User-defined Rosenbrock distribution

This examples shows the use of the multivariate normal distributions class. In particular:

import numpy as np
from UQpy.distributions import DistributionND
import matplotlib.pyplot as plt

Example with a custom distribution

In order to define a new distribution, the user must extend the one of the abstract base classes DistributionContinuous1D, DistributionDiscrete1D or DistributionND. For the purpose of this example a new multivariate Rosenbrock distribution is defined. Note that three methods are implemented, namely, the __init__ which allows the user to define custom distribution arguments, as well as the pdf and log_pdf of this new distribution. Note that it is required for the user to call the __init__ method of the baseclass by providing all arguments names and values required in the custom distribution initializer. In our case, the parameter name p and its values are provided to the super().__init__ method.

class Rosenbrock(DistributionND):
    def __init__(self, p=20.):
        super().__init__(p=p)

    def pdf(self, x):
        return np.exp(-(100 * (x[:, 1] - x[:, 0] ** 2) ** 2 + (1 - x[:, 0]) ** 2) / self.parameters['p'])

    def log_pdf(self, x):
        return -(100 * (x[:, 1] - x[:, 0] ** 2) ** 2 + (1 - x[:, 0]) ** 2) / self.parameters['p']

Initialize custom distribution

Given the newly defined distribution class, a Rosenbrock distribution object can be defined by providing to the initializer the user-defined argument p. Since the Rosenbrock distribution extends the DistributionND class, methods and attributes of the baseclass are already available. For instance, the user can retrieve the already defined parameters using the parameters attribute and subsequently update them using the update_parameters method.

dist = Rosenbrock(p=20)
print(dist.parameters)
dist.update_parameters(p=40)
print(dist.parameters)

dist = Rosenbrock(p=20)
print(dist.parameters)

{'p': 20}
{'p': 40}
{'p': 20}

Plot pdf of the user defined distribution

fig, ax = plt.subplots(figsize=(8, 5))
x = np.arange(-5, 8, 0.1)
y = np.arange(-5, 50, 0.1)
X, Y = np.meshgrid(x, y)
Z = dist.pdf(x=np.concatenate([X.reshape((-1, 1)), Y.reshape((-1, 1))], axis=1))
CS = ax.contour(X, Y, Z.reshape(X.shape))
ax.clabel(CS, inline=1, fontsize=10)
ax.set_title('Contour plot of custom pdf - Rosenbrock')
plt.show()

Check if the user-defined distribution has rvs, pdf and update_parameters method

print('Does the rosenbrock distribution have an rvs method?')
print(hasattr(dist, 'rvs'))

print('Does the rosenbrock distribution have an pdf method?')
print(hasattr(dist, 'pdf'))

print('Does the rosenbrock distribution have an update_parameters method?')
print(hasattr(dist, 'update_parameters'))

Does the rosenbrock distribution have an rvs method?
False
Does the rosenbrock distribution have an pdf method?
True
Does the rosenbrock distribution have an update_parameters method?
True