## 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.

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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