#include "ESMF_LapackBlas.inc" !> \brief \b DORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm). ! ! =========== DOCUMENTATION =========== ! ! Online html documentation available at ! http://www.netlib.org/lapack/explore-html/ ! !> \htmlonly !> Download DORG2R + dependencies !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorg2r.f"> !> [TGZ]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorg2r.f"> !> [ZIP]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorg2r.f"> !> [TXT]</a> !> \endhtmlonly ! ! Definition: ! =========== ! ! SUBROUTINE DORG2R( M, N, K, A, LDA, TAU, WORK, INFO ) ! ! .. Scalar Arguments .. ! INTEGER INFO, K, LDA, M, N ! .. ! .. Array Arguments .. ! DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) ! .. ! ! !> \par Purpose: ! ============= !> !> \verbatim !> !> DORG2R 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 (N) !> \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 DORG2R( M, N, K, A, LDA, TAU, WORK, 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, M, N ! .. ! .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) ! .. ! ! ===================================================================== ! ! .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) ! .. ! .. Local Scalars .. INTEGER I, J, L ! .. ! .. External Subroutines .. EXTERNAL DLARF, DSCAL, XERBLA ! .. ! .. Intrinsic Functions .. INTRINSIC MAX ! .. ! .. Executable Statements .. ! ! Test the input arguments ! INFO = 0 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 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DORG2R', -INFO ) RETURN END IF ! ! Quick return if possible ! IF( N.LE.0 ) & RETURN ! ! Initialise columns k+1:n to columns of the unit matrix ! DO 20 J = K + 1, N DO 10 L = 1, M A( L, J ) = ZERO 10 CONTINUE A( J, J ) = ONE 20 CONTINUE ! DO 40 I = K, 1, -1 ! ! Apply H(i) to A(i:m,i:n) from the left ! IF( I.LT.N ) THEN A( I, I ) = ONE CALL DLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ), & A( I, I+1 ), LDA, WORK ) END IF IF( I.LT.M ) & CALL DSCAL( M-I, -TAU( I ), A( I+1, I ), 1 ) A( I, I ) = ONE - TAU( I ) ! ! Set A(1:i-1,i) to zero ! DO 30 L = 1, I - 1 A( L, I ) = ZERO 30 CONTINUE 40 CONTINUE RETURN ! ! End of DORG2R ! END