version 1.1.1.1, 2010/01/26 15:22:46
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version 1.17, 2018/05/29 07:18:01
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*> \brief \b DLATZM |
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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 DLATZM + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlatzm.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/dlatzm.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/dlatzm.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 DLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, 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 C1( LDC, * ), C2( 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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*> This routine is deprecated and has been replaced by routine DORMRZ. |
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*> |
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*> DLATZM applies a Householder matrix generated by DTZRQF to a matrix. |
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*> |
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*> Let P = I - tau*u*u**T, u = ( 1 ), |
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*> ( v ) |
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*> where v is an (m-1) vector if SIDE = 'L', or a (n-1) vector if |
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*> SIDE = 'R'. |
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*> |
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*> If SIDE equals 'L', let |
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*> C = [ C1 ] 1 |
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*> [ C2 ] m-1 |
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*> n |
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*> Then C is overwritten by P*C. |
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*> |
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*> If SIDE equals 'R', let |
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*> C = [ C1, C2 ] m |
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*> 1 n-1 |
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*> Then C is overwritten by C*P. |
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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 P * C |
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*> = 'R': form C * P |
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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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*> (1 + (N-1)*abs(INCV)) if SIDE = 'R' |
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*> The vector v in the representation of P. V is not used |
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*> if 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 P. |
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*> \endverbatim |
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*> |
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*> \param[in,out] C1 |
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*> \verbatim |
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*> C1 is DOUBLE PRECISION array, dimension |
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*> (LDC,N) if SIDE = 'L' |
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*> (M,1) if SIDE = 'R' |
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*> On entry, the n-vector C1 if SIDE = 'L', or the m-vector C1 |
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*> if SIDE = 'R'. |
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*> |
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*> On exit, the first row of P*C if SIDE = 'L', or the first |
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*> column of C*P if SIDE = 'R'. |
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*> \endverbatim |
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*> |
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*> \param[in,out] C2 |
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*> \verbatim |
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*> C2 is DOUBLE PRECISION array, dimension |
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*> (LDC, N) if SIDE = 'L' |
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*> (LDC, N-1) if SIDE = 'R' |
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*> On entry, the (m - 1) x n matrix C2 if SIDE = 'L', or the |
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*> m x (n - 1) matrix C2 if SIDE = 'R'. |
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*> |
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*> On exit, rows 2:m of P*C if SIDE = 'L', or columns 2:m of C*P |
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*> 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 arrays C1 and C2. LDC >= (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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*> (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 December 2016 |
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* |
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*> \ingroup doubleOTHERcomputational |
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* |
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* ===================================================================== |
SUBROUTINE DLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK ) |
SUBROUTINE DLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational routine (version 3.7.0) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
* December 2016 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER SIDE |
CHARACTER SIDE |
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DOUBLE PRECISION C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * ) |
DOUBLE PRECISION C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* This routine is deprecated and has been replaced by routine DORMRZ. |
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* |
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* DLATZM applies a Householder matrix generated by DTZRQF to a matrix. |
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* |
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* Let P = I - tau*u*u', u = ( 1 ), |
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* ( v ) |
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* where v is an (m-1) vector if SIDE = 'L', or a (n-1) vector if |
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* SIDE = 'R'. |
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* |
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* If SIDE equals 'L', let |
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* C = [ C1 ] 1 |
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* [ C2 ] m-1 |
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* n |
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* Then C is overwritten by P*C. |
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* |
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* If SIDE equals 'R', let |
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* C = [ C1, C2 ] m |
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* 1 n-1 |
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* Then C is overwritten by C*P. |
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* |
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* Arguments |
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* ========= |
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* |
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* SIDE (input) CHARACTER*1 |
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* = 'L': form P * C |
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* = 'R': form C * P |
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* |
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* M (input) INTEGER |
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* The number of rows of the matrix C. |
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* |
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* N (input) INTEGER |
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* The number of columns of the matrix C. |
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* |
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* V (input) DOUBLE PRECISION array, dimension |
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* (1 + (M-1)*abs(INCV)) if SIDE = 'L' |
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* (1 + (N-1)*abs(INCV)) if SIDE = 'R' |
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* The vector v in the representation of P. V is not used |
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* if TAU = 0. |
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* |
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* INCV (input) INTEGER |
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* The increment between elements of v. INCV <> 0 |
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* |
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* TAU (input) DOUBLE PRECISION |
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* The value tau in the representation of P. |
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* |
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* C1 (input/output) DOUBLE PRECISION array, dimension |
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* (LDC,N) if SIDE = 'L' |
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* (M,1) if SIDE = 'R' |
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* On entry, the n-vector C1 if SIDE = 'L', or the m-vector C1 |
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* if SIDE = 'R'. |
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* |
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* On exit, the first row of P*C if SIDE = 'L', or the first |
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* column of C*P if SIDE = 'R'. |
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* |
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* C2 (input/output) DOUBLE PRECISION array, dimension |
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* (LDC, N) if SIDE = 'L' |
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* (LDC, N-1) if SIDE = 'R' |
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* On entry, the (m - 1) x n matrix C2 if SIDE = 'L', or the |
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* m x (n - 1) matrix C2 if SIDE = 'R'. |
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* |
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* On exit, rows 2:m of P*C if SIDE = 'L', or columns 2:m of C*P |
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* if SIDE = 'R'. |
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* |
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* LDC (input) INTEGER |
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* The leading dimension of the arrays C1 and C2. LDC >= (1,M). |
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* |
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* WORK (workspace) DOUBLE PRECISION array, dimension |
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* (N) if SIDE = 'L' |
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* (M) if SIDE = 'R' |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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* |
* |
IF( LSAME( SIDE, 'L' ) ) THEN |
IF( LSAME( SIDE, 'L' ) ) THEN |
* |
* |
* w := C1 + v' * C2 |
* w := (C1 + v**T * C2)**T |
* |
* |
CALL DCOPY( N, C1, LDC, WORK, 1 ) |
CALL DCOPY( N, C1, LDC, WORK, 1 ) |
CALL DGEMV( 'Transpose', M-1, N, ONE, C2, LDC, V, INCV, ONE, |
CALL DGEMV( 'Transpose', M-1, N, ONE, C2, LDC, V, INCV, ONE, |
$ WORK, 1 ) |
$ WORK, 1 ) |
* |
* |
* [ C1 ] := [ C1 ] - tau* [ 1 ] * w' |
* [ C1 ] := [ C1 ] - tau* [ 1 ] * w**T |
* [ C2 ] [ C2 ] [ v ] |
* [ C2 ] [ C2 ] [ v ] |
* |
* |
CALL DAXPY( N, -TAU, WORK, 1, C1, LDC ) |
CALL DAXPY( N, -TAU, WORK, 1, C1, LDC ) |
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CALL DGEMV( 'No transpose', M, N-1, ONE, C2, LDC, V, INCV, ONE, |
CALL DGEMV( 'No transpose', M, N-1, ONE, C2, LDC, V, INCV, ONE, |
$ WORK, 1 ) |
$ WORK, 1 ) |
* |
* |
* [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v'] |
* [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v**T] |
* |
* |
CALL DAXPY( M, -TAU, WORK, 1, C1, 1 ) |
CALL DAXPY( M, -TAU, WORK, 1, C1, 1 ) |
CALL DGER( M, N-1, -TAU, WORK, 1, V, INCV, C2, LDC ) |
CALL DGER( M, N-1, -TAU, WORK, 1, V, INCV, C2, LDC ) |