/********************************************************************
*   Find a real root of a real function F(x) by the Zeroin method   *
* ----------------------------------------------------------------- *
* SAMPLE RUN:                                                       *
* (Example 1: Find a root of function 5x - exp(x) between 0 and 1)  *
*                                                                   *
* The output file tzeroin.lst contains:                             *
*                                                                   *
* ----------------------------------------------------------------- *
* Zeroin method for real valued, nonlinear functions                *
*------------------------------------------------------------------ *
* Example n° 1                                                      *
*                                                                   *
* f = 5 * x - exp (x)                                               *
* Starting value x0 =  0.000000                                     *
* Return code       =  0                                            *
* Root              =   0.2591711018190740                          *
* Function value    =  6.661338e-016                                *
* Function calls    =  8                                            *
*                                                                   *
* Absolute error    = 0.000000                                      *
* Relative error    = 0.000000                                      *
*                                                                   *
* ----------------------------------------------------------------- * 
* Ref.: "Numerical Algorithms with C By G. Engeln-Mueller and       *
*        F. Uhlig, Springer-Verlag, 1996" [BIBLI 11].               *
*                                                                   *
*                                C++ version by J-P Moreau, Paris.  *
*                                       (www.jpmoreau.fr)           *
********************************************************************/
#include "basis.h"           // uses file fzeroin.cpp
#include "tfunc1.h"          // ---------------------
          

int zeroin (REALFCT, REAL *, REAL *, int, char *, REAL, REAL *, REAL *, int * );  


int main (void)
{
  int i, rc, nmax, niter;
  REAL abserr=100*MACH_EPS,relerr=1000*MACH_EPS,x1,x2, f;
  REAL (*fct) (REAL);
  char *text;
  FILE *fp;
  
  fp=fopen("tzeroin.lst","w"); // output file
  WriteHead(fp," Zeroin method for real valued, nonlinear functions"); 

  nmax = 100;

  for (i = 1; i <= 6; i++)
  {
    switch (i)
    {
      case 1: x1 = ZERO;
		      x2 = ONE;
              fct  = f1;
              text = "f = 5 * x - exp (x)";
              break;
      case 2: x1 = 0.5;
		      x2 = 1.5;
              fct  = f2;
              text = "f = (((((x-6)*x+15)*x-20)*x+15)*x-6)*x+1";
              break;
      case 3: x1 = 3.0;
		      x2 = 3.5;
              fct  = f3;
              text = "f = sin (x)";
              break;
      case 4: x1 = -2.0;
		      x2 = -1.5;
              fct  = f4;
              text = "f = 1 + sin (x)";
              break;
      case 5: x1 = TWO;
		      x2 = 3.0; 
              fct  = f5;
              text = "f = exp(x) -(1.0 + x + x*x*0.5)";
              break;
      case 6: x1 = TWO;
		      x2 = 3.0;
              fct  = f6;
              text = "f = (x-1.0)*(x-1.0)*( sin(PI*x)  - "
                     "log(fabs(2.0*x/(x+1.0)))";
              break;
      default: return (1);
    }

    fprintf (fp," Example n° %d\n\n",i);
    fprintf (fp," %s\n", text);
    fprintf (fp," Starting value x0 = ");
    fprintf (fp,FORMAT_LF, x1);
    fprintf (fp,"\n");

    rc = zeroin (fct, &abserr, &relerr, nmax, "tzeroin.log", x1, &x2, &f, &niter);

    fprintf (fp," Return code       = % d\n", rc);
    fprintf (fp," Root              = "); fprintf (fp,FORMAT_2016LF, x2);
    fprintf (fp,"\n Function value    = "); fprintf (fp,FORMAT_LE, f);
    fprintf (fp,"\n Function calls    = % d\n", niter);
	fprintf (fp,"\n Absolute error    = %f",abserr); 
    fprintf (fp,"\n Relative error    = %f\n\n",relerr); 
    WriteEnd(fp);
  } 
  
  fclose(fp);

  printf("\nResults in tzeroin.lst.\n\n");
  return (0);
}

//end of file tzeroin.cpp