# How Shape Information is Handled by Aesara¶

Currently, information regarding shape is used in the following ways by Aesara:

• To remove computations in the graph when we only want to know the shape, but not the actual value of a variable. This is done with the `Op.infer_shape()` method.
• To generate faster compiled code (e.g. for a 2D convolution).

Example:

```>>> import aesara
>>> x = aesara.tensor.matrix('x')
>>> f = aesara.function([x], (x ** 2).shape)
>>> aesara.dprint(f)
MakeVector{dtype='int64'} [id A] ''   2
|Shape_i{0} [id B] ''   1
| |x [id C]
|Shape_i{1} [id D] ''   0
|x [id C]
```

The output of this compiled function does not contain any multiplication or power computations; Aesara has removed them to compute the shape of the output directly.

Aesara propagates information about shapes within a graph using specialized `Op`s and static `Type` information (see Types).

## Specifying Exact Shape¶

You can create variables with static shape information as follows:

```aesara.tensor.tensor("float64", shape=(4, 3, 2))
```

You can also pass shape infomation directly to some `Op`s, like `RandomVariables`

```aesara.tensor.random.normal(size=(7, 3, 5, 5))
```
• You can use the `SpecifyShape``Op` to add shape information anywhere in the graph. This allows to perform some optimizations. In the following example, this makes it possible to precompute the Aesara function to a constant.
```>>> import aesara
>>> x = aesara.tensor.matrix()
>>> x_specify_shape = aesara.tensor.specify_shape(x, (2, 2))
>>> f = aesara.function([x], (x_specify_shape ** 2).shape)
>>> aesara.printing.debugprint(f)
DeepCopyOp [id A] ''   0
|TensorConstant{(2,) of 2} [id B]
```

## Problems with Shape inference¶

Sometimes this can lead to errors. Consider this example:

```>>> import numpy as np
>>> import aesara
>>> x = aesara.tensor.matrix('x')
>>> y = aesara.tensor.matrix('y')
>>> z = aesara.tensor.join(0, x, y)
>>> xv = np.random.random((5, 4))
>>> yv = np.random.random((3, 3))
```
```>>> f = aesara.function([x, y], z.shape)
>>> aesara.printing.debugprint(f)
MakeVector{dtype='int64'} [id A] ''   4
|Elemwise{Add}[(0, 0)] [id B] ''   3
| |Shape_i{0} [id C] ''   2
| | |x [id D]
| |Shape_i{0} [id E] ''   1
|   |y [id F]
|Shape_i{1} [id G] ''   0
|x [id D]
```
```>>> f(xv, yv) # DOES NOT RAISE AN ERROR AS SHOULD BE.
array([8, 4])
```
```>>> f = aesara.function([x,y], z)# Do not take the shape.
>>> aesara.printing.debugprint(f)
Join [id A] ''   0
|TensorConstant{0} [id B]
|x [id C]
|y [id D]
```
```>>> f(xv, yv)
Traceback (most recent call last):
...
ValueError: ...
```

As you can see, when asking only for the shape of some computation (`join` in the example above), an inferred shape is computed directly, without executing the computation itself (there is no `join` in the first output or debugprint).

This makes the computation of the shape faster, but it can also hide errors. In this example, the computation of the shape of the output of `join` is done only based on the first input Aesara variable, which leads to an error.

This might happen with other `Op`s such as `Elemwise` and `Dot`, for example. Indeed, to perform some optimizations/rewrites (for speed or stability, for instance), Aesara assumes that the computation is correct and consistent in the first place, as it does here.

You can detect those problems by running the code without this optimization, using the Aesara flag `optimizer_excluding=local_shape_to_shape_i`. You can also obtain the same effect by running in the modes `FAST_COMPILE` or `DebugMode`.