How to fill a sparse matrix efficiently? - c++

Question

I use the eigen library to perform the sparse matrix operations, particularly, to fill a sparse matirx. But the rows and cols are very large in our case, which results in a long time for filling the sparse matrix. Is there any efficient way to do this (maybe by the other libraries)?
Below is the my code:
SparseMatrix mat(rows,cols);
mat.reserve(VectorXi::Constant(cols,6));
for each i,j such that v_ij != 0
mat.insert(i,j) = v_ij;
mat.makeCompressed();

Answer 1

The order in which a SparseMatrix is filled can make an enormous difference in computation time. To fill a SparseMatrix matrix quickly, the elements should be addressed in a sequence that corresponds to the storage order of the SparseMatrix. By default, the storage order in Eigen's SparseMatrix is column major, but it is easy to change this.
The following code demonstrates the time difference between a rowwise filling of two sparse matrices with different storage order. The square sparse matrices are relatively small and nominally identical. While the RowMajor matrix is almost instantly filled, it takes a much longer time (about 30 seconds on my desktop computer) in the case of ColMajor storage format.
#include <iostream>
#include <Eigen/Dense>
#include <Eigen/SparseCore>
#include <random>
using namespace Eigen;
typedef SparseMatrix<double, RowMajor> SpMat_RM;
typedef SparseMatrix<double, ColMajor> SpMat_CM;
// compile with -std=c++11 -O3
int main() {
const int n = 1e4;
const int nnzpr = 50;
std::random_device rd;
std::mt19937 gen(rd());
std::uniform_int_distribution<> randInt(0, n-1);
SpMat_RM m_RM(n,n);
m_RM.reserve(n);
SpMat_CM m_CM(n,n);
m_CM.reserve(n);
std::cout << "Row-wise filling of [" << n << " x " << n << "] sparse matrix (RowMajor) ..." << std::flush;
for (int i = 0; i < n; ++i) {
for (int j = 0; j < nnzpr; ++j) {
int col = randInt(gen);
double val = 1. ; // v_ij
m_RM.coeffRef(i,col) = val ;
}
}
m_RM.makeCompressed();
std::cout << "done." << std::endl;
std::cout << "Row-wise filling of [" << n << " x " << n << "] sparse matrix (ColMajor) ..." << std::flush;
for (int i = 0; i < n; ++i) {
for (int j = 0; j < nnzpr; ++j) {
int col = randInt(gen);
double val = 1.; // v_ij
m_CM.coeffRef(i,col) = val ;
}
}
m_CM.makeCompressed();
std::cout << "done." << std::endl;
}