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SUBROUTINE MB04WR( JOB, TRANS, N, ILO, Q1, LDQ1, Q2, LDQ2, CS,
$ TAU, DWORK, LDWORK, INFO )
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 generate orthogonal symplectic matrices U or V, defined as
C products of symplectic reflectors and Givens rotators
C
C U = diag( HU(1),HU(1) ) GU(1) diag( FU(1),FU(1) )
C diag( HU(2),HU(2) ) GU(2) diag( FU(2),FU(2) )
C ....
C diag( HU(n),HU(n) ) GU(n) diag( FU(n),FU(n) ),
C
C V = diag( HV(1),HV(1) ) GV(1) diag( FV(1),FV(1) )
C diag( HV(2),HV(2) ) GV(2) diag( FV(2),FV(2) )
C ....
C diag( HV(n-1),HV(n-1) ) GV(n-1) diag( FV(n-1),FV(n-1) ),
C
C as returned by the SLICOT Library routines MB04TS or MB04TB. The
C matrices U and V are returned in terms of their first N/2 rows:
C
C [ U1 U2 ] [ V1 V2 ]
C U = [ ], V = [ ].
C [ -U2 U1 ] [ -V2 V1 ]
C
C ARGUMENTS
C
C Input/Output Parameters
C
C JOB CHARACTER*1
C Specifies whether the matrix U or the matrix V is
C required:
C = 'U': generate U;
C = 'V': generate V.
C
C TRANS CHARACTER*1
C If JOB = 'U' then TRANS must have the same value as
C the argument TRANA in the previous call of MB04TS or
C MB04TB.
C If JOB = 'V' then TRANS must have the same value as
C the argument TRANB in the previous call of MB04TS or
C MB04TB.
C
C N (input) INTEGER
C The order of the matrices Q1 and Q2. N >= 0.
C
C ILO (input) INTEGER
C ILO must have the same value as in the previous call of
C MB04TS or MB04TB. U and V are equal to the unit matrix
C except in the submatrices
C U([ilo:n n+ilo:2*n], [ilo:n n+ilo:2*n]) and
C V([ilo+1:n n+ilo+1:2*n], [ilo+1:n n+ilo+1:2*n]),
C respectively.
C 1 <= ILO <= N, if N > 0; ILO = 1, if N = 0.
C
C Q1 (input/output) DOUBLE PRECISION array, dimension (LDQ1,N)
C On entry, if JOB = 'U' and TRANS = 'N' then the
C leading N-by-N part of this array must contain in its i-th
C column the vector which defines the elementary reflector
C FU(i).
C If JOB = 'U' and TRANS = 'T' or TRANS = 'C' then the
C leading N-by-N part of this array must contain in its i-th
C row the vector which defines the elementary reflector
C FU(i).
C If JOB = 'V' and TRANS = 'N' then the leading N-by-N
C part of this array must contain in its i-th row the vector
C which defines the elementary reflector FV(i).
C If JOB = 'V' and TRANS = 'T' or TRANS = 'C' then the
C leading N-by-N part of this array must contain in its i-th
C column the vector which defines the elementary reflector
C FV(i).
C On exit, if JOB = 'U' and TRANS = 'N' then the leading
C N-by-N part of this array contains the matrix U1.
C If JOB = 'U' and TRANS = 'T' or TRANS = 'C' then the
C leading N-by-N part of this array contains the matrix
C U1**T.
C If JOB = 'V' and TRANS = 'N' then the leading N-by-N
C part of this array contains the matrix V1**T.
C If JOB = 'V' and TRANS = 'T' or TRANS = 'C' then the
C leading N-by-N part of this array contains the matrix V1.
C
C LDQ1 INTEGER
C The leading dimension of the array Q1. LDQ1 >= MAX(1,N).
C
C Q2 (input/output) DOUBLE PRECISION array, dimension (LDQ2,N)
C On entry, if JOB = 'U' then the leading N-by-N part of
C this array must contain in its i-th column the vector
C which defines the elementary reflector HU(i).
C If JOB = 'V' then the leading N-by-N part of this array
C must contain in its i-th row the vector which defines the
C elementary reflector HV(i).
C On exit, if JOB = 'U' then the leading N-by-N part of
C this array contains the matrix U2.
C If JOB = 'V' then the leading N-by-N part of this array
C contains the matrix V2**T.
