# Source code for ufl.sorting

```# -*- coding: utf-8 -*-
"""This module contains a sorting rule for expr objects that
is more robust w.r.t. argument numbering than using repr."""

# Copyright (C) 2008-2016 Martin Sandve Alnæs
#
# This file is part of UFL (https://www.fenicsproject.org)
#
#
# Modified by Anders Logg, 2009-2010.
# Modified by Johan Hake, 2010.

from functools import cmp_to_key

from ufl.core.expr import Expr
from ufl.argument import Argument
from ufl.coefficient import Coefficient
from ufl.core.multiindex import FixedIndex, MultiIndex
from ufl.variable import Label

def _cmp_multi_index(a, b):
# Careful not to depend on Index.count() here!
# This is placed first because it is most frequent.
# Make decision based on the first index pair possible
for i, j in zip(a._indices, b._indices):
fix1 = isinstance(i, FixedIndex)
fix2 = isinstance(j, FixedIndex)
if fix1 and fix2:
# Both are FixedIndex, sort by value
x, y = i._value, j._value
if x < y:
return -1
elif x > y:
return +1
else:
# Same value, no decision
continue
elif fix1:
# Sort fixed before free
return -1
elif fix2:
# Sort fixed before free
return +1
else:
# Both are Index, no decision, do not depend on count!
pass
# Failed to make a decision, return 0 by default
# (this does not mean equality, it could be e.g.
# [i,0] vs [j,0] because the counts of i,j cannot be used)
return 0

def _cmp_label(a, b):
# Don't compare counts! Causes circular problems when renumbering to get a canonical form.
# Therefore, even though a and b are not equal in general (__eq__ won't be True),
# but for this sorting they are considered equal and we return 0.
return 0

def _cmp_coefficient(a, b):
# It's ok to compare relative counts for Coefficients,
# since their ordering is a property of the form
x, y = a._count, b._count
if x < y:
return -1
elif x > y:
return +1
else:
return 0

def _cmp_argument(a, b):
# It's ok to compare relative number and part for Arguments,
# since their ordering is a property of the form
x = (a._number, a._part)
y = (b._number, b._part)
if x < y:
return -1
elif x > y:
return +1
else:
return 0

def _cmp_terminal_by_repr(a, b):
# The cost of repr on a terminal is fairly small, and bounded
x = repr(a)
y = repr(b)
return -1 if x < y else (0 if x == y else +1)

# Hack up a MultiFunction-like type dispatch for terminal comparisons
_terminal_cmps = [_cmp_terminal_by_repr] * Expr._ufl_num_typecodes_
_terminal_cmps[MultiIndex._ufl_typecode_] = _cmp_multi_index
_terminal_cmps[Argument._ufl_typecode_] = _cmp_argument
_terminal_cmps[Coefficient._ufl_typecode_] = _cmp_coefficient
_terminal_cmps[Label._ufl_typecode_] = _cmp_label

def cmp_expr(a, b):
"Replacement for cmp(a, b), removed in Python 3, for Expr objects."

# Modelled after pre_traversal to avoid recursion:
left = [(a, b)]
while left:
a, b = left.pop()

# First sort quickly by type code
x, y = a._ufl_typecode_, b._ufl_typecode_
if x != y:
return -1 if x < y else +1

# Now we know that the type is the same, check further based
# on type specific properties.
if a._ufl_is_terminal_:
c = _terminal_cmps[x](a, b)
if c:
return c
else:
# If the hash is the same, assume equal for the purpose of
# sorting.  This introduces a minor chance of
# nondeterministic behaviour, just as with MultiIndex.
# Although collected statistics for complicated forms
# suggest that the hash function is pretty good so there
# shouldn't be collisions.
# if hash(a) == hash(b): # FIXME: Test this for performance improvement.
#    return 0

# Delve into subtrees
aops = a.ufl_operands
bops = b.ufl_operands

# Sort by children in natural order
for (r, s) in zip(aops, bops):
# Skip subtree if objects are the same
if r is s:
continue
# Append subtree for further inspection
left.append((r, s))

# All children compare as equal, a and b must be
# equal. Except for...  A few types, notably ExprList and
# ExprMapping, can have a different number of operands.
# Sort by the length if it's different. Doing this after
# sorting by children because these types are rare so we
# try to avoid the cost of this check for most nodes.
x, y = len(aops), len(bops)
if x != y:
return -1 if x < y else +1

# Equal if we get out of the above loop!
return 0

def sorted_expr(sequence):
"Return a canonically sorted list of Expr objects in sequence."
return sorted(sequence, key=cmp_to_key(cmp_expr))

[docs]def sorted_expr_sum(seq):
seq2 = sorted(seq, key=cmp_to_key(cmp_expr))
s = seq2[0]
for e in seq2[1:]:
s = s + e
return s
```