MA02GD - SLICOT Library Routine Documentation

## MA02GD

### Column interchanges in a matrix

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

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.

Specification

          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, * )

Arguments

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.

Method

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

Further Comments

      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 )

Example

Program Text

      None

Program Data

      None

Program Results

      None

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