slar2v.f

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*> \brief \b SLAR2V 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.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
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*> \endhtmlonly 
*
*  Definition:
*  ===========
*
*       SUBROUTINE SLAR2V( N, X, Y, Z, INCX, C, S, INCC )
* 
*       .. Scalar Arguments ..
*       INTEGER            INCC, INCX, N
*       ..
*       .. Array Arguments ..
*       REAL               C( * ), S( * ), X( * ), Y( * ), Z( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SLAR2V applies a vector of real plane rotations from both sides to
*> a sequence of 2-by-2 real symmetric matrices, defined by the elements
*> of the vectors x, y and z. For i = 1,2,...,n
*>
*>    ( x(i)  z(i) ) := (  c(i)  s(i) ) ( x(i)  z(i) ) ( c(i) -s(i) )
*>    ( z(i)  y(i) )    ( -s(i)  c(i) ) ( 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 REAL array,
*>                         dimension (1+(N-1)*INCX)
*>          The vector x.
*> \endverbatim
*>
*> \param[in,out] Y
*> \verbatim
*>          Y is REAL array,
*>                         dimension (1+(N-1)*INCX)
*>          The vector y.
*> \endverbatim
*>
*> \param[in,out] Z
*> \verbatim
*>          Z is REAL 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 REAL 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 September 2012
*
*> \ingroup realOTHERauxiliary
*
*  =====================================================================
      SUBROUTINE slar2v( N, X, Y, Z, INCX, C, S, INCC )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            incc, incx, n
*     ..
*     .. Array Arguments ..
      REAL               c( * ), s( * ), x( * ), y( * ), z( * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      INTEGER            i, ic, ix
      REAL               ci, si, t1, t2, t3, t4, t5, t6, xi, yi, zi
*     ..
*     .. Executable Statements ..
*
      ix = 1
      ic = 1
      DO 10 i = 1, n
         xi = x( ix )
         yi = y( ix )
         zi = z( ix )
         ci = c( ic )
         si = s( ic )
         t1 = si*zi
         t2 = ci*zi
         t3 = t2 - si*xi
         t4 = t2 + si*yi
         t5 = ci*xi + t1
         t6 = ci*yi - t1
         x( ix ) = ci*t5 + si*t4
         y( ix ) = ci*t6 - si*t3
         z( ix ) = ci*t4 - si*t5
         ix = ix + incx
         ic = ic + incc
   10 continue
*
*     End of SLAR2V
*
      return
      END