numpy.zeros with multiple dimensions

Question

h = numpy.zeros((2,2,2))

What is the last 2 for? Is it creating a multidimensional array or something?

Output:

array([[[ 0.,  0.],
    [ 0.,  0.]],
   [[ 0.,  0.],
    [ 0.,  0.]]])

If it is creating number of copies, then what is happening when i do the following?

h = numpy.zeros((2,2,1))

Output:

array([[[ 0.],
    [ 0.]],
   [[ 0.],
    [ 0.]]])

I understand that it is getting filled by zeros, and the first two values are specifying the row and column, what about the third? Thank you in advance. And I tried Google, but I could not word my questions.

docs.scipy.org/doc/numpy/reference/generated/numpy.zeros.html — devnull
– devnull, Commented Jan 30, 2014 at 12:11
Your shape has 3 dimensions, so you have a three-dimensional array. What part is unclear? — Wooble
– Wooble, Commented Jan 30, 2014 at 12:12
Why the downvote on my very first question on this website. About the link, it does not specify anything about the third part. — hlkstuv_23900
– hlkstuv_23900, Commented Jan 30, 2014 at 12:14

Nils Werner · Accepted Answer · 2014-01-30 12:25:51Z

12

by giving three arguments you're creating a three-dimensional array:

numpy.array((2,2,2)) results in an array of size 2x2x2:

  0---0
 /   /|
0---0 0
|   |/
0---0

numpy.array((2,2,1)) results in an array of size 2x2x1:

0---0
|   |
0---0

numpy.array((2,1,2)) results in an array of size 2x2x1:

  0---0
 /   /
0---0

numpy.array((1,2,2)) results in an array of size 2x2x1:

  0
 /|
0 0
|/
0

in these representations the matrix "might look like numpy.array((2,2))" (a 2x2 array) however the underlying structure is still three dimensional.

edited Jan 30, 2014 at 12:25

answered Jan 30, 2014 at 12:16

Nils Werner

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3 Comments

hlkstuv_23900 Over a year ago

The brackets are utterly confusing, wish they could print as a 3D matrix. Thanks again.

usethedeathstar Over a year ago

wish i could +2 this, since this makes it very clear for people who have only seen matrices in 2D and do not know about higher dimensions (tensors etc), especially to the difference between (2,2,1) vs (2,1,2) vs (1,2,2)

hlkstuv_23900 Over a year ago

It is not like I have not seen matrices in 3D. I have not used numpy and I am not familiar with the print output. And yea, the difference between the (2,1,2) and (2,2,1) are pretty distinct by the visualizations presented by @Nils Werner. However, I wonder the applications of the three different shapes of (2,1,2) and the (2,2,1) type.

Ashwini Chaudhary · Accepted Answer · 2014-01-30 12:14:58Z

Read (4,3,2) as: There's a building with 4 floors, each floor has 3 rows and 2 columns of rooms. Hence it is a 3-D array.

In [4]: np.zeros((4, 3, 2))                                                                      
Out[4]: 
array([[[ 0.,  0.],                                                                              
        [ 0.,  0.],                                                                              
        [ 0.,  0.]],                                                                             

       [[ 0.,  0.],                                                                              
        [ 0.,  0.],                                                                              
        [ 0.,  0.]],                                                                             

       [[ 0.,  0.],                                                                              
        [ 0.,  0.],                                                                              
        [ 0.,  0.]],                                                                             

       [[ 0.,  0.],                                                                              
        [ 0.,  0.],                                                                              
        [ 0.,  0.]]])

unutbu · Accepted Answer · 2014-01-30 12:20:11Z

The argument is specifying the shape of the array:

In [72]: import numpy as np

In [73]: h = np.zeros((2,2,2))

In [74]: h.shape
Out[74]: (2, 2, 2)

In [75]: h = np.zeros((2,2,1))

In [76]: h.shape
Out[76]: (2, 2, 1)

If the shape of an array is (a,b,c), then it has in NumPy parlance 3 "axes" (or in common English, 3 "dimensions"). Axis 0 has length a, axis 1 has length b, and axis 2 has length c.

When you define h = np.zeros((2,2,1)) notice that the result has 3 levels of brackets:

In [77]: h
Out[77]: 
array([[[ 0.],
        [ 0.]],

       [[ 0.],
        [ 0.]]])

The outermost bracket contains 2 items, the middle brackets also contain 2 items each. The innermost bracket contains just a single item. Thus, the shape is (2, 2, 1).

Thank you all for providing the visualization that I could not get my mind to.

Anil Myne · Accepted Answer · 2021-03-11 10:21:02Z

The last digit always means number of elements. All the others are arrays or lists So, (3, 4, 3) means I need a list with 3 arrays each of the 3 containing 4 arrays, each of those 4 contains 3 elements.

{ [[0,0,0,], [0,0,0], [0,0,0], [0,0,0]],
[[0,0,0], [0,0,0], [0,0,0], [0,0,0]],
[[0,0,0], [0,0,0], [0,0,0], [0,0,0]] }

2, 2, 1 means , list with 2 arrays each containing 2 arrays each with 1 element

{ [[0], [0}],
[[0], [0]] }

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