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clarfb.f
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*> \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