Question

Part 1: Matrix Multiplication with OpenMP (30 points)

Write a program that calculates the product of two matrices, using a parallel for loop. Note that this
requires writing a triply-nested for loop, and making one of the for loops parallel.
Part 2a: Finding Pythagorean Triples with OpenMP (15 points)
Write a program that calculates Pythagorean triples using nested for loops. The Pythagorean Theorem
states the following:
2 + 2 = c2
Where a, b, and c are whole numbers.
Part 2b: Modifying the Pythagorean Theorem (5 points)
Modify the Pythagorean Theorem by either adding or subtracting a times b on the left-hand-side, and
run the program again. Are there integer solutions for this?
2 + 2 + = c2

Answer 1

To calculate the product of two matrices using a parallel for loop in C++, you can use the OpenMP library. The 'parallel for' directive is used to parallelize the outermost loop of the matrix multiplication, with the iterations divided among multiple threads. An example code snippet is provided to illustrate the implementation.

Step-by-step explanation:

To calculate the product of two matrices using a parallel for loop, we can use the OpenMP library in C++. OpenMP provides directives that allow us to parallelize certain sections of code easily. In this case, we can use the 'parallel for' directive to parallelize the outermost loop of the matrix multiplication. By doing this, the iterations of the outer loop are divided among multiple threads, allowing for concurrent execution. Here is an example of how the code might look:

#include<iostream>
#include<omp.h>

int main() {
int matrix1[3][3] = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
int matrix2[3][3] = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
int result[3][3] = {0};

#pragma omp parallel for
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
for (int k = 0; k < 3; k++) {
result[i][j] += matrix1[i][k] * matrix2[k][j];
}
}
}

// Print the result
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
std::cout << result[i][j] << ' ';
}
std::cout << std::endl;
}

return 0;
}

In this code, we define two matrices (matrix1 and matrix2) and initialize them. We also define a result matrix to store the product. The 'parallel for' directive is used to parallelize the outer for loop, which iterates over the rows of the first matrix. The inner two for loops iterate over the columns of the second matrix and perform the matrix multiplication. Finally, we print the result matrix.