Build the Polynomial Interpolator in Python

[paulvxx]

Relates to #16.

[ ] - The interpolator should take in the parameters row, col, interp_weights, Nf Nc as input [ ] - The interpolator should find a good polynomial basis to up sample the points on the 2d grid (undoing the coarsening)

[paulvxx]

• Performed a full analyzation of the buildInterpOp.m code, which required also looking at a different matlab file to understand it better
• Started working on the python implementation of buildInterpOp.

[t:110]

[paulvxx]

• Worked on more of the interpolator implementation
• Had to manually experiment and incrementally check a few lines of code were working (due to differences in MATLAB v.s. Python library calls)

[t:70]

[paulvxx]

• Worked on more of the interpolator implementation
• Stepped through the code in MATLAB line by line to figure out what it does (manually)

Note: It takes a lot of time to replicated code because you need to understand and compare lines of code (not just building the whole thing and testing, it should be done manually and incrementally)

[t:90]

[paulvxx]

• Tried to make sense of some more complex functions in the interpolator.m MATLAB code
• Encountered some problems with the MATLAB code I wasn't sure how to fix (or at least without having to modify it significantly
• Planning to likely address these issues with my sponsor (end result/conclusion for time spent)

[t:60]

[paulvxx]

• Did some more work on the Python code (brought it up to speed as far as I can with my comparative understanding of the MATLAB code; that is, I coded as much as I was able to directly understand and translate from MATLAB)

[t:60]

[paulvxx]

• Stepped through MATLAB code for the interpolator, specifically with the data Dr. Wright provided [helpful for a side-by-side comparison of Python implementation]
• Also had to (start to) implement a separate function in Python needed for part of the interpolator (for Dr. W's specific test case)

[t:90]

[paulvxx]

• Implemented more of the interpolator function (one of the two interpolation methods)

[t:25]

[paulvxx]

• Implemented the second interpolator method
• Modified MATLAB code to easily test the expected outcome of the second interpolator method
• Almost finished the rest of the interpolator python implementation (just need to create a final sparse matrix)

[t:70]

[paulvxx]

• Implemented the sparse matrix part of the Interpolator
• I ran into a rounding error problem that probably arose from some discrepancies in MATLAB and python data ("MOST" data is accurate enough, but a small percentage --- less than 0.01% or so, has zero entries in Python construction of the matrix, while MATLAB has non-zero entries.). It is hard (and haven't been able to) detect why they are occurring. This makes it difficult to test the interpolator code.
• Wasn't able to fix the technical issue

[t:120]

[paulvxx]

• Tested an alternative solution to the technical issue I described earlier

[t:15]

[paulvxx]

• Investigated more deeply the technical issue I was facing
• Realized it was more complex than I thought
• Part of the issues were due to using built in python functions (e.g. the KNN node search in Python and MATLAB differ)

[t:100]

[paulvxx]

• Finished writing tests for the interpolator
• Cleaned up code for the interpolator (debug statements, other debugging lines, etc.)

[t:65]