#include "ESMF_LapackBlas.inc" !> \brief \b DORMBR ! ! =========== DOCUMENTATION =========== ! ! Online html documentation available at ! http://www.netlib.org/lapack/explore-html/ ! !> \htmlonly !> Download DORMBR + dependencies !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dormbr.f"> !> [TGZ]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dormbr.f"> !> [ZIP]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dormbr.f"> !> [TXT]</a> !> \endhtmlonly ! ! Definition: ! =========== ! ! SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, ! LDC, WORK, LWORK, INFO ) ! ! .. Scalar Arguments .. ! CHARACTER SIDE, TRANS, VECT ! INTEGER INFO, K, LDA, LDC, LWORK, M, N ! .. ! .. Array Arguments .. ! DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) ! .. ! ! !> \par Purpose: ! ============= !> !> \verbatim !> !> If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C !> with !> SIDE = 'L' SIDE = 'R' !> TRANS = 'N': Q * C C * Q !> TRANS = 'T': Q**T * C C * Q**T !> !> If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C !> with !> SIDE = 'L' SIDE = 'R' !> TRANS = 'N': P * C C * P !> TRANS = 'T': P**T * C C * P**T !> !> Here Q and P**T are the orthogonal matrices determined by DGEBRD when !> reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and !> P**T are defined as products of elementary reflectors H(i) and G(i) !> respectively. !> !> Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the !> order of the orthogonal matrix Q or P**T that is applied. !> !> If VECT = 'Q', A is assumed to have been an NQ-by-K matrix: !> if nq >= k, Q = H(1) H(2) . . . H(k); !> if nq < k, Q = H(1) H(2) . . . H(nq-1). !> !> If VECT = 'P', A is assumed to have been a K-by-NQ matrix: !> if k < nq, P = G(1) G(2) . . . G(k); !> if k >= nq, P = G(1) G(2) . . . G(nq-1). !> \endverbatim ! ! Arguments: ! ========== ! !> \param[in] VECT !> \verbatim !> VECT is CHARACTER*1 !> = 'Q': apply Q or Q**T; !> = 'P': apply P or P**T. !> \endverbatim !> !> \param[in] SIDE !> \verbatim !> SIDE is CHARACTER*1 !> = 'L': apply Q, Q**T, P or P**T from the Left; !> = 'R': apply Q, Q**T, P or P**T from the Right. !> \endverbatim !> !> \param[in] TRANS !> \verbatim !> TRANS is CHARACTER*1 !> = 'N': No transpose, apply Q or P; !> = 'T': Transpose, apply Q**T or P**T. !> \endverbatim !> !> \param[in] M !> \verbatim !> M is INTEGER !> The number of rows of the matrix C. M >= 0. !> \endverbatim !> !> \param[in] N !> \verbatim !> N is INTEGER !> The number of columns of the matrix C. N >= 0. !> \endverbatim !> !> \param[in] K !> \verbatim !> K is INTEGER !> If VECT = 'Q', the number of columns in the original !> matrix reduced by DGEBRD. !> If VECT = 'P', the number of rows in the original !> matrix reduced by DGEBRD. !> K >= 0. !> \endverbatim !> !> \param[in] A !> \verbatim !> A is DOUBLE PRECISION array, dimension !> (LDA,min(nq,K)) if VECT = 'Q' !> (LDA,nq) if VECT = 'P' !> The vectors which define the elementary reflectors H(i) and !> G(i), whose products determine the matrices Q and P, as !> returned by DGEBRD. !> \endverbatim !> !> \param[in] LDA !> \verbatim !> LDA is INTEGER !> The leading dimension of the array A. !> If VECT = 'Q', LDA >= max(1,nq); !> if VECT = 'P', LDA >= max(1,min(nq,K)). !> \endverbatim !> !> \param[in] TAU !> \verbatim !> TAU is DOUBLE PRECISION array, dimension (min(nq,K)) !> TAU(i) must contain the scalar factor of the elementary !> reflector H(i) or G(i) which determines Q or P, as returned !> by DGEBRD in the array argument TAUQ or TAUP. !> \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 Q*C or Q**T*C or C*Q**T or C*Q !> or P*C or P**T*C or C*P or C*P**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 (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !> \endverbatim !> !> \param[in] LWORK !> \verbatim !> LWORK is INTEGER !> The dimension of the array WORK. !> If SIDE = 'L', LWORK >= max(1,N); !