Initial commit

Divers/descente_gradient/comparaison.py

@@ -0,0 +1,52 @@
+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)
+plt.xlabel("Paramètre 1 (x)")
+plt.ylabel("Paramètre 2 (y)")
+
+x1=x2=np.random.random_integers(-2, 2)+np.random.rand(1)[0]
+y1=y2=np.random.random_integers(-2, 2)+np.random.rand(1)[0]
+
+lr=0.2
+lr2=0.9
+correction_x1=0
+correction_y1=0
+i=0
+while True:
+    g_x1, g_y1=gradient_fonction(x1, y1)
+    g_x2, g_y2=gradient_fonction(x2, y2)
+
+    correction_x1=lr2*correction_x1-lr*g_x1
+    x1=x1+correction_x1
+    correction_y1=lr2*correction_y1-lr*g_y1
+    y1=y1+correction_y1
+
+    x2=x2-lr*g_x2
+    y2=y2-lr*g_y2
+
+    ax.scatter(x1, y1, fonction(x1, y1), marker='o', s=10, color='#FF0000')
+    ax.scatter(x2, y2, fonction(x2, y2), marker='o', s=10, color='#00FF00')
+    plt.draw()
+    print("iteration= {} x1={:+7.5f} y1={:+7.5f} x2={:+7.5f} y2={:+7.5f}".format(i, x1, y1, x2, y2))
+    plt.pause(0.05)
+    i+=1