# setup tensor vector u = prepare_vectors(J, FS) u = FullTensor.from_list(u) print "FullTensor u", u.dim() print "u as matrix shape", u.as_matrix().shape, u.flatten().as_array().shape # test tensor operator # ==================== # test application of operator w = A * u # print matricisation of tensor operator M = A.as_matrix() print M.shape, norm(M) # plot mesh #import dolfin #dolfin.plot(mesh, interactive=True) # plot sparsity pattern #fig = figure() ##spy(M) #spy(K[0].as_matrix()) #show() from spuq.application.egsz.pcg import pcg P = TensorOperator([K0inv], [D[0]]) print 0*w
# prepare "stochastic" matrices
D = [sps.csr_matrix(np.random.rand(d,d)) for _ in range(m)]
# convert to efficient sparse format
D = [ScipyOperator(D_.asformat('csr'), domain=CanonicalBasis(D_.shape[0]), codomain=CanonicalBasis(D_.shape[1])) for D_ in D]
# prepare vector
u = [np.random.rand(k) for _ in range(d)]
return K, D, u
# test tensor operator application
# ================================
I, J = 100, 15
for M in [1,2,5]:
# prepare data
K, D, u = construct_data(I, J, M)
A = TensorOperator(K, D)
u = FullTensor.from_list(u)
# print matricisation of tensor operator
Amat = A.as_matrix()
print Amat.shape
# compare with numpy kronecker product
M2 = [sps.kron(K_.matrix, D_.matrix) for K_, D_ in zip(K, D)]
M2 = np.sum(M2)
print "error norm: ", norm(Amat-M2.todense()), " == ", norm(Amat-M2)
# test application of operator
w = A * u
