731 lines
22 KiB
Fortran
731 lines
22 KiB
Fortran
*> \brief \b CLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
*> \htmlonly
|
|
*> Download CLARFB + dependencies
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clarfb.f">
|
|
*> [TGZ]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clarfb.f">
|
|
*> [ZIP]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clarfb.f">
|
|
*> [TXT]</a>
|
|
*> \endhtmlonly
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE CLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,
|
|
* T, LDT, C, LDC, WORK, LDWORK )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* CHARACTER DIRECT, SIDE, STOREV, TRANS
|
|
* INTEGER K, LDC, LDT, LDV, LDWORK, M, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* COMPLEX C( LDC, * ), T( LDT, * ), V( LDV, * ),
|
|
* $ WORK( LDWORK, * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> CLARFB applies a complex block reflector H or its transpose H**H to a
|
|
*> complex M-by-N matrix C, from either the left or the right.
|
|
*> \endverbatim
|
|
*
|
|
* Arguments:
|
|
* ==========
|
|
*
|
|
*> \param[in] SIDE
|
|
*> \verbatim
|
|
*> SIDE is CHARACTER*1
|
|
*> = 'L': apply H or H**H from the Left
|
|
*> = 'R': apply H or H**H from the Right
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] TRANS
|
|
*> \verbatim
|
|
*> TRANS is CHARACTER*1
|
|
*> = 'N': apply H (No transpose)
|
|
*> = 'C': apply H**H (Conjugate transpose)
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] DIRECT
|
|
*> \verbatim
|
|
*> DIRECT is CHARACTER*1
|
|
*> Indicates how H is formed from a product of elementary
|
|
*> reflectors
|
|
*> = 'F': H = H(1) H(2) . . . H(k) (Forward)
|
|
*> = 'B': H = H(k) . . . H(2) H(1) (Backward)
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] STOREV
|
|
*> \verbatim
|
|
*> STOREV is CHARACTER*1
|
|
*> Indicates how the vectors which define the elementary
|
|
*> reflectors are stored:
|
|
*> = 'C': Columnwise
|
|
*> = 'R': Rowwise
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] M
|
|
*> \verbatim
|
|
*> M is INTEGER
|
|
*> The number of rows of the matrix C.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] N
|
|
*> \verbatim
|
|
*> N is INTEGER
|
|
*> The number of columns of the matrix C.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] K
|
|
*> \verbatim
|
|
*> K is INTEGER
|
|
*> The order of the matrix T (= the number of elementary
|
|
*> reflectors whose product defines the block reflector).
|
|
*> If SIDE = 'L', M >= K >= 0;
|
|
*> if SIDE = 'R', N >= K >= 0.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] V
|
|
*> \verbatim
|
|
*> V is COMPLEX array, dimension
|
|
*> (LDV,K) if STOREV = 'C'
|
|
*> (LDV,M) if STOREV = 'R' and SIDE = 'L'
|
|
*> (LDV,N) if STOREV = 'R' and SIDE = 'R'
|
|
*> The matrix V. See Further Details.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDV
|
|
*> \verbatim
|
|
*> LDV is INTEGER
|
|
*> The leading dimension of the array V.
|
|
*> If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
|
|
*> if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
|
|
*> if STOREV = 'R', LDV >= K.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] T
|
|
*> \verbatim
|
|
*> T is COMPLEX array, dimension (LDT,K)
|
|
*> The triangular K-by-K matrix T in the representation of the
|
|
*> block reflector.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDT
|
|
*> \verbatim
|
|
*> LDT is INTEGER
|
|
*> The leading dimension of the array T. LDT >= K.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in,out] C
|
|
*> \verbatim
|
|
*> C is COMPLEX array, dimension (LDC,N)
|
|
*> On entry, the M-by-N matrix C.
|
|
*> On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.
|
|
*> \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 COMPLEX array, dimension (LDWORK,K)
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDWORK
|
|
*> \verbatim
|
|
*> LDWORK is INTEGER
|
|
*> The leading dimension of the array WORK.
|
|
*> If SIDE = 'L', LDWORK >= max(1,N);
|
|
*> if SIDE = 'R', LDWORK >= max(1,M).
|
|
*> \endverbatim
|
|
*
|
|
* Authors:
|
|
* ========
|
|
*
|
|
*> \author Univ. of Tennessee
|
|
*> \author Univ. of California Berkeley
|
|
*> \author Univ. of Colorado Denver
|
|
*> \author NAG Ltd.
