# Higher Order Operators

TensorFlow provides several higher order operators to simplify the common map-reduce programming patterns.

### tf.map_fn(fn, elems, dtype=None, parallel_iterations=10, back_prop=True, swap_memory=False, infer_shape=True, name=None)

map on the list of tensors unpacked from elems on dimension 0.

The simplest version of map repeatedly applies the callable fn to a sequence of elements from first to last. The elements are made of the tensors unpacked from elems. dtype is the data type of the return value of fn. Users must provide dtype if it is different from the data type of elems.

Suppose that elems is unpacked into values, a list of tensors. The shape of the result tensor is [values.shape[0]] + fn(values[0]).shape.

This method also allows multi-arity elems and output of fn. If elems is a (possibly nested) list or tuple of tensors, then each of these tensors must have a matching first (unpack) dimension. The signature of fn may match the structure of elems. That is, if elems is (t1, [t2, t3, [t4, t5]]), then an appropriate signature for fn is: fn = lambda (t1, [t2, t3, [t4, t5]]):.

Furthermore, fn may emit a different structure than its input. For example, fn may look like: fn = lambda t1: return (t1 + 1, t1 - 1). In this case, the dtype parameter is not optional: dtype must be a type or (possibly nested) tuple of types matching the output of fn.

##### Args:
• fn: The callable to be performed. It accepts one argument, which will have the same (possibly nested) structure as elems. Its output must have the same structure as dtype if one is provided, otherwise it must have the same structure as elems.
• elems: A tensor or (possibly nested) sequence of tensors, each of which will be unpacked along their first dimension. The nested sequence of the resulting slices will be applied to fn.
• dtype: (optional) The output type(s) of fn. If fn returns a structure of Tensors differing from the structure of elems, then dtype is not optional and must have the same structure as the output of fn.
• parallel_iterations: (optional) The number of iterations allowed to run in parallel.
• back_prop: (optional) True enables support for back propagation.
• swap_memory: (optional) True enables GPU-CPU memory swapping.
• infer_shape: (optional) False disables tests for consistent output shapes.
• name: (optional) Name prefix for the returned tensors.
##### Returns:

A tensor or (possibly nested) sequence of tensors. Each tensor packs the results of applying fn to tensors unpacked from elems along the first dimension, from first to last.

##### Raises:
• TypeError: if fn is not callable or the structure of the output of fn and dtype do not match.
• ValueError: if the lengths of the output of fn and dtype do not match.
##### Examples:

python elems = np.array([1, 2, 3, 4, 5, 6]) squares = map_fn(lambda x: x * x, elems) # squares == [1, 4, 9, 16, 25, 36]

python elems = (np.array([1, 2, 3]), np.array([-1, 1, -1])) alternate = map_fn(lambda x: x[0] * x[1], elems, dtype=tf.int64) # alternate == [-1, 2, -3]

python elems = np.array([1, 2, 3]) alternates = map_fn(lambda x: (x, -x), elems, dtype=(tf.int64, tf.int64)) # alternates[0] == [1, 2, 3] # alternates[1] == [-1, -2, -3]

### tf.foldl(fn, elems, initializer=None, parallel_iterations=10, back_prop=True, swap_memory=False, name=None)

foldl on the list of tensors unpacked from elems on dimension 0.

This foldl operator repeatedly applies the callable fn to a sequence of elements from first to last. The elements are made of the tensors unpacked from elems on dimension 0. The callable fn takes two tensors as arguments. The first argument is the accumulated value computed from the preceding invocation of fn. If initializer is None, elems must contain at least one element, and its first element is used as the initializer.

Suppose that elems is unpacked into values, a list of tensors. The shape of the result tensor is fn(initializer, values[0]).shape.

##### Args:
• fn: The callable to be performed.
• elems: A tensor to be unpacked on dimension 0.
• initializer: (optional) The initial value for the accumulator.
• parallel_iterations: (optional) The number of iterations allowed to run in parallel.
• back_prop: (optional) True enables support for back propagation.
• swap_memory: (optional) True enables GPU-CPU memory swapping.
• name: (optional) Name prefix for the returned tensors.
##### Returns:

A tensor resulting from applying fn consecutively to the list of tensors unpacked from elems, from first to last.

##### Raises:
• TypeError: if fn is not callable.
##### Example:

python elems = [1, 2, 3, 4, 5, 6] sum = foldl(lambda a, x: a + x, elems) # sum == 21

### tf.foldr(fn, elems, initializer=None, parallel_iterations=10, back_prop=True, swap_memory=False, name=None)

foldr on the list of tensors unpacked from elems on dimension 0.

