TutorialInplaceLU.cpp
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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;

	}