/usr/lib/python2.7/dist-packages/ffc/quadrature/symbol.py is in python-ffc 1.4.0-1.
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 | "This file implements a class to represent a symbol."
# Copyright (C) 2009-2011 Kristian B. Oelgaard
#
# This file is part of FFC.
#
# FFC 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.
#
# FFC 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 FFC. If not, see <http://www.gnu.org/licenses/>.
#
# First added: 2009-07-12
# Last changed: 2011-06-28
# FFC modules.
from ffc.log import error
from ffc.cpp import format
# FFC quadrature modules.
from symbolics import type_to_string
from symbolics import create_float
from symbolics import create_product
from symbolics import create_sum
from symbolics import create_fraction
from expr import Expr
class Symbol(Expr):
__slots__ = ("v", "base_expr", "base_op", "exp", "cond")
def __init__(self, variable, symbol_type, base_expr=None, base_op=0):
"""Initialise a Symbols object, it derives from Expr and contains
the additional variables:
v - string, variable name
base_expr - Other expression type like 'x*y + z'
base_op - number of operations for the symbol itself if it's a math
operation like std::cos(.) -> base_op = 1.
NOTE: self._prec = 1."""
# Dummy value, a symbol is always one.
self.val = 1.0
# Initialise variable, type and class.
self.v = variable
self.t = symbol_type
self._prec = 1
# Needed for symbols like std::cos(x*y + z),
# where base_expr = x*y + z.
# ops = base_expr.ops() + base_ops = 2 + 1 = 3
self.base_expr = base_expr
self.base_op = base_op
# If type of the base_expr is lower than the given symbol_type change type.
# TODO: Should we raise an error here? Or simply require that one
# initalise the symbol by Symbol('std::cos(x*y)', (x*y).t, x*y, 1).
if base_expr and base_expr.t < self.t:
self.t = base_expr.t
# Compute the representation now, such that we can use it directly
# in the __eq__ and __ne__ methods (improves performance a bit, but
# only when objects are cached).
if self.base_expr:# and self.exp is None:
self._repr = "Symbol('%s', %s, %s, %d)" % (self.v, type_to_string[self.t],\
self.base_expr._repr, self.base_op)
else:
self._repr = "Symbol('%s', %s)" % (self.v, type_to_string[self.t])
# Use repr as hash value.
self._hash = hash(self._repr)
# Print functions.
def __str__(self):
"Simple string representation which will appear in the generated code."
# print "sym str: ", self.v
return self.v
# Binary operators.
def __add__(self, other):
"Addition by other objects."
# NOTE: We expect expanded objects
# symbols, if other is a product, try to let product handle the addition.
# Returns x + x -> 2*x, x + 2*x -> 3*x.
if self._repr == other._repr:
return create_product([create_float(2), self])
elif other._prec == 2: # prod
return other.__add__(self)
return create_sum([self, other])
def __sub__(self, other):
"Subtract other objects."
# NOTE: We expect expanded objects
# symbols, if other is a product, try to let product handle the addition.
if self._repr == other._repr:
return create_float(0)
elif other._prec == 2: # prod
if other.get_vrs() == (self,):
return create_product([create_float(1.0 - other.val), self]).expand()
return create_sum([self, create_product([create_float(-1), other])])
def __mul__(self, other):
"Multiplication by other objects."
# NOTE: We assume expanded objects.
# If product will be zero.
if self.val == 0.0 or other.val == 0.0:
return create_float(0)
# If other is Sum or Fraction let them handle the multiply.
if other._prec in (3, 4): # sum or frac
return other.__mul__(self)
# If other is a float or symbol, create simple product.
if other._prec in (0, 1): # float or sym
return create_product([self, other])
# Else add variables from product.
return create_product([self] + other.vrs)
def __div__(self, other):
"Division by other objects."
# NOTE: We assume expanded objects.
# If division is illegal (this should definitely not happen).
if other.val == 0.0:
error("Division by zero.")
# Return 1 if the two symbols are equal.
if self._repr == other._repr:
return create_float(1)
# If other is a Sum we can only return a fraction.
# TODO: Refine this later such that x / (x + x*y) -> 1 / (1 + y)?
if other._prec == 3: # sum
return create_fraction(self, other)
# Handle division by FloatValue, Symbol, Product and Fraction.
# Create numerator and list for denominator.
num = [self]
denom = []
# Add floatvalue, symbol and products to the list of denominators.
if other._prec in (0, 1): # float or sym
denom = [other]
elif other._prec == 2: # prod
# Need copies, so can't just do denom = other.vrs.
denom += other.vrs
# fraction.
else:
# TODO: Should we also support division by fraction for generality?
# It should not be needed by this module.
error("Did not expected to divide by fraction.")
# Remove one instance of self in numerator and denominator if
# present in denominator i.e., x/(x*y) --> 1/y.
if self in denom:
denom.remove(self)
num.remove(self)
# Loop entries in denominator and move float value to numerator.
for d in denom:
# Add the inverse of a float to the numerator, remove it from
# the denominator and continue.
if d._prec == 0: # float
num.append(create_float(1.0/other.val))
denom.remove(d)
continue
# Create appropriate return value depending on remaining data.
# Can only be for x / (2*y*z) -> 0.5*x / (y*z).
if len(num) > 1:
num = create_product(num)
# x / (y*z) -> x/(y*z),
elif num:
num = num[0]
# else x / (x*y) -> 1/y.
else:
num = create_float(1)
# If we have a long denominator, create product and fraction.
if len(denom) > 1:
return create_fraction(num, create_product(denom))
# If we do have a denominator, but only one variable don't create a
# product, just return a fraction using the variable as denominator.
elif denom:
return create_fraction(num, denom[0])
# If we don't have any donominator left, return the numerator.
# x / 2.0 -> 0.5*x.
return num.expand()
# Public functions.
def get_unique_vars(self, var_type):
"Get unique variables (Symbols) as a set."
# Return self if type matches, also return base expression variables.
s = set()
if self.t == var_type:
s.add(self)
if self.base_expr:
s.update(self.base_expr.get_unique_vars(var_type))
return s
def get_var_occurrences(self):
"""Determine the number of times all variables occurs in the expression.
Returns a dictionary of variables and the number of times they occur."""
# There is only one symbol.
return {self:1}
def ops(self):
"Returning the number of floating point operation for symbol."
# Get base ops, typically 1 for sin() and then add the operations
# for the base (sin(2*x + 1)) --> 2 + 1.
if self.base_expr:
return self.base_op + self.base_expr.ops()
return self.base_op
from floatvalue import FloatValue
from product import Product
from sumobj import Sum
from fraction import Fraction
|