test_eigen-lu.cpp

// Coompilation:
// g++ -I/usr/include/eigen3 -O3 -march=native -fopenmp -o test-eigen-lu test-eigen-lu.cpp
//
// Run:
// export OMP_NUM_THREADS=N ; time ./test-eigen-lu

//#include <iostream>
#include <Eigen/Dense>
#include <Eigen/Core>
using namespace std;
using namespace Eigen;

int main() {
        Eigen::initParallel();
	MatrixXd A = MatrixXd::Random(8000, 8000);
	VectorXd B = VectorXd::Random(8000);
	//cout << "Here is the invertible matrix A:" << endl << A << endl;
	//cout << "Here is the matrix B:" << endl << B << endl;
	VectorXd X = A.lu().solve(B);
	//cout << "Here is the (unique) solution X to the equation AX=B:" << endl << X << endl;
	//cout << "Relative error: " << (A*X-B).norm() / B.norm() << endl;
}

Run in a cycle with 8000×8000 matrices:

$ for i in {1..10} ; do
    > echo "THREADS=1" ; export OMP_NUM_THREADS=1 ; command time ./test-eigen-lu
    > echo "THREADS=2" ; export OMP_NUM_THREADS=2 ; command time ./test-eigen-lu
    > echo "THREADS=3" ; export OMP_NUM_THREADS=3 ; command time ./test-eigen-lu
    > echo "THREADS=4" ; export OMP_NUM_THREADS=4 ; command time ./test-eigen-lu
    > done
(output edited manually to make it more terse)

THREADS=1: 33.41user 0.52system 0:34.11elapsed 99%CPU
THREADS=2: 38.01user 0.38system 0:21.66elapsed 177%CPU
THREADS=3: 54.56user 0.52system 0:23.14elapsed 238%CPU
THREADS=4: 67.61user 0.47system 0:22.41elapsed 303%CPU
THREADS=1: 33.43user 0.40system 0:33.89elapsed 99%CPU
THREADS=2: 41.22user 0.38system 0:23.31elapsed 178%CPU
THREADS=3: 55.22user 0.43system 0:23.61elapsed 235%CPU
THREADS=4: 67.43user 0.67system 0:22.75elapsed 299%CPU
THREADS=1: 33.57user 0.29system 0:33.92elapsed 99%CPU
THREADS=2: 40.62user 0.52system 0:23.11elapsed 178%CPU
THREADS=3: 55.07user 0.39system 0:23.58elapsed 235%CPU
THREADS=4: 67.88user 0.46system 0:22.96elapsed 297%CPU
THREADS=1: 33.45user 0.63system 0:34.32elapsed 99%CPU
THREADS=2: 39.39user 0.35system 0:22.20elapsed 179%CPU
THREADS=3: 56.28user 0.41system 0:23.80elapsed 238%CPU
THREADS=4: 67.34user 0.53system 0:22.70elapsed 298%CPU
THREADS=1: 33.55user 0.41system 0:34.07elapsed 99%CPU
THREADS=2: 40.40user 0.37system 0:23.00elapsed 177%CPU
THREADS=3: 55.33user 0.57system 0:23.90elapsed 233%CPU
THREADS=4: 68.02user 0.43system 0:23.05elapsed 296%CPU
THREADS=1: 34.39user 0.35system 0:34.81elapsed 99%CPU
THREADS=2: 41.68user 0.56system 0:23.50elapsed 179%CPU
THREADS=3: 54.78user 0.39system 0:23.39elapsed 235%CPU
THREADS=4: 67.47user 0.49system 0:22.99elapsed 295%CPU
THREADS=1: 33.57user 0.44system 0:33.99elapsed 100%CPU
THREADS=2: 42.08user 0.50system 0:23.59elapsed 180%CPU
THREADS=3: 54.63user 0.46system 0:23.40elapsed 235%CPU
THREADS=4: 67.51user 0.47system 0:22.03elapsed 308%CPU
THREADS=1: 33.38user 0.36system 0:33.88elapsed 99%CPU
THREADS=2: 40.27user 0.47system 0:22.68elapsed 179%CPU
THREADS=3: 55.34user 0.52system 0:23.67elapsed 236%CPU
THREADS=4: 66.96user 0.45system 0:22.24elapsed 303%CPU
THREADS=1: 33.44user 0.40system 0:33.90elapsed 99%CPU
THREADS=2: 40.18user 0.39system 0:22.67elapsed 178%CPU
THREADS=3: 54.46user 0.41system 0:23.31elapsed 235%CPU
THREADS=4: 67.54user 0.58system 0:22.93elapsed 297%CPU
THREADS=1: 33.40user 0.44system 0:34.01elapsed 99%CPU
THREADS=2: 42.29user 0.38system 0:23.74elapsed 179%CPU
THREADS=3: 54.81user 0.52system 0:23.59elapsed 234%CPU
THREADS=4: 66.57user 0.56system 0:22.76elapsed 294%CPU