Add solvers submodule and clean up examples.

Solvers submodule includes a generic solver in case you already have a
sparse matrix solver, or in case you have no solver at all.

Example file now uses alternate solvers if available, and has a nicer
way of picking which solver gets used.

examples/test.py

@@ -1,18 +1,22 @@
+import importlib
 import numpy
+from numpy.linalg import norm
 
 from fdfd_tools import vec, unvec, waveguide_mode
-import fdfd_tools, fdfd_tools.functional, fdfd_tools.grid
+import fdfd_tools
+import fdfd_tools.functional
+import fdfd_tools.grid
+from fdfd_tools.solvers import generic as generic_solver
+
 import gridlock
 
 from matplotlib import pyplot
 
-#import magma_fdfd
-from opencl_fdfd import cg_solver, csr
 
 __author__ = 'Jan Petykiewicz'
 
 
-def test0():
+def test0(solver=generic_solver):
     dx = 50                # discretization (nm/cell)
     pml_thickness = 10     # (number of cells)
 
@@ -59,21 +63,27 @@ def test0():
     J = [numpy.zeros_like(grid.grids[0], dtype=complex) for _ in range(3)]
     J[1][15, grid.shape[1]//2, grid.shape[2]//2] = 1e5
 
+    '''
+    Solve!
+    '''
+    x = solver(J=vec(J), **sim_args)
+
     A = fdfd_tools.functional.e_full(omega, dxes, vec(grid.grids)).tocsr()
     b = -1j * omega * vec(J)
+    print('Norm of the residual is ', norm(A @ x - b))
 
-    x = solve_A(A, b)
     E = unvec(x, grid.shape)
 
-    print('Norm of the residual is {}'.format(numpy.linalg.norm(A.dot(x) - b)/numpy.linalg.norm(b)))
-
+    '''
+    Plot results
+    '''
     pyplot.figure()
     pyplot.pcolor(numpy.real(E[1][:, :, grid.shape[2]//2]), cmap='seismic')
     pyplot.axis('equal')
     pyplot.show()
 
 
-def test1():
+def test1(solver=generic_solver):
     dx = 40                 # discretization (nm/cell)
     pml_thickness = 10      # (number of cells)
 
@@ -142,17 +152,14 @@ def test1():
         'pmc': vec(pmcg.grids),
     }
 
+    x = solver(J=vec(J), **sim_args)
+
     b = -1j * omega * vec(J)
     A = fdfd_tools.operators.e_full(**sim_args).tocsr()
-#    x = magma_fdfd.solve_A(A, b)
-
-#    x = csr.cg_solver(J=vec(J), **sim_args)
-    x = cg_solver(J=vec(J), **sim_args)
+    print('Norm of the residual is ', norm(A @ x - b))
 
     E = unvec(x, grid.shape)
 
-    print('Norm of the residual is ', numpy.linalg.norm(A @ x - b))
-
     '''
     Plot results
     '''
@@ -197,6 +204,22 @@ def test1():
     pyplot.show()
     print('Average overlap with mode:', sum(q)/len(q))
 
+
+def module_available(name):
+    return importlib.util.find_spec(name) is not None
+
+
 if __name__ == '__main__':
     # test0()
-    test1()
+
+    if module_available('opencl_fdfd'):
+        from opencl_fdfd import cg_solver as opencl_solver
+        test1(opencl_solver)
+        # from opencl_fdfd.csr import fdfd_cg_solver as opencl_csr_solver
+        # test1(opencl_csr_solver)
+    # elif module_available('magma_fdfd'):
+    #     from magma_fdfd import solver as magma_solver
+    #     test1(magma_solver)
+    else:
+        test1()
+