pytutorial/numpy/stack_split/README.md

# Stack and Split, Compress
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## The goal


Questions to [David Rotermund](mailto:davrot@uni-bremen.de)

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This is an optional topic!


## [numpy.column_stack](https://numpy.org/doc/stable/reference/generated/numpy.column_stack.html)

```python
numpy.column_stack(tup)
```

> Stack 1-D arrays as columns into a 2-D array.
> 
> Take a sequence of 1-D arrays and stack them as columns to make a single 2-D array. 2-D arrays are stacked as-is, just like with hstack. 1-D arrays are turned into 2-D columns first.

```python
import numpy as np

a = np.arange(0, 10)
print(a) # -> [0 1 2 3 4 5 6 7 8 9]
print(a.shape)  # -> (10,)

b = np.column_stack((a, a))
print(b)
print(b.shape) # -> (10, 2)
```
Output:

```python
[[0 0]
 [1 1]
 [2 2]
 [3 3]
 [4 4]
 [5 5]
 [6 6]
 [7 7]
 [8 8]
 [9 9]]
```

## [numpy.row_stack](https://numpy.org/doc/stable/reference/generated/numpy.row_stack.html)

```python
numpy.row_stack(tup, *, dtype=None, casting='same_kind')
```

> Stack arrays in sequence vertically (row wise).
> 
> This is equivalent to concatenation along the first axis after 1-D arrays of shape (N,) have been reshaped to (1,N). Rebuilds arrays divided by vsplit.
> 
> This function makes most sense for arrays with up to 3 dimensions. For instance, for pixel-data with a height (first axis), width (second axis), and r/g/b channels (third axis). The functions concatenate, stack and block provide more general stacking and concatenation operations.
> 
> np.row_stack is an alias for vstack. They are the same function.

```python
import numpy as np

a = np.arange(0, 10)
print(a)  # -> [0 1 2 3 4 5 6 7 8 9]
print(a.shape)  # -> (10,)

b = np.row_stack((a, a))
print(b)
print(b.shape)  # -> (2, 10)
```

Output:

```python
[[0 1 2 3 4 5 6 7 8 9]
 [0 1 2 3 4 5 6 7 8 9]]
```

## [numpy.vstack](https://numpy.org/doc/stable/reference/generated/numpy.vstack.html)

```python
numpy.vstack(tup, *, dtype=None, casting='same_kind')
```

> Stack arrays in sequence vertically (row wise).
> 
> This is equivalent to concatenation along the first axis after 1-D arrays of shape (N,) have been reshaped to (1,N). Rebuilds arrays divided by vsplit.
> 
> This function makes most sense for arrays with up to 3 dimensions. For instance, for pixel-data with a height (first axis), width (second axis), and r/g/b channels (third axis). The functions concatenate, stack and block provide more general stacking and concatenation operations.
> 
> np.row_stack is an alias for vstack. They are the same function.

```python
import numpy as np

a = np.zeros((2, 3, 4))
print(a.shape)  # -> (2, 3, 4)

b = np.vstack((a, a))
print(b.shape)  # -> (4, 3, 4)
```

## [numpy.vsplit](https://numpy.org/doc/stable/reference/generated/numpy.vsplit.html)

```python
numpy.vsplit(ary, indices_or_sections)[source]
```

> Split an array into multiple sub-arrays vertically (row-wise).
> 
> vsplit is equivalent to split with axis=0 (default), the array is always split along the first axis regardless of the array dimension.


## [numpy.hstack](https://numpy.org/doc/stable/reference/generated/numpy.hstack.html)

```python
numpy.hstack(tup, *, dtype=None, casting='same_kind')
```

> Stack arrays in sequence horizontally (column wise).
> 
> This is equivalent to concatenation along the second axis, except for 1-D arrays where it concatenates along the first axis. Rebuilds arrays divided by hsplit.
> 
> This function makes most sense for arrays with up to 3 dimensions. For instance, for pixel-data with a height (first axis), width (second axis), and r/g/b channels (third axis). The functions concatenate, stack and block provide more general stacking and concatenation operations.

```python
import numpy as np

a = np.zeros((2, 3, 4))
print(a.shape)  # -> (2, 3, 4)

b = np.hstack((a, a))
print(b.shape)  # -> (2, 6, 4)
```

## [numpy.hsplit](https://numpy.org/doc/stable/reference/generated/numpy.hsplit.html)

```python
numpy.hsplit(ary, indices_or_sections)[source]
```

> Split an array into multiple sub-arrays horizontally (column-wise).
>
> hsplit is equivalent to split with axis=1, the array is always split along the second axis except for 1-D arrays, where it is split at axis=0.

## [numpy.dstack](https://numpy.org/doc/stable/reference/generated/numpy.dstack.html)

```python
numpy.dstack(tup)
```

> Stack arrays in sequence depth wise (along third axis).
> 
> This is equivalent to concatenation along the third axis after 2-D arrays of shape (M,N) have been reshaped to (M,N,1) and 1-D arrays of shape (N,) have been reshaped to (1,N,1). Rebuilds arrays divided by dsplit.
> 
> This function makes most sense for arrays with up to 3 dimensions. For instance, for pixel-data with a height (first axis), width (second axis), and r/g/b channels (third axis). The functions concatenate, stack and block provide more general stacking and concatenation operations.

```python
import numpy as np

a = np.zeros((2, 3, 4))
print(a.shape)  # -> (2, 3, 4)

b = np.dstack((a, a))
print(b.shape)  # -> (2, 3, 8)
```

## [numpy.dsplit](https://numpy.org/doc/stable/reference/generated/numpy.dsplit.html)

```python
numpy.dsplit(ary, indices_or_sections)
```

> Split array into multiple sub-arrays along the 3rd axis (depth).
> 
> dsplit is equivalent to split with axis=2, the array is always split along the third axis provided the array dimension is greater than or equal to 3.


