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

1.1     ! bertrand    1:       DOUBLE PRECISION FUNCTION DLA_GBRPVGRW( N, KL, KU, NCOLS, AB,
        !             2:      $                                        LDAB, AFB, LDAFB )
        !             3: *
        !             4: *     -- LAPACK routine (version 3.2.2)                                 --
        !             5: *     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
        !             6: *     -- Jason Riedy of Univ. of California Berkeley.                 --
        !             7: *     -- June 2010                                                    --
        !             8: *
        !             9: *     -- LAPACK is a software package provided by Univ. of Tennessee, --
        !            10: *     -- Univ. of California Berkeley and NAG Ltd.                    --
        !            11: *
        !            12:       IMPLICIT NONE
        !            13: *     ..
        !            14: *     .. Scalar Arguments ..
        !            15:       INTEGER            N, KL, KU, NCOLS, LDAB, LDAFB
        !            16: *     ..
        !            17: *     .. Array Arguments ..
        !            18:       DOUBLE PRECISION   AB( LDAB, * ), AFB( LDAFB, * )
        !            19: *     ..
        !            20: *
        !            21: *  Purpose
        !            22: *  =======
        !            23: *
        !            24: *  DLA_GBRPVGRW computes the reciprocal pivot growth factor
        !            25: *  norm(A)/norm(U). The "max absolute element" norm is used. If this is
        !            26: *  much less than 1, the stability of the LU factorization of the
        !            27: *  (equilibrated) matrix A could be poor. This also means that the
        !            28: *  solution X, estimated condition numbers, and error bounds could be
        !            29: *  unreliable.
        !            30: *
        !            31: *  Arguments
        !            32: *  =========
        !            33: *
        !            34: *     N       (input) INTEGER
        !            35: *     The number of linear equations, i.e., the order of the
        !            36: *     matrix A.  N >= 0.
        !            37: *
        !            38: *     KL      (input) INTEGER
        !            39: *     The number of subdiagonals within the band of A.  KL >= 0.
        !            40: *
        !            41: *     KU      (input) INTEGER
        !            42: *     The number of superdiagonals within the band of A.  KU >= 0.
        !            43: *
        !            44: *     NCOLS   (input) INTEGER
        !            45: *     The number of columns of the matrix A.  NCOLS >= 0.
        !            46: *
        !            47: *     AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
        !            48: *     On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
        !            49: *     The j-th column of A is stored in the j-th column of the
        !            50: *     array AB as follows:
        !            51: *     AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
        !            52: *
        !            53: *     LDAB    (input) INTEGER
        !            54: *     The leading dimension of the array AB.  LDAB >= KL+KU+1.
        !            55: *
        !            56: *     AFB     (input) DOUBLE PRECISION array, dimension (LDAFB,N)
        !            57: *     Details of the LU factorization of the band matrix A, as
        !            58: *     computed by DGBTRF.  U is stored as an upper triangular
        !            59: *     band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
        !            60: *     and the multipliers used during the factorization are stored
        !            61: *     in rows KL+KU+2 to 2*KL+KU+1.
        !            62: *
        !            63: *     LDAFB   (input) INTEGER
        !            64: *     The leading dimension of the array AFB.  LDAFB >= 2*KL+KU+1.
        !            65: *
        !            66: *  =====================================================================
        !            67: *
        !            68: *     .. Local Scalars ..
        !            69:       INTEGER            I, J, KD
        !            70:       DOUBLE PRECISION   AMAX, UMAX, RPVGRW
        !            71: *     ..
        !            72: *     .. Intrinsic Functions ..
        !            73:       INTRINSIC          ABS, MAX, MIN
        !            74: *     ..
        !            75: *     .. Executable Statements ..
        !            76: *
        !            77:       RPVGRW = 1.0D+0
        !            78: 
        !            79:       KD = KU + 1
        !            80:       DO J = 1, NCOLS
        !            81:          AMAX = 0.0D+0
        !            82:          UMAX = 0.0D+0
        !            83:          DO I = MAX( J-KU, 1 ), MIN( J+KL, N )
        !            84:             AMAX = MAX( ABS( AB( KD+I-J, J)), AMAX )
        !            85:          END DO
        !            86:          DO I = MAX( J-KU, 1 ), J
        !            87:             UMAX = MAX( ABS( AFB( KD+I-J, J ) ), UMAX )
        !            88:          END DO
        !            89:          IF ( UMAX /= 0.0D+0 ) THEN
        !            90:             RPVGRW = MIN( AMAX / UMAX, RPVGRW )
        !            91:          END IF
        !            92:       END DO
        !            93:       DLA_GBRPVGRW = RPVGRW
        !            94:       END