*> \brief \b ZLAR2V 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 ZLAR2V + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLAR2V( N, X, Y, Z, INCX, C, S, INCC ) * * .. Scalar Arguments .. * INTEGER INCC, INCX, N * .. * .. Array Arguments .. * DOUBLE PRECISION C( * ) * COMPLEX*16 S( * ), X( * ), Y( * ), Z( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLAR2V 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*16 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*16 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*16 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 DOUBLE PRECISION array, dimension (1+(N-1)*INCC) *> The cosines of the plane rotations. *> \endverbatim *> *> \param[in] S *> \verbatim *> S is COMPLEX*16 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 complex16OTHERauxiliary * * ===================================================================== SUBROUTINE ZLAR2V( 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 .. DOUBLE PRECISION C( * ) COMPLEX*16 S( * ), X( * ), Y( * ), Z( * ) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER I, IC, IX DOUBLE PRECISION CI, SII, SIR, T1I, T1R, T5, T6, XI, YI, ZII, \$ ZIR COMPLEX*16 SI, T2, T3, T4, ZI * .. * .. Intrinsic Functions .. INTRINSIC DBLE, DCMPLX, DCONJG, DIMAG * .. * .. Executable Statements .. * IX = 1 IC = 1 DO 10 I = 1, N XI = DBLE( X( IX ) ) YI = DBLE( Y( IX ) ) ZI = Z( IX ) ZIR = DBLE( ZI ) ZII = DIMAG( ZI ) CI = C( IC ) SI = S( IC ) SIR = DBLE( SI ) SII = DIMAG( SI ) T1R = SIR*ZIR - SII*ZII T1I = SIR*ZII + SII*ZIR T2 = CI*ZI T3 = T2 - DCONJG( SI )*XI T4 = DCONJG( T2 ) + SI*YI T5 = CI*XI + T1R T6 = CI*YI - T1R X( IX ) = CI*T5 + ( SIR*DBLE( T4 )+SII*DIMAG( T4 ) ) Y( IX ) = CI*T6 - ( SIR*DBLE( T3 )-SII*DIMAG( T3 ) ) Z( IX ) = CI*T3 + DCONJG( SI )*DCMPLX( T6, T1I ) IX = IX + INCX IC = IC + INCC 10 CONTINUE RETURN * * End of ZLAR2V * END