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