def find_points_in_element(self, el, el_tolerance):
from pyrticle._internal import ElementOnGrid
eog = ElementOnGrid()
eog.element_number = el.id
points = self.backend.find_points_in_element(
eog, el_tolerance * la.norm(el.map.matrix, 2))
return eog, list(points)
def find_points_in_element(self, el, el_tolerance):
from pyrticle._internal import ElementOnGrid
eog = ElementOnGrid()
eog.element_number = el.id
points = self.backend.find_points_in_element(
eog, el_tolerance * la.norm(el.map.matrix, 2))
return eog, list(points)
def prepare_with_brick_interpolation(self):
class TensorProductLegendreBasisFunc:
def __init__(self, n):
from hedge.polynomial import LegendreFunction
self.funcs = [LegendreFunction(n_i) for n_i in n]
def __call__(self, x):
result = 1
for f_i, x_i in zip(self.funcs, x):
result *= f_i(x_i)
return result
def make_legendre_basis(dimensions):
from pytools import generate_nonnegative_integer_tuples_below
return [
TensorProductLegendreBasisFunc(n)
for n in generate_nonnegative_integer_tuples_below(dimensions)
]
discr = self.method.discretization
backend = self.backend
backend.elements_on_grid.reserve(
sum(len(eg.members) for eg in discr.element_groups))
from pyrticle._internal import ElementOnGrid, BoxFloat
total_points = 0
# Iterate over all elements
for eg in discr.element_groups:
ldis = eg.local_discretization
for el in eg.members:
el_bbox = BoxFloat(*el.bounding_box(discr.mesh.points))
scaled_tolerance = self.el_tolerance * la.norm(
el.map.matrix, 2)
el_bbox.lower -= scaled_tolerance
el_bbox.upper += scaled_tolerance
# For each brick, find all element nodes that lie in it
for brk in backend.bricks:
eog = ElementOnGrid()
eog.element_number = el.id
brk_bbox = brk.bounding_box()
brk_and_el = brk_bbox.intersect(el_bbox)
if brk_and_el.is_empty():
continue
el_nodes = []
el_node_indices = []
el_slice = discr.find_el_range(el.id)
el_length = el_slice.stop - el_slice.start
if brk_and_el == el_bbox:
# whole element in brick? fantastic.
el_nodes = discr.nodes[el_slice]
el_node_indices = range(el_length)
else:
# no? go through the nodes one by one.
for i, node in enumerate(discr.nodes[el_slice]):
# this containment check has to be exact,
# we positively cannot have nodes belong to
# two bricks
if brk_bbox.contains(node, threshold=0):
el_nodes.append(node)
el_node_indices.append(i)
idx_range = brk.index_range(brk_and_el)
lb = make_legendre_basis(idx_range.upper - idx_range.lower)
from hedge.polynomial import generic_vandermonde
brk_and_el_points = [
brk.point(c)
for c in self.iterator_type(brk, idx_range)
]
svdm = generic_vandermonde(points=brk_and_el_points,
functions=lb)
total_points += len(brk_and_el_points)
mixed_vdm_pre = generic_vandermonde(points=el_nodes,
functions=lb)
if len(el_nodes) < el_length:
mixed_vdm = numpy.zeros((el_length, len(lb)),
dtype=float)
for i, vdm_row in enumerate(mixed_vdm_pre):
mixed_vdm[el_node_indices[i]] = vdm_row
else:
mixed_vdm = mixed_vdm_pre
from hedge.tools import leftsolve
eog.interpolation_matrix = numpy.asarray(leftsolve(
svdm, mixed_vdm),
order="Fortran")
#print eog.interpolation_matrix.shape
#raw_input()
eog.grid_nodes.extend(
brk.index(c)
for c in self.iterator_type(brk, idx_range))
eog.weight_factors = numpy.ones((len(eog.grid_nodes), ),
dtype=numpy.float64)
backend.elements_on_grid.append(eog)
# we don't need no stinkin' extra points
backend.extra_point_brick_starts.extend([0] *
(len(backend.bricks) + 1))
# stats
self.generate_point_statistics(0)
def prepare_with_brick_interpolation(self):
class TensorProductLegendreBasisFunc:
def __init__(self, n):
from hedge.polynomial import LegendreFunction
self.funcs = [LegendreFunction(n_i) for n_i in n]
def __call__(self, x):
result = 1
for f_i, x_i in zip(self.funcs, x):
result *= f_i(x_i)
return result
def make_legendre_basis(dimensions):
from pytools import generate_nonnegative_integer_tuples_below
return [TensorProductLegendreBasisFunc(n)
for n in generate_nonnegative_integer_tuples_below(dimensions)]
discr = self.method.discretization
backend = self.backend
backend.elements_on_grid.reserve(
sum(len(eg.members) for eg in discr.element_groups))
from pyrticle._internal import ElementOnGrid, BoxFloat
total_points = 0
# Iterate over all elements
for eg in discr.element_groups:
ldis = eg.local_discretization
for el in eg.members:
el_bbox = BoxFloat(*el.bounding_box(discr.mesh.points))
scaled_tolerance = self.el_tolerance * la.norm(el.map.matrix, 2)
el_bbox.lower -= scaled_tolerance
el_bbox.upper += scaled_tolerance
# For each brick, find all element nodes that lie in it
for brk in backend.bricks:
eog = ElementOnGrid()
eog.element_number = el.id
brk_bbox = brk.bounding_box()
brk_and_el = brk_bbox.intersect(el_bbox)
if brk_and_el.is_empty():
continue
el_nodes = []
el_node_indices = []
el_slice = discr.find_el_range(el.id)
el_length = el_slice.stop-el_slice.start
if brk_and_el == el_bbox:
# whole element in brick? fantastic.
el_nodes = discr.nodes[el_slice]
el_node_indices = range(el_length)
else:
# no? go through the nodes one by one.
for i, node in enumerate(discr.nodes[el_slice]):
# this containment check has to be exact,
# we positively cannot have nodes belong to
# two bricks
if brk_bbox.contains(node, threshold=0):
el_nodes.append(node)
el_node_indices.append(i)
idx_range = brk.index_range(brk_and_el)
lb = make_legendre_basis(idx_range.upper-idx_range.lower)
from hedge.polynomial import generic_vandermonde
brk_and_el_points = [brk.point(c)
for c in self.iterator_type(brk, idx_range)]
svdm = generic_vandermonde(
points=brk_and_el_points,
functions=lb)
total_points += len(brk_and_el_points)
mixed_vdm_pre = generic_vandermonde(
points=el_nodes, functions=lb)
if len(el_nodes) < el_length:
mixed_vdm = numpy.zeros((el_length, len(lb)),
dtype=float)
for i, vdm_row in enumerate(mixed_vdm_pre):
mixed_vdm[el_node_indices[i]] = vdm_row
else:
mixed_vdm = mixed_vdm_pre
from hedge.tools import leftsolve
eog.interpolation_matrix = numpy.asarray(
leftsolve(svdm, mixed_vdm),
order="Fortran")
#print eog.interpolation_matrix.shape
#raw_input()
eog.grid_nodes.extend(brk.index(c)
for c in self.iterator_type(brk, idx_range))
eog.weight_factors = numpy.ones(
(len(eog.grid_nodes),), dtype=numpy.float64)
backend.elements_on_grid.append(eog)
# we don't need no stinkin' extra points
backend.extra_point_brick_starts.extend([0]*(len(backend.bricks)+1))
# stats
self.generate_point_statistics(0)
