I have this code: #include

#include

#include

#include

#define N $1000//$ Size of the matrices

void multiplyMatrices$($double$**$ A$,$ double$**$ B$,$ double$**$ C$,$ int n$)\{$

for $($int i $=0$; i $<$ n; i$++)\{$

for $($int j $=0$; j $<$ n; j$++)\{$

C$[$i$][$j$]=0$;

for $($int k $=0$; k $<$ n; k$++)\{$

C$[$i$][$j$]+=$ A$[$i$][$k$]*$ B$[$k$][$j$]$;

$\}$

$\}$

$\}$

$\}$

int main$()\{$

$//$ Allocate and initialize matrices A$,$ B$,$ C

double$**$ A $=$ new double$*[$N$]$;

double$**$ B $=$ new double$*[$N$]$;

double$**$ C $=$ new double$*[$N$]$;

for $($int i $=0$; i $<$ N; i$++)\{$

A$[$i$]=$ new double$[$N$]$;

B$[$i$]=$ new double$[$N$]$;

C$[$i$]=$ new double$[$N$]$;

for $($int j $=0$; j $<$ N; j$++)\{$

A$[$i$][$j$]=$ rand$()\%100$;

B$[$i$][$j$]=$ rand$()\%100$;

$\}$

$\}$

$//$ Record start time

auto start $=$ std::chrono::high$\_$resolution$\_$clock::now$()$;

$//$ Matrix multiplication

multiplyMatrices$($A$,$ B$,$ C$,$ N$)$;

$//$ Record end time

auto end $=$ std::chrono::high$\_$resolution$\_$clock::now$()$;

std::chrono::duration duration $=$ end $-$ start;

std::cout $<<$ "Execution time: $"<<$ duration.count$()<<"$ seconds" $<<$ std::endl;

$//$ Write result to file

std::ofstream resultFile$("$matrix$\_$output.txt$")$;

for $($int i $=0$; i $<$ N; i$++)\{$

for $($int j $=0$; j $<$ N; j$++)\{$

resultFile $<<$ C$[$i$][$j$]<<""$;

$\}$

resultFile $<<"$

$"$;

$\}$

resultFile.close$()$;

$//$ Free memory

for $($int i $=0$; i $<$ N; i$++)\{$

delete$[]$ A$[$i$]$;

delete$[]$ B$[$i$]$;

delete$[]$ C$[$i$]$;

$\}$

delete$[]$ A;

delete$[]$ B;

delete$[]$ C;

return $0$;

$\}$ I need to do these tasks $-$ Instructions

Modify your matrix multiplication program to use MPI to distribute work on nodes.

Evaluate the performance of your program vs sequential and multi$-$threaded solution.

Modify your code to use OpenMP on the nodes.

Evaluate the performance of your program vs the other two.

Modify your code to use OpenCL.

Evaluate the performance of your programs.

Document your results and present your findings

Submit your task as detailed on the submission details section above to OnTrack.

Please make sure to provide the following:

Source code of the MPI matrix multiplication program,

Source code of the MPI and OpenMP $($hybrid MPI to nodes and OpenMP in the nodes$)$ program,

Source code of the MPI and OpenCL $($hybrid MPI to nodes and OpenCL in the nodes$)$ program, and

Evaluation of your program on different input sizes and number of threads in each of these three

programs.