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docs/tutorials/control_flow/ControlFlowTutorial.md

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+MXNet currently provides three control flow operators: `cond`, `foreach` and `while_loop`. Like other MXNet operators, they all have a version for NDArray and a version for Symbol. These two versions have exactly the same semantics. We can take advantage of this and use Gluon hybrid blocks and switch between hybrid and non-hybrid modes seamleessly.
+
+In this tutorial, we use a few examples to demonstrate the use of control flow operators in Gluon and show how a model that requires control flow is hybridized.
+
+# Prepare running the code
+
+
+```python
+import mxnet as mx
+from mxnet.gluon import HybridBlock
+```
+
+# foreach
+`foreach` is defined with the following signature:
+
+```python
+foreach(body, data, init_states, name) => (outputs, states)
+```
+
+It iterates over the first dimension of the input data (it can be an array or multiple arrays) and run the Python function defined in `body` for every slice from the input arrays. The signature of the `body` function is defined as follows:
+
+```python
+body(data, states) => (outputs, states)
+```
+
+The inputs of the `body` function have two parts: `data` is a slice of an array (if there is only one input array in `foreach`) or a list of slices (if there are multiple input arrays); `states` are the arrays from the previous iteration. The outputs of the `body` function also have two parts: `outputs` is an array or a list of arrays; `states` is the computation states of the current iteration. `outputs` from all iterations are concatenated as the outputs of `foreach`.
+
+The pseudocode below illustrates the execution of `foreach`.
+
+```python
+def foreach(body, data, init_states):
+    states = init_states
+    outs = []
+
+    for i in range(data.shape[0]):
+        s = data[i]
+        out, states = body(s, states)
+        outs.append(out)
+    outs = mx.nd.stack(*outs)
+    return outs, states
+```
+
+### Example 1: foreach works like map
+`foreach` can work like a map function in a functional language. In this case, the states of foreach can be an empty list, which means the computation doesn't carry computation states across iterations.
+
+In this example, we use `foreach` to add each element in an array by one.
+
+
+```python
+data = mx.nd.arange(5)
+print(data)
+```
+
+
+    [ 0.  1.  2.  3.  4.]
+    <NDArray 5 @cpu(0)>
+
+
+
+```python
+def add1(data, _):
+    return data + 1, []
+
+class Map(HybridBlock):
+    def hybrid_forward(self, F, data):
+        out, _ = F.contrib.foreach(add1, data, [])
+        return out
+
+map_layer = Map()
+out = map_layer(data)
+print(out)
+```
+
+
+    [[ 1.]
+     [ 2.]
+     [ 3.]
+     [ 4.]
+     [ 5.]]
+    <NDArray 5x1 @cpu(0)>
+
+
+We can hybridize the block and run the computation again. It should generate the same result.
+
+
+```python
+map_layer.hybridize()
+out = map_layer(data)
+print(out)
+```
+
+
+    [[ 1.]
+     [ 2.]
+     [ 3.]
+     [ 4.]
+     [ 5.]]
+    <NDArray 5x1 @cpu(0)>
+
+
+### Example 2: foreach works like scan
+`foreach` can work like a scan function in a functional language. In this case, the outputs of the Python function is an empty list.
+
+
+```python
+def sum(data, state):
+    return [], state + data
+
+class Scan(HybridBlock):
+    def hybrid_forward(self, F, data):
+        _, state = F.contrib.foreach(sum, data, F.zeros((1)))
+        return state
+scan_layer = Scan()
+state = scan_layer(data)
+print(data)
+print(state)
+```
+
+
+    [ 0.  1.  2.  3.  4.]
+    <NDArray 5 @cpu(0)>
+
+    [ 10.]
+    <NDArray 1 @cpu(0)>
+
+
+
+```python
+scan_layer.hybridize()
+state = scan_layer(data)
+print(state)
+```
+
+
+    [ 10.]
+    <NDArray 1 @cpu(0)>
+
+
+### Example 3: foreach with both outputs and states
+This is probably the most common use case of `foreach`. We extend the scan example above and return both output and states.
+
+
+```python
+def sum(data, state):
+    return state + data, state + data
+
+class ScanV2(HybridBlock):
+    def hybrid_forward(self, F, data):
+        out, state = F.contrib.foreach(sum, data, F.zeros((1)))
+        return out, state
+scan_layer = ScanV2()
+out, state = scan_layer(data)
+print(out)
+print(state)
+```
+
+
+    [[  0.]
