sebchvxx.f - Man Page

subroutine sebchvxx (thresh, path)
SEBCHVXX

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.