import torch
from torch import tensor, rand
import pyro
import torch.distributions.constraints as constraints
import pyro.distributions as dist


def model(N=None, sigma_y=None, y=None):
    eta = sample('eta', ImproperUniform(shape=N))
    mu_theta = sample('mu_theta', ImproperUniform())
    sigma_eta = sample('sigma_eta', dist.Uniform(0.0, 100.0))
    xi = sample('xi', ImproperUniform())
    theta = zeros(N)
    theta = mu_theta + xi * eta
    sample('mu_theta' + '__1', dist.Normal(0, 100), obs=mu_theta)
    sample('sigma_eta' + '__2', dist.InverseGamma(1, 1), obs=sigma_eta)
    sample('eta' + '__3', dist.Normal(zeros(N), sigma_eta), obs=eta)
    sample('xi' + '__4', dist.Normal(0, 5), obs=xi)
    sample('y' + '__5', dist.Normal(theta, sigma_y), obs=y)


def generated_quantities(N=None, sigma_y=None, y=None, parameters=None):
    eta = parameters['eta']
    mu_theta = parameters['mu_theta']
    sigma_eta = parameters['sigma_eta']
    xi = parameters['xi']
    theta = zeros(N)
    theta = mu_theta + xi * eta
    return {'theta': theta}
