//
//  I4 Utilities.
//
int i4_log_10 ( int i );
int i4_max ( int i1, int i2 );
int i4_min ( int i1, int i2 );
//
//  R8 Utilities.
//
double r8_uniform_ab ( double rlo, double rhi, int &seed );
//
//  Real double precision Tridiagonal Scalar.
//
void r83s_cg ( int n, double a[], double b[], double x[] );
double *r83s_dif2 ( int m, int n );
void r83s_gs_sl ( int n, double a[], double b[], double x[], int it_max );
double *r83s_indicator ( int m, int n );
void r83s_jac_sl ( int n, double a[], double b[], double x[], int it_max );
double *r83s_mtv ( int m, int n, double a[], double x[] );
double *r83s_mv ( int m, int n, double a[], double x[] );
void r83s_print ( int m, int n, double a[], string title );
void r83s_print_some ( int m, int n, double a[], int ilo, int jlo, int ihi, 
  int jhi, string title );
double *r83s_random ( int m, int n, int &seed );
double *r83s_res ( int m, int n, double a[], double x[], double b[] );
double *r83s_to_r8ge ( int m, int n, double a[] );
double *r83s_zeros ( int m, int n );
//
//  Real double precision General.
//
double *r8ge_mtv ( int m, int n, double a[], double x[] );
double *r8ge_mv ( int m, int n, double a[], double x[] );
void r8ge_print ( int m, int n, double a[], string title );
void r8ge_print_some ( int m, int n, double a[], int ilo, int jlo, int ihi, 
  int jhi, string title );
//
//  R8VEC utilities.
//
double r8vec_dot_product ( int n, double x[], double y[] );
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[], string title );
double *r8vec_uniform_01_new ( int n, int &seed );

void r8vec2_print ( int n, double a1[], double a2[], string title );
//
//  Utility to print the time.
//
void timestamp ( );