fix

Author: KevinZonda

Function_test.py

@@ -2,6 +2,7 @@
 from Variable import Variable
 import numpy as np
 import unittest
+import Utils as u
 
 def Test1():
     x = Variable(11)
@@ -87,3 +88,13 @@ def test_backward(self):
 
         expected = np.array(6.)
         self.assertEqual(X.grad, expected)
+
+    def test_backward_auto(self):
+        X = Variable(np.array(np.random.rand(1)))
+        y = square(X)
+        y.backward()
+        expected = u.numerical_diff(square, X)
+        print(expected)
+        print(X.grad)
+        flag = np.allclose(X.grad, expected)
+        self.assertTrue(flag)

Utils.py

@@ -1,6 +1,14 @@
 import numpy as np
+from Variable import Variable
 
 def as_array(x) -> np.ndarray:
     if np.isscalar(x):
         return np.array(x)
     return x
+
+def numerical_diff(fx, x: Variable, eps=1e-4):
+    x_l = Variable(as_array(x.data-eps))
+    x_r = Variable(as_array(x.data+eps))
+    y_l = fx(x_l)
+    y_r = fx(x_r)
+    return (y_r.data - y_l.data) / (2*eps)