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227 lines
6.0 KiB
227 lines
6.0 KiB
*> \brief \b DLARF |
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* |
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* =========== DOCUMENTATION =========== |
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* |
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* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
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* |
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*> \htmlonly |
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*> Download DLARF + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarf.f"> |
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*> [TGZ]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarf.f"> |
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*> [ZIP]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarf.f"> |
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*> [TXT]</a> |
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*> \endhtmlonly |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE DLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER SIDE |
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* INTEGER INCV, LDC, M, N |
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* DOUBLE PRECISION TAU |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * ) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> DLARF applies a real elementary reflector H to a real m by n matrix |
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*> C, from either the left or the right. H is represented in the form |
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*> |
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*> H = I - tau * v * v**T |
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*> |
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*> where tau is a real scalar and v is a real vector. |
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*> |
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*> If tau = 0, then H is taken to be the unit matrix. |
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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] SIDE |
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*> \verbatim |
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*> SIDE is CHARACTER*1 |
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*> = 'L': form H * C |
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*> = 'R': form C * H |
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*> \endverbatim |
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*> |
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*> \param[in] M |
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*> \verbatim |
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*> M is INTEGER |
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*> The number of rows of the matrix C. |
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*> \endverbatim |
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*> |
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*> \param[in] N |
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*> \verbatim |
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*> N is INTEGER |
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*> The number of columns of the matrix C. |
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*> \endverbatim |
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*> |
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*> \param[in] V |
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*> \verbatim |
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*> V is DOUBLE PRECISION array, dimension |
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*> (1 + (M-1)*abs(INCV)) if SIDE = 'L' |
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*> or (1 + (N-1)*abs(INCV)) if SIDE = 'R' |
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*> The vector v in the representation of H. V is not used if |
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*> TAU = 0. |
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*> \endverbatim |
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*> |
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*> \param[in] INCV |
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*> \verbatim |
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*> INCV is INTEGER |
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*> The increment between elements of v. INCV <> 0. |
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*> \endverbatim |
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*> |
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*> \param[in] TAU |
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*> \verbatim |
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*> TAU is DOUBLE PRECISION |
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*> The value tau in the representation of H. |
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*> \endverbatim |
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*> |
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*> \param[in,out] C |
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*> \verbatim |
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*> C is DOUBLE PRECISION array, dimension (LDC,N) |
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*> On entry, the m by n matrix C. |
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*> On exit, C is overwritten by the matrix H * C if SIDE = 'L', |
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*> or C * H if SIDE = 'R'. |
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*> \endverbatim |
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*> |
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*> \param[in] LDC |
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*> \verbatim |
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*> LDC is INTEGER |
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*> The leading dimension of the array C. LDC >= max(1,M). |
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*> \endverbatim |
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*> |
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*> \param[out] WORK |
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*> \verbatim |
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*> WORK is DOUBLE PRECISION array, dimension |
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*> (N) if SIDE = 'L' |
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*> or (M) if SIDE = 'R' |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
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* |
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*> \date November 2011 |
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* |
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*> \ingroup doubleOTHERauxiliary |
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* |
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* ===================================================================== |
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SUBROUTINE DLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) |
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* |
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* -- LAPACK auxiliary routine (version 3.4.0) -- |
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* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
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* November 2011 |
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* |
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* .. Scalar Arguments .. |
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CHARACTER SIDE |
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INTEGER INCV, LDC, M, N |
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DOUBLE PRECISION TAU |
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* .. |
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* .. Array Arguments .. |
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DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * ) |
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* .. |
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* |
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* ===================================================================== |
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* |
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* .. Parameters .. |
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DOUBLE PRECISION ONE, ZERO |
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) |
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* .. |
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* .. Local Scalars .. |
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LOGICAL APPLYLEFT |
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INTEGER I, LASTV, LASTC |
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* .. |
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* .. External Subroutines .. |
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EXTERNAL DGEMV, DGER |
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* .. |
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* .. External Functions .. |
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LOGICAL LSAME |
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INTEGER ILADLR, ILADLC |
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EXTERNAL LSAME, ILADLR, ILADLC |
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* .. |
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* .. Executable Statements .. |
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* |
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APPLYLEFT = LSAME( SIDE, 'L' ) |
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LASTV = 0 |
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LASTC = 0 |
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IF( TAU.NE.ZERO ) THEN |
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! Set up variables for scanning V. LASTV begins pointing to the end |
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! of V. |
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IF( APPLYLEFT ) THEN |
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LASTV = M |
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ELSE |
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LASTV = N |
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END IF |
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IF( INCV.GT.0 ) THEN |
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I = 1 + (LASTV-1) * INCV |
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ELSE |
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I = 1 |
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END IF |
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! Look for the last non-zero row in V. |
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DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO ) |
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LASTV = LASTV - 1 |
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I = I - INCV |
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END DO |
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IF( APPLYLEFT ) THEN |
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! Scan for the last non-zero column in C(1:lastv,:). |
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LASTC = ILADLC(LASTV, N, C, LDC) |
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ELSE |
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! Scan for the last non-zero row in C(:,1:lastv). |
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LASTC = ILADLR(M, LASTV, C, LDC) |
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END IF |
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END IF |
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! Note that lastc.eq.0 renders the BLAS operations null; no special |
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! case is needed at this level. |
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IF( APPLYLEFT ) THEN |
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* |
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* Form H * C |
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* |
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IF( LASTV.GT.0 ) THEN |
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* |
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* w(1:lastc,1) := C(1:lastv,1:lastc)**T * v(1:lastv,1) |
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* |
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CALL DGEMV( 'Transpose', LASTV, LASTC, ONE, C, LDC, V, INCV, |
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$ ZERO, WORK, 1 ) |
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* |
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* C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**T |
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* |
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CALL DGER( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC ) |
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END IF |
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ELSE |
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* |
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* Form C * H |
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* |
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IF( LASTV.GT.0 ) THEN |
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* |
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* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1) |
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* |
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CALL DGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC, |
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$ V, INCV, ZERO, WORK, 1 ) |
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* |
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* C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**T |
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* |
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CALL DGER( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC ) |
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END IF |
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END IF |
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RETURN |
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* |
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* End of DLARF |
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* |
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END
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