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Mise à jour de lapack vers la version 3.3.0.

    1:       SUBROUTINE DLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )
    2: *
    3: *     -- LAPACK routine (version 3.2.2)                                 --
    4: *     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
    5: *     -- Jason Riedy of Univ. of California Berkeley.                 --
    6: *     -- June 2010                                                    --
    7: *
    8: *     -- LAPACK is a software package provided by Univ. of Tennessee, --
    9: *     -- Univ. of California Berkeley and NAG Ltd.                    --
   10: *
   11:       IMPLICIT NONE
   12: *     ..
   13: *     .. Scalar Arguments ..
   14:       INTEGER            N, NZ, NRHS
   15: *     ..
   16: *     .. Array Arguments ..
   17:       DOUBLE PRECISION   AYB( N, NRHS ), BERR( NRHS )
   18:       DOUBLE PRECISION   RES( N, NRHS )
   19: *     ..
   20: *
   21: *  Purpose
   22: *  =======
   23: *
   24: *     DLA_LIN_BERR computes component-wise relative backward error from
   25: *     the formula
   26: *         max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
   27: *     where abs(Z) is the component-wise absolute value of the matrix
   28: *     or vector Z.
   29: *
   30: *  Arguments
   31: *  ==========
   32: *
   33: *     N       (input) INTEGER
   34: *     The number of linear equations, i.e., the order of the
   35: *     matrix A.  N >= 0.
   36: *
   37: *     NZ      (input) INTEGER
   38: *     We add (NZ+1)*SLAMCH( 'Safe minimum' ) to R(i) in the numerator to
   39: *     guard against spuriously zero residuals. Default value is N.
   40: *
   41: *     NRHS    (input) INTEGER
   42: *     The number of right hand sides, i.e., the number of columns
   43: *     of the matrices AYB, RES, and BERR.  NRHS >= 0.
   44: *
   45: *     RES     (input) DOUBLE PRECISION array, dimension (N,NRHS)
   46: *     The residual matrix, i.e., the matrix R in the relative backward
   47: *     error formula above.
   48: *
   49: *     AYB     (input) DOUBLE PRECISION array, dimension (N, NRHS)
   50: *     The denominator in the relative backward error formula above, i.e.,
   51: *     the matrix abs(op(A_s))*abs(Y) + abs(B_s). The matrices A, Y, and B
   52: *     are from iterative refinement (see dla_gerfsx_extended.f).
   53: *     
   54: *     BERR    (output) DOUBLE PRECISION array, dimension (NRHS)
   55: *     The component-wise relative backward error from the formula above.
   56: *
   57: *  =====================================================================
   58: *
   59: *     .. Local Scalars ..
   60:       DOUBLE PRECISION   TMP
   61:       INTEGER            I, J
   62: *     ..
   63: *     .. Intrinsic Functions ..
   64:       INTRINSIC          ABS, MAX
   65: *     ..
   66: *     .. External Functions ..
   67:       EXTERNAL           DLAMCH
   68:       DOUBLE PRECISION   DLAMCH
   69:       DOUBLE PRECISION   SAFE1
   70: *     ..
   71: *     .. Executable Statements ..
   72: *
   73: *     Adding SAFE1 to the numerator guards against spuriously zero
   74: *     residuals.  A similar safeguard is in the SLA_yyAMV routine used
   75: *     to compute AYB.
   76: *
   77:       SAFE1 = DLAMCH( 'Safe minimum' )
   78:       SAFE1 = (NZ+1)*SAFE1
   79: 
   80:       DO J = 1, NRHS
   81:          BERR(J) = 0.0D+0
   82:          DO I = 1, N
   83:             IF (AYB(I,J) .NE. 0.0D+0) THEN
   84:                TMP = (SAFE1+ABS(RES(I,J)))/AYB(I,J)
   85:                BERR(J) = MAX( BERR(J), TMP )
   86:             END IF
   87: *
   88: *     If AYB is exactly 0.0 (and if computed by SLA_yyAMV), then we know
   89: *     the true residual also must be exactly 0.0.
   90: *
   91:          END DO
   92:       END DO
   93:       END