+     [  1.]
+     [  3.]
+     [  6.]
+     [ 10.]]
+    <NDArray 5x1 @cpu(0)>
+
+    [ 10.]
+    <NDArray 1 @cpu(0)>
+
+
+
+```python
+scan_layer.hybridize()
+out, state = scan_layer(data)
+print(out)
+print(state)
+```
+
+
+    [[  0.]
+     [  1.]
+     [  3.]
+     [  6.]
+     [ 10.]]
+    <NDArray 5x1 @cpu(0)>
+
+    [ 10.]
+    <NDArray 1 @cpu(0)>
+
+
+### Example 4: use foreach to run RNN on a variable-length sequence
+Previous examples illustrate `foreach` with simple use cases. Here I show an example of processing variable-length sequences with `foreach`. The same idea is used by dynamic_rnn in TensorFlow for processing variable-length sequences.
+
+
+```python
+class DynamicRNNLayer(HybridBlock):
+    def __init__(self, cell, prefix=None, params=None):
+        super(DynamicRNNLayer, self).__init__(prefix=prefix, params=params)
+        self.cell = cell
+    def hybrid_forward(self, F, inputs, begin_state, valid_length):
+        states = begin_state
+        zeros = []
+        for s in states:
+            zeros.append(F.zeros_like(s))
+        # the last state is the iteration number.
+        states.append(F.zeros((1)))
+        def loop_body(inputs, states):
+            cell_states = states[:-1]
+            # Get the iteration number from the states.
+            iter_no = states[-1]
+            out, new_states = self.cell(inputs, cell_states)
+            # Copy the old state if we have reached the end of a sequence.
+            for i, state in enumerate(cell_states):
+                new_states[i] = F.where(F.broadcast_greater(valid_length, iter_no),
+                                        new_states[i], state)
+            new_states.append(iter_no + 1)
+            return out, new_states
+
+        outputs, states = F.contrib.foreach(loop_body, inputs, states)
+        outputs = F.SequenceMask(outputs, sequence_length=valid_length,
+                                 use_sequence_length=True, axis=0)
+        # the last state is the iteration number. We don't need it.
+        return outputs, states[:-1]
+```
+
+
+```python
+seq_len = 10
+batch_size = 2
+input_size = 5
+hidden_size = 6
+
+rnn_data = mx.nd.normal(loc=0, scale=1, shape=(seq_len, batch_size, input_size))
+init_states = [mx.nd.normal(loc=0, scale=1, shape=(batch_size, hidden_size)) for i in range(2)]
+valid_length = mx.nd.round(mx.nd.random.uniform(low=1, high=10, shape=(batch_size))) 
+
+lstm = DynamicRNNLayer(mx.gluon.rnn.LSTMCell(hidden_size))
+lstm.initialize()
+res, states = lstm(rnn_data, [x for x in init_states], valid_length)
+
+lstm.hybridize()
+res, states = lstm(rnn_data, [x for x in init_states], valid_length)
+```
+
+# while_loop
+`while_loop` is defined with the following signature:
+
+```python
+while_loop(cond, body, loop_vars, max_iterations, name) => (outputs, states)
+```
+Instead of running over the first dimension of an array, `while_loop` checks a condition function in every iteration and runs a `body` function for computation. The signature of the `body` function is defined as follows:
+
+```python
+body(state1, state2, ...) => (outputs, states)
+```
+
+The inputs of the `body` function in `while_loop` are a little different from the one in `foreach`. It has a variable number of input arguments. Each input argument is a loop variable and the number of arguments is determined by the number of loop variables. The outputs of the `body` function also have two parts: `outputs` is an array or a list of arrays; `states` is the computation states of the current iteration. Like `foreach`, both `outputs` and `states` can be an empty list. `outputs` from all iterations are concatenated as the outputs of `while_loop`.
+
+### Example 5: scan with while_loop
+`while_loop` is more general than `foreach`. We can also use it to iterate over an array and sum all of its values together. In this example, instead of summing over the entire array, we only sum over the first 4 elements.
