reversed tensordot arguments to remove transpose for xgrad. updated comments.

theano/tensor/basic.py

@@ -6977,34 +6977,33 @@ class Dot(Op):
 
         # x or y is tensor, grad is tensor
         #
-        # the grad has the same dim as the dot product output, namely
-        # (x.shape[:-1] + y.shape[:-2] + [y.shape[-1]]). To get the grad
+        # the output grad has the same dim as the dot product output, namely
+        # x.shape[:-1] + y.shape[:-2] + y.shape[-1:]. To get the grad
         # wrt x or y, a tensordot is used to sum out non-compatible dims.
         #
-        # for grad x:
-        #     gradient is a tensordot over y and grad, summing out all but
-        #     the second-to-last dim of y (if it exists) and transposed
-        #     such that the first resulting dim goes last.
+        # for grad wrt x:
+        #     grad is a tensordot of the output grad and y, summing out all but
+        #     the second-to-last dim of y. If y is a vector, no sum is taken.
         #
-        # for grad y:
-        #     gradient is a tensordot over x and grad, summing out all but
-        #     the last dim of x and transposed such that the first
-        #     resulting dim goes second-to-last (unless ydim == 1, when
-        #     it goes last).
+        # for grad wrt y:
+        #     grad is a tensordot of the output grad and x, summing out
+        #     all but the last dim of x. If y is not a vector, the tensordot is
+        #     transposed so that its last dim becomes its second-to-last.
         else:
-            x_axes0 = range(ydim-2)
-            x_axes1 = range(xdim - 1, gdim)
-            x_tdims = range(1, xdim) + [0]
-            if ydim >= 2:
-                x_axes0 += [ydim - 1]
-            xgrad = tensordot(y, gz, [x_axes0, x_axes1]).transpose(x_tdims)
-
-            y_axes0 = range(xdim - 1)
-            y_axes1 = range(xdim - 1)
-            y_tdims = range(1, ydim - 1) + [0]
-            if ydim >= 2:
-                y_tdims += [ydim - 1]
-            ygrad = tensordot(x, gz, [y_axes0, y_axes1]).transpose(y_tdims)
+            gy_axes = range(xdim - 1, gdim)
+            if ydim != 1:
+                y_axes = [ax for ax in range(ydim) if ax != ydim - 2]
+            else:
+                y_axes = []
+            xgrad = tensordot(gz, y, [gy_axes, y_axes])
+
+            gx_axes = y_axes = range(xdim - 1)
+            if ydim != 1:
+                t_dims = range(ydim)
+                t_dims[-2], t_dims[-1] = t_dims[-1], t_dims[-2]
+                ygrad = tensordot(gz, x, [gx_axes, y_axes]).transpose(t_dims)
+            else:
+                ygrad = tensordot(gz, x, [gx_axes, y_axes])
 
         rval = xgrad, ygrad