4.2. Array Slice

4.2.1. SetUp

>>> import numpy as np

4.2.2. Recap

  • slice(start:stop:step)

  • data[start:stop:step]

  • By default start=0

  • By default stop=len(data)

  • By default step=1

>>> data = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> data[1:5:2]  # slice(start=1, stop=5, step=2)
array([2, 4])
>>> data[:5:2]  # slice(start=0, stop=5, step=2)
array([1, 3, 5])
>>> data[1::2]  # slice(start=1, stop=len(data), step = 2)
array([2, 4, 6, 8])
>>> data[1:5]  # slice(start=1, stop=5, step=1)
array([2, 3, 4, 5])
>>> data[::2]  # slice(start=0, stop=len(data), step=2)
array([1, 3, 5, 7, 9])
>>> data[:]  # slice(start=0, stop=len(data), step=1)
array([1, 2, 3, 4, 5, 6, 7, 8, 9])

4.2.3. Rationale

>>> 
... a[ 0 ]                              # int
... a[ [0,1] ]                          # list[int]
... a[ [True,False] ]                   # list[bool]
... a[ [[True,False], [True,False]] ]   # list[list[bool]]
... a[ 0:1 ]                            # slice(start,stop)
... a[ 0:1:2 ]                          # slice(start,stop,step)
...
... a[ 0,1 ]                            # tuple[int]
... a[ (0,1) ]                          # tuple[int]
... a[ [0,1], [2,3] ]                   # tuple[list[int]]
... a[ :,: ]                            # tuple[slice]
... a[ [True,False], [False,True] ]     # tuple[list[bool]]

1-dimensional Array:

  • int

  • list[int]

  • list[bool]

  • list[list[bool]]

  • slice(start,stop)

  • slice(start,stop,step)

2-dimensional Array:

  • tuple[int]

  • tuple[list[int]]

  • tuple[slice]

  • tuple[list[bool]]

4.2.4. 1-dimensional Array

>>> import numpy as np

1-dimensional Array:

>>> a = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9])
>>>
>>> a[1:5]
array([2, 3, 4, 5])
>>> a[3:8]
array([4, 5, 6, 7, 8])
>>>
>>> a[0:5]
array([1, 2, 3, 4, 5])
>>> a[:5]
array([1, 2, 3, 4, 5])
>>> a[5:9]
array([6, 7, 8, 9])
>>>
>>> a[5:len(a)]
array([6, 7, 8, 9])
>>> a[5:]
array([6, 7, 8, 9])
>>> a[-2:]
array([8, 9])
>>> a[-5:]
array([5, 6, 7, 8, 9])
>>> a[-6:-2]
array([4, 5, 6, 7])
>>>
>>> a[3:8:2]
array([4, 6, 8])
>>> a[-8:-3:2]
array([2, 4, 6])
>>> a[::2]
array([1, 3, 5, 7, 9])
>>> a[1::2]
array([2, 4, 6, 8])
>>>
>>> a[0:len(a)]
array([1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> a[0:]
array([1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> a[:len(a)]
array([1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> a[:]
array([1, 2, 3, 4, 5, 6, 7, 8, 9])

4.2.5. 2-dimensional Array

>>> import numpy as np

Rows:

>>> a = np.array([[1, 2, 3],
...               [4, 5, 6],
...               [7, 8, 9]])
>>>
>>> a[:]
array([[1, 2, 3],
       [4, 5, 6],
       [7, 8, 9]])
>>>
>>> a[1:]
array([[4, 5, 6],
       [7, 8, 9]])
>>>
>>> a[:1]
array([[1, 2, 3]])
>>>
>>> a[1:3]
array([[4, 5, 6],
       [7, 8, 9]])
>>>
>>> a[::2]
array([[1, 2, 3],
       [7, 8, 9]])
>>>
>>> a[1::2]
array([[4, 5, 6]])

Columns:

>>> a = np.array([[1, 2, 3],
...               [4, 5, 6],
...               [7, 8, 9]])
>>>
>>> a[:, 0]
array([1, 4, 7])
>>>
>>> a[:, 1]
array([2, 5, 8])
>>>
>>> a[:, 2]
array([3, 6, 9])
>>>
>>> a[:, -1]
array([3, 6, 9])
>>>
>>> a[:, 0:1]
array([[1],
       [4],
       [7]])
>>>
>>> a[:, 0:2]
array([[1, 2],
       [4, 5],
       [7, 8]])
>>>
>>> a[:, :2]
array([[1, 2],
       [4, 5],
       [7, 8]])
>>>
>>> a[:, ::2]
array([[1, 3],
       [4, 6],
       [7, 9]])
>>>
>>> a[:, 1::2]
array([[2],
       [5],
       [8]])

Rows and Columns:

