/usr/share/pyshared/ffc/tensor/monomialextraction.py is in python-ffc 1.0.0-1.
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# Copyright (C) 2008-2009 Anders Logg
#
# 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/>.
#
# Modified by Martin Alnes, 2008
# Modified by Kristian B. Oelgaard
#
# First added: 2008-08-01
# Last changed: 2010-01-25
# UFL modules
from ufl.classes import Form, Argument, Coefficient, ScalarValue, IntValue
from ufl.algorithms import purge_list_tensors, apply_transformer, ReuseTransformer
# FFC modules
from ffc.log import info, debug, ffc_assert
# Cache for computed integrand representations
_cache = {}
def extract_monomial_form(integrals):
"""
Extract monomial representation of form (if possible). When
successful, the form is represented as a sum of products of scalar
components of basis functions or derivatives of basis functions.
If unsuccessful, MonomialException is raised.
"""
info("Extracting monomial form representation from UFL form")
# Iterate over all integrals
monomial_form = MonomialForm()
for integral in integrals:
# Get measure and integrand
measure = integral.measure()
integrand = integral.integrand()
# Extract monomial representation if possible
integrand = extract_monomial_integrand(integrand)
monomial_form.append(integrand, measure)
return monomial_form
def extract_monomial_integrand(integrand):
"Extract monomial integrand (if possible)."
# Check cache
if integrand in _cache:
debug("Reusing monomial integrand from cache")
return _cache[integrand]
# Purge list tensors
integrand = purge_list_tensors(integrand)
# Apply monomial transformer
monomial_integrand = apply_transformer(integrand, MonomialTransformer())
# Store in cache
_cache[integrand] = monomial_integrand
return monomial_integrand
class MonomialException(Exception):
"Exception raised when monomial extraction fails."
def __init__(self, *args, **kwargs):
Exception.__init__(self, *args, **kwargs)
class MonomialFactor:
"""
This class represents a monomial factor, that is, a derivative of
a scalar component of a basis function.
"""
def __init__(self, arg=None):
if isinstance(arg, MonomialFactor):
self.function = arg.function
self.components = arg.components
self.derivatives = arg.derivatives
self.restriction = arg.restriction
elif isinstance(arg, (Argument, Coefficient)):
self.function = arg
self.components = []
self.derivatives = []
self.restriction = None
elif arg is None:
self.function = None
self.components = []
self.derivatives = []
self.restriction = None
else:
raise MonomialException, ("Unable to create monomial from expression: " + str(arg))
def element(self):
return self.function.element()
def count(self):
return self.function.count()
def apply_derivative(self, indices):
self.derivatives += indices
def apply_restriction(self, restriction):
self.restriction = restriction
def replace_indices(self, old_indices, new_indices):
if old_indices is None:
self.components = new_indices
else:
_replace_indices(self.components, old_indices, new_indices)
_replace_indices(self.derivatives, old_indices, new_indices)
def __str__(self):
if len(self.components) == 0:
c = ""
else:
c = "[%s]" % ", ".join(str(c) for c in self.components)
if len(self.derivatives) == 0:
d0 = ""
d1 = ""
else:
d0 = "(" + " ".join("d/dx_%s" % str(d) for d in self.derivatives) + " "
d1 = ")"
if self.restriction is None:
r = ""
else:
r = "(%s)" % str(self.restriction)
return d0 + str(self.function) + r + c + d1
class Monomial:
"This class represents a product of monomial factors."
def __init__(self, arg=None):
if isinstance(arg, Monomial):
self.float_value = arg.float_value
self.factors = [MonomialFactor(v) for v in arg.factors]
self.index_slots = arg.index_slots
elif isinstance(arg, (MonomialFactor, Argument, Coefficient)):
self.float_value = 1.0
self.factors = [MonomialFactor(arg)]
self.index_slots = None
elif isinstance(arg, ScalarValue):
self.float_value = float(arg)
self.factors = []
self.index_slots = None
elif arg is None:
self.float_value = 1.0
self.factors = []
self.index_slots = None
else:
raise MonomialException, ("Unable to create monomial from expression: " + str(arg))
def apply_derivative(self, indices):
if not len(self.factors) == 1:
raise MonomialException, "Expecting a single factor."
self.factors[0].apply_derivative(indices)
def apply_tensor(self, indices):
if not self.index_slots is None:
raise MonomialException, "Expecting scalar-valued expression."
