def map_sum(self, expr, other, urecs):
if (not isinstance(other, type(expr))
or len(expr.children) != len(other.children)):
return []
result = []
from pytools import generate_permutations
had_structural_match = False
for perm in generate_permutations(range(len(expr.children))):
it_assignments = urecs
for my_child, other_child in zip(
expr.children,
(other.children[i] for i in perm)):
it_assignments = self.rec(my_child, other_child, it_assignments)
if not it_assignments:
break
if it_assignments:
had_structural_match = True
result.extend(it_assignments)
if not had_structural_match:
return self.treat_mismatch(expr, other, urecs)
return result
def map_sum(self, expr, other, urecs):
if (not isinstance(other, type(expr))
or len(expr.children) != len(other.children)):
return []
result = []
from pytools import generate_permutations
had_structural_match = False
for perm in generate_permutations(range(len(expr.children))):
it_assignments = urecs
for my_child, other_child in zip(expr.children, (other.children[i]
for i in perm)):
it_assignments = self.rec(my_child, other_child,
it_assignments)
if not it_assignments:
break
if it_assignments:
had_structural_match = True
result.extend(it_assignments)
if not had_structural_match:
return self.treat_mismatch(expr, other, urecs)
return result
def size(k, string):
minimum = 'inf'
size = 0
for permutation in generate_permutations(range(k)):
result = []
for i in range(len(string) / k):
result.append(permute(permutation, string[k * i:k * (i + 1)]))
minimum = min(minimum, compressed_size(''.join(result)))
return minimum
def test_mapping_differences_tri():
"""Check that triangle interpolation is independent of mapping to reference
"""
from hedge.discretization.local import TriangleDiscretization
from random import random
from pytools import generate_permutations
def shift(list):
return list[1:] + [list[0]]
class LinearCombinationOfFunctions:
def __init__(self, coefficients, functions, premap):
self.coefficients = coefficients
self.functions = functions
self.premap = premap
def __call__(self, x):
return sum(coeff * f(self.premap(x))
for coeff, f in zip(self.coefficients, self.functions))
def random_barycentric_coordinates(dim):
remain = 1
coords = []
for i in range(dim):
coords.append(random() * remain)
remain -= coords[-1]
coords.append(remain)
return coords
tri = TriangleDiscretization(5)
for trial_number in range(10):
vertices = [numpy.random.randn(2) for vi in range(3)]
map = tri.geometry.get_map_unit_to_global(vertices)
nodes = [map(node) for node in tri.unit_nodes()]
node_values = numpy.array([random() for node in nodes])
functions = []
for pvertices in generate_permutations(vertices):
pmap = tri.geometry.get_map_unit_to_global(pvertices)
pnodes = [pmap(node) for node in tri.unit_nodes()]
# map from pnode# to node#
nodematch = {}
for pi, pn in enumerate(pnodes):
for i, n in enumerate(nodes):
if la.norm(n - pn) < 1e-13:
nodematch[pi] = i
break
pnode_values = numpy.array(
[node_values[nodematch[pi]] for pi in range(len(nodes))])
interp_f = LinearCombinationOfFunctions(
la.solve(tri.vandermonde(), pnode_values),
tri.basis_functions(), pmap.inverted())
# verify interpolation property
#for n, nv in zip(pnodes, pnode_values):
#assert abs(interp_f(n) - nv) < 1e-13
functions.append(interp_f)
for subtrial_number in range(15):
pt_in_element = sum(coeff * vertex for coeff, vertex in zip(
random_barycentric_coordinates(2), vertices))
f_values = [f(pt_in_element) for f in functions]
avg = sum(f_values) / len(f_values)
err = [abs(fv - avg) for fv in f_values]
assert max(err) < 1e-12
def test_mapping_differences_tri():
"""Check that triangle interpolation is independent of mapping to reference
"""
from hedge.discretization.local import TriangleDiscretization
from random import random
from pytools import generate_permutations
def shift(list):
return list[1:] + [list[0]]
class LinearCombinationOfFunctions:
def __init__(self, coefficients, functions, premap):
self.coefficients = coefficients
self.functions = functions
self.premap = premap
def __call__(self, x):
return sum(coeff * f(self.premap(x)) for coeff, f in zip(self.coefficients, self.functions))
def random_barycentric_coordinates(dim):
remain = 1
coords = []
for i in range(dim):
coords.append(random() * remain)
remain -= coords[-1]
coords.append(remain)
return coords
tri = TriangleDiscretization(5)
for trial_number in range(10):
vertices = [numpy.random.randn(2) for vi in range(3)]
map = tri.geometry.get_map_unit_to_global(vertices)
nodes = [map(node) for node in tri.unit_nodes()]
node_values = numpy.array([random() for node in nodes])
functions = []
for pvertices in generate_permutations(vertices):
pmap = tri.geometry.get_map_unit_to_global(pvertices)
pnodes = [pmap(node) for node in tri.unit_nodes()]
# map from pnode# to node#
nodematch = {}
for pi, pn in enumerate(pnodes):
for i, n in enumerate(nodes):
if la.norm(n - pn) < 1e-13:
nodematch[pi] = i
break
pnode_values = numpy.array([node_values[nodematch[pi]] for pi in range(len(nodes))])
interp_f = LinearCombinationOfFunctions(
la.solve(tri.vandermonde(), pnode_values), tri.basis_functions(), pmap.inverted()
)
# verify interpolation property
# for n, nv in zip(pnodes, pnode_values):
# assert abs(interp_f(n) - nv) < 1e-13
functions.append(interp_f)
for subtrial_number in range(15):
pt_in_element = sum(coeff * vertex for coeff, vertex in zip(random_barycentric_coordinates(2), vertices))
f_values = [f(pt_in_element) for f in functions]
avg = sum(f_values) / len(f_values)
err = [abs(fv - avg) for fv in f_values]
assert max(err) < 5e-13
