposition of an array, created by the LA_LUDC procedure.

Index

An n-element input vector, created by the LA_LUDC procedure, containing the row permutations which occurred as a result of partial pivoting.

B

An n-element input vector containing the right-hand side of the linear system, or a k-by-n array, where each of the k columns represents a different linear system.

Keywords

DOUBLE

Set this keyword to use double-precision for computations and to return a double-precision (real or complex) result. Set DOUBLE = 0 to use single-precision for computations and to return a single-precision (real or complex) result. The default is /DOUBLE if A is double precision, otherwise the default is DOUBLE = 0.

Examples

Given the system of equations:

4u + 16000v + 17000w = 100.1  
2u +     5v +     8w = 0.1  
3u +     6v +    10w = 0.01  

find the solution can be derived by using the following program:

PRO ExLA_LUSOL  
; Define the coefficient array:  
a = [[4, 16000, 17000], $  
     [2, 5, 8], $  
     [3, 6, 10]]  
; Compute the LU decomposition:  
aludc = a  
; make a copy  
LA_LUDC, aludc, index  
  
; Define the right-hand side vector B:  
b = [100.1, 0.1, 0.01]  
  
; Compute and print the solution to Ax=b:  
x = LA_LUSOL(aludc, index, b)  
PRINT, 'LA_LUSOL Solution:', x  
END  

When this program is compiled and run, IDL prints:

LA_LUSOL solution:    -0.397355    -0.334742     0.321033  

The exact solution to 6 decimal places is [-0.397432, -0.334865, 0.321149].

Version History

See Also

LA_LINEAR_EQUATION, LA_LUDC, LA_LUMPROVE, LUSOL

  IDL Online Help (March 06, 2007)