.. _theano_type:
======================
Making the double type
======================
.. _type_contract:
Type's contract
===============
In Theano's framework, a ``Type`` (:class:`.gof.type.Type`)
is any object which defines the following
methods. To obtain the default methods described below, the Type should
be an instance of ``Type`` or should be an instance of a
subclass of ``Type``. If you will write all methods yourself,
you need not use an instance of ``Type``.
Methods with default arguments must be defined with the same signature,
i.e. the same default argument names and values. If you wish to add
extra arguments to any of these methods, these extra arguments must have
default values.
.. class:: PureType
.. method:: filter(value, strict=False, allow_downcast=None)
This casts a value to match the Type and returns the
cast value. If ``value`` is incompatible with the Type,
the method must raise an exception. If ``strict`` is True, ``filter`` must return a
reference to ``value`` (i.e. casting prohibited).
If ``strict`` is False, then casting may happen, but downcasting should
only be used in two situations:
* if ``allow_downcast`` is True
* if ``allow_downcast`` is ``None`` and the default behavior for this
type allows downcasting for the given ``value`` (this behavior is
type-dependent, you may decide what your own type does by default)
We need to define ``filter`` with three arguments. The second argument
must be called ``strict`` (Theano often calls it by keyword) and must
have a default value of ``False``. The third argument must be called
``allow_downcast`` and must have a default value of ``None``.
.. method:: filter_inplace(value, storage, strict=False, allow_downcast=None)
If filter_inplace is defined, it will be called instead of
filter() This is to allow reusing the old allocated memory. As
of this writing this is used only when we transfer new data to a
shared variable on the gpu.
``storage`` will be the old value. i.e. The old numpy array,
CudaNdarray, ...
.. method:: is_valid_value(value)
Returns True iff the value is compatible with the Type. If
``filter(value, strict = True)`` does not raise an exception, the
value is compatible with the Type.
*Default:* True iff ``filter(value, strict=True)`` does not raise
an exception.
.. method:: values_eq(a, b)
Returns True iff ``a`` and ``b`` are equal.
*Default:* ``a == b``
.. method:: values_eq_approx(a, b)
Returns True iff ``a`` and ``b`` are approximately equal, for a
definition of "approximately" which varies from Type to Type.
*Default:* ``values_eq(a, b)``
.. method:: make_variable(name=None)
Makes a :term:`Variable` of this Type with the specified name, if
``name`` is not ``None``. If ``name`` is ``None``, then the Variable does
not have a name. The Variable will have its ``type`` field set to
the Type object.
*Default:* there is a generic definition of this in Type. The
Variable's ``type`` will be the object that defines this method (in
other words, ``self``).
.. method:: __call__(name=None)
Syntactic shortcut to ``make_variable``.
*Default:* ``make_variable``
.. method:: __eq__(other)
Used to compare Type instances themselves
*Default:* ``object.__eq__``
.. method:: __hash__()
Types should not be mutable, so it should be OK to define a hash
function. Typically this function should hash all of the terms
involved in ``__eq__``.
*Default:* ``id(self)``
.. method:: get_shape_info(obj)
Optional. Only needed to profile the memory of this Type of object.
Return the information needed to compute the memory size of ``obj``.
The memory size is only the data, so this excludes the container.
For an ndarray, this is the data, but not the ndarray object and
other data structures such as shape and strides.
``get_shape_info()`` and ``get_size()`` work in tandem for the memory profiler.
``get_shape_info()`` is called during the execution of the function.
So it is better that it is not too slow.
``get_size()`` will be called on the output of this function
when printing the memory profile.
:param obj: The object that this Type represents during execution
:return: Python object that ``self.get_size()`` understands
.. method:: get_size(shape_info)
Number of bytes taken by the object represented by shape_info.
Optional. Only needed to profile the memory of this Type of object.
:param shape_info: the output of the call to get_shape_info()
:return: the number of bytes taken by the object described by
``shape_info``.
.. method:: clone(dtype=None, broadcastable=None)
Optional, for TensorType-alikes.
Return a copy of the type with a possibly changed value for
dtype and broadcastable (if they aren't `None`).
:param dtype: New dtype for the copy.
:param broadcastable: New broadcastable tuple for the copy.
.. method:: may_share_memory(a, b)
Optional to run, but mandatory for DebugMode. Return True if the Python
objects `a` and `b` could share memory. Return False
otherwise. It is used to debug when Ops did not declare memory
aliasing between variables. Can be a static method.
It is highly recommended to use and is mandatory for Type in Theano
as our buildbot runs in DebugMode.
For each method, the *default* is what ``Type`` defines
for you. So, if you create an instance of ``Type`` or an
instance of a subclass of ``Type``, you
must define ``filter``. You might want to override ``values_eq_approx``,
as well as ``values_eq``. The other defaults generally need not be
overridden.
For more details you can go see the documentation for :ref:`type`.
Additional definitions
----------------------
For certain mechanisms, you can register functions and other such
things to plus your type into theano's mechanisms. These are optional
but will allow people to use you type with familiar interfaces.
`transfer()`
~~~~~~~~~~~~
To plug in additional options for the transfer target, define a
function which takes a theano variable and a target argument and
returns eitehr a new transferred variable (which can be the same as
the input if no transfer is nessecary) or returns None if the transfer
can't be done.
Then register that function by calling :func:`register_transfer()`
with it as argument.
Defining double
===============
We are going to base Type ``double`` on Python's ``float``. We
must define ``filter`` and shall override ``values_eq_approx``.
**filter**
.. testcode::
# Note that we shadow Python's function ``filter`` with this
# definition.
def filter(x, strict=False, allow_downcast=None):
if strict:
if isinstance(x, float):
return x
else:
raise TypeError('Expected a float!')
elif allow_downcast:
return float(x)
else: # Covers both the False and None cases.
x_float = float(x)
if x_float == x:
return x_float
else:
raise TypeError('The double type cannot accurately represent '
'value %s (of type %s): you must explicitly '
'allow downcasting if you want to do this.'
% (x, type(x)))
If ``strict`` is True we need to return ``x``. If ``strict`` is True and ``x`` is not a
``float`` (for example, ``x`` could easily be an ``int``) then it is
incompatible with our Type and we must raise an exception.
If ``strict is False`` then we are allowed to cast ``x`` to a ``float``,
so if ``x`` is an ``int`` it we will return an equivalent ``float``.
However if this cast triggers a precision loss (``x != float(x)``) and
``allow_downcast`` is not True, then we also raise an exception.
Note that here we decided that the default behavior of our type
(when ``allow_downcast`` is set to ``None``) would be the same as
when ``allow_downcast`` is False, i.e. no precision loss is allowed.
**values_eq_approx**
.. testcode::
def values_eq_approx(x, y, tolerance=1e-4):
return abs(x - y) / (abs(x) + abs(y)) < tolerance
The second method we define is ``values_eq_approx``. This method
allows approximate comparison between two values respecting our Type's
constraints. It might happen that an optimization changes the computation
graph in such a way that it produces slightly different variables, for
example because of numerical instability like rounding errors at the
end of the mantissa. For instance, ``a + a + a + a + a + a`` might not
actually produce the exact same output as ``6 * a`` (try with a=0.1),
but with ``values_eq_approx`` we do not necessarily mind.
We added an extra ``tolerance`` argument here. Since this argument is
not part of the API, it must have a default value, which we
chose to be 1e-4.
.. note::
``values_eq`` is never actually used by Theano, but it might be used
internally in the future. Equality testing in
:ref:`DebugMode <debugmode>` is done using ``values_eq_approx``.
**Putting them together**
What we want is an object that respects the aforementioned
contract. Recall that Type defines default implementations for all
required methods of the interface, except ``filter``. One way to make
the Type is to instantiate a plain Type and set the needed fields:
.. testcode::
from theano import gof
double = gof.Type()
double.filter = filter
double.values_eq_approx = values_eq_approx
Another way to make this Type is to make a subclass of ``gof.Type``
and define ``filter`` and ``values_eq_approx`` in the subclass:
.. code-block:: python
from theano import gof
class Double(gof.Type):
def filter(self, x, strict=False, allow_downcast=None):
# See code above.
...
def values_eq_approx(self, x, y, tolerance=1e-4):
# See code above.
...
double = Double()
``double`` is then an instance of Type ``Double``, which in turn is a
subclass of ``Type``.
