tf.scan

TensorFlow 2 version View source on GitHub

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

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

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, and the second is the value at the current position of elems. 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. If reverse=True, it's fn(initializer, values[-1]).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.

fn The callable to be performed. It accepts two arguments. The first will have the same structure as initializer if one is provided, otherwise it will have the same structure as elems. The second will have the same (possibly nested) 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.
reverse (optional) True scans the tensor last to first (instead of first to last).
name (optional) Name prefix for the returned tensors.

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 (or last to first, if reverse=True).

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:

elems = np.array([1, 2, 3, 4, 5, 6])
sum = scan(lambda a, x: a + x, elems)
# sum == [1, 3, 6, 10, 15, 21]
sum = scan(lambda a, x: a + x, elems, reverse=True)
# sum == [21, 20, 18, 15, 11, 6]

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]

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])