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SUBROUTINE MA02GD( N, A, LDA, K1, K2, IPIV, INCX )
C
C SLICOT RELEASE 5.0.
C
C Copyright (c) 2002-2009 NICONET e.V.
C
C This program is free software: you can redistribute it and/or
C modify it under the terms of the GNU General Public License as
C published by the Free Software Foundation, either version 2 of
C the License, or (at your option) any later version.
C
C This program is distributed in the hope that it will be useful,
C but WITHOUT ANY WARRANTY; without even the implied warranty of
C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
C GNU General Public License for more details.
C
C You should have received a copy of the GNU General Public License
C along with this program. If not, see
C <http://www.gnu.org/licenses/>.
C
C PURPOSE
C
C To perform a series of column interchanges on the matrix A.
C One column interchange is initiated for each of columns K1 through
C K2 of A. This is useful for solving linear systems X*A = B, when
C the matrix A has already been factored by LAPACK Library routine
C DGETRF.
C
C ARGUMENTS
C
C Input/Output Parameters
C
C N (input) INTEGER
C The number of rows of the matrix A. N >= 0.
C
C A (input/output) DOUBLE PRECISION array, dimension (LDA,*)
C On entry, the leading N-by-M part of this array must
C contain the matrix A to which the column interchanges will
C be applied, where M is the largest element of IPIV(K), for
C K = K1, ..., K2.
C On exit, the leading N-by-M part of this array contains
C the permuted matrix.
C
C LDA INTEGER
C The leading dimension of the array A. LDA >= MAX(1,N).
C
C K1 (input) INTEGER
C The first element of IPIV for which a column interchange
C will be done.
C
C K2 (input) INTEGER
C The last element of IPIV for which a column interchange
C will be done.
C
C IPIV (input) INTEGER array, dimension (K1+(K2-K1)*abs(INCX))
C The vector of interchanging (pivot) indices. Only the
C elements in positions K1 through K2 of IPIV are accessed.
C IPIV(K) = L implies columns K and L are to be
C interchanged.
C
C INCX (input) INTEGER
C The increment between successive values of IPIV.
C If INCX is negative, the interchanges are applied in
C reverse order.
C
C METHOD
C
C The columns IPIV(K) and K are swapped for K = K1, ..., K2, for
C INCX = 1 (and similarly, for INCX <> 1).
C
C FURTHER COMMENTS
C
C This routine is the column-oriented counterpart of the LAPACK
C Library routine DLASWP. The LAPACK Library routine DLAPMT cannot
C be used in this context. To solve the system X*A = B, where A and
C B are N-by-N and M-by-N, respectively, the following statements
C can be used:
C
C CALL DGETRF( N, N, A, LDA, IPIV, INFO )
C CALL DTRSM( 'R', 'U', 'N', 'N', M, N, ONE, A, LDA, B, LDB )
C CALL DTRSM( 'R', 'L', 'N', 'U', M, N, ONE, A, LDA, B, LDB )
C CALL MA02GD( M, B, LDB, 1, N, IPIV, -1 )
C
C CONTRIBUTOR
C
C V. Sima, Research Institute for Informatics, Bucharest, Mar. 2000.
C
C REVISIONS
C
C V. Sima, Research Institute for Informatics, Bucharest, Apr. 2008.
C
C KEYWORDS
C
C Elementary matrix operations, linear algebra.
C
C ******************************************************************
C
C .. Scalar Arguments ..
INTEGER INCX, K1, K2, LDA, N
C ..
C .. Array Arguments ..
INTEGER IPIV( * )
DOUBLE PRECISION A( LDA, * )
C ..
C .. Local Scalars ..
INTEGER J, JP, JX
C ..
C .. External Subroutines ..
EXTERNAL DSWAP
C ..
C .. Executable Statements ..
C
C Quick return if possible.
C
IF( INCX.EQ.0 .OR. N.EQ.0 )
$ RETURN
C
C Interchange column J with column IPIV(J) for each of columns K1
C through K2.
C
IF( INCX.GT.0 ) THEN
JX = K1
ELSE
JX = 1 + ( 1-K2 )*INCX
END IF
C
IF( INCX.EQ.1 ) THEN
C
DO 10 J = K1, K2
JP = IPIV( J )
IF( JP.NE.J )
$ CALL DSWAP( N, A( 1, J ), 1, A( 1, JP ), 1 )
10 CONTINUE
C
ELSE IF( INCX.GT.1 ) THEN
C
DO 20 J = K1, K2
JP = IPIV( JX )
IF( JP.NE.J )
$ CALL DSWAP( N, A( 1, J ), 1, A( 1, JP ), 1 )
JX = JX + INCX
20 CONTINUE
C
ELSE IF( INCX.LT.0 ) THEN
C
DO 30 J = K2, K1, -1
JP = IPIV( JX )
IF( JP.NE.J )
$ CALL DSWAP( N, A( 1, J ), 1, A( 1, JP ), 1 )
JX = JX + INCX
30 CONTINUE
C
END IF
C
RETURN
C
C *** Last line of MA02GD ***
END
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