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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)
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