# Glossary¶

- Apply¶
- Instances of
`Apply`

represent the application of an Op to some input Variable (or variables) to produce some output 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 (i.e. element-wise) computations. It works by (virtually) replicating the smaller tensor along the dimensions that it is lacking.

For more detail, see Broadcasting, 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 = at.ivector() >>> y = x + 3

Then a

`constant`

is created to represent the`3`

in the graph.See also:

`graph.basic.Constant`

- Elemwise¶
An element-wise 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 element-wise operation is like a scalar operation generalized along several dimensions. Element-wise operations are defined for tensors of different numbers of dimensions by broadcasting the smaller ones. The`Op`

responsible for performing element-wise computations is`Elemwise`

.- Expression¶
- See Apply
- Expression Graph¶
A directed, acyclic set of connected Variable and Apply nodes that express symbolic functional relationship between variables. You use Aesara by defining expression graphs, and then compiling them with aesara.function.

See also Variable, Op, Apply, and Type, or read more about Graph Structures.

- Destructive¶
An Op is destructive (of particular input[s]) if its computation requires that one or more inputs be overwritten or otherwise invalidated. For example, inplace

`Op`

s are destructive. Destructive`Op`

s can sometimes be faster than non-destructive alternatives. Aesara encourages users not to put destructive`Op`

s into graphs that are given to aesara.function, but instead to trust the optimizations to insert destructive ops judiciously.Destructive

`Op`

s are indicated via a`Op.destroy_map`

attribute. (See`Op`

.- Graph¶
- see 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.
`Op`

s representing inplace computations are destructive, and by default these can only be inserted by optimizations, not user code. - Linker¶
- Part of a function 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 optimizer and a linker that is passed to aesara.function. It parametrizes how an expression graph is converted to a callable object.
- Op¶
The

`.op`

of an 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 (i.e.`aesara.tensor.add()`

) and indexing`x[i]`

are`Op`

s in Aesara. Much of the library documentation is devoted to describing the various`Op`

s that are provided with Aesara, but you can add more.See also Variable, Type, and Apply, or read more about Graph Structures.

- Rewriter¶
- A function or class that transforms an Aesara graph.
- Optimizer¶
- An instance of a rewriter that has the capacity to provide an improvement to the performance of a graph.
- Optimization¶
- A graph transformation applied by an optimizer during the compilation of a graph by aesara.function. These are graph rewrites that are intended to improve the performance of a compiled Graph.
- Pure¶
- An Op is
*pure*if it has no 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 constant and shared variable the storage is not internal. - A Variable whose value may be shared between multiple functions. See
`shared`

and`aesara.function`

. - aesara.function¶
- The interface for Aesara’s compilation from symbolic expression graphs
to callable objects. See
`function.function()`

. - Type¶
The

`.type`

of a Variable indicates what kinds of values might be computed for it in a compiled graph. An instance that inherits from`Type`

, and is used as the`.type`

attribute of a Variable.See also Variable, Op, and Apply, or read more about Graph Structures.

- Variable¶
The the main data structure you work with when using Aesara. For example,

>>> x = at.ivector() >>> y = -x**2

`x`

and`y`

are both`Variable`

s, i.e. instances of the`Variable`

class.See also Type, Op, and Apply, or read more about Graph Structures.

- View¶
Some tensor

`Op`

s (such as`Subtensor`

and`DimShuffle`

) can be computed in constant time by simply re-indexing their inputs. The outputs of such`Op`

s are views because their storage might be aliased to the storage of other variables (the inputs of the`Apply`

). It is important for Aesara to know which`Variable`

s are views of which other ones in order to introduce Destructive`Op`

s correctly.`Op`

s that are views have their`Op.view_map`

attributes set.