def initialise_multivector(mv, M):
# initial multiindices
mis = [Multiindex(mis) for mis in MultiindexSet.createCompleteOrderSet(M, 1)]
# intialise fem vectors
N = 15
mesh = UnitSquareMesh(N, N)
V = FunctionSpace(mesh, 'CG', 1)
ex = Expression('sin(2*pi*A*x[0])', A=0)
for i, mi in enumerate(mis):
ex.A = i+1
f = interpolate(ex, V)
mv[mi] = FEniCSVector(f)
def teXXXst_fenics_vector():
# quad_degree = 13
# dolfin.parameters["form_compiler"]["quadrature_degree"] = quad_degree
pi = 3.14159265358979323
k1, k2 = 2, 3
EV = pi * pi * (k1 * k1 + k2 * k2)
N = 11
degree = 1
mesh = UnitSquare(N, N)
fs = FunctionSpace(mesh, "CG", degree)
ex = Expression("A*sin(k1*pi*x[0])*sin(k2*pi*x[1])", k1=k1, k2=k2, A=1.0)
x = FEniCSVector(interpolate(ex, fs))
# print "x.coeff", x.coeffs.array()
ex.A = EV
b_ex = assemble_rhs(ex, fs)
bexg = interpolate(ex, fs)
# print b_ex.array()
# print b_ex.array() / (2 * pi * pi * x.coeffs.array())
Afe = assemble_lhs(Expression('1'), fs)
# apply discrete operator on (interpolated) x
A = FEniCSOperator(Afe, x.basis)
b = A * x
# evaluate solution for eigenfunction rhs
if False:
b_num = Function(fs)
solve(A, b_num.vector(), b_ex)
bnv = A * b_num.vector()
b3 = Function(fs, bnv / EV)
np.set_printoptions(threshold='nan', suppress=True)
print b.coeffs.array()
print np.abs((b_ex.array() - b.coeffs.array()) / np.max(b_ex.array()))
print np.max(np.abs((b_ex.array() - b.coeffs.array()) / np.max(b_ex.array())))
#print b_ex.array() / (M * interpolate(ex1, fs).vector()).array()
# #assert_array_almost_equal(b.coeffs, b_ex.coeffs)
b2 = Function(fs, b_ex.copy())
bg = Function(fs, b_ex.copy())
b2g = Function(fs, b_ex.copy())
G = assemble_gramian(x.basis)
dolfin.solve(G, bg.vector(), b.coeffs)
dolfin.solve(G, b2g.vector(), b2.vector())
# # compute eigenpairs numerically
# eigensolver = evaluate_evp(FEniCSBasis(fs))
# # Extract largest (first) eigenpair
# r, c, rx, cx = eigensolver.get_eigenpair(0)
# print "Largest eigenvalue: ", r
# # Initialize function and assign eigenvector
# ef0 = Function(fs)
# ef0.vector()[:] = rx
if False:
# export
out_b = dolfin.File(__name__ + "_b.pvd", "compressed")
out_b << b._fefunc
out_b_ex = dolfin.File(__name__ + "_b_ex.pvd", "compressed")
out_b_ex << b2
out_b_num = dolfin.File(__name__ + "_b_num.pvd", "compressed")
out_b_num << b_num
#dolfin.plot(x._fefunc, title="interpolant x", rescale=False, axes=True, legend=True)
dolfin.plot(bg, title="b", rescale=False, axes=True, legend=True)
dolfin.plot(b2g, title="b_ex (ass/G)", rescale=False, axes=True, legend=True)
dolfin.plot(bexg, title="b_ex (dir)", rescale=False, axes=True, legend=True)
#dolfin.plot(b_num, title="b_num", rescale=False, axes=True, legend=True)
# dolfin.plot(b3, title="M*b_num", rescale=False, axes=True, legend=True)
#dolfin.plot(ef0, title="ef0", rescale=False, axes=True, legend=True)
print dolfin.errornorm(u=b._fefunc, uh=b2) #, norm_type, degree, mesh)
dolfin.interactive()
from spuq.fem.fenics.fenics_vector import FEniCSVector
from spuq.application.egsz.multi_vector import MultiVector, MultiVectorWithProjection
from spuq.math_utils.multiindex import Multiindex
from spuq.math_utils.multiindex_set import MultiindexSet
from dolfin import UnitSquare, FunctionSpace, Function, refine, Expression, plot, interactive
from math import pi
import pickle
mis = [Multiindex(mis) for mis in MultiindexSet.createCompleteOrderSet(3, 1)]
N = len(mis)
meshes = [UnitSquare(10 + 2 * i, 10 + 2 * i) for i in range(N)]
functions = [Function(FunctionSpace(m, "CG", d + 1)) for d, m in enumerate(meshes)]
ex = Expression('sin(A*x[0])*sin(A*x[1])', A=1)
for i, f in enumerate(functions):
ex.A = 2 * pi * (i + 1)
f.interpolate(ex)
# test FEniCSVector
# =================
vectors = [FEniCSVector(f) for f in functions]
with open('test-vector.pkl', 'wb') as f:
pickle.dump(vectors[1], f)
with open('test-vector.pkl', "rb") as f:
v1 = pickle.load(f)
# test MultiVector
# ================
#mv1 = MultiVector()