self.index_slots = indices
def apply_indices(self, indices):
for v in self.factors:
v.replace_indices(self.index_slots, indices)
self.index_slots = None
def apply_restriction(self, restriction):
for v in self.factors:
v.apply_restriction(restriction)
def __mul__(self, other):
m = Monomial()
m.float_value = self.float_value * other.float_value
m.factors = self.factors + other.factors
return m
def __str__(self):
if self.float_value == 1.0:
float_value = ""
else:
float_value = "%g * " % self.float_value
return float_value + " * ".join(str(v) for v in self.factors)
class MonomialSum:
"This class represents a sum of monomials."
def __init__(self, arg=None):
if isinstance(arg, MonomialSum):
self.monomials = [Monomial(m) for m in arg.monomials]
elif arg is None:
self.monomials = []
else:
self.monomials = [Monomial(arg)]
def apply_derivative(self, indices):
for m in self.monomials:
m.apply_derivative(indices)
def apply_tensor(self, indices):
for m in self.monomials:
m.apply_tensor(indices)
def apply_indices(self, indices):
for m in self.monomials:
m.apply_indices(indices)
def apply_restriction(self, restriction):
for m in self.monomials:
m.apply_restriction(restriction)
def __add__(self, other):
m0 = [Monomial(m) for m in self.monomials]
m1 = [Monomial(m) for m in other.monomials]
sum = MonomialSum()
sum.monomials = m0 + m1
return sum
def __mul__(self, other):
sum = MonomialSum()
for m0 in self.monomials:
for m1 in other.monomials:
sum.monomials.append(m0 * m1)
return sum
def __str__(self):
return " + ".join(str(m) for m in self.monomials)
class MonomialForm:
"""
This class represents a monomial form, that is, a sum of
integrals, each represented as a MonomialSum.
"""
def __init__(self):
self.integrals = []
def append(self, integral, measure):
self.integrals.append((integral, measure))
def __len__(self):
return len(self.integrals)
def __getitem__(self, i):
return self.integrals[i]
def __iter__(self):
return iter(self.integrals)
def __str__(self):
if len(self.integrals) == 0:
return "<Empty form>"
s = "Monomial form of %d integral(s)\n" % len(self.integrals)
s += len(s) * "-" + "\n"
for (integrand, measure) in self.integrals:
s += "Integrand: " + str(integrand) + "\n"
s += "Measure: " + str(measure) + "\n"
return s
class MonomialTransformer(ReuseTransformer):
"""
This class defines the transformation rules for extraction of a
monomial form represented as a MonomialSum from a UFL integral.
"""
def __init__(self):
ReuseTransformer.__init__(self)
def expr(self, o, *ops):
raise MonomialException, ("No handler defined for expression %s." % o._uflclass.__name__)
def terminal(self, o):
raise MonomialException, ("No handler defined for terminal %s." % o._uflclass.__name__)
def variable(self, o):
return self.visit(o.expression())
#--- Operator handles ---
def sum(self, o, s0, s1):
s = s0 + s1
return s
def product(self, o, s0, s1):
s = s0 * s1
return s
def index_sum(self, o, s, index):
return s
def indexed(self, o, s, indices):
s = MonomialSum(s)
s.apply_indices(indices)
return s
def component_tensor(self, o, s, indices):
s = MonomialSum(s)
s.apply_tensor(indices)
return s
def spatial_derivative(self, o, s, indices):
s = MonomialSum(s)
s.apply_derivative(indices)
return s
def positive_restricted(self, o, s):
s.apply_restriction("+")
return s
def negative_restricted(self, o, s):
s.apply_restriction("-")
return s
def power(self, o, s, ignored_exponent_expressed_as_sum):
(expr, exponent) = o.operands()
if not isinstance(exponent, IntValue):
raise MonomialException, "Cannot handle non-integer exponents."
p = MonomialSum(Monomial())
for i in range(int(exponent)):
p = p * s
return p
#--- Terminal handlers ---
def multi_index(self, multi_index):
indices = [index for index in multi_index]
return indices
def index(self, o):
raise MonomialException, "Not expecting to see an Index terminal."
def argument(self, v):
s = MonomialSum(v)
return s
def coefficient(self, v):
s = MonomialSum(v)
return s
def scalar_value(self, x):
s = MonomialSum(x)
return s
def _replace_indices(indices, old_indices, new_indices):
"Handle replacement of subsets of multi indices."
# Old and new indices must match
if not len(old_indices) == len(new_indices):
raise MonomialException, "Unable to replace indices, mismatching index dimensions."
# Build index map
index_map = {}
for (i, index) in enumerate(old_indices):
index_map[index] = new_indices[i]
# Check all indices and replace
for (i, index) in enumerate(indices):
if index in old_indices:
indices[i] = index_map[index]
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