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

@@ -3609,16 +3609,16 @@ class T_Join_and_Split(unittest.TestCase):
         f = function([a, b], s, mode=self.mode)
         v = numpy.zeros((2, 3, 2))
         v[:,:,0] = v1
-        v[:,:,1] = v2 
-        out = f(v1, v2) 
+        v[:,:,1] = v2
+        out = f(v1, v2)
         self.assertTrue(v.shape == out.shape)
         self.assertTrue(numpy.all(v == out))
         s = stack([a, b], axis=-2)
         f = function([a, b], s, mode=self.mode)
         v = numpy.zeros((2, 2, 3))
         v[:,0,:] = v1
-        v[:,1,:] = v2 
-        out = f(v1, v2) 
+        v[:,1,:] = v2
+        out = f(v1, v2)
         self.assertTrue(v.shape == out.shape)
         self.assertTrue(numpy.all(v == out))
         # Testing out-of-bounds axis
@@ -5437,7 +5437,7 @@ def test_tile():
     # Test 1,2,3,4-dimensional cases.
     # Test input x has the shape [2], [2, 4], [2, 4, 3], [2, 4, 3, 5].
     test_shape = [2, 4, 3, 5]
-    k = 0 
+    k = 0
     for xtype in [vector(), matrix(), tensor3(), tensor4()]:
         x = xtype
         k = k+1
@@ -5495,7 +5495,7 @@ def test_tile():
             reps_ = r[:k-1]
             f = function([x], tile(x, reps_, ndim_))
             assert numpy.all( f(x_) == numpy.tile(x_, [1, 1] + reps_))
-           
+
         # error raising test: ndim not specified when reps is vector
         reps = ivector()
         numpy.testing.assert_raises(ValueError, tile, x, reps)
@@ -5503,7 +5503,7 @@ def test_tile():
         # error raising test: not a integer
         for reps in [2.5, fscalar(), fvector()]:
             numpy.testing.assert_raises(ValueError, tile, x, reps)
-        
+
         # error raising test: the dimension of reps exceeds 1
         reps = imatrix()
         numpy.testing.assert_raises(ValueError, tile, x, reps)
@@ -5514,14 +5514,14 @@ def test_tile():
             if k > 1:
                 ndim = k-1
                 numpy.testing.assert_raises(ValueError, tile, x, reps, ndim)
-        
+
         # error raising test: reps is list, len(reps) > ndim
         r = [2, 3, 4, 5, 6]
         reps = r[:k+1]
         ndim = k
         numpy.testing.assert_raises(ValueError, tile, x, reps, ndim)
 
-        # error raising test: 
+        # error raising test:
         # reps is tensor.vector and len(reps_value) > ndim,
         # reps_value is the real value when excuting the function.
         reps = ivector()
@@ -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):