C
C LDQ2 INTEGER
C The leading dimension of the array Q2. LDQ2 >= MAX(1,N).
C
C CS (input) DOUBLE PRECISION array, dimension (2N)
C On entry, if JOB = 'U' then the first 2N elements of
C this array must contain the cosines and sines of the
C symplectic Givens rotators GU(i).
C If JOB = 'V' then the first 2N-2 elements of this array
C must contain the cosines and sines of the symplectic
C Givens rotators GV(i).
C
C TAU (input) DOUBLE PRECISION array, dimension (N)
C On entry, if JOB = 'U' then the first N elements of
C this array must contain the scalar factors of the
C elementary reflectors FU(i).
C If JOB = 'V' then the first N-1 elements of this array
C must contain the scalar factors of the elementary
C reflectors FV(i).
C
C Workspace
C
C DWORK DOUBLE PRECISION array, dimension (LDWORK)
C On exit, if INFO = 0, DWORK(1) returns the optimal
C value of LDWORK.
C On exit, if INFO = -12, DWORK(1) returns the minimum
C value of LDWORK.
C
C LDWORK INTEGER
C The length of the array DWORK.
C LDWORK >= MAX(1,2*(N-ILO+1)).
C
C Error Indicator
C
C INFO INTEGER
C = 0: successful exit;
C < 0: if INFO = -i, the i-th argument had an illegal
C value.
C
C REFERENCES
C
C [1] Benner, P., Mehrmann, V., and Xu, H.
C A numerically stable, structure preserving method for
C computing the eigenvalues of real Hamiltonian or symplectic
C pencils. Numer. Math., Vol 78 (3), pp. 329-358, 1998.
C
C [2] Kressner, D.
C Block algorithms for orthogonal symplectic factorizations.
C BIT, 43 (4), pp. 775-790, 2003.
C
C CONTRIBUTORS
C
C D. Kressner, Technical Univ. Berlin, Germany, and
C P. Benner, Technical Univ. Chemnitz, Germany, December 2003.
C
C REVISIONS
C
C V. Sima, June 2008 (SLICOT version of the HAPACK routine DOSGSU).
C
C KEYWORDS
C
C Elementary matrix operations, Hamiltonian matrix, orthogonal
C symplectic matrix.
C
C ******************************************************************
C
C .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
C .. Scalar Arguments ..
CHARACTER JOB, TRANS
INTEGER ILO, INFO, LDQ1, LDQ2, LDWORK, N
C .. Array Arguments ..
DOUBLE PRECISION CS(*), DWORK(*), Q1(LDQ1,*), Q2(LDQ2,*), TAU(*)
C .. Local Scalars ..
LOGICAL COMPU, LTRAN
INTEGER I, IERR, J, NH
C .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
C .. External Subroutines ..
EXTERNAL DLASET, MB04WD, XERBLA
C .. Intrinsic Functions ..
INTRINSIC DBLE, MAX
C
C .. Executable Statements ..
C
C Check the scalar input parameters.
C
INFO = 0
LTRAN = LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' )
COMPU = LSAME( JOB, 'U' )
IF ( .NOT.COMPU .AND. .NOT.LSAME( JOB, 'V' ) ) THEN
INFO = -1
ELSE IF ( .NOT.LTRAN .AND. .NOT.LSAME( TRANS, 'N' ) ) THEN
INFO = -2
ELSE IF ( N.LT.0 ) THEN
INFO = -3
ELSE IF ( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN
INFO = -4
ELSE IF ( LDQ1.LT.MAX( 1, N ) ) THEN
INFO = -6
ELSE IF ( LDQ2.LT.MAX( 1, N ) ) THEN
INFO = -8
ELSE IF ( LDWORK.LT.MAX( 1, 2*( N-ILO+1 ) ) ) THEN
DWORK(1) = DBLE( MAX( 1, 2*( N-ILO+1 ) ) )
INFO = -12
END IF
C
C Return if there were illegal values.
C
IF ( INFO.NE.0 ) THEN
CALL XERBLA( 'MB04WR', -INFO )
RETURN
END IF
C
C Quick return if possible.
