void recenter(double, vector<vector<double> >, vector<vector<double> >&);
void tred2(vector<vector<double> >&, vector<double>&, vector<double>&);
void qtli(vector<double>&, vector<double>&, vector<vector<double> >&);
void recenter(double, vector<vector<double> >, vector<vector<double> >&);
void tred2(vector<vector<double> >&, vector<double>&, vector<double>&);
void qtli(vector<double>&, vector<double>&, vector<vector<double> >&);