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Annotation of rpl/lapack/lapack/zlarfy.f, revision 1.5

1.1       bertrand    1: *> \brief \b ZLARFY
                      2: *
                      3: *  =========== DOCUMENTATION ===========
                      4: *
                      5: * Online html documentation available at
                      6: *            http://www.netlib.org/lapack/explore-html/
                      7: *
                      8: *  Definition:
                      9: *  ===========
                     10: *
                     11: *       SUBROUTINE ZLARFY( UPLO, N, V, INCV, TAU, C, LDC, WORK )
                     12: *
                     13: *       .. Scalar Arguments ..
                     14: *       CHARACTER          UPLO
                     15: *       INTEGER            INCV, LDC, N
                     16: *       COMPLEX*16         TAU
                     17: *       ..
                     18: *       .. Array Arguments ..
                     19: *       COMPLEX*16         C( LDC, * ), V( * ), WORK( * )
                     20: *       ..
                     21: *
                     22: *
                     23: *> \par Purpose:
                     24: *  =============
                     25: *>
                     26: *> \verbatim
                     27: *>
                     28: *> ZLARFY applies an elementary reflector, or Householder matrix, H,
                     29: *> to an n x n Hermitian matrix C, from both the left and the right.
                     30: *>
                     31: *> H is represented in the form
                     32: *>
                     33: *>    H = I - tau * v * v'
                     34: *>
                     35: *> where  tau  is a scalar and  v  is a vector.
                     36: *>
                     37: *> If  tau  is  zero, then  H  is taken to be the unit matrix.
                     38: *> \endverbatim
                     39: *
                     40: *  Arguments:
                     41: *  ==========
                     42: *
                     43: *> \param[in] UPLO
                     44: *> \verbatim
                     45: *>          UPLO is CHARACTER*1
                     46: *>          Specifies whether the upper or lower triangular part of the
                     47: *>          Hermitian matrix C is stored.
                     48: *>          = 'U':  Upper triangle
                     49: *>          = 'L':  Lower triangle
                     50: *> \endverbatim
                     51: *>
                     52: *> \param[in] N
                     53: *> \verbatim
                     54: *>          N is INTEGER
                     55: *>          The number of rows and columns of the matrix C.  N >= 0.
                     56: *> \endverbatim
                     57: *>
                     58: *> \param[in] V
                     59: *> \verbatim
                     60: *>          V is COMPLEX*16 array, dimension
                     61: *>                  (1 + (N-1)*abs(INCV))
                     62: *>          The vector v as described above.
                     63: *> \endverbatim
                     64: *>
                     65: *> \param[in] INCV
                     66: *> \verbatim
                     67: *>          INCV is INTEGER
                     68: *>          The increment between successive elements of v.  INCV must
                     69: *>          not be zero.
                     70: *> \endverbatim
                     71: *>
                     72: *> \param[in] TAU
                     73: *> \verbatim
                     74: *>          TAU is COMPLEX*16
                     75: *>          The value tau as described above.
                     76: *> \endverbatim
                     77: *>
                     78: *> \param[in,out] C
                     79: *> \verbatim
                     80: *>          C is COMPLEX*16 array, dimension (LDC, N)
                     81: *>          On entry, the matrix C.
                     82: *>          On exit, C is overwritten by H * C * H'.
                     83: *> \endverbatim
                     84: *>
                     85: *> \param[in] LDC
                     86: *> \verbatim
                     87: *>          LDC is INTEGER
                     88: *>          The leading dimension of the array C.  LDC >= max( 1, N ).
                     89: *> \endverbatim
                     90: *>
                     91: *> \param[out] WORK
                     92: *> \verbatim
                     93: *>          WORK is COMPLEX*16 array, dimension (N)
                     94: *> \endverbatim
                     95: *
                     96: *  Authors:
                     97: *  ========
                     98: *
                     99: *> \author Univ. of Tennessee
                    100: *> \author Univ. of California Berkeley
                    101: *> \author Univ. of Colorado Denver
                    102: *> \author NAG Ltd.
                    103: *
1.4       bertrand  104: *> \ingroup complex16OTHERauxiliary
1.1       bertrand  105: *
                    106: *  =====================================================================
                    107:       SUBROUTINE ZLARFY( UPLO, N, V, INCV, TAU, C, LDC, WORK )
                    108: *
1.5     ! bertrand  109: *  -- LAPACK test routine --
1.1       bertrand  110: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                    111: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
                    112: *
                    113: *     .. Scalar Arguments ..
                    114:       CHARACTER          UPLO
                    115:       INTEGER            INCV, LDC, N
                    116:       COMPLEX*16         TAU
                    117: *     ..
                    118: *     .. Array Arguments ..
                    119:       COMPLEX*16         C( LDC, * ), V( * ), WORK( * )
                    120: *     ..
                    121: *
                    122: *  =====================================================================
                    123: *
                    124: *     .. Parameters ..
                    125:       COMPLEX*16         ONE, ZERO, HALF
                    126:       PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ),
                    127:      $                   ZERO = ( 0.0D+0, 0.0D+0 ),
                    128:      $                   HALF = ( 0.5D+0, 0.0D+0 ) )
                    129: *     ..
                    130: *     .. Local Scalars ..
                    131:       COMPLEX*16         ALPHA
                    132: *     ..
                    133: *     .. External Subroutines ..
                    134:       EXTERNAL           ZAXPY, ZHEMV, ZHER2
                    135: *     ..
                    136: *     .. External Functions ..
                    137:       COMPLEX*16         ZDOTC
                    138:       EXTERNAL           ZDOTC
                    139: *     ..
                    140: *     .. Executable Statements ..
                    141: *
                    142:       IF( TAU.EQ.ZERO )
                    143:      $   RETURN
                    144: *
                    145: *     Form  w:= C * v
                    146: *
                    147:       CALL ZHEMV( UPLO, N, ONE, C, LDC, V, INCV, ZERO, WORK, 1 )
                    148: *
                    149:       ALPHA = -HALF*TAU*ZDOTC( N, WORK, 1, V, INCV )
                    150:       CALL ZAXPY( N, ALPHA, V, INCV, WORK, 1 )
                    151: *
                    152: *     C := C - v * w' - w * v'
                    153: *
                    154:       CALL ZHER2( UPLO, N, -TAU, V, INCV, WORK, 1, C, LDC )
                    155: *
                    156:       RETURN
                    157: *
                    158: *     End of ZLARFY
                    159: *
                    160:       END