如何将 OpenMp 添加到三重嵌套 for 循环

Question

目标是将尽可能多的 OpenMP 添加到以下 Cholesky 因子函数以增加并行化。到目前为止，我只有一个 #pragma omp parallel for 正确实施。 vector<vector<double>> 表示二维矩阵。我已经尝试为
添加 #pragma omp parallel for for (int i = 0; i < n; ++i)、for (int k = 0; k < i; ++k) 和 for (int j = 0; j < k; ++j) 但并行化出错了。 makeMatrix(n, n) 初始化大小为 nxn.

的所有零的 vector<vector<double>>

vector<vector<double>> cholesky_factor(vector<vector<double>> input)
{
    int n = input.size();
    vector<vector<double>> result = makeMatrix(n, n);
        
    for (int i = 0; i < n; ++i) 
    {
        for (int k = 0; k < i; ++k)
        {
            double value = input[i][k];
            for (int j = 0; j < k; ++j)
            {
                value -= result[i][j] * result[k][j];
            }
            result[i][k] = value / result[k][k];
        }
        double value = input[i][i];
        #pragma omp parallel for
        for (int j = 0; j < i; ++j)
        {
            value -= result[i][j] * result[i][j];
        }
        result[i][i] = std::sqrt(value);
    }

    return result;
}

Answer 1

我不认为你可以用这个算法并行化更多的东西，因为外循环的第 i 次迭代取决于第 i - 1 次迭代的结果和 k次内循环迭代取决于第k - 1次迭代的结果。

vector<vector<double>> cholesky_factor(vector<vector<double>> input)
{
    int n = input.size();
    vector<vector<double>> result = makeMatrix(n, n);
        
    for (int i = 0; i < n; ++i) 
    {
        for (int k = 0; k < i; ++k)
        {
            double value = input[i][k];
            // reduction(-: value) does the same 
            // (private instances of value are initialized to zero and
            // added to the initial instance of value when the threads are joining
            #pragma omp parallel for reduction(+: value)
            for (int j = 0; j < k; ++j)
            {
                value -= result[i][j] * result[k][j];
            }
            result[i][k] = value / result[k][k];
        }
        double value = input[i][i];
        #pragma omp parallel for reduction(+: value)
        for (int j = 0; j < i; ++j)
        {
            value -= result[i][j] * result[i][j];
        }
        result[i][i] = std::sqrt(value);
    }

    return result;
}

如何将 OpenMp 添加到三重嵌套 for 循环

How to add OpenMp to triple nested for-loop

c++

parallel-processing

performance

multithreading

openmp