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|
*> \brief \b SORM22 multiplies a general matrix by a banded orthogonal matrix.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download SORM22 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sorm22.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sorm22.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sorm22.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE SORM22( SIDE, TRANS, M, N, N1, N2, Q, LDQ, C, LDC,
* $ WORK, LWORK, INFO )
*
* .. Scalar Arguments ..
* CHARACTER SIDE, TRANS
* INTEGER M, N, N1, N2, LDQ, LDC, LWORK, INFO
* ..
* .. Array Arguments ..
* REAL Q( LDQ, * ), C( LDC, * ), WORK( * )
* ..
*
*> \par Purpose
* ============
*>
*> \verbatim
*>
*>
*> SORM22 overwrites the general real M-by-N matrix C with
*>
*> SIDE = 'L' SIDE = 'R'
*> TRANS = 'N': Q * C C * Q
*> TRANS = 'T': Q**T * C C * Q**T
*>
*> where Q is a real orthogonal matrix of order NQ, with NQ = M if
*> SIDE = 'L' and NQ = N if SIDE = 'R'.
*> The orthogonal matrix Q processes a 2-by-2 block structure
*>
*> [ Q11 Q12 ]
*> Q = [ ]
*> [ Q21 Q22 ],
*>
*> where Q12 is an N1-by-N1 lower triangular matrix and Q21 is an
*> N2-by-N2 upper triangular matrix.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] SIDE
*> \verbatim
*> SIDE is CHARACTER*1
*> = 'L': apply Q or Q**T from the Left;
*> = 'R': apply Q or Q**T from the Right.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> = 'N': apply Q (No transpose);
*> = 'C': apply Q**T (Conjugate transpose).
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix C. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix C. N >= 0.
*> \endverbatim
*>
*> \param[in] N1
*> \param[in] N2
*> \verbatim
*> N1 is INTEGER
*> N2 is INTEGER
*> The dimension of Q12 and Q21, respectively. N1, N2 >= 0.
*> The following requirement must be satisfied:
*> N1 + N2 = M if SIDE = 'L' and N1 + N2 = N if SIDE = 'R'.
*> \endverbatim
*>
*> \param[in] Q
*> \verbatim
*> Q is REAL array, dimension
*> (LDQ,M) if SIDE = 'L'
*> (LDQ,N) if SIDE = 'R'
*> \endverbatim
*>
*> \param[in] LDQ
*> \verbatim
*> LDQ is INTEGER
*> The leading dimension of the array Q.
*> LDQ >= max(1,M) if SIDE = 'L'; LDQ >= max(1,N) if SIDE = 'R'.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is REAL array, dimension (LDC,N)
*> On entry, the M-by-N matrix C.
*> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*> LDC is INTEGER
*> The leading dimension of the array C. LDC >= max(1,M).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array, dimension (MAX(1,LWORK))
*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The dimension of the array WORK.
*> If SIDE = 'L', LWORK >= max(1,N);
*> if SIDE = 'R', LWORK >= max(1,M).
*> For optimum performance LWORK >= M*N.
*>
*> If LWORK = -1, then a workspace query is assumed; the routine
*> only calculates the optimal size of the WORK array, returns
*> this value as the first entry of the WORK array, and no error
*> message related to LWORK is issued by XERBLA.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date January 2015
*
*> \ingroup complexOTHERcomputational
*
* =====================================================================
SUBROUTINE SORM22( SIDE, TRANS, M, N, N1, N2, Q, LDQ, C, LDC,
$ WORK, LWORK, INFO )
*
* -- LAPACK computational routine (version 3.7.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* January 2015
*
IMPLICIT NONE
*
* .. Scalar Arguments ..
CHARACTER SIDE, TRANS
INTEGER M, N, N1, N2, LDQ, LDC, LWORK, INFO
* ..
* .. Array Arguments ..
REAL Q( LDQ, * ), C( LDC, * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ONE
PARAMETER ( ONE = 1.0E+0 )
*
* .. Local Scalars ..
LOGICAL LEFT, LQUERY, NOTRAN
INTEGER I, LDWORK, LEN, LWKOPT, NB, NQ, NW
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL SGEMM, SLACPY, STRMM, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC REAL, MAX, MIN
* ..
* .. Executable Statements ..
