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Annotation of rpl/lapack/lapack/dlarfy.f, revision 1.1

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: *
        !           106: *> \ingroup double_eig
        !           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