from __future__ import division
from hedge.discretization.local import TriangleDiscretization
tri = TriangleDiscretization(5)
import Gnuplot
gp = Gnuplot.Gnuplot()
import numpy
xpts = numpy.arange(-1.5, 1.5, 0.1)
ypts = numpy.arange(-1.5, 1.5, 0.1)
gp("set zrange [-3:3]")
for bfi, bf in zip(tri.generate_mode_identifiers(), tri.basis_functions()):
lines = []
for x in xpts:
values = []
for y in ypts:
values.append((x, y, bf(numpy.array((x, y)))))
lines.append(Gnuplot.Data(values, with_="lines"))
for y in xpts:
values = []
for x in ypts:
values.append((x, y, bf(numpy.array((x, y)))))
lines.append(Gnuplot.Data(values, with_="lines"))
tri = numpy.array([
(-1, -1, 0),
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
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
from hedge.discretization.local import TriangleDiscretization
tri = TriangleDiscretization(5)
import Gnuplot
gp = Gnuplot.Gnuplot()
import numpy
xpts = numpy.arange(-1.5, 1.5, 0.1)
ypts = numpy.arange(-1.5, 1.5, 0.1)
gp("set zrange [-3:3]")
for bfi, bf in zip(tri.generate_mode_identifiers(), tri.basis_functions()):
lines = []
for x in xpts:
values = []
for y in ypts:
values.append((x, y, bf(numpy.array((x, y)))))
lines.append(Gnuplot.Data(values, with_="lines"))
for y in xpts:
values = []
for x in ypts:
values.append((x, y, bf(numpy.array((x, y)))))
lines.append(Gnuplot.Data(values, with_="lines"))
tri = numpy.array([(-1, -1, 0), (-1, 1, 0), (1, -1, 0), (-1, -1, 0)])
lines.append(Gnuplot.Data(tri, with_="lines"))
