void find_level(int *inf, int k, int m, int ell);
double interp(double** u, int ell, int n0, int interp_points, int k, int m);
void spr_data_to_sparse(double **u, int ell, int n0, int interp_points, double eps);
void spr_sparse_to_data(double **u, int ell, int n0, int interp_points);
double spr_derivXE(double** u, int ell, int n0, int interp_points, double dx, int k, int m);
double spr_derivYE(double** u, int ell, int n0, int interp_points, double dx, int k, int m);
void spr_refine(double** u, int ell, int n0, int interp_points);
double interpEx(double** u, int ell, int n0, int interp_points, int k, int m);
void spr_data_to_sparseEx(double **u, int ell, int n0, int interp_points, double eps);
void spr_sparse_to_dataEx(double **u, int ell, int n0, int interp_points);
void derivYEx(double** u,int ell, int n0, int interp_points, double dx, double **du,  double** v);
void spr_refineEx(double** u, int ell, int n0, int interp_points);
void spr_refineEy(double** u, int ell, int n0, int interp_points);
double spr_derivYEx(double** u, int ell, int n0, int interp_points, double dx, int k, int m);
double interpEy(double** u, int ell, int n0, int interp_points, int k, int m);
void spr_data_to_sparseEy(double **u, int ell, int n0, int interp_points, double eps);
void spr_sparse_to_dataEy(double **u, int ell, int n0, int interp_points);
void derivXEy(double** u, int ell, int n0, int interp_points, double dx, double **du,  double** v);
double spr_derivXEy(double** u, int ell, int n0, int interp_points, double dx, int k, int m);
double interpEy(double** u, int ell, int n0, int interp_points, int k, int m);
double interpH(double** u, int ell, int n0, int interp_points, int k, int m);
void spr_data_to_sparseH(double** u, int ell, int n0, int interp_points, double eps);
void spr_sparse_to_dataH(double **u, int ell, int n0, int interp_points);
void derivXH(double** u, int ell, int n0, int interp_points, double dx, double **du,  double** v);
void derivYH(double** u, int ell, int n0, int interp_points, double dx, double **du,  double** v);
void spr_refineH(double** u, int ell, int n0, int interp_points);
int find_level_max(double** u, int ell, int n0, int ell_atual);