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);
double spr_derivXH(double** u, int ell, int n0, int interp_points, double dx, int k, int m);
double spr_derivYH(double** u, int ell, int n0, int interp_points, double dx, int k, int m);
void spr_coneH(double** u, int ell, int n0, int interp_points);
void spr_coneHSimp(double** u, int ell, int n0, int interp_points);
int local_scalex(double** u,  int k, int m, int ell,  int n0);
int local_scaley(double** u,  int k, int m, int ell,  int n0);
int find_level_max(double** u, int ell, int n0, int ell_atual);
int mostra_cont();

/* UTILITY ROUTINES */

void fatal(char* s);

double** dvector(int nl, int nc);
  /* Allocates an array with {nl} rows and {nc} columns. */

void wait_for_user(void);
  /* Writes "Hit return to continue" and waits for user to do so. */

double get_double_from_user(char *prompt, double defval);
int get_int_from_user(char *prompt, int defval);
  /*  Writes a message "Enter {promt} [{defval}]:" to {stderr}; then
    waits for the user to type a number ({double} or {int},
    rspectively) + 'ENTER', and returns that number. Returns {defval}
    if the user just types 'ENTER'. */
void libera(int nl, int nc, double **A);