def test_n_samples(self):
#
# 1D
#
# Define mesh
mesh = Mesh1D(resolution=(10,))
# Define function
f = Explicit([lambda x: x, lambda x: -2+2*x**2], dim=1)
n_samples = f.n_samples()
k = Kernel(f)
n_points = 101
x0, x1 = mesh.bounding_box()
x = np.linspace(x0,x1,n_points)
self.assertEqual(k.eval(x).shape, (n_points, n_samples))
self.assertTrue(np.allclose(k.eval(x)[:,0],x))
self.assertTrue(np.allclose(k.eval(x)[:,1], -2+2*x**2))
def test_eval(self):
#
# Evaluate single univariate/bivariate functions in 1 or 2 dimensions
#
fns = {
1: {
1: lambda x: x**2,
2: lambda x, y: x + y
},
2: {
1: lambda x: x[:, 0]**2 + x[:, 1]**2,
2: lambda x, y: x[:, 0] * y[:, 0] + x[:, 1] * y[:, 1]
}
}
# Singletons
x = {1: {1: 2, 2: (3, 4)}, 2: {1: (1, 2), 2: ((1, 2), (3, 4))}}
vals = {1: {1: 4, 2: 7}, 2: {1: 5, 2: 11}}
for dim in [1, 2]:
#
# Iterate over dimension
#
for n_variables in [1, 2]:
#
# Iterate over number of variables
#
fn = fns[dim][n_variables]
f = Explicit(fn, n_variables=n_variables, dim=dim)
xn = x[dim][n_variables]
self.assertEqual(f.eval(xn), vals[dim][n_variables])
#
# Evaluate sampled functions
#
fns = {
1: {
1: lambda x, a: a * x**2,
2: lambda x, y, a: a * (x + y)
},
2: {
1: lambda x, a: a * (x[:, 0]**2 + x[:, 1]**2),
2: lambda x, y, a: a * (x[:, 0] * y[:, 0] + x[:, 1] * y[:, 1])
}
}
pars = [{'a': 1}, {'a': 2}]
#
# Singletons
#
x = {1: {1: 2, 2: (3, 4)}, 2: {1: (1, 2), 2: ((1, 2), (3, 4))}}
vals = {1: {1: 4, 2: 7}, 2: {1: 5, 2: 11}}
for dim in [1, 2]:
#
# Iterate over dimension
#
for n_variables in [1, 2]:
#
# Iterate over number of variables
#
fn = fns[dim][n_variables]
f = Explicit(fn,
parameters=pars,
n_variables=n_variables,
dim=dim)
xn = x[dim][n_variables]
self.assertEqual(f.eval(xn)[0][0], vals[dim][n_variables])
self.assertEqual(f.eval(xn)[0][1], 2 * vals[dim][n_variables])
#
# 2 points
#
n_points = 2
x = {
1: {
1: [(2, ), (2, )],
2: ([(3, ), (3, )], [(4, ), (4, )])
},
2: {
1: [(1, 2), (1, 2)],
2: ([(1, 2), (1, 2)], [(3, 4), (3, 4)])
}
}
for dim in [1, 2]:
#
# Iterate over dimension
#
for n_variables in [1, 2]:
#
# Iterate over number of variables
#
fn = fns[dim][n_variables]
f = Explicit(fn,
parameters=pars,
n_variables=n_variables,
dim=dim)
xn = x[dim][n_variables]
self.assertEqual(f.eval(xn).shape[0], n_points)
self.assertEqual(f.eval(xn).shape[1], f.n_samples())
for i in range(f.n_samples()):
for j in range(2):
val = pars[i]['a'] * vals[dim][n_variables]
self.assertEqual(f.eval(xn)[j, i], val)