Shapes & dimensions

• NumPy
• Shape = the number of elements in each dimension
  • NumPy arrays have an attribute called shape that returns a tuple with each index having the number of corresponding elements
  • Generally:
    • shape = ( …, # of 3D arrays, # of 2D arrays, rows, columns)
• Dimension = the number of axes it has
  • The number of levels of nesting the array has (the number of square brackets!!)
  • Example
    • an np array with shape (5,6,3) → dimension of 3
    • np.array([[1,2,3],[1,2,3]]) → dimension of 2
• This page explains the shapes and dimensions
  • More covered in Matrices

Pro tip! Count the number of square brackets [

1D array

import numpy as np
 
arr = np.array([1,2,3,4])
# one dimensional array of 4 elements
print(arr.shape) # (4,)

• concept of rows and columns apply to NumPy arrays only if the dimension is more than 1
  • For a 1D array like this, there are no rows and cols, so .shape just returns the # of elements

2D array

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

• arr has 3 rows and 4 columns
• There are 2 square brackets [[→ this indicates that this is a 2D array
• A 2D array is just a collection of 1D arrays.
  • A 3D array is a collection of 2D arrays and goes on
• So arr is a 2D array made out of 3 1D arrays

3D array

arr = np.array([[[1,2,3],[4,5,6],[7,8,9],[11,12,13]],[[10,20,30],[40,50,60],[70,80,90],[11,12,13]]])
print(arr.shape) # (2,4,3)
print(arr)
#[[[ 1  2  3]  
#  [ 4  5  6]  
#  [ 7  8  9]  
#  [11 12 13]] 
# [[10 20 30]  
#  [40 50 60]  
#  [70 80 90]  
#  [11 12 13]]]

• arr.shape is (2,4,3)
  • arr now has 2 2D arrays.
  • Each of those 2D arrays is made up of 4 1D arrays (rows).
  • Each of those 1D arrays contains 3 elements.