Conquering Row-wise Division in NumPy Arrays using Broadcasting

Broadcasting:

NumPy's broadcasting mechanism allows performing element-wise operations between arrays of different shapes under certain conditions. When an array and a vector with compatible shapes are used for division, NumPy automatically broadcasts the vector to match the dimensions of the array, enabling row-wise division.

Reshaping the Vector (if necessary):

• If the vector has the same number of elements as the number of columns in the array, it already has the compatible shape for broadcasting.
• If the vector has a different size, we need to reshape it to have one column with the same number of rows as the array. This can be done using techniques like:
  • vector[:, None]: This adds a new axis at the second dimension (column-wise) with size 1, effectively creating a column vector.
  • np.newaxis: This is similar to None but provides more explicit control over the new axis insertion.

Example:

import numpy as np

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

# Create a vector to divide by
divisor = np.array([2, 3, 4])

# Dividing each row by the corresponding element in the divisor vector
divided_arr = arr / divisor[:, np.newaxis]  # Reshape for broadcasting

# Print the original array and the divided array
print("Original array:\n", arr)
print("\nDivided array:\n", divided_arr)

This code will output:

Original array:
 [[1 2 3]
 [4 5 6]
 [7 8 9]]

Divided array:
 [[0.5        1.         1.5       ]
 [1.33333333 1.66666667 2.        ]
 [1.75       2.         2.25      ]]

As you can see, each row of the original array is divided by the corresponding element in the divisor vector, resulting in a new array with element-wise division performed along the rows.

Key Points:

• Broadcasting is crucial for achieving row-wise division in NumPy.
• Reshape the divisor vector if its size doesn't match the number of columns in the array.
• This technique allows efficient vectorized division without using loops.

Example 1: Vector with matching number of columns

import numpy as np

# Sample array
arr = np.array([[2, 4, 6], [8, 10, 12], [14, 16, 18]])

# Divisor vector (same number of elements as columns)
divisor = np.array([2, 5, 3])

# Divide each row by the divisor
divided_arr = arr / divisor

# Print results
print("Original array:\n", arr)
print("\nDivided array:\n", divided_arr)

Example 2: Reshaping a shorter vector

import numpy as np

# Sample array
arr = np.array([[1, 3, 5], [7, 9, 11], [13, 15, 17]])

# Divisor vector (shorter than columns)
divisor = np.array([2])

# Reshape and divide
divided_arr = arr / divisor[:, np.newaxis]

# Print results
print("Original array:\n", arr)
print("\nDivided array:\n", divided_arr)

Example 3: Using np.divide for explicit control

import numpy as np

# Sample array
arr = np.array([[4, 8, 12], [16, 20, 24], [28, 32, 36]])

# Divisor vector
divisor = np.array([3, 4, 5])

# Divide using np.divide
divided_arr = np.divide(arr, divisor[:, None])

# Print results
print("Original array:\n", arr)
print("\nDivided array:\n", divided_arr)

These examples showcase different scenarios for dividing rows by a vector. Remember to choose the method that best suits your specific vector size and desired operation.

np.apply_along_axis:

This function allows applying a custom function along a specified axis of the array. We can define a division function and use it with np.apply_along_axis to achieve row-wise division.

import numpy as np

def divide_by_vector(row, divisor):
  return row / divisor

# Sample array
arr = np.array([[2, 4, 6], [8, 10, 12], [14, 16, 18]])

# Divisor vector
divisor = np.array([3, 2, 1])

# Divide each row using apply_along_axis (axis 1 for rows)
divided_arr = np.apply_along_axis(divide_by_vector, 1, arr, divisor)

# Print results
print("Original array:\n", arr)
print("\nDivided array:\n", divided_arr)

List comprehension (for smaller arrays):

For small arrays, you can use a list comprehension to iterate over each row and perform division. This might be less efficient for larger arrays compared to vectorized methods.

import numpy as np

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

# Divisor vector
divisor = np.array([2, 3])

# Divide each row using list comprehension
divided_arr = np.array([row / divisor for row in arr])

# Print results
print("Original array:\n", arr)
print("\nDivided array:\n", divided_arr)

Choosing the right method:

• Broadcasting with reshaping is the most efficient and recommended approach for larger arrays.
• np.apply_along_axis offers more flexibility for custom division logic but might be slower.
• List comprehension is suitable for very small arrays but not ideal for performance-critical tasks.