Correct mistake in trellis evaluation in accordance with the CTC paper

examples/tutorials/forced_alignment_tutorial.py

@@ -146,10 +146,11 @@ def plot():
 #
 # To generate, the probability of time step :math:`t+1`, we look at the
 # trellis from time step :math:`t` and emission at time step :math:`t+1`.
-# There are two path to reach to time step :math:`t+1` with label
-# :math:`c_{j+1}`. The first one is the case where the label was
+# There are three paths to reach to time step :math:`t+1` with label
+# :math:`c_{j+1}`. The first two are the cases where the label was
 # :math:`c_{j+1}` at :math:`t` and there was no label change from
-# :math:`t` to :math:`t+1`. The other case is where the label was
+# :math:`t` to :math:`t+1`. For this we use he probability of 'blank' 
+# emission and repeating the same letter. The last case is where the label was
 # :math:`c_j` at :math:`t` and it transitioned to the next label
 # :math:`c_{j+1}` at :math:`t+1`.
 #
@@ -160,7 +161,7 @@ def plot():
 # Since we are looking for the most likely transitions, we take the more
 # likely path for the value of :math:`k_{(t+1, j+1)}`, that is
 #
-# :math:`k_{(t+1, j+1)} = max( k_{(t, j)} p(t+1, c_{j+1}), k_{(t, j+1)} p(t+1, repeat) )`
+# :math:`k_{(t+1, j+1)} = max( k_{(t, j)} p(t+1, c_{j+1}), k_{(t, j+1)} p(t+1, blank), k_{(t, j+1)} p(t+1, c_{j+1}))`
 #
 # where :math:`k` represents is trellis matrix, and :math:`p(t, c_j)`
 # represents the probability of label :math:`c_j` at time step :math:`t`.
@@ -194,6 +195,10 @@ def get_trellis(emission, tokens, blank_id=0):
             # Score for changing to the next token
             trellis[t, :-1] + emission[t, tokens[1:]],
         )
+        trellis[t+1,1:] = torch.maximum(
+            trellis[t+1,1:],
+            trellis[t, 1:] + emission[t, tokens[1:]],
+        )
     return trellis