Esempio n. 1
0
    def _eval_apply_evalf(self, arg):
        arg = arg.evalf()

        if isinstance(arg, Basic.Number):
            # Temporary hack
            from sympy.core.numbers import Real
            from sympy.numerics import evalf
            from sympy.numerics.functions2 import erf
            e = erf(evalf(arg))
            return Real(str(e))
Esempio n. 2
0
    def confidence(s, p):
        """Return a symmetric (p*100)% confidence interval. For example,
        p=0.95 gives a 95% confidence interval. Currently this function
        only handles numerical values except in the trivial case p=1.

        Examples usage:
            # One standard deviation
            >>> N = Normal(0, 1)
            >>> N.confidence(0.68)
            (-0.994457883209753, 0.994457883209753)
            >>> N.probability(*_).evalf()
            0.68

            # Two standard deviations
            >>> N = Normal(0, 1)
            >>> N.confidence(0.95)
            (-1.95996398454005, 1.95996398454005)
            >>> N.probability(*_).evalf()
            0.95
        """

        if p == 1:
            return (-oo, oo)

        assert p <= 1

        # In terms of n*sigma, we have n = sqrt(2)*ierf(p). The inverse
        # error function is not yet implemented in SymPy but can easily be
        # computed numerically

        from sympy.numerics import Float, secant, evalf
        from sympy.numerics.functions2 import erf
        p = evalf(p)
        # calculate y = ierf(p) by solving erf(y) - p = 0
        y = secant(lambda y: erf(y) - p, 0)
        t = Real(str(evalf(s.sigma) * Float(2)**0.5 * y))
        mu = s.mu.evalf()
        return (mu-t, mu+t)