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*> \brief \b SLARFB** =========== DOCUMENTATION ===========** Online html documentation available at * http://www.netlib.org/lapack/explore-html/ **> \htmlonly*> Download SLARFB + dependencies *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slarfb.f"> *> [TGZ]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slarfb.f"> *> [ZIP]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slarfb.f"> *> [TXT]</a>*> \endhtmlonly ** Definition:* ===========** SUBROUTINE SLARFB( 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 ..* REAL C( LDC, * ), T( LDT, * ), V( LDV, * ),* $ WORK( LDWORK, * )* ..* **> \par Purpose:* =============*>*> \verbatim*>*> SLARFB applies a real block reflector H or its transpose H**T to a*> real 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**T from the Left*> = 'R': apply H or H**T from the Right*> \endverbatim*>*> \param[in] TRANS*> \verbatim*> TRANS is CHARACTER*1*> = 'N': apply H (No transpose)*> = 'T': apply H**T (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).*> \endverbatim*>*> \param[in] V*> \verbatim*> V is REAL 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 REAL 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 REAL array, dimension (LDC,N)*> On entry, the m by n matrix C.*> On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T.*> \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 (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. **> \date November 2011**> \ingroup realOTHERauxiliary**> \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 SLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, $ T, LDT, C, LDC, WORK, LDWORK )** -- LAPACK auxiliary routine (version 3.4.0) --* -- LAPACK is a software package provided by Univ. of Tennessee, --* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--* November 2011** .. Scalar Arguments .. CHARACTER DIRECT, SIDE, STOREV, TRANS INTEGER K, LDC, LDT, LDV, LDWORK, M, N* ..* .. Array Arguments .. REAL C( LDC, * ), T( LDT, * ), V( LDV, * ), $ WORK( LDWORK, * )* ..** =====================================================================** .. Parameters .. REAL ONE PARAMETER ( ONE = 1.0E+0 )* ..* .. Local Scalars .. CHARACTER TRANST INTEGER I, J, LASTV, LASTC* ..* .. External Functions .. LOGICAL LSAME INTEGER ILASLR, ILASLC EXTERNAL LSAME, ILASLR, ILASLC* ..* .. External Subroutines .. EXTERNAL SCOPY, SGEMM, STRMM* ..* .. Executable Statements ..** Quick return if possible* IF( M.LE.0 .OR. N.LE.0 ) $ RETURN* IF( LSAME( TRANS, 'N' ) ) THEN TRANST = 'T' 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**T * C where C = ( C1 )* ( C2 )* LASTV = MAX( K, ILASLR( M, K, V, LDV ) ) LASTC = ILASLC( LASTV, N, C, LDC )** W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK)** W := C1**T* DO 10 J = 1, K CALL SCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 ) 10 CONTINUE** W := W * V1* CALL STRMM( 'Right', 'Lower', 'No transpose', 'Unit', $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) IF( LASTV.GT.K ) THEN** W := W + C2**T *V2* CALL SGEMM( 'Transpose', 'No transpose', $ LASTC, K, LASTV-K, $ ONE, C( K+1, 1 ), LDC, V( K+1, 1 ), LDV, $ ONE, WORK, LDWORK ) END IF** W := W * T**T or W * T* CALL STRMM( 'Right', 'Upper', TRANST, 'Non-unit', $ LASTC, K, ONE, T, LDT, WORK, LDWORK )** C := C - V * W**T* IF( LASTV.GT.K ) THEN** C2 := C2 - V2 * W**T* CALL SGEMM( 'No transpose', 'Transpose', $ LASTV-K, LASTC, K, $ -ONE, V( K+1, 1 ), LDV, WORK, LDWORK, ONE, $ C( K+1, 1 ), LDC ) END IF** W := W * V1**T* CALL STRMM( 'Right', 'Lower', 'Transpose', 'Unit', $ LASTC, K, ONE, V, LDV, WORK, LDWORK )** C1 := C1 - W**T* DO 30 J = 1, K DO 20 I = 1, LASTC C( J, I ) = C( J, I ) - WORK( I, J ) 20 CONTINUE 30 CONTINUE* ELSE IF( LSAME( SIDE, 'R' ) ) THEN** Form C * H or C * H**T where C = ( C1 C2 )* LASTV = MAX( K, ILASLR( N, K, V, LDV ) ) LASTC = ILASLR( M, LASTV, C, LDC )** W := C * V = (C1*V1 + C2*V2) (stored in WORK)** W := C1* DO 40 J = 1, K CALL SCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 ) 40 CONTINUE** W := W * V1* CALL STRMM( 'Right', 'Lower', 'No transpose', 'Unit', $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) IF( LASTV.GT.K ) THEN** W := W + C2 * V2* CALL SGEMM( 'No transpose', 'No transpose', $ LASTC, K, LASTV-K, $ ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV, $ ONE, WORK, LDWORK ) END IF** W := W * T or W * T**T* CALL STRMM( 'Right', 'Upper', TRANS, 'Non-unit', $ LASTC, K, ONE, T, LDT, WORK, LDWORK )** C := C - W * V**T* IF( LASTV.GT.K ) THEN** C2 := C2 - W * V2**T* CALL SGEMM( 'No transpose', 'Transpose', $ LASTC, LASTV-K, K, $ -ONE, WORK, LDWORK, V( K+1, 1 ), LDV, ONE, $ C( 1, K+1 ), LDC ) END IF** W := W * V1**T* CALL STRMM( 'Right', 'Lower', 'Transpose', 'Unit', $ LASTC, K, ONE, V, LDV, WORK, LDWORK )** C1 := C1 - W* DO 60 J = 1, K DO 50 I = 1, LASTC 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**T * C where C = ( C1 )* ( C2 )* LASTV = MAX( K, ILASLR( M, K, V, LDV ) ) LASTC = ILASLC( LASTV, N, C, LDC )** W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK)** W := C2**T* DO 70 J = 1, K CALL SCOPY( LASTC, C( LASTV-K+J, 1 ), LDC, $ WORK( 1, J ), 1 ) 70 CONTINUE** W := W * V2* CALL STRMM( 'Right', 'Upper', 'No transpose', 'Unit', $ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, $ WORK, LDWORK ) IF( LASTV.GT.K ) THEN** W := W + C1**T*V1* CALL SGEMM( 'Transpose', 'No transpose', $ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, $ ONE, WORK, LDWORK ) END IF** W := W * T**T or W * T* CALL STRMM( 'Right', 'Lower', TRANST, 'Non-unit', $ LASTC, K, ONE, T, LDT, WORK, LDWORK )** C := C - V * W**T* IF( LASTV.GT.K ) THEN** C1 := C1 - V1 * W**T* CALL SGEMM( 'No transpose', 'Transpose', $ LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK, $ ONE, C, LDC ) END IF** W := W * V2**T* CALL STRMM( 'Right', 'Upper', 'Transpose', 'Unit', $ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, $ WORK, LDWORK )** C2 := C2 - W**T* DO 90 J = 1, K DO 80 I = 1, LASTC C( LASTV-K+J, I ) = C( LASTV-K+J, I ) - WORK(I, J) 80 CONTINUE 90 CONTINUE* ELSE IF( LSAME( SIDE, 'R' ) ) THEN** Form C * H or C * H**T where C = ( C1 C2 )* LASTV = MAX( K, ILASLR( N, K, V, LDV ) ) LASTC = ILASLR( M, LASTV, C, LDC )** W := C * V = (C1*V1 + C2*V2) (stored in WORK)** W := C2* DO 100 J = 1, K CALL SCOPY( LASTC, C( 1, N-K+J ), 1, WORK( 1, J ), 1 ) 100 CONTINUE** W := W * V2* CALL STRMM( 'Right', 'Upper', 'No transpose', 'Unit', $ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, $ WORK, LDWORK ) IF( LASTV.GT.K ) THEN** W := W + C1 * V1* CALL SGEMM( 'No transpose', 'No transpose', $ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, $ ONE, WORK, LDWORK ) END IF** W := W * T or W * T**T* CALL STRMM( 'Right', 'Lower', TRANS, 'Non-unit', $ LASTC, K, ONE, T, LDT, WORK, LDWORK )** C := C - W * V**T* IF( LASTV.GT.K ) THEN** C1 := C1 - W * V1**T* CALL SGEMM( 'No transpose', 'Transpose', $ LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV, $ ONE, C, LDC ) END IF** W := W * V2**T* CALL STRMM( 'Right', 'Upper', 'Transpose', 'Unit', $ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, $ WORK, LDWORK )** C2 := C2 - W* DO 120 J = 1, K DO 110 I = 1, LASTC C( I, LASTV-K+J ) = C( I, LASTV-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**T * C where C = ( C1 )* ( C2 )* LASTV = MAX( K, ILASLC( K, M, V, LDV ) ) LASTC = ILASLC( LASTV, N, C, LDC )** W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK)** W := C1**T* DO 130 J = 1, K CALL SCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 ) 130 CONTINUE** W := W * V1**T* CALL STRMM( 'Right', 'Upper', 'Transpose', 'Unit', $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) IF( LASTV.GT.K ) THEN** W := W + C2**T*V2**T* CALL SGEMM( 'Transpose', 'Transpose', $ LASTC, K, LASTV-K, $ ONE, C( K+1, 1 ), LDC, V( 1, K+1 ), LDV, $ ONE, WORK, LDWORK ) END IF** W := W * T**T or W * T* CALL STRMM( 'Right', 'Upper', TRANST, 'Non-unit', $ LASTC, K, ONE, T, LDT, WORK, LDWORK )** C := C - V**T * W**T* IF( LASTV.GT.K ) THEN** C2 := C2 - V2**T * W**T* CALL SGEMM( 'Transpose', 'Transpose', $ LASTV-K, LASTC, K, $ -ONE, V( 1, K+1 ), LDV, WORK, LDWORK, $ ONE, C( K+1, 1 ), LDC ) END IF** W := W * V1* CALL STRMM( 'Right', 'Upper', 'No transpose', 'Unit', $ LASTC, K, ONE, V, LDV, WORK, LDWORK )** C1 := C1 - W**T* DO 150 J = 1, K DO 140 I = 1, LASTC C( J, I ) = C( J, I ) - WORK( I, J ) 140 CONTINUE 150 CONTINUE* ELSE IF( LSAME( SIDE, 'R' ) ) THEN** Form C * H or C * H**T where C = ( C1 C2 )* LASTV = MAX( K, ILASLC( K, N, V, LDV ) ) LASTC = ILASLR( M, LASTV, C, LDC )** W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK)** W := C1* DO 160 J = 1, K CALL SCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 ) 160 CONTINUE** W := W * V1**T* CALL STRMM( 'Right', 'Upper', 'Transpose', 'Unit', $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) IF( LASTV.GT.K ) THEN** W := W + C2 * V2**T* CALL SGEMM( 'No transpose', 'Transpose', $ LASTC, K, LASTV-K, $ ONE, C( 1, K+1 ), LDC, V( 1, K+1 ), LDV, $ ONE, WORK, LDWORK ) END IF** W := W * T or W * T**T* CALL STRMM( 'Right', 'Upper', TRANS, 'Non-unit', $ LASTC, K, ONE, T, LDT, WORK, LDWORK )** C := C - W * V* IF( LASTV.GT.K ) THEN** C2 := C2 - W * V2* CALL SGEMM( 'No transpose', 'No transpose', $ LASTC, LASTV-K, K, $ -ONE, WORK, LDWORK, V( 1, K+1 ), LDV, $ ONE, C( 1, K+1 ), LDC ) END IF** W := W * V1* CALL STRMM( 'Right', 'Upper', 'No transpose', 'Unit', $ LASTC, K, ONE, V, LDV, WORK, LDWORK )** C1 := C1 - W* DO 180 J = 1, K DO 170 I = 1, LASTC 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**T * C where C = ( C1 )* ( C2 )* LASTV = MAX( K, ILASLC( K, M, V, LDV ) ) LASTC = ILASLC( LASTV, N, C, LDC )** W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK)** W := C2**T* DO 190 J = 1, K CALL SCOPY( LASTC, C( LASTV-K+J, 1 ), LDC, $ WORK( 1, J ), 1 ) 190 CONTINUE** W := W * V2**T* CALL STRMM( 'Right', 'Lower', 'Transpose', 'Unit', $ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, $ WORK, LDWORK ) IF( LASTV.GT.K ) THEN** W := W + C1**T * V1**T* CALL SGEMM( 'Transpose', 'Transpose', $ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, $ ONE, WORK, LDWORK ) END IF** W := W * T**T or W * T* CALL STRMM( 'Right', 'Lower', TRANST, 'Non-unit', $ LASTC, K, ONE, T, LDT, WORK, LDWORK )** C := C - V**T * W**T* IF( LASTV.GT.K ) THEN** C1 := C1 - V1**T * W**T* CALL SGEMM( 'Transpose', 'Transpose', $ LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK, $ ONE, C, LDC ) END IF** W := W * V2* CALL STRMM( 'Right', 'Lower', 'No transpose', 'Unit', $ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, $ WORK, LDWORK )** C2 := C2 - W**T* DO 210 J = 1, K DO 200 I = 1, LASTC C( LASTV-K+J, I ) = C( LASTV-K+J, I ) - WORK(I, J) 200 CONTINUE 210 CONTINUE* ELSE IF( LSAME( SIDE, 'R' ) ) THEN** Form C * H or C * H**T where C = ( C1 C2 )* LASTV = MAX( K, ILASLC( K, N, V, LDV ) ) LASTC = ILASLR( M, LASTV, C, LDC )** W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK)** W := C2* DO 220 J = 1, K CALL SCOPY( LASTC, C( 1, LASTV-K+J ), 1, $ WORK( 1, J ), 1 ) 220 CONTINUE** W := W * V2**T* CALL STRMM( 'Right', 'Lower', 'Transpose', 'Unit', $ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, $ WORK, LDWORK ) IF( LASTV.GT.K ) THEN** W := W + C1 * V1**T* CALL SGEMM( 'No transpose', 'Transpose', $ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, $ ONE, WORK, LDWORK ) END IF** W := W * T or W * T**T* CALL STRMM( 'Right', 'Lower', TRANS, 'Non-unit', $ LASTC, K, ONE, T, LDT, WORK, LDWORK )** C := C - W * V* IF( LASTV.GT.K ) THEN** C1 := C1 - W * V1* CALL SGEMM( 'No transpose', 'No transpose', $ LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV, $ ONE, C, LDC ) END IF** W := W * V2* CALL STRMM( 'Right', 'Lower', 'No transpose', 'Unit', $ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, $ WORK, LDWORK )** C1 := C1 - W* DO 240 J = 1, K DO 230 I = 1, LASTC C( I, LASTV-K+J ) = C( I, LASTV-K+J ) $ - WORK( I, J ) 230 CONTINUE 240 CONTINUE* END IF* END IF END IF* RETURN** End of SLARFB* END
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