sympy/functions/special/error_functions.py

   1
   2 from sympy.core.basic import Basic, S, cache_it, cache_it_immutable
   3 from sympy.core.function import SingleValuedFunction
   4
   5 ###############################################################################
   6 ################################ ERROR FUNCTION ###############################
   7 ###############################################################################
   8
   9 class erf(SingleValuedFunction):
  10
  11     nofargs = 1
  12
  13     def fdiff(self, argindex=1):
  14         if argindex == 1:
  15             return 2*Basic.exp(-self[0]**2)/Basic.sqrt(S.Pi)
  16         else:
  17             raise ArgumentIndexError(self, argindex)
  18
  19     @classmethod
  20     def _eval_apply_subs(cls, *args):
  21         return
  22
  23     @classmethod
  24     def _eval_apply(self, arg):
  25         arg = Basic.sympify(arg)
  26
  27         if isinstance(arg, Basic.Number):
  28             if isinstance(arg, Basic.NaN):
  29                 return S.NaN
  30             elif isinstance(arg, Basic.Infinity):
  31                 return S.One
  32             elif isinstance(arg, Basic.NegativeInfinity):
  33                 return S.NegativeOne
  34             elif isinstance(arg, Basic.Zero):
  35                 return S.Zero
  36             elif arg.is_negative:
  37                 return -self(-arg)
  38         elif isinstance(arg, Basic.Mul):
  39             coeff, terms = arg.as_coeff_terms()
  40
  41             if coeff.is_negative:
  42                 return -self(-arg)
  43
  44     @classmethod
  45     @cache_it_immutable
  46     def taylor_term(self, n, x, *previous_terms):
  47         if n < 0 or n % 2 == 0:
  48             return S.Zero
  49         else:
  50             x = Basic.sympify(x)
  51
  52             k = (n - 1)/2
  53
  54             if len(previous_terms) > 2:
  55                 return -previous_terms[-2] * x**2 * (n-2)/(n*k)
  56             else:
  57                 return 2*(-1)**k * x**n/(n*Basic.Factorial(k)*Basic.sqrt(S.Pi))
  58
  59     def _eval_as_leading_term(self, x):
  60         arg = self[0].as_leading_term(x)
  61
  62         if Basic.Order(1,x).contains(arg):
  63             return arg
  64         else:
  65             return self.func(arg)
  66
  67     def _eval_is_real(self):
  68         return self[0].is_real
  69
  70     @classmethod
  71     def _eval_apply_evalf(self, arg):
  72         arg = arg.evalf()
  73
  74         if isinstance(arg, Basic.Number):
  75             # Temporary hack
  76             from sympy.core.numbers import Real
  77             from sympy.numerics import evalf
  78             from sympy.numerics.functions2 import erf
  79             e = erf(evalf(arg))
  80             return Real(str(e))
  81