Open MP with gsl_matrix is slower than sequential - openmp

Question

I've created a simple c program using gsl(GNU Scienctific Library) and open mp. In this simple program, I want to test the execution time for sequential and parallel. Here is the program snippets, main.c.
#include "omp.h"
#include <stdio.h>
#include <gsl/gsl_matrix.h>
#include <time.h>
int main()
{
omp_set_num_threads(4);
int n1=10000, n2=10000;
gsl_matrix *A = gsl_matrix_alloc(n1, n2);
int i,j;
struct timeval tv1, tv2, tv3, tv4;
gettimeofday(&tv1, 0);
for(i=0; i<n1; i++)
{
for(j=0; j<n2; j++)
{
gsl_matrix_set(A, i, j, i*j*1000000);
}
}
gettimeofday(&tv2, 0);
long elapsed = (tv2.tv_sec-tv1.tv_sec)*1000000 + tv2.tv_usec-tv1.tv_usec;
printf("Sequential Duration:%ldms\n", elapsed);
gettimeofday(&tv3, 0);
#pragma omp parallel for private(i,j)
for(i=0; i<n1; i++)
{
for(j=0; j<n2; j++)
{
gsl_matrix_set(A, i, j, i*j*1000000);
}
}
gettimeofday(&tv4, 0);
elapsed = (tv4.tv_sec-tv3.tv_sec)*1000000 + tv4.tv_usec-tv3.tv_usec;
printf(" Parallel Duration:%ldms\n", elapsed);
return 0;
}
Then I compiled the above code, using this command:
gcc -fopenmp main.c -o test -lgsl -lgslcblas -lm
Here is the program's result:
Sequential Duration:11980106ms
Parallel Duration:20624043ms
Why, the parallel part slower than the sequential part. How can I optimize this code? Thanks

Answer 1

as you have written it the j variable is shared between all threads so the threads are overwritting other threads state constantly, leading to them iterating values they have already covered.
You should always minimize the scope of variables when trying to parallelize with openmp. Either move the scope of j into the loop or mark it as private explicitly:
#pragma omp parallel for private(j)
also clock counts the processor time not the real time, you probably want to use gettimeofday
you matrix is too small to benefit much from parallelization, the threading overhead will dominate. Increase it to ~10000x10000 to start seeing something.

Answer 2

The problem here is that you do not know what the procedure gsl_matrix_set does with A. You do not know if it is thread safe. To change one element in that matrix you supply the whole matrix to the routine instead of only the indices of the element. This smells by false sharing (see e.g. this answer).
I would try this instead
gsl_matrix_set(A[i][j],i*j*1000000);
If that does not work and what you are interested in is only the time difference between serial and parallel I would just do
A[i][j] = i*j*1000000

Answer 3

In the thread part, try this:
#pragma omp parallel private(i,j)
for(i=0; i<n1; i++)
{
for(j=0; j<n2; j++)
{
gsl_matrix_set(A, i, j, i*j*1000000);
}
}
or
#pragma omp parallel for
for(i=0; i<n1; i++)
{
for(j=0; j<n2; j++)
{
gsl_matrix_set(A, i, j, i*j*1000000);
}
}