Initial commit

Divers/descente_gradient/exemple_3d_inertie.py

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+from mpl_toolkits.mplot3d import Axes3D
+from matplotlib import cm
+from matplotlib.colors import LogNorm
+import matplotlib.pyplot as plt
+import numpy as np
+import math
+
+def fonction(X, Y):
+    return X*np.exp(-X**2-Y**2)+(X**2+Y**2)/20
+
+def gradient_fonction(X, Y):
+    g_x=np.exp(-X**2-Y**2)+X*-2*X*np.exp(-X**2-Y**2)+X/10
+    g_y=-2*Y*X*np.exp(-X**2-Y**2)+Y/10
+    return g_x, g_y
+
+fig=plt.figure()
+fig.set_size_inches(9, 7, forward=True)
+ax=Axes3D(fig, azim=-29, elev=49)
+X=np.arange(-3, 3, 0.2)
+Y=np.arange(-3, 3, 0.2)
+X, Y=np.meshgrid(X, Y)
+Z=fonction(X, Y)
+ax.plot_wireframe(X, Y, Z, rstride=1, cstride=1)
+#ax.contour(X, Y, Z, 70, rstride=1, cstride=1, cmap='plasma')
+
+plt.xlabel("Paramètre 1 (x)")
+plt.ylabel("Paramètre 2 (y)")
+
+x=np.random.random_integers(-2, 2)+np.random.rand(1)[0]
+y=np.random.random_integers(-2, 2)+np.random.rand(1)[0]
+
+lr=0.2
+lr2=0.9
+correction_x=0
+correction_y=0
+i=0
+while True:
+    g_x, g_y=gradient_fonction(x, y)
+    correction_x=lr2*correction_x-lr*g_x
+    x=x+correction_x
+    correction_y=lr2*correction_y-lr*g_y
+    y=y+correction_y
+    ax.scatter(x, y, fonction(x, y), marker='o', s=10, color='#FF0000')
+    plt.draw()
+    print("itération {:3d}  -> x={:+7.5f} y={:+7.5f}".format(i, x, y))
+    plt.pause(0.05)
+    i+=1