/usr/share/pyshared/dolfin/functions/function.py is in python-dolfin 1.0.0-7.
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"""
# Copyright (C) 2009 Johan Hake
#
# This file is part of DOLFIN.
#
# DOLFIN 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.
#
# DOLFIN 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 DOLFIN. If not, see <http://www.gnu.org/licenses/>.
#
# First added: 2009-10-06
# Last changed: 2011-04-18
__all__ = ["Function", "TestFunction", "TrialFunction", "Argument",
"TestFunctions", "TrialFunctions"]
import types
# Import UFL and SWIG-generated extension module (DOLFIN C++)
import ufl
import dolfin.cpp as cpp
import numpy
from dolfin.functions.functionspace import FunctionSpaceBase
class MetaNoEvalOverloading(type):
def __init__(mcs, name, bases, dictionary):
if "eval" in dictionary:
raise TypeError, "cannot overload 'eval'"
class Function(ufl.Coefficient, cpp.Function):
"""
This class represents a function :math:`u_h` in a finite
element function space :math:`V_h`, given by
.. math::
u_h = \sum_{i=1}^n U_i \phi_i,
where :math:`\{\phi_i\}_{i=1}^n` is a basis for :math:`V_h`,
and :math:`U` is a vector of expansion coefficients for
:math:`u_h`.
*Arguments*
There is a maximum of two arguments. The first argument must be a
Function or a :py:class:`FunctionSpace
<dolfin.functions.functionspace.FunctionSpace>`.
If instantiated from another Function, the (optional)
second argument must be an integer denoting the number
of sub functions to extract.
*Examples*
Create a Function:
- from a :py:class:`FunctionSpace
<dolfin.functions.functionspace.FunctionSpace>` ``V``
.. code-block:: python
f = Function(V)
- from another Function ``f``
.. code-block:: python
g = Function(f)
- from a :py:class:`FunctionSpace
<dolfin.functions.functionspace.FunctionSpace>` ``V`` and a
:py:class:`GenericVector <dolfin.cpp.GenericVector>` ``v``
.. code-block:: python
g = Function(V, v)
- from a :py:class:`FunctionSpace
<dolfin.functions.functionspace.FunctionSpace>` and a
filename containg a :py:class:`GenericVector
<dolfin.cpp.GenericVector>`
.. code-block:: python
g = Function(V, 'MyVectorValues.xml')
"""
__metaclass__ = MetaNoEvalOverloading
def __init__(self, *args):
"""Initialize Function."""
# Check arguments
if len(args) == 0:
raise TypeError, "expected 1 or more arguments"
if not isinstance(args[0], (FunctionSpaceBase, Function)):
raise TypeError, "expected a FunctionSpace or a Function as argument 1"
# If using the copy constuctor
if isinstance(args[0], Function):
other = args[0]
# If using the copy constuctor
if len(args) == 1:
# Instantiate base classes
cpp.Function.__init__(self, other)
ufl.Coefficient.__init__(self, other._element)
return
# If using sub-function constructor
elif len(args) == 2 and isinstance(args[1], int):
i = args[1]
num_sub_spaces = other.function_space().num_sub_spaces()
if num_sub_spaces == 1:
raise RuntimeError, "No subfunctions to extract"
if not i < num_sub_spaces:
raise RuntimeError, "Can only extract subfunctions with i = 0..%d"% num_sub_spaces
cpp.Function.__init__(self, other, i)
ufl.Coefficient.__init__(self, self.function_space().ufl_element())
return
else:
raise TypeError, "expected one or two arguments when instantiating from another Function"
V = args[0]
# Instantiate ufl base class
ufl.Coefficient.__init__(self, V.ufl_element())
# Passing only the FunctionSpace
if len(args) == 1:
# Instantiate cpp base classes
cpp.Function.__init__(self, V)
elif len(args) == 2:
# If passing FunctionSpace together with cpp.Function
# Attached passed FunctionSpace and initialize the cpp.Function
# using the passed Function
if isinstance(args[1], cpp.Function):
if args[1].function_space().dim() != V.dim():
raise ValueError, "non matching dimensions on passed FunctionSpaces"
cpp.Function.__init__(self, args[1])
else:
cpp.Function.__init__(self, *args)
else:
raise TypeError, "too many arguments"
def _sub(self, i, deepcopy = False):
"""Return a sub function.
The sub functions are numbered from i = 0..N-1, where N is the
total number of sub spaces.
*Arguments*
i
The number of the sub function
"""
if not isinstance(i, int):
raise TypeError, "expects an 'int' as first argument"
num_sub_spaces = self.function_space().num_sub_spaces()
if num_sub_spaces == 1:
raise RuntimeError, "No subfunctions to extract"
if not i < num_sub_spaces:
raise RuntimeError, "Can only extract subfunctions with i = 0..%d"% num_sub_spaces
# Create and instantiate the Function
if deepcopy:
return Function(self.function_space().sub(i), cpp.Function._sub(self, i))
else:
return Function(self, i)
def split(self, deepcopy=False):
"""
Extract any sub functions.
A sub function can be extracted from a discrete function that
is in a :py:class:`MixedFunctionSpace
<dolfin.functions.functionspace.MixedFunctionSpace>` or in a
:py:class:`VectorFunctionSpace
<dolfin.functions.functionspace.VectorFunctionSpace>`. The sub
function resides in the subspace of the mixed space.
