version 1.2, 2010/04/21 13:45:35
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version 1.18, 2023/08/07 08:39:31
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*> \brief \b ZLARGV generates a vector of plane rotations with real cosines and complex sines. |
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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 ZLARGV + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlargv.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/zlargv.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/zlargv.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 ZLARGV( N, X, INCX, Y, INCY, C, INCC ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER INCC, INCX, INCY, N |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION C( * ) |
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* COMPLEX*16 X( * ), Y( * ) |
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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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*> ZLARGV generates a vector of complex plane rotations with real |
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*> cosines, determined by elements of the complex vectors x and y. |
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*> For i = 1,2,...,n |
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*> |
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*> ( c(i) s(i) ) ( x(i) ) = ( r(i) ) |
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*> ( -conjg(s(i)) c(i) ) ( y(i) ) = ( 0 ) |
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*> |
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*> where c(i)**2 + ABS(s(i))**2 = 1 |
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*> |
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*> The following conventions are used (these are the same as in ZLARTG, |
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*> but differ from the BLAS1 routine ZROTG): |
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*> If y(i)=0, then c(i)=1 and s(i)=0. |
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*> If x(i)=0, then c(i)=0 and s(i) is chosen so that r(i) 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] N |
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*> \verbatim |
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*> N is INTEGER |
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*> The number of plane rotations to be generated. |
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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 (1+(N-1)*INCX) |
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*> On entry, the vector x. |
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*> On exit, x(i) is overwritten by r(i), for i = 1,...,n. |
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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[in,out] Y |
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*> \verbatim |
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*> Y is COMPLEX*16 array, dimension (1+(N-1)*INCY) |
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*> On entry, the vector y. |
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*> On exit, the sines of the plane rotations. |
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*> \endverbatim |
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*> |
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*> \param[in] INCY |
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*> \verbatim |
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*> INCY is INTEGER |
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*> The increment between elements of Y. INCY > 0. |
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*> \endverbatim |
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*> |
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*> \param[out] C |
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*> \verbatim |
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*> C is DOUBLE PRECISION array, dimension (1+(N-1)*INCC) |
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*> The cosines of the plane rotations. |
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*> \endverbatim |
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*> |
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*> \param[in] INCC |
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*> \verbatim |
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*> INCC is INTEGER |
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*> The increment between elements of C. INCC > 0. |
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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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*> \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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*> 6-6-96 - 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 ZLARGV( N, X, INCX, Y, INCY, C, INCC ) |
SUBROUTINE ZLARGV( N, X, INCX, Y, INCY, C, INCC ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.2) -- |
* -- LAPACK auxiliary routine -- |
* -- 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 |
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* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER INCC, INCX, INCY, N |
INTEGER INCC, INCX, INCY, N |
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COMPLEX*16 X( * ), Y( * ) |
COMPLEX*16 X( * ), Y( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZLARGV generates a vector of complex plane rotations with real |
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* cosines, determined by elements of the complex vectors x and y. |
|
* For i = 1,2,...,n |
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* |
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* ( c(i) s(i) ) ( x(i) ) = ( r(i) ) |
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* ( -conjg(s(i)) c(i) ) ( y(i) ) = ( 0 ) |
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* |
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* where c(i)**2 + ABS(s(i))**2 = 1 |
|
* |
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* The following conventions are used (these are the same as in ZLARTG, |
|
* but differ from the BLAS1 routine ZROTG): |
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* If y(i)=0, then c(i)=1 and s(i)=0. |
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* If x(i)=0, then c(i)=0 and s(i) is chosen so that r(i) is real. |
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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 number of plane rotations to be generated. |
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* |
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* X (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCX) |
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* On entry, the vector x. |
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* On exit, x(i) is overwritten by r(i), for i = 1,...,n. |
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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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* Y (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCY) |
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* On entry, the vector y. |
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* On exit, the sines of the plane rotations. |
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* |
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* INCY (input) INTEGER |
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* The increment between elements of Y. INCY > 0. |
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* |
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* C (output) DOUBLE PRECISION array, dimension (1+(N-1)*INCC) |
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* The cosines of the plane rotations. |
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* |
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* INCC (input) INTEGER |
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* The increment between elements of C. INCC > 0. |
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* |
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* Further Details |
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* ======= ======= |
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* |
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* 6-6-96 - 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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FS = FS*SAFMN2 |
FS = FS*SAFMN2 |
GS = GS*SAFMN2 |
GS = GS*SAFMN2 |
SCALE = SCALE*SAFMN2 |
SCALE = SCALE*SAFMN2 |
IF( SCALE.GE.SAFMX2 ) |
IF( SCALE.GE.SAFMX2 .AND. COUNT .LT. 20 ) |
$ 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 ) THEN |