*TODO* Freshen up this old documentation

io - defines aesara.function [TODO]#


The inputs argument to aesara.function is a list, containing the Variable instances for which values will be specified at the time of the function call. But inputs can be more than just Variables. In instances let us attach properties to Variables to tell function more about how to use them.

__init__(variable, name=None, value=None, update=None, mutable=False, strict=False, autoname=True, implicit=None)[source]#

variable: a Variable instance. This will be assigned a value before running the function, not computed from its owner.

name: Any type. (If autoname_input==True, defaults to If name is a valid Python identifier, this input can be set by kwarg, and its value can be accessed by self.<name>. The default value is None.

value: literal or Container. The initial/default value for this

input. If update is`` None``, this input acts just like an argument with a default value in Python. If update is not None, changes to this value will “stick around”, whether due to an update or a user’s explicit action.

update: Variable instance. This expression Variable will replace value after each function call. The default value is None, indicating that no update is to be done.

mutable: Bool (requires value). If True, permit the compiled function to modify the Python object being used as the default value. The default value is False.

strict: Bool (default: False ). True means that the value you pass for this input must have exactly the right type. Otherwise, it may be cast automatically to the proper type.

autoname: Bool. If set to True, if name is None and the Variable has a name, it will be taken as the input’s name. If autoname is set to False, the name is the exact value passed as the name parameter (possibly None).

implicit: Bool or None (default: None)

True: This input is implicit in the sense that the user is not allowed to provide a value for it. Requires value to be set.

False: The user can provide a value for this input. Be careful when value is a container, because providing an input value will overwrite the content of this container.

None: Automatically choose between True or False depending on the situation. It will be set to False in all cases except if value is a container (so that there is less risk of accidentally overwriting its content without being aware of it).

Value: initial and default values#

A non-None value argument makes an In() instance an optional parameter of the compiled function. For example, in the following code we are defining an arity-2 function inc.

>>> import aesara.tensor as at
>>> from aesara import function
>>> from import In
>>> u, x, s = at.scalars('u', 'x', 's')
>>> inc = function([u, In(x, value=3), In(s, update=(s+x*u), value=10.0)], [])

Since we provided a value for s and x, we can call it with just a value for u like this:

>>> inc(5)         # update s with 10+3*5
>>> print(inc[s])

The effect of this call is to increment the storage associated to s in inc by 15.

If we pass two arguments to inc, then we override the value associated to x, but only for this one function call.

>>> inc(3, 4)      # update s with 25 + 3*4
>>> print(inc[s])
>>> print(inc[x])   # the override value of 4 was only temporary

If we pass three arguments to inc, then we override the value associated with x and u and s. Since s’s value is updated on every call, the old value of s will be ignored and then replaced.

>>> inc(3, 4, 7)      # update s with 7 + 3*4
>>> print(inc[s])

We can also assign to inc[s] directly:

>>> inc[s] = 10
>>> inc[s]

Input Argument Restrictions#

The following restrictions apply to the inputs to aesara.function:

  • Every input list element must be a valid In instance, or must be upgradable to a valid In instance. See the shortcut rules below.

  • The same restrictions apply as in Python function definitions: default arguments and keyword arguments must come at the end of the list. Un-named mandatory arguments must come at the beginning of the list.

  • Names have to be unique within an input list. If multiple inputs have the same name, then the function will raise an exception. [*Which exception?]

  • Two In instances may not name the same Variable. I.e. you cannot give the same parameter multiple times.

If no name is specified explicitly for an In instance, then its name will be taken from the Variable’s name. Note that this feature can cause harmless-looking input lists to not satisfy the two conditions above. In such cases, Inputs should be named explicitly to avoid problems such as duplicate names, and named arguments preceding unnamed ones. This automatic naming feature can be disabled by instantiating an In instance explicitly with the autoname flag set to False.

Access to function values and containers#

For each input, aesara.function will create a Container if value was not already a Container (or if implicit was False). At the time of a function call, each of these containers must be filled with a value. Each input (but especially ones with a default value or an update expression) may have a value between calls. The function interface defines a way to get at both the current value associated with an input, as well as the container which will contain all future values:

  • The value property accesses the current values. It is both readable and writable, but assignments (writes) may be implemented by an internal copy and/or casts.

  • The container property accesses the corresponding container. This property accesses is a read-only dictionary-like interface. It is useful for fetching the container associated with a particular input to share containers between functions, or to have a sort of pointer to an always up-to-date value.

Both value and container properties provide dictionary-like access based on three types of keys:

  • integer keys: you can look up a value/container by its position in the input list;

  • name keys: you can look up a value/container by its name;

  • Variable keys: you can look up a value/container by the Variable it corresponds to.

