/usr/lib/python3/dist-packages/FIAT/mixed.py is in python3-fiat 2017.2.0.0-2.
This file is owned by root:root, with mode 0o644.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 | # -*- coding: utf-8 -*-
#
# Copyright (C) 2005-2010 Anders Logg
#
# This file is part of FIAT.
#
# FIAT is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# FIAT is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with FIAT. If not, see <http://www.gnu.org/licenses/>.
from __future__ import absolute_import, print_function, division
from six import iteritems
from six.moves import map
import numpy
from operator import add
from functools import partial
from FIAT.dual_set import DualSet
from FIAT.finite_element import FiniteElement
class MixedElement(FiniteElement):
"""A FIAT-like representation of a mixed element.
:arg elements: An iterable of FIAT elements.
:arg ref_el: The reference element (optional).
This object offers tabulation of the concatenated basis function
tables along with an entity_dofs dict."""
def __init__(self, elements, ref_el=None):
elements = tuple(elements)
cells = set(e.get_reference_element() for e in elements)
if ref_el is not None:
cells.add(ref_el)
ref_el, = cells
# These functionals are absolutely wrong, they all map from
# functions of the wrong shape, and potentially of different
# shapes. However, they are wrong precisely as FFC hacks
# expect them to be. :(
nodes = [L for e in elements for L in e.dual_basis()]
entity_dofs = concatenate_entity_dofs(ref_el, elements)
dual = DualSet(nodes, ref_el, entity_dofs)
super(MixedElement, self).__init__(ref_el, dual, None, mapping=None)
self._elements = elements
def elements(self):
return self._elements
def num_sub_elements(self):
return len(self._elements)
def value_shape(self):
return (sum(numpy.prod(e.value_shape(), dtype=int) for e in self.elements()), )
def mapping(self):
return [m for e in self._elements for m in e.mapping()]
def get_nodal_basis(self):
raise NotImplementedError("get_nodal_basis not implemented")
def tabulate(self, order, points, entity=None):
"""Tabulate a mixed element by appropriately splatting
together the tabulation of the individual elements.
"""
shape = (self.space_dimension(),) + self.value_shape() + (len(points),)
output = {}
sub_dims = [0] + list(e.space_dimension() for e in self.elements())
sub_cmps = [0] + list(numpy.prod(e.value_shape(), dtype=int)
for e in self.elements())
irange = numpy.cumsum(sub_dims)
crange = numpy.cumsum(sub_cmps)
for i, e in enumerate(self.elements()):
table = e.tabulate(order, points, entity)
for d, tab in iteritems(table):
try:
arr = output[d]
except KeyError:
arr = numpy.zeros(shape, dtype=tab.dtype)
output[d] = arr
ir = irange[i:i+2]
cr = crange[i:i+2]
tab = tab.reshape(ir[1] - ir[0], cr[1] - cr[0], -1)
arr[slice(*ir), slice(*cr)] = tab
return output
def is_nodal(self):
"""True if primal and dual bases are orthogonal."""
return all(e.is_nodal() for e in self._elements)
def concatenate_entity_dofs(ref_el, elements):
"""Combine the entity_dofs from a list of elements into a combined
entity_dof containing the information for the concatenated DoFs of
all the elements."""
entity_dofs = {dim: {i: [] for i in entities}
for dim, entities in iteritems(ref_el.get_topology())}
offsets = numpy.cumsum([0] + list(e.space_dimension()
for e in elements), dtype=int)
for i, d in enumerate(e.entity_dofs() for e in elements):
for dim, dofs in iteritems(d):
for ent, off in iteritems(dofs):
entity_dofs[dim][ent] += list(map(partial(add, offsets[i]), off))
return entity_dofs
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