/usr/lib/python2.7/dist-packages/FIAT/newdubiner.py is in python-fiat 1.6.0-1.
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 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 | # 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/>.
import numpy
def jrc(a, b, n, num_type):
an = num_type((2*n+1+a+b)*(2*n+2+a+b)) \
/ num_type(2*(n+1)*(n+1+a+b))
bn = num_type((a*a-b*b) * (2*n+1+a+b)) \
/ num_type(2*(n+1)*(2*n+a+b)*(n+1+a+b))
cn = num_type((n+a)*(n+b)*(2*n+2+a+b)) \
/ num_type((n+1)*(n+1+a+b)*(2*n+a+b))
return an, bn, cn
def lattice_iter(start, finish, depth):
"""Generator iterating over the depth-dimensional lattice of
integers between start and (finish-1). This works on simplices in
1d, 2d, 3d, and beyond"""
if depth == 0:
return
elif depth == 1:
for ii in range(start, finish):
yield [ii]
else:
for ii in range(start, finish):
for jj in lattice_iter(start, finish-ii, depth - 1):
yield [ii] + jj
def make_lattice(n, vs, numtype):
hs = numpy.array([(vs[i] - vs[0]) / numtype(n)
for i in range(1, len(vs))]
)
result = []
m = len(hs)
for indices in lattice_iter(0, n+1, m):
res_cur = vs[0].copy()
for i in range(len(indices)):
res_cur += indices[i] * hs[m-i-1]
result.append(res_cur)
return numpy.array(result)
def make_triangle_lattice(n, numtype):
vs = numpy.array([(numtype(-1), numtype(-1)),
(numtype(1), numtype(-1)),
(numtype(-1), numtype(1))])
return make_lattice(n, vs, numtype)
def make_tetrahedron_lattice(n, numtype):
vs = numpy.array([(numtype(-1), numtype(-1), numtype(-1)),
(numtype(1), numtype(-1), numtype(-1)),
(numtype(-1), numtype(1), numtype(-1)),
(numtype(-1), numtype(-1), numtype(1))
])
return make_lattice(n, vs, numtype)
def make_lattice_dim(D, n, numtype):
if D == 2:
return make_triangle_lattice(n, numtype)
elif D == 3:
return make_tetrahedron_lattice(n, numtype)
def tabulate_triangle(n, pts, numtype):
return _tabulate_triangle_single(n, numpy.array(pts).T, numtype)
def _tabulate_triangle_single(n, pts, numtype):
if len(pts) == 0:
return numpy.array([], numtype)
def idx(p, q):
return (p+q)*(p+q+1)//2 + q
results = (n+1)*(n+2)//2 * [None]
results[0] = numtype(1) \
+ pts[0] - pts[0] \
+ pts[1] - pts[1]
if n == 0:
return results
x = pts[0]
y = pts[1]
one = numtype(1)
two = numtype(2)
three = numtype(3)
# foo = one + two*x + y
f1 = (one+two*x+y)/two
f2 = (one - y) / two
f3 = f2**2
results[idx(1, 0), :] = f1
for p in range(1, n):
a = (two * p + 1) / (1 + p)
# b = p / (p + one)
results[idx(p+1, 0)] = a * f1 * results[idx(p, 0), :] \
- p/(one+p) * f3 * results[idx(p-1, 0), :]
for p in range(n):
results[idx(p, 1)] = (one + two*p+(three+two*p)*y) / two \
* results[idx(p, 0)]
for p in range(n-1):
for q in range(1, n-p):
(a1, a2, a3) = jrc(2*p+1, 0, q, numtype)
results[idx(p, q+1)] = \
(a1 * y + a2) * results[idx(p, q)] \
- a3 * results[idx(p, q-1)]
return results
def tabulate_tetrahedron(n, pts, numtype):
return _tabulate_tetrahedron_single(n, numpy.array(pts).T, numtype)
def _tabulate_tetrahedron_single(n, pts, numtype):
def idx(p, q, r):
return (p+q+r)*(p+q+r+1)*(p+q+r+2)//6 + (q+r)*(q+r+1)//2 + r
results = (n+1)*(n+2)*(n+3)//6 * [None]
results[0] = 1.0 \
+ pts[0] - pts[0] \
+ pts[1] - pts[1] \
+ pts[2] - pts[2]
if n == 0:
return results
x = pts[0]
y = pts[1]
z = pts[2]
one = numtype(1)
two = numtype(2)
three = numtype(3)
factor1 = (two + two*x + y + z) / two
factor2 = ((y+z)/two)**2
factor3 = (one + two * y + z) / two
factor4 = (1 - z) / two
factor5 = factor4 ** 2
results[idx(1, 0, 0)] = factor1
for p in range(1, n):
a1 = (two * p + one) / (p + one)
a2 = p / (p + one)
results[idx(p+1, 0, 0)] = a1 * factor1 * results[idx(p, 0, 0)] \
- a2 * factor2 * results[idx(p-1, 0, 0)]
for p in range(0, n):
results[idx(p, 1, 0)] = results[idx(p, 0, 0)] \
* (p * (one + y) + (two + three * y + z) / two)
for p in range(0, n-1):
for q in range(1, n-p):
(aq, bq, cq) = jrc(2*p+1, 0, q, numtype)
qmcoeff = aq * factor3 + bq * factor4
qm1coeff = cq * factor5
results[idx(p, q+1, 0)] = qmcoeff * results[idx(p, q, 0)] \
- qm1coeff * results[idx(p, q-1, 0)]
for p in range(n):
for q in range(n-p):
results[idx(p, q, 1)] = results[idx(p, q, 0)] \
* (one + p + q + (two + q + p) * z)
for p in range(n-1):
for q in range(0, n-p-1):
for r in range(1, n-p-q):
ar, br, cr = jrc(2*p+2*q+2, 0, r, numtype)
results[idx(p, q, r+1)] = \
(ar * z + br) * results[idx(p, q, r)] \
- cr * results[idx(p, q, r-1)]
return results
def tabulate_tetrahedron_derivatives(n, pts, numtype):
D = 3
order = 1
return tabulate_jet(D, n, pts, order, numtype)
def tabulate(D, n, pts, numtype):
return _tabulate_single(D, n, numpy.array(pts).T, numtype)
def _tabulate_single(D, n, pts, numtype):
if D == 2:
return _tabulate_triangle_single(n, pts, numtype)
elif D == 3:
return _tabulate_tetrahedron_single(n, pts, numtype)
def tabulate_jet(D, n, pts, order, numtype):
from .expansions import _tabulate_dpts
# Wrap the tabulator to allow for nondefault numtypes
def tabulator_wrap(n, X):
return _tabulate_single(D, n, X, numtype)
data1 = _tabulate_dpts(tabulator_wrap, D, n, order, pts)
# Put data in the required data structure, i.e.,
# k-tuples which contain the value, and the k-1 derivatives
# (gradient, Hessian, ...)
m = data1[0].shape[0]
n = data1[0].shape[1]
data2 = [[tuple([data1[r][i][j] for r in range(order+1)])
for j in range(n)]
for i in range(m)]
return data2
if __name__ == "__main__":
import gmpy
latticeK = 2
D = 3
pts = make_tetrahedron_lattice(latticeK, gmpy.mpq)
vals = tabulate_tetrahedron_derivatives(D, pts, gmpy.mpq)
print(vals)
|