python-ufl 1.4.0-1 / usr / lib / python2.7 / dist-packages / ufl / algorithms / analysis.py

"""Utility algorithms for inspection of and information extraction from UFL objects in various ways."""

# Copyright (C) 2008-2014 Martin Sandve Alnes
#
# 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 Anders Logg, 2009-2010.
# Modified by Johan Hake, 2010.

from itertools import izip, chain
from collections import namedtuple

from ufl.log import error, warning, info
from ufl.assertions import ufl_assert
from ufl.sorting import topological_sorting
from ufl.common import sorted_by_count

from ufl.expr import Expr
from ufl.terminal import Terminal, FormArgument
from ufl.finiteelement import MixedElement, RestrictedElement
from ufl.argument import Argument
from ufl.coefficient import Coefficient
from ufl.variable import Variable
from ufl.indexing import Index, MultiIndex
from ufl.geometry import Domain
from ufl.integral import Measure, Integral
from ufl.form import Form
from ufl.algorithms.traversal import iter_expressions, post_traversal, post_walk, traverse_terminals

#--- Utilities to extract information from an expression ---

# TODO: Some of these can possibly be optimised by implementing inlined stack based traversal algorithms

def extract_classes(a):
    """Build a set of all unique Expr subclasses used in a.
    The argument a can be a Form, Integral or Expr."""
    return set(o._uflclass
               for e in iter_expressions(a)
               for o in post_traversal(e))

def extract_type(a, ufl_type):
    """Build a set of all objects of class ufl_type found in a.
    The argument a can be a Form, Integral or Expr."""
    if issubclass(ufl_type, Terminal):
        return set(o for e in iter_expressions(a)
                   for o in traverse_terminals(e)
                   if isinstance(o, ufl_type))
    return set(o for e in iter_expressions(a)
               for o in post_traversal(e)
               if isinstance(o, ufl_type))

def expr_has_terminal_types(expr, ufl_types):
    input = [expr]
    while input:
        e = input.pop()
        ops = e.operands()
        if ops:
            input.extend(ops)
        elif isinstance(e, ufl_types):
            return True
    return False

def expr_has_types(expr, ufl_types):
    input = [expr]
    while input:
        e = input.pop()
        if isinstance(e, ufl_types):
            return True
        input.extend(e.operands())
    return False

def has_type(a, ufl_types):
    """Check if any class from ufl_types is found in a.
    The argument a can be a Form, Integral or Expr."""
    if issubclass(ufl_types, Expr):
        ufl_types = (ufl_types,)
    if all(issubclass(ufl_type, Terminal) for ufl_type in ufl_types):
        return any(expr_has_terminal_types(e, ufl_types)
                   for e in iter_expressions(a))
    else:
        return any(expr_has_types(e, ufl_types)
                   for e in iter_expressions(a))

def extract_terminals(a):
    "Build a set of all Terminal objects in a."
    return set(o for e in iter_expressions(a) \
                 for o in post_traversal(e) \
                 if isinstance(o, Terminal))

def sorted_by_number_and_part(seq):
    return sorted(seq, key=lambda x: (x.number(), x.part()))

def extract_arguments(a):
    """Build a sorted list of all arguments in a,
    which can be a Form, Integral or Expr."""
    return sorted_by_number_and_part(extract_type(a, Argument))

def extract_coefficients(a):
    """Build a sorted list of all coefficients in a,
    which can be a Form, Integral or Expr."""
    return sorted_by_count(extract_type(a, Coefficient))

def extract_arguments_and_coefficients(a):
    """Build two sorted lists of all arguments and coefficients
    in a, which can be a Form, Integral or Expr."""

    # This function is faster than extract_arguments + extract_coefficients
    # for large forms, and has more validation built in.

    # Extract lists of all form argument instances
    terminals = extract_type(a, FormArgument)
    arguments = [f for f in terminals if isinstance(f, Argument)]
    coefficients = [f for f in terminals if isinstance(f, Coefficient)]

    # Build number,part: instance mappings, should be one to one
    bfnp = dict((f, (f.number(), f.part())) for f in arguments)
    if len(bfnp) != len(set(bfnp.values())):
        msg = """\
Found different Arguments with same number and part.
Did you combine test or trial functions from different spaces?
The Arguments found are:\n%s""" % "\n".join("  %s" % f for f in arguments)
        error(msg)

    # Build count: instance mappings, should be one to one
    fcounts = dict((f, f.count()) for f in coefficients)
    if len(fcounts) != len(set(fcounts.values())):
        msg = """\
Found different coefficients with same counts.
The arguments found are:\n%s""" % "\n".join("  %s" % f for f in coefficients)
        error(msg)

    # Passed checks, so we can safely sort the instances by count
    arguments = sorted_by_number_and_part(arguments)
    coefficients = sorted_by_count(coefficients)

    return arguments, coefficients

def build_coefficient_replace_map(coefficients, element_mapping=None):
    """Create new Coefficient objects
    with count starting at 0. Return mapping from old
    to new objects, and lists of the new objects."""
    if element_mapping is None:
        element_mapping = {}
    def remap(args):
        for (i, f) in enumerate(args):
            old_e = f.element()
            new_e = element_mapping.get(old_e, old_e)
            yield f.reconstruct(element=new_e, count=i)
    new_coefficients = list(remap(coefficients))
    replace_map = dict(izip(coefficients, new_coefficients))
    return new_coefficients, replace_map

