Eigen::SparseMatrix<double> Condi2Joint(Eigen::SparseMatrix<double> Condi, Eigen::SparseVector<double> Pa)
{	// second dimension of Condi is the parent
	Eigen::SparseMatrix<double> Joint;
	Joint.resize(Condi.rows(), Condi.cols());

	for (int cols = 0; cols < Condi.cols(); cols++)
	{
		Eigen::SparseVector<double> tmp_vec = Condi.block(0, cols, Condi.rows(), 1)*Pa.coeff(cols);
		for (int id_rows = 0; id_rows < tmp_vec.size(); id_rows++)
		{
			Joint.coeffRef(id_rows, cols) = tmp_vec.coeff(id_rows);
		}

	}
	Joint.prune(TOLERANCE);
	return Joint;

}
void place::scanToSparse(const cv::Mat &scan,
                         Eigen::SparseMatrix<double> &sparse) {
  std::vector<Eigen::Triplet<double>> tripletList;

  for (int i = 0; i < scan.rows; ++i) {
    const uchar *src = scan.ptr<uchar>(i);
    for (int j = 0; j < scan.cols; ++j) {
      if (src[j] == 255)
        continue;
      double confidence = 1.0 - (double)src[j] / 255.0;
      tripletList.push_back(Eigen::Triplet<double>(i, j, confidence));
    }
  }
  sparse = Eigen::SparseMatrix<double>(scan.rows, scan.cols);
  sparse.setFromTriplets(tripletList.begin(), tripletList.end());
  sparse.makeCompressed();
  sparse.prune(1.0);
}
Eigen::SparseMatrix<double> joint2conditional(Eigen::SparseMatrix<double> edgePot)// pa is the second dimension
{	// second dimension of edgePot is the parent
	Eigen::SparseMatrix<double> Conditional;
	Conditional.resize(edgePot.rows(), edgePot.cols());

	Eigen::SparseVector<double> Parent_Marginal;
	Parent_Marginal.resize(edgePot.cols());
	for (int id_col = 0; id_col < edgePot.cols(); id_col++)
	{
		Eigen::SparseVector<double> tmp_vec = edgePot.block(0, id_col, edgePot.rows(), 1);
		Parent_Marginal.coeffRef(id_col) = tmp_vec.sum();
		if (Parent_Marginal.coeff(id_col)>TOLERANCE)
			for (int id_row = 0; id_row < edgePot.rows(); id_row++)
			{
				Conditional.coeffRef(id_row, id_col) = edgePot.coeff(id_row, id_col) / Parent_Marginal.coeff(id_col);
			}
	}
	Conditional.makeCompressed();
	Conditional.prune(TOLERANCE);
	return Conditional;
}