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Patches pour OS/2

    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