def get_projection_error_function(self, mu_src, mu_dest, reference_degree, refine_mesh=0):
"""Construct projection error function by projecting mu_src vector to mu_dest space of dest_degree.
From this, the projection of mu_src onto the mu_dest space, then to the mu_dest space of dest_degree is subtracted.
If refine_mesh > 0, the destination mesh is refined uniformly n times."""
from spuq.fem.fenics.fenics_utils import create_joint_mesh
from dolfin import FunctionSpace, VectorFunctionSpace
from spuq.fem.fenics.fenics_basis import FEniCSBasis
# get joint mesh based on destination space
basis_src = self[mu_src].basis
basis_dest = self[mu_dest].basis
mesh_reference, parents = create_joint_mesh([basis_src.mesh], basis_dest.mesh)
# create function space on destination mesh
if basis_dest._fefs.num_sub_spaces() > 0:
fs_reference = VectorFunctionSpace(mesh_reference, basis_dest._fefs.ufl_element().family(), reference_degree)
else:
fs_reference = FunctionSpace(mesh_reference, basis_dest._fefs.ufl_element().family(), reference_degree)
basis_reference = FEniCSBasis(fs_reference, basis_dest._ptype)
# project both vectors to reference space
w_reference = basis_reference.project_onto(self[mu_src])
w_dest = self.get_projection(mu_src, mu_dest)
w_dest = basis_reference.project_onto(w_dest)
# define summation function to get values on original destination mesh from function space on joint mesh
def sum_up(vals):
sum_vals = [sum(vals[v]) for _, v in parents.iteritems()]
return np.array(sum_vals)
return w_dest - w_reference, sum_up
def get_projection_basis(mesh0, mesh_refinements=None, maxh=None, degree=1, sub_spaces=None, family='CG'):
if mesh_refinements is not None:
mesh = mesh0
for _ in range(mesh_refinements):
mesh = refine(mesh)
if sub_spaces is None or sub_spaces == 0:
V = FunctionSpace(mesh, family, degree)
else:
V = VectorFunctionSpace(mesh, family, degree)
assert V.num_sub_spaces() == sub_spaces
return FEniCSBasis(V)
else:
assert maxh is not None
if sub_spaces is None or sub_spaces == 0:
V = FunctionSpace(mesh0, family, degree)
else:
V = VectorFunctionSpace(mesh0, family, degree)
assert V.num_sub_spaces() == sub_spaces
B = FEniCSBasis(V)
return B.refine_maxh(maxh, True)[0]
def test4():
print "TEST 4"
mis = (Multiindex(), Multiindex([1]), Multiindex([0, 1]), Multiindex([1, 1]))
mv = MultiVectorWithProjection()
V1 = FEniCSBasis(FunctionSpace(UnitSquare(5, 5), 'CG', 1))
V2, _, _ = V1.refine()
V3, _, _ = V2.refine()
V4 = V1.refine_maxh(1 / 30, uniform=True)
print "mesh1", V1.mesh, "maxh,minh=", V1.maxh, V1.minh
print "mesh2", V2.mesh, "maxh,minh=", V2.maxh, V2.minh
print "mesh3", V3.mesh, "maxh,minh=", V3.maxh, V3.minh
print "mesh4", V4.mesh, "maxh,minh=", V4.maxh, V4.minh
F2 = FEniCSVector.from_basis(V2)
F3 = FEniCSVector.from_basis(V3)
F4 = FEniCSVector.from_basis(V4)
mv[mis[0]] = FEniCSVector.from_basis(V1)
mv[mis[1]] = F2
mv[mis[2]] = F3
mv[mis[3]] = F4
for j, ex in enumerate(EX):
print "ex[", j, "] =================="
for degree in range(1, 4):
print "\t=== degree ", degree, "==="
F2.interpolate(ex)
F3.interpolate(ex)
F4.interpolate(ex)
err1 = mv.get_projection_error_function(mis[1], mis[0], degree, refine_mesh=False)
