def get_face_index_shuffle_lookup_map_for_nodes(self, face_nodes):
first_face_vertex_node_index_lists = \
self.geometry.face_vertices(self.vertex_indices())[0]
def check_and_chop(pt):
assert abs(pt[-1] - (-1)) < 1e-13
return pt[:-1]
unodes = self.unit_nodes()
face_unit_vertices = [
check_and_chop(unodes[i])
for i in first_face_vertex_node_index_lists
]
class FaceIndexShuffle:
def __init__(self, vert_perm, idx_map):
self.vert_perm = vert_perm
self.idx_map = idx_map
def __hash__(self):
return hash(self.vert_perm)
def __eq__(self, other):
return self.vert_perm == other.vert_perm
def __call__(self, indices):
return tuple(indices[i] for i in self.idx_map)
result = {}
from pytools import generate_unique_permutations
for vert_perm in generate_unique_permutations(
tuple(range(self.dimensions))):
permuted_face_unit_vertices = [
face_unit_vertices[i] for i in vert_perm
]
from hedge.tools.affine import identify_affine_map
amap = identify_affine_map(face_unit_vertices,
permuted_face_unit_vertices)
from hedge.tools.indexing import find_index_map_from_node_sets
imap = find_index_map_from_node_sets(
face_nodes, [amap(node) for node in face_nodes])
result[vert_perm] = FaceIndexShuffle(vert_perm, imap)
return result
def get_face_index_shuffle_lookup_map_for_nodes(self, face_nodes):
first_face_vertex_node_index_lists = \
self.geometry.face_vertices(self.vertex_indices())[0]
def check_and_chop(pt):
assert abs(pt[-1] - (-1)) < 1e-13
return pt[:-1]
unodes = self.unit_nodes()
face_unit_vertices = [check_and_chop(unodes[i])
for i in first_face_vertex_node_index_lists]
class FaceIndexShuffle:
def __init__(self, vert_perm, idx_map):
self.vert_perm = vert_perm
self.idx_map = idx_map
def __hash__(self):
return hash(self.vert_perm)
def __eq__(self, other):
return self.vert_perm == other.vert_perm
def __call__(self, indices):
return tuple(indices[i] for i in self.idx_map)
result = {}
from pytools import generate_unique_permutations
for vert_perm in generate_unique_permutations(
tuple(range(self.dimensions))):
permuted_face_unit_vertices = [
face_unit_vertices[i] for i in vert_perm]
from hedge.tools.affine import identify_affine_map
amap = identify_affine_map(
face_unit_vertices, permuted_face_unit_vertices)
from hedge.tools.indexing import find_index_map_from_node_sets
imap = find_index_map_from_node_sets(
face_nodes, [amap(node) for node in face_nodes])
result[vert_perm] = FaceIndexShuffle(vert_perm, imap)
return result
def test_identify_affine_map():
n = 5
randn = numpy.random.randn
for i in range(10):
a = numpy.eye(n) + 0.3*randn(n,n)
b = randn(n)
from hedge.tools.affine import AffineMap, identify_affine_map
amap = AffineMap(a, b)
from_points = [randn(n) for i in range(n+1)]
to_points = [amap(fp) for fp in from_points]
amap2 = identify_affine_map(from_points, to_points)
assert la.norm(a-amap2.matrix) < 1e-12
assert la.norm(b-amap2.vector) < 1e-12
def test_identify_affine_map():
n = 5
randn = numpy.random.randn
for i in range(10):
a = numpy.eye(n) + 0.3*randn(n,n)
b = randn(n)
from hedge.tools.affine import AffineMap, identify_affine_map
amap = AffineMap(a, b)
from_points = [randn(n) for i in range(n+1)]
to_points = [amap(fp) for fp in from_points]
amap2 = identify_affine_map(from_points, to_points)
assert la.norm(a-amap2.matrix) < 1e-12
assert la.norm(b-amap2.vector) < 1e-12
def face_affine_maps(self):
"""Return an affine map for each face that maps the (n-1)-dimensional
face unit coordinates to their volume coordintes.
"""
face_vertex_node_index_lists = \
self.geometry.face_vertices(self.vertex_indices())
from pytools import flatten, one
vertex_node_indices = set(flatten(face_vertex_node_index_lists))
def find_missing_node(face_vertex_node_indices):
return unit_nodes[one(vertex_node_indices -
set(face_vertex_node_indices))]
unit_nodes = self.unit_nodes()
sets_of_to_points = [
[unit_nodes[fvni] for fvni in face_vertex_node_indices] +
[find_missing_node(face_vertex_node_indices)]
for face_vertex_node_indices in face_vertex_node_index_lists
]
from_points = sets_of_to_points[0]
# Construct an affine map that promotes face nodes into volume
# by appending -1, this should end up on the first face
dim = self.dimensions
from hedge.tools.affine import AffineMap
from hedge.tools.linalg import unit_vector
to_face_1 = AffineMap(
numpy.vstack([
numpy.eye(dim - 1, dtype=numpy.float64),
numpy.zeros(dim - 1)
]), -unit_vector(dim, dim - 1, dtype=numpy.float64))
def finish_affine_map(amap):
return amap.post_compose(to_face_1)
from hedge.tools.affine import identify_affine_map
return [
finish_affine_map(identify_affine_map(from_points, to_points))
for to_points in sets_of_to_points
]
def face_affine_maps(self):
"""Return an affine map for each face that maps the (n-1)-dimensional
face unit coordinates to their volume coordintes.
"""
face_vertex_node_index_lists = \
self.geometry.face_vertices(self.vertex_indices())
from pytools import flatten, one
vertex_node_indices = set(flatten(face_vertex_node_index_lists))
def find_missing_node(face_vertex_node_indices):
return unit_nodes[one(
vertex_node_indices - set(face_vertex_node_indices))]
unit_nodes = self.unit_nodes()
sets_of_to_points = [[unit_nodes[fvni]
for fvni in face_vertex_node_indices]
+ [find_missing_node(face_vertex_node_indices)]
for face_vertex_node_indices in face_vertex_node_index_lists]
from_points = sets_of_to_points[0]
# Construct an affine map that promotes face nodes into volume
# by appending -1, this should end up on the first face
dim = self.dimensions
from hedge.tools.affine import AffineMap
from hedge.tools.linalg import unit_vector
to_face_1 = AffineMap(
numpy.vstack([
numpy.eye(dim-1, dtype=numpy.float64),
numpy.zeros(dim-1)]),
-unit_vector(dim, dim-1, dtype=numpy.float64))
def finish_affine_map(amap):
return amap.post_compose(to_face_1)
from hedge.tools.affine import identify_affine_map
return [
finish_affine_map(
identify_affine_map(from_points, to_points))
for to_points in sets_of_to_points]
