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
CPP
// 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 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
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
C
// C Program to multiply two matrix using pthreads without // use of global variables #include<stdio.h> #include<pthread.h> #include<unistd.h> #include<stdlib.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; } |
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