def estimate(self, U, mu=None):
assert len(U) == 1, 'Can estimate only one solution vector'
if not self.rhs.parametric or self.rhs.operator_affine_part is not None:
CRA = np.ones(1)
else:
CRA = np.ones(0)
if self.rhs.parametric:
CRL = self.rhs.evaluate_coefficients(self.map_parameter(mu, 'rhs'))
else:
CRL = np.ones(0)
CR = np.hstack((CRA, CRL))
if not self.operator.parametric or self.operator.operator_affine_part is not None:
COA = np.ones(1)
else:
COA = np.ones(0)
if self.operator.parametric:
COL = self.operator.evaluate_coefficients(self.map_parameter(mu, 'operator'))
else:
COL = np.ones(0)
C = np.hstack((CR, np.dot(np.hstack((COA, COL))[..., np.newaxis], U.data).ravel()))
return induced_norm(self.estimator_matrix)(NumpyVectorArray(C))
def test_induced():
grid = TriaGrid(num_intervals=(10, 10))
boundary_info = AllDirichletBoundaryInfo(grid)
product = L2ProductP1(grid, boundary_info)
zero = la.NumpyVectorArray(np.zeros(grid.size(2)))
norm = la.induced_norm(product)
value = norm(zero)
np.testing.assert_almost_equal(value, 0.0)
def estimate(self, U, mu, discretization):
d = discretization
if len(U) > 1:
raise NotImplementedError
if not d.rhs.parametric:
CR = np.ones(1)
else:
CR = d.rhs.evaluate_coefficients(mu)
if not d.operator.parametric:
CO = np.ones(1)
else:
CO = d.operator.evaluate_coefficients(mu)
C = np.hstack((CR, np.dot(CO[..., np.newaxis], U.data).ravel()))
return induced_norm(self.estimator_matrix)(NumpyVectorArray(C))
def __init__(self, operators, functionals, vector_operators, products=None, estimator=None, visualizer=None,
cache_region='disk', name=None):
self.operators = FrozenDict(operators)
self.functionals = FrozenDict(functionals)
self.vector_operators = FrozenDict(vector_operators)
self.linear = all(op is None or op.linear for op in chain(operators.itervalues(), functionals.itervalues()))
self.products = products
self.estimator = estimator
self.visualizer = visualizer
self.cache_region = cache_region
self.name = name
if products:
for k, v in products.iteritems():
setattr(self, '{}_product'.format(k), v)
setattr(self, '{}_norm'.format(k), induced_norm(v))
if estimator is not None:
self.estimate = self.__estimate
if visualizer is not None:
self.visualize = self.__visualize
def __init__(self, parameter_range=(0.1, 1.), name=None):
super(DuneLinearEllipticCGDiscretization, self).__init__()
Cachable.__init__(self, config=NO_CACHE_CONFIG)
self.example = dune.LinearEllipticExampleCG()
ops = list(self.example.operators())
f = self.example.functional()
self.solution_dim = f.len()
ops = [DuneLinearOperator(op, dim=self.solution_dim) for op in ops]
operator = LinearAffinelyDecomposedOperator(ops[:-1], ops[-1], name='diffusion')
operator.rename_parameter({'.coefficients': 'diffusion'})
functional = DuneLinearFunctional(f)
self.operators = {'operator': operator, 'rhs': functional}
self.build_parameter_type(inherits={'operator': operator})
self.h1_product = operator.assemble(mu={'diffusion': np.ones(self.example.paramSize())})
self.h1_norm = induced_norm(self.h1_product)
self.parameter_space = CubicParameterSpace({'diffusion': self.example.paramSize()}, *parameter_range)
self.name = name
def discretize_elliptic_cg(analytical_problem, diameter=None, domain_discretizer=None,
grid=None, boundary_info=None):
'''Discretize an `EllipticProblem` using finite elements.
Since operators are not assembled during instatiation, calling this function is
cheap if the domain discretization proceeds quickly.
Parameters
----------
analytical_problem
The `EllipticProblem` to discretize.
diameter
If not None, is passed to the domain_discretizer.
domain_discretizer
Discretizer to be used for discretizing the analytical domain. This has
to be function `domain_discretizer(domain_description, diameter=...)`.
If further arguments should be passed to the discretizer, use
functools.partial. If None, `discretize_domain_default` is used.
grid
Instead of using a domain discretizer, the grid can be passed directly.
boundary_info
A `BoundaryInfo` specifying the boundary types of the grid boundary
entities. Must be provided is `grid` is provided.
Returns
-------
discretization
The discretization that has been generated.
data
Dict with the following entries:
grid
The generated grid.
boundary_info
The generated `BoundaryInfo`.
'''
assert isinstance(analytical_problem, EllipticProblem)
assert grid is None or boundary_info is not None
assert boundary_info is None or grid is not None
assert grid is None or domain_discretizer is None
if grid is None:
domain_discretizer = domain_discretizer or discretize_domain_default
if diameter is None:
grid, boundary_info = domain_discretizer(analytical_problem.domain)
else:
grid, boundary_info = domain_discretizer(analytical_problem.domain, diameter=diameter)
assert isinstance(grid, (OnedGrid, TriaGrid))
Operator = DiffusionOperatorP1
Functional = L2ProductFunctionalP1
p = analytical_problem
if p.diffusion_functionals is not None or len(p.diffusion_functions) > 1:
L0 = Operator(grid, boundary_info, diffusion_constant=0, name='diffusion_boundary_part')
Li = tuple(Operator(grid, boundary_info, diffusion_function=df, dirichlet_clear_diag=True,
name='diffusion_{}'.format(i))
for i, df in enumerate(p.diffusion_functions))
if p.diffusion_functionals is None:
L = LinearAffinelyDecomposedOperator(Li, L0, name='diffusion')
L.rename_parameter({'.coefficients': '.diffusion_coefficients'})
else:
L = LinearAffinelyDecomposedOperator(Li, L0, p.diffusion_functionals, name='diffusion')
else:
L = Operator(grid, boundary_info, diffusion_function=p.diffusion_functions[0],
name='diffusion')
F = Functional(grid, p.rhs, boundary_info, dirichlet_data=p.dirichlet_data)
import matplotlib.pyplot as pl
if isinstance(grid, TriaGrid):
def visualize(U):
assert len(U) == 1
pl.tripcolor(grid.centers(2)[:, 0], grid.centers(2)[:, 1], grid.subentities(0, 2), U.data.ravel())
pl.colorbar()
pl.show()
else:
def visualize(U):
assert len(U) == 1
pl.plot(grid.centers(1), U.data.ravel())
pl.show()
pass
discretization = StationaryLinearDiscretization(L, F, visualizer=visualize, name='{}_CG'.format(p.name))
discretization.h1_product = Operator(grid, boundary_info)
discretization.h1_norm = induced_norm(discretization.h1_product)
discretization.l2_product = L2ProductP1(grid, boundary_info)
if hasattr(p, 'parameter_space'):
discretization.parameter_space = p.parameter_space
return discretization, {'grid': grid, 'boundary_info': boundary_info}
def __init__(self, estimator_matrix, coercivity_estimator):
self.estimator_matrix = estimator_matrix
self.coercivity_estimator = coercivity_estimator
self.norm = induced_norm(estimator_matrix)
def __init__(self, product):
self.norm = induced_norm(product) if product else None