slargv.f

Go to the documentation of this file.

*> \brief \b SLARGV generates a vector of plane rotations with real cosines and real sines.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download SLARGV + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slargv.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slargv.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slargv.f">
*> [TXT]</a>
*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE SLARGV( N, X, INCX, Y, INCY, C, INCC )
*
*       .. Scalar Arguments ..
*       INTEGER            INCC, INCX, INCY, N
*       ..
*       .. Array Arguments ..
*       REAL               C( * ), X( * ), Y( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SLARGV generates a vector of real plane rotations, determined by
*> elements of the real vectors x and y. For i = 1,2,...,n
*>
*>    (  c(i)  s(i) ) ( x(i) ) = ( a(i) )
*>    ( -s(i)  c(i) ) ( y(i) ) = (   0  )
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of plane rotations to be generated.
*> \endverbatim
*>
*> \param[in,out] X
*> \verbatim
*>          X is REAL array,
*>                         dimension (1+(N-1)*INCX)
*>          On entry, the vector x.
*>          On exit, x(i) is overwritten by a(i), for i = 1,...,n.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*>          INCX is INTEGER
*>          The increment between elements of X. INCX > 0.
*> \endverbatim
*>
*> \param[in,out] Y
*> \verbatim
*>          Y is REAL array,
*>                         dimension (1+(N-1)*INCY)
*>          On entry, the vector y.
*>          On exit, the sines of the plane rotations.
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*>          INCY is INTEGER
*>          The increment between elements of Y. INCY > 0.
*> \endverbatim
*>
*> \param[out] C
*> \verbatim
*>          C is REAL array, dimension (1+(N-1)*INCC)
*>          The cosines of the plane rotations.
*> \endverbatim
*>
*> \param[in] INCC
*> \verbatim
*>          INCC is INTEGER
*>          The increment between elements of C. INCC > 0.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup largv
*
*  =====================================================================
      SUBROUTINE slargv( N, X, INCX, Y, INCY, C, 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, INCY, N
*     ..
*     .. Array Arguments ..
      REAL               C( * ), X( * ), Y( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE
      parameter( zero = 0.0e+0, one = 1.0e+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, IC, IX, IY
      REAL               F, G, T, TT
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, sqrt
*     ..
*     .. Executable Statements ..
*
      ix = 1
      iy = 1
      ic = 1
      DO 10 i = 1, n
         f = x( ix )
         g = y( iy )
         IF( g.EQ.zero ) THEN
            c( ic ) = one
         ELSE IF( f.EQ.zero ) THEN
            c( ic ) = zero
            y( iy ) = one
            x( ix ) = g
         ELSE IF( abs( f ).GT.abs( g ) ) THEN
            t = g / f
            tt = sqrt( one+t*t )
            c( ic ) = one / tt
            y( iy ) = t*c( ic )
            x( ix ) = f*tt
         ELSE
            t = f / g
            tt = sqrt( one+t*t )
            y( iy ) = one / tt
            c( ic ) = t*y( iy )
            x( ix ) = g*tt
         END IF
         ic = ic + incc
         iy = iy + incy
         ix = ix + incx
   10 CONTINUE
      RETURN
*
*     End of SLARGV
*
      END