C
IF( N.EQ.0 ) THEN
DWORK(1) = ONE
RETURN
END IF
C
IF ( COMPU ) THEN
CALL DLASET( 'All', N, ILO-1, ZERO, ONE, Q1, LDQ1 )
CALL DLASET( 'All', ILO-1, N-ILO+1, ZERO, ZERO, Q1(1,ILO),
$ LDQ1 )
CALL DLASET( 'All', N, ILO-1, ZERO, ZERO, Q2, LDQ2 )
CALL DLASET( 'All', ILO-1, N-ILO+1, ZERO, ZERO, Q2(1,ILO),
$ LDQ2 )
NH = N - ILO + 1
END IF
IF ( COMPU .AND. .NOT.LTRAN ) THEN
C
C Generate U1 and U2.
C
IF ( NH.GT.0 ) THEN
CALL MB04WD( 'No Transpose', 'No Transpose', NH, NH, NH,
$ Q1(ILO,ILO), LDQ1, Q2(ILO,ILO), LDQ2, CS(ILO),
$ TAU(ILO), DWORK, LDWORK, IERR )
END IF
ELSE IF ( COMPU.AND.LTRAN ) THEN
C
C Generate U1**T and U2.
C
IF ( NH.GT.0 ) THEN
CALL MB04WD( 'Transpose', 'No Transpose', NH, NH, NH,
$ Q1(ILO,ILO), LDQ1, Q2(ILO,ILO), LDQ2, CS(ILO),
$ TAU(ILO), DWORK, LDWORK, IERR )
END IF
ELSE IF ( .NOT.COMPU .AND. .NOT.LTRAN ) THEN
C
C Generate V1**T and V2**T.
C
C Shift the vectors which define the elementary reflectors one
C column to the bottom, and set the first ilo rows and
C columns to those of the unit matrix.
C
DO 40 I = 1, N
DO 10 J = N, MAX( I, ILO )+1, -1
Q1(J,I) = ZERO
10 CONTINUE
DO 20 J = MAX( I, ILO ), ILO+1, -1
Q1(J,I) = Q1(J-1,I)
20 CONTINUE
DO 30 J = ILO, 1, -1
Q1(J,I) = ZERO
30 CONTINUE
IF ( I.LE.ILO ) Q1(I,I) = ONE
40 CONTINUE
DO 80 I = 1, N
DO 50 J = N, MAX( I, ILO )+1, -1
Q2(J,I) = ZERO
50 CONTINUE
DO 60 J = MAX( I, ILO ), ILO+1, -1
Q2(J,I) = Q2(J-1,I)
60 CONTINUE
DO 70 J = ILO, 1, -1
Q2(J,I) = ZERO
70 CONTINUE
80 CONTINUE
C
NH = N - ILO
IF ( NH.GT.0 ) THEN
CALL MB04WD( 'Transpose', 'Transpose', NH, NH, NH,
$ Q1(ILO+1,ILO+1), LDQ1, Q2(ILO+1,ILO+1), LDQ2,
$ CS(ILO), TAU(ILO), DWORK, LDWORK, IERR )
END IF
ELSE IF ( .NOT.COMPU .AND. LTRAN ) THEN
C
C Generate V1 and V2**T.
C
C Shift the vectors which define the elementary reflectors one
C column to the right/bottom, and set the first ilo rows and
C columns to those of the unit matrix.
C
DO 110 J = N, ILO + 1, -1
DO 90 I = 1, J-1
Q1(I,J) = ZERO
90 CONTINUE
DO 100 I = J+1, N
Q1(I,J) = Q1(I,J-1)
100 CONTINUE
110 CONTINUE
CALL DLASET( 'All', N, ILO, ZERO, ONE, Q1, LDQ1 )
DO 150 I = 1, N
DO 120 J = N, MAX( I, ILO )+1, -1
Q2(J,I) = ZERO
120 CONTINUE
DO 130 J = MAX( I, ILO ), ILO+1, -1
Q2(J,I) = Q2(J-1,I)
130 CONTINUE
DO 140 J = ILO, 1, -1
Q2(J,I) = ZERO
140 CONTINUE
150 CONTINUE
NH = N - ILO
C
IF ( NH.GT.0 ) THEN
CALL MB04WD( 'No Transpose', 'Transpose', NH, NH, NH,
$ Q1(ILO+1,ILO+1), LDQ1, Q2(ILO+1,ILO+1), LDQ2,
$ CS(ILO), TAU(ILO), DWORK, LDWORK, IERR )
END IF
END IF
RETURN
C *** Last line of MB04WR ***
END
|
