Sparse Jacobians for DVGeometryMulti

[sseraj]

Purpose

I changed the total Jacobian computation in DVGeometryMulti to use sparse matrices instead of dense matrices. I followed one of SciPy's recommended approaches by using lil_matrix for construction and then converting to csr_matrix for faster arithmetic. This approach required minimal changes to the code.

The memory usage was not dramatically different for the cases I tested because the Jacobian is usually not very sparse. Still, the memory used by the sparse Jacobian was about 60% of the memory used by the dense Jacobian for the largest case I tested (around 140k surface points and 270 geometric DVs).

Expected time until merged

1 week

Type of change

• [ ] Bugfix (non-breaking change which fixes an issue)
• [ ] New feature (non-breaking change which adds functionality)
• [ ] Breaking change (non-backwards-compatible fix or feature)
• [ ] Code style update (formatting, renaming)
• [x] Refactoring (no functional changes, no API changes)
• [ ] Documentation update
• [ ] Maintenance update
• [ ] Other (please describe)

Testing

The current DVGeometryMulti test passes, which shows that the derivatives are still correct.

Checklist

• [x] I have run flake8 and black to make sure the Python code adheres to PEP-8 and is consistently formatted
• [ ] I have formatted the Fortran code with fprettify or C/C++ code with clang-format as applicable
• [x] I have run unit and regression tests which pass locally with my changes
• [ ] I have added new tests that prove my fix is effective or that my feature works
• [ ] I have added necessary documentation

[codecov[bot]]

Codecov Report

Merging #187 (49d6108) into main (b7f1bfb) will increase coverage by 0.00%. The diff coverage is 100.00%.

@@           Coverage Diff           @@
##             main     #187   +/-   ##
=======================================
  Coverage   64.76%   64.77%           
=======================================
  Files          47       47           
  Lines       11949    11951    +2     
=======================================
+ Hits         7739     7741    +2     
  Misses       4210     4210           

Impacted Files	Coverage Δ
pygeo/parameterization/DVGeoMulti.py	91.05% <100.00%> (+0.01%)	:arrow_up:

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