There is a small issue with defining ``double`` this way. All
instances of ``Double`` are technically the same Type. However, different
``Double`` Type instances do not compare the same:
.. testsetup::
from theano import gof
class Double(gof.Type):
def filter(self, x, strict=False, allow_downcast=None):
if strict:
if isinstance(x, float):
return x
else:
raise TypeError('Expected a float!')
elif allow_downcast:
return float(x)
else: # Covers both the False and None cases.
x_float = float(x)
if x_float == x:
return x_float
else:
raise TypeError('The double type cannot accurately represent '
'value %s (of type %s): you must explicitly '
'allow downcasting if you want to do this.'
% (x, type(x)))
def values_eq_approx(self, x, y, tolerance=1e-4):
return abs(x - y) / (abs(x) + abs(y)) < tolerance
def __str__(self):
return "double"
double = Double()
>>> double1 = Double()
>>> double2 = Double()
>>> double1 == double2
False
Theano compares Types using ``==`` to see if they are the same.
This happens in DebugMode. Also, Ops can (and should) ensure that their inputs
have the expected Type by checking something like ``if x.type == lvector``.
There are several ways to make sure that equality testing works properly:
#. Define ``Double.__eq__`` so that instances of type Double
are equal. For example:
.. testcode::
def __eq__(self, other):
return type(self) is Double and type(other) is Double
#. Override ``Double.__new__`` to always return the same instance.
#. Hide the Double class and only advertise a single instance of it.
Here we will prefer the final option, because it is the simplest.
Ops in the Theano code often define the ``__eq__`` method though.
Untangling some concepts
========================
Initially, confusion is common on what an instance of Type is versus
a subclass of Type or an instance of Variable. Some of this confusion is
syntactic. A Type is any object which has fields corresponding to the
functions defined above. The Type class provides sensible defaults for
all of them except ``filter``, so when defining new Types it is natural
to subclass Type. Therefore, we often end up with Type subclasses and
it is can be confusing what these represent semantically. Here is an
attempt to clear up the confusion:
* An **instance of Type** (or an instance of a subclass)
is a set of constraints on real data. It is
akin to a primitive type or class in C. It is a *static*
annotation.
* An **instance of Variable** symbolizes data nodes in a data flow
graph. If you were to parse the C expression ``int x;``, ``int``
would be a Type instance and ``x`` would be a Variable instance of
that Type instance. If you were to parse the C expression ``c = a +
b;``, ``a``, ``b`` and ``c`` would all be Variable instances.
* A **subclass of Type** is a way of implementing
a set of Type instances that share
structural similarities. In the ``double`` example that we are doing,
there is actually only one Type in that set, therefore the subclass
does not represent anything that one of its instances does not. In this
case it is a singleton, a set with one element. However, the
:class:`TensorType`
class in Theano (which is a subclass of Type)
represents a set of types of tensors
parametrized by their data type or number of dimensions. We could say
that subclassing Type builds a hierarchy of Types which is based upon
structural similarity rather than compatibility.
Final version
=============
.. testcode::
from theano import gof
class Double(gof.Type):
def filter(self, x, strict=False, allow_downcast=None):
if strict:
if isinstance(x, float):
return x
else:
raise TypeError('Expected a float!')
elif allow_downcast:
return float(x)
else: # Covers both the False and None cases.
x_float = float(x)
if x_float == x:
return x_float
else:
raise TypeError('The double type cannot accurately represent '
'value %s (of type %s): you must explicitly '
'allow downcasting if you want to do this.'
% (x, type(x)))
def values_eq_approx(self, x, y, tolerance=1e-4):
return abs(x - y) / (abs(x) + abs(y)) < tolerance
def __str__(self):
return "double"
double = Double()
We add one utility function, ``__str__``. That way, when we print
``double``, it will print out something intelligible.