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    1: *> \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.
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at
    6: *            http://www.netlib.org/lapack/explore-html/
    7: *
    8: *> \htmlonly
    9: *> Download ZLAR2V + dependencies
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlar2v.f">
   11: *> [TGZ]</a>
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlar2v.f">
   13: *> [ZIP]</a>
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlar2v.f">
   15: *> [TXT]</a>
   16: *> \endhtmlonly
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE ZLAR2V( N, X, Y, Z, INCX, C, S, INCC )
   22: *
   23: *       .. Scalar Arguments ..
   24: *       INTEGER            INCC, INCX, N
   25: *       ..
   26: *       .. Array Arguments ..
   27: *       DOUBLE PRECISION   C( * )
   28: *       COMPLEX*16         S( * ), X( * ), Y( * ), Z( * )
   29: *       ..
   30: *
   31: *
   32: *> \par Purpose:
   33: *  =============
   34: *>
   35: *> \verbatim
   36: *>
   37: *> ZLAR2V applies a vector of complex plane rotations with real cosines
   38: *> from both sides to a sequence of 2-by-2 complex Hermitian matrices,
   39: *> defined by the elements of the vectors x, y and z. For i = 1,2,...,n
   40: *>
   41: *>    (       x(i)  z(i) ) :=
   42: *>    ( conjg(z(i)) y(i) )
   43: *>
   44: *>      (  c(i) conjg(s(i)) ) (       x(i)  z(i) ) ( c(i) -conjg(s(i)) )
   45: *>      ( -s(i)       c(i)  ) ( conjg(z(i)) y(i) ) ( s(i)        c(i)  )
   46: *> \endverbatim
   47: *
   48: *  Arguments:
   49: *  ==========
   50: *
   51: *> \param[in] N
   52: *> \verbatim
   53: *>          N is INTEGER
   54: *>          The number of plane rotations to be applied.
   55: *> \endverbatim
   56: *>
   57: *> \param[in,out] X
   58: *> \verbatim
   59: *>          X is COMPLEX*16 array, dimension (1+(N-1)*INCX)
   60: *>          The vector x; the elements of x are assumed to be real.
   61: *> \endverbatim
   62: *>
   63: *> \param[in,out] Y
   64: *> \verbatim
   65: *>          Y is COMPLEX*16 array, dimension (1+(N-1)*INCX)
   66: *>          The vector y; the elements of y are assumed to be real.
   67: *> \endverbatim
   68: *>
   69: *> \param[in,out] Z
   70: *> \verbatim
   71: *>          Z is COMPLEX*16 array, dimension (1+(N-1)*INCX)
   72: *>          The vector z.
   73: *> \endverbatim
   74: *>
   75: *> \param[in] INCX
   76: *> \verbatim
   77: *>          INCX is INTEGER
   78: *>          The increment between elements of X, Y and Z. INCX > 0.
   79: *> \endverbatim
   80: *>
   81: *> \param[in] C
   82: *> \verbatim
   83: *>          C is DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
   84: *>          The cosines of the plane rotations.
   85: *> \endverbatim
   86: *>
   87: *> \param[in] S
   88: *> \verbatim
   89: *>          S is COMPLEX*16 array, dimension (1+(N-1)*INCC)
   90: *>          The sines of the plane rotations.
   91: *> \endverbatim
   92: *>
   93: *> \param[in] INCC
   94: *> \verbatim
   95: *>          INCC is INTEGER
   96: *>          The increment between elements of C and S. INCC > 0.
   97: *> \endverbatim
   98: *
   99: *  Authors:
  100: *  ========
  101: *
  102: *> \author Univ. of Tennessee
  103: *> \author Univ. of California Berkeley
  104: *> \author Univ. of Colorado Denver
  105: *> \author NAG Ltd.
  106: *
  107: *> \date December 2016
  108: *
  109: *> \ingroup complex16OTHERauxiliary
  110: *
  111: *  =====================================================================
  112:       SUBROUTINE ZLAR2V( N, X, Y, Z, INCX, C, S, INCC )
  113: *
  114: *  -- LAPACK auxiliary routine (version 3.7.0) --
  115: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  116: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  117: *     December 2016
  118: *
  119: *     .. Scalar Arguments ..
  120:       INTEGER            INCC, INCX, N
  121: *     ..
  122: *     .. Array Arguments ..
  123:       DOUBLE PRECISION   C( * )
  124:       COMPLEX*16         S( * ), X( * ), Y( * ), Z( * )
  125: *     ..
  126: *
  127: *  =====================================================================
  128: *
  129: *     .. Local Scalars ..
  130:       INTEGER            I, IC, IX
  131:       DOUBLE PRECISION   CI, SII, SIR, T1I, T1R, T5, T6, XI, YI, ZII,
  132:      $                   ZIR
  133:       COMPLEX*16         SI, T2, T3, T4, ZI
  134: *     ..
  135: *     .. Intrinsic Functions ..
  136:       INTRINSIC          DBLE, DCMPLX, DCONJG, DIMAG
  137: *     ..
  138: *     .. Executable Statements ..
  139: *
  140:       IX = 1
  141:       IC = 1
  142:       DO 10 I = 1, N
  143:          XI = DBLE( X( IX ) )
  144:          YI = DBLE( Y( IX ) )
  145:          ZI = Z( IX )
  146:          ZIR = DBLE( ZI )
  147:          ZII = DIMAG( ZI )
  148:          CI = C( IC )
  149:          SI = S( IC )
  150:          SIR = DBLE( SI )
  151:          SII = DIMAG( SI )
  152:          T1R = SIR*ZIR - SII*ZII
  153:          T1I = SIR*ZII + SII*ZIR
  154:          T2 = CI*ZI
  155:          T3 = T2 - DCONJG( SI )*XI
  156:          T4 = DCONJG( T2 ) + SI*YI
  157:          T5 = CI*XI + T1R
  158:          T6 = CI*YI - T1R
  159:          X( IX ) = CI*T5 + ( SIR*DBLE( T4 )+SII*DIMAG( T4 ) )
  160:          Y( IX ) = CI*T6 - ( SIR*DBLE( T3 )-SII*DIMAG( T3 ) )
  161:          Z( IX ) = CI*T3 + DCONJG( SI )*DCMPLX( T6, T1I )
  162:          IX = IX + INCX
  163:          IC = IC + INCC
  164:    10 CONTINUE
  165:       RETURN
  166: *
  167: *     End of ZLAR2V
  168: *
  169:       END