Objective:

$$ Implement a robust matrix class using object$-$oriented programming principles in

C$++.$

$$ Apply multithreading std::thread to enhance computational efficiency for large matrix

multiplication.

$$ Compare the performance of single$-$threaded and multithreaded computations.

Tasks: Design Matrix Class for Matrix Multplication

$1.$ Design and implement a Matrix class that supports dynamic memory management to handle large matrices.

$2.$ The class should include default constructors and destructor.

$3.$ The default constructor is used to initialize a matrix with $0.$

$4.$ A member function fill$\_$rand$\_$value to initialize a matrix with random values.

$5.$ Include methods for matrix multiplication in mathematics, ensuring the class can

handle non$-$square matrices as well.a$.$ Extend the matrix multiplication method to use multithreading, where each thread computes a portion of the result matrix.

$6.$ Single$-$threaded Multiplication Implementation

a$.$ Implement the standard matrix multiplication algorithm in a single$-$threaded

manner within the Matrix class.

b$.$ Ensure the method handles exceptions $($e$.$g$.,$ mismatched size$)$ correctly.

$7.$ Multithreaded Multiplication Implementation

a$.$ Extend the matrix multiplication method to use multithreading, where each

thread computes a portion of the result matrix

b$.$ Consider dividing the workload by rows or blocks of rows to distribute the multiplication tasks among threads.

c$.$ Ensure the method handles exceptions $($e$.$g$.,$ mismatched size$)$ correctly.

The input and output should be like below:

Input:

Based on the given week$8.$cpp to develop your program. Must not change the supplied

code.

Output

Test at least three cases, as shown below. Please note that the running time may vary

depending on the specifications of different computers.

Enter the number of rows of Matrix A: $10$

Enter the number of cols of Matrix A: $20$

Enter the number of rows of Matrix B: $10$

Enter the number of cols of Matrix B: $20$

Enter the number of threads: $2$

Matrix dimensions must match!

Quit $(\frac{Y}{N})$:$n$

Enter the number of rows of Matrix A: $100$

Enter the number of cols of Matrix A: $50$

Enter the number of rows of Matrix B: $50$

Enter the number of cols of Matrix B: $100$

Enter the number of threads: $2$

Single$-$threaded multiplication took $3\mathrm{.}355ms.$

Multithreaded multiplication took $18\mathrm{.}6884$ ms$.$

Validating results...

Results are identical!

Quit $(\frac{Y}{N})$:$n$

Enter the number of rows of Matrix A: $500$

Enter the number of cols of Matrix A: $500$

Enter the number of rows of Matrix B: $500$

Enter the number of cols of Matrix B: $500$

Enter the number of threads: $2$

Single$-$threaded multiplication took $973\mathrm{.}992ms.$

Multithreaded multiplication took $482\mathrm{.}789ms.$

Validating results...

Results are identical!

Quit $($Y$/$N$)$: y