|
|
*
|
|
*> \ingroup complexOTHERauxiliary
|
|
*
|
|
*> \par Further Details:
|
|
* =====================
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> The shape of the matrix V and the storage of the vectors which define
|
|
*> the H(i) is best illustrated by the following example with n = 5 and
|
|
*> k = 3. The elements equal to 1 are not stored; the corresponding
|
|
*> array elements are modified but restored on exit. The rest of the
|
|
*> array is not used.
|
|
*>
|
|
*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R':
|
|
*>
|
|
*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 )
|
|
*> ( v1 1 ) ( 1 v2 v2 v2 )
|
|
*> ( v1 v2 1 ) ( 1 v3 v3 )
|
|
*> ( v1 v2 v3 )
|
|
*> ( v1 v2 v3 )
|
|
*>
|
|
*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':
|
|
*>
|
|
*> V = ( v1 v2 v3 ) V = ( v1 v1 1 )
|
|
*> ( v1 v2 v3 ) ( v2 v2 v2 1 )
|
|
*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 )
|
|
*> ( 1 v3 )
|
|
*> ( 1 )
|
|
*> \endverbatim
|
|
*>
|
|
* =====================================================================
|
|
SUBROUTINE CLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,
|
|
$ T, LDT, C, LDC, WORK, LDWORK )
|
|
*
|
|
* -- LAPACK auxiliary routine --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
*
|
|
* .. Scalar Arguments ..
|
|
CHARACTER DIRECT, SIDE, STOREV, TRANS
|
|
INTEGER K, LDC, LDT, LDV, LDWORK, M, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
COMPLEX C( LDC, * ), T( LDT, * ), V( LDV, * ),
|
|
$ WORK( LDWORK, * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
COMPLEX ONE
|
|
PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
CHARACTER TRANST
|
|
INTEGER I, J
|
|
* ..
|
|
* .. External Functions ..
|
|
LOGICAL LSAME
|
|
EXTERNAL LSAME
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL CCOPY, CGEMM, CLACGV, CTRMM
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC CONJG
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
* Quick return if possible
|
|
*
|
|
IF( M.LE.0 .OR. N.LE.0 )
|
|
$ RETURN
|
|
*
|
|
IF( LSAME( TRANS, 'N' ) ) THEN
|
|
TRANST = 'C'
|
|
ELSE
|
|
TRANST = 'N'
|
|
END IF
|
|
*
|
|
IF( LSAME( STOREV, 'C' ) ) THEN
|
|
*
|
|
IF( LSAME( DIRECT, 'F' ) ) THEN
|
|
*
|
|
* Let V = ( V1 ) (first K rows)
|
|
* ( V2 )
|
|
* where V1 is unit lower triangular.
|
|
*
|
|
IF( LSAME( SIDE, 'L' ) ) THEN
|
|
*
|
|
* Form H * C or H**H * C where C = ( C1 )
|
|
* ( C2 )
|
|
*
|
|
* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK)
|
|
*
|
|
* W := C1**H
|
|
*
|
|
DO 10 J = 1, K
|
|
CALL CCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
|
|
CALL CLACGV( N, WORK( 1, J ), 1 )
|
|
10 CONTINUE
|
|
*
