Multiplication of Matrix using threads
Multiplication of matrix does take time surely. Time complexity of matrix multiplication is O(n^3) using normal matrix multiplication. And Strassen algorithm improves it and its time complexity is O(n^(2.8074)).
But, Is there any way to improve the performance of matrix multiplication using the normal method.
Multi-threading can be done to improve it. In multi-threading, instead of utilizing a single core of your processor, we utilizes all or more core to solve the problem.
We create different threads, each thread evaluating some part of matrix multiplication.
Depending upon the number of cores your processor has, you can create the number of threads required. Although you can create as many threads as you need, a better way is to create each thread for one core.
In second approach,we create a separate thread for each element in resultant matrix. Using pthread_exit() we return computed value from each thread which is collected by pthread_join(). This approach does not make use of any global variables.
Examples:
Input :
Matrix A
1 0 0
0 1 0
0 0 1
Matrix B
2 3 2
4 5 1
7 8 6
Output : Multiplication of A and B
2 3 2
4 5 1
7 8 6
NOTE* It is advised to execute the program in linux based system
Compile in linux using following code:
g++ -pthread program_name.cpp
Implementation:
import java.util.Random;
public class MatrixMultiplication {
static final int MAX = 4;
static final int MAX_THREAD = 4;
static int[][] matA = new int[MAX][MAX];
static int[][] matB = new int[MAX][MAX];
static int[][] matC = new int[MAX][MAX];
static int step_i = 0;
static class Worker implements Runnable {
int i;
Worker(int i) {
this.i = i;
}
@Override
public void run() {
for (int j = 0; j < MAX; j++) {
for (int k = 0; k < MAX; k++) {
matC[i][j] += matA[i][k] * matB[k][j];
}
}
}
}
public static void main(String[] args) {
Random rand = new Random();
// Generating random values in matA and matB
for (int i = 0; i < MAX; i++) {
for (int j = 0; j < MAX; j++) {
matA[i][j] = rand.nextInt(10);
matB[i][j] = rand.nextInt(10);
}
}
// Displaying matA
System.out.println("Matrix A");
for (int i = 0; i < MAX; i++) {
for (int j = 0; j < MAX; j++) {
System.out.print(matA[i][j] + " ");
}
System.out.println();
}
// Displaying matB
System.out.println("Matrix B");
for (int i = 0; i < MAX; i++) {
for (int j = 0; j < MAX; j++) {
System.out.print(matB[i][j] + " ");
}
System.out.println();
}
// declaring four threads
Thread[] threads = new Thread[MAX_THREAD];
// Creating four threads, each evaluating its own part
for (int i = 0; i < MAX_THREAD; i++) {
threads[i] = new Thread(new Worker(step_i++));
threads[i].start();
}
// joining and waiting for all threads to complete
for (int i = 0; i < MAX_THREAD; i++) {
try {
threads[i].join();
} catch (InterruptedException e) {
e.printStackTrace();
}
}
// Displaying the result matrix
System.out.println("Multiplication of A and B");
for (int i = 0; i < MAX; i++) {
for (int j = 0; j < MAX; j++) {
System.out.print(matC[i][j] + " ");
}
System.out.println();
}
}
}
// This code is written by Sundaram.
