Python iterables.preorder_traversal函数代码示例

def _aresame(a, b):
    """Return True if a and b are structurally the same, else False.

    Examples
    ========

    To SymPy, 2.0 == 2:

    >>> from sympy import S, Symbol, cos, sin
    >>> 2.0 == S(2)
    True

    Since a simple 'same or not' result is sometimes useful, this routine was
    written to provide that query:

    >>> from sympy.core.basic import _aresame
    >>> _aresame(S(2.0), S(2))
    False

    """
    from sympy.utilities.iterables import preorder_traversal
    from itertools import izip

    for i, j in izip(preorder_traversal(a), preorder_traversal(b)):
        if i != j or type(i) != type(j):
            return False
    else:
        return True

def test_preorder_traversal():
    expr = z+w*(x+y)
    expected1 = [z + w*(x + y), z, w*(x + y), w, x + y, y, x]
    expected2 = [z + w*(x + y), z, w*(x + y), w, x + y, x, y]
    expected3 = [z + w*(x + y), w*(x + y), w, x + y, y, x, z]
    assert list(preorder_traversal(expr)) in [expected1, expected2, expected3]

    expr = Piecewise((x,x<1),(x**2,True))
    assert list(preorder_traversal(expr)) == [
        Piecewise((x, x < 1), (x**2, True)), ExprCondPair(x, x < 1), x, x < 1,
        x, 1, ExprCondPair(x**2, True), x**2, x, 2, True
    ]
    assert list(postorder_traversal(Integral(x**2, (x, 0, 1)))) == [
        x, 2, x**2, x, 0, 1, Tuple(x, 0, 1),
        Integral(x**2, Tuple(x, 0, 1))
    ]
    assert list(postorder_traversal(('abc', ('d', 'ef')))) == [
        'abc', 'd', 'ef', ('d', 'ef'), ('abc', ('d', 'ef'))]

    expr = (x**(y**z)) ** (x**(y**z))
    expected = [(x**(y**z))**(x**(y**z)), x**(y**z), x**(y**z)]
    result = []
    pt = preorder_traversal(expr)
    for i in pt:
        result.append(i)
        if i == x**(y**z):
            pt.skip()
    assert result == expected

def _aresame(a, b):
    """Return True if a and b are structurally the same, else False.

    Examples
    ========

    To SymPy, 2.0 == 2:

    >>> from sympy import S, Symbol, cos, sin
    >>> 2.0 == S(2)
    True

    The Basic.compare method will indicate that these are not the same, but
    the same method allows symbols with different assumptions to compare the
    same:

    >>> S(2).compare(2.0)
    -1
    >>> Symbol('x').compare(Symbol('x', positive=True))
    0

    The Basic.compare method will not work with instances of FunctionClass:

    >>> sin.compare(cos)
    Traceback (most recent call last):
     File "<stdin>", line 1, in <module>
    TypeError: unbound method compare() must be called with sin instance as first ar
    gument (got FunctionClass instance instead)

    Since a simple 'same or not' result is sometimes useful, this routine was
    written to provide that query.

    """
    from sympy.utilities.iterables import preorder_traversal
    from itertools import izip

    try:
        if a.compare(b) == 0 and a.is_Symbol and b.is_Symbol:
            return a.assumptions0 == b.assumptions0
    except (TypeError, AttributeError):
        pass

    for i, j in izip(preorder_traversal(a), preorder_traversal(b)):
        if i == j and type(i) == type(j):
            continue
        return False
    return True

def test_postorder_traversal():
    expr = z+w*(x+y)
    expected1 = [z, w, y, x, x + y, w*(x + y), z + w*(x + y)]
    expected2 = [z, w, x, y, x + y, w*(x + y), z + w*(x + y)]
    expected3 = [w, y, x, x + y, w*(x + y), z, z + w*(x + y)]
    assert list(postorder_traversal(expr)) in [expected1, expected2, expected3]

    expr = Piecewise((x,x<1),(x**2,True))
    assert list(postorder_traversal(expr)) == [
        x, x, 1, x < 1, ExprCondPair(x, x < 1), x, 2, x**2, True,
        ExprCondPair(x**2, True), Piecewise((x, x < 1), (x**2, True))
    ]
    assert list(preorder_traversal(Integral(x**2, (x, 0, 1)))) == [
        Integral(x**2, (x, 0, 1)), x**2, x, 2, Tuple(x, 0, 1), x, 0, 1
    ]
    assert list(preorder_traversal(('abc', ('d', 'ef')))) == [
        ('abc', ('d', 'ef')), 'abc', ('d', 'ef'), 'd', 'ef']

def test_preorder_traversal():
    expr = z+w*(x+y)
    expected1 = [z + w*(x + y), z, w*(x + y), w, x + y, y, x]
    expected2 = [z + w*(x + y), z, w*(x + y), w, x + y, x, y]
    expected3 = [z + w*(x + y), w*(x + y), w, x + y, y, x, z]
    assert list(preorder_traversal(expr)) in [expected1, expected2, expected3]

