MA02GD

Column interchanges in a matrix

Purpose

  To perform a series of column interchanges on the matrix A.
  One column interchange is initiated for each of columns K1 through
  K2 of A. This is useful for solving linear systems X*A = B, when
  the matrix A has already been factored by LAPACK Library routine
  DGETRF.

      SUBROUTINE MA02GD( N, A, LDA, K1, K2, IPIV, INCX )
C     .. Scalar Arguments ..
      INTEGER            INCX, K1, K2, LDA, N
C     .. Array Arguments ..
      INTEGER            IPIV( * )
      DOUBLE PRECISION   A( LDA, * )

Input/Output Parameters

  N       (input) INTEGER
          The number of rows of the matrix A.  N >= 0.

  A       (input/output) DOUBLE PRECISION array, dimension (LDA,*)
          On entry, the leading N-by-M part of this array must
          contain the matrix A to which the column interchanges will
          be applied, where M is the largest element of IPIV(K), for
          K = K1, ..., K2.
          On exit, the leading N-by-M part of this array contains
          the permuted matrix.

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

  K1      (input) INTEGER
          The first element of IPIV for which a column interchange
          will be done.

  K2      (input) INTEGER
          The last element of IPIV for which a column interchange
          will be done.

  IPIV    (input) INTEGER array, dimension (K1+(K2-K1)*abs(INCX))
          The vector of interchanging (pivot) indices.  Only the
          elements in positions K1 through K2 of IPIV are accessed.
          IPIV(K) = L implies columns K and L are to be
          interchanged.

  INCX    (input) INTEGER
          The increment between successive values of IPIV.
          If INCX is negative, the interchanges are applied in
          reverse order.

  The columns IPIV(K) and K are swapped for K = K1, ..., K2, for
  INCX = 1 (and similarly, for INCX <> 1).

  This routine is the column-oriented counterpart of the LAPACK
  Library routine DLASWP. The LAPACK Library routine DLAPMT cannot
  be used in this context. To solve the system X*A = B, where A and
  B are N-by-N and M-by-N, respectively, the following statements
  can be used:

      CALL DGETRF( N, N, A, LDA, IPIV, INFO )
      CALL DTRSM( 'R', 'U', 'N', 'N', M, N, ONE, A, LDA, B, LDB )
      CALL DTRSM( 'R', 'L', 'N', 'U', M, N, ONE, A, LDA, B, LDB )
      CALL MA02GD( M, B, LDB, 1, N, IPIV, -1 )

Program Text

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