Tutorial_sparse_example.cpp File Reference

#include <Eigen/Sparse>
#include <vector>
#include <iostream>

Typedefs
typedef Eigen::SparseMatrix< double >	SpMat
typedef Eigen::Triplet< double >	T

Functions
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)

Typedef Documentation

SpMat

typedef Eigen::SparseMatrix<double> SpMat

T

typedef Eigen::Triplet<double> T

Function Documentation

buildProblem()

void buildProblem	(	std::vector< T > &	coefficients,
		Eigen::VectorXd &	b,
		int	n
	)

                                                                       {
  b.setZero();
  Eigen::ArrayXd boundary = Eigen::ArrayXd::LinSpaced(n, 0, M_PI).sin().pow(2);
  for (int j = 0; j < n; ++j) {
    for (int i = 0; i < n; ++i) {
      int id = i + j * n;
      insertCoefficient(id, i - 1, j, -1, coefficients, b, boundary);
      insertCoefficient(id, i + 1, j, -1, coefficients, b, boundary);
      insertCoefficient(id, i, j - 1, -1, coefficients, b, boundary);
      insertCoefficient(id, i, j + 1, -1, coefficients, b, boundary);
      insertCoefficient(id, i, j, 4, coefficients, b, boundary);
    }
  }
}

References b, i, insertCoefficient(), j, M_PI, and n.

Referenced by main().

main()

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;
}

References b, buildProblem(), m, n, saveAsBitmap(), Eigen::SparseSolverBase< Derived >::solve(), and plotDoE::x.

saveAsBitmap()

void saveAsBitmap	(	const Eigen::VectorXd &	x,
		int	n,
		const char *	filename
	)

                                                                       {
  Eigen::Array<unsigned char, Eigen::Dynamic, Eigen::Dynamic> bits = (x * 255).cast<unsigned char>();
  QImage img(bits.data(), n, n, QImage::Format_Indexed8);
  img.setColorCount(256);
  for (int i = 0; i < 256; i++) img.setColor(i, qRgb(i, i, i));
  img.save(filename);
}

References Eigen::test::bits(), MergeRestartFiles::filename, i, n, and plotDoE::x.

Referenced by main().