#include "ESMF_LapackBlas.inc" !> \brief \b DLARFB ! ! =========== DOCUMENTATION =========== ! ! Online html documentation available at ! http://www.netlib.org/lapack/explore-html/ ! !> \htmlonly !> Download DLARFB + dependencies !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarfb.f"> !> [TGZ]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarfb.f"> !> [ZIP]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarfb.f"> !> [TXT]</a> !> \endhtmlonly ! ! Definition: ! =========== ! ! SUBROUTINE DLARFB( 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 .. ! DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ), ! $ WORK( LDWORK, * ) ! .. ! ! !> \par Purpose: ! ============= !> !> \verbatim !> !> DLARFB 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 doubleOTHERauxiliary ! !> \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 DLARFB( 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 .. DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ), & & WORK( LDWORK, * ) ! .. ! ! ===================================================================== ! ! .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) ! .. ! .. Local Scalars .. CHARACTER TRANST INTEGER I, J, LASTV, LASTC ! .. ! .. External Functions .. LOGICAL LSAME INTEGER ILADLR, ILADLC EXTERNAL LSAME, ILADLR, ILADLC ! .. ! .. External Subroutines .. EXTERNAL DCOPY, DGEMM, DTRMM ! .. ! .. 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, ILADLR( M, K, V, LDV ) ) LASTC = ILADLC( 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 DCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 ) 10 CONTINUE ! ! W := W * V1 ! CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', & & LASTC, K, ONE, V, LDV, WORK, LDWORK ) IF( LASTV.GT.K ) THEN ! ! W := W + C2**T *V2 ! CALL DGEMM( '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 DTRMM( '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 DGEMM( '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 DTRMM( '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, ILADLR( N, K, V, LDV ) ) LASTC = ILADLR( M, LASTV, C, LDC ) ! ! W := C * V = (C1*V1 + C2*V2) (stored in WORK) ! ! W := C1 ! DO 40 J = 1, K CALL DCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 ) 40 CONTINUE ! ! W := W * V1 ! CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', & & LASTC, K, ONE, V, LDV, WORK, LDWORK ) IF( LASTV.GT.K ) THEN ! ! W := W + C2 * V2 ! CALL DGEMM( '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 DTRMM( '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 DGEMM( '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 DTRMM( '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, ILADLR( M, K, V, LDV ) ) LASTC = ILADLC( 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 DCOPY( LASTC, C( LASTV-K+J, 1 ), LDC, & & WORK( 1, J ), 1 ) 70 CONTINUE ! ! W := W * V2 ! CALL DTRMM( '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 DGEMM( '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 DTRMM( '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 DGEMM( 'No transpose', 'Transpose', & & LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK, & & ONE, C, LDC ) END IF ! ! W := W * V2**T ! CALL DTRMM( '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, ILADLR( N, K, V, LDV ) ) LASTC = ILADLR( M, LASTV, C, LDC ) ! ! W := C * V = (C1*V1 + C2*V2) (stored in WORK) ! ! W := C2 ! DO 100 J = 1, K CALL DCOPY( LASTC, C( 1, N-K+J ), 1, WORK( 1, J ), 1 ) 100 CONTINUE ! ! W := W * V2 ! CALL DTRMM( '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 DGEMM( '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 DTRMM( '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 DGEMM( 'No transpose', 'Transpose', & & LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV, & & ONE, C, LDC ) END IF ! ! W := W * V2**T ! CALL DTRMM( '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, ILADLC( K, M, V, LDV ) ) LASTC = ILADLC( 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 DCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 ) 130 CONTINUE ! ! W := W * V1**T ! CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', & & LASTC, K, ONE, V, LDV, WORK, LDWORK ) IF( LASTV.GT.K ) THEN ! ! W := W + C2**T*V2**T ! CALL DGEMM( '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 DTRMM( '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 DGEMM( '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 DTRMM( '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, ILADLC( K, N, V, LDV ) ) LASTC = ILADLR( 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 DCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 ) 160 CONTINUE ! ! W := W * V1**T ! CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', & & LASTC, K, ONE, V, LDV, WORK, LDWORK ) IF( LASTV.GT.K ) THEN ! ! W := W + C2 * V2**T ! CALL DGEMM( '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 DTRMM( '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 DGEMM( '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 DTRMM( '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, ILADLC( K, M, V, LDV ) ) LASTC = ILADLC( 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 DCOPY( LASTC, C( LASTV-K+J, 1 ), LDC, & & WORK( 1, J ), 1 ) 190 CONTINUE ! ! W := W * V2**T ! CALL DTRMM( '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 DGEMM( 'Transpose', 'Transpose', & & LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, & & ONE, WORK, LDWORK ) END IF ! ! W := W * T**T or W * T ! CALL DTRMM( '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 DGEMM( 'Transpose', 'Transpose', & & LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK, & & ONE, C, LDC ) END IF ! ! W := W * V2 ! CALL DTRMM( '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, ILADLC( K, N, V, LDV ) ) LASTC = ILADLR( 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 DCOPY( LASTC, C( 1, LASTV-K+J ), 1, & & WORK( 1, J ), 1 ) 220 CONTINUE ! ! W := W * V2**T ! CALL DTRMM( '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 DGEMM( '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 DTRMM( '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 DGEMM( 'No transpose', 'No transpose', & & LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV, & & ONE, C, LDC ) END IF ! ! W := W * V2 ! CALL DTRMM( '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 DLARFB ! END