225 lines
6.7 KiB
Fortran
225 lines
6.7 KiB
Fortran
SUBROUTINE AB07MD( JOBD, N, M, P, A, LDA, B, LDB, C, LDC, D, LDD,
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$ INFO )
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C
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C SLICOT RELEASE 5.0.
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C
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C Copyright (c) 2002-2009 NICONET e.V.
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C
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C This program is free software: you can redistribute it and/or
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C modify it under the terms of the GNU General Public License as
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C published by the Free Software Foundation, either version 2 of
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C the License, or (at your option) any later version.
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C
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C This program is distributed in the hope that it will be useful,
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C but WITHOUT ANY WARRANTY; without even the implied warranty of
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C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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C GNU General Public License for more details.
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C
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C You should have received a copy of the GNU General Public License
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C along with this program. If not, see
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C <http://www.gnu.org/licenses/>.
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C
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C PURPOSE
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C
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C To find the dual of a given state-space representation.
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C
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C ARGUMENTS
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C
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C Mode Parameters
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C
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C JOBD CHARACTER*1
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C Specifies whether or not a non-zero matrix D appears in
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C the given state space model:
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C = 'D': D is present;
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C = 'Z': D is assumed a zero matrix.
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C
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C Input/Output Parameters
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C
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C N (input) INTEGER
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C The order of the state-space representation. N >= 0.
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C
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C M (input) INTEGER
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C The number of system inputs. M >= 0.
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C
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C P (input) INTEGER
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C The number of system outputs. P >= 0.
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C
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C A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
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C On entry, the leading N-by-N part of this array must
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C contain the original state dynamics matrix A.
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C On exit, the leading N-by-N part of this array contains
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C the dual state dynamics matrix A'.
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C
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C LDA INTEGER
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C The leading dimension of array A. LDA >= MAX(1,N).
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C
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C B (input/output) DOUBLE PRECISION array, dimension
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C (LDB,MAX(M,P))
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C On entry, the leading N-by-M part of this array must
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C contain the original input/state matrix B.
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C On exit, the leading N-by-P part of this array contains
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C the dual input/state matrix C'.
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C
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C LDB INTEGER
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C The leading dimension of array B. LDB >= MAX(1,N).
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C
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C C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
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C On entry, the leading P-by-N part of this array must
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C contain the original state/output matrix C.
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C On exit, the leading M-by-N part of this array contains
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C the dual state/output matrix B'.
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C
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C LDC INTEGER
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C The leading dimension of array C.
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C LDC >= MAX(1,M,P) if N > 0.
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C LDC >= 1 if N = 0.
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C
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C D (input/output) DOUBLE PRECISION array, dimension
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C (LDD,MAX(M,P))
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C On entry, if JOBD = 'D', the leading P-by-M part of this
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C array must contain the original direct transmission
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C matrix D.
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C On exit, if JOBD = 'D', the leading M-by-P part of this
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C array contains the dual direct transmission matrix D'.
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C The array D is not referenced if JOBD = 'Z'.
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C
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C LDD INTEGER
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C The leading dimension of array D.
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C LDD >= MAX(1,M,P) if JOBD = 'D'.
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C LDD >= 1 if JOBD = 'Z'.
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C
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C Error Indicator
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C
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C INFO INTEGER
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C = 0: successful exit;
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C < 0: if INFO = -i, the i-th argument had an illegal
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C value.
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C
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C METHOD
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C
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C If the given state-space representation is the M-input/P-output
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C (A,B,C,D), its dual is simply the P-input/M-output (A',C',B',D').
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C
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C REFERENCES
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C
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C None
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C
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C NUMERICAL ASPECTS
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C
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C None
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C
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C CONTRIBUTOR
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C
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C Release 3.0: V. Sima, Katholieke Univ. Leuven, Belgium, Dec. 1996.
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C Supersedes Release 2.0 routine AB07AD by T.W.C.Williams, Kingston
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C Polytechnic, United Kingdom, March 1982.
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C
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C REVISIONS
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C
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C V. Sima, Research Institute for Informatics, Bucharest, Feb. 2004.
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C
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C KEYWORDS
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C
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C Dual system, state-space model, state-space representation.
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C
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C ******************************************************************
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C
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C .. Scalar Arguments ..
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CHARACTER JOBD
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INTEGER INFO, LDA, LDB, LDC, LDD, M, N, P
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C .. Array Arguments ..
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DOUBLE PRECISION A(LDA,*), B(LDB,*), C(LDC,*), D(LDD,*)
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C .. Local Scalars ..
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LOGICAL LJOBD
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INTEGER J, MINMP, MPLIM
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C .. External functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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C .. External subroutines ..
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EXTERNAL DCOPY, DSWAP, XERBLA
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C .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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C .. Executable Statements ..
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C
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INFO = 0
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LJOBD = LSAME( JOBD, 'D' )
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MPLIM = MAX( M, P )
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MINMP = MIN( M, P )
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C
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C Test the input scalar arguments.
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C
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IF( .NOT.LJOBD .AND. .NOT.LSAME( JOBD, 'Z' ) ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( M.LT.0 ) THEN
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INFO = -3
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ELSE IF( P.LT.0 ) THEN
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INFO = -4
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -6
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ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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INFO = -8
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ELSE IF( ( N.GT.0 .AND. LDC.LT.MAX( 1, MPLIM ) ) .OR.
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$ ( N.EQ.0 .AND. LDC.LT.1 ) ) THEN
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INFO = -10
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ELSE IF( ( LJOBD .AND. LDD.LT.MAX( 1, MPLIM ) ) .OR.
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$ ( .NOT.LJOBD .AND. LDD.LT.1 ) ) THEN
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INFO = -12
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END IF
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C
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IF ( INFO.NE.0 ) THEN
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C
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C Error return.
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C
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CALL XERBLA( 'AB07MD', -INFO )
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RETURN
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END IF
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C
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C Quick return if possible.
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C
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IF ( MAX( N, MINMP ).EQ.0 )
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$ RETURN
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C
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IF ( N.GT.0 ) THEN
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C
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C Transpose A, if non-scalar.
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C
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DO 10 J = 1, N - 1
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CALL DSWAP( N-J, A(J+1,J), 1, A(J,J+1), LDA )
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10 CONTINUE
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C
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C Replace B by C' and C by B'.
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C
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DO 20 J = 1, MPLIM
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IF ( J.LE.MINMP ) THEN
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CALL DSWAP( N, B(1,J), 1, C(J,1), LDC )
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ELSE IF ( J.GT.P ) THEN
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CALL DCOPY( N, B(1,J), 1, C(J,1), LDC )
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ELSE
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CALL DCOPY( N, C(J,1), LDC, B(1,J), 1 )
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END IF
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20 CONTINUE
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C
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END IF
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C
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IF ( LJOBD .AND. MINMP.GT.0 ) THEN
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C
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C Transpose D, if non-scalar.
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C
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DO 30 J = 1, MPLIM
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IF ( J.LT.MINMP ) THEN
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CALL DSWAP( MINMP-J, D(J+1,J), 1, D(J,J+1), LDD )
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ELSE IF ( J.GT.P ) THEN
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CALL DCOPY( P, D(1,J), 1, D(J,1), LDD )
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ELSE IF ( J.GT.M ) THEN
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CALL DCOPY( M, D(J,1), LDD, D(1,J), 1 )
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END IF
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30 CONTINUE
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C
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END IF
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C
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RETURN
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C *** Last line of AB07MD ***
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END
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