我试图解决Ax = b,其中矩阵A可以大到接近1M x 1M的大小,稀疏且对称,但可能没有明确定义.

问题在于,使用本征中的sparseLU object来计算分解可能会花费很长时间,并且可以存储一个sparseLU矩阵而不是原始矩阵,这样,只要我们使用相同的矩阵A执行类似的运算,我们就可以无需重新计算

在*上进行的快速搜索和google返回了this、this和this的稀疏矩阵,用于本征矩阵的序列化.但是,我不确定是否可以将相同的代码应用于sparseLU对象.

也许我应该改一下我的问题：

如何将分解后的矩阵存储到文件中？

当前的方法都集中于存储原始矩阵,但是我想存储分解后的矩阵.有什么办法吗？谢谢.

解决方法:

下面的示例应帮助您实现自己的序列化.

编辑更改示例以回答改写的问题.

#include <Eigen/Dense>
#include <Eigen/Core>
#include <Eigen/Sparse>
#include <Eigen/SparseLU>
#include <iostream>
#include <fstream>

using namespace Eigen;
using namespace std;

typedef Triplet<int> Trip;

template <typename T, int whatever, typename IND>
void Serialize(SparseMatrix<T, whatever, IND>& m) {
    std::vector<Trip> res;
    int sz = m.nonZeros();
    m.makeCompressed();

    fstream writeFile;
    writeFile.open("matrix", ios::binary | ios::out);

    if(writeFile.is_open())
    {
        IND rows, cols, nnzs, outS, innS;
        rows = m.rows()     ;
        cols = m.cols()     ;
        nnzs = m.nonZeros() ;
        outS = m.outerSize();
        innS = m.innerSize();

        writeFile.write((const char *)&(rows), sizeof(IND));
        writeFile.write((const char *)&(cols), sizeof(IND));
        writeFile.write((const char *)&(nnzs), sizeof(IND));
        writeFile.write((const char *)&(outS), sizeof(IND));
        writeFile.write((const char *)&(innS), sizeof(IND));

        writeFile.write((const char *)(m.valuePtr()),       sizeof(T  ) * m.nonZeros());
        writeFile.write((const char *)(m.outerIndexPtr()),  sizeof(IND) * m.outerSize());
        writeFile.write((const char *)(m.innerIndexPtr()),  sizeof(IND) * m.nonZeros());

        writeFile.close();
    }
}

template <typename T, int whatever, typename IND>
void Deserialize(SparseMatrix<T, whatever, IND>& m) {
    fstream readFile;
    readFile.open("matrix", ios::binary | ios::in);
    if(readFile.is_open())
    {
        IND rows, cols, nnz, inSz, outSz;
        readFile.read((char*)&rows , sizeof(IND));
        readFile.read((char*)&cols , sizeof(IND));
        readFile.read((char*)&nnz  , sizeof(IND));
        readFile.read((char*)&outSz, sizeof(IND));
        readFile.read((char*)&inSz , sizeof(IND));

        m.resize(rows, cols);
        m.makeCompressed();
        m.resizeNonZeros(nnz);

        readFile.read((char*)(m.valuePtr())     , sizeof(T  ) * nnz  );
        readFile.read((char*)(m.outerIndexPtr()), sizeof(IND) * outSz);
        readFile.read((char*)(m.innerIndexPtr()), sizeof(IND) * nnz );

        m.finalize();
        readFile.close();

    } // file is open
}


int main(int argc, char *argv[]){
    int rows, cols;
    rows = cols = 6;
    SparseMatrix<double> A(rows,cols), B;

    std::vector<Trip> trp, tmp;

    trp.push_back(Trip(0, 0, rand()));
    trp.push_back(Trip(1, 1, rand()));
    trp.push_back(Trip(2, 2, rand()));
    trp.push_back(Trip(3, 3, rand()));
    trp.push_back(Trip(4, 4, rand()));
    trp.push_back(Trip(5, 5, rand()));
    trp.push_back(Trip(2, 4, rand()));
    trp.push_back(Trip(3, 1, rand()));

    A.setFromTriplets(trp.begin(), trp.end());
    cout << A.nonZeros() << endl;   // Prints 8
    cout << A.size() << endl;       // Prints 36
    cout << A << endl;              // Prints the matrix along with the sparse matrix stuff

    Serialize(A);

    Deserialize(B);

    cout << B.nonZeros() << endl;   // Prints 8
    cout << B.size() << endl;       // Prints 36
    cout << B << endl;              // Prints the reconstructed matrix along with the sparse matrix stuff


    SparseLU<SparseMatrix<double>, COLAMDOrdering<int> > solver;
    solver.isSymmetric(true);
    solver.compute(A);  // Works...
    /*
    ...
    */

    return 0;
}

另外,nonZeros是Matrix的成员,而不是SparseLU.