def cg2_demo(nrhs, n, plot):
rhs0 = GenericFunction(lambda X: np.ones(X.shape[:-1]) * 10, dim_domain=2) # NOQA
rhs1 = GenericFunction(lambda X: (X[..., 0] - 0.5) ** 2 * 1000, dim_domain=2) # NOQA
assert 0 <= nrhs <= 1, ValueError('Invalid rhs number.')
rhs = eval('rhs{}'.format(nrhs))
d0 = GenericFunction(lambda X: 1 - X[..., 0], dim_domain=2)
d1 = GenericFunction(lambda X: X[..., 0], dim_domain=2)
parameter_space = CubicParameterSpace({'diffusionl': 0}, 0.1, 1)
f0 = ProjectionParameterFunctional('diffusionl', 0)
f1 = GenericParameterFunctional(lambda mu: 1, {})
print('Solving on TriaGrid(({0},{0}))'.format(n))
print('Setup Problem ...')
problem = EllipticProblem(domain=RectDomain(), rhs=rhs, diffusion_functions=(d0, d1),
diffusion_functionals=(f0, f1), name='2DProblem')
print('Discretize ...')
discretization, _ = discretize_elliptic_cg(problem, diameter=m.sqrt(2) / n)
print('The parameter type is {}'.format(discretization.parameter_type))
U = discretization.type_solution.empty(discretization.dim_solution)
for mu in parameter_space.sample_uniformly(10):
U.append(discretization.solve(mu))
if plot:
print('Plot ...')
discretization.visualize(U, title='Solution for diffusionl in [0.1, 1]')
def cg_oned_demo(nrhs, n, plot):
rhs0 = GenericFunction(lambda X: np.ones(X.shape) * 10, dim_domain=1)
rhs1 = GenericFunction(lambda X: (X[..., 0] - 0.5) ** 2 * 1000, dim_domain=1)
assert 0 <= nrhs <= 1, ValueError('Invalid rhs number.')
rhs = eval('rhs{}'.format(nrhs))
d0 = GenericFunction(lambda X: 1 - X[..., 0], dim_domain=1)
d1 = GenericFunction(lambda X: X[..., 0], dim_domain=1)
parameter_space = CubicParameterSpace({'diffusionl': 1}, 0.1, 1)
f0 = ProjectionParameterFunctional(parameter_space, 'diffusionl')
f1 = GenericParameterFunctional(parameter_space, lambda mu: 1)
print('Solving on OnedGrid(({0},{0}))'.format(n))
print('Setup Problem ...')
problem = EllipticProblem(domain=LineDomain(), rhs=rhs, diffusion_functions=(d0, d1), diffusion_functionals=(f0, f1),
dirichlet_data=ConstantFunction(value=0, dim_domain=1))
print('Discretize ...')
discretization, _ = discretize_elliptic_cg(problem, diameter=1 / n)
print(discretization.parameter_info())
for mu in parameter_space.sample_uniformly(4):
print('Solving for mu = {} ...'.format(mu))
U = discretization.solve(mu)
if plot:
print('Plot ...')
discretization.visualize(U)
print('')