/usr/lib/python2.7/dist-packages/ufl/__init__.py is in python-ufl 1.4.0-1.
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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 | """The Unified Form Language is an embedded domain specific language
for definition of variational forms intended for finite element
discretization. More precisely, it defines a fixed interface for choosing
finite element spaces and defining expressions for weak forms in a
notation close to mathematical notation.
This Python module contains the language as well as algorithms to work
with it.
* To import the language, type::
from ufl import *
* To import the underlying classes an UFL expression tree is built
from, type::
from ufl.classes import *
* Various algorithms for working with UFL expression trees can be
found in::
from ufl.algorithms import *
The classes and algorithms are considered implementation details and
should not be used in form definitions.
For more details on the language, see
http://www.fenicsproject.org
and
http://arxiv.org/abs/1211.4047
The development version can be found in the repository at
https://www.bitbucket.org/fenics-project/ufl
A very brief overview of the language contents follows:
* Domains::
Domain, ProductDomain
* Cells::
Cell, ProductCell, OuterProductCell,
interval, triangle, tetrahedron,
quadrilateral, hexahedron,
cell1D, cell2D, cell3D,
* Sobolev spaces::
L2, H1, H2, HDiv, HCurl
* Elements::
FiniteElement,
MixedElement, VectorElement, TensorElement
EnrichedElement, RestrictedElement,
TensorProductElement, OuterProductElement,
OuterProductVectorElement, HDiv, HCurl
* Arguments::
Argument, TestFunction, TrialFunction
* Coefficients::
Coefficient, Constant, VectorConstant, TensorConstant
* Splitting form arguments in mixed spaces::
split
* Literal constants::
Identity, PermutationSymbol
* Geometric quantities::
SpatialCoordinate,
FacetNormal, CellNormal,
CellVolume, Circumradius,
FacetArea, MinFacetEdgeLength, MaxFacetEdgeLength,
* Indices::
Index, indices,
i, j, k, l, p, q, r, s
* Scalar to tensor expression conversion::
as_tensor, as_vector, as_matrix
* Unit vectors and matrices::
unit_vector, unit_vectors,
unit_matrix, unit_matrices
* Tensor algebra operators::
outer, inner, dot, cross, perp,
det, inv, cofac,
transpose, tr, diag, diag_vector,
dev, skew, sym
* Elementwise tensor operators::
elem_mult, elem_div, elem_pow, elem_op
* Differential operators::
variable, diff,
grad, div, nabla_grad, nabla_div,
Dx, Dn, curl, rot
* Nonlinear functions::
Max, Min,
abs, sign, sqrt,
exp, ln, erf,
cos, sin, tan,
acos, asin, atan, atan_2,
cosh, sinh, tanh,
bessel_J, bessel_Y, bessel_I, bessel_K
* Discontinuous Galerkin operators:
jump, avg, v('+'), v('-'), cell_avg, facet_avg
* Conditional operators::
eq, ne, le, ge, lt, gt,
<, >, <=, >=,
And, Or, Not,
conditional
* Integral measures::
dx, ds, ds_b, ds_t, ds_tb, ds_v, dS, dS_h, dS_v, dP, dc, dE
* Form transformations::
rhs, lhs, system, functional,
replace, replace_integral_domains,
adjoint, action, energy_norm,
sensitivity_rhs, derivative
"""