|
|
* W := W * V1
|
|
*
|
|
CALL CTRMM( 'Right', 'Lower', 'No transpose', 'Unit', N,
|
|
$ K, ONE, V, LDV, WORK, LDWORK )
|
|
IF( M.GT.K ) THEN
|
|
*
|
|
* W := W + C2**H *V2
|
|
*
|
|
CALL CGEMM( 'Conjugate transpose', 'No transpose', N,
|
|
$ K, M-K, ONE, C( K+1, 1 ), LDC,
|
|
$ V( K+1, 1 ), LDV, ONE, WORK, LDWORK )
|
|
END IF
|
|
*
|
|
* W := W * T**H or W * T
|
|
*
|
|
CALL CTRMM( 'Right', 'Upper', TRANST, 'Non-unit', N, K,
|
|
$ ONE, T, LDT, WORK, LDWORK )
|
|
*
|
|
* C := C - V * W**H
|
|
*
|
|
IF( M.GT.K ) THEN
|
|
*
|
|
* C2 := C2 - V2 * W**H
|
|
*
|
|
CALL CGEMM( 'No transpose', 'Conjugate transpose',
|
|
$ M-K, N, K, -ONE, V( K+1, 1 ), LDV, WORK,
|
|
$ LDWORK, ONE, C( K+1, 1 ), LDC )
|
|
END IF
|
|
*
|
|
* W := W * V1**H
|
|
*
|
|
CALL CTRMM( 'Right', 'Lower', 'Conjugate transpose',
|
|
$ 'Unit', N, K, ONE, V, LDV, WORK, LDWORK )
|
|
*
|
|
* C1 := C1 - W**H
|
|
*
|
|
DO 30 J = 1, K
|
|
DO 20 I = 1, N
|
|
C( J, I ) = C( J, I ) - CONJG( WORK( I, J ) )
|
|
20 CONTINUE
|
|
30 CONTINUE
|
|
*
|
|
ELSE IF( LSAME( SIDE, 'R' ) ) THEN
|
|
*
|
|
* Form C * H or C * H**H where C = ( C1 C2 )
|
|
*
|
|
* W := C * V = (C1*V1 + C2*V2) (stored in WORK)
|
|
*
|
|
* W := C1
|
|
*
|
|
DO 40 J = 1, K
|
|
CALL CCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 )
|
|
40 CONTINUE
|
|
*
|
|
* W := W * V1
|
|
*
|
|
CALL CTRMM( 'Right', 'Lower', 'No transpose', 'Unit', M,
|
|
$ K, ONE, V, LDV, WORK, LDWORK )
|
|
IF( N.GT.K ) THEN
|
|
*
|
|
* W := W + C2 * V2
|
|
*
|
|
CALL CGEMM( 'No transpose', 'No transpose', M, K, N-K,
|
|
$ ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV,
|
|
$ ONE, WORK, LDWORK )
|
|
END IF
|
|
*
|
|
* W := W * T or W * T**H
|
|
*
|
|
CALL CTRMM( 'Right', 'Upper', TRANS, 'Non-unit', M, K,
|
|
$ ONE, T, LDT, WORK, LDWORK )
|
|
*
|
|
* C := C - W * V**H
|
|
*
|
|
IF( N.GT.K ) THEN
|
|
*
|
|
* C2 := C2 - W * V2**H
|
|
*
|
|
CALL CGEMM( 'No transpose', 'Conjugate transpose', M,
|
|
$ N-K, K, -ONE, WORK, LDWORK, V( K+1, 1 ),
|
|
$ LDV, ONE, C( 1, K+1 ), LDC )
|
|
END IF
|
|
*
|
|
* W := W * V1**H
|
|
*
|
|
CALL CTRMM( 'Right', 'Lower', 'Conjugate transpose',
|
|
$ 'Unit', M, K, ONE, V, LDV, WORK, LDWORK )
|
|
*
|
|
* C1 := C1 - W
|
|
*
|
|
DO 60 J = 1, K
|
|
DO 50 I = 1, M
|
|
C( I, J ) = C( I, J ) - WORK( I, J )
|
|
50 CONTINUE
|
|
60 CONTINUE
|
|
END IF
|
|
*
|
|
ELSE
|
|
*
|
|
* Let V = ( V1 )
|
|
* ( V2 ) (last K rows)
|
|
* where V2 is unit upper triangular.
|
|
*
|
|
IF( LSAME( SIDE, 'L' ) ) THEN
|
|
*
|
|
* Form H * C or H**H * C where C = ( C1 )
|
|
* ( C2 )
|
|
*
|
|
* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK)
|
|
*
|
|
* W := C2**H
|
|
*
|
|
DO 70 J = 1, K
