zdana

list04/mutations.py

@@ -1,3 +1,5 @@
+from matplotlib.patches import Ellipse
+from scipy.stats import norm, chi2
 import numpy as np
 import matplotlib.pyplot as plt
 
@@ -12,16 +14,19 @@ def plot_mutation(
         domain_Y=np.arange(-5, 5, 0.25),
         objective_function=objective_function_F1a,
         original_individual=np.array([[1, 1]]),
+        conv_elipse=False,
 ):
     X, Y = np.meshgrid(domain_X, domain_Y)
     Z = - objective_function(np.vstack([X.ravel(),
                                         Y.ravel()]).T).reshape(X.shape[0], X.shape[1])
     plt.figure(figsize=(6, 6))
-    plt.contour(X, Y, Z, 50)
-    plt.plot(mutations[:, 0], mutations[:, 1], 'ro')
+    plt.contour(X, Y, Z, 50, alpha=0.5)
+    plt.plot(mutations[:, 0], mutations[:, 1], 'ro', markersize=2)
     plt.plot(original_individual[0, 0],
              original_individual[0, 1], 'k*', markersize=24)
     # plt.title('Mutation 1')
+    if conv_elipse:
+        plot_point_cov(mutations)
     plt.show()
 
 
@@ -53,9 +58,10 @@ def benchmark_mutation(
     original_individual=np.array([[1, 1]])
 ):
     indv_res = objective_function(original_individual)[0]
-
-    x = np.array([objective_function(mutate(sigma)) for i in range(100)])
-    better_than_indv = (x < indv_res).sum(axis=1)
+    mutations = np.array([(mutate(sigma)) for i in range(100)])
+    x = np.array([objective_function(i) for i in mutations])
+    plot_mutation(mutations[0], objective_function=objective_function, conv_elipse=True)
+    better_than_indv = (x < indv_res).sum(axis=1)    
     best_from_pop = x.max(axis=1)
 
     fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(6, 3))
@@ -73,3 +79,31 @@ def benchmark_mutation(
     )
     fig.tight_layout()
     plt.show()
+
+
+def plot_point_cov(points, q=0.95, ax=None, **kwargs):
+    pos = points.mean(axis=0)
+    cov = np.cov(points, rowvar=False)
+    return plot_cov_ellipse(cov, pos, q, ax, **kwargs)
+
+
+def plot_cov_ellipse(cov, pos, q=0.95, ax=None, **kwargs):
+    def eigsorted(cov):
+        vals, vecs = np.linalg.eigh(cov)
+        order = vals.argsort()[::-1]
+        return vals[order], vecs[:, order]
+
+    if ax is None:
+        ax = plt.gca()
+
+    q = np.asarray(q)
+    r2 = chi2.ppf(q, 2)
+    val, vec = np.linalg.eigh(cov)
+    width, height = 2 * np.sqrt(val[:, None] * r2)
+    rotation = np.degrees(np.arctan2(*vec[::-1, 0]))
+
+    ellip = Ellipse(xy=pos, width=width, height=height,
+                    angle=rotation, color='green', **kwargs)
+
+    ax.add_artist(ellip)
+    return width, height

list04/notebook_utils.py

@@ -162,6 +162,7 @@ def run_es(
     plot=True,
     sigma=50.0,
     verbose=True,
+    K=1
 
 ):
     result = es(
@@ -172,8 +173,8 @@ def run_es(
         number_of_offspring=2*N,
         number_of_parents=number_of_parents,
         sigma=sigma,
-        tau=1/np.sqrt(2*d),
-        tau_0=1/np.sqrt(2*np.sqrt(d)),
+        tau=K/np.sqrt(2*d),
+        tau_0=K/np.sqrt(2*np.sqrt(d)),
         log_frequency=log_frequency,
         verbose=verbose
     )