/***********************************************************************
*     Test program: Numerical differentation according to  Romberg     *
* -------------------------------------------------------------------- *
* SAMPLE RUN:                                                          *
* (Find first derivative of function f(x)=1/x, for x=0.12).            *
*                                                                      *
* Numerical differentation according to Romberg                        *
*                                                                      *
* Test function   f(x) = 1/x                                           *
*                                                                      *
* Put in x-value at which you want to evaluate derivative: 0.12        *
* Put in desired accuracy: 1e-10                                       *
* Maximal number of columns in Romberg scheme: 4                       *
* Starting step size: 0.005                                            *
*                                                                      *
* Results:                                                             *
*                                                                      *
* er_app=  8.8917317953019e-11                                         *
* res   = -6.9444444444444e+01                                         *
* nend  =  3                                                           *
* hend  =  6.2500000000000e-04                                         *
*                                                                      *
* -------------------------------------------------------------------- *
* "Numerical Algorithms with C, By Gisela Engeln-Muellges              *
*  and Frank Uhlig, Springer-Verlag, 1996" [BIBLI 11].                 *
*                                                                      *
*                                C++ Release 1.0 By J-P Moreau, Paris. *
*                                         (www.jpmoreau.fr)            *
************************************************************************
Note: to link with files: basis_r.cpp, difrom.cpp, vmblock.cpp.
--------------------------------------------------------------- */ 
#include <basis.h>    // For REAL, etc.


//test function to derivate
REAL func (REAL x)
{
  return (1 / x);
}

//print results
void aus (int  n,   REAL prec,  REAL h,
          REAL x,   int  error, REAL schaetz,
          REAL res, int  nend,  REAL hend)
{
  if (error != 1) {
    printf ("\n Results:\n\n");
    printf (" er_app= %20.13"LZP"e\n"
            " res   = %20.13"LZP"e\n"
            " nend  = %2d\n"
            " hend  = %20.13"LZP"e\n\n",
             schaetz, res, nend, hend);
  }
}

//input one data item
#define input(Question,EinFormat,AusFormat,Variable)              \
   ( printf (Question" "),              /* Write out question */  \
     scanf  (EinFormat,    &Variable))  /* read value */          \


int difrom (REAL  x0,
            REAL  eps,
            int   n,
            REAL  h,
            REAL* res,
            REAL* er_app,
            int*  nend,
            REAL* hend);


void main()  {

  int  error, nend, n;
  REAL x, prec, h;
  REAL res, schaetz, hend;

  printf ("\n Numerical differentation according to Romberg\n\n");
  printf (" Test function   f(x) = 1/x\n\n");

  input (" Put in x-value at which you want to evaluate derivative:",
         "%"LZS"f", "%"LZP"f", x);

  input (" Put in desired accuracy:", "%"LZS"f", "%"LZP"f", prec);

  input(" Maximal number of columns in Romberg scheme:", "%d", "%d", n);

  input (" Starting step size:", "%"LZS"f", "%"LZP"f", h);

  error = difrom (x,prec,n,h,&res,&schaetz,&nend,&hend);

  aus (n,prec,h,x,error,schaetz,res,nend,hend);

  return;
}

//end of file tdifrom.cpp