/****************************************************
* Program to demonstrate Newton's 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 (x+1)^5)            *
*                                                   *
* Input the initial guess:                          *
*                                                   *
*    X0 = 0                                         *
*                                                   *
* Convergence factor: 1e-6                          *
*                                                   *
* Maximum number of iterations: 30                  *
*                                                   *
*                                                   *
* The calculated zero is X = -0.998729              *
*                                                   *
* The associated Y value is Y = 0.000000            *
*                                                   *
* The number of steps was: 30                       *
*                                                   *
****************************************************/
#include <stdio.h>
#include <math.h>

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

/**************************************************
  Function subroutine                            */
  double Y(double x, double *y1) {
    //derivative
    *y1 = 5+20*x+30*x*x+20*x*x*x+5*x*x*x*x;
    return (1+5*x+10*x*x+10*x*x*x+5*x*x*x*x+x*x*x*x*x);
  }
/**************************************************/

/**********************************************
*         Newton's method subroutine          *
* ------------------------------------------- *
* This routine calculates the zeroes of a     *
* function Y(x) by Newton's method.           *
* The routine requires an initial guess, x0,  *
* and a convergence factor, e. Also required  *
* is alimit on the number of iterations, m.   *
**********************************************/
void  Newton()  {
  double y1;
  n=0;
  // Get y and y1
e100: yy=Y(x0,&y1);
  // Update estimate
  x0=x0-(yy/y1);
  n++;
  if (n>=m) return;
  if (fabs(yy/y1)>e) goto e100;
}


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

  Newton();   // Call Newton routine

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

// End of file Newton.cpp