#include "ESMF_LapackBlas.inc" !> \brief \b DORMTR ! ! =========== DOCUMENTATION =========== ! ! Online html documentation available at ! http://www.netlib.org/lapack/explore-html/ ! !> \htmlonly !> Download DORMTR + dependencies !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dormtr.f"> !> [TGZ]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dormtr.f"> !> [ZIP]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dormtr.f"> !> [TXT]</a> !> \endhtmlonly ! ! Definition: ! =========== ! ! SUBROUTINE DORMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, ! WORK, LWORK, INFO ) ! ! .. Scalar Arguments .. ! CHARACTER SIDE, TRANS, UPLO ! INTEGER INFO, LDA, LDC, LWORK, M, N ! .. ! .. Array Arguments .. ! DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) ! .. ! ! !> \par Purpose: ! ============= !> !> \verbatim !> !> DORMTR 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 !> !> where Q is a real orthogonal matrix of order nq, with nq = m if !> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of !> nq-1 elementary reflectors, as returned by DSYTRD: !> !> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); !> !> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1). !> \endverbatim ! ! Arguments: ! ========== ! !> \param[in] SIDE !> \verbatim !> SIDE is CHARACTER*1 !> = 'L': apply Q or Q**T from the Left; !> = 'R': apply Q or Q**T from the Right. !> \endverbatim !> !> \param[in] UPLO !> \verbatim !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A contains elementary reflectors !> from DSYTRD; !> = 'L': Lower triangle of A contains elementary reflectors !> from DSYTRD. !> \endverbatim !> !> \param[in] TRANS !> \verbatim !> TRANS is CHARACTER*1 !> = 'N': No transpose, apply Q; !> = 'T': Transpose, apply Q**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] A !> \verbatim !> A is DOUBLE PRECISION array, dimension !> (LDA,M) if SIDE = 'L' !> (LDA,N) if SIDE = 'R' !> The vectors which define the elementary reflectors, as !> returned by DSYTRD. !> \endverbatim !> !> \param[in] LDA !> \verbatim !> LDA is INTEGER !> The leading dimension of the array A. !> LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'. !> \endverbatim !> !> \param[in] TAU !> \verbatim !> TAU is DOUBLE PRECISION array, dimension !> (M-1) if SIDE = 'L' !> (N-1) if SIDE = 'R' !> TAU(i) must contain the scalar factor of the elementary !> reflector H(i), as returned by DSYTRD. !> \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. !> \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 December 2016 ! !> \ingroup doubleOTHERcomputational ! ! ===================================================================== SUBROUTINE DORMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, & WORK, LWORK, INFO ) ! ! -- LAPACK computational routine (version 3.7.0) -- ! -- LAPACK is a software package provided by Univ. of Tennessee, -- ! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- ! December 2016 ! ! .. Scalar Arguments .. CHARACTER SIDE, TRANS, UPLO INTEGER INFO, LDA, LDC, LWORK, M, N ! .. ! .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) ! .. ! ! ===================================================================== ! ! .. Local Scalars .. LOGICAL LEFT, LQUERY, UPPER INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW ! .. ! .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV ! .. ! .. External Subroutines .. EXTERNAL DORMQL, DORMQR, XERBLA ! .. ! .. Intrinsic Functions .. INTRINSIC MAX ! .. ! .. Executable Statements .. ! ! Test the input arguments ! INFO = 0 LEFT = LSAME( SIDE, 'L' ) UPPER = LSAME( UPLO, 'U' ) LQUERY = ( LWORK.EQ.-1 ) ! ! NQ is the order of Q and NW is the minimum dimension of WORK ! IF( LEFT ) THEN NQ = M NW = N ELSE NQ = N NW = M END IF IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN INFO = -1 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -2 ELSE IF( .NOT.LSAME( TRANS, 'N' ) .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( LDA.LT.MAX( 1, NQ ) ) THEN INFO = -7 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -10 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN INFO = -12 END IF ! IF( INFO.EQ.0 ) THEN IF( UPPER ) THEN IF( LEFT ) THEN NB = ILAENV( 1, 'DORMQL', SIDE // TRANS, M-1, N, M-1, & -1 ) ELSE NB = ILAENV( 1, 'DORMQL', SIDE // TRANS, M, N-1, N-1, & -1 ) END IF ELSE 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 END IF LWKOPT = MAX( 1, NW )*NB WORK( 1 ) = LWKOPT END IF ! IF( INFO.NE.0 ) THEN CALL XERBLA( 'DORMTR', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF ! ! Quick return if possible ! IF( M.EQ.0 .OR. N.EQ.0 .OR. NQ.EQ.1 ) THEN WORK( 1 ) = 1 RETURN END IF ! IF( LEFT ) THEN MI = M - 1 NI = N ELSE MI = M NI = N - 1 END IF ! IF( UPPER ) THEN ! ! Q was determined by a call to DSYTRD with UPLO = 'U' ! CALL DORMQL( SIDE, TRANS, MI, NI, NQ-1, A( 1, 2 ), LDA, TAU, C, & LDC, WORK, LWORK, IINFO ) ELSE ! ! Q was determined by a call to DSYTRD with UPLO = 'L' ! IF( LEFT ) THEN I1 = 2 I2 = 1 ELSE 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 WORK( 1 ) = LWKOPT RETURN ! ! End of DORMTR ! END