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*> \brief \b CLAR2V applies a vector of plane rotations with real cosines and complex sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CLAR2V + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clar2v.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clar2v.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clar2v.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CLAR2V( N, X, Y, Z, INCX, C, S, INCC )
*
* .. Scalar Arguments ..
* INTEGER INCC, INCX, N
* ..
* .. Array Arguments ..
* REAL C( * )
* COMPLEX S( * ), X( * ), Y( * ), Z( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CLAR2V applies a vector of complex plane rotations with real cosines
*> from both sides to a sequence of 2-by-2 complex Hermitian matrices,
*> defined by the elements of the vectors x, y and z. For i = 1,2,...,n
*>
*> ( x(i) z(i) ) :=
*> ( conjg(z(i)) y(i) )
*>
*> ( c(i) conjg(s(i)) ) ( x(i) z(i) ) ( c(i) -conjg(s(i)) )
*> ( -s(i) c(i) ) ( conjg(z(i)) y(i) ) ( s(i) c(i) )
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of plane rotations to be applied.
*> \endverbatim
*>
*> \param[in,out] X
*> \verbatim
*> X is COMPLEX array, dimension (1+(N-1)*INCX)
*> The vector x; the elements of x are assumed to be real.
*> \endverbatim
*>
*> \param[in,out] Y
*> \verbatim
*> Y is COMPLEX array, dimension (1+(N-1)*INCX)
*> The vector y; the elements of y are assumed to be real.
*> \endverbatim
*>
*> \param[in,out] Z
*> \verbatim
*> Z is COMPLEX array, dimension (1+(N-1)*INCX)
*> The vector z.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> The increment between elements of X, Y and Z. INCX > 0.
*> \endverbatim
*>
*> \param[in] C
*> \verbatim
*> C is REAL array, dimension (1+(N-1)*INCC)
*> The cosines of the plane rotations.
*> \endverbatim
*>
*> \param[in] S
*> \verbatim
*> S is COMPLEX array, dimension (1+(N-1)*INCC)
*> The sines of the plane rotations.
*> \endverbatim
*>
*> \param[in] INCC
*> \verbatim
*> INCC is INTEGER
*> The increment between elements of C and S. 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 complexOTHERauxiliary
*
* =====================================================================
SUBROUTINE CLAR2V( N, X, Y, Z, INCX, C, S, 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, N
* ..
* .. Array Arguments ..
REAL C( * )
COMPLEX S( * ), X( * ), Y( * ), Z( * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I, IC, IX
REAL CI, SII, SIR, T1I, T1R, T5, T6, XI, YI, ZII,
$ ZIR
COMPLEX SI, T2, T3, T4, ZI
* ..
* .. Intrinsic Functions ..
INTRINSIC AIMAG, CMPLX, CONJG, REAL
* ..
* .. Executable Statements ..
*
IX = 1
IC = 1
DO 10 I = 1, N
XI = REAL( X( IX ) )
YI = REAL( Y( IX ) )
ZI = Z( IX )
ZIR = REAL( ZI )
ZII = AIMAG( ZI )
CI = C( IC )
SI = S( IC )
SIR = REAL( SI )
SII = AIMAG( SI )
T1R = SIR*ZIR - SII*ZII
T1I = SIR*ZII + SII*ZIR
T2 = CI*ZI
T3 = T2 - CONJG( SI )*XI
T4 = CONJG( T2 ) + SI*YI
T5 = CI*XI + T1R
T6 = CI*YI - T1R
X( IX ) = CI*T5 + ( SIR*REAL( T4 )+SII*AIMAG( T4 ) )
Y( IX ) = CI*T6 - ( SIR*REAL( T3 )-SII*AIMAG( T3 ) )
Z( IX ) = CI*T3 + CONJG( SI )*CMPLX( T6, T1I )
IX = IX + INCX
IC = IC + INCC
10 CONTINUE
RETURN
*
* End of CLAR2V
*
END
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