version 1.5, 2010/08/07 13:22:40
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version 1.14, 2014/01/27 09:28:39
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*> \brief \b ZLARFG generates an elementary reflector (Householder matrix). |
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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 ZLARFG + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarfg.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/zlarfg.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/zlarfg.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 ZLARFG( N, ALPHA, X, INCX, TAU ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER INCX, N |
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* COMPLEX*16 ALPHA, TAU |
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* .. |
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* .. Array Arguments .. |
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* COMPLEX*16 X( * ) |
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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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*> ZLARFG generates a complex elementary reflector H of order n, such |
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*> that |
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*> |
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*> H**H * ( alpha ) = ( beta ), H**H * H = I. |
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*> ( x ) ( 0 ) |
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*> |
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*> where alpha and beta are scalars, with beta real, and x is an |
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*> (n-1)-element complex vector. H is represented in the form |
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*> |
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*> H = I - tau * ( 1 ) * ( 1 v**H ) , |
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*> ( v ) |
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*> |
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*> where tau is a complex scalar and v is a complex (n-1)-element |
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*> vector. Note that H is not hermitian. |
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*> |
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*> If the elements of x are all zero and alpha is real, then tau = 0 |
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*> and H is taken to be the unit matrix. |
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*> |
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*> Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 . |
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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] N |
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*> \verbatim |
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*> N is INTEGER |
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*> The order of the elementary reflector. |
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*> \endverbatim |
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*> |
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*> \param[in,out] ALPHA |
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*> \verbatim |
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*> ALPHA is COMPLEX*16 |
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*> On entry, the value alpha. |
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*> On exit, it is overwritten with the value beta. |
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*> \endverbatim |
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*> |
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*> \param[in,out] X |
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*> \verbatim |
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*> X is COMPLEX*16 array, dimension |
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*> (1+(N-2)*abs(INCX)) |
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*> On entry, the vector x. |
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*> On exit, it is overwritten with the vector v. |
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*> \endverbatim |
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*> |
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*> \param[in] INCX |
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*> \verbatim |
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*> INCX is INTEGER |
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*> The increment between elements of X. INCX > 0. |
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*> \endverbatim |
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*> |
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*> \param[out] TAU |
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*> \verbatim |
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*> TAU is COMPLEX*16 |
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*> The value tau. |
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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 September 2012 |
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* |
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*> \ingroup complex16OTHERauxiliary |
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* |
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* ===================================================================== |
SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU ) |
SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.2) -- |
* -- LAPACK auxiliary routine (version 3.4.2) -- |
* -- 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 |
* September 2012 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER INCX, N |
INTEGER INCX, N |
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COMPLEX*16 X( * ) |
COMPLEX*16 X( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZLARFG generates a complex elementary reflector H of order n, such |
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* that |
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* |
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* H' * ( alpha ) = ( beta ), H' * H = I. |
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* ( x ) ( 0 ) |
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* |
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* where alpha and beta are scalars, with beta real, and x is an |
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* (n-1)-element complex vector. H is represented in the form |
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* |
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* H = I - tau * ( 1 ) * ( 1 v' ) , |
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* ( v ) |
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* |
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* where tau is a complex scalar and v is a complex (n-1)-element |
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* vector. Note that H is not hermitian. |
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* |
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* If the elements of x are all zero and alpha is real, then tau = 0 |
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* and H is taken to be the unit matrix. |
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* |
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* Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 . |
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* |
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* Arguments |
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* ========= |
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* |
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* N (input) INTEGER |
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* The order of the elementary reflector. |
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* |
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* ALPHA (input/output) COMPLEX*16 |
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* On entry, the value alpha. |
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* On exit, it is overwritten with the value beta. |
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* |
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* X (input/output) COMPLEX*16 array, dimension |
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* (1+(N-2)*abs(INCX)) |
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* On entry, the vector x. |
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* On exit, it is overwritten with the vector v. |
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* |
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* INCX (input) INTEGER |
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* The increment between elements of X. INCX > 0. |
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* |
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* TAU (output) COMPLEX*16 |
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* The value tau. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |