/usr/lib/python2.7/dist-packages/FIAT/hermite.py is in python-fiat 2016.2.0-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 | # Copyright (C) 2008 Robert C. Kirby (Texas Tech University)
#
# 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 FIAT import finite_element, polynomial_set, dual_set, functional
class CubicHermiteDualSet(dual_set.DualSet):
"""The dual basis for Lagrange elements. This class works for
simplices of any dimension. Nodes are point evaluation at
equispaced points."""
def __init__(self, ref_el):
entity_ids = {}
nodes = []
cur = 0
# make nodes by getting points
# need to do this dimension-by-dimension, facet-by-facet
top = ref_el.get_topology()
verts = ref_el.get_vertices()
sd = ref_el.get_spatial_dimension()
# get jet at each vertex
entity_ids[0] = {}
for v in sorted(top[0]):
nodes.append(functional.PointEvaluation(ref_el, verts[v]))
pd = functional.PointDerivative
for i in range(sd):
alpha = [0] * sd
alpha[i] = 1
nodes.append(pd(ref_el, verts[v], alpha))
entity_ids[0][v] = list(range(cur, cur + 1 + sd))
cur += sd + 1
# no edge dof
entity_ids[1] = {}
# face dof
# point evaluation at barycenter
entity_ids[2] = {}
for f in sorted(top[2]):
pt = ref_el.make_points(2, f, 3)[0]
n = functional.PointEvaluation(ref_el, pt)
nodes.append(n)
entity_ids[2] = list(range(cur, cur + 1))
cur += 1
for dim in range(3, sd + 1):
entity_ids[dim] = {}
for facet in top[dim]:
entity_ids[dim][facet] = []
super(CubicHermiteDualSet, self).__init__(nodes, ref_el, entity_ids)
class CubicHermite(finite_element.CiarletElement):
"""The cubic Hermite finite element. It is what it is."""
def __init__(self, ref_el):
poly_set = polynomial_set.ONPolynomialSet(ref_el, 3)
dual = CubicHermiteDualSet(ref_el)
super(CubicHermite, self).__init__(poly_set, dual, 3)
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