Dear Eigen community,

I am a new guy using Eigen and so far I am really satisfied using it, because I have had a good performance using the Full-Matrix module compared to Matlab. However, this is not the same if I use The Sparse Module. I have tried using MKL (9.38 s)and other libraries in order to improve my performance and I have got a worse performance than Matlab (0.82 s). I would like to know what I am doing wrong, please find bellow the code I am employing.

If somebody can help me, I would really appreciate it!

Thanks for taking time in answering,

Code: Select all

#include <cstdlib>
#include <sstream>
#include <fstream>
#include <iostream>

#include <ctime>

#include <eigen3/Eigen/Core>
#include <eigen3/Eigen/Sparse>

int main() {

    clock_t start, finish;
    const int dim = 10000;

  //First Test:
    Eigen::SparseMatrix<double> ccc(dim,dim);
    Eigen::SparseMatrix<double> ddd(dim,dim);
    ccc.reserve(2*dim);
    ddd.reserve(dim*dim);

    for(int i = 0; i < dim; i++)
        ccc.insert(i,i) = 1;

    for(int i = 1; i < dim; i++)
        ccc.insert(1,i) = 1;

    start = clock();

    ddd = Eigen::SparseMatrix<double>(ccc.transpose())*ccc;

    finish = clock();
    std::cout << "Time for Multiplication (a'*a) (seconds): " << ((double)(finish - start))/CLOCKS_PER_SEC << std::endl;
   

    return 0;

}


Your example is quite unusual because the result is completely dense. With Eigen, you can use a different product algorithm by calling .pruned():

ddd = (ccc.transpose()*ccc).pruned();

It should be faster for your use case.

Dear ggael,

Thanks for your answer. Actually ".pruned()" IS FASTER than my method. I have got 2.47 (s) instead of 9.38 (s). However, I still don't understand why Matlab gets 0.82 (s); what does make Matlab so fast? is it possible to get that performance in Eigen?

P.S: That sort of multiplication, you will find it very often in Finite Element Analysis to assemble stiffness matrices and force vectors, in fact, they are not as the example I gave above, the idea is to check if at least I get the same performance like Matlab, because I want to change Matlab to C++, and Eigen is the most suitable library so far.

It does not make sense to bench sparse algebra on non representative sparse structures.