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

1.1     ! bertrand    1: *> \brief \b ZLA_GERPVGRW
        !             2: *
        !             3: *  =========== DOCUMENTATION ===========
        !             4: *
        !             5: * Online html documentation available at 
        !             6: *            http://www.netlib.org/lapack/explore-html/ 
        !             7: *
        !             8: *> \htmlonly
        !             9: *> Download ZLA_GERPVGRW + dependencies 
        !            10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_gerpvgrw.f"> 
        !            11: *> [TGZ]</a> 
        !            12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_gerpvgrw.f"> 
        !            13: *> [ZIP]</a> 
        !            14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_gerpvgrw.f"> 
        !            15: *> [TXT]</a>
        !            16: *> \endhtmlonly 
        !            17: *
        !            18: *  Definition:
        !            19: *  ===========
        !            20: *
        !            21: *       DOUBLE PRECISION FUNCTION ZLA_GERPVGRW( N, NCOLS, A, LDA, AF,
        !            22: *                LDAF )
        !            23: * 
        !            24: *       .. Scalar Arguments ..
        !            25: *       INTEGER            N, NCOLS, LDA, LDAF
        !            26: *       ..
        !            27: *       .. Array Arguments ..
        !            28: *       COMPLEX*16         A( LDA, * ), AF( LDAF, * )
        !            29: *       ..
        !            30: *  
        !            31: *
        !            32: *> \par Purpose:
        !            33: *  =============
        !            34: *>
        !            35: *> \verbatim
        !            36: *>
        !            37: *> 
        !            38: *> ZLA_GERPVGRW computes the reciprocal pivot growth factor
        !            39: *> norm(A)/norm(U). The "max absolute element" norm is used. If this is
        !            40: *> much less than 1, the stability of the LU factorization of the
        !            41: *> (equilibrated) matrix A could be poor. This also means that the
        !            42: *> solution X, estimated condition numbers, and error bounds could be
        !            43: *> unreliable.
        !            44: *> \endverbatim
        !            45: *
        !            46: *  Arguments:
        !            47: *  ==========
        !            48: *
        !            49: *> \param[in] N
        !            50: *> \verbatim
        !            51: *>          N is INTEGER
        !            52: *>     The number of linear equations, i.e., the order of the
        !            53: *>     matrix A.  N >= 0.
        !            54: *> \endverbatim
        !            55: *>
        !            56: *> \param[in] NCOLS
        !            57: *> \verbatim
        !            58: *>          NCOLS is INTEGER
        !            59: *>     The number of columns of the matrix A. NCOLS >= 0.
        !            60: *> \endverbatim
        !            61: *>
        !            62: *> \param[in] A
        !            63: *> \verbatim
        !            64: *>          A is DOUBLE PRECISION array, dimension (LDA,N)
        !            65: *>     On entry, the N-by-N matrix A.
        !            66: *> \endverbatim
        !            67: *>
        !            68: *> \param[in] LDA
        !            69: *> \verbatim
        !            70: *>          LDA is INTEGER
        !            71: *>     The leading dimension of the array A.  LDA >= max(1,N).
        !            72: *> \endverbatim
        !            73: *>
        !            74: *> \param[in] AF
        !            75: *> \verbatim
        !            76: *>          AF is DOUBLE PRECISION array, dimension (LDAF,N)
        !            77: *>     The factors L and U from the factorization
        !            78: *>     A = P*L*U as computed by ZGETRF.
        !            79: *> \endverbatim
        !            80: *>
        !            81: *> \param[in] LDAF
        !            82: *> \verbatim
        !            83: *>          LDAF is INTEGER
        !            84: *>     The leading dimension of the array AF.  LDAF >= max(1,N).
        !            85: *> \endverbatim
        !            86: *
        !            87: *  Authors:
        !            88: *  ========
        !            89: *
        !            90: *> \author Univ. of Tennessee 
        !            91: *> \author Univ. of California Berkeley 
        !            92: *> \author Univ. of Colorado Denver 
        !            93: *> \author NAG Ltd. 
        !            94: *
        !            95: *> \date November 2011
        !            96: *
        !            97: *> \ingroup complex16GEcomputational
        !            98: *
        !            99: *  =====================================================================
        !           100:       DOUBLE PRECISION FUNCTION ZLA_GERPVGRW( N, NCOLS, A, LDA, AF,
        !           101:      $         LDAF )
        !           102: *
        !           103: *  -- LAPACK computational routine (version 3.4.0) --
        !           104: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
        !           105: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
        !           106: *     November 2011
        !           107: *
        !           108: *     .. Scalar Arguments ..
        !           109:       INTEGER            N, NCOLS, LDA, LDAF
        !           110: *     ..
        !           111: *     .. Array Arguments ..
        !           112:       COMPLEX*16         A( LDA, * ), AF( LDAF, * )
        !           113: *     ..
        !           114: *
        !           115: *  =====================================================================
        !           116: *
        !           117: *     .. Local Scalars ..
        !           118:       INTEGER            I, J
        !           119:       DOUBLE PRECISION   AMAX, UMAX, RPVGRW
        !           120:       COMPLEX*16         ZDUM
        !           121: *     ..
        !           122: *     .. Intrinsic Functions ..
        !           123:       INTRINSIC          MAX, MIN, ABS, REAL, DIMAG
        !           124: *     ..
        !           125: *     .. Statement Functions ..
        !           126:       DOUBLE PRECISION   CABS1
        !           127: *     ..
        !           128: *     .. Statement Function Definitions ..
        !           129:       CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
        !           130: *     ..
        !           131: *     .. Executable Statements ..
        !           132: *
        !           133:       RPVGRW = 1.0D+0
        !           134: 
        !           135:       DO J = 1, NCOLS
        !           136:          AMAX = 0.0D+0
        !           137:          UMAX = 0.0D+0
        !           138:          DO I = 1, N
        !           139:             AMAX = MAX( CABS1( A( I, J ) ), AMAX )
        !           140:          END DO
        !           141:          DO I = 1, J
        !           142:             UMAX = MAX( CABS1( AF( I, J ) ), UMAX )
        !           143:          END DO
        !           144:          IF ( UMAX /= 0.0D+0 ) THEN
        !           145:             RPVGRW = MIN( AMAX / UMAX, RPVGRW )
        !           146:          END IF
        !           147:       END DO
        !           148:       ZLA_GERPVGRW = RPVGRW
        !           149:       END