#include "ESMF_LapackBlas.inc" !> \brief \b DGEQR2 ! ! =========== DOCUMENTATION =========== ! ! Online html documentation available at ! http://www.netlib.org/lapack/explore-html/ ! !> \htmlonly !> Download DGEQR2 + dependencies !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgeqr2.f"> !> [TGZ]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgeqr2.f"> !> [ZIP]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgeqr2.f"> !> [TXT]</a> !> \endhtmlonly ! ! Definition: ! =========== ! ! SUBROUTINE DGEQR2( M, N, A, LDA, TAU, WORK, INFO ) ! ! .. Scalar Arguments .. ! INTEGER INFO, LDA, M, N ! .. ! .. Array Arguments .. ! DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) ! .. ! ! !> \par Purpose: ! ============= !> !> \verbatim !> !> DGEQR2 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 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 (N) !> \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 DGEQR2( M, N, A, LDA, TAU, WORK, 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, M, N ! .. ! .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) ! .. ! ! ===================================================================== ! ! .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) ! .. ! .. Local Scalars .. INTEGER I, K DOUBLE PRECISION AII ! .. ! .. External Subroutines .. EXTERNAL DLARF, DLARFG, XERBLA ! .. ! .. Intrinsic Functions .. INTRINSIC MAX, MIN ! .. ! .. Executable Statements .. ! ! Test the input arguments ! INFO = 0 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 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DGEQR2', -INFO ) RETURN END IF ! K = MIN( M, N ) ! DO 10 I = 1, K ! ! Generate elementary reflector H(i) to annihilate A(i+1:m,i) ! CALL DLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1, & & TAU( I ) ) IF( I.LT.N ) THEN ! ! Apply H(i) to A(i:m,i+1:n) from the left ! AII = A( I, I ) A( I, I ) = ONE CALL DLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ), & & A( I, I+1 ), LDA, WORK ) A( I, I ) = AII END IF 10 CONTINUE RETURN ! ! End of DGEQR2 ! END