MB02UV

LU factorization with complete pivoting of a general matrix

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.

      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, * )

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).

  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.

Program Text

  None

  None

  None