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from sympy.core.function import Add, ArgumentIndexError, Function
from sympy.core.power import Pow
from sympy.core.singleton import S
from sympy.core.sorting import default_sort_key
from sympy.functions.elementary.exponential import exp, log
def _logaddexp(x1, x2, *, evaluate=True):
return log(Add(exp(x1, evaluate=evaluate), exp(x2, evaluate=evaluate), evaluate=evaluate))
_two = S.One*2
_ln2 = log(_two)
def _lb(x, *, evaluate=True):
return log(x, evaluate=evaluate)/_ln2
def _exp2(x, *, evaluate=True):
return Pow(_two, x, evaluate=evaluate)
def _logaddexp2(x1, x2, *, evaluate=True):
return _lb(Add(_exp2(x1, evaluate=evaluate),
_exp2(x2, evaluate=evaluate), evaluate=evaluate))
class logaddexp(Function):
""" Logarithm of the sum of exponentiations of the inputs.
Helper class for use with e.g. numpy.logaddexp
See Also
========
https://numpy.org/doc/stable/reference/generated/numpy.logaddexp.html
"""
nargs = 2
def __new__(cls, *args):
return Function.__new__(cls, *sorted(args, key=default_sort_key))
def fdiff(self, argindex=1):
"""
Returns the first derivative of this function.
"""
if argindex == 1:
wrt, other = self.args
elif argindex == 2:
other, wrt = self.args
else:
raise ArgumentIndexError(self, argindex)
return S.One/(S.One + exp(other-wrt))
def _eval_rewrite_as_log(self, x1, x2, **kwargs):
return _logaddexp(x1, x2)
def _eval_evalf(self, *args, **kwargs):
return self.rewrite(log).evalf(*args, **kwargs)
def _eval_simplify(self, *args, **kwargs):
a, b = (x.simplify(**kwargs) for x in self.args)
candidate = _logaddexp(a, b)
if candidate != _logaddexp(a, b, evaluate=False):
return candidate
else:
return logaddexp(a, b)
class logaddexp2(Function):
""" Logarithm of the sum of exponentiations of the inputs in base-2.
Helper class for use with e.g. numpy.logaddexp2
See Also
========
https://numpy.org/doc/stable/reference/generated/numpy.logaddexp2.html
"""
nargs = 2
def __new__(cls, *args):
return Function.__new__(cls, *sorted(args, key=default_sort_key))
def fdiff(self, argindex=1):
"""
Returns the first derivative of this function.
"""
if argindex == 1:
wrt, other = self.args
elif argindex == 2:
other, wrt = self.args
else:
raise ArgumentIndexError(self, argindex)
return S.One/(S.One + _exp2(other-wrt))
def _eval_rewrite_as_log(self, x1, x2, **kwargs):
return _logaddexp2(x1, x2)
def _eval_evalf(self, *args, **kwargs):
return self.rewrite(log).evalf(*args, **kwargs)
def _eval_simplify(self, *args, **kwargs):
a, b = (x.simplify(**kwargs).factor() for x in self.args)
candidate = _logaddexp2(a, b)
if candidate != _logaddexp2(a, b, evaluate=False):
return candidate
else:
return logaddexp2(a, b)
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