add the recursice_least_square

MC9529 · MC9529 · commit caed5353752e · 2019-12-08T17:33:22.000+08:00
diff --git a/examples/python_test.py b/examples/python_test.py
@@ -1,14 +1,25 @@
 import os
 import numpy as np 
 import matplotlib.pyplot as plt 
+import numpy.matlib 
 
 e = np.array([1, 2, 3])
 f = np.array([2, 3, 4])
+p = np.matlib.eye(3, 3)
+#print("the fist rows:", p[0,:])
+print ("the type of p:", type(p))
+g = np.zeros(3)
+print("the g:", g)
+#h = np.matrix.ye(3)
+
+print("the_res: ", p * f.transpose())
+
+
 a = np.append(e[1:3], f,axis = 0)
 m = np.array([[1,2,3], [2,2,3], [2,3,4]])
 print("the inverse:", type(np.linalg.inv(m)))
-g = np.vdot(e, f.transpose())
-print("the g: ", g)
+#g = np.vdot(e, f.transpose())
+print("the g: ", e.transpose() * f)
 
 print("the a: ", a)
 
diff --git a/examples/recursive_least_square.py b/examples/recursive_least_square.py
@@ -0,0 +1,86 @@
+import os
+import numpy as np 
+import matplotlib.pyplot as plt 
+import numpy.matlib 
+
+#the least_square
+a = np.array([1, -1.5, 0.7]); b = np.array([1, 0.5]); d = 3 #
+
+len_a = len(a) -1; len_b = len(b) - 1 ; L =400
+Input_init = np.zeros(d + len_b) #the init_value of input
+Output_init = np.zeros(len_a) # the init_value of ouput
+
+
+white_noise = np.random.normal(0, 1, L) # the white_noise
+white_noise_1 = np.sqrt(0.1) * np.random.normal(0, 1, L)
+
+theta = np.append(a[1: len_a + 1], b) #the permeter of object
+print("the shape of theat:", np.shape(theta))
+
+theta_1 = np.zeros(len_a + len_b + 1)
+print("the theta_1:", np.shape(theta_1))
+P = np.eye(len_a + len_b + 1, len_a + len_b + 1)
+
+phi = np.array([]) # the 
+y = np.array([])
+U = np.array([]) #the inverse_M_sequence
+thetae_1 = []
+thetae_2 = []
+thetae_3 = []
+thetae_4 = []
+
+
+for i in range(L):
+    # Y = AX + xi(noise)
+    temp = np.append(-Output_init, Input_init[d - 1: d + len_b]) # X
+    temp_y = np.dot(temp, theta.transpose()) + white_noise_1[i] # Y
+
+    phi = np.concatenate((phi, temp)) 
+    #print("the phi: ", phi)
+    temp_matrix = np.matrix(temp)
+    print("the shape of temp_matrix:", np.shape(temp_matrix))
+    P_matrix = np.matrix(P)
+    print("the shape of temp*P*temp:", np.shape(temp_matrix * P_matrix *temp_matrix.transpose()))
+    K = (P_matrix * temp_matrix.transpose()) /(1 + temp_matrix * P_matrix *temp_matrix.transpose())
+    print("the shape of K: ", np.shape(K))
+    thetae_temp = theta_1 + K * (temp_y - temp * theta_1)
+    print("the shape of theta_1", np.shape(theta_1))
+    print("the shape of theate_temp:", np.shape(thetae_temp))
+
+    print("the value of theta_temp[0,0]:", thetae_temp[0,0])
+    
+    thetae_1.append(thetae_temp[0,0])
+    thetae_2.append(thetae_temp[1,1])
+    thetae_3.append(thetae_temp[2,2])
+    thetae_4.append(thetae_temp[3,3])
+    P = (np.eye(len_a + len_b  + 1) - K * temp) * P 
+
+    #update the data
+    theta_1 = thetae_temp
+
+    for k in range(d + len_b - 1, 0, -1):
+        Input_init[k] = Input_init[k - 1]
+    Input_init[0] = white_noise[i]
+
+    for j in range(len_a - 1, 0, -1):
+        Output_init[j] = Output_init[j - 1]
+    Output_init[0] = temp_y
+
+# the np.narray to np.matrix
+
+plt.figure(1)
+ax = plt.subplot(1, 1, 1)
+
+plt.sca(ax)
+ax.plot(thetae_1, 'Red', label = 'thetae_1')
+ax.plot(thetae_2, 'Blue', label = 'thetae_2')
+ax.plot(thetae_3, 'Green', label = 'thetae_3')
+ax.plot(thetae_4, 'Yellow', label = 'thetae_4')
+plt.title('thetae')
+#plt.xlabel("L")
+plt.ylabel("thetae_1")
+
+ax.legend()
+plt.show()
+
+
