E- and H-field interpolation tests, frequency domain interpolation

[willGraham01]

Interpolation Tests for the $E$- and $H$-fields.

Dependent on #74 | Dependent on #108 (namespacing issues)

Completes the following tasks in #44:

• Closes Unit tests for BLi interpolation methods. #111
• Closes Unit tests for interpolate{TimeDomain,FrequencyDomain}{E,H}{x,y,z} functions. #110

Tests the performance of the BLi interpolation methods against the MATLAB function the scheme is based off. MATLAB scripts which output the error for particular field choices are included in the tests/unit/matlab_benchmark_scripts directory. The output error values are currently hard-coded into the respective tests; this is not an ideal solution, however in light of #70 is an adequate testing method until the MATLAB dependency question is answered.

The tests themselves are against MATLAB's interp function. Using predefined functional forms for the components of the two fields; and a particular grid setup to mimic the Yee cells and stored field components, the maximum pointwise-error of the interpolation to the Yee cell centres is computed, and compared to that from MATLAB.

Tests of the BLi method for complex data has been added to test_interpolation_functions.
A field-wide time-domain interpolation test has been added to test_field_interpolation.cpp.

Completes the following task in #44:

• Closes Write interpolation methods for the E- and H- fields in the frequency domain. Compared to the time-domain, this scheme must be able to handle complex data. #112

The codebase currently uses mxArrays to encode complex fields, and the functions mxInterpolateFieldCentral{E,H} to handle the interpolation. The new functions use complex as the datatype for the inputs. This is to be consistent with test_numerical_derivative and field.h, and to use a complex datatype we are importing already (and which won't be removed by #70). However, these functions will be are unused by the code, as the mxInterpolate functions are still used until iterator's refactor is complete.

It is also worth noting that interpolation in the frequency domain does not appear to use split-field components, unlike that in the time domain. As such, the functionality of the time domain and frequency domain functions are slightly different (which doesn't permit templating).

A test on the frequency-domain interpolation has been added to test_field_interpolation.cpp.

Key Files to Check:

• test_field_interpolation.cpp
• test_BLi_vs_cubic_interpolation.cpp
• interpolate_{E,H}.h (although these changes just turn the field-interpolation functions into template functions, so we can use double (time domain) or std::complex<double> (freq domain) data in each.

[prmunro]

This broadly looks great. I have made some comments which I think need some attention. Apologies if I have misunderstood something!

[samcunliffe]

Approving, for my part.
Obv. subject to Peter's change requests as above.