Reduction with OpenMP

Question

I am trying to compute mean of a 2d matrix using openmp. This 2d matrix is actually an image.

I am doing the thread-wise division of data. For example, if I have

Answer 1

Yes, you can - the reduction clause is applicable to the whole parallel region as well as to individual for worksharing constructs. This allows for e.g. reduction over computations done in different parallel sections (the preferred way to restructure the code):

#pragma omp parallel sections private(val) reduction(+:sum)
{
   #pragma omp section
   {
      bla bla code
      sum += val;
   }
   #pragma omp section
   {
      bla bla code
      sum += val;
   }
}

You can also use the OpenMP for worksharing construct to automatically distribute the loop iterations among the threads in the team instead of reimplementing it using sections:

#pragma omp parallel for private(val) reduction(+:sum)
for (row = 0; row < Rows; row++)
{
   bla bla code
   sum += val;
}

Note that reduction variables are private and their intermediate values (i.e. the value they hold before the reduction at the end of the parallel region) are only partial and not very useful. For example the following serial loop cannot be (easily?) transformed to a parallel one with reduction operation:

for (row = 0; row < Rows; row++)
{
   bla bla code
   sum += val;
   if (sum > threshold)
      yada yada code
}

Here the yada yada code should be executed in each iteration once the accumulated value of sum has passed the value of threshold. When the loop is run in parallel, the private values of sum might never reach threshold, even if their sum does.

Answer 2

In your case, the sum = sum + val could interpreted as val[i] = val[i-1] + val[i] in 1-d array (or val[rows][cols] = val[rows][cols-1] + val[rows][cols] in 2-d array) which is a prefix sum calculation.

Reduction is one of solution for prefix sum, you can use reduction to any commutative-associative operators like '+', '-', '*', '/'.