def test_get_rbf_matrix(self):
"""Test basic properties of the RBF matrix (e.g. symmetry, size).
Verify that the RBF matrix is symmetric and it has the correct
size for all types of RBF.
"""
settings = RbfoptSettings()
for i in range(50):
dim = random.randint(1, 20)
num_points = random.randint(10, 50)
node_pos = np.array(
[[random.uniform(-100, 100) for j in range(dim)]
for k in range(num_points)])
# Possible shapes of the matrix
for rbf_type in self.rbf_types:
settings.rbf = rbf_type
mat = ru.get_rbf_matrix(settings, dim, num_points, node_pos)
self.assertIsInstance(mat, np.matrix)
self.assertAlmostEqual(np.max(mat - mat.transpose()),
0.0,
msg='RBF matrix is not symmetric')
size = num_points + 1
if (ru.get_degree_polynomial(settings) > 0):
size += dim**ru.get_degree_polynomial(settings)
self.assertEqual(mat.shape, (size, size))
# Check that exception is raised for unknown RBF types
settings.rbf = 'unknown'
self.assertRaises(ValueError, ru.get_rbf_matrix, settings, dim,
num_points, node_pos)
def test_get_degree_polynomial(self):
"""Verify that the degree is always between 0 and 1."""
settings = RbfoptSettings()
for rbf_type in self.rbf_types:
settings.rbf = rbf_type
degree = ru.get_degree_polynomial(settings)
self.assertTrue(degree == 0 or degree == 1)
def test_get_size_P_matrix(self):
"""Verify that the size is always between 0 and n+1."""
settings = RbfoptSettings()
for rbf_type in self.rbf_types:
settings.rbf = rbf_type
for n in range(20):
size = ru.get_size_P_matrix(settings, n)
self.assertTrue(0 <= size <= n + 1)
def test_get_rbf_function(self):
"""Check that all RBFs are properly computed at 0 and at 1."""
settings = RbfoptSettings()
# Set up values of the RBF at 0 and at 1
rbf_values = dict()
rbf_values['linear'] = (0.0, 1.0)
rbf_values['multiquadric'] = (1.0, math.sqrt(1 + 1.0))
rbf_values['cubic'] = (0.0, 1.0)
rbf_values['thin_plate_spline'] = (0.0, 0.0)
for rbf_type in self.rbf_types:
settings.rbf = rbf_type
rbf = ru.get_rbf_function(settings)
rbf_at_0, rbf_at_1 = rbf_values[rbf_type]
msg = 'RBF {:s} is not {:f} at 0'.format(rbf_type, rbf_at_0)
self.assertEqual(rbf_at_0, rbf(0.0), msg=msg)
msg = 'RBF {:s} is not {:f} at 1'.format(rbf_type, rbf_at_1)
self.assertEqual(rbf_at_1, rbf(1.0), msg=msg)
