#include "ESMF_LapackBlas.inc" !> \brief \b DORGQR ! ! =========== DOCUMENTATION =========== ! ! Online html documentation available at ! http://www.netlib.org/lapack/explore-html/ ! !> \htmlonly !> Download DORGQR + dependencies !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorgqr.f"> !> [TGZ]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorgqr.f"> !> [ZIP]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorgqr.f"> !> [TXT]</a> !> \endhtmlonly ! ! Definition: ! =========== ! ! SUBROUTINE DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) ! ! .. Scalar Arguments .. ! INTEGER INFO, K, LDA, LWORK, M, N ! .. ! .. Array Arguments .. ! DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) ! .. ! ! !> \par Purpose: ! ============= !> !> \verbatim !> !> DORGQR generates an M-by-N real matrix Q with orthonormal columns, !> which is defined as the first N columns of a product of K elementary !> reflectors of order M !> !> Q = H(1) H(2) . . . H(k) !> !> as returned by DGEQRF. !> \endverbatim ! ! Arguments: ! ========== ! !> \param[in] M !> \verbatim !> M is INTEGER !> The number of rows of the matrix Q. M >= 0. !> \endverbatim !> !> \param[in] N !> \verbatim !> N is INTEGER !> The number of columns of the matrix Q. M >= N >= 0. !> \endverbatim !> !> \param[in] K !> \verbatim !> K is INTEGER !> The number of elementary reflectors whose product defines the !> matrix Q. N >= K >= 0. !> \endverbatim !> !> \param[in,out] A !> \verbatim !> A is DOUBLE PRECISION array, dimension (LDA,N) !> On entry, the i-th column must contain the vector which !> defines the elementary reflector H(i), for i = 1,2,...,k, as !> returned by DGEQRF in the first k columns of its array !> argument A. !> On exit, the M-by-N matrix Q. !> \endverbatim !> !> \param[in] LDA !> \verbatim !> LDA is INTEGER !> The first dimension of the array A. LDA >= max(1,M). !> \endverbatim !> !> \param[in] TAU !> \verbatim !> TAU is DOUBLE PRECISION array, dimension (K) !> TAU(i) must contain the scalar factor of the elementary !> reflector H(i), as returned by DGEQRF. !> \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. LWORK >= max(1,N). !> For optimum performance LWORK >= N*NB, 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 has 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 DORGQR( M, N, K, A, LDA, TAU, 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 .. INTEGER INFO, K, LDA, LWORK, M, N ! .. ! .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) ! .. ! ! ===================================================================== ! ! .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) ! .. ! .. Local Scalars .. LOGICAL LQUERY INTEGER I, IB, IINFO, IWS, J, KI, KK, L, LDWORK, & LWKOPT, NB, NBMIN, NX ! .. ! .. External Subroutines .. EXTERNAL DLARFB, DLARFT, DORG2R, XERBLA ! .. ! .. Intrinsic Functions .. INTRINSIC MAX, MIN ! .. ! .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV ! .. ! .. Executable Statements .. ! ! Test the input arguments ! INFO = 0 NB = ILAENV( 1, 'DORGQR', ' ', M, N, K, -1 ) LWKOPT = MAX( 1, N )*NB WORK( 1 ) = LWKOPT LQUERY = ( LWORK.EQ.-1 ) IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN INFO = -2 ELSE IF( K.LT.0 .OR. K.GT.N ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -5 ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN INFO = -8 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DORGQR', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF ! ! Quick return if possible ! IF( N.LE.0 ) THEN WORK( 1 ) = 1 RETURN END IF ! NBMIN = 2 NX = 0 IWS = N IF( NB.GT.1 .AND. NB.LT.K ) THEN ! ! Determine when to cross over from blocked to unblocked code. ! NX = MAX( 0, ILAENV( 3, 'DORGQR', ' ', M, N, K, -1 ) ) IF( NX.LT.K ) THEN ! ! Determine if workspace is large enough for blocked code. ! LDWORK = N IWS = LDWORK*NB IF( LWORK.LT.IWS ) THEN ! ! Not enough workspace to use optimal NB: reduce NB and ! determine the minimum value of NB. ! NB = LWORK / LDWORK NBMIN = MAX( 2, ILAENV( 2, 'DORGQR', ' ', M, N, K, -1 ) ) END IF END IF END IF ! IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN ! ! Use blocked code after the last block. ! The first kk columns are handled by the block method. ! KI = ( ( K-NX-1 ) / NB )*NB KK = MIN( K, KI+NB ) ! ! Set A(1:kk,kk+1:n) to zero. ! DO 20 J = KK + 1, N DO 10 I = 1, KK A( I, J ) = ZERO 10 CONTINUE 20 CONTINUE ELSE KK = 0 END IF ! ! Use unblocked code for the last or only block. ! IF( KK.LT.N ) & CALL DORG2R( M-KK, N-KK, K-KK, A( KK+1, KK+1 ), LDA, & TAU( KK+1 ), WORK, IINFO ) ! IF( KK.GT.0 ) THEN ! ! Use blocked code ! DO 50 I = KI + 1, 1, -NB IB = MIN( NB, K-I+1 ) IF( I+IB.LE.N ) THEN ! ! Form the triangular factor of the block reflector ! H = H(i) H(i+1) . . . H(i+ib-1) ! CALL DLARFT( 'Forward', 'Columnwise', M-I+1, IB, & A( I, I ), LDA, TAU( I ), WORK, LDWORK ) ! ! Apply H to A(i:m,i+ib:n) from the left ! CALL DLARFB( 'Left', 'No transpose', 'Forward', & 'Columnwise', M-I+1, N-I-IB+1, IB, & A( I, I ), LDA, WORK, LDWORK, A( I, I+IB ), & LDA, WORK( IB+1 ), LDWORK ) END IF ! ! Apply H to rows i:m of current block ! CALL DORG2R( M-I+1, IB, IB, A( I, I ), LDA, TAU( I ), WORK, & IINFO ) ! ! Set rows 1:i-1 of current block to zero ! DO 40 J = I, I + IB - 1 DO 30 L = 1, I - 1 A( L, J ) = ZERO 30 CONTINUE 40 CONTINUE 50 CONTINUE END IF ! WORK( 1 ) = IWS RETURN ! ! End of DORGQR ! END