diff --git a/HDC_library.py b/HDC_library.py
index e167bb1..aa6f9eb 100644
--- a/HDC_library.py
+++ b/HDC_library.py
@@ -99,9 +99,11 @@ def train_HDC_RFF(n_class, N_train, Y_train_init, HDC_cont_train, gamma, D_b):
         omega = np.zeros(N_train, N_train)
         #Fill Beta:
         
+            
         for i in range(N_train):
             for j in range(N_train):
-                omega[i][j] = Y_train[i]*Y_train[j]*(np.transpose(HDC_cont_train))[i]*HDC_cont_train[j]
+                omega[i, j] = Y_train[i] * Y_train[j] * HDC_cont_train[i] * HDC_cont_train[j]
+        
         Beta[1:N_train+1,0] = Y_train
         Beta[0,1:N_train+1] = np.transpose(Y_train)
         Beta[1:N_train+1,1:N_train+1] = omega + pow(gamma,-1) * np.identity(N_train)
diff --git a/playground.py b/playground.py
index 4cf36b4..ff41587 100644
--- a/playground.py
+++ b/playground.py
@@ -1,6 +1,7 @@
 # Here the unit tests are performed
 import numpy as np
 import sys
+from scipy.linalg import lu_factor, lu_solve
 np.set_printoptions(threshold=sys.maxsize)
 
 def lookup_generate(dim, n_keys, mode = 1):
@@ -23,4 +24,37 @@ def lookup_generate(dim, n_keys, mode = 1):
 xor_result = (xor_result != 0).astype(int)
 xor_result[xor_result == 0] = -1
 counter = xor_result.sum(axis=0)
-print(counter)
+
+N_train =200
+Y_train =  np.random.choice([-1, 1], size=(N_train))
+#print(Y_train)
+HDC_cont_train = np.random.choice([-1,0,1], size=(N_train,1))
+gamma = 2
+Beta = np.zeros((N_train+1, N_train+1)) #LS-SVM regression matrix
+omega = np.zeros((N_train, N_train))
+
+for i in range(N_train):
+    for j in range(N_train):
+        omega[i, j] = Y_train[i] * Y_train[j] * HDC_cont_train[i] * HDC_cont_train[j]
+        
+Beta[1:N_train+1,0] = Y_train
+Beta[0,1:N_train+1] = np.transpose(Y_train)
+Beta[1:N_train+1,1:N_train+1] = omega + pow(gamma,-1) * np.identity(N_train)
+
+
+        
+#Target vector L:
+            
+L = np.zeros(N_train+1)
+L[1:N_train+1] = np.ones(N_train)
+        
+#Solve the system of equations to get the vector alpha:
+            
+v = np.zeros(N_train+1)
+lu, piv = lu_factor(Beta)
+v = lu_solve((lu,piv),L)
+alpha = v[1:N_train+1]
+b = v[0]
+print(v)
+print(len(alpha))     
+print(b) 
\ No newline at end of file