98 lines
2.4 KiB
Python
98 lines
2.4 KiB
Python
import numpy as np
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import matplotlib.pyplot as plt
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from mpl_toolkits.mplot3d.art3d import Poly3DCollection
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from quapy.functional import uniform_prevalence_sampling
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# Vertices of a regular tetrahedron
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v1 = np.array([0, 0, 0])
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v2 = np.array([1, 0, 0])
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v3 = np.array([0.5, np.sqrt(3)/2, 0])
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v4 = np.array([0.5, np.sqrt(3)/6, np.sqrt(6)/3])
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vertices = np.array([v1, v2, v3, v4])
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# Function to map (p1,p2,p3,p4) to 3D coordinates
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def prob_to_xyz(p):
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return p[0]*v1 + p[1]*v2 + p[2]*v3 + p[3]*v4
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# --- Example: 5 random distributions inside the simplex
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rand_probs = uniform_prevalence_sampling(n_classes=4, size=3000)
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points_xyz = np.array([prob_to_xyz(p) for p in rand_probs])
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# --- Plotting
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fig = plt.figure(figsize=(8, 8))
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ax = fig.add_subplot(111, projection='3d')
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# Draw tetrahedron faces
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faces = [
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[v1, v2, v3],
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[v1, v2, v4],
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[v1, v3, v4],
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[v2, v3, v4]
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]
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poly = Poly3DCollection(faces, alpha=0.15, edgecolor='k', facecolor=None)
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# poly = Poly3DCollection(faces, alpha=0.15, edgecolor='k', facecolor=None)
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ax.add_collection3d(poly)
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edges = [
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[v1, v2],
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[v1, v3],
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[v1, v4],
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[v2, v3],
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[v2, v4],
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[v3, v4]
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]
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for edge in edges:
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xs, ys, zs = zip(*edge)
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ax.plot(xs, ys, zs, color='black', linewidth=1)
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# Draw vertices
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# ax.scatter(vertices[:,0], vertices[:,1], vertices[:,2], s=60, color='red')
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# Labels
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offset = 0.08
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labels = ["$y_1$", "$y_2$", "$y_3$", "$y_4$"]
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for i, v in enumerate(vertices):
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direction = v / np.linalg.norm(v)
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label_pos = v + offset * direction
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ax.text(label_pos[0], label_pos[1], label_pos[2], labels[i], fontsize=14, color='black')
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# Plot random points
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ax.scatter(points_xyz[:,0], points_xyz[:,1], points_xyz[:,2], s=10, c='blue', alpha=0.2)
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# Axes formatting
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ax.set_xlabel("X")
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ax.set_ylabel("Y")
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ax.set_zlabel("Z")
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ax.set_title("4-Class Probability Simplex (Tetrahedron)")
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# ax.view_init(elev=65, azim=20)
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ax.set_xticks([])
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ax.set_yticks([])
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ax.set_zticks([])
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ax.set_xticklabels([])
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ax.set_yticklabels([])
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ax.set_zticklabels([])
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ax.xaxis.set_ticks_position('none') # evita que dibuje marcas
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ax.yaxis.set_ticks_position('none')
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ax.zaxis.set_ticks_position('none')
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ax.xaxis.pane.set_visible(False)
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ax.yaxis.pane.set_visible(False)
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ax.zaxis.pane.set_visible(False)
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ax.set_xlabel('')
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ax.set_ylabel('')
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ax.set_zlabel('')
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ax.grid(False)
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plt.tight_layout()
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# plt.show()
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plt.savefig('plots_ieee/tetrahedron.pdf')
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