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    1: *> \brief \b DLAR2V applies a vector of plane rotations with real cosines and real 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 DLAR2V + dependencies
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlar2v.f">
   11: *> [TGZ]</a>
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlar2v.f">
   13: *> [ZIP]</a>
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlar2v.f">
   15: *> [TXT]</a>
   16: *> \endhtmlonly
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE DLAR2V( 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( * ), S( * ), X( * ), Y( * ), Z( * )
   28: *       ..
   29: *
   30: *
   31: *> \par Purpose:
   32: *  =============
   33: *>
   34: *> \verbatim
   35: *>
   36: *> DLAR2V applies a vector of real plane rotations from both sides to
   37: *> a sequence of 2-by-2 real symmetric matrices, defined by the elements
   38: *> of the vectors x, y and z. For i = 1,2,...,n
   39: *>
   40: *>    ( x(i)  z(i) ) := (  c(i)  s(i) ) ( x(i)  z(i) ) ( c(i) -s(i) )
   41: *>    ( z(i)  y(i) )    ( -s(i)  c(i) ) ( z(i)  y(i) ) ( s(i)  c(i) )
   42: *> \endverbatim
   43: *
   44: *  Arguments:
   45: *  ==========
   46: *
   47: *> \param[in] N
   48: *> \verbatim
   49: *>          N is INTEGER
   50: *>          The number of plane rotations to be applied.
   51: *> \endverbatim
   52: *>
   53: *> \param[in,out] X
   54: *> \verbatim
   55: *>          X is DOUBLE PRECISION array,
   56: *>                         dimension (1+(N-1)*INCX)
   57: *>          The vector x.
   58: *> \endverbatim
   59: *>
   60: *> \param[in,out] Y
   61: *> \verbatim
   62: *>          Y is DOUBLE PRECISION array,
   63: *>                         dimension (1+(N-1)*INCX)
   64: *>          The vector y.
   65: *> \endverbatim
   66: *>
   67: *> \param[in,out] Z
   68: *> \verbatim
   69: *>          Z is DOUBLE PRECISION array,
   70: *>                         dimension (1+(N-1)*INCX)
   71: *>          The vector z.
   72: *> \endverbatim
   73: *>
   74: *> \param[in] INCX
   75: *> \verbatim
   76: *>          INCX is INTEGER
   77: *>          The increment between elements of X, Y and Z. INCX > 0.
   78: *> \endverbatim
   79: *>
   80: *> \param[in] C
   81: *> \verbatim
   82: *>          C is DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
   83: *>          The cosines of the plane rotations.
   84: *> \endverbatim
   85: *>
   86: *> \param[in] S
   87: *> \verbatim
   88: *>          S is DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
   89: *>          The sines of the plane rotations.
   90: *> \endverbatim
   91: *>
   92: *> \param[in] INCC
   93: *> \verbatim
   94: *>          INCC is INTEGER
   95: *>          The increment between elements of C and S. INCC > 0.
   96: *> \endverbatim
   97: *
   98: *  Authors:
   99: *  ========
  100: *
  101: *> \author Univ. of Tennessee
  102: *> \author Univ. of California Berkeley
  103: *> \author Univ. of Colorado Denver
  104: *> \author NAG Ltd.
  105: *
  106: *> \ingroup doubleOTHERauxiliary
  107: *
  108: *  =====================================================================
  109:       SUBROUTINE DLAR2V( N, X, Y, Z, INCX, C, S, INCC )
  110: *
  111: *  -- LAPACK auxiliary routine --
  112: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  113: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  114: *
  115: *     .. Scalar Arguments ..
  116:       INTEGER            INCC, INCX, N
  117: *     ..
  118: *     .. Array Arguments ..
  119:       DOUBLE PRECISION   C( * ), S( * ), X( * ), Y( * ), Z( * )
  120: *     ..
  121: *
  122: *  =====================================================================
  123: *
  124: *     .. Local Scalars ..
  125:       INTEGER            I, IC, IX
  126:       DOUBLE PRECISION   CI, SI, T1, T2, T3, T4, T5, T6, XI, YI, ZI
  127: *     ..
  128: *     .. Executable Statements ..
  129: *
  130:       IX = 1
  131:       IC = 1
  132:       DO 10 I = 1, N
  133:          XI = X( IX )
  134:          YI = Y( IX )
  135:          ZI = Z( IX )
  136:          CI = C( IC )
  137:          SI = S( IC )
  138:          T1 = SI*ZI
  139:          T2 = CI*ZI
  140:          T3 = T2 - SI*XI
  141:          T4 = T2 + SI*YI
  142:          T5 = CI*XI + T1
  143:          T6 = CI*YI - T1
  144:          X( IX ) = CI*T5 + SI*T4
  145:          Y( IX ) = CI*T6 - SI*T3
  146:          Z( IX ) = CI*T4 - SI*T5
  147:          IX = IX + INCX
  148:          IC = IC + INCC
  149:    10 CONTINUE
  150: *
  151: *     End of DLAR2V
  152: *
  153:       RETURN
  154:       END