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Annotation of rpl/lapack/lapack/dlar2v.f, revision 1.13

1.11      bertrand    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.
1.8       bertrand    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: *
1.11      bertrand  106: *> \date September 2012
1.8       bertrand  107: *
                    108: *> \ingroup doubleOTHERauxiliary
                    109: *
                    110: *  =====================================================================
1.1       bertrand  111:       SUBROUTINE DLAR2V( N, X, Y, Z, INCX, C, S, INCC )
                    112: *
1.11      bertrand  113: *  -- LAPACK auxiliary routine (version 3.4.2) --
1.1       bertrand  114: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                    115: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.11      bertrand  116: *     September 2012
1.1       bertrand  117: *
                    118: *     .. Scalar Arguments ..
                    119:       INTEGER            INCC, INCX, N
                    120: *     ..
                    121: *     .. Array Arguments ..
                    122:       DOUBLE PRECISION   C( * ), S( * ), X( * ), Y( * ), Z( * )
                    123: *     ..
                    124: *
                    125: *  =====================================================================
                    126: *
                    127: *     .. Local Scalars ..
                    128:       INTEGER            I, IC, IX
                    129:       DOUBLE PRECISION   CI, SI, T1, T2, T3, T4, T5, T6, XI, YI, ZI
                    130: *     ..
                    131: *     .. Executable Statements ..
                    132: *
                    133:       IX = 1
                    134:       IC = 1
                    135:       DO 10 I = 1, N
                    136:          XI = X( IX )
                    137:          YI = Y( IX )
                    138:          ZI = Z( IX )
                    139:          CI = C( IC )
                    140:          SI = S( IC )
                    141:          T1 = SI*ZI
                    142:          T2 = CI*ZI
                    143:          T3 = T2 - SI*XI
                    144:          T4 = T2 + SI*YI
                    145:          T5 = CI*XI + T1
                    146:          T6 = CI*YI - T1
                    147:          X( IX ) = CI*T5 + SI*T4
                    148:          Y( IX ) = CI*T6 - SI*T3
                    149:          Z( IX ) = CI*T4 - SI*T5
                    150:          IX = IX + INCX
                    151:          IC = IC + INCC
                    152:    10 CONTINUE
                    153: *
                    154: *     End of DLAR2V
                    155: *
                    156:       RETURN
                    157:       END