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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) | |