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*> \brief \b ZLARGV generates a vector of plane rotations with real cosines and complex sines.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ZLARGV + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlargv.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlargv.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlargv.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE ZLARGV( N, X, INCX, Y, INCY, C, INCC )
*
* .. Scalar Arguments ..
* INTEGER INCC, INCX, INCY, N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION C( * )
* COMPLEX*16 X( * ), Y( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZLARGV generates a vector of complex plane rotations with real
*> cosines, determined by elements of the complex vectors x and y.
*> For i = 1,2,...,n
*>
*> ( c(i) s(i) ) ( x(i) ) = ( r(i) )
*> ( -conjg(s(i)) c(i) ) ( y(i) ) = ( 0 )
*>
*> where c(i)**2 + ABS(s(i))**2 = 1
*>
*> The following conventions are used (these are the same as in ZLARTG,
*> but differ from the BLAS1 routine ZROTG):
*> If y(i)=0, then c(i)=1 and s(i)=0.
*> If x(i)=0, then c(i)=0 and s(i) is chosen so that r(i) is real.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of plane rotations to be generated.
*> \endverbatim
*>
*> \param[in,out] X
*> \verbatim
*> X is COMPLEX*16 array, dimension (1+(N-1)*INCX)
*> On entry, the vector x.
*> On exit, x(i) is overwritten by r(i), for i = 1,...,n.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> The increment between elements of X. INCX > 0.
*> \endverbatim
*>
*> \param[in,out] Y
*> \verbatim
*> Y is COMPLEX*16 array, dimension (1+(N-1)*INCY)
*> On entry, the vector y.
*> On exit, the sines of the plane rotations.
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*> INCY is INTEGER
*> The increment between elements of Y. INCY > 0.
*> \endverbatim
*>
*> \param[out] C
*> \verbatim
*> C is DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
*> The cosines of the plane rotations.
*> \endverbatim
*>
*> \param[in] INCC
*> \verbatim
*> INCC is INTEGER
*> The increment between elements of C. INCC > 0.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complex16OTHERauxiliary
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 6-6-96 - Modified with a new algorithm by W. Kahan and J. Demmel
*>
*> This version has a few statements commented out for thread safety
*> (machine parameters are computed on each entry). 10 feb 03, SJH.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZLARGV( N, X, INCX, Y, INCY, C, INCC )
*
* -- LAPACK auxiliary routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
INTEGER INCC, INCX, INCY, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION C( * )
COMPLEX*16 X( * ), Y( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION TWO, ONE, ZERO
PARAMETER ( TWO = 2.0D+0, ONE = 1.0D+0, ZERO = 0.0D+0 )
COMPLEX*16 CZERO
PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
* LOGICAL FIRST
INTEGER COUNT, I, IC, IX, IY, J
DOUBLE PRECISION CS, D, DI, DR, EPS, F2, F2S, G2, G2S, SAFMIN,
$ SAFMN2, SAFMX2, SCALE
COMPLEX*16 F, FF, FS, G, GS, R, SN
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, DLAPY2
EXTERNAL DLAMCH, DLAPY2
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, DCMPLX, DCONJG, DIMAG, INT, LOG,
$ MAX, SQRT
* ..
* .. Statement Functions ..
DOUBLE PRECISION ABS1, ABSSQ
* ..
* .. Save statement ..
* SAVE FIRST, SAFMX2, SAFMIN, SAFMN2
* ..
* .. Data statements ..
* DATA FIRST / .TRUE. /
* ..
* .. Statement Function definitions ..
ABS1( FF ) = MAX( ABS( DBLE( FF ) ), ABS( DIMAG( FF ) ) )
ABSSQ( FF ) = DBLE( FF )**2 + DIMAG( FF )**2
* ..
* .. Executable Statements ..
*
* IF( FIRST ) THEN
* FIRST = .FALSE.
