Output Files

Once the interpolation is done, TestInterp prints various error norms to standard output, and can optionally produce 3 main types of output file:

• We can print any single interpolation result in detail, in a generic ASCII format which can be inspected by hand or ploted with gnuplot or other graphics programs. This is controlled by the plot_output_type and plot_file_name parameters.
• We can print the Jacobian of the interpolation (as obtained by querying the interpolator, as estimated by numerical perturbations, or both) to a data file, again in a generic ASCII format which is convenient for gnuplot. This is controlled by the print_Jacobian_file and Jacobian_file_name parameters.
• For a Cactus test suite, both of the previous options are a bit inconvenient because they produce fairly large output files for 3-D interpolation, and because they attempt to write the same output files on each processor of a multiprocessor run. (This latter point is really a bug.) Instead, for test-suite purposes, we can also ``hash'' all the interpolation results of a given Cactus data type down into a single number (this makes the test-suite data files nice and small!), check that this is identical on each processor of a multiprocessor run, and (only on processor #0) write this to a data file. This is controlled by the print_hash_files, hash_difference_file_name, hash_data_file_name_real, hash_data_file_name_real4, and hash_data_file_name_real8 parameters.

  The ``hashing'' here is really just a linear combination
  

  $$\text{hash} = \frac{1}{N} \sum_{k=1}^N w_k \times \text{result}_k$$ (part954)

  
  
  where the weights $w_k$ are chosen to be pseudorandom numbers fairly close to unity, typically in the range $[0.5,1.5)$. This definition has the properties that
  • the hash is a continuous (in fact linear) function of the interpolation results
  • the Jacobian of the hash with respect to any given result is reasonably close to unity
  • if the hash matches the archived value for a test suite, then it's highly likely that all the individual interpolation results also matched their archived values (i.e. it's highly unlikely that the errors in the different interpolation results just happened to cancel out in the linear combination  $(\ref{CactusTest/TestInterp/eqn-hash})$).