Distributions.py

'''
Copyright 2020 Amanpreet Singh,
               Martin Bauer,
               Sarang Joshi

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

'''


import torch
import numpy as np
import math


'''
gauss - Gaussian function -with default parameters this is a unit gaussian.

Parametrs -    x -------- Input points (should come from the geometry class in our implementation).
               c -------- Constant never used.
               mu ------- Mean of the gaussian.
               sigma ---- Variance of the gaussian.

Outputs ---    1. Value of the Gaussian at the given points 

Note ------    Was used in the testing of our formulation in continuous domain.
'''
def gauss(x, c, mu=[0, 0], sigma=1):
    ret = torch.exp(-(torch.pow(x[:, 1:] - mu[0], 2) + torch.pow(x[:, 0:1] - mu[1], 2)) /(2 * (sigma**2))).squeeze()
    ret = ret/((sigma**2)*(2*torch.from_numpy(np.array(np.pi))))
    return ret


'''
gass_md ------ A multi dimensional gaussian function.

Parameters  -- x -------- Input points (should come from the geometry class in our implementation).
               c -------- Constant never used.
               mu ------- Mean of the gaussian.
               sigma ---- Variance of the gaussian.

Outputs ---    1. Value of the Gaussian at the given points 

'''
def gauss_md(x, c):

    dim = x.shape[1]

    mu = torch.zeros(dim, 1)
    sigma = torch.eye(dim)

    x = x.unsqueeze(-1)

    mu = mu.reshape(1, dim, 1).repeat(x.shape[0], 1, 1).cuda()
    sigma_r = sigma.reshape(1, dim, dim).repeat(x.shape[0], 1, 1).cuda()
    ret = torch.matmul(torch.matmul(torch.transpose(x - mu, 1, 2), torch.inverse(sigma_r)), x - mu)

    ret = torch.exp(-0.5 * ret)

    ret = ret/torch.sqrt((2 * math.pi)**dim * torch.det(sigma))

    return ret.squeeze()


'''
gass_md ------ A multi-dimensional unit gaussian function. 

Parameters  -- x -------- Input points (should come from the geometry class in our implementation).
               c -------- Constant never used.

Outputs ---    1. Log probability at the given point

'''
def gauss_md_2(x, c):

    dim = x.shape[1]

    mu = torch.zeros(dim).cuda()
    sigma = torch.eye(dim).cuda()

    m = torch.distributions.multivariate_normal.MultivariateNormal(mu, sigma)

    ret = m.log_prob(x)

    return ret


'''
gass_md ------ A multi gaussian function. With default parameters this is the unit gaussian.

Parameters  -- x -------- Input points (should come from the geometry class in our implementation).
               c -------- Constant never used.
               mu ------- Mean of the gaussian.
               sigma ---- Should be named covariance. Takes in the Covariance Matrix.

Outputs ---    1. Log probability at the given point

'''
def gauss_md_2ms(x, mu=None, sigma=None):

    dim = x.shape[1]

    if mu is None:
        mu = torch.zeros(dim).cuda()
    else:
        mu = torch.from_numpy(mu).cuda()
    if sigma is None:
        sigma = torch.eye(dim).cuda()
    else:
        sigma = torch.from_numpy(sigma).cuda()

    m = torch.distributions.multivariate_normal.MultivariateNormal(mu, sigma)

    ret = m.log_prob(x)

    return ret