Tutorial_sparse_example.cpp
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	#include <Eigen/Sparse>
	#include <vector>
	#include <iostream>

	typedef Eigen::SparseMatrix<double> SpMat; // declares a column-major sparse matrix type of double
	typedef Eigen::Triplet<double> T;

	void buildProblem(std::vector<T>& coefficients, Eigen::VectorXd& b, int n);
	void saveAsBitmap(const Eigen::VectorXd& x, int n, const char* filename);

	int main(int argc, char** argv)
	{
	if(argc!=2) {
	std::cerr << "Error: expected one and only one argument.\n";
	return -1;
	}

	int n = 300; // size of the image
	int m = n*n; // number of unknowns (=number of pixels)

	// Assembly:
	std::vector<T> coefficients; // list of non-zeros coefficients
	Eigen::VectorXd b(m); // the right hand side-vector resulting from the constraints
	buildProblem(coefficients, b, n);

	SpMat A(m,m);
	A.setFromTriplets(coefficients.begin(), coefficients.end());

	// Solving:
	Eigen::SimplicialCholesky<SpMat> chol(A); // performs a Cholesky factorization of A
	Eigen::VectorXd x = chol.solve(b); // use the factorization to solve for the given right hand side

	// Export the result to a file:
	saveAsBitmap(x, n, argv[1]);

	return 0;
	}