void clip_matrix ( double **a, int m, int n, int M );
double matrix_norm_frobenius ( double **a, int m, int n );
int prune_pgm ( double **a, int m, int n, double rel_err );
int prune_ppm ( double **r, double **g, double **b, int m, int n, 
  double rel_err );
void reduce_pgm_image ( struct image *img, double rel_err );
void reduce_ppm_image ( struct image *img, double rel_err );
void show_usage ( char *progname );
double truncation_error ( double t, double **a, int m, int n );