# Python3 Program to multiply two matrix using multi-threading
from threading import Thread
MAX = 4
MAX_THREAD = 4
matC = [[0 for i in range(MAX)] for j in range(MAX)]
step_i = 0
# Function to print matrix in readable format
def printMatrix(mat):
for row in mat:
print(row)
# Function to multiply a row of matrix A
# with entire matrix B to get a row of matrix C
def multi():
global step_i, matC
i = step_i
step_i = step_i + 1
for j in range(MAX):
for k in range(MAX):
matC[i][j] = matC[i][j] + matA[i][k] * matB[k][j]
if __name__ == "__main__":
# matrix A used for muliplication
matA = [[3,7,3,6],
[9,2,0,3],
[0,2,1,7],
[2,2,7,9]]
# matrix B used for multiplication
matB = [[6,5,5,2],
[1,7,9,6],
[6,6,8,9],
[0,3,5,2]]
# creating list of size MAX_THREAD
thread = list(range(MAX_THREAD))
# creating MAX_THEAD number of threads
for i in range(MAX_THREAD):
thread[i] = Thread(target=multi)
thread[i].start()
# Waiting for all threads to finish
for i in range(MAX_THREAD):
thread[i].join()
# Printing the resultant matrix C = A x B
printMatrix(matC)
using System;
using System.Threading;
public class MatrixMultiplication
{
static readonly int MAX = 4;
static readonly int MAX_THREAD = 4;
static int[,] matA = new int[MAX, MAX];
static int[,] matB = new int[MAX, MAX];
static int[,] matC = new int[MAX, MAX];
static int step_i = 0;
class Worker
{
int i;
public Worker(int i)
{
this.i = i;
}
public void Run()
{
for (int j = 0; j < MAX; j++)
{
for (int k = 0; k < MAX; k++)
{
matC[i, j] += matA[i, k] * matB[k, j];
}
}
}
}
public static void Main(string[] args)
{
Random rand = new Random();
// Generating random values in matA and matB
for (int i = 0; i < MAX; i++)
{
for (int j = 0; j < MAX; j++)
{
matA[i, j] = rand.Next(10);
matB[i, j] = rand.Next(10);
}
}
// Displaying matA
Console.WriteLine("Matrix A");
for (int i = 0; i < MAX; i++)
{
for (int j = 0; j < MAX; j++)
{
Console.Write(matA[i, j] + " ");
}
Console.WriteLine();
}
// Displaying matB
Console.WriteLine("Matrix B");
for (int i = 0; i < MAX; i++)
{
for (int j = 0; j < MAX; j++)
{
Console.Write(matB[i, j] + " ");
}
Console.WriteLine();
}
// declaring four threads
Thread[] threads = new Thread[MAX_THREAD];
// Creating four threads, each evaluating its own part
for (int i = 0; i < MAX_THREAD; i++)
{
threads[i] = new Thread(new Worker(step_i++).Run);
threads[i].Start();
}
// joining and waiting for all threads to complete
for (int i = 0; i < MAX_THREAD; i++)
{
threads[i].Join();
}
// Displaying the result matrix
Console.WriteLine("Multiplication of A and B");
for (int i = 0; i < MAX; i++)
{
for (int j = 0; j < MAX; j++)
{
Console.Write(matC[i, j] + " ");
}
Console.WriteLine();
}
}
}
const MAX = 4;
const MAX_THREAD = 4;
const matA = new Array(MAX).fill().map(() => new Array(MAX).fill(0));
const matB = new Array(MAX).fill().map(() => new Array(MAX).fill(0));
const matC = new Array(MAX).fill().map(() => new Array(MAX).fill(0));
let step_i = 0;
class Worker {
constructor(i) {
this.i = i;
}
run() {
for (let j = 0; j < MAX; j++) {
for (let k = 0; k < MAX; k++) {
matC[this.i][j] += matA[this.i][k] * matB[k][j];
}
}
}
}
// Generating random values in matA and matB
for (let i = 0; i < MAX; i++) {
for (let j = 0; j < MAX; j++) {
matA[i][j] = Math.floor(Math.random() * 10);
