control_systems_torbox 0.2.1

Control systems toolbox
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<HEAD><TITLE>MA02GD - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>

<H2><A Name="MA02GD">MA02GD</A></H2>
<H3>
Column interchanges in a matrix
</H3>
<A HREF ="#Specification"><B>[Specification]</B></A>
<A HREF ="#Arguments"><B>[Arguments]</B></A>
<A HREF ="#Method"><B>[Method]</B></A>
<A HREF ="#References"><B>[References]</B></A>
<A HREF ="#Comments"><B>[Comments]</B></A>
<A HREF ="#Example"><B>[Example]</B></A>

<P>
<B><FONT SIZE="+1">Purpose</FONT></B>
<PRE>
  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.

</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
      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, * )

</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>

</PRE>
<B>Input/Output Parameters</B>
<PRE>
  N       (input) INTEGER
          The number of rows of the matrix A.  N &gt;= 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 &gt;= 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.

</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
  The columns IPIV(K) and K are swapped for K = K1, ..., K2, for
  INCX = 1 (and similarly, for INCX &lt;&gt; 1).

</PRE>
<A name="Comments"><B><FONT SIZE="+1">Further Comments</FONT></B></A>
<PRE>
  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 )

</PRE>

<A name="Example"><B><FONT SIZE="+1">Example</FONT></B></A>
<P>
<B>Program Text</B>
<PRE>
  None
</PRE>
<B>Program Data</B>
<PRE>
  None
</PRE>
<B>Program Results</B>
<PRE>
  None
</PRE>

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