def estimate_resid(inner_n):
nodes = mp.warp_and_blend_nodes(dims, inner_n)
basis = mp.orthonormal_basis_for_space(
mp.PN(dims, inner_n), mp.Simplex(dims))
vdm = mp.vandermonde(basis.functions, nodes)
f = test_func(nodes[0])
coeffs = la.solve(vdm, f)
from modepy.modal_decay import estimate_relative_expansion_residual
return estimate_relative_expansion_residual(
coeffs.reshape(1, -1), dims, inner_n)
def get_simplex_element_flip_matrix(order, unit_nodes, permutation=None):
"""
Generate a resampling matrix that corresponds to a
permutation of the barycentric coordinates being applied.
The default permutation is to swap the
first two barycentric coordinates.
:param order: The order of the function space on the simplex,
(see second argument in
:fun:`modepy.simplex_best_available_basis`)
:param unit_nodes: A np array of unit nodes with shape
*(dim, nunit_nodes)*
:param permutation: Either *None*, or a tuple of shape
storing a permutation:
the *i*th barycentric coordinate gets mapped to
the *permutation[i]*th coordinate.
:return: A numpy array of shape *(nunit_nodes, nunit_nodes)*
which, when its transpose is right-applied
to the matrix of nodes (shaped *(dim, nunit_nodes)*),
corresponds to the permutation being applied
"""
from modepy.tools import barycentric_to_unit, unit_to_barycentric
bary_unit_nodes = unit_to_barycentric(unit_nodes)
flipped_bary_unit_nodes = bary_unit_nodes.copy()
if permutation is None:
flipped_bary_unit_nodes[0, :] = bary_unit_nodes[1, :]
flipped_bary_unit_nodes[1, :] = bary_unit_nodes[0, :]
else:
flipped_bary_unit_nodes[permutation, :] = bary_unit_nodes
flipped_unit_nodes = barycentric_to_unit(flipped_bary_unit_nodes)
dim = unit_nodes.shape[0]
shape = mp.Simplex(dim)
space = mp.PN(dim, order)
basis = mp.basis_for_space(space, shape)
flip_matrix = mp.resampling_matrix(basis.functions, flipped_unit_nodes,
unit_nodes)
flip_matrix[np.abs(flip_matrix) < 1e-15] = 0
# Flipping twice should be the identity
if permutation is None:
assert la.norm(
np.dot(flip_matrix, flip_matrix) -
np.eye(len(flip_matrix))) < 1e-13
return flip_matrix
def test_diff_matrix_permutation(dims):
order = 5
space = mp.PN(dims, order)
from pytools import \
generate_nonnegative_integer_tuples_summing_to_at_most as gnitstam
node_tuples = list(gnitstam(order, dims))
simplex_onb = mp.orthonormal_basis_for_space(space, mp.Simplex(dims))
nodes = np.array(mp.warp_and_blend_nodes(dims, order, node_tuples=node_tuples))
diff_matrices = mp.differentiation_matrices(
simplex_onb.functions, simplex_onb.gradients, nodes)
for iref_axis in range(dims):
perm = mp.diff_matrix_permutation(node_tuples, iref_axis)
assert la.norm(
diff_matrices[iref_axis]
- diff_matrices[0][perm][:, perm]) < 1e-10
def test_modal_decay(case_name, test_func, dims, n, expected_expn):
space = mp.PN(dims, n)
nodes = mp.warp_and_blend_nodes(dims, n)
basis = mp.orthonormal_basis_for_space(space, mp.Simplex(dims))
vdm = mp.vandermonde(basis.functions, nodes)
f = test_func(nodes[0])
coeffs = la.solve(vdm, f)
if 0:
from modepy.tools import plot_element_values
plot_element_values(n, nodes, f, resample_n=70,
show_nodes=True)
from modepy.modal_decay import fit_modal_decay
expn, _ = fit_modal_decay(coeffs.reshape(1, -1), dims, n)
expn = expn[0]
print(f"{case_name}: computed: {expn:g}, expected: {expected_expn:g}")
assert abs(expn-expected_expn) < 0.1
def space(self):
return mp.PN(self.dim, self.order)
def from_mesh_interp_matrix(self):
meg = self.mesh_el_group
meg_space = mp.PN(meg.dim, meg.order)
return mp.resampling_matrix(
mp.basis_for_space(meg_space, self._shape).functions,
self.unit_nodes, meg.unit_nodes)