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

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