def _assemble_and_evaluate(self, x0, d0, active_nodes,
fixed_and_handle_nodes,
no_of_fixed_and_handle_nodes,
delta_d_handler, delta_d):
# 2. Assemble m
logging.info('Assemble interpolation matrix...')
m = assemble(self._rbffunc, x0[fixed_and_handle_nodes, :] +
d0[fixed_and_handle_nodes, :],
self._polynomial_order)
logging.info('Solve weights for interpolation...')
if self._extra_columns == 0:
gamma = solve(m, delta_d_handler[fixed_and_handle_nodes, :])
else:
gamma = solve(m, np.concatenate(
(delta_d_handler[fixed_and_handle_nodes, :],
np.zeros((self._extra_columns, 3), dtype=np.float64)),
axis=0))
# 3. Evaluate
logging.info('Evaluate interpolation...')
s = evaluate(self._rbffunc, x0[active_nodes, :] +
d0[active_nodes, :],
x0[fixed_and_handle_nodes, :] +
d0[fixed_and_handle_nodes, :],
gamma[:no_of_fixed_and_handle_nodes],
gamma[no_of_fixed_and_handle_nodes:])
delta_d[active_nodes, :] = s
def test_assembly_with_polynomial_order_1():
"""
Test assembly with polynomial order = 1
"""
s = r'r**3'
# Define two nodes
x = np.array([[1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.2, 0.5, 0.6]])
actual = assemble(s, x, 1)
desired = np.array([[
0.0,
np.sqrt(5.0)**3,
np.sqrt(0.8**2 + 0.5**2 + 0.6**2)**3, 1.0, 1.0, 0.0, 0.0
],
[
np.sqrt(5.0)**3, 0.0,
np.sqrt(0.2**2 + 1.5**2 + 0.6**2)**3, 1.0, 0.0,
2.0, 0.0
],
[
np.sqrt(0.8**2 + 0.5**2 + 0.6**2)**3,
np.sqrt(0.2**2 + 1.5**2 + 0.6**2)**3, 0.0, 1.0,
0.2, 0.5, 0.6
], [1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0],
[1.0, 0.0, 0.2, 0.0, 0.0, 0.0, 0.0],
[0.0, 2.0, 0.5, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.6, 0.0, 0.0, 0.0, 0.0]])
assert_allclose(actual, desired)
def test_assembly():
"""
Test assembly with simple rbf function f(r) = r**3
"""
s = r'r**3'
# Define two nodes
x = np.array([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0]])
actual = assemble(s, x)
desired = np.array([[0.0, np.sqrt(2.0)**3], [np.sqrt(2.0)**3, 0.0]])
assert_allclose(actual, desired)
def test_assembly_with_polynomial_order_0_2d():
"""
Test assembly with polynomial order = 0
"""
s = r'r**3'
# Define two nodes
x = np.array([[1.0, 0.0], [0.0, 1.0]])
actual = assemble(s, x, 0)
desired = np.array([[0.0, np.sqrt(2.0)**3, 1.0],
[np.sqrt(2.0)**3, 0.0, 1.0], [1.0, 1.0, 0.0]])
assert_allclose(actual, desired)