#include "ESMF_LapackBlas.inc" !> \brief \b DGEQRF ! ! =========== DOCUMENTATION =========== ! ! Online html documentation available at ! http://www.netlib.org/lapack/explore-html/ ! !> \htmlonly !> Download DGEQRF + dependencies !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgeqrf.f"> !> [TGZ]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgeqrf.f"> !> [ZIP]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgeqrf.f"> !> [TXT]</a> !> \endhtmlonly ! ! Definition: ! =========== ! ! SUBROUTINE DGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) ! ! .. Scalar Arguments .. ! INTEGER INFO, LDA, LWORK, M, N ! .. ! .. Array Arguments .. ! DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) ! .. ! ! !> \par Purpose: ! ============= !> !> \verbatim !> !> DGEQRF computes a QR factorization of a real M-by-N matrix A: !> A = Q * R. !> \endverbatim ! ! Arguments: ! ========== ! !> \param[in] M !> \verbatim !> M is INTEGER !> The number of rows of the matrix A. M >= 0. !> \endverbatim !> !> \param[in] N !> \verbatim !> N is INTEGER !> The number of columns of the matrix A. N >= 0. !> \endverbatim !> !> \param[in,out] A !> \verbatim !> A is DOUBLE PRECISION array, dimension (LDA,N) !> On entry, the M-by-N matrix A. !> On exit, the elements on and above the diagonal of the array !> contain the min(M,N)-by-N upper trapezoidal matrix R (R is !> upper triangular if m >= n); the elements below the diagonal, !> with the array TAU, represent the orthogonal matrix Q as a !> product of min(m,n) elementary reflectors (see Further !> Details). !> \endverbatim !> !> \param[in] LDA !> \verbatim !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,M). !> \endverbatim !> !> \param[out] TAU !> \verbatim !> TAU is DOUBLE PRECISION array, dimension (min(M,N)) !> The scalar factors of the elementary reflectors (see Further !> Details). !> \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 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 doubleGEcomputational ! !> \par Further Details: ! ===================== !> !> \verbatim !> !> The matrix Q is represented as a product of elementary reflectors !> !> Q = H(1) H(2) . . . H(k), where k = min(m,n). !> !> Each H(i) has the form !> !> H(i) = I - tau * v * v**T !> !> where tau is a real scalar, and v is a real vector with !> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), !> and tau in TAU(i). !> \endverbatim !> ! ===================================================================== SUBROUTINE DGEQRF( M, N, A, LDA, TAU, 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 .. INTEGER INFO, LDA, LWORK, M, N ! .. ! .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) ! .. ! ! ===================================================================== ! ! .. Local Scalars .. LOGICAL LQUERY INTEGER I, IB, IINFO, IWS, K, LDWORK, LWKOPT, NB, & & NBMIN, NX ! .. ! .. External Subroutines .. EXTERNAL DGEQR2, DLARFB, DLARFT, XERBLA ! .. ! .. Intrinsic Functions .. INTRINSIC MAX, MIN ! .. ! .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV ! .. ! .. Executable Statements .. ! ! Test the input arguments ! INFO = 0 NB = ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 ) LWKOPT = N*NB WORK( 1 ) = LWKOPT LQUERY = ( LWORK.EQ.-1 ) IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -4 ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN INFO = -7 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DGEQRF', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF ! ! Quick return if possible ! K = MIN( M, N ) IF( K.EQ.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, 'DGEQRF', ' ', M, N, -1, -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, 'DGEQRF', ' ', M, N, -1, & & -1 ) ) END IF END IF END IF ! IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN ! ! Use blocked code initially ! DO 10 I = 1, K - NX, NB IB = MIN( K-I+1, NB ) ! ! Compute the QR factorization of the current block ! A(i:m,i:i+ib-1) ! CALL DGEQR2( M-I+1, IB, A( I, I ), LDA, TAU( I ), WORK, & & IINFO ) 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**T to A(i:m,i+ib:n) from the left ! CALL DLARFB( 'Left', '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 10 CONTINUE ELSE I = 1 END IF ! ! Use unblocked code to factor the last or only block. ! IF( I.LE.K ) & & CALL DGEQR2( M-I+1, N-I+1, A( I, I ), LDA, TAU( I ), WORK, & & IINFO ) ! WORK( 1 ) = IWS RETURN ! ! End of DGEQRF ! END