# 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]]
```