112 lines
2.9 KiB
Markdown
112 lines
2.9 KiB
Markdown
# Slices and views
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{:.no_toc}
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<nav markdown="1" class="toc-class">
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* TOC
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{:toc}
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</nav>
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## The goal
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Sometimes we want to use or see only a part of the matrix. This can be done via slices and views
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Questions to [David Rotermund](mailto:davrot@uni-bremen.de)
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## 1-d slices
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We assume N as the number of elements and 1d:
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* A valid index starts at **0** and runs until N-1
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* [start:stop:step]
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start = 1, stop=N, step=1 -> this results in the sequence 1,2,3,...,(N-1)
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* [start:stop:1] can be shortened to [start:stop]
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* [0:stop] can be shortened to [:stop]
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* [start:N] can be shortened to [start:]
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* B = A[:] or B = A[...] gives you a view of A. B has the same shape and size of A.
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```python
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import numpy as np
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a = np.arange(0, 10)
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print(a[1:10:1]) # -> [1 2 3 4 5 6 7 8 9]
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print(a[3:7:2]) # -> [3 5]
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print(a[3:6]) # -> [3 4 5]
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print(a[:6]) # -> [0 1 2 3 4 5]
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print(a[5:]) # -> [5 6 7 8 9]
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print(a[:]) # -> [0 1 2 3 4 5 6 7 8 9]
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print(a[...]) # -> [0 1 2 3 4 5 6 7 8 9]
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print(a[:9999]) # -> [0 1 2 3 4 5 6 7 8 9]
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print(a[9999:]) # ->[]
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```
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* Negative values for start and stop are understood as N-\|start\| and N-\|stop\|
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* N-1 is the last valid index.
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* Thus A[-1] gives us the last element of A.
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Extracting a value based on a negative index:
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```python
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import numpy as np
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a = np.arange(0, 10)
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print(a[-1]) # -> 9
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print(a[-2]) # -> 8
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print(a[-9]) # -> 1
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print(a[-10]) # -> 0
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print(a[-11]) # IndexError: index -11 is out of bounds for axis 0 with size 10
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```
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Extracting a slice based on a negative stop point:
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```python
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import numpy as np
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a = np.arange(0, 10)
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print(a) # -> [0 1 2 3 4 5 6 7 8 9]
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print(a[:-1]) # -> [0 1 2 3 4 5 6 7 8]
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print(a[:-5]) # -> [0 1 2 3 4]
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print(a[:-8]) # -> [0 1]
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print(a[:-11]) # -> []
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print(a[:-12]) # -> []
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print(a[:-999]) # -> []
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```
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Extracting a slice based on a negative start point:
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```python
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import numpy as np
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a = np.arange(0, 10)
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print(a) # -> [0 1 2 3 4 5 6 7 8 9]
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print(a[-3:-1]) # -> [7 8]
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print(a[-1:-8]) # -> []
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print(a[-9999:]) # -> [0 1 2 3 4 5 6 7 8 9]
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```
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Negative step sizes:
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```python
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import numpy as np
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a = np.arange(0, 10)
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print(a) # -> [0 1 2 3 4 5 6 7 8 9]
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print(a[::-1]) # -> [9 8 7 6 5 4 3 2 1 0]
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print(a[4:-2:-1]) # -> []
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print(a[-1:5:-1]) # -> [9 8 7 6]
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```
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### [... (Ellipsis)](https://docs.python.org/dev/library/constants.html#Ellipsis)
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> The same as the ellipsis literal “...”. Special value used mostly in conjunction with extended slicing syntax for user-defined container data types. Ellipsis is the sole instance of the types.EllipsisType type.
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```python
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import numpy as np
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a = np.empty((2, 3, 4, 5, 6, 7, 8))
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print(a.shape) # -> (2, 3, 4, 5, 6, 7, 8)
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print(a[..., 1:2].shape) # -> (2, 3, 4, 5, 6, 7, 1)
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print(a[:, :, 1:2, ...].shape) # -> (2, 3, 1, 5, 6, 7, 8)
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print(a[0, ...].shape) # -> (3, 4, 5, 6, 7, 8)
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print(a[0, ..., 0].shape) # -> (3, 4, 5, 6, 7)
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```
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## Views
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