Section 1.1: What is Vectorization?

Vectorization refers to the approach of applying operations to entire arrays or data columns simultaneously. In the context of Pandas, you can leverage vectorized operations to execute a function across an entire column instead of looping through individual rows.

For instance, suppose you have a DataFrame that includes a column with temperature values in Celsius, and you wish to convert these to Fahrenheit. You might consider either looping through each row to apply the conversion or utilizing vectorization to process the entire column at once:

# Using a loop

for i, row in df.iterrows():

df.loc[i, 'Temperature (F)'] = (row['Temperature (C)'] * 9/5) + 32

# Using vectorization

df['Temperature (F)'] = (df['Temperature (C)'] * 9/5) + 32

As illustrated, vectorization significantly outperforms traditional looping methods in terms of speed and efficiency.

Subsection 1.1.1: Visual Explanation of Vectorization

Section 1.2: What is Broadcasting?

Broadcasting is another powerful technique used to execute operations across entire arrays, particularly when dealing with arrays of differing shapes. In Pandas, broadcasting allows you to perform calculations between a DataFrame and a Series, with the Series being applied across each row of the DataFrame.

For example, if you have a DataFrame with 'Price' and 'Tax Rate' columns and you want to compute the total price including tax for each entry, you could either loop through the DataFrame or employ broadcasting:

# Using a loop

for i, row in df.iterrows():

df.loc[i, 'Total Price'] = row['Price'] * (1 + row['Tax Rate'])

# Using broadcasting

df['Total Price'] = df['Price'] * (1 + df['Tax Rate'])

Again, broadcasting is a more efficient alternative to using loops.