# alternative implementation, kept as an example:
def _extract_coefficients(a):
    """Build a sorted list of all coefficients in a,
    which can be a Form, Integral or Expr."""
    # build set of all unique coefficients
    s = set()
    def func(o):
        if isinstance(o, Coefficient):
            s.add(o)
    post_walk(a, func)
    # sort by count
    return sorted_by_count(s)

def extract_elements(form):
    "Build sorted tuple of all elements used in form."
    args = chain(extract_arguments(form), extract_coefficients(form))
    return tuple(f.element() for f in args)

def extract_unique_elements(form):
    "Build sorted tuple of all unique elements used in form."
    return unique_tuple(extract_elements(form))

def extract_sub_elements(elements):
    "Build sorted tuple of all sub elements (including parent element)."
    sub_elements = tuple(chain(*[e.sub_elements() for e in elements]))
    if not sub_elements: return tuple(elements)
    return tuple(elements) + extract_sub_elements(sub_elements)

def extract_unique_sub_elements(elements):
    "Build sorted tuple of all unique sub elements (including parent element)."
    return unique_tuple(extract_sub_elements(elements))

def extract_element_map(elements):
    "Build map from elements to element index in ordered tuple."
    element_map = {}
    unique_elements = unique_tuple(elements)
    for element in elements:
        indices = [i for (i, e) in enumerate(unique_elements) if e == element]
        ufl_assert(len(indices) == 1, "Unable to find unique index for element.")
        element_map[element] = i
    return element_map

def extract_indices(expression):
    "Build a set of all Index objects used in expression."
    warning("Is this used for anything? Doesn't make much sense.")
    multi_indices = extract_type(expression, MultiIndex)
    indices = set()
    for mi in multi_indices:
        indices.update(i for i in mi if isinstance(i, Index))
    return indices

def extract_variables(a):
    """Build a list of all Variable objects in a,
    which can be a Form, Integral or Expr.
    The ordering in the list obeys dependency order."""
    handled = set()
    variables = []
    for e in iter_expressions(a):
        for o in post_traversal(e):
            if isinstance(o, Variable):
                expr, label = o.operands()
                if not label in handled:
                    variables.append(o)
                    handled.add(label)
    return variables

def extract_duplications(expression):
    "Build a set of all repeated expressions in expression."
    # TODO: Handle indices in a canonical way, maybe create a transformation that does this to apply before extract_duplications?
    ufl_assert(isinstance(expression, Expr), "Expecting UFL expression.")
    handled = set()
    duplicated = set()
    for o in post_traversal(expression):
        if o in handled:
            duplicated.add(o)
        handled.add(o)
    return duplicated

def count_nodes(expr, ids=None):
    "Count the number of unique Expr instances in expression."
    i = id(expr)
    if ids is None:
        ids = set()
    elif i in ids:
        # Skip already visited subtrees
        return
    # Extend set with children recursively
    for o in expr.operands():
        count_nodes(o, ids)
    ids.add(i)
    return len(ids)

def extract_max_quadrature_element_degree(integral):
    """Extract quadrature integration order from quadrature
    elements in integral. Returns None if not found."""
    quadrature_elements = [e for e in extract_elements(integral) if "Quadrature" in e.family()]
    degrees = [element.degree() for element in quadrature_elements]
    degrees = [q for q in degrees if not q is None]
    if not degrees:
        return None
    max_degree = quadrature_elements[0].degree()
    ufl_assert(all(max_degree == q for q in degrees),
               "Incompatible quadrature elements specified (orders must be equal).")
    return max_degree

def estimate_quadrature_degree(integral):
    "Estimate the necessary quadrature order for integral using the sum of argument degrees."
    arguments = extract_arguments(integral)
    degrees = [v.element().degree() for v in arguments]
    if len(arguments) == 0:
        return None
    if len(arguments) == 1:
        return 2*degrees[0]
    return sum(degrees)

def unique_tuple(objects):
    "Return tuple of unique objects."
    unique_objects = []
    for object in objects:
        if not object in unique_objects:
            unique_objects.append(object)
    return tuple(unique_objects)

def extract_num_sub_domains(form):
    "Extract the upper limit of sub domain ids for each domain label/domain type."
    num_sub_domains = {}
    for integral in form.integrals():
        domain = integral.domain()
        label = None if domain is None else domain.label()
        if label not in num_sub_domains:
            num_sub_domains[label] = {}

        subdomain_id = integral.subdomain_id()
        max_subdomain_id = None
        if isinstance(subdomain_id, int):
            max_subdomain_id = subdomain_id
        elif isinstance(subdomain_id, tuple):
            max_subdomain_id = max(did for did in subdomain_id)

        integral_type = integral.integral_type()
        if max_subdomain_id is not None:
            prev = num_sub_domains[label].get(integral_type, 0)
            num_sub_domains[label][integral_type] = max(prev, max_subdomain_id + 1)

    return num_sub_domains

def sort_elements(elements):
    """
    Sort elements so that any sub elements appear before the
    corresponding mixed elements. This is useful when sub elements
    need to be defined before the corresponding mixed elements.

    The ordering is based on sorting a directed acyclic graph.
    """

    # Set nodes
    nodes = elements

    # Set edges
    edges = dict((node, []) for node in nodes)
    for element in elements:
        for sub_element in element.sub_elements():
            edges[element].append(sub_element)

    # Sort graph
    sorted_elements = topological_sorting(nodes, edges)

    # Reverse list of elements
    sorted_elements.reverse()

    return sorted_elements