"""Nataf (normal) copula."""
import numpy
from scipy import special
from .baseclass import Copula
from ..baseclass import Dist
class nataf(Dist):
"""Nataf (normal) copula."""
def __init__(self, R, ordering=None):
if ordering is None:
ordering = range(len(R))
ordering = numpy.array(ordering)
P = numpy.eye(len(R))[ordering]
R = numpy.dot(P, numpy.dot(R, P.T))
R = numpy.linalg.cholesky(R)
R = numpy.dot(P.T, numpy.dot(R, P))
Ci = numpy.linalg.inv(R)
Dist.__init__(self, C=R, Ci=Ci)
self.length = len(R)
def __len__(self):
return self.length
def _cdf(self, x, C, Ci):
out = special.ndtr(numpy.dot(Ci, special.ndtri(x)))
return out
def _ppf(self, q, C, Ci):
out = special.ndtr(numpy.dot(C, special.ndtri(q)))
return out
def _lower(self, C, Ci):
return 0.
def _upper(self, C, Ci):
return 1.
class Nataf(Copula):
"""
Nataf (normal) copula.
Args:
dist (Dist):
The Distribution to wrap.
R (numpy.ndarray):
Covariance matrix.
Examples:
>>> distribution = chaospy.Nataf(
... chaospy.Iid(chaospy.Uniform(-1, 1), 2), R=[[1, .5], [.5, 1]])
>>> distribution
Nataf(Iid(Uniform(lower=-1, upper=1), 2), R=[[1, 0.5], [0.5, 1]])
>>> samples = distribution.sample(3)
>>> samples.round(4)
array([[ 0.3072, -0.77 , 0.9006],
[ 0.1262, 0.3001, 0.1053]])
>>> distribution.pdf(samples).round(4)
array([0.292 , 0.1627, 0.2117])
>>> distribution.fwd(samples).round(4)
array([[0.6536, 0.115 , 0.9503],
[0.4822, 0.8725, 0.2123]])
>>> mesh = numpy.meshgrid([.4, .5, .6], [.4, .5, .6])
>>> distribution.inv(mesh).round(4)
array([[[-0.2 , 0. , 0.2 ],
[-0.2 , 0. , 0.2 ],
[-0.2 , 0. , 0.2 ]],
<BLANKLINE>
[[-0.2707, -0.1737, -0.0739],
[-0.1008, 0. , 0.1008],
[ 0.0739, 0.1737, 0.2707]]])
>>> distribution.mom([1, 1]).round(4)
0.1609
"""
def __init__(self, dist, R, ordering=None):
self._repr = {"R": R}
assert len(dist) == len(R)
return Copula.__init__(self, dist=dist, trans=nataf(R, ordering))
