PYMPS: Method of Particular Solutions, in Python, for Eigenvalue Problems

Adapted from Betcke-Trevethen, 2003, Reviving the Method of Particular Solutions.

Implementation of code from Betcke-Trevethen 2003 is 95% complete. Still an issue with the magnitude of the eigenvalues --- suspect problem is in the scaling of the domain. To plot the points in the domain, pipe the output of Ldrum.py to a file and then plot with gnuplot. To plot the lowest singular value, comment the printing of r and t, uncomment the printing of lamvec and S, pipe to a file, and plot with gnuplot.

Current status: Have implemented a Polygon class.

To-do:

-[x] Implement Polygon class -[ ] Implement cosine/sine MPS matrix and test it -[ ] Implement Neumann boundary conditions (matrix of normal derivatives to boundary) -[ ] Automate the generation of the dense matrix $A(\lambda)$ -[ ] Implement bracketing solver to pinpoint local minima of sing value function -[ ] Write code that reads JSON inputs to Polygons -[ ] Survey rectangles and triangles for subspectrality -[ ] Code specifying the subspectral cone of a fixed rectangle or triangle -[ ] Code guaranteeing eigenvalues fall within \eps of output -[ ] Hyperbolic and spherical domains