Question

我试图为矩阵乘法编写并行分治算法，矩阵为2 ^ N x 2 ^ n。我的解决方案适用于较小的矩阵，但是当我尝试将两个2 ^ 6 x 2 ^ 6或更大的矩阵相乘时，它开始写入随机0，并且计算结果非常糟糕。我认为问题是太多的线程可能从那个大小开始，但我不知道如何解决它的一天。谢谢你的帮助。这是我到目前为止的尝试：

bool ParallelMultiply(const std::vector<std::vector<int> > &m1, const std::vector<std::vector<int> > &m2, std::vector<std::vector<int> > &dest)
{
if((m1.size() == 1) && m1.size() == m1[0].size())
    dest[0][0] = m1[0][0]*m2[0][0];
else
{
    std::vector<std::vector<int> > temp(m1.size());
    for(int i=0; i < temp.size(); i++)
        temp[i].resize(temp.size());

    int subSize = m1.size()/2;

    std::vector<std::vector<int> > A11 = SubMatrix(m1, 0, 0);
    std::vector<std::vector<int> > A12 = SubMatrix(m1, 0, subSize);
    std::vector<std::vector<int> > A21 = SubMatrix(m1, subSize, 0);
    std::vector<std::vector<int> > A22 = SubMatrix(m1, subSize, subSize);
    std::vector<std::vector<int> > B11 = SubMatrix(m2, 0, 0);
    std::vector<std::vector<int> > B12 = SubMatrix(m2, 0, subSize);
    std::vector<std::vector<int> > B21 = SubMatrix(m2, subSize, 0);
    std::vector<std::vector<int> > B22 = SubMatrix(m2, subSize, subSize);
    std::vector<std::vector<int> > dest11 = SubMatrix(dest, 0, 0);
    std::vector<std::vector<int> > dest12 = SubMatrix(dest, 0, subSize);
    std::vector<std::vector<int> > dest21 = SubMatrix(dest, subSize, 0);
    std::vector<std::vector<int> > dest22 = SubMatrix(dest, subSize, subSize);
    std::vector<std::vector<int> > temp11 = SubMatrix(temp, 0, 0);
    std::vector<std::vector<int> > temp12 = SubMatrix(temp, 0, subSize);
    std::vector<std::vector<int> > temp21 = SubMatrix(temp, subSize, 0);
    std::vector<std::vector<int> > temp22 = SubMatrix(temp, subSize, subSize);


    std::future<bool> f1 = std::async(std::launch::async, ParallelMultiply, std::cref(A11), std::cref(B11), std::ref(dest11));
    std::future<bool> f2 = std::async(std::launch::async, ParallelMultiply, std::cref(A12), std::cref(B21), std::ref(temp11));

    std::future<bool> f3 = std::async(std::launch::async, ParallelMultiply, std::cref(A11), std::cref(B12), std::ref(dest12));
    std::future<bool> f4 = std::async(std::launch::async, ParallelMultiply, std::cref(A12), std::cref(B22), std::ref(temp12));


    std::future<bool> f5 = std::async(std::launch::async, ParallelMultiply, std::cref(A21), std::cref(B11), std::ref(dest21));
    std::future<bool> f6 = std::async(std::launch::async, ParallelMultiply, std::cref(A22), std::cref(B21), std::ref(temp21));

    std::future<bool> f7 = std::async(std::launch::async, ParallelMultiply, std::cref(A21), std::cref(B12), std::ref(dest22));
    std::future<bool> f8 = std::async(std::launch::async, ParallelMultiply, std::cref(A22), std::cref(B22), std::ref(temp22));

    f1.wait(); f2.wait(); f3.wait(); f4.wait(); f5.wait(); f6.wait(); f7.wait(); f8.wait();

    AddMatrices(temp11, dest11);
    AddMatrices(temp12, dest12);
    AddMatrices(temp21, dest21);
    AddMatrices(temp22, dest22);

    MergeMatrices(dest11, dest12, dest21, dest22, dest);

}

return true;
}

另外两个功能：

void AddMatrices(const std::vector<std::vector<int> > &m, std::vector<std::vector<int> > &res)
{
for(int i=0; i < m.size(); i++)
    for(int j=0; j < m.size(); j++)
        res[i][j] += m[i][j];
}

void MergeMatrices(const std::vector<std::vector<int> > &m1, const std::vector<std::vector<int> > &m2, const std::vector<std::vector<int> > &m3, const std::vector<std::vector<int> > &m4, std::vector<std::vector<int> > &res)
{
int x = res.size()/2;
for(int i=0; i<x; i++)
    for(int j=0; j<x; j++)
    {
        res[i][j] = m1[i][j];
        res[i][x+j] = m2[i][j];
        res[x+i][j] = m3[i][j];
        res[x+i][x+j] = m4[i][j];
    }
}

如何使用c ++ 11使线程安全成为异步矩阵乘法？

0 个答案: