Ob 5 scripts agregados

ob5/ej1.py

@@ -0,0 +1,71 @@
+# -*- coding: utf-8 -*-
+
+import numpy as np
+import matplotlib.pyplot as plt
+np.random.seed(5)
+
+
+class ConstantStep:
+    def __init__(self, const):
+        self.const = const
+    def step(self, *k1, **k2):
+        return self.const
+    def __str__(self):
+        return fr'$\alpha_k = {self.const}$'
+class DecreasingStep:
+    def __init__(self, const, *k1, **k2):
+        self.const = const
+    def step(self, k):
+        return self.const/k
+    def __str__(self):
+        return fr'$\alpha_k = {self.const}/k$'
+
+A = np.array([[2, 1],
+              [1, 2]])
+theta_0 = np.array([[1],
+                    [1]])
+
+
+X = lambda :A + np.random.randn(2,2)
+y = lambda X: X@theta_0 + np.random.randn(2,1)
+
+Ff = lambda X, y, theta: 2*X.T @ (X@theta - y)
+
+stepsTypes = [ConstantStep(0.1), ConstantStep(0.01), ConstantStep(0.001),
+         DecreasingStep(0.1)]
+
+
+plt.figure(figsize=(7,7))
+plt.xlabel('x')
+plt.ylabel('y')
+plt.title(r'Trayectoria $\theta_k$')
+
+for step_type in stepsTypes:
+    thetas = list()
+    theta_k = np.zeros((2,1))
+    thetas.append(theta_k)
+
+    alpha_const = 0.1
+
+    K = 10000
+    for k in range(K):
+        X_ = X()
+        y_ = y(X_)
+        F = Ff(X_, y_, theta_k)
+        alpha_k = step_type.step(k+1)
+        theta_k = theta_k - alpha_k * F
+        thetas.append(theta_k)
+
+    print(theta_k)
+
+    thetas_ = np.array(thetas)[:,:,0]
+
+    plt.plot(thetas_[:, 0], thetas_[:, 1], label=str(step_type))
+
+    plt.scatter(1, 1, c='r')
+plt.xlim(-.25,2.25)
+plt.ylim(-.25,2.25)
+plt.grid(True)
+
+plt.legend()
+plt.savefig('figures/ej1.png')

ob5/ej2.py

@@ -0,0 +1,94 @@
+# -*- coding: utf-8 -*-
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+gatos = np.loadtxt('Gatos.asc').astype(np.uint8)
+conejos = np.loadtxt('Conejos.asc').astype(np.uint8)
+
+#%%
+def vect2img(x):
+    return np.transpose((x[:-1].reshape(3, 256,256)), (2,1,0))
+
+
+plt.figure()
+plt.imshow(vect2img(gatos[:, 1]))
+#%%
+
+plt.figure()
+plt.imshow(np.transpose((conejos[:-1, 10].reshape(3, 256,256)), (2,1,0)))
+#%%
+
+class ConstantStep:
+    def __init__(self, const):
+        self.const = const
+    def step(self, *k1, **k2):
+        return self.const
+    def __str__(self):
+        return fr'Paso constante $\alpha_k = {self.const}$'
+
+epsilon = 0.1
+
+def ReLU(x, epsilon):
+    if x>0:
+        return x
+    else:
+        return epsilon * x
+
+def F(x, y, a):
+    if a.T@x <= 0:
+        value = epsilon
+    else:
+        value = 1
+    return 2 * (-y + ReLU(a.T@x, epsilon)) * value * x
+
+# gatos   : label=0
+# conejos : label=1
+gato_label = 0
+conejo_label = 1
+
+step = ConstantStep(1e-9)
+
+a = np.zeros((gatos.shape[0],1))
+
+#%%
+K = 20
+N_EPOCHS = 50
+for n in range(N_EPOCHS):
+    for k in range(K):
+        gato = gatos[:, k:k+1]
+        conejo = conejos[:, k:k+1]
+
+        a = a - step.step()*F(gato, gato_label, a)
+        a = a - step.step()*F(conejo, conejo_label, a)
+
+#%%
+# Train
+label = lambda x: 'gato' if x<0.5 else 'conejo'
+
+print('GATOS')
+for k in range(0,10):
+    gato = gatos[:, k:k+1]
+    v = a.T@gato
+    print(v, label(v))
+
+print('\n\nCONEJOS')
+for k in range(0,10):
+    conejo = conejos[:, k:k+1]
+    v = a.T@conejo
+    print(v, label(v))
+#%%
+# Test
+label = lambda x: 'gato' if x<0.5 else 'conejo'
+
+print('GATOS')
+for k in range(20,30):
+    gato = gatos[:, k:k+1]
+    v = a.T@gato
+    print(v, label(v))
+
+print('\n\nCONEJOS')
+for k in range(20,30):
+    conejo = conejos[:, k:k+1]
+    v = a.T@conejo
+    print(v, label(v))