import meshes as msh
import FEM
h0 = 0.1
qo = 3
r = lambda x, y: sqrt(x * x + y * y)
u = lambda x, y: x * sin(pi * r(x, y))
f = lambda x, y: pi * pi * u(x, y) - 3.0 * pi * (x / r(x, y)) * cos(pi * r(x, y))
g = lambda x, y: -pi * x
m = lambda x, y: 1.0
[p, t] = msh.circle(1, h0, 1)
be = FEM.boundaryEdges(p, t)
A = FEM.stiffness(p, t).tocsr()
F = FEM.load(p, t, qo, f)
G = FEM.loadNeumann(p, be, qo, g)
M = sparse.lil_matrix(FEM.load(p, t, 1, m))
S = sparse.bmat([[A, M.transpose()], [M, None]]).tocsr()
F = np.hstack([F + G, 0.0])
U_n = spsolve(S, F)
lambda_n = U_n[-1]
print "lambda", lambda_n
FEM.plot(p, t, U_n[0:-1])
U = np.zeros((p.shape[0]))
for i in range(0, p.shape[0]):
U[i] = u(p[i, 0], p[i, 1])
FEM.plot(p, t, U - U_n[0:-1])
