/*
  I4 utilities.
*/
int i4_log_10 ( int i );
int i4_max ( int i1, int i2 );
int i4_min ( int i1, int i2 );
int i4_power ( int i, int j );
/*
  Real double precision General.
*/
void r8ge_print ( int m, int n, double a[], char *title );
void r8ge_print_some ( int m, int n, double a[], int ilo, int jlo, int ihi, 
  int jhi, char *title );
/*
  Real double precision Nonsymmetric Coordinate Format.
*/
void r8ncf_print ( int m, int n, int nz_num, int rowcol[], double a[], 
  char *title );
void r8ncf_print_some ( int m, int n, int nz_num, int rowcol[], 
  double a[], int ilo, int jlo, int ihi, int jhi, char *title );
/*
  Real double precision Sparse storage.
*/
void r8sp_cg ( int n, int nz_num, int row[], int col[], double a[], 
  double b[], double x[] );
int r8sp_check ( int m, int n, int nz_num, int row[], int col[] );
void r8sp_diagonal ( int m, int n, int nz_num, int row[], int col[], double a[] );
double *r8sp_dif2 ( int m, int n, int nz_num, int row[], int col[] );
int r8sp_ij_to_k ( int nz_num, int row[], int col[], int i, int j );
double *r8sp_indicator ( int m, int n, int nz_num, int row[], int col[] );
void r8sp_jac_sl ( int n, int nz_num, int row[], int col[], 
  double a[], double b[], double x[], int it_max );
double *r8sp_mtv ( int m, int n, int nz_num, int row[], int col[], 
  double a[], double x[] );
double *r8sp_mv ( int m, int n, int nz_num, int row[], int col[], 
  double a[], double x[] );
void r8sp_print ( int m, int n, int nz_num, int row[], int col[], 
  double a[], char *title );
void r8sp_print_some ( int m, int n, int nz_num, int row[], int col[], 
  double a[], int ilo, int jlo, int ihi, int jhi, char *title );
double *r8sp_random ( int m, int n, int nz_num, int row[], int col[], 
  int *seed );
void r8sp_read ( char *input_file, int m, int n, int nz_num, int row[], 
  int col[], double a[] );
void r8sp_read_size ( char *input_file, int *m, int *n, int *nz_num );
double *r8sp_res ( int m, int n, int nz_num, int row[], int col[], double a[], 
  double x[], double b[] );
double *r8sp_to_r8ge ( int m, int n, int nz_num, int row[], int col[], 
  double a[] );
void r8sp_to_r8ncf ( int m, int n, int nz_num, int row[], int col[], 
  double a[], int rowcol[] );
void r8sp_write ( int m, int n, int nz_num, int row[], int col[], double a[], 
  char *output_file );
double *r8sp_zeros ( int m, int n, int nz_num, int row[], int col[] );
/*
  R8VEC Utilities.
*/
double r8vec_dot_product ( int n, double a1[], double a2[] );
double *r8vec_indicator1_new ( int n );
double r8vec_norm ( int n, double a[] );
double r8vec_norm_affine ( int n, double v0[], double v1[] );
void r8vec_print ( int n, double a[], char *title );
double *r8vec_uniform_01_new ( int n, int *seed );
double *r8vec_zeros_new ( int n );
/*
  Utility to print the time.
*/
void timestamp ( );