def evalf_log(expr, prec, options):
arg = expr.args[0]
workprec = prec + 10
xre, xim, xacc, _ = evalf(arg, workprec, options)
if xim:
# XXX: use get_abs etc instead
re = evalf_log(
C.log(C.Abs(arg, evaluate=False), evaluate=False), prec, options)
im = mpf_atan2(xim, xre or fzero, prec)
return re[0], im, re[2], prec
imaginary_term = (mpf_cmp(xre, fzero) < 0)
re = mpf_log(mpf_abs(xre), prec, rnd)
size = fastlog(re)
if prec - size > workprec:
# We actually need to compute 1+x accurately, not x
arg = C.Add(S.NegativeOne, arg, evaluate=False)
xre, xim, _, _ = evalf_add(arg, prec, options)
prec2 = workprec - fastlog(xre)
# xre is now x - 1 so we add 1 back here to calculate x
re = mpf_log(mpf_abs(mpf_add(xre, fone, prec2)), prec, rnd)
re_acc = prec
if imaginary_term:
return re, mpf_pi(prec), re_acc, prec
else:
return re, None, re_acc, None
def _matches_commutative(self, expr, repl_dict={}, old=False):
"""
Matches Add/Mul "pattern" to an expression "expr".
repl_dict ... a dictionary of (wild: expression) pairs, that get
returned with the results
This function is the main workhorse for Add/Mul.
For instance:
>>> from sympy import symbols, Wild, sin
>>> a = Wild("a")
>>> b = Wild("b")
>>> c = Wild("c")
>>> x, y, z = symbols("x y z")
>>> (a+sin(b)*c)._matches_commutative(x+sin(y)*z)
{a_: x, b_: y, c_: z}
In the example above, "a+sin(b)*c" is the pattern, and "x+sin(y)*z" is
the expression.
The repl_dict contains parts that were already matched. For example
here:
>>> (x+sin(b)*c)._matches_commutative(x+sin(y)*z, repl_dict={a: x})
{a_: x, b_: y, c_: z}
the only function of the repl_dict is to return it in the
result, e.g. if you omit it:
>>> (x+sin(b)*c)._matches_commutative(x+sin(y)*z)
{b_: y, c_: z}
the "a: x" is not returned in the result, but otherwise it is
equivalent.
"""
# handle simple patterns
if self == expr:
return repl_dict
d = self._matches_simple(expr, repl_dict)
if d is not None:
return d
# eliminate exact part from pattern: (2+a+w1+w2).matches(expr) -> (w1+w2).matches(expr-a-2)
from .function import WildFunction
from .symbol import Wild
wild_part = []
exact_part = []
for p in ordered(self.args):
if p.has(Wild, WildFunction) and (not expr.has(p)):
# not all Wild should stay Wilds, for example:
# (w2+w3).matches(w1) -> (w1+w3).matches(w1) -> w3.matches(0)
wild_part.append(p)
else:
exact_part.append(p)
if exact_part:
exact = self.func(*exact_part)
free = expr.free_symbols
if free and (exact.free_symbols - free):
# there are symbols in the exact part that are not
# in the expr; but if there are no free symbols, let
# the matching continue
return None
newpattern = self.func(*wild_part)
newexpr = self._combine_inverse(expr, exact)
if not old and (expr.is_Add or expr.is_Mul):
if newexpr.count_ops() > expr.count_ops():
return None
return newpattern.matches(newexpr, repl_dict)
# now to real work ;)
i = 0
saw = set()
while expr not in saw:
saw.add(expr)
expr_list = (self.identity,) + tuple(ordered(self.make_args(expr)))
for last_op in reversed(expr_list):
for w in reversed(wild_part):
d1 = w.matches(last_op, repl_dict)
if d1 is not None:
d2 = self.xreplace(d1).matches(expr, d1)
if d2 is not None:
return d2
if i == 0:
if self.is_Mul:
# make e**i look like Mul
if expr.is_Pow and expr.exp.is_Integer:
if expr.exp > 0:
expr = C.Mul(*[expr.base, expr.base**(expr.exp - 1)], evaluate=False)
else:
expr = C.Mul(*[1/expr.base, expr.base**(expr.exp + 1)], evaluate=False)
i += 1
continue
elif self.is_Add:
# make i*e look like Add
c, e = expr.as_coeff_Mul()
if abs(c) > 1:
if c > 0:
expr = C.Add(*[e, (c - 1)*e], evaluate=False)
else:
expr = C.Add(*[-e, (c + 1)*e], evaluate=False)
i += 1
continue
# try collection on non-Wild symbols
from sympy.simplify.simplify import collect
was = expr
did = set()
for w in reversed(wild_part):
c, w = w.as_coeff_mul(Wild)
free = c.free_symbols - did
if free:
did.update(free)
expr = collect(expr, free)
if expr != was:
i += 0
continue
break # if we didn't continue, there is nothing more to do
return