*
* Test the input arguments
*
INFO = 0
LEFT = LSAME( SIDE, 'L' )
NOTRAN = LSAME( TRANS, 'N' )
LQUERY = ( LWORK.EQ.-1 )
*
* NQ is the order of Q;
* NW is the minimum dimension of WORK.
*
IF( LEFT ) THEN
NQ = M
ELSE
NQ = N
END IF
NW = NQ
IF( N1.EQ.0 .OR. N2.EQ.0 ) NW = 1
IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
INFO = -1
ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.LSAME( TRANS, 'T' ) )
$ THEN
INFO = -2
ELSE IF( M.LT.0 ) THEN
INFO = -3
ELSE IF( N.LT.0 ) THEN
INFO = -4
ELSE IF( N1.LT.0 .OR. N1+N2.NE.NQ ) THEN
INFO = -5
ELSE IF( N2.LT.0 ) THEN
INFO = -6
ELSE IF( LDQ.LT.MAX( 1, NQ ) ) THEN
INFO = -8
ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
INFO = -10
ELSE IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN
INFO = -12
END IF
*
IF( INFO.EQ.0 ) THEN
LWKOPT = M*N
WORK( 1 ) = REAL( LWKOPT )
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SORM22', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Quick return if possible
*
IF( M.EQ.0 .OR. N.EQ.0 ) THEN
WORK( 1 ) = 1
RETURN
END IF
*
* Degenerate cases (N1 = 0 or N2 = 0) are handled using STRMM.
*
IF( N1.EQ.0 ) THEN
CALL STRMM( SIDE, 'Upper', TRANS, 'Non-Unit', M, N, ONE,
$ Q, LDQ, C, LDC )
WORK( 1 ) = ONE
RETURN
ELSE IF( N2.EQ.0 ) THEN
CALL STRMM( SIDE, 'Lower', TRANS, 'Non-Unit', M, N, ONE,
$ Q, LDQ, C, LDC )
WORK( 1 ) = ONE
RETURN
END IF
*
* Compute the largest chunk size available from the workspace.
*
NB = MAX( 1, MIN( LWORK, LWKOPT ) / NQ )
*
IF( LEFT ) THEN
IF( NOTRAN ) THEN
DO I = 1, N, NB
LEN = MIN( NB, N-I+1 )
LDWORK = M
*
* Multiply bottom part of C by Q12.
*
CALL SLACPY( 'All', N1, LEN, C( N2+1, I ), LDC, WORK,
$ LDWORK )
CALL STRMM( 'Left', 'Lower', 'No Transpose', 'Non-Unit',
$ N1, LEN, ONE, Q( 1, N2+1 ), LDQ, WORK,
$ LDWORK )
*
* Multiply top part of C by Q11.
*
CALL SGEMM( 'No Transpose', 'No Transpose', N1, LEN, N2,
$ ONE, Q, LDQ, C( 1, I ), LDC, ONE, WORK,
$ LDWORK )
*
* Multiply top part of C by Q21.
*
CALL SLACPY( 'All', N2, LEN, C( 1, I ), LDC,
$ WORK( N1+1 ), LDWORK )
CALL STRMM( 'Left', 'Upper', 'No Transpose', 'Non-Unit',
$ N2, LEN, ONE, Q( N1+1, 1 ), LDQ,
$ WORK( N1+1 ), LDWORK )
*
* Multiply bottom part of C by Q22.
*
CALL SGEMM( 'No Transpose', 'No Transpose', N2, LEN, N1,
$ ONE, Q( N1+1, N2+1 ), LDQ, C( N2+1, I ), LDC,
$ ONE, WORK( N1+1 ), LDWORK )
*
* Copy everything back.
*
CALL SLACPY( 'All', M, LEN, WORK, LDWORK, C( 1, I ),
$ LDC )
END DO
ELSE
DO I = 1, N, NB
LEN = MIN( NB, N-I+1 )
LDWORK = M
*
* Multiply bottom part of C by Q21**T.
*
CALL SLACPY( 'All', N2, LEN, C( N1+1, I ), LDC, WORK,
$ LDWORK )
CALL STRMM( 'Left', 'Upper', 'Transpose', 'Non-Unit',
$ N2, LEN, ONE, Q( N1+1, 1 ), LDQ, WORK,
$ LDWORK )
*
* Multiply top part of C by Q11**T.
*
CALL SGEMM( 'Transpose', 'No Transpose', N2, LEN, N1,
$ ONE, Q, LDQ, C( 1, I ), LDC, ONE, WORK,
$ LDWORK )
*
* Multiply top part of C by Q12**T.
