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