matB[i][j] = Math.floor(Math.random() * 10);
}
}
// Displaying matA
console.log("Matrix A");
for (let i = 0; i < MAX; i++) {
console.log(matA[i].join(" "));
}
// Displaying matB
console.log("Matrix B");
for (let i = 0; i < MAX; i++) {
console.log(matB[i].join(" "));
}
// declaring four threads
const threads = new Array(MAX_THREAD).fill();
// Creating four threads, each evaluating its own part
for (let i = 0; i < MAX_THREAD; i++) {
threads[i] = new Worker(step_i++);
threads[i].run();
}
// Displaying the result matrix
console.log("Multiplication of A and B");
for (let i = 0; i < MAX; i++) {
console.log(matC[i].join(" "));
}
// CPP Program to multiply two matrix using pthreads
#include <bits/stdc++.h>
using namespace std;
// maximum size of matrix
#define MAX 4
// maximum number of threads
#define MAX_THREAD 4
int matA[MAX][MAX];
int matB[MAX][MAX];
int matC[MAX][MAX];
int step_i = 0;
void* multi(void* arg)
{
int i = step_i++; //i denotes row number of resultant matC
for (int j = 0; j < MAX; j++)
for (int k = 0; k < MAX; k++)
matC[i][j] += matA[i][k] * matB[k][j];
}
// Driver Code
int main()
{
// Generating random values in matA and matB
for (int i = 0; i < MAX; i++) {
for (int j = 0; j < MAX; j++) {
matA[i][j] = rand() % 10;
matB[i][j] = rand() % 10;
}
}
// Displaying matA
cout << endl
<< "Matrix A" << endl;
for (int i = 0; i < MAX; i++) {
for (int j = 0; j < MAX; j++)
cout << matA[i][j] << " ";
cout << endl;
}
// Displaying matB
cout << endl
<< "Matrix B" << endl;
for (int i = 0; i < MAX; i++) {
for (int j = 0; j < MAX; j++)
cout << matB[i][j] << " ";
cout << endl;
}
// declaring four threads
pthread_t threads[MAX_THREAD];
// Creating four threads, each evaluating its own part
for (int i = 0; i < MAX_THREAD; i++) {
int* p;
pthread_create(&threads[i], NULL, multi, (void*)(p));
}
// joining and waiting for all threads to complete
for (int i = 0; i < MAX_THREAD; i++)
pthread_join(threads[i], NULL);
// Displaying the result matrix
cout << endl
<< "Multiplication of A and B" << endl;
for (int i = 0; i < MAX; i++) {
for (int j = 0; j < MAX; j++)
cout << matC[i][j] << " ";
cout << endl;
}
return 0;
}
Output
Matrix A 7 2 6 8 7 0 6 6 6 1 7 5 3 7 7 2 Matrix B 3 5 3 6 5 7 5 8 8 9 4 9 6 5 7 2 Multiplication of A and B 127 143 111 128 105 119 87 108 109 125 86 117 112 137 86 141
Time Complexity: O(1)
Auxiliary Space: O(1)
An approach without using global variables:
NOTE* It is advised to execute the program in linux based system
Compile in linux using following code:
g++ -pthread program_name.cpp
Implementation:
#include <iostream>
#include <vector>
std::vector<std::vector<int> > matrixMultiplication(
const std::vector<std::vector<int> >& matA,
const std::vector<std::vector<int> >& matB)
{
int rowsA = matA.size();
int colsA = matA[0].size();
int colsB = matB[0].size();
if (colsA != matB.size()) {
throw std::invalid_argument(
"Matrices cannot be multiplied: columns of "
"matrix A must be equal to rows of matrix B");
}
std::vector<std::vector<int> > result(
rowsA, std::vector<int>(colsB, 0));
for (int i = 0; i < rowsA; i++) {
for (int j = 0; j < colsB; j++) {
int sum = 0;
for (int k = 0; k < colsA; k++) {
sum += matA[i][k] * matB[k][j];
}
result[i][j] = sum;
}
}
return result;
}
int main()
{
// Example matrices
std::vector<std::vector<int> > matA
