3.2. Array Shape

  • Any shape operation changes only np.ndarray.shape and np.ndarray.strides and does not touch data

3.2.1. SetUp

>>> import numpy as np

3.2.2. Recap

>>> obj = [1, 2, 3]
>>>
>>> len(obj)
3
>>> obj1 = [1, 2, 3]
>>> obj2 = [4, 5, 6]
>>>
>>> len([obj1, obj2])
2
>>> len([ [1,2,3], [4,5,6] ])
2
>>> len([[1,2,3],
...      [4,5,6]])
2
>>> obj1 = [1, 2, 3]
>>> obj2 = [4, 5, 6]
>>> obj3 = [7, 8, 9]
>>> obj4 = [10, 11, 12]
>>>
>>> len([ [obj1, obj2], [obj3, obj4] ])
2
>>> len([[obj1, obj2],
...      [obj3, obj4]])
2

3.2.3. Shape

1-dimensional:

>>> a = np.array([1, 2, 3])
>>> a.shape
(3,)

2-dimensional:

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

3-dimensional:

>>> a = np.array([[[ 1,  2,  3],
...                [ 4,  5,  6],
...                [ 5,  6,  7]],
...               [[11, 22, 33],
...                [44, 55, 66],
...                [77, 88, 99]]])
>>> a.shape
(2, 3, 3)

3.2.4. Reshape

  • Returns new array

  • Does not modify inplace

  • a.reshape(1, 2) is equivalent to a.reshape((1, 2))

>>> a = np.array([1, 2, 3])
>>>
>>> a.reshape(1, 3)
array([[1, 2, 3]])
>>>
>>> a.reshape(3, 1)
array([[1],
       [2],
       [3]])
>>> a = np.array([[1, 2, 3],
...               [4, 5, 6]])
>>>
>>> a.reshape(3, 2)
array([[1, 2],
       [3, 4],
       [5, 6]])
>>>
>>> a.reshape(1, 6)
array([[1, 2, 3, 4, 5, 6]])
>>>
>>> a.reshape(6, 1)
array([[1],
       [2],
       [3],
       [4],
       [5],
       [6]])
>>>
>>> a.reshape(5, 2)
Traceback (most recent call last):
ValueError: cannot reshape array of size 6 into shape (5,2)
>>> a = np.array([1, 2, 3, 4, 5, 6, 7, 8])
>>>
>>> a.reshape(2, 4)
array([[1, 2, 3, 4],
       [5, 6, 7, 8]])
>>>
>>> a.reshape(2, 4, 1)
array([[[1],
        [2],
        [3],
        [4]],

       [[5],
        [6],
        [7],
        [8]]])
>>>
>>> a.reshape(2, 2, 2)
array([[[1, 2],
        [3, 4]],

       [[5, 6],
        [7, 8]]])
>>>
>>> a.reshape(1, 2, 4)
array([[[1, 2, 3, 4],
        [5, 6, 7, 8]]])
>>>
>>> a.reshape(4, 2, 1)
array([[[1],
        [2]],

       [[3],
        [4]],

       [[5],
        [6]],

       [[7],
        [8]]])
>>>
>>> a.reshape(1, 8, 1)
array([[[1],
        [2],
        [3],
        [4],
        [5],
        [6],
        [7],
        [8]]])
>>>
>>> a.reshape(2, 3, 1)
Traceback (most recent call last):
ValueError: cannot reshape array of size 8 into shape (2,3,1)

3.2.5. Flatten

  • Returns new array (makes memory copy - expensive)

  • Does not modify inplace

>>> a = np.array([1, 2, 3])
>>>
>>> a.flatten()
array([1, 2, 3])
>>> a = np.array([[1, 2, 3],
...               [4, 5, 6],
...               [7, 8, 9]])
>>>
>>> a.flatten()
array([1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> a = np.array([[[ 1,  2,  3],
...                [ 4,  5,  6],
...                [ 5,  6,  7]],
...
...               [[11, 22, 33],
...                [44, 55, 66],
...                [77, 88, 99]]])
>>>
>>> a.flatten()  
array([ 1,  2,  3,  4,  5,  6,  5,  6,  7, 11, 22, 33, 44, 55, 66, 77, 88, 99])

3.2.6. Ravel

  • Ravel is the same as Flatten but returns a reference (or view) of the array if possible (i.e. memory is contiguous)

  • Otherwise returns new array (makes memory copy)

>>> a = np.array([1, 2, 3])
>>>
>>> a.ravel()
array([1, 2, 3])
>>> a = np.array([[1, 2, 3],
...               [4, 5, 6],
...               [7, 8, 9]])
>>>
>>> a.ravel()
array([1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> a = np.array([[[ 1,  2,  3],
...                [ 4,  5,  6],
...                [ 5,  6,  7]],
...
...               [[11, 22, 33],
...                [44, 55, 66],
...                [77, 88, 99]]])
>>>
>>>
>>> a.ravel()  
array([ 1,  2,  3,  4,  5,  6,  5,  6,  7, 11, 22, 33, 44, 55, 66, 77, 88, 99])

3.2.7. Flatten vs Ravel

>>> a = np.array([1, 2, 3])
>>> b = a.ravel()
>>> c = a.flatten()
>>> a[0] = 99
>>> a  # original
array([99,  2,  3])
>>>
>>> b  # flatten
array([99,  2,  3])
>>>
>>> c  # ravel
array([1, 2, 3])

3.2.8. Recap

../../_images/array-shape-ravel-vs-flatten.png

3.2.9. Assignments

Code 3.55. Solution
"""
* Assignment: Numpy Shape 1d
* Complexity: easy
* Lines of code: 2 lines
* Time: 3 min

English:
    1. Define `result_ravel` with result of flattening `DATA` using `.ravel()` method
    2. Define `result_flatten` with result of flattening `DATA` using `.flatten()` method
    3. Define `result_reshape` with result of reshaping `DATA` into 1x9
    4. Run doctests - all must succeed

Polish:
    1. Zdefiniuj `result_ravel` z wynikiem spłaszczenia `DATA` używając metody `.ravel()`
    2. Zdefiniuj `result_flatten` z wynikiem spłaszczenia `DATA` używając metody `.flatten()`
    3. Zdefiniuj `result_reshape` z wynikiem zmiany kształtu `DATA` na 1x9
    4. Uruchom doctesty - wszystkie muszą się powieść

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

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

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

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

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

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

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

import numpy as np


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


result_ravel = ...
result_flatten = ...
result_reshape = ...