Updated documentation, added test

theano/tensor/basic.py

@@ -3142,11 +3142,13 @@ def var(input, axis=None, keepdims=False, corrected=False):
     corrected : bool
         If this is set to True, the 'corrected_two_pass' algorithm is
         used to compute the variance.
+        Refer : http://www.cs.yale.edu/publications/techreports/tr222.pdf
 
     Notes
     -----
-    It uses the two-pass algorithm for more stable results.
+    By default, uses the two-pass algorithm for more stable results.
     https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Two-pass_algorithm
+    Also supports 'corrected_two_pass' algorithm, as mentioned above.
     There exist other implementations that are even more stable, but probably
     slower.
 

theano/tensor/tests/test_basic.py

@@ -6319,8 +6319,6 @@ def test_var():
     f = function([a], var(a))
 
     a_val = numpy.arange(60).reshape(3, 4, 5)
-    # print numpy.var(a_val)
-    # print f(a_val)
     assert numpy.allclose(numpy.var(a_val), f(a_val))
 
     f = function([a], var(a, axis=0))
@@ -6333,7 +6331,13 @@ def test_var():
     assert numpy.allclose(numpy.var(a_val, axis=2), f(a_val))
 
     f = function([a], var(a, corrected=True))
-    assert numpy.allclose(numpy.var(a_val), f(a_val))
+    mean_a = numpy.mean(a_val)
+    centered_a = a_val - mean_a
+    v = numpy.mean(centered_a ** 2)
+    error = (numpy.mean(centered_a)) ** 2
+    v = v - error
+    assert numpy.allclose(v, f(a_val))
+
 
 class T_sum(unittest.TestCase):
     def test_sum_overflow(self):