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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.functions.elementary.exponential import log | |
| from sympy.functions.elementary.trigonometric import cos, sin | |
| def _cosm1(x, *, evaluate=True): | |
| return Add(cos(x, evaluate=evaluate), -S.One, evaluate=evaluate) | |
| class cosm1(Function): | |
| """ Minus one plus cosine of x, i.e. cos(x) - 1. For use when x is close to zero. | |
| Helper class for use with e.g. scipy.special.cosm1 | |
| See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.cosm1.html | |
| """ | |
| nargs = 1 | |
| def fdiff(self, argindex=1): | |
| """ | |
| Returns the first derivative of this function. | |
| """ | |
| if argindex == 1: | |
| return -sin(*self.args) | |
| else: | |
| raise ArgumentIndexError(self, argindex) | |
| def _eval_rewrite_as_cos(self, x, **kwargs): | |
| return _cosm1(x) | |
| def _eval_evalf(self, *args, **kwargs): | |
| return self.rewrite(cos).evalf(*args, **kwargs) | |
| def _eval_simplify(self, **kwargs): | |
| x, = self.args | |
| candidate = _cosm1(x.simplify(**kwargs)) | |
| if candidate != _cosm1(x, evaluate=False): | |
| return candidate | |
| else: | |
| return cosm1(x) | |
| def _powm1(x, y, *, evaluate=True): | |
| return Add(Pow(x, y, evaluate=evaluate), -S.One, evaluate=evaluate) | |
| class powm1(Function): | |
| """ Minus one plus x to the power of y, i.e. x**y - 1. For use when x is close to one or y is close to zero. | |
| Helper class for use with e.g. scipy.special.powm1 | |
| See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.powm1.html | |
| """ | |
| nargs = 2 | |
| def fdiff(self, argindex=1): | |
| """ | |
| Returns the first derivative of this function. | |
| """ | |
| if argindex == 1: | |
| return Pow(self.args[0], self.args[1])*self.args[1]/self.args[0] | |
| elif argindex == 2: | |
| return log(self.args[0])*Pow(*self.args) | |
| else: | |
| raise ArgumentIndexError(self, argindex) | |
| def _eval_rewrite_as_Pow(self, x, y, **kwargs): | |
| return _powm1(x, y) | |
| def _eval_evalf(self, *args, **kwargs): | |
| return self.rewrite(Pow).evalf(*args, **kwargs) | |
| def _eval_simplify(self, **kwargs): | |
| x, y = self.args | |
| candidate = _powm1(x.simplify(**kwargs), y.simplify(**kwargs)) | |
| if candidate != _powm1(x, y, evaluate=False): | |
| return candidate | |
| else: | |
| return powm1(x, y) | |