# debchvxx.f - Man Page

TESTING/LIN/debchvxx.f

## Synopsis

### Functions/Subroutines

subroutine debchvxx (thresh, path)
DEBCHVXX

## Function/Subroutine Documentation

### subroutine debchvxx (double precision thresh, character*3 path)

DEBCHVXX

Purpose:

```  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.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 95 of file debchvxx.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page debchvxx(3) is an alias of debchvxx.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK