使用 openMP 并行化矩阵向量乘法的最佳方法

Question

I have the following code, which I have parallelized using openMP:

#pragma omp parallel shared(matrix, result, vector) private(i, j)
  {
#pragma omp for schedule(static)
    for (i = 0; i < n; i++)
    {
      for (j = 0; j <= i && j < n; k++)
      {

        result[i] += matrix[i * n + j] * vector[j];
      }
    }
  }

I have added the above pragma directive to the for loop, which calculates the product of a Matrix and a column vector. It does speed up things. But, could there be a more efficient way to
speed things up using OpenMP? I tried with the different types of schedules static, dynamic, runtime, guided, auto. Static and auto seem to give the best results nearly for matrices as large as 30000 x 30000. The Matrix has the property that matrix[i][j]=0 if j>i

Answer 1

1. It may help the compiler to optimize the code if you use a local temporary variable to sum the result of j loop. Your compiler may also do this, but if not, it will be much faster.

2. Always use your variables in their minimum required scope, it also helps the compiler to optimize.

3. Make sure your compiler can effectively vectorize your code: use the appropriate compiler flags, and if you use pointers tell the compiler that there is no loop carried dependency by using restrict keyword or by adding #pragma ivdep (Intel compiler), #pragma gcc ivdep (GCC), #pargma loop(ivdep) (MSVC), #pragma clang loop vectorize(assume_safety) (clang) before the inner loop.

So, your code should look something like this:

#pragma omp parallel for shared(matrix, result, vector) schedule(static)
    for (size_t i = 0; i < n; i++)
    {
      double sum=0;
      #pragma GCC ivdep
      for (size_t j = 0; j <= i; j++) //as suggested by @tstanisl
      {
        sum += matrix[i * n + j] * vector[j];
      }
      result[i] += sum;
    }
  }