ENH, TST: Misc changes to ODE and matrix solvers

[nawtrey]

Description

• Changes ode.ode_solver() to use "LSODA" integration method for automatic stiffness detection, faster calculation, and better accuracy

• Adds new matrix solver to svd.py module which uses the standard np.linalg.solve() and produces more accurate results for some problem cases

• Adds a test for a known problem case that illustrates the accuracy of SVD vs. ODE vs. a standard matrix solver

Status

• [x] Ready to go

[codecov[bot]]

Codecov Report

Merging #29 (71c958e) into master (9450edf) will increase coverage by 0.10%. The diff coverage is 100.00%.

[nawtrey]

Another messy PR with misc changes.. Luckily the vast majority of the changes here have no affect on the functionality of the main code. The new matrix function is a copy/paste of the SVD solver with some minor changes to allow for the use of np.linalg.solve(), which is then used in verification.py. The new test is a copy/paste of the test above it, but instead of leveraging hypothesis it only runs a specific "bad apple" case that causes issues for SVD and ODE (if ran without LSODA, or another stiff solver). I was going to add it as a hypothesis @example but I would have had to do adjust the tolerances based on whether or not it was using the example or the hypothesis-generated datasets, and that just didn't seem worth it.

[nawtrey]

All tests/checks are passing. Merging.