Routines (alphabetical) > Routines: L > LUSOL

# 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.

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

## 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.

## 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.

## Version History

Pre 4.0 | Introduced

## Resources and References

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.

## See Also

CHOLSOL, CRAMER, GS_ITER, LA_LUSOL, LU_COMPLEX, LUDC, SVSOL, TRISOL