correct GP/GPR to work with Python3 and add example

examples/models/gpr.py

@@ -0,0 +1,98 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+"""Provide some examples using GPR.
+"""
+
+import sys  # to check if Python 3 or 2
+import numpy as np
+import matplotlib.pyplot as plt
+
+from pyrobolearn.models.gp import GPR
+from pyrobolearn.utils.converter import torch_to_numpy
+
+
+# create data: Generate random sample following a sine curve
+# Ref: https://scikit-learn.org/stable/auto_examples/mixture/plot_gmm_sin.html#sphx-glr-auto-examples-mixture-\
+# plot-gmm-sin-py
+n_samples = 100
+np.random.seed(0)
+X = np.zeros((n_samples, 2))
+step = 4. * np.pi / n_samples
+
+for i in range(X.shape[0]):
+    x = i * step - 6.
+    X[i, 0] = x + np.random.normal(0, 0.1)
+    X[i, 1] = 3. * (np.sin(x) + np.random.normal(0, .2))
+
+x, y = X[:, 0], X[:, 1]
+xlim, ylim = [-8, 8], [-8, 8]
+
+# plot data
+plt.title('Training data')
+plt.scatter(x, y)
+plt.xlim(xlim)
+plt.ylim(ylim)
+plt.show()
+
+# create GPR
+model = GPR()
+
+# plot prior possible functions
+f = model.sample(x, num_samples=10, to_numpy=True)
+plt.title('Sampled functions from prior distribution')
+plt.scatter(x, y, alpha=0.3)
+plt.plot(x, f.T)
+plt.xlim(xlim)
+plt.ylim(ylim)
+plt.show()
+
+# compute log likelihoods
+print("\nBefore training:")
+print("Log likelihood: {}".format(model.log_likelihood(x, y, to_numpy=True)))
+print("Log marginal likelihood: {}".format(model.log_marginal_likelihood(x, y, to_numpy=True)))
+
+# fit the data
+optimizer = 'adam'  # 'lbfgs'
+model.fit(x, y, num_iters=100, optimizer=optimizer, verbose=True)
+
+# compute log likelihoods
+print("\nAfter training:")
+print("Log likelihood: {}".format(model.log_likelihood(x, y, to_numpy=True)))
+print("Log marginal likelihood: {}".format(model.log_marginal_likelihood(x, y, to_numpy=True)))
+
+# sample function and plot it
+f = model.sample(x, num_samples=1, to_numpy=True)
+plt.title('one sampled function after training')
+plt.scatter(x, y)
+plt.plot(x, f.T, 'k', linewidth=2.)
+plt.xlim(xlim)
+plt.ylim(ylim)
+plt.show()
+
+# predict prob
+x_test = np.linspace(-10, 10, 101)
+xlim, ylim = [-10, 10], [-10, 10]
+mean_y, var_y = model.predict_prob(x_test, to_numpy=True)
+std_y = np.sqrt(var_y)
+plt.title('Prediction')
+plt.scatter(x, y)
+plt.plot(x_test, mean_y, 'b')
+plt.fill_between(x_test, mean_y-2*std_y, mean_y+2*std_y, facecolor='green', alpha=0.3)
+plt.xlim(xlim)
+plt.ylim(ylim)
+plt.show()
+
+# Another way to predict
+pred = model.forward(x_test)
+lower, upper = pred.confidence_region()
+
+plt.title("Another way to predict (see code)")
+plt.plot(x, y, 'k*')
+if sys.version_info[0] < 3:  # Python 2
+    plt.plot(x_test, torch_to_numpy(pred.mean()), 'b')
+else:  # Python 3
+    plt.plot(x_test, torch_to_numpy(pred.mean), 'b')
+plt.fill_between(x_test, torch_to_numpy(lower), torch_to_numpy(upper), alpha=0.5)
+plt.xlim(xlim)
+plt.ylim(ylim)
+plt.show()