Abstract MGM port: solve function

[seanbsu]

References #49

• [x] port over the solve function file
• [x] test should test the 'none' acceleration method other accelerations methods to be implemented/tests in later task
• [x] all sovle function tests with no acceleration pass

[seanbsu]

• began getting and parsing data from matlab inot mat files and parsing into python structs
• created a new fixture for the levels data so the multilevel tests and the solve tests have seperate and independent strucutres that are loaded from different files
• rewrote the first solve test to load the input data and compare the expected values to the returned ones [t:60]

[seanbsu]

• started implementation for the solve method
• after getting the no acceleration method passing started to work on the bigcstab acceleration
• the way that matlab does bigcstab is different than how scipy's sparse module does it. so the calls aren't a 1:1 call and the returned results are not the same amount of variables returned. like python will give the resulting uh and the convergence flag but nothing else. I had to start looking into how matlab gets the iters, relres, and resvec and am currently trying to implement that to get those but my answers dont match the matlab so I wonder if those are changed inside matlab's bigcstab which will make it a lot harder to implement. the uh result is the same and the convergence flag is the same I just don't know how important those are and if they are crucial to return.
• I had to refactor my tests for the afun because to use bigcstab in python I had to make the matvecOp a LinearOperator and I need to have the afun tests use the mgm objects that are used in the other functions (a list of dictionaries) so i had to refactor those tests to use that structure. This means that the mgm classes need to store this information in the same way and pass that structure to the functions

[t:240]

[seanbsu]

• rewrote last solve test to have it test the gmres acceleration method. For now this just raises and not implemented error since it will rely on the gmres_r function that will be implemented in a later task
• changed the return values for bigcstab for relres,resvec and iters to None. pythons Bigcstab doesnt return these like matlab. future development will look into getting these but Dr Wright says that for now the uh and flag are ok

[t:45]