.. _glossary: Glossary ======== .. testsetup:: import theano from theano import tensor .. glossary:: Apply Instances of :class:`Apply` represent the application of an :term:`Op` to some input :term:`Variable` (or variables) to produce some output :term:`Variable` (or variables). They are like the application of a [symbolic] mathematical function to some [symbolic] inputs. Broadcasting Broadcasting is a mechanism which allows tensors with different numbers of dimensions to be used in element-by-element (elementwise) computations. It works by (virtually) replicating the smaller tensor along the dimensions that it is lacking. For more detail, see :ref:`libdoc_tensor_broadcastable`, and also * `SciPy documentation about numpy's broadcasting `_ * `OnLamp article about numpy's broadcasting `_ Constant A variable with an immutable value. For example, when you type >>> x = tensor.ivector() >>> y = x + 3 Then a `constant` is created to represent the ``3`` in the graph. See also: :class:`gof.Constant` Elementwise An elementwise operation ``f`` on two tensor variables ``M`` and ``N`` is one such that: ``f(M, N)[i, j] == f(M[i, j], N[i, j])`` In other words, each element of an input matrix is combined with the corresponding element of the other(s). There are no dependencies between elements whose ``[i, j]`` coordinates do not correspond, so an elementwise operation is like a scalar operation generalized along several dimensions. Elementwise operations are defined for tensors of different numbers of dimensions by :term:`broadcasting` the smaller ones. Expression See :term:`Apply` Expression Graph A directed, acyclic set of connected :term:`Variable` and :term:`Apply` nodes that express symbolic functional relationship between variables. You use Theano by defining expression graphs, and then compiling them with :term:`theano.function`. See also :term:`Variable`, :term:`Op`, :term:`Apply`, and :term:`Type`, or read more about :ref:`tutorial_graphstructures`. Destructive An :term:`Op` is destructive (of particular input[s]) if its computation requires that one or more inputs be overwritten or otherwise invalidated. For example, :term:`inplace` Ops are destructive. Destructive Ops can sometimes be faster than non-destructive alternatives. Theano encourages users not to put destructive Ops into graphs that are given to :term:`theano.function`, but instead to trust the optimizations to insert destructive ops judiciously. Destructive Ops are indicated via a ``destroy_map`` Op attribute. (See :class:`gof.Op`. Graph see :term:`expression graph` Inplace Inplace computations are computations that destroy their inputs as a side-effect. For example, if you iterate over a matrix and double every element, this is an inplace operation because when you are done, the original input has been overwritten. Ops representing inplace computations are :term:`destructive`, and by default these can only be inserted by optimizations, not user code. Linker Part of a function :term:`Mode` -- an object responsible for 'running' the compiled function. Among other things, the linker determines whether computations are carried out with C or Python code. Mode An object providing an :term:`optimizer` and a :term:`linker` that is passed to :term:`theano.function`. It parametrizes how an expression graph is converted to a callable object. Op The ``.op`` of an :term:`Apply`, together with its symbolic inputs fully determines what kind of computation will be carried out for that ``Apply`` at run-time. Mathematical functions such as addition (``T.add``) and indexing ``x[i]`` are Ops in Theano. Much of the library documentation is devoted to describing the various Ops that are provided with Theano, but you can add more. See also :term:`Variable`, :term:`Type`, and :term:`Apply`, or read more about :ref:`tutorial_graphstructures`. Optimizer An instance of :class:`Optimizer`, which has the capacity to provide an :term:`optimization` (or optimizations). Optimization A :term:`graph` transformation applied by an :term:`optimizer` during the compilation of a :term:`graph` by :term:`theano.function`. Pure An :term:`Op` is *pure* if it has no :term:`destructive` side-effects. Storage The memory that is used to store the value of a Variable. In most cases storage is internal to a compiled function, but in some cases (such as :term:`constant` and :term:`shared variable ` the storage is not internal. Shared Variable A :term:`Variable` whose value may be shared between multiple functions. See :func:`shared ` and :func:`theano.function `. theano.function The interface for Theano's compilation from symbolic expression graphs to callable objects. See :func:`function.function`. Type The ``.type`` of a :term:`Variable` indicates what kinds of values might be computed for it in a compiled graph. An instance that inherits from :class:`Type`, and is used as the ``.type`` attribute of a :term:`Variable`. See also :term:`Variable`, :term:`Op`, and :term:`Apply`, or read more about :ref:`tutorial_graphstructures`. Variable The the main data structure you work with when using Theano. For example, >>> x = theano.tensor.ivector() >>> y = -x**2 ``x`` and ``y`` are both `Variables`, i.e. instances of the :class:`Variable` class. See also :term:`Type`, :term:`Op`, and :term:`Apply`, or read more about :ref:`tutorial_graphstructures`. View Some Tensor Ops (such as Subtensor and Transpose) can be computed in constant time by simply re-indexing their inputs. The outputs from [the Apply instances from] such Ops are called `Views` because their storage might be aliased to the storage of other variables (the inputs of the Apply). It is important for Theano to know which Variables are views of which other ones in order to introduce :term:`Destructive` Ops correctly. View Ops are indicated via a ``view_map`` Op attribute. (See :class:`gof.Op`.