> if SIDE = 'R', LWORK >= max(1,M). !> For optimum performance LWORK >= N*NB if SIDE = 'L', and !> LWORK >= M*NB if SIDE = 'R', where NB is the optimal !> blocksize. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA. !> \endverbatim !> !> \param[out] INFO !> \verbatim !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> \endverbatim ! ! Authors: ! ======== ! !> \author Univ. of Tennessee !> \author Univ. of California Berkeley !> \author Univ. of Colorado Denver !> \author NAG Ltd. ! !> \date November 2011 ! !> \ingroup doubleOTHERcomputational ! ! ===================================================================== SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, & & LDC, WORK, LWORK, INFO ) ! ! -- 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 SIDE, TRANS, VECT INTEGER INFO, K, LDA, LDC, LWORK, M, N ! .. ! .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) ! .. ! ! ===================================================================== ! ! .. Local Scalars .. LOGICAL APPLYQ, LEFT, LQUERY, NOTRAN CHARACTER TRANST INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW ! .. ! .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV ! .. ! .. External Subroutines .. EXTERNAL DORMLQ, DORMQR, XERBLA ! .. ! .. Intrinsic Functions .. INTRINSIC MAX, MIN ! .. ! .. Executable Statements .. ! ! Test the input arguments ! INFO = 0 APPLYQ = LSAME( VECT, 'Q' ) LEFT = LSAME( SIDE, 'L' ) NOTRAN = LSAME( TRANS, 'N' ) LQUERY = ( LWORK.EQ.-1 ) ! ! NQ is the order of Q or P and NW is the minimum dimension of WORK ! IF( LEFT ) THEN NQ = M NW = N ELSE NQ = N NW = M END IF IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN INFO = -1 ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN INFO = -2 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN INFO = -3 ELSE IF( M.LT.0 ) THEN INFO = -4 ELSE IF( N.LT.0 ) THEN INFO = -5 ELSE IF( K.LT.0 ) THEN INFO = -6 ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR. & & ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) ) & & THEN INFO = -8 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -11 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN INFO = -13 END IF ! IF( INFO.EQ.0 ) THEN IF( APPLYQ ) THEN IF( LEFT ) THEN NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M-1, N, M-1, & & -1 ) ELSE NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M, N-1, N-1, & & -1 ) END IF ELSE IF( LEFT ) THEN NB = ILAENV( 1, 'DORMLQ', SIDE // TRANS, M-1, N, M-1, & & -1 ) ELSE NB = ILAENV( 1, 'DORMLQ', SIDE // TRANS, M, N-1, N-1, & & -1 ) END IF END IF LWKOPT = MAX( 1, NW )*NB WORK( 1 ) = LWKOPT END IF ! IF( INFO.NE.0 ) THEN CALL XERBLA( 'DORMBR', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF ! ! Quick return if possible ! WORK( 1 ) = 1 IF( M.EQ.0 .OR. N.EQ.0 ) & & RETURN ! IF( APPLYQ ) THEN ! ! Apply Q ! IF( NQ.GE.K ) THEN ! ! Q was determined by a call to DGEBRD with nq >= k ! CALL DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, & & WORK, LWORK, IINFO ) ELSE IF( NQ.GT.1 ) THEN ! ! Q was determined by a call to DGEBRD with nq < k ! IF( LEFT ) THEN MI = M - 1 NI = N I1 = 2 I2 = 1 ELSE MI = M NI = N - 1 I1 = 1 I2 = 2 END IF CALL DORMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU, & & C( I1, I2 ), LDC, WORK, LWORK, IINFO ) END IF ELSE ! ! Apply P ! IF( NOTRAN ) THEN TRANST = 'T' ELSE TRANST = 'N' END IF IF( NQ.GT.K ) THEN ! ! P was determined by a call to DGEBRD with nq > k ! CALL DORMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC, & & WORK, LWORK, IINFO ) ELSE IF( NQ.GT.1 ) THEN ! ! P was determined by a call to DGEBRD with nq <= k ! IF( LEFT ) THEN MI = M - 1 NI = N I1 = 2 I2 = 1 ELSE MI = M NI = N - 1 I1 = 1 I2 = 2 END IF CALL DORMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA, & & TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO ) END IF END IF WORK( 1 ) = LWKOPT RETURN ! ! End of DORMBR ! END