add 2D letters data + GMR example with 2D letter

data/2Dletters/README.md

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+
+This document contains the data (trajectories) to draw 2D letters. The data is provided by Sylvain Calinon.

examples/models/gmr.py

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+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+"""Provide some examples using GMR.
+
+See also the `gmm.py` example beforehand. In this example, we delve a bit deeper into GMR using 2D letters as training
+data.
+"""
+
+import numpy as np
+from scipy.io import loadmat
+import matplotlib.pyplot as plt
+
+from pyrobolearn.models.gmm import Gaussian, GMM, plot_gmm, plot_gmr
+
+
+# load the training data
+G = loadmat('../../data/2Dletters/G.mat')  # dict
+demos = G['demos']  # shape (1,N)
+n_demos = demos.shape[1]
+dim = demos[0, 0][0, 0][0].shape[0]
+length = demos[0, 0][0, 0][0].shape[1]
+
+# plot the training data (x,y)
+X = []
+xlim, ylim = [-10, 10], [-10, 10]
+plt.xlim(xlim)
+plt.ylim(ylim)
+for i in range(0, n_demos, 2):
+    demo = demos[0, i][0, 0][0]  # shape (2, 200)
+    plt.plot(demo[0], demo[1])
+    X.append(demo.T)
+plt.show()
+
+# reshape training data (add time in addition to (x,y), thus we now have (t,x,y))
+time_linspace = np.linspace(0, 2., length)
+times = np.asarray([time_linspace for _ in range(len(X))]).reshape(-1, 1)
+X = np.vstack(X)  # shape (N*200, 2)
+X = np.hstack((times, X))  # shape (N*200, 3)
+print(X.shape)
+
+# create GMM
+dim, num_components = X.shape[1], 7
+gmm = GMM(gaussians=[Gaussian(mean=np.concatenate((np.random.uniform(0, 2., size=1),
+                                                   np.random.uniform(-8., 8., size=dim-1))),
+                              covariance=0.1*np.identity(dim)) for _ in range(num_components)])
+
+# init GMM
+init_method = 'k-means'  # 'random', 'k-means', 'uniform', 'sklearn', 'curvature'
+gmm.init(X, method=init_method)
+fig, ax = plt.subplots(1, 1)
+plot_gmm(gmm, dims=[1, 2], X=X, ax=ax, title='GMM after ' + init_method.capitalize(), xlim=xlim, ylim=ylim)
+plt.show()
+
+# fit a GMM on it
+result = gmm.fit(X, init=None, num_iters=200)
+
+# plot EM optimization
+plt.plot(result['losses'])
+plt.title('EM per iteration')
+plt.show()
+
+# plot trained GMM
+fig, ax = plt.subplots(1, 1)
+plot_gmm(gmm, dims=[1, 2], X=X, label=True, ax=ax, title='Our Trained GMM', option=1, xlim=xlim, ylim=ylim)
+plt.show()
+
+# GMR: condition on the input variable and plot
+gaussians = []
+for t in time_linspace:
+    g = gmm.condition(np.array([t]), idx_out=[1, 2], idx_in=[0]).approximate_by_single_gaussian()
+    gaussians.append(g)
+
+# plot figures for GMR
+plot_gmr(time_linspace, gaussians=gaussians, xlim=xlim, ylim=ylim)
+plt.show()