math_util.h

multipleshooting to find the roots of the non-linear functions

/*

   This file contains the prototypes for mshoot
   
*/
#define MACH_EPS 1.0e-19
#define FD_TOL 1.0e-8
#define max_num(x,y) ((x)>(y)?(x):(y))
#define sgn_num(x) (((x)<0.0)?-1.0:1.0)
#define dmax(x,y) (((x)>(y))?(x):(y))
#define dmin(x,y) (((x)>(y))?(y):(x))
      long double *a1d_allo_dbl( int );
      long double **a2d_allo_dbl( int, int );
      long double ***a3d_allo_dbl( int, int, int );
      void a1d_free_dbl( long double * );
      void a2d_free_dbl( long double **, int );
      void a3d_free_dbl( long double ***, int, int );
      
      int *a1d_allo_int( int );
      void a1d_free_int( int * );
      
      int  factor( long double **, int, int * );
      long double enorm( long double *, int );
      long double sec( long double );
      void solve( long double **, int *, long double *, int, long double * );
     
      void mat_add( long double **, long double **, long double **, int, int );
      void mat_copy( long double **, long double **, int, int );
      void mat_null( long double **, int, int );
      void mat_mul( long double **, long double **, long double **, int, int, int );
      void mat_muls( long double **, long double **, long double, int, int );
      void mat_mulv( long double *, long double **, long double *, int, int );
      long double mat_norm_a( long double **, int );
      long double mat_norm_b( long double **, int );
      long double mat_norm_c( long double **, int );     
      int  mat_solve( long double **, long double **, long double **, int, int );
      void mat_sub( long double **, long double **, long double **, int, int );
      void mat_tran( long double **, long double **, int, int );
      void mat_tran_bc( long double **,long double **,long double **,int, int, int );
  
      void vec_column( long double *, long double **, int, int );      
      void vec_copy( long double *, long double *, int );
      void vec_mul_bct( long double **, long double *, long double *, int );
      long double vec_mul_btc( long double *, long double *, int );
      void vec_mul_s( long double *, long double *, long double, int );
      void vec_null( long double *, int );
      void vec_sub(long double *, long double *, long double *, int);

      int qr_fac( long double **, int, int );
      void qr_qtc( long double **, long double **, int, int, int);

      void print_mat( long double **, int, int );
      void print_vec_dbl( long double *, int ); 
      void print_vec_int( int *, int );
      void file_read_vec_dbl( FILE *, long double *, int );