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#include <iostream>
struct init {
init() { std::cout << "[" << "init" << "]" << std::endl; }
};
init init_obj;
// [init]
#include <iostream>
#include <Eigen/Dense>
using namespace std;
using namespace Eigen;
int main()
{
MatrixXd A(2,2);
A << 2, -1, 1, 3;
cout << "Here is the input matrix A before decomposition:\n" << A << endl;
cout << "[init]" << endl;
cout << "[declaration]" << endl;
PartialPivLU<Ref<MatrixXd> > lu(A);
cout << "Here is the input matrix A after decomposition:\n" << A << endl;
cout << "[declaration]" << endl;
cout << "[matrixLU]" << endl;
cout << "Here is the matrix storing the L and U factors:\n" << lu.matrixLU() << endl;
cout << "[matrixLU]" << endl;
cout << "[solve]" << endl;
MatrixXd A0(2,2); A0 << 2, -1, 1, 3;
VectorXd b(2); b << 1, 2;
VectorXd x = lu.solve(b);
cout << "Residual: " << (A0 * x - b).norm() << endl;
cout << "[solve]" << endl;
cout << "[modifyA]" << endl;
A << 3, 4, -2, 1;
x = lu.solve(b);
cout << "Residual: " << (A0 * x - b).norm() << endl;
cout << "[modifyA]" << endl;
cout << "[recompute]" << endl;
A0 = A; // save A
lu.compute(A);
x = lu.solve(b);
cout << "Residual: " << (A0 * x - b).norm() << endl;
cout << "[recompute]" << endl;
cout << "[recompute_bis0]" << endl;
MatrixXd A1(2,2);
A1 << 5,-2,3,4;
lu.compute(A1);
cout << "Here is the input matrix A1 after decomposition:\n" << A1 << endl;
cout << "[recompute_bis0]" << endl;
cout << "[recompute_bis1]" << endl;
x = lu.solve(b);
cout << "Residual: " << (A1 * x - b).norm() << endl;
cout << "[recompute_bis1]" << endl;
}
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