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If the array x is declared as:

x = np.array([[1, 2], [3, 4]])

the shape of x is (2, 2) because it is a 2x2 matrix.

However, for a 1-dimensional vector, such as:

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

why does the shape of x gives (3,) and not (1,3)?

Is it my mistake to understand the shape as (row, column)?

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  • 1
    [1,2,3] is 1-dimensional, [[1,2],[3,4]] is 2-dimensional. Compare [[[1,2],[3,4]],[[5, 6], [7, 8]]]. "(row, column)" describes a matrix, not an n-dimensional array. Commented Aug 4, 2020 at 11:09
  • 2
    Your only "mistake" is confining your thinking to matrixes (2x2 arrays). In that case yes, you can think of it as 2 rows and 2 columns, but what if you have 63 dimensions? Rows and columns don't have much meaning. More simply, a 1-dimensional vector doesn't have rows, just elements. It is not the same as a 1x3 array Commented Aug 4, 2020 at 11:41
  • As a general understanding rule, you can think of it as the number of levels of brackets represents the amount of numbers in the shape, and the number itself is how many elements are inside each corresponding set of brackets Commented Aug 4, 2020 at 11:45
  • Because it has only 1 dimension Commented Aug 4, 2020 at 12:32

3 Answers 3

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5

Because np.array([1,2,3]) is one-dimensional array. (3,) means that this is single dimension with three elements.

(1,3) means that this is a two-dimensional array. If you use reshape() method on the array, and give it arguments (1,3), additional brackets will be added to it.

>>> np.array([1,2,3]).reshape(1,3)
array([[1, 2, 3]])
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1 Comment

aha the reason the vector returns (3,)is because it is just an one dimension! Thank you so much :)
1

As per the docs, np.array's are multidimensional containers. Consider:

np.array([[[0, 1], [2, 3]], [[4, 5], [6, 7]]]).shape
# (2, 2, 2)

Also, np.shape always returns a tuple. In your example, (3,) is the representation of a one-element tuple, which is the correct value for the shape of a one-dimensional array.

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1

np.array represents an n-dimensional array. This may include a 2-dimensional array to represent a matrix, for which (row, column) is appropriate. It may also include 1-dimensional, 3-dimensional or other arrays for which (row, column) are too many/few dimensions. Compare:

>>> # 1-dimensional
>>> np.array([1, 2, 3]).shape
(3,)
>>> np.array([1, 2, 3])[1]
2
>>> # 2-dimensional
>>> np.array([[1, 2, 3]]).shape
(1, 3)
>>> np.array([[1, 2, 3]])[0,1]
2
>>> np.array([[1], [2], [3]]).shape
(3, 1)
>>> np.array([[1], [2], [3]])[1, 0]
2
>>> # 3-dimensional
>>> np.array([[[1, 2, 3]]]).shape
(1, 1, 3)
>>> np.array([[[1, 2, 3]]])[0,0,1]
2
>>> np.array([[[1,2],[3,4]],[[5, 6], [7, 8]]]).shape
(2, 2, 2)

Note how the shapes (3,), (1, 3), (3, 1), (1, 1, 3), ... represent different logical layouts, as exemplified by the different position at which a specific element resides.

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1 Comment

is it okay to understand np.array([[1,2], [3,4]]) returns (2,2) is just a coincidence of (row,column)? actually it means 2 dimensions with 2 tuples?

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