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Annotation of rpl/lapack/lapack/dlarfy.f, revision 1.4

1.1       bertrand    1: *> \brief \b DLARFY
                      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 DLARFY( UPLO, N, V, INCV, TAU, C, LDC, WORK )
                     12: *
                     13: *       .. Scalar Arguments ..
                     14: *       CHARACTER          UPLO
                     15: *       INTEGER            INCV, LDC, N
                     16: *       DOUBLE PRECISION   TAU
                     17: *       ..
                     18: *       .. Array Arguments ..
                     19: *       DOUBLE PRECISION   C( LDC, * ), V( * ), WORK( * )
                     20: *       ..
                     21: *
                     22: *
                     23: *> \par Purpose:
                     24: *  =============
                     25: *>
                     26: *> \verbatim
                     27: *>
                     28: *> DLARFY applies an elementary reflector, or Householder matrix, H,
                     29: *> to an n x n symmetric 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: *>          symmetric 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 DOUBLE PRECISION 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 DOUBLE PRECISION
                     75: *>          The value tau as described above.
                     76: *> \endverbatim
                     77: *>
                     78: *> \param[in,out] C
                     79: *> \verbatim
                     80: *>          C is DOUBLE PRECISION 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 DOUBLE PRECISION 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: *
                    104: *> \date December 2016
                    105: *
1.4     ! bertrand  106: *> \ingroup doubleOTHERauxiliary
1.1       bertrand  107: *
                    108: *  =====================================================================
                    109:       SUBROUTINE DLARFY( UPLO, N, V, INCV, TAU, C, LDC, WORK )
                    110: *
                    111: *  -- LAPACK test routine (version 3.7.0) --
                    112: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                    113: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
                    114: *     December 2016
                    115: *
                    116: *     .. Scalar Arguments ..
                    117:       CHARACTER          UPLO
                    118:       INTEGER            INCV, LDC, N
                    119:       DOUBLE PRECISION   TAU
                    120: *     ..
                    121: *     .. Array Arguments ..
                    122:       DOUBLE PRECISION   C( LDC, * ), V( * ), WORK( * )
                    123: *     ..
                    124: *
                    125: *  =====================================================================
                    126: *
                    127: *     .. Parameters ..
                    128:       DOUBLE PRECISION   ONE, ZERO, HALF
                    129:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0, HALF = 0.5D+0 )
                    130: *     ..
                    131: *     .. Local Scalars ..
                    132:       DOUBLE PRECISION   ALPHA
                    133: *     ..
                    134: *     .. External Subroutines ..
                    135:       EXTERNAL           DAXPY, DSYMV, DSYR2
                    136: *     ..
                    137: *     .. External Functions ..
                    138:       DOUBLE PRECISION   DDOT
                    139:       EXTERNAL           DDOT
                    140: *     ..
                    141: *     .. Executable Statements ..
                    142: *
                    143:       IF( TAU.EQ.ZERO )
                    144:      $   RETURN
                    145: *
                    146: *     Form  w:= C * v
                    147: *
                    148:       CALL DSYMV( UPLO, N, ONE, C, LDC, V, INCV, ZERO, WORK, 1 )
                    149: *
                    150:       ALPHA = -HALF*TAU*DDOT( N, WORK, 1, V, INCV )
                    151:       CALL DAXPY( N, ALPHA, V, INCV, WORK, 1 )
                    152: *
                    153: *     C := C - v * w' - w * v'
                    154: *
                    155:       CALL DSYR2( UPLO, N, -TAU, V, INCV, WORK, 1, C, LDC )
                    156: *
                    157:       RETURN
                    158: *
                    159: *     End of DLARFY
                    160: *
                    161:       END