Broadcasting rules in Data Analysis Python

Introduction

Broadcasting lets you do math on arrays of different sizes easily. It saves time and code by matching shapes automatically.

Adding a single number to every element in a list of numbers.

Multiplying each row of a table by a different number.

Subtracting a small array from a bigger array without writing loops.

Applying a formula to all data points with different shapes.

Combining data from different sources with compatible sizes.

Syntax

Data Analysis Python

result = array1 + array2

Arrays must have compatible shapes for broadcasting.

Smaller arrays are 'stretched' to match bigger ones without copying data.

Examples

Adds 5 to each element of the array.

Data Analysis Python

import numpy as np

# Add a number to an array
arr = np.array([1, 2, 3])
result = arr + 5
print(result)

Each row of arr2d is multiplied element-wise by arr1d.

Data Analysis Python

import numpy as np

# Multiply a 2D array by a 1D array
arr2d = np.array([[1, 2, 3], [4, 5, 6]])
arr1d = np.array([10, 20, 30])
result = arr2d * arr1d
print(result)

Subtracts each element of col_vec from corresponding row in arr2d.

Data Analysis Python

import numpy as np

# Subtract a column vector from a 2D array
arr2d = np.array([[5, 5, 5], [10, 10, 10]])
col_vec = np.array([[1], [2]])
result = arr2d - col_vec
print(result)

Sample Program

This program adds the 1D vector to each row of the 3x3 matrix. Broadcasting stretches the vector to match the matrix shape.

Data Analysis Python

import numpy as np

# Create a 3x3 array
matrix = np.array([[1, 2, 3],
                   [4, 5, 6],
                   [7, 8, 9]])

# Create a 1D array with 3 elements
vector = np.array([10, 20, 30])

# Add vector to each row of matrix using broadcasting
result = matrix + vector

print(result)

Important Notes

Broadcasting works when trailing dimensions are equal or one of them is 1.

If shapes are not compatible, Python will raise an error.

Broadcasting does not copy data, so it is memory efficient.

Summary

Broadcasting lets you do math on arrays with different shapes easily.

Smaller arrays are stretched to match bigger ones without copying data.

It saves time and makes code simpler for array operations.