import numpy
import numpy as np
from beartype import beartype
from UQpy.utilities.ValidationTypes import Numpy2DFloatArray
from UQpy.distributions.baseclass import Copula
[docs]class Frank(Copula):
@beartype
def __init__(self, theta: float):
"""
:param theta: Parameter of the copula, real number in :math:`\mathbb{R}`
"""
super().__init__(theta=theta)
[docs] def evaluate_cdf(self, unit_uniform_samples: Numpy2DFloatArray) -> numpy.ndarray:
"""
Compute the copula cdf :math:`C(u_1, u_2, ..., u_d)` for a `d`-variate uniform distribution.
For a generic multivariate distribution with marginal cdfs :math:`F_1, ..., F_d` the joint cdf is computed as:
:math:`F(x_1, ..., x_d) = C(u_1, u_2, ..., u_d)`
where :math:`u_i = F_i(x_i)` is uniformly distributed. This computation is performed in the
:meth:`.JointCopula.cdf` method.
:param unit_uniform_samples: Points (uniformly distributed) at which to evaluate the copula cdf, must be of
shape :code:`(npoints, dimension)`.
:return: Values of the cdf.
"""
theta, u, v = self.extract_data(unit_uniform_samples)
tmp_ratio = ((np.exp(-theta * u) - 1.0) * (np.exp(-theta * v) - 1.0) / (np.exp(-theta) - 1.0))
cdf_val = -1.0 / theta * np.log(1.0 + tmp_ratio)
return cdf_val
def extract_data(self, unit_uniform_samples: Numpy2DFloatArray):
u = unit_uniform_samples[:, 0]
v = unit_uniform_samples[:, 1]
theta = self.parameters["theta"]
return theta, u, v