>>> a = np.array([[1, 2, 3],
...               [4, 5, 6],
...               [7, 8, 9]])
>>>
>>> a[0:1, 0:1]
array([[1]])
>>>
>>> a[0:1, 0:2]
array([[1, 2]])
>>>
>>> a[0:1, 0:3]
array([[1, 2, 3]])
>>>
>>> a[0:2, 0:2]
array([[1, 2],
       [4, 5]])
>>>
>>> a[-1:, -2:]
array([[8, 9]])
>>>
>>> a[::2, ::2]
array([[1, 3],
       [7, 9]])
>>>
>>> a[1::2, 1::2]
array([[5]])
>>>
>>> a[[2,1], ::2]
array([[7, 9],
       [4, 6]])

4.2.6. Assignments

Code 4.67. Solution
"""
* Assignment: Numpy Slice 1
* Complexity: easy
* Lines of code: 3 lines
* Time: 3 min

English:
    1. Print inner 2x2 elements
    2. Run doctests - all must succeed

Polish:
    1. Wybierz wewnętrzne 2x2 elementy
    2. Uruchom doctesty - wszystkie muszą się powieść

Tests:
    >>> import sys; sys.tracebacklimit = 0

    >>> assert result is not Ellipsis, \
    'Assign result to variable: `result`'
    >>> assert type(result) is np.ndarray, \
    'Variable `result` has invalid type, expected: np.ndarray'

    >>> result
    array([[8, 4],
           [5, 2]])
"""

import numpy as np


DATA = np.array([
    [2, 8, 1, 5],
    [8, 8, 4, 4],
    [5, 5, 2, 5],
    [1, 0, 6, 0],
])


result = ...


Code 4.68. Solution
"""
* Assignment: Numpy Slice 2
* Complexity: easy
* Lines of code: 3 lines
* Time: 3 min

English:
    1. Print inner 4x4 elements
    2. Inner matrix is exactly in the middle of outer
    3. Run doctests - all must succeed

Polish:
    1. Wypisz środkowe 4x4 elementy
    2. Środkowa macierz jest dokładnie w środku większej
    3. Uruchom doctesty - wszystkie muszą się powieść

Tests:
    >>> import sys; sys.tracebacklimit = 0

    >>> assert result is not Ellipsis, \
    'Assign result to variable: `result`'
    >>> assert type(result) is np.ndarray, \
    'Variable `result` has invalid type, expected: np.ndarray'

    >>> result
    array([[2, 0, 7, 5],
           [1, 2, 9, 1],
           [8, 8, 8, 2],
           [4, 3, 6, 9]])
"""

import numpy as np

DATA = np.array([[5, 0, 3, 3, 7, 9, 3, 5, 2, 4, 7, 6, 8, 8, 1, 6],
                 [7, 7, 8, 1, 5, 9, 8, 9, 4, 3, 0, 3, 5, 0, 2, 3],
                 [8, 1, 3, 3, 3, 7, 0, 1, 9, 9, 0, 4, 7, 3, 2, 7],
                 [2, 0, 0, 4, 5, 5, 6, 8, 4, 1, 4, 9, 8, 1, 1, 7],
                 [9, 9, 3, 6, 7, 2, 0, 3, 5, 9, 4, 4, 6, 4, 4, 3],
                 [4, 4, 8, 4, 3, 7, 5, 5, 0, 1, 5, 9, 3, 0, 5, 0],
                 [1, 2, 4, 2, 0, 3, 2, 0, 7, 5, 9, 0, 2, 7, 2, 9],
                 [2, 3, 3, 2, 3, 4, 1, 2, 9, 1, 4, 6, 8, 2, 3, 0],
                 [0, 6, 0, 6, 3, 3, 8, 8, 8, 2, 3, 2, 0, 8, 8, 3],
                 [8, 2, 8, 4, 3, 0, 4, 3, 6, 9, 8, 0, 8, 5, 9, 0],
                 [9, 6, 5, 3, 1, 8, 0, 4, 9, 6, 5, 7, 8, 8, 9, 2],
                 [8, 6, 6, 9, 1, 6, 8, 8, 3, 2, 3, 6, 3, 6, 5, 7],
                 [0, 8, 4, 6, 5, 8, 2, 3, 9, 7, 5, 3, 4, 5, 3, 3],
                 [7, 9, 9, 9, 7, 3, 2, 3, 9, 7, 7, 5, 1, 2, 2, 8],
                 [1, 5, 8, 4, 0, 2, 5, 5, 0, 8, 1, 1, 0, 3, 8, 8],
                 [4, 4, 0, 9, 3, 7, 3, 2, 1, 1, 2, 1, 4, 2, 5, 5]])

result = ...


../../_images/random-inner-sum1.png

Figure 4.4. Inner 4x4 elements