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version 1.15, 2017/06/17 11:06:24
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*> \brief \b DLARFGP generates an elementary reflector (Householder matrix) with non-negative beta. |
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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 DLARFGP + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarfgp.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/dlarfgp.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/dlarfgp.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 DLARFGP( 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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* DOUBLE PRECISION ALPHA, TAU |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION 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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*> DLARFGP generates a real elementary reflector H of order n, such |
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*> that |
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*> |
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*> H * ( alpha ) = ( beta ), H**T * H = I. |
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*> ( x ) ( 0 ) |
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*> |
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*> where alpha and beta are scalars, beta is non-negative, and x is |
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*> an (n-1)-element real vector. H is represented in the form |
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*> |
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*> H = I - tau * ( 1 ) * ( 1 v**T ) , |
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*> ( v ) |
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*> |
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*> where tau is a real scalar and v is a real (n-1)-element |
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*> vector. |
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*> |
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*> If the elements of x are all zero, then tau = 0 and H is taken to be |
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*> 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] 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 DOUBLE PRECISION |
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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 DOUBLE PRECISION 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 DOUBLE PRECISION |
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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 December 2016 |
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* |
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*> \ingroup doubleOTHERauxiliary |
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* |
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* ===================================================================== |
SUBROUTINE DLARFGP( N, ALPHA, X, INCX, TAU ) |
SUBROUTINE DLARFGP( N, ALPHA, X, INCX, TAU ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.3.1) -- |
* -- LAPACK auxiliary 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..-- |
* -- April 2011 -- |
* December 2016 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER INCX, N |
INTEGER INCX, N |
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DOUBLE PRECISION X( * ) |
DOUBLE PRECISION X( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DLARFGP generates a real elementary reflector H of order n, such |
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* that |
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* |
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* H * ( alpha ) = ( beta ), H**T * H = I. |
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* ( x ) ( 0 ) |
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* |
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* where alpha and beta are scalars, beta is non-negative, and x is |
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* an (n-1)-element real vector. H is represented in the form |
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* |
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* H = I - tau * ( 1 ) * ( 1 v**T ) , |
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* ( v ) |
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* |
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* where tau is a real scalar and v is a real (n-1)-element |
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* vector. |
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* |
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* If the elements of x are all zero, then tau = 0 and H is taken to be |
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* the unit matrix. |
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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) DOUBLE PRECISION |
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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) DOUBLE PRECISION 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) DOUBLE PRECISION |
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* The value tau. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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IF ( ABS(TAU).LE.SMLNUM ) THEN |
IF ( ABS(TAU).LE.SMLNUM ) THEN |
* |
* |
* In the case where the computed TAU ends up being a denormalized number, |
* In the case where the computed TAU ends up being a denormalized number, |
* it loses relative accuracy. This is a BIG problem. Solution: flush TAU |
* it loses relative accuracy. This is a BIG problem. Solution: flush TAU |
* to ZERO. This explains the next IF statement. |
* to ZERO. This explains the next IF statement. |
* |
* |
* (Bug report provided by Pat Quillen from MathWorks on Jul 29, 2009.) |
* (Bug report provided by Pat Quillen from MathWorks on Jul 29, 2009.) |
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BETA = -SAVEALPHA |
BETA = -SAVEALPHA |
END IF |
END IF |
* |
* |
ELSE |
ELSE |
* |
* |
* This is the general case. |
* This is the general case. |
* |
* |