|
|
CALL CCOPY( N, C( M-K+J, 1 ), LDC, WORK( 1, J ), 1 )
|
|
CALL CLACGV( N, WORK( 1, J ), 1 )
|
|
70 CONTINUE
|
|
*
|
|
* W := W * V2
|
|
*
|
|
CALL CTRMM( 'Right', 'Upper', 'No transpose', 'Unit', N,
|
|
$ K, ONE, V( M-K+1, 1 ), LDV, WORK, LDWORK )
|
|
IF( M.GT.K ) THEN
|
|
*
|
|
* W := W + C1**H * V1
|
|
*
|
|
CALL CGEMM( 'Conjugate transpose', 'No transpose', N,
|
|
$ K, M-K, ONE, C, LDC, V, LDV, ONE, WORK,
|
|
$ LDWORK )
|
|
END IF
|
|
*
|
|
* W := W * T**H or W * T
|
|
*
|
|
CALL CTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K,
|
|
$ ONE, T, LDT, WORK, LDWORK )
|
|
*
|
|
* C := C - V * W**H
|
|
*
|
|
IF( M.GT.K ) THEN
|
|
*
|
|
* C1 := C1 - V1 * W**H
|
|
*
|
|
CALL CGEMM( 'No transpose', 'Conjugate transpose',
|
|
$ M-K, N, K, -ONE, V, LDV, WORK, LDWORK,
|
|
$ ONE, C, LDC )
|
|
END IF
|
|
*
|
|
* W := W * V2**H
|
|
*
|
|
CALL CTRMM( 'Right', 'Upper', 'Conjugate transpose',
|
|
$ 'Unit', N, K, ONE, V( M-K+1, 1 ), LDV, WORK,
|
|
$ LDWORK )
|
|
*
|
|
* C2 := C2 - W**H
|
|
*
|
|
DO 90 J = 1, K
|
|
DO 80 I = 1, N
|
|
C( M-K+J, I ) = C( M-K+J, I ) -
|
|
$ CONJG( WORK( I, J ) )
|
|
80 CONTINUE
|
|
90 CONTINUE
|
|
*
|
|
ELSE IF( LSAME( SIDE, 'R' ) ) THEN
|
|
*
|
|
* Form C * H or C * H**H where C = ( C1 C2 )
|
|
*
|
|
* W := C * V = (C1*V1 + C2*V2) (stored in WORK)
|
|
*
|
|
* W := C2
|
|
*
|
|
DO 100 J = 1, K
|
|
CALL CCOPY( M, C( 1, N-K+J ), 1, WORK( 1, J ), 1 )
|
|
100 CONTINUE
|
|
*
|
|
* W := W * V2
|
|
*
|
|
CALL CTRMM( 'Right', 'Upper', 'No transpose', 'Unit', M,
|
|
$ K, ONE, V( N-K+1, 1 ), LDV, WORK, LDWORK )
|
|
IF( N.GT.K ) THEN
|
|
*
|
|
* W := W + C1 * V1
|
|
*
|
|
CALL CGEMM( 'No transpose', 'No transpose', M, K, N-K,
|
|
$ ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )
|
|
END IF
|
|
*
|
|
* W := W * T or W * T**H
|
|
*
|
|
CALL CTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K,
|
|
$ ONE, T, LDT, WORK, LDWORK )
|
|
*
|
|
* C := C - W * V**H
|
|
*
|
|
IF( N.GT.K ) THEN
|
|
*
|
|
* C1 := C1 - W * V1**H
|
|
*
|
|
CALL CGEMM( 'No transpose', 'Conjugate transpose', M,
|
|
$ N-K, K, -ONE, WORK, LDWORK, V, LDV, ONE,
|
|
$ C, LDC )
|
|
END IF
|
|
*
|
|
* W := W * V2**H
|
|
*
|
|
CALL CTRMM( 'Right', 'Upper', 'Conjugate transpose',
|
|
$ 'Unit', M, K, ONE, V( N-K+1, 1 ), LDV, WORK,
|
|
$ LDWORK )
|
|
*
|
|
* C2 := C2 - W
|
|
*
|
|
DO 120 J = 1, K
|
|
DO 110 I = 1, M
|
|
C( I, N-K+J ) = C( I, N-K+J ) - WORK( I, J )
|
|
110 CONTINUE
|
|
120 CONTINUE
|
|
END IF
|
|
END IF
|
|
*
|
|
ELSE IF( LSAME( STOREV, 'R' ) ) THEN
|
|
*
|
|
IF( LSAME( DIRECT, 'F' ) ) THEN
|
|
*
|
|
* Let V = ( V1 V2 ) (V1: first K columns)
|
|
* where V1 is unit upper triangular.
|
|
*
|
|
IF( LSAME( SIDE, 'L' ) ) THEN
|
|
*
|
|
* Form H * C or H**H * C where C = ( C1 )
|
|
* ( C2 )
|
|
*
|
|
* W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK)
|
|
*
|
|
* W := C1**H
|
|
*
|
|
DO 130 J = 1, K
|
|
CALL CCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
|
|
CALL CLACGV( N, WORK( 1, J ), 1 )
|
|
130 CONTINUE
|
|
*
|
|
* W := W * V1**H
|
|
*
|
|
CALL CTRMM( 'Right', 'Upper', 'Conjugate transpose',
|
|
$ 'Unit', N, K, ONE, V, LDV, WORK, LDWORK )
|
|
IF( M.GT.K ) THEN
|
|
*
|
|
* W := W + C2**H * V2**H
|
|
*
|
|
CALL CGEMM( 'Conjugate transpose',
|
|
$ 'Conjugate transpose', N, K, M-K, ONE,
|
|
$ C( K+1, 1 ), LDC, V( 1, K+1 ), LDV, ONE,
|
|
$ WORK, LDWORK )
|
|
END IF
|
|
*
|
|
* W := W * T**H or W * T
|
|
*
|
|
CALL CTRMM( 'Right', 'Upper', TRANST, 'Non-unit', N, K,
|
|
$ ONE, T, LDT, WORK, LDWORK )
|
|
*
|
|
* C := C - V**H * W**H
|
|
*
|
|
IF( M.GT.K ) THEN
|
|
*
|
|
* C2 := C2 - V2**H * W**H
|
|
*
|
|
CALL CGEMM( 'Conjugate transpose',
|
|
$ 'Conjugate transpose', M-K, N, K, -ONE,
|
|
$ V( 1, K+1 ), LDV, WORK, LDWORK, ONE,
|
|
$ C( K+1, 1 ), LDC )
|
|
END IF
|
|
*
|
|
* W := W * V1
|
|
*
|
|
CALL CTRMM( 'Right', 'Upper', 'No transpose', 'Unit', N,
|
|
$ K, ONE, V, LDV, WORK, LDWORK )
|
|
*
|
|
* C1 := C1 - W**H
|
|
*
|
|
DO 150 J = 1, K
|
|
DO 140 I = 1, N
|
|
C( J, I ) = C( J, I ) - CONJG( WORK( I, J ) )
|
|
140 CONTINUE
|
|
150 CONTINUE
|
|
*
|
|
ELSE IF( LSAME( SIDE, 'R' ) ) THEN
|
|
*
|
|
* Form C * H or C * H**H where C = ( C1 C2 )
|
|
*
|
|
* W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK)
|
|
*
|
|
* W := C1
|
|
*
|
|
DO 160 J = 1, K
|
|
CALL CCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 )
|
|
160 CONTINUE
|
|
*
|
|
* W := W * V1**H
|
|
*
|
|
CALL CTRMM( 'Right', 'Upper', 'Conjugate transpose',
|
|
$ 'Unit', M, K, ONE, V, LDV, WORK, LDWORK )
|
|
IF( N.GT.K ) THEN
|
|
*
|
|
* W := W + C2 * V2**H
|
|
*
|
|
CALL CGEMM( 'No transpose', 'Conjugate transpose', M,
|
|
$ K, N-K, ONE, C( 1, K+1 ), LDC,
|
|
$ V( 1, K+1 ), LDV, ONE, WORK, LDWORK )
|
|
END IF
|
|
*
|
|
* W := W * T or W * T**H
|
|
*
|
|
CALL CTRMM( 'Right', 'Upper', TRANS, 'Non-unit', M, K,
|
|
$ ONE, T, LDT, WORK, LDWORK )
|
|
*
|
|
* C := C - W * V
|
|
*
|
|
IF( N.GT.K ) THEN
|
|
*
|
|
* C2 := C2 - W * V2
|
|
*
|
|
CALL CGEMM( 'No transpose', 'No transpose', M, N-K, K,
|
|
$ -ONE, WORK, LDWORK, V( 1, K+1 ), LDV, ONE,
|
|
$ C( 1, K+1 ), LDC )
|
|
END IF
|
|
*
|
|
* W := W * V1
|
|
*
|
|
CALL CTRMM( 'Right', 'Upper', 'No transpose', 'Unit', M,
|
|
$ K, ONE, V, LDV, WORK, LDWORK )
|
|
*
|
|
* C1 := C1 - W
|
|
*
|
|
DO 180 J = 1, K
|
|
DO 170 I = 1, M
|
|
C( I, J ) = C( I, J ) - WORK( I, J )
|
|
170 CONTINUE
|
|
180 CONTINUE
|
|
*
|
|
END IF
|
|
*
|
|
ELSE
|
|
*
|
|
* Let V = ( V1 V2 ) (V2: last K columns)
|
|
* where V2 is unit lower triangular.
