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:

Output Type |
LAPACK Routine |

Float |
sgetrs |

Double |
dgetrs |

Complex |
cgetrs |

Double complex |
zgetrs |

## Examples

Given the system of equations:

4u + 16000v + 17000w = 100.1

2u + 5v + 8w = 0.1

3u + 6v + 10w = 0.01

the solution can be derived with the following code:

`; 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

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].

**Note: **UNIX users may see slightly different output results.

## 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.

**Note: **LA_LUSOL cannot accept any non-square output generated by LA_LUDC.

### 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.

## Version History

5.6 |
Introduced |

## Resources and References

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

## See Also

LA_LINEAR_EQUATION, LA_LUDC, LA_LUMPROVE, LUSOL

## Notes

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