    expr = Piecewise((x,x<1),(x**2,True))
    assert list(preorder_traversal(expr)) == [
        Piecewise((x, x < 1), (x**2, True)), ExprCondPair(x, x < 1), x, x < 1,
        x, 1, ExprCondPair(x**2, True), x**2, x, 2, True
    ]
    assert list(postorder_traversal(Integral(x**2, (x, 0, 1)))) == [
        x, 2, x**2, x, 0, 1, (0, 1), (x, (0, 1)), ((x, (0, 1)),),
        Integral(x**2, (x, 0, 1))
    ]
    assert list(postorder_traversal(('abc', ('d', 'ef')))) == [
        'abc', 'd', 'ef', ('d', 'ef'), ('abc', ('d', 'ef'))]

def sub_post(e):
    """ Replace Neg(x) with -x.
    """
    replacements = []
    for node in preorder_traversal(e):
        if isinstance(node, Neg):
            replacements.append((node, -node.args[0]))
    for node, replacement in replacements:
        e = e.xreplace({node: replacement})

    return e

def sub_post(e):
    """ Replace Sub(x,y) with the canonical form Add(x, Mul(NegativeOne(-1), y)).
    """
    replacements = []
    for node in preorder_traversal(e):
        if assumed(node, 'is_Sub'):
            replacements.append((node, Add(node.args[0], Mul(-1, node.args[1]))))
    for node, replacement in replacements:
        e = e.subs(node, replacement)

    return e

def mycollectsimp(expr):
    from sympy import collect
    counts = {}
    for subtree in preorder_traversal(expr):
        if isinstance(subtree, Symbol):
            counts[subtree] = counts.get(subtree, 0)+1
    counts = [(count, symbol) for symbol, count in counts.iteritems()]
    counts.sort()
    for count, symbol in counts:
        expr = collect(expr, symbol)
    return expr

def denoms(eq, x=None):
    """Return (recursively) set of all denominators that appear in eq
    that contain any symbol in x; if x is None (default) then all
    denominators with symbols will be returned."""
    from sympy.utilities.iterables import preorder_traversal

    if x is None:
        x = eq.free_symbols
    dens = set()
    pt = preorder_traversal(eq)
    for e in pt:
        if e.is_Pow or e.func is exp:
            n, d = e.as_numer_denom()
            if d in dens:
                pt.skip()
            elif d.has(*x):
                dens.add(d.as_base_exp()[0])
    return dens

def peel_terms(s):
    lim_min = None
    lim_max = None
    for p in preorder_traversal(s):
        if isinstance(p,Sum):
            lmin = p.limits[0][1]
            lmax = p.limits[0][2]
            if lim_min:
                lim_min = max(lmin,lim_min)
            else:
                lim_min = lmin
            if lim_max:
                lim_max = min(lmax,lim_max)
            else:
                lim_max = lmax
         
    p = peel_sum_terms(lim_min, lim_max)     
    new_s = rewrite(s,[(Sum,p)])
    return new_s

def _atomic(e):
    """Return atom-like quantities as far as substitution is
    concerned: Derivatives, Functions and Symbols. Don't
    return any 'atoms' that are inside such quantities unless
    they also appear outside, too.

    Examples
    ========
    >>> from sympy import Derivative, Function, cos
    >>> from sympy.abc import x, y
    >>> from sympy.core.basic import _atomic
    >>> f = Function('f')
    >>> _atomic(x + y)
    set([x, y])
    >>> _atomic(x + f(y))
    set([x, f(y)])
    >>> _atomic(Derivative(f(x), x) + cos(x) + y)
    set([y, cos(x), Derivative(f(x), x)])

    """
    from sympy import Derivative, Function, Symbol
    from sympy.utilities.iterables import preorder_traversal
    pot = preorder_traversal(e)
    seen = set()
    try:
        free = e.free_symbols
    except AttributeError:
        return set([e])
    atoms = set()
    for p in pot:
        if p in seen:
            pot.skip()
            continue
        seen.add(p)
        if isinstance(p, Symbol) and p in free:
            atoms.add(p)
        elif isinstance(p, (Derivative, Function)):
            pot.skip()
            atoms.add(p)
    return atoms

def sub_pre(e):
    """ Replace Add(x, Mul(NegativeOne(-1), y)) with Sub(x, y).
    """
    replacements = []
    for node in preorder_traversal(e):
        if assumed(node, 'is_Add'):
            positives = []
            negatives = []
            for arg in node.args:
                if (assumed(arg, 'is_Mul') and
                    assumed(arg.args[0], 'is_number') and
                    assumed(arg.args[0], 'is_negative')):
                    negatives.append(Mul(-arg.args[0], *arg.args[1:]))
                else:
                    positives.append(arg)
            if len(negatives) > 0:
                replacement = Sub(Add(*positives), Add(*negatives))
                replacements.append((node, replacement))
    for node, replacement in replacements:
        e = e.subs(node, replacement)

