*> \brief \b DLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLARZ + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \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 December 2016 * *> \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 3.7.0) -- * -- 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 .. 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