*> \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/ * *> \htmlonly *> Download SLAR2V + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \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 December 2016 * *> \ingroup realOTHERauxiliary * * ===================================================================== SUBROUTINE SLAR2V( N, X, Y, Z, INCX, C, S, INCC ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. 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