SAFMIN = DLAMCH( 'S' )
EPS = DLAMCH( 'E' )
SAFMN2 = DLAMCH( 'B' )**INT( LOG( SAFMIN / EPS ) /
$ LOG( DLAMCH( 'B' ) ) / TWO )
SAFMX2 = ONE / SAFMN2
* END IF
IX = 1
IY = 1
IC = 1
DO 60 I = 1, N
F = X( IX )
G = Y( IY )
*
* Use identical algorithm as in ZLARTG
*
SCALE = MAX( ABS1( F ), ABS1( G ) )
FS = F
GS = G
COUNT = 0
IF( SCALE.GE.SAFMX2 ) THEN
10 CONTINUE
COUNT = COUNT + 1
FS = FS*SAFMN2
GS = GS*SAFMN2
SCALE = SCALE*SAFMN2
IF( SCALE.GE.SAFMX2 )
$ GO TO 10
ELSE IF( SCALE.LE.SAFMN2 ) THEN
IF( G.EQ.CZERO ) THEN
CS = ONE
SN = CZERO
R = F
GO TO 50
END IF
20 CONTINUE
COUNT = COUNT - 1
FS = FS*SAFMX2
GS = GS*SAFMX2
SCALE = SCALE*SAFMX2
IF( SCALE.LE.SAFMN2 )
$ GO TO 20
END IF
F2 = ABSSQ( FS )
G2 = ABSSQ( GS )
IF( F2.LE.MAX( G2, ONE )*SAFMIN ) THEN
*
* This is a rare case: F is very small.
*
IF( F.EQ.CZERO ) THEN
CS = ZERO
R = DLAPY2( DBLE( G ), DIMAG( G ) )
* Do complex/real division explicitly with two real
* divisions
D = DLAPY2( DBLE( GS ), DIMAG( GS ) )
SN = DCMPLX( DBLE( GS ) / D, -DIMAG( GS ) / D )
GO TO 50
END IF
F2S = DLAPY2( DBLE( FS ), DIMAG( FS ) )
* G2 and G2S are accurate
* G2 is at least SAFMIN, and G2S is at least SAFMN2
G2S = SQRT( G2 )
* Error in CS from underflow in F2S is at most
* UNFL / SAFMN2 .lt. sqrt(UNFL*EPS) .lt. EPS
* If MAX(G2,ONE)=G2, then F2 .lt. G2*SAFMIN,
* and so CS .lt. sqrt(SAFMIN)
* If MAX(G2,ONE)=ONE, then F2 .lt. SAFMIN
* and so CS .lt. sqrt(SAFMIN)/SAFMN2 = sqrt(EPS)
* Therefore, CS = F2S/G2S / sqrt( 1 + (F2S/G2S)**2 ) = F2S/G2S
CS = F2S / G2S
* Make sure abs(FF) = 1
* Do complex/real division explicitly with 2 real divisions
IF( ABS1( F ).GT.ONE ) THEN
D = DLAPY2( DBLE( F ), DIMAG( F ) )
FF = DCMPLX( DBLE( F ) / D, DIMAG( F ) / D )
ELSE
DR = SAFMX2*DBLE( F )
DI = SAFMX2*DIMAG( F )
D = DLAPY2( DR, DI )
FF = DCMPLX( DR / D, DI / D )
END IF
SN = FF*DCMPLX( DBLE( GS ) / G2S, -DIMAG( GS ) / G2S )
R = CS*F + SN*G
ELSE
*
* This is the most common case.
* Neither F2 nor F2/G2 are less than SAFMIN
* F2S cannot overflow, and it is accurate
*
F2S = SQRT( ONE+G2 / F2 )
* Do the F2S(real)*FS(complex) multiply with two real
* multiplies
R = DCMPLX( F2S*DBLE( FS ), F2S*DIMAG( FS ) )
CS = ONE / F2S
D = F2 + G2
* Do complex/real division explicitly with two real divisions
SN = DCMPLX( DBLE( R ) / D, DIMAG( R ) / D )
SN = SN*DCONJG( GS )
IF( COUNT.NE.0 ) THEN
IF( COUNT.GT.0 ) THEN
DO 30 J = 1, COUNT
R = R*SAFMX2
30 CONTINUE
ELSE
DO 40 J = 1, -COUNT
R = R*SAFMN2
40 CONTINUE
END IF
END IF
END IF
50 CONTINUE
C( IC ) = CS
Y( IY ) = SN
X( IX ) = R
IC = IC + INCC
IY = IY + INCY
IX = IX + INCX
60 CONTINUE
RETURN
*
* End of ZLARGV
*
END
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