Step by Step solution about How to resolve the algorithm Pragmatic directives step by step in the Julia programming language

The provided Julia code performs operations on two matrices, x and y, using nested loops. The @inbounds macro is used to ensure that the loop indices remain within the bounds of the matrices. Here's a detailed explanation of the code:

1. Matrix Initialization:

   • x = rand(100, 100): This line generates a random matrix x with 100 rows and 100 columns. Each element of x is a random floating-point number.
   • y = rand(100, 100): Similarly, this line generates a random matrix y with the same dimensions as x.

2. @inbounds Macro:

   • The @inbounds macro is used to ensure that the loop indices i and j remain within the valid range of indices for the matrices x and y. This macro is required because otherwise, the code may attempt to access elements outside the bounds of the matrices, which would result in an error.

3. Nested Loops:

   • The code contains two nested loops using the for statement:
     • The outer loop iterates over the rows of both matrices using the index variable i. It ranges from 1 to 100.
     • The inner loop iterates over the columns of both matrices using the index variable j. It also ranges from 1 to 100.

4. Matrix Operations:

   • Within the nested loops, two operations are performed on corresponding elements of x and y:
     • x[i, j] *= y[i, j]: This line performs element-wise multiplication. It multiplies the element in row i and column j of x by the corresponding element in y.
     • y[i, j] += x[i, j]: This line performs element-wise addition. It adds the element in row i and column j of x to the corresponding element in y.

x = rand(100, 100)
y = rand(100, 100)

@inbounds begin
    for i = 1:100
        for j = 1:100
            x[i, j] *= y[i, j]
            y[i, j] += x[i, j]
        end
    end
end