import pints
import pints.toy
import numpy as np
import matplotlib.pyplot as plt

# Create log pdf
log_pdf = pints.toy.GaussianLogPDF([2, 4], [[1, 0], [0, 3]])

# Contour plot of pdf
levels = np.linspace(-3,12,20)
num_points = 100
x = np.linspace(-1, 5, num_points)
y = np.linspace(-0, 8, num_points)
X, Y = np.meshgrid(x, y)
Z = np.zeros(X.shape)
Z = np.exp([[log_pdf([i, j]) for i in x] for j in y])
plt.contour(X, Y, Z)
plt.xlabel('x')
plt.ylabel('y')
plt.show()

"""
Explanation: Inference: Relativistic Monte Carlo
This example shows you how to perform Bayesian inference on a Gaussian distribution and a time-series problem, using Relativistic MCMC.
First, we create a simple normal distribution
End of explanation
"""


# Choose starting points for 3 mcmc chains
xs = [
    [2, 1],
    [3, 3],
    [5, 4],
]

# Create mcmc routine
sigma = [1, 1]
mcmc = pints.MCMCController(log_pdf, 3, xs, method=pints.RelativisticMCMC, sigma0=sigma)

# Add stopping criterion
mcmc.set_max_iterations(1000)

# Set up modest logging
mcmc.set_log_to_screen(True)
mcmc.set_log_interval(100)

# Run!
print('Running...')
full_chains = mcmc.run()
print('Done!')

# Show traces and histograms
import pints.plot
pints.plot.trace(full_chains)
plt.show()

# Discard warm up
chains = full_chains[:, 200:]

# Check convergence and other properties of chains
results = pints.MCMCSummary(chains=chains, time=mcmc.time(), parameter_names=['mean_x', 'mean_y'])
print(results)

# Look at distribution in chain 0
pints.plot.pairwise(chains[0], kde=True)
plt.show()

# Check Kullback-Leibler divergence of chains
print(log_pdf.kl_divergence(chains[0]))
print(log_pdf.kl_divergence(chains[1]))
print(log_pdf.kl_divergence(chains[2]))

"""
Explanation: Now we set up and run a sampling routine using Relativistic MCMC.
End of explanation
"""


import pints
import pints.toy as toy
import pints.plot
import numpy as np
import matplotlib.pyplot as plt

# Load a forward model
model = toy.LogisticModel()

# Create some toy data
times = np.linspace(0, 1000, 50)
real_parameters = np.array([0.015, 500])
org_values = model.simulate(real_parameters, times)

# Add noise
np.random.seed(1)
noise = 10
values = org_values + np.random.normal(0, noise, org_values.shape)

# Create an object with links to the model and time series
problem = pints.SingleOutputProblem(model, times, values)

# Create a log-likelihood function
log_likelihood = pints.GaussianKnownSigmaLogLikelihood(problem, noise)

# Create a uniform prior over the parameters
log_prior = pints.UniformLogPrior(
    [0.01, 400],
    [0.02, 600]
)

# Create a posterior log-likelihood (log(likelihood * prior))
log_posterior = pints.LogPosterior(log_likelihood, log_prior)

# Choose starting points for 3 mcmc chains
xs = [
    real_parameters * 1.01,
    real_parameters * 0.9,
    real_parameters * 1.1,
]

# Create mcmc routine
mcmc = pints.MCMCController(log_posterior, len(xs), xs, method=pints.RelativisticMCMC)

# Add stopping criterion
mcmc.set_max_iterations(1000)

# Set up modest logging
mcmc.set_log_to_screen(True)
mcmc.set_log_interval(100)

# Run!
print('Running...')
chains = mcmc.run()
print('Done!')

"""
Explanation: Relativistic Monte Carlo on a time-series problem
We now try the same method on a time-series problem
End of explanation
"""


# Check convergence and other properties of chains
results = pints.MCMCSummary(chains=chains[:, 200:], time=mcmc.time(), parameter_names=['growth rate', 'capacity'])
print(results)

# Show traces and histograms
pints.plot.trace(chains)
plt.show()

"""
Explanation: The chains do not take long to reach equilibrium with this method.
End of explanation
"""


div = len(mcmc.samplers()[0].divergent_iterations())
print("There were " + str(div) + " divergent iterations in the 1st chain.")

"""
Explanation: Chains have converged!
Extract any divergent iterations -- looks fine as there were none.
End of explanation
"""


