2.3. Array Shape

2.3.1. 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

2.3.2. Rationale

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

2.3.3. Shape

import numpy as np


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

a.shape
# (3,)
import numpy as np


a = np.array([[1, 2, 3],
              [4, 5, 6]])

a.shape
# (2, 3)
import numpy as np


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

a.shape
# (3, 3)
import numpy as np


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)

2.3.4. Reshape

  • Returns new array

  • Does not modify inplace

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

import numpy as np


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

a.reshape(1, 3)
# array([[1, 2, 3]])

a.reshape(3, 1)
# array([[1],
#        [2],
#        [3]])
import numpy as np


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)
import numpy as np


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)

2.3.5. Flatten

  • Returns new array (makes memory copy - expensive)

  • Does not modify inplace

import numpy as np


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

a.flatten()
# array([1, 2, 3])
import numpy as np


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

a.flatten()
# array([1, 2, 3, 4, 5, 6, 7, 8, 9])
import numpy as np

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])

2.3.6. 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)

import numpy as np


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

a.ravel()
# array([1, 2, 3])
import numpy as np


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

a.ravel()
# array([1, 2, 3, 4, 5, 6, 7, 8, 9])
import numpy as np

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])

2.3.7. Recap

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

2.3.8. Assignments

Code 2.33. 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

    >>> type(result_ravel) is np.ndarray
    True
    >>> type(result_flatten) is np.ndarray
    True
    >>> type(result_reshape) is np.ndarray
    True
    >>> 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 = ...