In addition to these access mechanisms, there is an even more convenient method to access values by indexing a Function directly by typing fn[<name>], as in the examples above.

To show some examples of these access methods…

>>> from aesara import tensor as at, function
>>> a, b, c = at.scalars('xys') # set the internal names of graph nodes
>>> # Note that the name of c is 's', not 'c'!
>>> fn = function([a, b, ((c, c+a+b), 10.0)], [])
>>> # the value associated with c is accessible in 3 ways
>>> fn['s'] is fn.value[c]
>>> fn['s'] is fn.container[c].value
>>> fn['s']
>>> fn(1, 2)
>>> fn['s']
>>> fn['s'] = 99.0
>>> fn(1, 0)
>>> fn['s']
>>> fn.value[c] = 99.0
>>> fn(1,0)
>>> fn['s']
>>> fn['s'] == fn.value[c]
>>> fn['s'] == fn.container[c].value

Input Shortcuts#

Every element of the inputs list will be upgraded to an In instance if necessary.

  • a Variable instance r will be upgraded like In(r)

  • a tuple (name, r) will be In(r, name=name)

  • a tuple (r, val) will be In(r, value=value, autoname=True)

  • a tuple ((r,up), val) will be In(r, value=value, update=up, autoname=True)

  • a tuple (name, r, val) will be In(r, name=name, value=value)

  • a tuple (name, (r,up), val) will be In(r, name=name, value=val, update=up, autoname=True)


>>> import aesara
>>> from aesara import tensor as at
>>> from import In
>>> x = at.scalar()
>>> y = at.scalar('y')
>>> z = at.scalar('z')
>>> w = at.scalar('w')
>>> fn = aesara.function(inputs=[x, y, In(z, value=42), ((w, w+x), 0)],
...                      outputs=x + y + z)
>>> # the first two arguments are required and the last two are
>>> # optional and initialized to 42 and 0, respectively.
>>> # The last argument, w, is updated with w + x each time the
>>> # function is called.
>>> fn(1)               # illegal because there are two required arguments 
Traceback (most recent call last):
TypeError: Missing required input: y
>>> fn(1, 2)            # legal, z is 42, w goes 0 -> 1 (because w <- w + x)
>>> fn(1, y=2)        # legal, z is 42, w goes 1 -> 2
>>> fn(x=1, y=2)    # illegal because x was not named 
Traceback (most recent call last):
TypeError: Unknown input or state: x. The function has 3 named inputs (y, z, w), and 1 unnamed input which thus cannot be accessed through keyword argument (use 'name=...' in a variable's constructor to give it a name).
>>> fn(1, 2, 3)         # legal, z is 3, w goes 2 -> 3
>>> fn(1, z=3, y=2) # legal, z is 3, w goes 3 -> 4
>>> fn(1, 2, w=400)   # legal, z is 42 again, w goes 400 -> 401
>>> fn(1, 2)            # legal, z is 42, w goes 401 -> 402

In the example above, z has value 42 when no value is explicitly given. This default value is potentially used at every function invocation, because z has no update or storage associated with it.


The outputs argument to function can be one of

  • None, or

  • a Variable or Out instance, or

  • a list of Variables or Out instances.

An Out instance is a structure that lets us attach options to individual output Variable instances, similarly to how In lets us attach options to individual input Variable instances.

Out(variable, borrow=False) returns an Out instance:

  • borrow

    If True, a reference to function’s internal storage is OK. A value returned for this output might be clobbered by running the function again, but the function might be faster.

    Default: False

If a single Variable or Out instance is given as argument, then the compiled function will return a single value.

If a list of Variable or Out instances is given as argument, then the compiled function will return a list of their values.

>>> import numpy
>>> from import Out
>>> x, y, s = at.matrices('xys')
>>> # print a list of 2 ndarrays
>>> fn1 = aesara.function([x], [x+x, Out((x+x).T, borrow=True)])
>>> fn1(numpy.asarray([[1,0],[0,1]]))
[array([[ 2.,  0.],
       [ 0.,  2.]]), array([[ 2.,  0.],
       [ 0.,  2.]])]
>>> # print a list of 1 ndarray
>>> fn2 = aesara.function([x], [x+x])
>>> fn2(numpy.asarray([[1,0],[0,1]]))
[array([[ 2.,  0.],
       [ 0.,  2.]])]
>>> # print an ndarray
>>> fn3 = aesara.function([x], outputs=x+x)
>>> fn3(numpy.asarray([[1,0],[0,1]]))
array([[ 2.,  0.],
       [ 0.,  2.]])