def test_n_samples(self):
#
# Sampled Case
#
meshes = {1: Mesh1D(), 2: QuadMesh()}
elements = {1: QuadFE(1, 'Q2'), 2: QuadFE(2, 'Q2')}
# Use function to set data
fns = {
1: {
1: lambda x: 2 * x[:, 0]**2,
2: lambda x, y: 2 * x[:, 0] + 2 * y[:, 0]
},
2: {
1: lambda x: x[:, 0]**2 + x[:, 1],
2: lambda x, y: x[:, 0] * y[:, 0] + x[:, 1] * y[:, 1]
}
}
# n_samples = 2
parms = {1: {1: [{}, {}], 2: [{}, {}]}, 2: {1: [{}, {}], 2: [{}, {}]}}
for dim in [1, 2]:
mesh = meshes[dim]
element = elements[dim]
dofhandler = DofHandler(mesh, element)
dofhandler.distribute_dofs()
basis = Basis(dofhandler)
for n_variables in [1, 2]:
fn = fns[dim][n_variables]
parm = parms[dim][n_variables]
#
# Deterministic
#
f = Nodal(f=fn,
mesh=mesh,
basis=basis,
element=element,
dim=dim,
n_variables=n_variables)
self.assertEqual(f.n_samples(), 1)
#
# Sampled
#
f = Nodal(f=fn,
parameters=parm,
basis=basis,
mesh=mesh,
element=element,
dim=dim,
n_variables=n_variables)
self.assertEqual(f.n_samples(), 2)
def test_eval_x(self):
#
# Evaluate Nodal function at a given set of x-values
#
# Meshes and elements
meshes = {1: Mesh1D(resolution=(2, )), 2: QuadMesh(resolution=(2, 1))}
elements = {1: QuadFE(1, 'Q2'), 2: QuadFE(2, 'Q2')}
# Use function to set data
fns = {
1: {
1: lambda x: 2 * x[:, 0]**2,
2: lambda x, y: 2 * x[:, 0] + 2 * y[:, 0]
},
2: {
1: lambda x: x[:, 0]**2 + x[:, 1],
2: lambda x, y: x[:, 0] * y[:, 0] + x[:, 1] * y[:, 1]
}
}
# n_samples = 2
parms = {1: {1: [{}, {}], 2: [{}, {}]}, 2: {1: [{}, {}], 2: [{}, {}]}}
n_points = 1
for dim in [1, 2]:
mesh = meshes[dim]
element = elements[dim]
dofhandler = DofHandler(mesh, element)
dofhandler.distribute_dofs()
#dofhandler.get_region_dofs()
basis = Basis(dofhandler)
#
# Define random points in domain
#
if dim == 1:
x_min, x_max = mesh.bounding_box()
x = x_min + 0.5 * (x_max - x_min) * np.random.rand(n_points)
x = x[:, np.newaxis]
y = x_min + (x_max - x_min) * np.random.rand(n_points)
y = y[:, np.newaxis]
elif dim == 2:
x_min, x_max, y_min, y_max = mesh.bounding_box()
x = np.zeros((n_points, 2))
x[:, 0] = x_min + (x_max - x_min) * np.random.rand(n_points)
x[:, 1] = y_min + (y_max - y_min) * np.random.rand(n_points)
y = np.zeros((n_points, 2))
y[:, 0] = x_min + (x_max - x_min) * np.random.rand(n_points)
y[:, 1] = y_min + (y_max - y_min) * np.random.rand(n_points)
for n_variables in [1, 2]:
fn = fns[dim][n_variables]
parm = parms[dim][n_variables]
#
# Deterministic
#
f = Nodal(f=fn,
basis=basis,
mesh=mesh,
element=element,
dim=dim,
n_variables=n_variables)
if n_variables == 1:
xx = x
fe = fn(x)
elif n_variables == 2:
xx = (x, y)
fe = fn(*xx)
fx = f.eval(x=xx)
self.assertTrue(np.allclose(fx, fe))
#
# Sampled
#
f = Nodal(f=fn,
parameters=parm,
basis=basis,
mesh=mesh,
element=element,
dim=dim,
n_variables=n_variables)
self.assertEqual(f.n_samples(), 2)
fx = f.eval(x=xx)
self.assertTrue(np.allclose(fx[:, 0], fe))
self.assertTrue(np.allclose(fx[:, 1], fe))