This foldr operator repeatedly applies the callable fn to a sequence of elements from last to first. The elements are made of the tensors unpacked from elems. The callable fn takes two tensors as arguments. The first argument is the accumulated value computed from the preceding invocation of fn. If initializer is None, elems must contain at least one element, and its first element is used as the initializer.

Suppose that elems is unpacked into values, a list of tensors. The shape of the result tensor is fn(initializer, values[0]).shape.

##### Args:
• fn: The callable to be performed.
• elems: A tensor that is unpacked into a sequence of tensors to apply fn.
• initializer: (optional) The initial value for the accumulator.
• parallel_iterations: (optional) The number of iterations allowed to run in parallel.
• back_prop: (optional) True enables support for back propagation.
• swap_memory: (optional) True enables GPU-CPU memory swapping.
• name: (optional) Name prefix for the returned tensors.
##### Returns:

A tensor resulting from applying fn consecutively to the list of tensors unpacked from elems, from last to first.

##### Raises:
• TypeError: if fn is not callable.
##### Example:

python elems = [1, 2, 3, 4, 5, 6] sum = foldr(lambda a, x: a + x, elems) # sum == 21

### tf.scan(fn, elems, initializer=None, parallel_iterations=10, back_prop=True, swap_memory=False, infer_shape=True, name=None)

scan on the list of tensors unpacked from elems on dimension 0.

The simplest version of scan repeatedly applies the callable fn to a sequence of elements from first to last. The elements are made of the tensors unpacked from elems on dimension 0. The callable fn takes two tensors as arguments. The first argument is the accumulated value computed from the preceding invocation of fn. If initializer is None, elems must contain at least one element, and its first element is used as the initializer.

Suppose that elems is unpacked into values, a list of tensors. The shape of the result tensor is [len(values)] + fn(initializer, values[0]).shape.

This method also allows multi-arity elems and accumulator. If elems is a (possibly nested) list or tuple of tensors, then each of these tensors must have a matching first (unpack) dimension. The second argument of fn must match the structure of elems.

If no initializer is provided, the output structure and dtypes of fn are assumed to be the same as its input; and in this case, the first argument of fn must match the structure of elems.

If an initializer is provided, then the output of fn must have the same structure as initializer; and the first argument of fn must match this structure.

For example, if elems is (t1, [t2, t3]) and initializer is [i1, i2] then an appropriate signature for fn in python2 is: fn = lambda (acc_p1, acc_p2), (t1 [t2, t3]): and fn must return a list, [acc_n1, acc_n2]. An alternative correct signature for fn, and the one that works in python3, is: fn = lambda a, t:, where a and t correspond to the input tuples.

##### Args:
• fn: The callable to be performed. It accepts two arguments. The first will have the same (possibly nested) structure as elems. The second will have the same structure as initializer if one is provided, otherwise it will have the same structure as elems. Its output must have the same structure as initializer if one is provided, otherwise it must have the same structure as elems.
• elems: A tensor or (possibly nested) sequence of tensors, each of which will be unpacked along their first dimension. The nested sequence of the resulting slices will be the first argument to fn.
• initializer: (optional) A tensor or (possibly nested) sequence of tensors, initial value for the accumulator, and the expected output type of fn.
• parallel_iterations: (optional) The number of iterations allowed to run in parallel.
• back_prop: (optional) True enables support for back propagation.
• swap_memory: (optional) True enables GPU-CPU memory swapping.
• infer_shape: (optional) False disables tests for consistent output shapes.
• name: (optional) Name prefix for the returned tensors.
##### Returns:

A tensor or (possibly nested) sequence of tensors. Each tensor packs the results of applying fn to tensors unpacked from elems along the first dimension, and the previous accumulator value(s), from first to last.

##### Raises:
• TypeError: if fn is not callable or the structure of the output of fn and initializer do not match.
• ValueError: if the lengths of the output of fn and initializer do not match.
##### Examples:

python elems = np.array([1, 2, 3, 4, 5, 6]) sum = scan(lambda a, x: a + x, elems) # sum == [1, 3, 6, 10, 15, 21]

python elems = np.array([1, 2, 3, 4, 5, 6]) initializer = np.array(0) sum_one = scan( lambda a, x: x[0] - x[1] + a, (elems + 1, elems), initializer) # sum_one == [1, 2, 3, 4, 5, 6]

python elems = np.array([1, 0, 0, 0, 0, 0]) initializer = (np.array(0), np.array(1)) fibonaccis = scan(lambda a, _: (a[1], a[0] + a[1]), elems, initializer) # fibonaccis == ([1, 1, 2, 3, 5, 8], [1, 2, 3, 5, 8, 13])`