TESTING/LIN/cebchvxx.f(3)  Library Functions Manual  TESTING/LIN/cebchvxx.f(3)

NAME
       TESTING/LIN/cebchvxx.f

SYNOPSIS
   Functions/Subroutines
       subroutine cebchvxx (thresh, path)
           CEBCHVXX

Function/Subroutine Documentation
   subroutine cebchvxx (real thresh, character*3 path)
       CEBCHVXX Purpose:

         CEBCHVXX will run CGESVXX on a series of Hilbert matrices and then
         compare the error bounds returned by CGESVXX 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 CGESVXX
                 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

           Univ. of Colorado Denver

           NAG Ltd.

       Definition at line 95 of file cebchvxx.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0       TESTING/LIN/cebchvxx.f(3)