= { { 3, 7, 3, 6 },
{ 9, 2, 0, 3 },
{ 0, 2, 1, 7 },
{ 2, 2, 7, 9 } };
std::vector<std::vector<int> > matB
= { { 6, 5, 5, 2 },
{ 1, 7, 9, 6 },
{ 6, 6, 8, 9 },
{ 0, 3, 5, 2 } };
// Perform matrix multiplication
std::vector<std::vector<int> > result
= matrixMultiplication(matA, matB);
// Display the result
std::cout << "Multiplication of A and B:" << std::endl;
for (const auto& row : result) {
for (int num : row) {
std::cout << num << " ";
}
std::cout << std::endl;
}
return 0;
}
// C Program to multiply two matrix using pthreads without
// use of global variables
#include <pthread.h>
#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>
#define MAX 4
// Each thread computes single element in the resultant
// matrix
void* mult(void* arg)
{
int* data = (int*)arg;
int k = 0, i = 0;
int x = data[0];
for (i = 1; i <= x; i++)
k += data[i] * data[i + x];
int* p = (int*)malloc(sizeof(int));
*p = k;
// Used to terminate a thread and the return value is
// passed as a pointer
pthread_exit(p);
}
// Driver code
int main()
{
int matA[MAX][MAX];
int matB[MAX][MAX];
int r1 = MAX, c1 = MAX, r2 = MAX, c2 = MAX, i, j, k;
// Generating random values in matA
for (i = 0; i < r1; i++)
for (j = 0; j < c1; j++)
matA[i][j] = rand() % 10;
// Generating random values in matB
for (i = 0; i < r1; i++)
for (j = 0; j < c1; j++)
matB[i][j] = rand() % 10;
// Displaying matA
for (i = 0; i < r1; i++) {
for (j = 0; j < c1; j++)
printf("%d ", matA[i][j]);
printf("\n");
}
// Displaying matB
for (i = 0; i < r2; i++) {
for (j = 0; j < c2; j++)
printf("%d ", matB[i][j]);
printf("\n");
}
int max = r1 * c2;
// declaring array of threads of size r1*c2
pthread_t* threads;
threads = (pthread_t*)malloc(max * sizeof(pthread_t));
int count = 0;
int* data = NULL;
for (i = 0; i < r1; i++)
for (j = 0; j < c2; j++) {
// storing row and column elements in data
data = (int*)malloc((20) * sizeof(int));
data[0] = c1;
for (k = 0; k < c1; k++)
data[k + 1] = matA[i][k];
for (k = 0; k < r2; k++)
data[k + c1 + 1] = matB[k][j];
// creating threads
pthread_create(&threads[count++], NULL, mult,
(void*)(data));
}
printf("RESULTANT MATRIX IS :- \n");
for (i = 0; i < max; i++) {
void* k;
// Joining all threads and collecting return value
pthread_join(threads[i], &k);
int* p = (int*)k;
printf("%d ", *p);
if ((i + 1) % c2 == 0)
printf("\n");
}
return 0;
}
import java.util.Random;
class MatrixMultiplier implements Runnable {
private final int[][] matA;
private final int[][] matB;
private final int row;
private final int col;
private final int[] resultRow;
public MatrixMultiplier(int[][] matA, int[][] matB,
int row, int col,
int[] resultRow)
{
this.matA = matA;
this.matB = matB;
this.row = row;
this.col = col;
this.resultRow = resultRow;
}
@Override public void run()
{
int sum = 0;
for (int i = 0; i < matA[0].length; i++) {
sum += matA[row][i] * matB[i][col];
}
resultRow[col] = sum;
}
}
public class MatrixMultiplication {
public static void main(String[] args)
throws InterruptedException
{
final int MAX = 4;
int[][] matA = new int[MAX][MAX];
int[][] matB = new int[MAX][MAX];
int[][] result = new int[MAX][MAX];
Random rand = new Random();
// Generating random values in matA
for (int i = 0; i < MAX; i++) {
for (int j = 0; j < MAX; j++) {
matA[i][j] = rand.nextInt(10);
}
}
// Generating random values in matB
for (int i = 0; i < MAX; i++) {
for (int j = 0; j < MAX; j++) {
matB[i][j] = rand.nextInt(10);
}
}
// Displaying matA
System.out.println("Matrix A:");
for (int[] row : matA) {
for (int val : row) {
System.out.print(val + " ");
}
System.out.println();
}
// Displaying matB
System.out.println("Matrix B:");
for (int[] row : matB) {
for (int val : row) {
System.out.print(val + " ");
}
System.out.println();
}
Thread[][] threads = new Thread[MAX][MAX];
// Multiplying matrices
for (int i = 0; i < MAX; i++) {
for (int j = 0; j < MAX; j++) {
threads[i][j]
= new Thread(new MatrixMultiplier(
matA, matB, i, j, result[i]));
threads[i][j].start();
}
}
// Waiting for all threads to finish
for (int i = 0; i < MAX; i++) {
for (int j = 0; j < MAX; j++) {
threads[i][j].join();
}
}
// Displaying result matrix
System.out.println("Resultant Matrix:");
for (int[] row : result) {
for (int val : row) {
System.out.print(val + " ");
}
System.out.println();
}
}
}
import threading
import random
MAX = 4
# Function to multiply two matrices
def multiply(data):
result = 0
x = data[0]
for i in range(1, x + 1):
result += data[i] * data[i + x]
return result
# Thread function
def mult_thread(data, results, index):
result = multiply(data)
results[index] = result
# Main function
def main():
matA = [[random.randint(0, 9) for _ in range(MAX)] for _ in range(MAX)]
matB = [[random.randint(0, 9) for _ in range(MAX)] for _ in range(MAX)]
# Displaying matA
print("Matrix A:")
for row in matA:
print(row)
# Displaying matB
print("\nMatrix B:")
for row in matB:
print(row)
results = [None] * (MAX * MAX)
threads = []
count = 0
for i in range(MAX):
for j in range(MAX):
# Storing row and column elements in data
data = [MAX] + matA[i] + [row[j] for row in matB]
# Creating thread
thread = threading.Thread(
target=mult_thread, args=(data, results, count))
thread.start()
threads.append(thread)
count += 1
# Waiting for all threads to complete
for thread in threads:
thread.join()
print("\nResultant Matrix:")
for i, result in enumerate(results):
print(result, end=" ")
if (i + 1) % MAX == 0:
print()
if __name__ == "__main__":
main()
function matrixMultiplication(matA, matB) {
const rowsA = matA.length;
const colsA = matA[0].length;
const colsB = matB[0].length;
if (colsA !== matB.length) {
throw new Error("Matrices cannot be multiplied: columns of matrix A must be equal to rows of matrix B");
}
const result = new Array(rowsA).fill(0).map(() => new Array(colsB).fill(0));
for (let i = 0; i < rowsA; i++) {
for (let j = 0; j < colsB; j++) {
let sum = 0;
for (let k = 0; k < colsA; k++) {
sum += matA[i][k] * matB[k][j];
}
result[i][j] = sum;
}
}
return result;
}
// Example matrices
const matA = [
[3, 7, 3, 6],
[9, 2, 0, 3],
[0, 2, 1, 7],
[2, 2, 7, 9]
];
const matB = [
[6, 5, 5, 2],
[1, 7, 9, 6],
[6, 6, 8, 9],
[0, 3, 5, 2]
];
// Perform matrix multiplication
const result = matrixMultiplication(matA, matB);
// Display the result
console.log("Multiplication of A and B:");
result.forEach(row => console.log(row.join(" ")));
Output:
Matrix A
3 7 3 6
9 2 0 3
0 2 1 7
2 2 7 9
Matrix B
6 5 5 2
1 7 9 6
6 6 8 9
0 3 5 2
Multiplication of A and B
43 100 132 87
56 68 78 36
8 41 61 35
56 93 129 97
Time Complexity: O(MAX*MAX)
Auxiliary Space: O(MAX*MAX)