clar2v.f

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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/
*
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*
*  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.
*
*> \ingroup lar2v
*
*  =====================================================================
      SUBROUTINE clar2v( N, X, Y, Z, INCX, C, S, INCC )
*
*  -- LAPACK auxiliary routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. 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