#include "ESMF_LapackBlas.inc" !> \brief \b DTZRZF ! ! =========== DOCUMENTATION =========== ! ! Online html documentation available at ! http://www.netlib.org/lapack/explore-html/ ! !> \htmlonly !> Download DTZRZF + dependencies !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtzrzf.f"> !> [TGZ]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtzrzf.f"> !> [ZIP]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtzrzf.f"> !> [TXT]</a> !> \endhtmlonly ! ! Definition: ! =========== ! ! SUBROUTINE DTZRZF( 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 !> !> DTZRZF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A !> to upper triangular form by means of orthogonal transformations. !> !> The upper trapezoidal matrix A is factored as !> !> A = ( R 0 ) * Z, !> !> where Z is an N-by-N orthogonal matrix and R is an M-by-M upper !> triangular matrix. !> \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 >= M. !> \endverbatim !> !> \param[in,out] A !> \verbatim !> A is DOUBLE PRECISION array, dimension (LDA,N) !> On entry, the leading M-by-N upper trapezoidal part of the !> array A must contain the matrix to be factorized. !> On exit, the leading M-by-M upper triangular part of A !> contains the upper triangular matrix R, and elements M+1 to !> N of the first M rows of A, with the array TAU, represent the !> orthogonal matrix Z as a product of M elementary reflectors. !> \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 (M) !> The scalar factors of the elementary reflectors. !> \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,M). !> For optimum performance LWORK >= M*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 doubleOTHERcomputational ! !> \par Contributors: ! ================== !> !> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA ! !> \par Further Details: ! ===================== !> !> \verbatim !> !> The factorization is obtained by Householder's method. The kth !> transformation matrix, Z( k ), which is used to introduce zeros into !> the ( m - k + 1 )th row of A, is given in the form !> !> Z( k ) = ( I 0 ), !> ( 0 T( k ) ) !> !> where !> !> T( k ) = I - tau*u( k )*u( k )**T, u( k ) = ( 1 ), !> ( 0 ) !> ( z( k ) ) !> !> tau is a scalar and z( k ) is an ( n - m ) element vector. !> tau and z( k ) are chosen to annihilate the elements of the kth row !> of X. !> !> The scalar tau is returned in the kth element of TAU and the vector !> u( k ) in the kth row of A, such that the elements of z( k ) are !> in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in !> the upper triangular part of A. !> !> Z is given by !> !> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). !> \endverbatim !> ! ===================================================================== SUBROUTINE DTZRZF( 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( * ) ! .. ! ! ===================================================================== ! ! .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) ! .. ! .. Local Scalars .. LOGICAL LQUERY INTEGER I, IB, IWS, KI, KK, LDWORK, LWKMIN, LWKOPT, & & M1, MU, NB, NBMIN, NX ! .. ! .. External Subroutines .. EXTERNAL XERBLA, DLARZB, DLARZT, DLATRZ ! .. ! .. Intrinsic Functions .. INTRINSIC MAX, MIN ! .. ! .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV ! .. ! .. Executable Statements .. ! ! Test the input arguments ! INFO = 0 LQUERY = ( LWORK.EQ.-1 ) IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.M ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -4 END IF ! IF( INFO.EQ.0 ) THEN IF( M.EQ.0 .OR. M.EQ.N ) THEN LWKOPT = 1 LWKMIN = 1 ELSE ! ! Determine the block size. ! NB = ILAENV( 1, 'DGERQF', ' ', M, N, -1, -1 ) LWKOPT = M*NB LWKMIN = MAX( 1, M ) END IF WORK( 1 ) = LWKOPT ! IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN INFO = -7 END IF END IF ! IF( INFO.NE.0 ) THEN CALL XERBLA( 'DTZRZF', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF ! ! Quick return if possible ! IF( M.EQ.0 ) THEN RETURN ELSE IF( M.EQ.N ) THEN DO 10 I = 1, N TAU( I ) = ZERO 10 CONTINUE RETURN END IF ! NBMIN = 2 NX = 1 IWS = M IF( NB.GT.1 .AND. NB.LT.M ) THEN ! ! Determine when to cross over from blocked to unblocked code. ! NX = MAX( 0, ILAENV( 3, 'DGERQF', ' ', M, N, -1, -1 ) ) IF( NX.LT.M ) THEN ! ! Determine if workspace is large enough for blocked code. ! LDWORK = M 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, 'DGERQF', ' ', M, N, -1, & & -1 ) ) END IF END IF END IF ! IF( NB.GE.NBMIN .AND. NB.LT.M .AND. NX.LT.M ) THEN ! ! Use blocked code initially. ! The last kk rows are handled by the block method. ! M1 = MIN( M+1, N ) KI = ( ( M-NX-1 ) / NB )*NB KK = MIN( M, KI+NB ) ! DO 20 I = M - KK + KI + 1, M - KK + 1, -NB IB = MIN( M-I+1, NB ) ! ! Compute the TZ factorization of the current block ! A(i:i+ib-1,i:n) ! CALL DLATRZ( IB, N-I+1, N-M, A( I, I ), LDA, TAU( I ), & & WORK ) IF( I.GT.1 ) THEN ! ! Form the triangular factor of the block reflector ! H = H(i+ib-1) . . . H(i+1) H(i) ! CALL DLARZT( 'Backward', 'Rowwise', N-M, IB, A( I, M1 ), & & LDA, TAU( I ), WORK, LDWORK ) ! ! Apply H to A(1:i-1,i:n) from the right ! CALL DLARZB( 'Right', 'No transpose', 'Backward', & & 'Rowwise', I-1, N-I+1, IB, N-M, A( I, M1 ), & & LDA, WORK, LDWORK, A( 1, I ), LDA, & & WORK( IB+1 ), LDWORK ) END IF 20 CONTINUE MU = I + NB - 1 ELSE MU = M END IF ! ! Use unblocked code to factor the last or only block ! IF( MU.GT.0 ) & & CALL DLATRZ( MU, N, N-M, A, LDA, TAU, WORK ) ! WORK( 1 ) = LWKOPT ! RETURN ! ! End of DTZRZF ! END