*
CALL SLACPY( 'All', N1, LEN, C( 1, I ), LDC,
$ WORK( N2+1 ), LDWORK )
CALL STRMM( 'Left', 'Lower', 'Transpose', 'Non-Unit',
$ N1, LEN, ONE, Q( 1, N2+1 ), LDQ,
$ WORK( N2+1 ), LDWORK )
*
* Multiply bottom part of C by Q22**T.
*
CALL SGEMM( 'Transpose', 'No Transpose', N1, LEN, N2,
$ ONE, Q( N1+1, N2+1 ), LDQ, C( N1+1, I ), LDC,
$ ONE, WORK( N2+1 ), LDWORK )
*
* Copy everything back.
*
CALL SLACPY( 'All', M, LEN, WORK, LDWORK, C( 1, I ),
$ LDC )
END DO
END IF
ELSE
IF( NOTRAN ) THEN
DO I = 1, M, NB
LEN = MIN( NB, M-I+1 )
LDWORK = LEN
*
* Multiply right part of C by Q21.
*
CALL SLACPY( 'All', LEN, N2, C( I, N1+1 ), LDC, WORK,
$ LDWORK )
CALL STRMM( 'Right', 'Upper', 'No Transpose', 'Non-Unit',
$ LEN, N2, ONE, Q( N1+1, 1 ), LDQ, WORK,
$ LDWORK )
*
* Multiply left part of C by Q11.
*
CALL SGEMM( 'No Transpose', 'No Transpose', LEN, N2, N1,
$ ONE, C( I, 1 ), LDC, Q, LDQ, ONE, WORK,
$ LDWORK )
*
* Multiply left part of C by Q12.
*
CALL SLACPY( 'All', LEN, N1, C( I, 1 ), LDC,
$ WORK( 1 + N2*LDWORK ), LDWORK )
CALL STRMM( 'Right', 'Lower', 'No Transpose', 'Non-Unit',
$ LEN, N1, ONE, Q( 1, N2+1 ), LDQ,
$ WORK( 1 + N2*LDWORK ), LDWORK )
*
* Multiply right part of C by Q22.
*
CALL SGEMM( 'No Transpose', 'No Transpose', LEN, N1, N2,
$ ONE, C( I, N1+1 ), LDC, Q( N1+1, N2+1 ), LDQ,
$ ONE, WORK( 1 + N2*LDWORK ), LDWORK )
*
* Copy everything back.
*
CALL SLACPY( 'All', LEN, N, WORK, LDWORK, C( I, 1 ),
$ LDC )
END DO
ELSE
DO I = 1, M, NB
LEN = MIN( NB, M-I+1 )
LDWORK = LEN
*
* Multiply right part of C by Q12**T.
*
CALL SLACPY( 'All', LEN, N1, C( I, N2+1 ), LDC, WORK,
$ LDWORK )
CALL STRMM( 'Right', 'Lower', 'Transpose', 'Non-Unit',
$ LEN, N1, ONE, Q( 1, N2+1 ), LDQ, WORK,
$ LDWORK )
*
* Multiply left part of C by Q11**T.
*
CALL SGEMM( 'No Transpose', 'Transpose', LEN, N1, N2,
$ ONE, C( I, 1 ), LDC, Q, LDQ, ONE, WORK,
$ LDWORK )
*
* Multiply left part of C by Q21**T.
*
CALL SLACPY( 'All', LEN, N2, C( I, 1 ), LDC,
$ WORK( 1 + N1*LDWORK ), LDWORK )
CALL STRMM( 'Right', 'Upper', 'Transpose', 'Non-Unit',
$ LEN, N2, ONE, Q( N1+1, 1 ), LDQ,
$ WORK( 1 + N1*LDWORK ), LDWORK )
*
* Multiply right part of C by Q22**T.
*
CALL SGEMM( 'No Transpose', 'Transpose', LEN, N2, N1,
$ ONE, C( I, N2+1 ), LDC, Q( N1+1, N2+1 ), LDQ,
$ ONE, WORK( 1 + N1*LDWORK ), LDWORK )
*
* Copy everything back.
*
CALL SLACPY( 'All', LEN, N, WORK, LDWORK, C( I, 1 ),
$ LDC )
END DO
END IF
END IF
*
WORK( 1 ) = REAL( LWKOPT )
RETURN
*
* End of SORM22
*
END
|
