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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.

**Further Comments**
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

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