## MB02UV

### LU factorization with complete pivoting of a general matrix

[Specification] [Arguments] [Method] [References] [Comments] [Example]

Purpose

```  To compute an LU factorization, using complete pivoting, of the
N-by-N matrix A. The factorization has the form A = P * L * U * Q,
where P and Q are permutation matrices, L is lower triangular with
unit diagonal elements and U is upper triangular.

```
Specification
```      SUBROUTINE MB02UV( N, A, LDA, IPIV, JPIV, INFO )
C     .. Scalar Arguments ..
INTEGER            INFO, LDA, N
C     .. Array Arguments ..
INTEGER            IPIV( * ), JPIV( * )
DOUBLE PRECISION   A( LDA, * )

```
Arguments

Input/Output Parameters

```  N       (input) INTEGER
The order of the matrix A.

A       (input/output) DOUBLE PRECISION array, dimension (LDA, N)
On entry, the leading N-by-N part of this array must
contain the matrix A to be factored.
On exit, the leading N-by-N part of this array contains
the factors L and U from the factorization A = P*L*U*Q;
the unit diagonal elements of L are not stored. If U(k, k)
appears to be less than SMIN, U(k, k) is given the value
of SMIN, giving a nonsingular perturbed system.

LDA     INTEGER
The leading dimension of the array A.  LDA >= max(1, N).

IPIV    (output) INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= N, row i of the
matrix has been interchanged with row IPIV(i).

JPIV    (output) INTEGER array, dimension (N)
The pivot indices; for 1 <= j <= N, column j of the
matrix has been interchanged with column JPIV(j).

```
Error Indicator
```  INFO    INTEGER
= 0:  successful exit;
= k:  U(k, k) is likely to produce owerflow if one tries
to solve for x in Ax = b. So U is perturbed to get
a nonsingular system. This is a warning.

```
```  In the interests of speed, this routine does not check the input
for errors. It should only be used to factorize matrices A of
very small order.

```
Example

Program Text

```  None
```
Program Data
```  None
```
Program Results
```  None
```