version 1.7, 2010/12/21 13:53:52
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version 1.13, 2014/01/27 09:24:36
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*> \brief \b ZLARTG generates a plane rotation with real cosine and complex sine. |
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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 ZLARTG + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlartg.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/zlartg.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/zlartg.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 ZLARTG( F, G, CS, SN, R ) |
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* |
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* .. Scalar Arguments .. |
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* DOUBLE PRECISION CS |
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* COMPLEX*16 F, G, R, SN |
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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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*> ZLARTG generates a plane rotation so that |
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*> |
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*> [ CS SN ] [ F ] [ R ] |
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*> [ __ ] . [ ] = [ ] where CS**2 + |SN|**2 = 1. |
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*> [ -SN CS ] [ G ] [ 0 ] |
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*> |
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*> This is a faster version of the BLAS1 routine ZROTG, except for |
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*> the following differences: |
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*> F and G are unchanged on return. |
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*> If G=0, then CS=1 and SN=0. |
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*> If F=0, then CS=0 and SN is chosen so that R is real. |
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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] F |
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*> \verbatim |
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*> F is COMPLEX*16 |
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*> The first component of vector to be rotated. |
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*> \endverbatim |
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*> |
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*> \param[in] G |
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*> \verbatim |
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*> G is COMPLEX*16 |
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*> The second component of vector to be rotated. |
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*> \endverbatim |
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*> |
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*> \param[out] CS |
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*> \verbatim |
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*> CS is DOUBLE PRECISION |
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*> The cosine of the rotation. |
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*> \endverbatim |
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*> |
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*> \param[out] SN |
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*> \verbatim |
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*> SN is COMPLEX*16 |
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*> The sine of the rotation. |
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*> \endverbatim |
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*> |
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*> \param[out] R |
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*> \verbatim |
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*> R is COMPLEX*16 |
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*> The nonzero component of the rotated vector. |
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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 2013 |
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* |
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*> \ingroup complex16OTHERauxiliary |
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* |
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*> \par Further Details: |
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* ===================== |
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*> |
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*> \verbatim |
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*> |
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*> 3-5-96 - Modified with a new algorithm by W. Kahan and J. Demmel |
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*> |
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*> This version has a few statements commented out for thread safety |
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*> (machine parameters are computed on each entry). 10 feb 03, SJH. |
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*> \endverbatim |
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*> |
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* ===================================================================== |
SUBROUTINE ZLARTG( F, G, CS, SN, R ) |
SUBROUTINE ZLARTG( F, G, CS, SN, R ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.2) -- |
* -- LAPACK auxiliary routine (version 3.5.0) -- |
* -- 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 |
* November 2013 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
DOUBLE PRECISION CS |
DOUBLE PRECISION CS |
COMPLEX*16 F, G, R, SN |
COMPLEX*16 F, G, R, SN |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZLARTG generates a plane rotation so that |
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* |
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* [ CS SN ] [ F ] [ R ] |
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* [ __ ] . [ ] = [ ] where CS**2 + |SN|**2 = 1. |
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* [ -SN CS ] [ G ] [ 0 ] |
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* |
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* This is a faster version of the BLAS1 routine ZROTG, except for |
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* the following differences: |
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* F and G are unchanged on return. |
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* If G=0, then CS=1 and SN=0. |
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* If F=0, then CS=0 and SN is chosen so that R is real. |
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* |
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* Arguments |
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* ========= |
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* |
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* F (input) COMPLEX*16 |
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* The first component of vector to be rotated. |
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* |
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* G (input) COMPLEX*16 |
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* The second component of vector to be rotated. |
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* |
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* CS (output) DOUBLE PRECISION |
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* The cosine of the rotation. |
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* |
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* SN (output) COMPLEX*16 |
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* The sine of the rotation. |
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* |
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* R (output) COMPLEX*16 |
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* The nonzero component of the rotated vector. |
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* |
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* Further Details |
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* ======= ======= |
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* |
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* 3-5-96 - Modified with a new algorithm by W. Kahan and J. Demmel |
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* |
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* This version has a few statements commented out for thread safety |
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* (machine parameters are computed on each entry). 10 feb 03, SJH. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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* .. |
* .. |
* .. External Functions .. |
* .. External Functions .. |
DOUBLE PRECISION DLAMCH, DLAPY2 |
DOUBLE PRECISION DLAMCH, DLAPY2 |
EXTERNAL DLAMCH, DLAPY2 |
LOGICAL DISNAN |
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EXTERNAL DLAMCH, DLAPY2, DISNAN |
* .. |
* .. |
* .. Intrinsic Functions .. |
* .. Intrinsic Functions .. |
INTRINSIC ABS, DBLE, DCMPLX, DCONJG, DIMAG, INT, LOG, |
INTRINSIC ABS, DBLE, DCMPLX, DCONJG, DIMAG, INT, LOG, |
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* .. Statement Functions .. |
* .. Statement Functions .. |
DOUBLE PRECISION ABS1, ABSSQ |
DOUBLE PRECISION ABS1, ABSSQ |
* .. |
* .. |
* .. Save statement .. |
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* SAVE FIRST, SAFMX2, SAFMIN, SAFMN2 |
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* .. |
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* .. Data statements .. |
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* DATA FIRST / .TRUE. / |
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* .. |
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* .. Statement Function definitions .. |
* .. Statement Function definitions .. |
ABS1( FF ) = MAX( ABS( DBLE( FF ) ), ABS( DIMAG( FF ) ) ) |
ABS1( FF ) = MAX( ABS( DBLE( FF ) ), ABS( DIMAG( FF ) ) ) |
ABSSQ( FF ) = DBLE( FF )**2 + DIMAG( FF )**2 |
ABSSQ( FF ) = DBLE( FF )**2 + DIMAG( FF )**2 |
* .. |
* .. |
* .. Executable Statements .. |
* .. Executable Statements .. |
* |
* |
* IF( FIRST ) THEN |
SAFMIN = DLAMCH( 'S' ) |
SAFMIN = DLAMCH( 'S' ) |
EPS = DLAMCH( 'E' ) |
EPS = DLAMCH( 'E' ) |
SAFMN2 = DLAMCH( 'B' )**INT( LOG( SAFMIN / EPS ) / |
SAFMN2 = DLAMCH( 'B' )**INT( LOG( SAFMIN / EPS ) / |
$ LOG( DLAMCH( 'B' ) ) / TWO ) |
$ LOG( DLAMCH( 'B' ) ) / TWO ) |
SAFMX2 = ONE / SAFMN2 |
SAFMX2 = ONE / SAFMN2 |
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* FIRST = .FALSE. |
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* END IF |
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SCALE = MAX( ABS1( F ), ABS1( G ) ) |
SCALE = MAX( ABS1( F ), ABS1( G ) ) |
FS = F |
FS = F |
GS = G |
GS = G |
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IF( SCALE.GE.SAFMX2 ) |
IF( SCALE.GE.SAFMX2 ) |
$ GO TO 10 |
$ GO TO 10 |
ELSE IF( SCALE.LE.SAFMN2 ) THEN |
ELSE IF( SCALE.LE.SAFMN2 ) THEN |
IF( G.EQ.CZERO ) THEN |
IF( G.EQ.CZERO.OR.DISNAN( ABS( G ) ) ) THEN |
CS = ONE |
CS = ONE |
SN = CZERO |
SN = CZERO |
R = F |
R = F |