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#include <iostream>
#include <Eigen/Dense>
using namespace std;
using namespace Eigen;
int main()
{
Matrix2d A;
FullPivLU<Matrix2d> lu;
A << 2, 1,
2, 0.9999999999;
lu.compute(A);
cout << "By default, the rank of A is found to be " << lu.rank() << endl;
cout << "Now recomputing the LU decomposition with threshold 1e-5" << endl;
lu.setThreshold(1e-5);
lu.compute(A);
cout << "The rank of A is found to be " << lu.rank() << endl;
}
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