192 lines
5.6 KiB
Markdown
192 lines
5.6 KiB
Markdown
# Dimensions and shape
|
||
{:.no_toc}
|
||
|
||
<nav markdown="1" class="toc-class">
|
||
* TOC
|
||
{:toc}
|
||
</nav>
|
||
|
||
## The goal
|
||
|
||
Matrices have dimensions. But how to add and remove extra dimensions (i.e. dimensions with length 1)?
|
||
|
||
Questions to [David Rotermund](mailto:davrot@uni-bremen.de)
|
||
|
||
## [numpy.ndarray.shape](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.shape.html)
|
||
|
||
```python
|
||
ndarray.shape
|
||
```
|
||
|
||
> Tuple of array dimensions.
|
||
>
|
||
> The shape property is usually used to get the current shape of an array, but may also be used to reshape the array in-place by assigning a tuple of array dimensions to it. As with numpy.reshape, one of the new shape dimensions can be -1, in which case its value is inferred from the size of the array and the remaining dimensions. Reshaping an array in-place will fail if a copy is required.
|
||
|
||
```python
|
||
import numpy as np
|
||
|
||
data = np.zeros((2, 4, 2, 7, 2))
|
||
print(data.shape) # -> (2, 4, 2, 7, 2)
|
||
```
|
||
|
||
## Vanishing dimensions
|
||
|
||
```python
|
||
import numpy as np
|
||
|
||
data = np.zeros((5, 3, 2))
|
||
|
||
# All the same dimensionwise
|
||
print(data.shape) # -> (5, 3, 2)
|
||
print(data[:].shape) # -> (5, 3, 2)
|
||
print(data[:, :, :].shape) # -> (5, 3, 2)
|
||
print(data[...].shape) # -> (5, 3, 2)
|
||
|
||
|
||
print(data[0, :, :].shape) # -> (3, 2)
|
||
print(data[:, 0, :].shape) # -> (5, 2)
|
||
print(data[:, :, 0].shape) # -> (5, 3)
|
||
|
||
print(data[:, 0, 0].shape) # -> (5,)
|
||
print(data[0, :, 0].shape) # -> (3,)
|
||
print(data[0, 0, :].shape) # -> (2,)
|
||
|
||
print(data[0, 0, 0].shape) # -> ()
|
||
print(type(data[0, 0, 0])) # -> <class 'numpy.float64'>
|
||
```
|
||
### keepdims
|
||
|
||
There are functions like
|
||
```python
|
||
ndarray.sum(axis=None, dtype=None, out=None, keepdims=False, initial=0, where=True)
|
||
ndarray.mean(axis=None, dtype=None, out=None, keepdims=False, *, where=True)
|
||
ndarray.prod(axis=None, dtype=None, out=None, keepdims=False, initial=1, where=True)
|
||
ndarray.max(axis=None, out=None, keepdims=False, initial=<no value>, where=True)
|
||
ndarray.min(axis=None, out=None, keepdims=False, initial=<no value>, where=True)
|
||
ndarray.argmax(axis=None, out=None, *, keepdims=False)
|
||
ndarray.argmin(axis=None, out=None, *, keepdims=False)
|
||
```
|
||
that normally make one dimension vanish. However, often this type of functions have an argument **keepdims** that keeps this dimension alive.
