/* -*-ePiX-*- */
#include "epix.h"
using namespace ePiX;

double alpha(-1.25), beta(1.3);

double g(double x)
{
  return 0.05*pow(fabs(x-alpha), 1.5)*pow(fabs(x-beta),1.25);
}

double f(double x)
{
  return tanh(x) - 0.05 - g(x);
}

Deriv fp(f);

double df(double x)
{
  return fp.eval(x);
}

double iter(double x)
{
  return x - f(x)/df(x);
}

int main()
{
  picture(P(-2,-1), P(2,1), "2.5 x 1.25in");

  begin();
  bold();

  set_crop();
  line(P(xmin()), P(xmax()));

  line(P(alpha,f(alpha)), P(alpha));
  line(P(alpha,f(alpha)), P(iter(alpha)));

  line(P(beta, f(beta)),  P(beta));
  line(P(beta, f(beta)),  P(iter(beta)));

  plot(f, alpha, beta, 60);

  label(P(alpha), P(-2,-2), "$\\alpha$", bl);
  label(P(beta),  P(2,  2), "$\\beta$",  tr);

  label(P(0, ymin()), P(0,-18), "\\textsc{Fig.~23}", b);

  tikz_format();

  end();
}