diff --git a/optimizer.py b/optimizer.py
index 4dd4cd5..d392cd1 100644
--- a/optimizer.py
+++ b/optimizer.py
@@ -1,33 +1,63 @@
 #!/usr/bin/env python3
 # -*- coding: utf-8 -*-
 """
 Created on Wed Oct 10 12:31:42 2018
 
 @author: alessia
 """
 
 import numpy as np
 import scipy.optimize as sopt
+from mpl_toolkits.mplot3d import Axes3D
+import matplotlib.pyplot as plt
+from matplotlib import cm
+from matplotlib.ticker import LinearLocator, FormatStrFormatter
+
 
 def S(x):
     x1 = x[0]
     x2 = x[1]
-    return 2. * x1 ** 2 + 3. / 2. * x2 ** 2 + x1 * x2 - x1 - 2 * x2 + 6
+    return 2. * (x1 ** 2) + 3. / 2. * (x2 ** 2) + x1 * x2 - x1 - 2 * x2 + 6
 
 path = []
-
 def getIterationSteps(x):
     path.append(x)
-
+    
+def plotFunc(S,path):
+    
+    fig = plt.figure()
+    ax = fig.gca(projection='3d')
+    
+    # Plot the surface.
+    X1 = np.arange(-3, 3, 0.1)
+    X2 = np.arange(-3, 3, 0.1)
+    X1, X2 = np.meshgrid(X1,X2)
+    X3 = S((X1,X2))
+    surf = ax.plot_surface(X1, X2, X3, cmap=cm.coolwarm,linewidth=0, antialiased=False)
+    
+    # Plot the path.
+    path=np.array(path)
+    x1 = path[:,0]
+    x2 = path[:,1]
+    x3 = S((x1,x2))
+    ax.plot(x1,x2,x3,'--k')
+    
+    fig.colorbar(surf, shrink=0.5, aspect=5)
+    plt.show()       
+    
+
+#-------------------------------------------------------------------------------------------------------------------
 
 method1 = 'BFGS'
 method2 = 'CG'
 
 x = np.random.rand(2)
 path.append(x)
+
 minimum = sopt.minimize(S,x,method=method2, tol=1e-14, callback=getIterationSteps)
 
-print (path[:])
 print ("starting point = ", path[0])
 print ("minimum = ", path[-1] )
-print ("# iterations = ", len(path))
\ No newline at end of file
+print ("# iterations = ", len(path))
+
+plotFunc(S,path)
\ No newline at end of file