/****************************************************
*  Program to demonstrate Secant method subroutine  *
* ------------------------------------------------- *
* Reference: BASIC Scientific Subroutines, Vol. II  *
* By F.R. Ruckdeschel, BYTE/McGRAWW-HILL, 1981 [1]. *
*                                                   *
*                C++ version by J-P Moreau, Paris.  *
*                      (www.jpmoreau.fr)            *
* ------------------------------------------------- *
* SAMPLE RUN:                                       *
*                                                   *
* ( Example: Find a real root of f(x)=(x+1)^5 )     *
*                                                   *
* Input the initial guesses:                        *
*                                                   *
*    X0 = -2                                        *
*    X1 = 0                                         *
*                                                   *
* Convergence factor: 1e-6                          *
* Maximum number of iterations: 50                  *
*                                                   *
*                                                   *
* The calculated zero is X = -1.000000              *
*                                                   *
* The associated Y value is Y = 0.000000            *
*                                                   *
* The number of steps was: 3                        *
*                                                   *
****************************************************/
#include <stdio.h>
#include <math.h>

double  e,x0,x1;
int     m,n;


/**************************************************
  Function subroutine                            */
  double Y(double x) {
    return (1+5*x+10*x*x+10*x*x*x+5*x*x*x*x+x*x*x*x*x);
  }
/**************************************************/


/**********************************************
*          Secant method subroutine           *
* ------------------------------------------- *
* This subroutine calculates the zeroes of a  *
* function Y(x) using the secant method.      *
* Two initial guesses are required, x0 and x1,*
* and a convergence criterion, e. Also requi- *
* red is the maximum number of iterations, m. *
* The root is returned in x, the number of    *
* iterations performed in n.                  *
**********************************************/
void Secant()  {
  double x,y0,y1;
  n=0;
  // Start iteration
e100: y0=Y(x0);
  y1=Y(x1);
  // Calculate new estimate
  // Guard against y1-y0 too small
  if (fabs(y1-y0)<0.001) y1 += 0.001;
  x=(x0*y1-x1*y0)/(y1-y0);
  n++;
  // Test for convergence
  if (n>=m) return;
  if (fabs(x1-x0)<e) return;
  // Update positions
  x0=x1; x1=x;
  goto e100;
}


void main()  {
  printf("\n Input the initial guess:\n\n");
  printf("    X0 = "); scanf("%lf",&x0);
  printf("    X1 = "); scanf("%lf",&x1);
  printf("\n Convergence factor: "); scanf("%lf",&e);
  printf("\n Maximum number of iterations: "); scanf("%d",&m);

  Secant();   // Call Secant routine

  printf("\n\n The calculated zero is X = %f\n\n",x0);
  printf(" The associated Y value is Y = %f\n\n",Y(x0));
  printf(" The number of steps was: %d\n\n",n);
}

// End of file Secant.cpp