LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
clar2v.f
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00001 *> \brief \b CLAR2V
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download CLAR2V + dependencies 
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00011 *> [TGZ]</a> 
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00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clar2v.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE CLAR2V( N, X, Y, Z, INCX, C, S, INCC )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       INTEGER            INCC, INCX, N
00025 *       ..
00026 *       .. Array Arguments ..
00027 *       REAL               C( * )
00028 *       COMPLEX            S( * ), X( * ), Y( * ), Z( * )
00029 *       ..
00030 *  
00031 *
00032 *> \par Purpose:
00033 *  =============
00034 *>
00035 *> \verbatim
00036 *>
00037 *> CLAR2V applies a vector of complex plane rotations with real cosines
00038 *> from both sides to a sequence of 2-by-2 complex Hermitian matrices,
00039 *> defined by the elements of the vectors x, y and z. For i = 1,2,...,n
00040 *>
00041 *>    (       x(i)  z(i) ) :=
00042 *>    ( conjg(z(i)) y(i) )
00043 *>
00044 *>      (  c(i) conjg(s(i)) ) (       x(i)  z(i) ) ( c(i) -conjg(s(i)) )
00045 *>      ( -s(i)       c(i)  ) ( conjg(z(i)) y(i) ) ( s(i)        c(i)  )
00046 *> \endverbatim
00047 *
00048 *  Arguments:
00049 *  ==========
00050 *
00051 *> \param[in] N
00052 *> \verbatim
00053 *>          N is INTEGER
00054 *>          The number of plane rotations to be applied.
00055 *> \endverbatim
00056 *>
00057 *> \param[in,out] X
00058 *> \verbatim
00059 *>          X is COMPLEX array, dimension (1+(N-1)*INCX)
00060 *>          The vector x; the elements of x are assumed to be real.
00061 *> \endverbatim
00062 *>
00063 *> \param[in,out] Y
00064 *> \verbatim
00065 *>          Y is COMPLEX array, dimension (1+(N-1)*INCX)
00066 *>          The vector y; the elements of y are assumed to be real.
00067 *> \endverbatim
00068 *>
00069 *> \param[in,out] Z
00070 *> \verbatim
00071 *>          Z is COMPLEX array, dimension (1+(N-1)*INCX)
00072 *>          The vector z.
00073 *> \endverbatim
00074 *>
00075 *> \param[in] INCX
00076 *> \verbatim
00077 *>          INCX is INTEGER
00078 *>          The increment between elements of X, Y and Z. INCX > 0.
00079 *> \endverbatim
00080 *>
00081 *> \param[in] C
00082 *> \verbatim
00083 *>          C is REAL array, dimension (1+(N-1)*INCC)
00084 *>          The cosines of the plane rotations.
00085 *> \endverbatim
00086 *>
00087 *> \param[in] S
00088 *> \verbatim
00089 *>          S is COMPLEX array, dimension (1+(N-1)*INCC)
00090 *>          The sines of the plane rotations.
00091 *> \endverbatim
00092 *>
00093 *> \param[in] INCC
00094 *> \verbatim
00095 *>          INCC is INTEGER
00096 *>          The increment between elements of C and S. INCC > 0.
00097 *> \endverbatim
00098 *
00099 *  Authors:
00100 *  ========
00101 *
00102 *> \author Univ. of Tennessee 
00103 *> \author Univ. of California Berkeley 
00104 *> \author Univ. of Colorado Denver 
00105 *> \author NAG Ltd. 
00106 *
00107 *> \date November 2011
00108 *
00109 *> \ingroup complexOTHERauxiliary
00110 *
00111 *  =====================================================================
00112       SUBROUTINE CLAR2V( N, X, Y, Z, INCX, C, S, INCC )
00113 *
00114 *  -- LAPACK auxiliary routine (version 3.4.0) --
00115 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00116 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00117 *     November 2011
00118 *
00119 *     .. Scalar Arguments ..
00120       INTEGER            INCC, INCX, N
00121 *     ..
00122 *     .. Array Arguments ..
00123       REAL               C( * )
00124       COMPLEX            S( * ), X( * ), Y( * ), Z( * )
00125 *     ..
00126 *
00127 *  =====================================================================
00128 *
00129 *     .. Local Scalars ..
00130       INTEGER            I, IC, IX
00131       REAL               CI, SII, SIR, T1I, T1R, T5, T6, XI, YI, ZII,
00132      $                   ZIR
00133       COMPLEX            SI, T2, T3, T4, ZI
00134 *     ..
00135 *     .. Intrinsic Functions ..
00136       INTRINSIC          AIMAG, CMPLX, CONJG, REAL
00137 *     ..
00138 *     .. Executable Statements ..
00139 *
00140       IX = 1
00141       IC = 1
00142       DO 10 I = 1, N
00143          XI = REAL( X( IX ) )
00144          YI = REAL( Y( IX ) )
00145          ZI = Z( IX )
00146          ZIR = REAL( ZI )
00147          ZII = AIMAG( ZI )
00148          CI = C( IC )
00149          SI = S( IC )
00150          SIR = REAL( SI )
00151          SII = AIMAG( SI )
00152          T1R = SIR*ZIR - SII*ZII
00153          T1I = SIR*ZII + SII*ZIR
00154          T2 = CI*ZI
00155          T3 = T2 - CONJG( SI )*XI
00156          T4 = CONJG( T2 ) + SI*YI
00157          T5 = CI*XI + T1R
00158          T6 = CI*YI - T1R
00159          X( IX ) = CI*T5 + ( SIR*REAL( T4 )+SII*AIMAG( T4 ) )
00160          Y( IX ) = CI*T6 - ( SIR*REAL( T3 )-SII*AIMAG( T3 ) )
00161          Z( IX ) = CI*T3 + CONJG( SI )*CMPLX( T6, T1I )
00162          IX = IX + INCX
00163          IC = IC + INCC
00164    10 CONTINUE
00165       RETURN
00166 *
00167 *     End of CLAR2V
00168 *
00169       END
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