Tutorial_sparse_example.cpp File Reference

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

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

Typedef Documentation

SpMat

typedef Eigen::SparseMatrix<double> SpMat

Definition at line 5 of file Tutorial_sparse_example.cpp.

T

typedef Eigen::Triplet<double> T

Definition at line 6 of file Tutorial_sparse_example.cpp.

Function Documentation

buildProblem()

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

Definition at line 19 of file Tutorial_sparse_example_details.cpp.

{
  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);
    }
  }
}

main()

int main	(	int	argc,
		char **	argv
	)

Definition at line 11 of file Tutorial_sparse_example.cpp.

{
  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;
}

saveAsBitmap()

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

Definition at line 37 of file Tutorial_sparse_example_details.cpp.

{
  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);
}