NumPy: Get the block-sum from a given array of shape 25x25
Compute block-sum of a 25x25 matrix (e.g., sum of each 5x5 block).
Write a NumPy program to get the block-sum (block size is 5x5) from a given array of shape 25x25.
Pictorial Presentation:
Sample Solution:
Python Code:
# Importing the NumPy library
import numpy as np
# Creating a NumPy array 'arra1' of shape (25, 25) filled with ones
arra1 = np.ones((25, 25))
# Setting the block size 'k' as 5
k = 5
# Displaying the original array 'arra1'
print("Original arrays:")
print(arra1)
# Calculating the block-sum (5x5) of the original array 'arra1'
result = np.add.reduceat(
np.add.reduceat(arra1, np.arange(0, arra1.shape[0], k), axis=0),
np.arange(0, arra1.shape[1], k), axis=1
)
# Displaying the block-sum result
print("\nBlock-sum (5x5) of the said array:")
print(result)
Sample Output:
Original arrays: [[1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]] Block-sum (5x5) of the said array: [[25. 25. 25. 25. 25.] [25. 25. 25. 25. 25.] [25. 25. 25. 25. 25.] [25. 25. 25. 25. 25.] [25. 25. 25. 25. 25.]]
Explanation:
In the above exercise -
arra1: A 2D NumPy array of shape (25, 25) filled with ones.
k: The size of the non-overlapping blocks to calculate the sum.
result = np.add.reduceat(np.add.reduceat(arra1, np.arange(0, arra1.shape[0], k), axis=0), np.arange(0, arra1.shape[1], k), axis=1)
In the above code -
- np.add.reduceat: This function performs a local reduce (in this case, addition) on the input array along the specified axis using the given indices.
- np.arange(0, arra1.shape[0], k): This creates an array of indices with a step of k for the rows. It will be [0, 5, 10, 15, 20].
- np.arange(0, arra1.shape[1], k): This creates an array of indices with a step of k for the columns. It will be [0, 5, 10, 15, 20].
- The first np.add.reduceat is applied to the rows, resulting in an intermediate array with summed blocks of size kxk along the rows.
- The second np.add.reduceat is applied to the columns of the intermediate array, resulting in the final array result, which has the summed blocks of size kxk.
print(result): Finally print() function prints the final result.
For more Practice: Solve these Related Problems:
- Write a NumPy program to divide a 25x25 matrix into non-overlapping 5x5 blocks and compute the sum of each block using np.add.reduceat.
- Create a function that reshapes the matrix into a 5x5 grid of blocks and then computes the block-sum for each.
- Implement a solution that uses slicing and loops to manually compute the sum of each 5x5 block.
- Test the block-sum function on matrices with different block sizes to verify its generality.
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