#include "ESMF_LapackBlas.inc" !> \brief \b DLARZB ! ! =========== DOCUMENTATION =========== ! ! Online html documentation available at ! http://www.netlib.org/lapack/explore-html/ ! !> \htmlonly !> Download DLARZB + dependencies !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarzb.f"> !> [TGZ]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarzb.f"> !> [ZIP]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarzb.f"> !> [TXT]</a> !> \endhtmlonly ! ! Definition: ! =========== ! ! SUBROUTINE DLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, ! LDV, T, LDT, C, LDC, WORK, LDWORK ) ! ! .. Scalar Arguments .. ! CHARACTER DIRECT, SIDE, STOREV, TRANS ! INTEGER K, L, LDC, LDT, LDV, LDWORK, M, N ! .. ! .. Array Arguments .. ! DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ), ! $ WORK( LDWORK, * ) ! .. ! ! !> \par Purpose: ! ============= !> !> \verbatim !> !> DLARZB applies a real block reflector H or its transpose H**T to !> a real distributed M-by-N C from the left or the right. !> !> Currently, only STOREV = 'R' and DIRECT = 'B' are supported. !> \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) !> = 'C': 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, not supported yet) !> = '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 (not supported yet) !> = '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] L !> \verbatim !> L is INTEGER !> The number of columns of the matrix V containing the !> meaningful part of the Householder reflectors. !> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. !> \endverbatim !> !> \param[in] V !> \verbatim !> V is DOUBLE PRECISION array, dimension (LDV,NV). !> If STOREV = 'C', NV = K; if STOREV = 'R', NV = L. !> \endverbatim !> !> \param[in] LDV !> \verbatim !> LDV is INTEGER !> The leading dimension of the array V. !> If STOREV = 'C', LDV >= L; 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 doubleOTHERcomputational ! !> \par Contributors: ! ================== !> !> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA ! !> \par Further Details: ! ===================== !> !> \verbatim !> \endverbatim !> ! ===================================================================== SUBROUTINE DLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, & & LDV, T, LDT, C, LDC, WORK, LDWORK ) ! ! -- LAPACK computational 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, L, 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, INFO, J ! .. ! .. External Functions .. LOGICAL LSAME EXTERNAL LSAME ! .. ! .. External Subroutines .. EXTERNAL DCOPY, DGEMM, DTRMM, XERBLA ! .. ! .. Executable Statements .. ! ! Quick return if possible ! IF( M.LE.0 .OR. N.LE.0 ) & & RETURN ! ! Check for currently supported options ! INFO = 0 IF( .NOT.LSAME( DIRECT, 'B' ) ) THEN INFO = -3 ELSE IF( .NOT.LSAME( STOREV, 'R' ) ) THEN INFO = -4 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DLARZB', -INFO ) RETURN END IF ! IF( LSAME( TRANS, 'N' ) ) THEN TRANST = 'T' ELSE TRANST = 'N' END IF ! IF( LSAME( SIDE, 'L' ) ) THEN ! ! Form H * C or H**T * C ! ! W( 1:n, 1:k ) = C( 1:k, 1:n )**T ! DO 10 J = 1, K CALL DCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 ) 10 CONTINUE ! ! W( 1:n, 1:k ) = W( 1:n, 1:k ) + ... ! C( m-l+1:m, 1:n )**T * V( 1:k, 1:l )**T ! IF( L.GT.0 ) & & CALL DGEMM( 'Transpose', 'Transpose', N, K, L, ONE, & & C( M-L+1, 1 ), LDC, V, LDV, ONE, WORK, LDWORK ) ! ! W( 1:n, 1:k ) = W( 1:n, 1:k ) * T**T or W( 1:m, 1:k ) * T ! CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, ONE, T, & & LDT, WORK, LDWORK ) ! ! C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )**T ! DO 30 J = 1, N DO 20 I = 1, K C( I, J ) = C( I, J ) - WORK( J, I ) 20 CONTINUE 30 CONTINUE ! ! C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ... ! V( 1:k, 1:l )**T * W( 1:n, 1:k )**T ! IF( L.GT.0 ) & & CALL DGEMM( 'Transpose', 'Transpose', L, N, K, -ONE, V, LDV, & & WORK, LDWORK, ONE, C( M-L+1, 1 ), LDC ) ! ELSE IF( LSAME( SIDE, 'R' ) ) THEN ! ! Form C * H or C * H**T ! ! W( 1:m, 1:k ) = C( 1:m, 1:k ) ! DO 40 J = 1, K CALL DCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 ) 40 CONTINUE ! ! W( 1:m, 1:k ) = W( 1:m, 1:k ) + ... ! C( 1:m, n-l+1:n ) * V( 1:k, 1:l )**T ! IF( L.GT.0 ) & & CALL DGEMM( 'No transpose', 'Transpose', M, K, L, ONE, & & C( 1, N-L+1 ), LDC, V, LDV, ONE, WORK, LDWORK ) ! ! W( 1:m, 1:k ) = W( 1:m, 1:k ) * T or W( 1:m, 1:k ) * T**T ! CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, ONE, T, & & LDT, WORK, LDWORK ) ! ! C( 1:m, 1:k ) = C( 1:m, 1:k ) - W( 1:m, 1:k ) ! DO 60 J = 1, K DO 50 I = 1, M C( I, J ) = C( I, J ) - WORK( I, J ) 50 CONTINUE 60 CONTINUE ! ! C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ... ! W( 1:m, 1:k ) * V( 1:k, 1:l ) ! IF( L.GT.0 ) & & CALL DGEMM( 'No transpose', 'No transpose', M, L, K, -ONE, & & WORK, LDWORK, V, LDV, ONE, C( 1, N-L+1 ), LDC ) ! END IF ! RETURN ! ! End of DLARZB ! END