debchvxx.f3

!>
!>  DEBCHVXX will run D**SVXX on a series of Hilbert matrices and then
!>  compare the error bounds returned by D**SVXX 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, CGESVXX 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 CGESVXX.  Let RCONDc be the RCOND returned by D**SVXX
!>          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 )).
!>
!>       6. 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.
!> 

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