multithreading - How to Parallelize Nested Loops in Fortran on a Shared Memory System with OpenMP, Assigning Threads Explicitly

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I am working on a Fortran program with nested loops that I want to parallelize using OpenMP. The program runs on a shared memory multi-processor system, and I want the following:

The inner loop to run on nearby threads, optimizing locality. The outer loop to run on spread-out threads. Here is the code snippet I am trying to parallelize:

program test
use omp_lib
implicit none

integer(8), parameter :: n = 2**5 +16 

real(8) :: A(n,n)
integer(8) :: threads_A(n,n)
integer(8) :: i, j

do j = int(1,8), int(n,8)
  do i = int(1,8), int(n,8)
    A(i,j) = 1.d0/real(i+j,8)
    threads_A(i,j) = omp_get_proc_num() ! physical thread number
  end do
end do

end program test

For example, if my CPU has 4 cores with one thread each, and I have 4 CPUs, the thread affinity matrix for a matrix A(9x9) should look like this:

threads_A(:,1) = [0, 1, 2, 3, 0, 1, 2, 3, 0]  (0,1,2,3 are threads of 1st CPU)
threads_A(:,2) = [4, 5, 6, 7, 4, 5, 6, 7, 4]  (4,5,6,7 are threads of 2nd CPU)
.
.

And so on for the other CPUs. This matrix shows how threads are assigned to the elements of the matrix A. How can I achieve this thread assignment and parallelize the loops using OpenMP in Fortran?

Can anyone help me with the OpenMP constructs for this, and also provide guidance on specifying the exact thread numbers or affinity for these loops in the program?

I am working on a Fortran program with nested loops that I want to parallelize using OpenMP. The program runs on a shared memory multi-processor system, and I want the following:

The inner loop to run on nearby threads, optimizing locality. The outer loop to run on spread-out threads. Here is the code snippet I am trying to parallelize:

program test
use omp_lib
implicit none

integer(8), parameter :: n = 2**5 +16 

real(8) :: A(n,n)
integer(8) :: threads_A(n,n)
integer(8) :: i, j

do j = int(1,8), int(n,8)
  do i = int(1,8), int(n,8)
    A(i,j) = 1.d0/real(i+j,8)
    threads_A(i,j) = omp_get_proc_num() ! physical thread number
  end do
end do

end program test

For example, if my CPU has 4 cores with one thread each, and I have 4 CPUs, the thread affinity matrix for a matrix A(9x9) should look like this:

threads_A(:,1) = [0, 1, 2, 3, 0, 1, 2, 3, 0]  (0,1,2,3 are threads of 1st CPU)
threads_A(:,2) = [4, 5, 6, 7, 4, 5, 6, 7, 4]  (4,5,6,7 are threads of 2nd CPU)
.
.

And so on for the other CPUs. This matrix shows how threads are assigned to the elements of the matrix A. How can I achieve this thread assignment and parallelize the loops using OpenMP in Fortran?

Can anyone help me with the OpenMP constructs for this, and also provide guidance on specifying the exact thread numbers or affinity for these loops in the program?

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