/***************************************************
*    Root of a non-linear Equation By Lagrange     *
* ------------------------------------------------ *
* REF.: "Méthode de calcul numérique - Programmes  *
*        en Basic By Claude Nowakowski, PS1 1981". *
*                                                  *
* ------------------------------------------------ *
* SAMPLE RUN:                                      *
*                                                  *
*  Find a root of equation: X - E SIN X            *
*                                                  *
*    Input Starting, Ending X: 1 10                *
*    Input max. error: 1e-5                        *
*                                                  *
*    Root = 2.199123                               *
*    Iterations: 7                                 *
*    Y = -5.409158e-007                            *
*                                                  *
*                                                  *
*                C++ Version By J-P Moreau, Paris. *
*                       (www.jpmoreau.fr)          *
***************************************************/
#include <stdio.h>
#include <math.h>

// Labels: e100, e200

#define  MAXITER  50

double   E,XB,X1,X2,YB,Y1,Y2;
int      K;
char     rep[2];

// User-defined non-linear function
double FUNC (double X) {
  return (X - 2.718281828 * sin(X));
}


void main() {

  printf("\n Input Starting, Ending X: "); scanf("%lf %lf", &X1, &X2);
  printf(" Input max.error: "); scanf("%lf", &E);
  printf("\n");

  Y1 = FUNC(X1);
  Y2 = FUNC(X2);

  if (Y1 * Y2 > 0) {
    printf(" Bad choice for X1, X2!\n");
    goto e200;
  }

  if (fabs(Y1 * Y2) < 1e-10) {
    printf(" X1 or X2 is a root!\n");
    goto e200;
  }

  // main iteration loop
  for (K=1; K<=MAXITER; K++) {
    XB = X2 - (X2 - X1) * Y2 / (Y2 - Y1);
    if (fabs(X1 - XB) < E) goto e100;  // normal exit
    YB = FUNC(XB);
    if (Y1 * YB < 0) {
      X2 = XB; Y2 = YB;
    }
    else {
      X1 = XB; Y1 = YB;
    }
  }

  printf(" No root found!\n");
  goto e200;

e100: printf(" Root = %f\n", XB);
  printf(" Iterations: %d\n", K);
  printf(" Y = %e\n\n", FUNC(XB));

e200: scanf("%s", rep);
}

// End of file Lagrange1.cpp