Logistic

autodiff/functions.py

@@ -359,6 +359,28 @@ def tanh(sclr):
     """
     return sinh(sclr) / cosh(sclr);
 
+
+@vectorize
+def logistic(sclr):
+    """
+    This function takes in an int, float, or Scalar object and applies the logistic function to the value. If the argument is an int or float, then the function returns a float. If the argument is a Scalar object, the function returns a new Scalar object with the updated value and derivative.
+    INPUTS
+    =======
+    sclr: An int, float, or Scalar object on which the the logistic function will be applied.
+    RETURNS
+    ========
+    float, Scalar
+    A float is returned if the input is an int/float. A new Scalar object, resulting from applying the logistic function to 'sclr', is returned if the input is a Scalar object .
+    NOTES
+    =====
+    POST:
+        - 'sclr' is not changed by the function
+        - returns a float or Scalar object, resulting from applying the logistic function to 'sclr'.
+    """
+
+    return 1 / (1 + exp(-sclr))
+
+
 @vectorize
 def log(sclr, base):
     """

tests/test_functions.py

@@ -125,6 +125,32 @@ def test_exp():
     assert(np.isclose(z.getDeriv()['x'],  5 * np.exp(-15)))
     assert(np.isclose(z.getDeriv()['y'],  -3 * np.exp(-15)))
 
+def test_logistic():
+    x = ad.Scalar('x', 8)
+    y = ad.logistic(x)
+    assert(np.isclose(y.getValue(), 1 / (1 + np.exp(-8))))
+    assert(np.isclose(y.getDeriv()['x'], (1 / (1 + np.exp(-8))) * (1 - 1 / (1 + np.exp(-8)))))
+
+    x = ad.Scalar('x', 0)
+    y = ad.logistic(x)
+    assert(np.isclose(y.getValue(), 0.5))
+    assert(np.isclose(y.getDeriv()['x'], (0.25)))   
+
+    x = ad.Scalar('x', 5)
+    y = ad.Scalar('y', 2)
+    z = ad.logistic(x * y)
+    assert(np.isclose(z.getValue(), 1 / (1 + np.exp(-10))))
+    assert(np.isclose(z.getDeriv()['x'], 2  * (1 / (1 + np.exp(-10))) * (1 - 1 / (1 + np.exp(-10)))))   
+    assert(np.isclose(z.getDeriv()['y'], 5  * (1 / (1 + np.exp(-10))) * (1 - 1 / (1 + np.exp(-10)))))   
+
+    x = ad.Scalar('x', 8)
+    y = ad.logistic(2 * x)
+    assert(np.isclose(y.getValue(), 1 / (1 + np.exp(-16))))
+    assert(np.isclose(y.getDeriv()['x'], 2  * (1 / (1 + np.exp(-16))) * (1 - 1 / (1 + np.exp(-16)))))
+
+    assert(np.isclose(ad.logistic(0), 0.5))
+
+
 
 def test_power():
     assert(ad.power(5, 3) == 125.0)