Fourier expansion

[tjlaboss]

Description

Addresses Part 1 of #3815 . Implements a new functional expansion tally basis in space: spatial Fourier. This borrows heavily from the implementation of spatial Legendre.

• Adds new class SpatialFourierFilter.
• Created a new base class SpatialExpansionFilter as a parent of SpatialFourierFilter and SpatialLegendreFilter on the Python side. Moved most of SpatialLegendreFilter to its parent.
• Added unit and regression tests.

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Checklist

• I have performed a self-review of my own code
• I have run clang-format (version 18) on any C++ source files (if applicable)
• I have followed the style guidelines for Python source files (if applicable)
• I have made corresponding changes to the documentation (if applicable)
• I have added tests that prove my fix is effective or that my feature works (if applicable)

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Discussion

• Should this filter have a flag for only odd (sin) or even (cos) modes?
• Is there a better convention for the bin labels?
• Should the SpatialExpansionFilter base class be implemented on the C++ side as well?
• This does filter does not normalize by the factor of sqrt(2). I believe that the convention for FETs in OpenMC is to normalize in postprocessing (though I'm not sure if this is explicitly established: see Return actual functional representation of funcational expansion tallies in Python API #3419).

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Details

Running on the example problem from example-filters.ipynb:

spatiallegendre	nuclide	score	mean	std. dev.
P0	total	flux	3.63e+01	8.06e-02
P1	total	flux	-2.60e-02	4.23e-02
P2	total	flux	-4.35e+00	2.69e-02
P3	total	flux	-1.36e-02	2.02e-02
P4	total	flux	-2.81e-01	1.40e-02
P5	total	flux	4.92e-03	1.15e-02
P6	total	flux	1.13e-01	9.69e-03
P7	total	flux	5.20e-03	8.94e-03
P8	total	flux	-7.84e-02	7.61e-03

spatialfourier	nuclide	score	mean	std. dev.
a0 (constant)	total	flux	3.63e+01	8.06e-02
a1 (cos)	total	flux	-6.45e+00	4.60e-02
b1 (sin)	total	flux	8.13e-03	6.10e-02
a2 (cos)	total	flux	-2.32e+00	2.96e-02
b2 (sin)	total	flux	2.65e-02	3.14e-02
a3 (cos)	total	flux	-6.38e-01	2.47e-02
b3 (sin)	total	flux	2.61e-02	2.51e-02
a4 (cos)	total	flux	-6.40e-01	2.42e-02
b4 (sin)	total	flux	2.72e-02	2.35e-02