TESTING/LIN/sebchvxx.f(3)

NAME
TESTING/LIN/sebchvxx.f

SYNOPSIS

  Functions/Subroutines
subroutine sebchvxx (thresh, path)
SEBCHVXX

Function/Subroutine Documentation

  subroutine sebchvxx (real thresh, character*3 path)

SEBCHVXX

Purpose:

    !>
    !>  SEBCHVXX will run S**SVXX on a series of Hilbert matrices and then
    !>  compare the error bounds returned by SGESVXX to see if the returned
    !>  answer indeed falls within those bounds.
    !>
    !>  Eight test ratios will be computed.  The tests will pass if they are .LT.
    !>  THRESH.  There are two cases that are determined by 1 / (SQRT( N ) * EPS).
    !>  If that value is .LE. to the component wise reciprocal condition number,
    !>  it uses the guaranteed case, other wise it uses the unguaranteed case.
    !>
    !>  Test ratios:
    !>     Let Xc be X_computed and Xt be X_truth.
    !>     The norm used is the infinity norm.
    !>
    !>     Let A be the guaranteed case and B be the unguaranteed case.
    !>
    !>       1. Normwise guaranteed forward error bound.
    !>       A: norm ( abs( Xc - Xt ) / norm ( Xt ) .LE. ERRBND( *, nwise_i, bnd_i ) and
    !>          ERRBND( *, nwise_i, bnd_i ) .LE. MAX(SQRT(N),10) * EPS.
    !>          If these conditions are met, the test ratio is set to be
    !>          ERRBND( *, nwise_i, bnd_i ) / MAX(SQRT(N), 10).  Otherwise it is 1/EPS.
    !>       B: For this case, SGESVXX should just return 1.  If it is less than
    !>          one, treat it the same as in 1A.  Otherwise it fails. (Set test
    !>          ratio to ERRBND( *, nwise_i, bnd_i ) * THRESH?)
    !>
    !>       2. Componentwise guaranteed forward error bound.
    !>       A: norm ( abs( Xc(j) - Xt(j) ) ) / norm (Xt(j)) .LE. ERRBND( *, cwise_i, bnd_i )
    !>          for all j .AND. ERRBND( *, cwise_i, bnd_i ) .LE. MAX(SQRT(N), 10) * EPS.
    !>          If these conditions are met, the test ratio is set to be
    !>          ERRBND( *, cwise_i, bnd_i ) / MAX(SQRT(N), 10).  Otherwise it is 1/EPS.
    !>       B: Same as normwise test ratio.
    !>
    !>       3. Backwards error.
    !>       A: The test ratio is set to BERR/EPS.
    !>       B: Same test ratio.
    !>
    !>       4. Reciprocal condition number.
    !>       A: A condition number is computed with Xt and compared with the one
    !>          returned from SGESVXX.  Let RCONDc be the RCOND returned by SGESVXX
    !>          and RCONDt be the RCOND from the truth value.  Test ratio is set to
    !>          MAX(RCONDc/RCONDt, RCONDt/RCONDc).
    !>       B: Test ratio is set to 1 / (EPS * RCONDc).
    !>
    !>       5. Reciprocal normwise condition number.
    !>       A: The test ratio is set to
    !>          MAX(ERRBND( *, nwise_i, cond_i ) / NCOND, NCOND / ERRBND( *, nwise_i, cond_i )).
    !>       B: Test ratio is set to 1 / (EPS * ERRBND( *, nwise_i, cond_i )).
    !>
    !>       7. Reciprocal componentwise condition number.
    !>       A: Test ratio is set to
    !>          MAX(ERRBND( *, cwise_i, cond_i ) / CCOND, CCOND / ERRBND( *, cwise_i, cond_i )).
    !>       B: Test ratio is set to 1 / (EPS * ERRBND( *, cwise_i, cond_i )).
    !>
    !>     .. Parameters ..
    !>     NMAX is determined by the largest number in the inverse of the Hilbert
    !>     matrix.  Precision is exhausted when the largest entry in it is greater
    !>     than 2 to the power of the number of bits in the fraction of the data
    !>     type used plus one, which is 24 for single precision.
    !>     NMAX should be 6 for single and 11 for double.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 95 of file sebchvxx.f.

Author

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