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38 lines
1.1 KiB
38 lines
1.1 KiB
from sympy.core.function import Add, ArgumentIndexError, Function
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from sympy.core.singleton import S
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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, x, **kwargs):
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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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