"""Folded normal distribution."""
import numpy
from scipy import special
from ..baseclass import SimpleDistribution, ShiftScaleDistribution
class folded_normal(SimpleDistribution):
"""Folded normal distribution."""
def __init__(self, c=1):
super(folded_normal, self).__init__(dict(c=c))
def _pdf(self, x, c):
return (
numpy.sqrt(2.0 / numpy.pi)
* numpy.cosh(c * x)
* numpy.exp(-(x * x + c * c) / 2.0)
)
def _cdf(self, x, c):
return special.ndtr(x - c) + special.ndtr(x + c) - 1.0
def _lower(self, c):
return 0.0
def _upper(self, c):
return 8 + c
[docs]class FoldedNormal(ShiftScaleDistribution):
"""
Folded normal distribution.
Args:
mu (float, Distribution):
Location parameter in normal distribution.
scale (float, Distribution):
Scaling parameter (in both normal and fold).
shift (float, Distribution):
Location of fold.
Examples:
>>> distribution = chaospy.FoldedNormal(1.5)
>>> distribution
FoldedNormal(1.5)
>>> uloc = numpy.linspace(0, 1, 6)
>>> uloc
array([0. , 0.2, 0.4, 0.6, 0.8, 1. ])
>>> xloc = distribution.inv(uloc)
>>> xloc.round(3)
array([0. , 0.706, 1.254, 1.755, 2.342, 9.5 ])
>>> numpy.allclose(distribution.fwd(xloc), uloc)
True
>>> distribution.pdf(xloc).round(3)
array([0.259, 0.326, 0.396, 0.388, 0.28 , 0. ])
>>> distribution.sample(4).round(3)
array([1.906, 2.225, 1.638, 2.701])
"""
[docs] def __init__(self, mu=0, scale=1, shift=0):
super(FoldedNormal, self).__init__(
dist=folded_normal(mu - shift),
scale=scale,
shift=shift,
repr_args=[mu],
)