    return e

def sub_pre(e):
    """ Replace Add(x, Mul(NegativeOne(-1), y)) with Sub(x, y).
    """
    replacements = []
    for node in preorder_traversal(e):
        if node.is_Add:
            positives = []
            negatives = []
            for arg in node.args:
                if arg.is_Mul:
                    a, b = arg.as_two_terms()
                    if (a.is_number and a.is_negative):
                        negatives.append(Mul(-a, b))
                        continue
                positives.append(arg)
            if len(negatives) > 0:
                replacement = Sub(Add(*positives), Add(*negatives))
                replacements.append((node, replacement))
    for node, replacement in replacements:
        e = e.subs(node, replacement)

    return e

 def singles(self):
     counter = self.size-1
     while counter >= 0:
         command = self.commands[counter]
         if command.tag != "final":
             # do not consider end results
             # check for usage
             used = 0
             tmp = None
             for later_command in self.commands[counter+1:]:
                 if command.symbol in later_command.expr:
                     for subtree in preorder_traversal(later_command.expr):
                         if subtree == command.symbol:
                             used += 1
                             tmp = later_command
                         if isinstance(subtree, C.Pow) and subtree.exp == 2 and subtree.base == command.symbol:
                             used += 1
                             tmp = later_command
             if used == 1:
                 tmp.expr = tmp.expr.subs(command.symbol, command.expr)
                 print "SINGLE", command
                 del self.commands[counter]
         counter -= 1

def cse(exprs, symbols=None, optimizations=None):
    """ Perform common subexpression elimination on an expression.

    Parameters:

    exprs : list of sympy expressions, or a single sympy expression
        The expressions to reduce.
    symbols : infinite iterator yielding unique Symbols
        The symbols used to label the common subexpressions which are pulled
        out. The `numbered_symbols` generator is useful. The default is a stream
        of symbols of the form "x0", "x1", etc. This must be an infinite
        iterator.
    optimizations : list of (callable, callable) pairs, optional
        The (preprocessor, postprocessor) pairs. If not provided,
        `sympy.simplify.cse.cse_optimizations` is used.

    Returns:

    replacements : list of (Symbol, expression) pairs
        All of the common subexpressions that were replaced. Subexpressions
        earlier in this list might show up in subexpressions later in this list.
    reduced_exprs : list of sympy expressions
        The reduced expressions with all of the replacements above.
    """
    if symbols is None:
        symbols = numbered_symbols()
    else:
        # In case we get passed an iterable with an __iter__ method instead of
        # an actual iterator.
        symbols = iter(symbols)
    seen_subexp = set()
    muls = set()
    adds = set()
    to_eliminate = []
    to_eliminate_ops_count = []

    if optimizations is None:
        # Pull out the default here just in case there are some weird
        # manipulations of the module-level list in some other thread.
        optimizations = list(cse_optimizations)

    # Handle the case if just one expression was passed.
    if isinstance(exprs, Basic):
        exprs = [exprs]
    # Preprocess the expressions to give us better optimization opportunities.
    exprs = [preprocess_for_cse(e, optimizations) for e in exprs]

    # Find all of the repeated subexpressions.
    def insert(subtree):
        '''This helper will insert the subtree into to_eliminate while
        maintaining the ordering by op count and will skip the insertion
        if subtree is already present.'''
        ops_count = subtree.count_ops()
        index_to_insert = bisect.bisect(to_eliminate_ops_count, ops_count)
        # all i up to this index have op count <= the current op count
        # so check that subtree is not yet present from this index down
        # (if necessary) to zero.
        for i in xrange(index_to_insert - 1, -1, -1):
            if to_eliminate_ops_count[i] == ops_count and \
               subtree == to_eliminate[i]:
                return # already have it
        to_eliminate_ops_count.insert(index_to_insert, ops_count)
        to_eliminate.insert(index_to_insert, subtree)

    for expr in exprs:
        pt = preorder_traversal(expr)
        for subtree in pt:
            if subtree.is_Atom:
                # Exclude atoms, since there is no point in renaming them.
                continue

            if subtree in seen_subexp:
                insert(subtree)
                pt.skip()
                continue

            if subtree.is_Mul:
                muls.add(subtree)
            elif subtree.is_Add:
                adds.add(subtree)

            seen_subexp.add(subtree)

    # process adds - any adds that weren't repeated might contain
    # subpatterns that are repeated, e.g. x+y+z and x+y have x+y in common
    adds = [set(a.args) for a in adds]
    for i in xrange(len(adds)):
        for j in xrange(i + 1, len(adds)):
            com = adds[i].intersection(adds[j])
            if len(com) > 1:
                insert(Add(*com))

                # remove this set of symbols so it doesn't appear again
                adds[i] = adds[i].difference(com)
                adds[j] = adds[j].difference(com)
                for k in xrange(j + 1, len(adds)):
                    if not com.difference(adds[k]):
                        adds[k] = adds[k].difference(com)

    # process muls - any muls that weren't repeated might contain
#.........这里部分代码省略.........