Return to zla_lin_berr.f CVS log

Up to [local] / rpl / lapack / lapack

Mise à jour globale de Lapack 3.2.2.

    1:       SUBROUTINE ZLA_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:       COMPLEX*16         RES( N, NRHS )
   19: *     ..
   20: *
   21: *  Purpose
   22: *  =======
   23: *
   24: *     ZLA_LIN_BERR computes componentwise 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 componentwise absolute value of the matrix
   28: *     or vector Z.
   29: *
   30: *     N       (input) INTEGER
   31: *     The number of linear equations, i.e., the order of the
   32: *     matrix A.  N >= 0.
   33: *
   34: *     NZ      (input) INTEGER
   35: *     We add (NZ+1)*SLAMCH( 'Safe minimum' ) to R(i) in the numerator to
   36: *     guard against spuriously zero residuals. Default value is N.
   37: *
   38: *     NRHS    (input) INTEGER
   39: *     The number of right hand sides, i.e., the number of columns
   40: *     of the matrices AYB, RES, and BERR.  NRHS >= 0.
   41: *
   42: *     RES    (input) DOUBLE PRECISION array, dimension (N,NRHS)
   43: *     The residual matrix, i.e., the matrix R in the relative backward
   44: *     error formula above.
   45: *
   46: *     AYB    (input) DOUBLE PRECISION array, dimension (N, NRHS)
   47: *     The denominator in the relative backward error formula above, i.e.,
   48: *     the matrix abs(op(A_s))*abs(Y) + abs(B_s). The matrices A, Y, and B
   49: *     are from iterative refinement (see zla_gerfsx_extended.f).
   50: *     
   51: *     BERR   (output) COMPLEX*16 array, dimension (NRHS)
   52: *     The componentwise relative backward error from the formula above.
   53: *
   54: *  =====================================================================
   55: *
   56: *     .. Local Scalars ..
   57:       DOUBLE PRECISION   TMP
   58:       INTEGER            I, J
   59:       COMPLEX*16         CDUM
   60: *     ..
   61: *     .. Intrinsic Functions ..
   62:       INTRINSIC          ABS, REAL, DIMAG, MAX
   63: *     ..
   64: *     .. External Functions ..
   65:       EXTERNAL           DLAMCH
   66:       DOUBLE PRECISION   DLAMCH
   67:       DOUBLE PRECISION   SAFE1
   68: *     ..
   69: *     .. Statement Functions ..
   70:       COMPLEX*16         CABS1
   71: *     ..
   72: *     .. Statement Function Definitions ..
   73:       CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) )
   74: *     ..
   75: *     .. Executable Statements ..
   76: *
   77: *     Adding SAFE1 to the numerator guards against spuriously zero
   78: *     residuals.  A similar safeguard is in the CLA_yyAMV routine used
   79: *     to compute AYB.
   80: *
   81:       SAFE1 = DLAMCH( 'Safe minimum' )
   82:       SAFE1 = (NZ+1)*SAFE1
   83: 
   84:       DO J = 1, NRHS
   85:          BERR(J) = 0.0D+0
   86:          DO I = 1, N
   87:             IF (AYB(I,J) .NE. 0.0D+0) THEN
   88:                TMP = (SAFE1 + CABS1(RES(I,J)))/AYB(I,J)
   89:                BERR(J) = MAX( BERR(J), TMP )
   90:             END IF
   91: *
   92: *     If AYB is exactly 0.0 (and if computed by CLA_yyAMV), then we know
   93: *     the true residual also must be exactly 0.0.
   94: *
   95:          END DO
   96:       END DO
   97:       END