# Copyright (C) 2008-2014 Martin Sandve Alnes and Anders Logg
#
# This file is part of UFL.
#
# UFL 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.
#
# UFL 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 UFL. If not, see <http://www.gnu.org/licenses/>.
#
# Modified by Kristian B. Oelgaard, 2009, 2011
# Modified by Anders Logg, 2009.
# Modified by Johannes Ring, 2014.
# Modified by Andrew T. T. McRae, 2014
# Modified by Lawrence Mitchell, 2014
__version__ = "1.4.0"
########## README
# Imports here should be what the user sees when doing "from ufl import *",
# which means we should _not_ import f.ex. "Grad", but "grad".
# This way we expose the language, the operation "grad", but less
# of the implementation, the particular class "Grad".
##########
# Utility functions (product is the counterpart of the built-in
# python function sum, can be useful for users as well?)
from ufl.common import product
# Output control
from ufl.log import get_handler, get_logger, set_handler, set_level, add_logfile, \
UFLException, DEBUG, INFO, WARNING, ERROR, CRITICAL
# Types for geometric quantities
from ufl.cell import as_cell, Cell, ProductCell, OuterProductCell
from ufl.domain import as_domain, Domain, ProductDomain
from ufl.geometry import (
SpatialCoordinate,
FacetNormal, CellNormal,
CellVolume, Circumradius,
FacetArea, MinFacetEdgeLength, MaxFacetEdgeLength,
)
# Sobolev spaces
from ufl.sobolevspace import L2, H1, H2, HDiv, HCurl
# Finite elements classes
from ufl.finiteelement import FiniteElementBase, FiniteElement, \
MixedElement, VectorElement, TensorElement, EnrichedElement, \
RestrictedElement, TensorProductElement, OuterProductElement, \
OuterProductVectorElement, HDiv, HCurl
# Hook to extend predefined element families
from ufl.finiteelement.elementlist import register_element, show_elements #, ufl_elements
# Arguments
from ufl.argument import Argument, TestFunction, TrialFunction, \
Arguments, TestFunctions, TrialFunctions
# Coefficients
from ufl.coefficient import Coefficient, Coefficients, \
Constant, VectorConstant, TensorConstant
# Split function
from ufl.split_functions import split
# Literal constants
from ufl.constantvalue import PermutationSymbol, Identity, zero, as_ufl
# Indexing of tensor expressions
from ufl.indexing import Index, indices
# Special functions for expression base classes
# (ensure this is imported, since it attaches operators to Expr)
import ufl.exproperators as __exproperators
# Containers for expressions with value rank > 0
from ufl.tensors import as_tensor, as_vector, as_matrix, relabel
from ufl.tensors import unit_vector, unit_vectors, unit_matrix, unit_matrices
# Operators
from ufl.operators import rank, shape, \
outer, inner, dot, cross, perp, \
det, inv, cofac, \
transpose, tr, diag, diag_vector, \
dev, skew, sym, \
sqrt, exp, ln, erf, \
cos, sin, tan, \
acos, asin, atan, atan_2, \
cosh, sinh, tanh, \
bessel_J, bessel_Y, bessel_I, bessel_K, \
eq, ne, le, ge, lt, gt, And, Or, Not, \
conditional, sign, Max, Min, \
variable, diff, \
Dx, grad, div, curl, rot, nabla_grad, nabla_div, Dn, exterior_derivative, \
jump, avg, cell_avg, facet_avg, \
elem_mult, elem_div, elem_pow, elem_op
# Measure classes
from ufl.measure import Measure, register_integral_type, integral_types
# Form class
from ufl.form import Form, replace_integral_domains
# Integral classes
from ufl.integral import Integral
# Special functions for Measure class
# (ensure this is imported, since it attaches operators to Measure)
import ufl.measureoperators as __measureoperators
# Representations of transformed forms
from ufl.formoperators import replace, derivative, action, energy_norm, rhs, lhs,\
system, functional, adjoint, sensitivity_rhs #, dirichlet_functional
# Predefined convenience objects
from ufl.objects import \
vertex, interval, triangle, tetrahedron, \
quadrilateral, hexahedron, facet, cell1D, cell2D, cell3D, \
i, j, k, l, p, q, r, s, \
dx, ds, ds_b, ds_t, ds_tb, ds_v, dS, dS_h, dS_v, dP, dc, dE
# Useful constants
from math import e, pi
__all__ = [
'product',
'get_handler', 'get_logger', 'set_handler', 'set_level', 'add_logfile',
'UFLException', 'DEBUG', 'INFO', 'WARNING', 'ERROR', 'CRITICAL',
'as_cell', 'Cell', 'ProductCell', 'OuterProductCell',
'as_domain', 'Domain', 'ProductDomain',
'L2', 'H1', 'H2', 'HCurl', 'HDiv',
'SpatialCoordinate',
'CellVolume', 'Circumradius',
'FacetArea', 'MinFacetEdgeLength', 'MaxFacetEdgeLength',
'FacetNormal', 'CellNormal',
'FiniteElementBase', 'FiniteElement',
'MixedElement', 'VectorElement', 'TensorElement', 'EnrichedElement',
'RestrictedElement', 'TensorProductElement', 'OuterProductElement',
'OuterProductVectorElement', 'HDiv', 'HCurl',
'register_element', 'show_elements',
'Argument', 'TestFunction', 'TrialFunction',
'Arguments', 'TestFunctions', 'TrialFunctions',
'Coefficient', 'Coefficients',
'Constant', 'VectorConstant', 'TensorConstant',
'split',
'PermutationSymbol', 'Identity', 'zero', 'as_ufl',
'Index', 'indices',
'as_tensor', 'as_vector', 'as_matrix', 'relabel',
'unit_vector', 'unit_vectors', 'unit_matrix', 'unit_matrices',
'rank', 'shape',
'outer', 'inner', 'dot', 'cross', 'perp',
'det', 'inv', 'cofac',
'transpose', 'tr', 'diag', 'diag_vector', 'dev', 'skew', 'sym',
'sqrt', 'exp', 'ln', 'erf',
'cos', 'sin', 'tan',
'acos', 'asin', 'atan', 'atan_2',
'cosh', 'sinh', 'tanh',
'bessel_J', 'bessel_Y', 'bessel_I', 'bessel_K',
'eq', 'ne', 'le', 'ge', 'lt', 'gt', 'And', 'Or', 'Not',
'conditional', 'sign', 'Max', 'Min',
'variable', 'diff',
'Dx', 'grad', 'div', 'curl', 'rot', 'nabla_grad', 'nabla_div', 'Dn', 'exterior_derivative',
'jump', 'avg', 'cell_avg', 'facet_avg',
'elem_mult', 'elem_div', 'elem_pow', 'elem_op',
'Form',
'Integral', 'Measure', 'register_integral_type', 'integral_types',
'replace', 'replace_integral_domains', 'derivative', 'action', 'energy_norm', 'rhs', 'lhs',
'system', 'functional', 'adjoint', 'sensitivity_rhs',
'dx', 'ds', 'ds_b', 'ds_t', 'ds_tb', 'ds_v', 'dS', 'dS_h', 'dS_v', 'dP', 'dc', 'dE',
'vertex', 'interval', 'triangle', 'tetrahedron',
'quadrilateral', 'hexahedron', 'facet',
'cell1D', 'cell2D', 'cell3D',
'i', 'j', 'k', 'l', 'p', 'q', 'r', 's',
'e', 'pi',
]
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