from dolfin import *

from scipy.sparse import csr_matrix

from scipy.sparse.linalg import inv

import matplotlib.pyplot as plt

# Choose backend that allows .data()

parameters.linear_algebra_backend = 'uBLAS'

mesh = UnitSquareMesh(30, 30)

V = FunctionSpace(mesh, 'CG', 1)

u = TrialFunction(V)

v = TestFunction(V)

a = inner(grad(u), grad(v))*dx

m = inner(u, v)*dx

L = Constant(0.)*v*dx

bc = DirichletBC(V, Constant(0), DomainBoundary())

A, _ = assemble_system(a, L, bc)

M, _ = assemble_system(m, L, bc)

# Prepare A and M for scipy

rows, cols, values = A.data()

A = csr_matrix((values, cols, rows))

rows, cols, values = M.data()

M = csr_matrix((values, cols, rows))

print 'Inverting %d by %d matrix' % (V.dim(), V.dim())

timer = Timer('inverse')

timer.start()

T = inv(M).dot(A)

timer.stop()

print '\t\t done in %g' % timing('inverse')

# Plot

plt.figure()

plt.subplot(131)

plt.spy(A)

plt.subplot(132)

plt.spy(M)

plt.subplot(133)

plt.spy(T)

plt.show()