|
|
*
|
|
IF( LSAME( SIDE, 'L' ) ) THEN
|
|
*
|
|
* Form H * C or H**H * C where C = ( C1 )
|
|
* ( C2 )
|
|
*
|
|
* W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK)
|
|
*
|
|
* W := C2**H
|
|
*
|
|
DO 190 J = 1, K
|
|
CALL CCOPY( N, C( M-K+J, 1 ), LDC, WORK( 1, J ), 1 )
|
|
CALL CLACGV( N, WORK( 1, J ), 1 )
|
|
190 CONTINUE
|
|
*
|
|
* W := W * V2**H
|
|
*
|
|
CALL CTRMM( 'Right', 'Lower', 'Conjugate transpose',
|
|
$ 'Unit', N, K, ONE, V( 1, M-K+1 ), LDV, WORK,
|
|
$ LDWORK )
|
|
IF( M.GT.K ) THEN
|
|
*
|
|
* W := W + C1**H * V1**H
|
|
*
|
|
CALL CGEMM( 'Conjugate transpose',
|
|
$ 'Conjugate transpose', N, K, M-K, ONE, C,
|
|
$ LDC, V, LDV, ONE, WORK, LDWORK )
|
|
END IF
|
|
*
|
|
* W := W * T**H or W * T
|
|
*
|
|
CALL CTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K,
|
|
$ ONE, T, LDT, WORK, LDWORK )
|
|
*
|
|
* C := C - V**H * W**H
|
|
*
|
|
IF( M.GT.K ) THEN
|
|
*
|
|
* C1 := C1 - V1**H * W**H
|
|
*
|
|
CALL CGEMM( 'Conjugate transpose',
|
|
$ 'Conjugate transpose', M-K, N, K, -ONE, V,
|
|
$ LDV, WORK, LDWORK, ONE, C, LDC )
|
|
END IF
|
|
*
|
|
* W := W * V2
|
|
*
|
|
CALL CTRMM( 'Right', 'Lower', 'No transpose', 'Unit', N,
|
|
$ K, ONE, V( 1, M-K+1 ), LDV, WORK, LDWORK )
|
|
*
|
|
* C2 := C2 - W**H
|
|
*
|
|
DO 210 J = 1, K
|
|
DO 200 I = 1, N
|
|
C( M-K+J, I ) = C( M-K+J, I ) -
|
|
$ CONJG( WORK( I, J ) )
|
|
200 CONTINUE
|
|
210 CONTINUE
|
|
*
|
|
ELSE IF( LSAME( SIDE, 'R' ) ) THEN
|
|
*
|
|
* Form C * H or C * H**H where C = ( C1 C2 )
|
|
*
|
|
* W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK)
|
|
*
|
|
* W := C2
|
|
*
|
|
DO 220 J = 1, K
|
|
CALL CCOPY( M, C( 1, N-K+J ), 1, WORK( 1, J ), 1 )
|
|
220 CONTINUE
|
|
*
|
|
* W := W * V2**H
|
|
*
|
|
CALL CTRMM( 'Right', 'Lower', 'Conjugate transpose',
|
|
$ 'Unit', M, K, ONE, V( 1, N-K+1 ), LDV, WORK,
|
|
$ LDWORK )
|
|
IF( N.GT.K ) THEN
|
|
*
|
|
* W := W + C1 * V1**H
|
|
*
|
|
CALL CGEMM( 'No transpose', 'Conjugate transpose', M,
|
|
$ K, N-K, ONE, C, LDC, V, LDV, ONE, WORK,
|
|
$ LDWORK )
|
|
END IF
|
|
*
|
|
* W := W * T or W * T**H
|
|
*
|
|
CALL CTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K,
|
|
$ ONE, T, LDT, WORK, LDWORK )
|
|
*
|
|
* C := C - W * V
|
|
*
|
|
IF( N.GT.K ) THEN
|
|
*
|
|
* C1 := C1 - W * V1
|
|
*
|
|
CALL CGEMM( 'No transpose', 'No transpose', M, N-K, K,
|
|
$ -ONE, WORK, LDWORK, V, LDV, ONE, C, LDC )
|
|
END IF
|
|
*
|
|
* W := W * V2
|
|
*
|
|
CALL CTRMM( 'Right', 'Lower', 'No transpose', 'Unit', M,
|
|
$ K, ONE, V( 1, N-K+1 ), LDV, WORK, LDWORK )
|
|
*
|
|
* C1 := C1 - W
|
|
*
|
|
DO 240 J = 1, K
|
|
DO 230 I = 1, M
|
|
C( I, N-K+J ) = C( I, N-K+J ) - WORK( I, J )
|
|
230 CONTINUE
|
|
240 CONTINUE
|
|
*
|
|
END IF
|
|
*
|
|
END IF
|
|
END IF
|
|
*
|
|
RETURN
|
|
*
|
|
* End of CLARFB
|
|
*
|
|
END
|