#include "ESMF_LapackBlas.inc" !> \brief \b DLARZ ! ! =========== DOCUMENTATION =========== ! ! Online html documentation available at ! http://www.netlib.org/lapack/explore-html/ ! !> \htmlonly !> Download DLARZ + dependencies !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarz.f"> !> [TGZ]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarz.f"> !> [ZIP]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarz.f"> !> [TXT]</a> !> \endhtmlonly ! ! Definition: ! =========== ! ! SUBROUTINE DLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK ) ! ! .. Scalar Arguments .. ! CHARACTER SIDE ! INTEGER INCV, L, LDC, M, N ! DOUBLE PRECISION TAU ! .. ! .. Array Arguments .. ! DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * ) ! .. ! ! !> \par Purpose: ! ============= !> !> \verbatim !> !> DLARZ applies a real elementary reflector H to a real M-by-N !> matrix C, from either the left or the right. H is represented in the !> form !> !> H = I - tau * v * v**T !> !> where tau is a real scalar and v is a real vector. !> !> If tau = 0, then H is taken to be the unit matrix. !> !> !> H is a product of k elementary reflectors as returned by DTZRZF. !> \endverbatim ! ! Arguments: ! ========== ! !> \param[in] SIDE !> \verbatim !> SIDE is CHARACTER*1 !> = 'L': form H * C !> = 'R': form C * H !> \endverbatim !> !> \param[in] M !> \verbatim !> M is INTEGER !> The number of rows of the matrix C. !> \endverbatim !> !> \param[in] N !> \verbatim !> N is INTEGER !> The number of columns of the matrix C. !> \endverbatim !> !> \param[in] L !> \verbatim !> L is INTEGER !> The number of entries of the vector V containing !> the meaningful part of the Householder vectors. !> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. !> \endverbatim !> !> \param[in] V !> \verbatim !> V is DOUBLE PRECISION array, dimension (1+(L-1)*abs(INCV)) !> The vector v in the representation of H as returned by !> DTZRZF. V is not used if TAU = 0. !> \endverbatim !> !> \param[in] INCV !> \verbatim !> INCV is INTEGER !> The increment between elements of v. INCV <> 0. !> \endverbatim !> !> \param[in] TAU !> \verbatim !> TAU is DOUBLE PRECISION !> The value tau in the representation of H. !> \endverbatim !> !> \param[in,out] C !> \verbatim !> C is DOUBLE PRECISION array, dimension (LDC,N) !> On entry, the M-by-N matrix C. !> On exit, C is overwritten by the matrix H * C if SIDE = 'L', !> or C * H if SIDE = 'R'. !> \endverbatim !> !> \param[in] LDC !> \verbatim !> LDC is INTEGER !> The leading dimension of the array C. LDC >= max(1,M). !> \endverbatim !> !> \param[out] WORK !> \verbatim !> WORK is DOUBLE PRECISION array, dimension !> (N) if SIDE = 'L' !> or (M) if SIDE = 'R' !> \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 !> \endverbatim !> ! ===================================================================== SUBROUTINE DLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK ) ! ! -- 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 .. CHARACTER SIDE INTEGER INCV, L, LDC, M, N DOUBLE PRECISION TAU ! .. ! .. Array Arguments .. DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * ) ! .. ! ! ===================================================================== ! ! .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) ! .. ! .. External Subroutines .. EXTERNAL DAXPY, DCOPY, DGEMV, DGER ! .. ! .. External Functions .. LOGICAL LSAME EXTERNAL LSAME ! .. ! .. Executable Statements .. ! IF( LSAME( SIDE, 'L' ) ) THEN ! ! Form H * C ! IF( TAU.NE.ZERO ) THEN ! ! w( 1:n ) = C( 1, 1:n ) ! CALL DCOPY( N, C, LDC, WORK, 1 ) ! ! w( 1:n ) = w( 1:n ) + C( m-l+1:m, 1:n )**T * v( 1:l ) ! CALL DGEMV( 'Transpose', L, N, ONE, C( M-L+1, 1 ), LDC, V, & & INCV, ONE, WORK, 1 ) ! ! C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n ) ! CALL DAXPY( N, -TAU, WORK, 1, C, LDC ) ! ! C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ... ! tau * v( 1:l ) * w( 1:n )**T ! CALL DGER( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ), & & LDC ) END IF ! ELSE ! ! Form C * H ! IF( TAU.NE.ZERO ) THEN ! ! w( 1:m ) = C( 1:m, 1 ) ! CALL DCOPY( M, C, 1, WORK, 1 ) ! ! w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l ) ! CALL DGEMV( 'No transpose', M, L, ONE, C( 1, N-L+1 ), LDC, & & V, INCV, ONE, WORK, 1 ) ! ! C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m ) ! CALL DAXPY( M, -TAU, WORK, 1, C, 1 ) ! ! C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ... ! tau * w( 1:m ) * v( 1:l )**T ! CALL DGER( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ), & & LDC ) ! END IF ! END IF ! RETURN ! ! End of DLARZ ! END