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