Dimensions in Arrays

M3-R5.1 · Chapter 9: NumPy Basics · 16 min read

Dimensions in Arrays : A dimension in arrays is one level of array depth (nested arrays).

Nested array: are arrays that have arrays as their elements.

0-D Arrays : 0-D arrays, or Scalars, are the elements in an array. Each value in an array is a 0-D array.

Example Create a 0-D array with value 42

import numpy as np

arr = np.array(42)

print(arr)

1-D Arrays: An array that has 0-D arrays as its elements is called uni-dimensional or 1-D array.these are the most common and basic arrays.

Example: Create a 1-D array containing the values 1,2,3,4,5:

import numpy as np

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

print(arr)

2-D Arrays : An array that has 1-D arrays as its elements is called a 2-D array.these are often used to represent matrix or 2nd order tensors.

NumPy has a whole sub module dedicated towards matrix operations called numpy.mat

Example: Create a 2-D array containing two arrays with the values 1,2,3 and 4,5,6:

import numpy as np

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

print(arr)

3-D arrays : An array that has 2-D arrays (matrices) as its elements is called 3-D array.these are often used to represent a 3rd order tensor.

Example: Create a 3-D array with two 2-D arrays, both containing two arrays with the values 1,2,3 and 4,5,6:

import numpy as np

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

print(arr)

Check Number of Dimensions? : NumPy Arrays provides the ndim attribute that returns an integer that tells us how many dimensions the array have.

Example: Check how many dimensions the arrays have:

import numpy as np

a = np.array(42)

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

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

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

print(a.ndim)

print(b.ndim)

print(c.ndim)

print(d.ndim)

Higher Dimensional Arrays: An array can have any number of dimensions. When the array is created, you can define the number of dimensions by using the ndmin argument.

Example: Create an array with 5 dimensions and verify that it has 5 dimensions:

import numpy as np

arr = np.array([1, 2, 3, 4], ndmin=5)

print(arr)

print('number of dimensions :', arr.ndim)

In this array the innermost dimension (5th dim) has 4 elements, the 4th dim has 1 element that is the vector, the 3rd dim has 1 element that is the matrix with the vector, the 2nd dim has 1 element that is 3D array and 1st dim has 1 element that is a 4D array.

NumPy Array Indexing

Access Array Elements: Array indexing is the same as accessing an array element. we can access an array element by referring to its index number. The indexes in NumPy arrays start with 0, meaning that the first element has index 0, and the second has index 1 etc.

Example: Get the first element from the following array:

import numpy as np

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

print(arr[0])

Example: Get the second element from the following array.

import numpy as np

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

print(arr[1])

Example: Get third and fourth elements from the following array and add them.

import numpy as np

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

print(arr[2] + arr[3])

Access 2-D Arrays : To access elements from 2-D arrays we can use comma separated integers representing

the dimension and the index of the element.

Think of 2-D arrays like a table with rows and columns, where the row represents the dimension and the

index represents the column.

Example: Access the element on the first row, second column:

import numpy as np

arr = np.array([[1,2,3,4,5], [6,7,8,9,10]])

print('2nd element on 1st row: ', arr[0, 1])

Example: Access the element on the 2nd row, 5th column:

import numpy as np

arr = np.array([[1,2,3,4,5], [6,7,8,9,10]])

print('5th element on 2nd row: ', arr[1, 4])

Access 3-D Arrays : To access elements from 3-D arrays we can use comma separated integers representing the dimensions and the index of the element.

Example: Access the third element of the second array of the first array:

import numpy as np

arr = np.array([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]])

print(arr[0, 1, 2])

Explained : arr[0, 1, 2] prints the value 6.

And this is why:

The first number represents the first dimension, which contains two arrays: [[1, 2, 3], [4, 5, 6]] and:

[[7, 8, 9], [10, 11, 12]] Since we selected 0, we are left with the first array: [[1, 2, 3], [4, 5, 6]]

The second number represents the second dimension, which also contains two arrays: [1, 2, 3] and: [4, 5, 6]
Since we selected 1, we are left with the second array: [4, 5, 6]
The third number represents the third dimension, which contains three values: 4 5 6 Since we selected 2, we end up with the third value: 6

:NumPy Array Slicing :

Slicing arrays : Slicing in python means taking elements from one given index to another given index.

We pass slice instead of index like this: [start:end].
We can also define the step, like this: [start:end:step].
If we don't pass start its considered 0
If we don't pass end its considered length of array in that dimension
If we don't pass step its considered 1

Example: Slice elements from index 1 to index 5 from the following array:

import numpy as np