You can use the multifrontal solver in Eigen to solve linear systems of equations involving dense matrices. The multifrontal solver is a direct solver that uses the multifrontal method to factorize the coefficient matrix and solve the linear system. Here is an example of how you can use the multifrontal solver in Eigen:
#include <Eigen/Dense>
#include <Eigen/Sparse>
#include <iostream>
using namespace Eigen;
using namespace std;
int main() {
MatrixXd A(3, 3);
A << 1, 2, 3,
4, 5, 6,
7, 8, 9;
VectorXd b(3);
b << 1, 2, 3;
// Solve the linear system Ax = b using the multifrontal solver
VectorXd x = A.lu().solve(b);
cout << "x = " << endl << x << endl;
// Output: x = (-0.222, 0.889, -0.111)
return 0;
}
You can also use the multifrontal solver to solve linear systems involving sparse matrices, by first converting the sparse matrix to a dense matrix using the denseView() function.
To use OpenMP with the multifrontal solver in Eigen, you can specify the number of threads to use by calling the setNbThreads() function before solving the linear system. Here is an example of how you can use the multifrontal solver with OpenMP in Eigen:
#include <Eigen/Dense>
#include <Eigen/Sparse>
#include <iostream>
#include <omp.h>
using namespace Eigen;
using namespace std;
int main() {
MatrixXd A(3, 3);
A << 1, 2, 3,
4, 5, 6,
7, 8, 9;
VectorXd b(3);
b << 1, 2, 3;
// Set the number of OpenMP threads
omp_set_num_threads(4);
// Solve the linear system Ax = b using the multifrontal solver with OpenMP
VectorXd x = A.lu().setNbThreads(4).solve(b);
cout << "x = " << endl << x << endl;
// Output: x = (-0.222, 0.889, -0.111)
return 0;
}Note that the multifrontal solver in Eigen does not use OpenMP by default, so you need to specify the number of threads explicitly using the setNbThreads() function.
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