import numpy as np
import sympy
from scipy import stats
from copul.family.elliptical.elliptical_copula import EllipticalCopula
from copul.family.other import LowerFrechet, UpperFrechet
[docs]
class multivariate_laplace:
"""
Simplified multivariate_laplace implementation for Laplace copula.
This is a minimal version that only includes what's needed for the copula.
"""
[docs]
@staticmethod
def rvs(mean=None, cov=1, size=1, random_state=None, **kwargs):
"""Generate random samples from multivariate Laplace distribution"""
# Simple implementation just for the copula's rvs method
dim = len(mean)
final_shape = [size, dim] if isinstance(size, int) else size + [dim]
# Generate standard Laplace random variables
if random_state is not None:
np.random.seed(random_state)
x = np.random.laplace(loc=0.0, scale=1.0, size=final_shape).reshape(-1, dim)
# Apply covariance structure
# We use a simplified approach: Cholesky decomposition
L = np.linalg.cholesky(cov)
x = np.dot(x, L.T)
x += mean
return x
[docs]
class Laplace(EllipticalCopula):
"""
Laplace copula implementation.
The Laplace copula is an elliptical copula based on the multivariate Laplace distribution.
It is characterized by a correlation parameter rho in [-1, 1].
Special cases:
- rho = -1: Lower Fréchet bound (countermonotonicity)
- rho = 1: Upper Fréchet bound (comonotonicity)
"""
def __call__(self, *args, **kwargs):
if args is not None and len(args) == 1:
kwargs["rho"] = args[0]
if "rho" in kwargs:
if kwargs["rho"] == -1:
del kwargs["rho"]
return LowerFrechet()(**kwargs)
elif kwargs["rho"] == 1:
del kwargs["rho"]
return UpperFrechet()(**kwargs)
return super().__call__(**kwargs)
@property
def is_symmetric(self) -> bool:
return True
rho = sympy.symbols("rho")
@property
def is_absolutely_continuous(self) -> bool:
return True
[docs]
def rvs(self, n=1):
"""
Generate random samples from the Laplace copula.
Args:
n (int): Number of samples to generate
Returns:
numpy.ndarray: Array of shape (n, 2) containing the samples
"""
mu = [0, 0]
cov = np.array(self.corr_matrix, dtype=float)
samples = multivariate_laplace.rvs(mean=mu, cov=cov, size=n)
u1 = stats.laplace.cdf(samples[:, 0])
u2 = stats.laplace.cdf(samples[:, 1])
return np.array([u1, u2]).T
@property
def cdf(self):
"""
Compute the cumulative distribution function of the Laplace copula.
Returns:
SymPyFuncWrapper: Wrapped CDF function
Note:
This method is not yet implemented.
"""
# Not implemented yet
raise NotImplementedError("CDF not implemented for Laplace copula")
@property
def pdf(self):
"""
Compute the probability density function of the Laplace copula.
Returns:
SymPyFuncWrapper: Wrapped PDF function
Note:
This method is not yet implemented.
"""
# Not implemented yet
raise NotImplementedError("PDF not implemented for Laplace copula")