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Annotation of rpl/lapack/lapack/dla_gbrpvgrw.f, revision 1.4

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