python source code of trunc_normal

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"""Truncated normal distribution."""
import numpy
from scipy import special

from ..baseclass import Dist


class TruncNormal(Dist):
    """
    Truncated normal distribution

    Args:
        lower (float, Dist):
            Location of lower threshold
        upper (float, Dist):
            Location of upper threshold
        mu (float, Dist):
            Mean of normal distribution
        sigma (float, Dist):
            Standard deviation of normal distribution

    Examples:
        >>> distribution = chaospy.TruncNormal(2, 4, 2, 2)
        >>> distribution
        TruncNormal(lower=2, mu=2, sigma=2, upper=4)
        >>> q = numpy.linspace(0, 1, 5)
        >>> distribution.inv(q).round(4)
        array([2.    , 2.4311, 2.8835, 3.387 , 4.    ])
        >>> distribution.fwd(distribution.inv(q)).round(4)
        array([0.  , 0.25, 0.5 , 0.75, 1.  ])
        >>> distribution.pdf(distribution.inv(q)).round(4)
        array([1.1687, 1.1419, 1.0601, 0.9189, 0.7089])
        >>> distribution.sample(4).round(4)
        array([3.1841, 2.1971, 3.8643, 2.8501])
    """

    def __init__(self, lower=-1, upper=1, mu=0, sigma=1):
        self._repr = {"lower": lower, "upper": upper, "mu": mu, "sigma": sigma}
        Dist.__init__(self, a=lower, b=upper, sigma=sigma, mu=mu)

    def _pdf(self, x, a, b, mu, sigma):
        fa = special.ndtr((a-mu)/sigma)
        fb = special.ndtr((b-mu)/sigma)
        x = (x-mu)/sigma
        norm = (2*numpy.pi)**(-.5)*numpy.e**(-x**2/2.)
        return norm/(fb-fa)

    def _cdf(self, x, a, b, mu, sigma):
        fa = special.ndtr((a-mu)/sigma)
        fb = special.ndtr((b-mu)/sigma)
        x = special.ndtr((x-mu)/sigma)
        return (x - fa) / (fb-fa)

    def _ppf(self, q, a, b, mu, sigma):
        fa = special.ndtr((a-mu)/sigma)
        fb = special.ndtr((b-mu)/sigma)
        return special.ndtri(q*(fb-fa) + fa)*sigma + mu

    def _lower(self, a, b, mu, sigma):
        return a

    def _upper(self, a, b, mu, sigma):
        return b