err2 = mv.get_projection_error_function(mis[2], mis[0], degree, refine_mesh=False)
err3 = mv.get_projection_error_function(mis[3], mis[0], degree, refine_mesh=False)
print "\t[NO DESTINATION MESH REFINEMENT]"
print "\t\tV2 L2", norm(err1._fefunc, 'L2'), "H1", norm(err1._fefunc, 'H1')
print "\t\tV3 L2", norm(err2._fefunc, 'L2'), "H1", norm(err2._fefunc, 'H1')
print "\t\tV4 L2", norm(err3._fefunc, 'L2'), "H1", norm(err3._fefunc, 'H1')
err1 = mv.get_projection_error_function(mis[1], mis[0], degree, refine_mesh=True)
err2 = mv.get_projection_error_function(mis[2], mis[0], degree, refine_mesh=True)
err3 = mv.get_projection_error_function(mis[3], mis[0], degree, refine_mesh=True)
print "\t[WITH DESTINATION MESH REFINEMENT]"
print "\t\tV2 L2", norm(err1._fefunc, 'L2'), "H1", norm(err1._fefunc, 'H1')
print "\t\tV3 L2", norm(err2._fefunc, 'L2'), "H1", norm(err2._fefunc, 'H1')
print "\t\tV4 L2", norm(err3._fefunc, 'L2'), "H1", norm(err3._fefunc, 'H1')
def get_projection_error_function_old(self, mu_src, mu_dest, reference_degree, refine_mesh=0):
"""Construct projection error function by projecting mu_src vector to mu_dest space of dest_degree.
From this, the projection of mu_src onto the mu_dest space, then to the mu_dest space of dest_degree is subtracted.
If refine_mesh > 0, the destination mesh is refined uniformly n times."""
# TODO: If refine_mesh is True, the destination space of mu_dest is ensured to include the space of mu_src by mesh refinement
# TODO: proper description
# TODO: separation of fenics specific code
from dolfin import refine, FunctionSpace, VectorFunctionSpace
from spuq.fem.fenics.fenics_basis import FEniCSBasis
if not refine_mesh:
w_reference = self.get_projection(mu_src, mu_dest, reference_degree)
w_dest = self.get_projection(mu_src, mu_dest)
w_dest = w_reference.basis.project_onto(w_dest)
sum_up = lambda vals: vals
else:
# uniformly refine destination mesh
# NOTE: the cell_marker based refinement used in FEniCSBasis is a bisection of elements
# while refine(mesh) carries out a red-refinement of all cells (split into 4)
# basis_src = self[mu_src].basis
basis_dest = self[mu_dest].basis
mesh_reference = basis_dest.mesh
for _ in range(refine_mesh):
mesh_reference = refine(mesh_reference)
# print "multi_vector::get_projection_error_function"
# print type(basis_src._fefs), type(basis_dest._fefs)
# print basis_src._fefs.num_sub_spaces(), basis_dest._fefs.num_sub_spaces()
# if isinstance(basis_dest, VectorFunctionSpace):
if basis_dest._fefs.num_sub_spaces() > 0:
fs_reference = VectorFunctionSpace(mesh_reference, basis_dest._fefs.ufl_element().family(), reference_degree)
else:
fs_reference = FunctionSpace(mesh_reference, basis_dest._fefs.ufl_element().family(), reference_degree)
basis_reference = FEniCSBasis(fs_reference, basis_dest._ptype)
# project both vectors to reference space
w_reference = basis_reference.project_onto(self[mu_src])
w_dest = self.get_projection(mu_src, mu_dest)
w_dest = basis_reference.project_onto(w_dest)
sum_up = lambda vals: np.array([sum(vals[i * 4:(i + 1) * 4]) for i in range(len(vals) / 4 ** refine_mesh)])
return w_dest - w_reference, sum_up