Create multivariate_gaussian.py

multivariate_gaussian.py

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+import numpy as np
+import matplotlib
+
+from scipy.stats import multivariate_normal
+from sklearn.linear_model import Ridge
+from sklearn.preprocessing import PolynomialFeatures
+from sklearn.pipeline import make_pipeline
+from mpl_toolkits.mplot3d import Axes3D
+
+matplotlib.rcParams['mathtext.fontset'] = 'stix'
+matplotlib.rcParams['font.family'] = 'STIXGeneral'
+matplotlib.rcParams.update({'font.size': 18})
+
+import matplotlib.pyplot as plt
+
+mean = [0, 0]
+cov = [[1, 4/5], [3/4, 2]]  # diagonal covariance
+
+x, y = np.random.multivariate_normal(mean, cov, 200).T
+fig = plt.figure(1)
+plt.plot(x, y, 'o')
+plt.axis('equal')
+plt.xlabel('$x^{(1)}$')
+plt.ylabel('$x^{(2)}$')
+
+fig.subplots_adjust(top = 0.98, bottom = 0.1, right = 0.98, left = 0.02, hspace = 0, wspace = 0)
+fig.savefig('../../Illustrations/multivariate-gaussian-0.eps', format='eps', dpi=1000, bbox_inches = 'tight', pad_inches = 0.1)
+fig.savefig('../../Illustrations/multivariate-gaussian-0.pdf', format='pdf', dpi=1000, bbox_inches = 'tight', pad_inches = 0.1)
+fig.savefig('../../Illustrations/multivariate-gaussian-0.png', dpi=1000, bbox_inches = 'tight', pad_inches = 0.1)
+
+fig1 = plt.figure(2)
+
+ax = Axes3D(fig1)
+
+x1, y1 = np.mgrid[-5:5:.2, -5:5:.2]
+pos = np.empty(x1.shape + (2,))
+pos[:, :, 0] = x1; pos[:, :, 1] = y1
+rv = multivariate_normal(mean, cov)
+#ax.plot_surface(x1, y1, rv.pdf(pos), rstride=1, cstride=1, alpha=0.8, cmap='viridis', edgecolor='none')
+ax.plot_wireframe(x1, y1, rv.pdf(pos), rstride=2, cstride=2, color='gray')
+
+z = [0] * len(x)
+ax.scatter(x, y, z)
+
+ax.set_xlabel('$x^{(1)}$')
+ax.set_ylabel('$x^{(2)}$')
+ax.set_zlabel('pdf');
+ax.set_zticks([])
+ax.set_xticks([])
+ax.set_yticks([])
+
+#ax.view_init(14, -77)
+
+fig1.subplots_adjust(top = 0.98, bottom = 0.1, right = 0.9, left = 0.08, hspace = 0, wspace = 0)
+fig1.savefig('../../Illustrations/multivariate-gaussian-1.eps', format='eps', dpi=1000, bbox_inches = 'tight', pad_inches = 0)
+fig1.savefig('../../Illustrations/multivariate-gaussian-1.pdf', format='pdf', dpi=1000, bbox_inches = 'tight', pad_inches = 0)
+fig1.savefig('../../Illustrations/multivariate-gaussian-1.png', dpi=1000, bbox_inches = 'tight', pad_inches = 0)
+
+#plt.show()