## [numpy.stack](https://numpy.org/doc/stable/reference/generated/numpy.stack.html)

```python
numpy.stack(arrays, axis=0, out=None, *, dtype=None, casting='same_kind')
```

> Join a sequence of arrays along a **new axis**.
> 
> The axis parameter specifies the index of the new axis in the dimensions of the result. For example, if axis=0 it will be the first dimension and if axis=-1 it will be the last dimension.

```python
import numpy as np

a = np.zeros((6, 8, 10))
print(a.shape)  # -> (6, 8, 10)

b = np.stack((a, a), axis=0)
print(b.shape)  # -> (2, 6, 8, 10)

b = np.stack((a, a), axis=1)
print(b.shape)  # -> (6, 2, 8, 10)

b = np.stack((a, a), axis=2)
print(b.shape)  # -> (6, 8, 2, 10)

b = np.stack((a, a), axis=3)
print(b.shape)  # -> (6, 8, 10, 2)

b = np.stack((a, a), axis=4) # AxisError: axis 4 is out of bounds for array of dimension 4
```

## [numpy.split](https://numpy.org/doc/stable/reference/generated/numpy.split.html) and [numpy.array_split](https://numpy.org/doc/stable/reference/generated/numpy.array_split.html)

```python
numpy.split(ary, indices_or_sections, axis=0)
```

> Split an array into multiple sub-arrays as **views** into ary.

```python
import numpy as np

a = np.arange(0, 20).reshape(10, 2)
print(a)
print(a.shape)  # -> (10, 2)
print()

b = np.split(a, 2, axis=0)
print(len(b))  # -> 2
print(b[0])
print(b[0].shape)  # -> (5, 2)
print()
print(b[1])
print(b[1].shape)  # -> (5, 2)

b = np.split(a, 3, axis=0)  # ValueError: array split does not result in an equal division
```

Output:

```python
[[ 0  1]
 [ 2  3]
 [ 4  5]
 [ 6  7]
 [ 8  9]
 [10 11]
 [12 13]
 [14 15]
 [16 17]
 [18 19]]

[[0 1]
 [2 3]
 [4 5]
 [6 7]
 [8 9]]

[[10 11]
 [12 13]
 [14 15]
 [16 17]
 [18 19]]
```

np.split(a, [2, 5, 8, 9], axis=0) can be used for the following corresponding slices​:

||
|---|
|[:2,:]|​
|[2:5,:]|​
|[5:8,:]|​
|[8:9,:]|​
|[9:,:]|

```python
import numpy as np

a = np.arange(0, 20).reshape(10, 2)
print(a.shape)  # -> (10, 2)
print()

b = np.split(a, [2, 5, 8, 9], axis=0)
print(len(b))  # -> 5
print(b[0])
print(b[0].shape)  # -> (2, 2)
print()
print(b[1])
print(b[1].shape)  # -> (3, 2)
print()
print(b[2])
print(b[2].shape)  # -> (3, 2)
print()
print(b[3])
print(b[3].shape)  # -> (1, 2)
print()
print(b[4])
print(b[4].shape)  # -> (1, 2)
```

Output:

```python
[[0 1]
 [2 3]]

[[4 5]
 [6 7]
 [8 9]]

[[10 11]
 [12 13]
 [14 15]]

[[16 17]]

[[18 19]]
```


```python
numpy.array_split(ary, indices_or_sections, axis=0)
```

> Split an array into multiple sub-arrays.
> 
> The only difference between these functions is that array_split allows indices_or_sections to be an integer that does not equally divide the axis. For an array of length l that should be split into n sections, it returns l % n sub-arrays of size l//n + 1 and the rest of size l//n.

```python
import numpy as np

a = np.arange(0, 20).reshape(10, 2)
print(a.shape)  # -> (10, 2)
print()

b = np.array_split(a, 3, axis=0)
print(len(b))  # -> 3
print(b[0])
print(b[0].shape)  # -> (4, 2)
print()
print(b[1])
print(b[1].shape)  # -> (3, 2)
print()
print(b[2])
print(b[2].shape)  # -> (3, 2)
```

Output:

```python
[[0 1]
 [2 3]
 [4 5]
 [6 7]]

[[ 8  9]
 [10 11]
 [12 13]]

[[14 15]
 [16 17]
 [18 19]]
```

## [numpy.compress](https://numpy.org/doc/stable/reference/generated/numpy.compress.html)

```python
numpy.compress(condition, a, axis=None, out=None)
```

> Return selected slices of an array along given axis.
> 
> When working along a given axis, a slice along that axis is returned in output for each index where condition evaluates to True. When working on a 1-D array, compress is equivalent to extract.

```python
import numpy as np

a = np.arange(0, 20).reshape(5, 4)
print(a)
print(a.shape)  # -> (5, 4)
print()

b = np.compress([True, False, False, True, True], a, axis=0)
print(b)
print(b.shape)  # -> (3, 4)
print()

b = np.compress([False, True, False, True], a, axis=1)
print(b)
print(b.shape)  # -> (5, 2)
```

Output:

```python
[[ 0  1  2  3]
 [ 4  5  6  7]
 [ 8  9 10 11]
 [12 13 14 15]
 [16 17 18 19]]

[[ 0  1  2  3]
 [12 13 14 15]
 [16 17 18 19]]

[[ 1  3]
 [ 5  7]
 [ 9 11]
 [13 15]
 [17 19]]
```