|
||
|
||
```python
|
||
import numpy as np
|
||
|
||
data = np.zeros((5, 3, 2))
|
||
|
||
# All the same dimensionwise
|
||
print(data.shape) # -> (5, 3, 2)
|
||
print(data.sum().shape) # -> ()
|
||
print(data.sum(axis=0).shape) # -> (3, 2)
|
||
print(data.sum(axis=1).shape) # -> (5, 2)
|
||
print(data.sum(axis=2).shape) # -> (5, 3)
|
||
|
||
# You can use keepdims:
|
||
|
||
print(data.sum(axis=0, keepdims=True).shape) # -> (1, 3, 2)
|
||
print(data.sum(axis=1, keepdims=True).shape) # -> (5, 1, 2)
|
||
print(data.sum(axis=2, keepdims=True).shape) # -> (5, 3, 1)
|
||
```
|
||
|
||
As as reminder, shape is only availabe for np.ndarray and torch.Tensor matrices:
|
||
|
||
```python
|
||
z = int(7)
|
||
print(np.array(z).shape) # -> ()
|
||
print(type(np.array(z))) # -> <class 'numpy.ndarray'>
|
||
print(type(z)) # -> <class 'int'>
|
||
print(z.shape) # -> AttributeError: 'int' object has no attribute 'shape'
|
||
```
|
||
|
||
## Stop vanishing dimensions
|
||
|
||
One way to do stop vanishing dimensions is to use slices of thickness 1. If you want the nth element, then use **n:n+1**:
|
||
|
||
```python
|
||
import numpy as np
|
||
|
||
data = np.zeros((5, 3, 2))
|
||
|
||
# All the same dimensionwise
|
||
print(data.shape) # -> (5, 3, 2)
|
||
|
||
print(data[0:1, :, :].shape) # -> (1, 3, 2)
|
||
print(data[:, 0:1, :].shape) # -> (5, 1, 2)
|
||
print(data[:, :, 0:1].shape) # -> (5, 3, 1)
|
||
|
||
print(data[:, 0:1, 0:1].shape) # -> (5, 1, 1)
|
||
print(data[0:1, :, 0:1].shape) # -> (1, 3, 1)
|
||
print(data[0:1, 0:1, :].shape) # -> (1, 1, 2)
|
||
|
||
print(data[0:1, 0:1, 0:1].shape) # -> (1, 1, 1)
|
||
print(type(data[0:1, 0:1, 0:1])) # -> <class 'numpy.ndarray'>
|
||
```
|
||
|
||
**Please understand this creates a view which is connected to original data.** If necessary make a **copy()**.
|
||
|
||
## Adding dimensions with [np.newaxis](https://numpy.org/doc/stable/reference/constants.html#numpy.newaxis)
|
||
|
||
```python
|
||
numpy.newaxis
|
||
```
|
||
|
||
> A convenient alias for None, useful for indexing arrays.
|
||
|
||
```python
|
||
import numpy as np
|
||
|
||
data = np.zeros((2))
|
||
print(data.shape) # -> (2,)
|
||
print(data[:, np.newaxis].shape) # -> (2, 1)
|
||
print(data[np.newaxis, :].shape) # -> (1, 2)
|
||
|
||
|
||
print(data[:, np.newaxis, np.newaxis].shape) # -> (2, 1, 1)
|
||
print(data[np.newaxis, :, np.newaxis].shape) # -> (1, 2, 1)
|
||
print(data[:, np.newaxis, np.newaxis].shape) # -> (2, 1, 1)
|
||
```
|
||
|
||
## Adding dimensions with [numpy.expand_dims](https://numpy.org/doc/stable/reference/generated/numpy.expand_dims.html)
|
||
|
||
In the case you don’t like newaxis for adding a new dimension...
|
||
|
||
```python
|
||
numpy.expand_dims(a, axis)
|
||
```
|
||
|
||
> Expand the shape of an array.
|
||
>
|
||
> Insert a new axis that will appear at the axis position in the expanded array shape.
|
||
|
||
```python
|
||
import numpy as np
|
||
|
||
data = np.zeros((2))
|
||
print(data.shape) # -> (2,)
|
||
print(np.expand_dims(data, axis=0).shape) # -> (1, 2)
|
||
print(np.expand_dims(data, axis=1).shape) # -> (2, 1)
|
||
print(np.expand_dims(data, axis=(1, 2, 3)).shape) # -> (2, 1, 1, 1)
|
||
```
|
||
## Removing dimensions with [numpy.squeeze](https://numpy.org/doc/stable/reference/generated/numpy.squeeze.html)
|
||
|
||
```python
|
||
numpy.squeeze(a, axis=None)
|
||
```
|
||
|
||
> Remove axes of length one from a.
|
||
|
||
```python
|
||
import numpy as np
|
||
|
||
data = np.zeros((1, 2, 1, 1))
|
||
print(data.shape) # -> (1, 2, 1, 1)
|
||
print(np.squeeze(data).shape) # -> (2,)
|
||
print(np.squeeze(data, axis=0).shape) # -> (2, 1, 1)
|
||
print(np.squeeze(data, axis=2).shape) # -> (1, 2, 1)
|
||
print(np.squeeze(data, axis=3).shape) # -> (1, 2, 1)
|
||
|
||
print(np.squeeze(data, axis=(0, -1)).shape) # -> (2, 1)
|
||
|
||
print(
|
||
np.squeeze(data, axis=1).shape
|
||
) # -> ValueError: cannot select an axis to squeeze out which has size not equal to one
|
||
```
|