*Arguments*
deepcopy
Copy sub function vector instead of sharing
"""
num_sub_spaces = self.function_space().num_sub_spaces()
if num_sub_spaces == 1:
raise RuntimeError, "No subfunctions to extract"
return tuple(self._sub(i, deepcopy) for i in xrange(num_sub_spaces))
def ufl_element(self):
"""Return ufl element"""
return self._element
def __str__(self):
"""Return a pertty print representation of it self.
Use ufl.__str__ is used for this.
"""
return ufl.Coefficient.__str__(self)
def __repr__(self):
"""Return a str repr of it self.
Must use ufl.__repr__ for this"""
return ufl.Coefficient.__repr__(self)
def str(self, verose=False):
"""Return an informative str representation of itself"""
# FIXME: We might change this using rank and dimension instead
return "<Function in %s>" % str(self.function_space())
def ufl_evaluate(self, x, component, derivatives):
"""Function used by ufl to evaluate the Function"""
import numpy
import ufl
assert derivatives == () # TODO: Handle derivatives
if component:
shape = self.shape()
assert len(shape) == len(component)
value_size = ufl.common.product(shape)
index = ufl.common.component_to_index(component, shape)
values = numpy.zeros(value_size)
self(*x, values=values)
return values[index]
else:
# Scalar evaluation
return self(*x)
def __call__(self, *args, **kwargs):
"""
Evaluates the Function.
*Examples*
1) Using an iterable as x:
.. code-block:: python
fs = Expression("sin(x[0])*cos(x[1])*sin(x[3])")
x0 = (1.,0.5,0.5)
x1 = [1.,0.5,0.5]
x2 = numpy.array([1.,0.5,0.5])
v0 = fs(x0)
v1 = fs(x1)
v2 = fs(x2)
2) Using multiple scalar args for x, interpreted as a
point coordinate
.. code-block:: python
v0 = f(1.,0.5,0.5)
3) Using a Point
.. code-block:: python
p0 = Point(1.,0.5,0.5)
v0 = f(p0)
3) Passing return array
.. code-block:: python
fv = Expression(("sin(x[0])*cos(x[1])*sin(x[3])",
"2.0","0.0"))
x0 = numpy.array([1.,0.5,0.5])
v0 = numpy.zeros(3)
fv(x0, values = v0)
.. note::
A longer values array may be passed. In this way one can fast
fill up an array with different evaluations.
.. code-block:: python
values = numpy.zeros(9)
for i in xrange(0,10,3):
fv(x[i:i+3], values = values[i:i+3])
"""
if len(args)==0:
raise TypeError, "expected at least 1 argument"
# Test for ufl restriction
if len(args) == 1 and args[0] in ('+','-'):
return ufl.Coefficient.__call__(self, *args)
# Test for ufl mapping
if len(args) == 2 and isinstance(args[1], dict) and self in args[1]:
return ufl.Coefficient.__call__(self, *args)
# Some help variables
value_size = ufl.common.product(self.ufl_element().value_shape())
# If values (return argument) is passed, check the type and length
values = kwargs.get("values", None)
if values is not None:
if not isinstance(values, numpy.ndarray):
raise TypeError, "expected a NumPy array for 'values'"
if len(values) != value_size or \
not numpy.issubdtype(values.dtype, 'd'):
raise TypeError, "expected a double NumPy array of length"\
" %d for return values."%value_size
values_provided = True
else:
values_provided = False
values = numpy.zeros(value_size, dtype='d')
# Get the dimension of the cell
dim = self.ufl_element().cell().geometric_dimension()
# Assume all args are x argument
x = args
# If only one x argument has been provided, unpack it if it's an iterable
if len(x) == 1:
if isinstance(x[0], cpp.Point):
x = (x[0][i] for i in xrange(dim))
elif hasattr(x[0], '__iter__'):
x = x[0]
# Convert it to an 1D numpy array
try:
x = numpy.fromiter(x, 'd')
except (TypeError, ValueError, AssertionError):
raise TypeError, "expected scalar arguments for the coordinates"
if len(x) == 0:
raise TypeError, "coordinate argument too short"
if len(x) != dim:
raise TypeError, "expected the geometry argument to be of "\
"length %d"%dim
# The actual evaluation
self.eval(values, x)
# If scalar return statement, return scalar value.
if value_size == 1 and not values_provided:
return values[0]
return values
#--- Subclassing of ufl.{Basis, Trial, Test}Function ---
class Argument(ufl.Argument):
"""An Argument represents a possibly differentiated component
of an argument on the reference cell.
"""
def __init__(self, V, index=None):
if not isinstance(V, FunctionSpaceBase):
raise TypeError, "Illegal argument for creation of Argument, not a FunctionSpace: " + str(V)
ufl.Argument.__init__(self, V.ufl_element(), index)
self._V = V
def function_space(self):
"Return the FunctionSpace"
return self._V
def TrialFunction(V):
"""A TrialFunction is the Argument with the next lowest primary
index. We simply pick an index lower than almost all others (-1).
"""
return Argument(V, -1)
def TestFunction(V):
"""A TestFunction is the Argument with the lowest primary
index. We simply pick an index lower than all others (-2).
"""
return Argument(V, -2)
#--- TestFunctions and TrialFunctions ---
def TestFunctions(V):
"Create test functions from mixed function space."
return ufl.split(TestFunction(V))
def TrialFunctions(V):
"Create trial functions from mixed function space."
return ufl.split(TrialFunction(V))
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