+
+**Note**: the output arrays of the current implementation of `while_loop` is determined by `max_iterations`. As such, even though the while loop in this example runs 4 iterations, it still outputs an array of 5 elements. The last element in the output array is actually filled with a random number.
+
+
+```python
+class ScanV2(HybridBlock):
+    def hybrid_forward(self, F, data):
+        def sum(state, i):
+            s = state + data[i]
+            return s, [s, i + 1]
+
+        def sum_cond(state, i):
+            return i < 4
+
+        out, state = F.contrib.while_loop(sum_cond, sum,
+                                          [F.zeros((1)), F.zeros((1))], max_iterations=5)
+        return out, state
+scan_layer = ScanV2()
+out, state = scan_layer(data)
+print(out)
+print(state)
+```
+
+
+    [[ 0.]
+     [ 1.]
+     [ 3.]
+     [ 6.]
+     [ 0.]]
+    <NDArray 5x1 @cpu(0)>
+    [
+    [ 6.]
+    <NDArray 1 @cpu(0)>, 
+    [ 4.]
+    <NDArray 1 @cpu(0)>]
+
+
+# cond
+`cond` is defined with the following signature:
+
+```python
+cond(pred, then_func, else_func, name)
+```
+
+`cond` checks `pred`, which is a symbol or an NDArray with one element. If its value is true, it calls `then_func`. Otherwise, it calls `else_func`. The signature of `then_func` and `else_func` are as follows:
+
+```python
+func() => [outputs]
+```
+
+`cond` requires all outputs from `then_func` and `else_func` have the same number of Symbols/NDArrays with the same shapes and data types.
+
+### Example 6: skip RNN computation with cond
+Example 4 shows how to process a batch with sequences of different lengths. In this example, we show how to skip computation after we have met the end of the sequence.
+
+
+```python
+class SkipRNNCell(HybridBlock):
+    def __init__(self, cell, prefix=None, params=None):
+        super(SkipRNNCell, self).__init__(prefix=prefix, params=params)
+        self.cell = cell
+    def hybrid_forward(self, F, i, length, data, states):
+        def run_rnn():
+            return self.cell(data, states)
+
+        def copy_states():
+            return F.zeros_like(data), states
+        out, state = F.contrib.cond(i < length, run_rnn, copy_states)
+        return out, state
+
+class RNNLayer(HybridBlock):
+    def __init__(self, cell, prefix=None, params=None):
+        super(RNNLayer, self).__init__(prefix=prefix, params=params)
+        self.cell = SkipRNNCell(cell)
+    def hybrid_forward(self, F, length, data, init_states):
+        def body(data, states):
+            i = states[0]
+            out, states = self.cell(i, length, data, states[1])
+            return out, [i + 1, states]
+
+        out, state = F.contrib.foreach(body, data, [F.zeros((1)), init_states])
+        return out, state
+```
+
+
+```python
+seq_len = 5
+batch_size = 1
+input_size = 3
+hidden_size = 3
+
+rnn_data = mx.nd.normal(loc=0, scale=1, shape=(seq_len, batch_size, input_size))
+init_states = [mx.nd.normal(loc=0, scale=1, shape=(batch_size, hidden_size)) for i in range(2)]
+
+cell = mx.gluon.rnn.LSTMCell(hidden_size)
+layer = RNNLayer(cell)
+layer.initialize()
+
+out, states = layer(mx.nd.array([3]), rnn_data, init_states)
+print(rnn_data)
+print(out)
+```
+
+
+    [[[-0.70893967  0.79505837  1.01872194]]
+
+     [[-0.15738758 -1.5379014  -0.78309226]]
+
+     [[ 0.5364728  -1.49940979  0.18817241]]
+
+     [[-0.52421683  0.29636207 -0.53233677]]
+
+     [[ 0.85569632 -0.87393355 -0.10898105]]]
+    <NDArray 5x1x3 @cpu(0)>
+
+    [[[ 0.32939154 -0.01365058 -0.25545752]]
+
+     [[ 0.15680683 -0.00335424 -0.14627317]]
+
+     [[ 0.07623718 -0.00953147 -0.09720358]]
+
+     [[ 0.          0.          0.        ]]
+
+     [[ 0.          0.          0.        ]]]
+    <NDArray 5x1x3 @cpu(0)>
+