/* 複素Newton法 */
/* complex_newton.c */
#include <stdio.h>
#include <complex.h>
#define NMAX 10 
#define EPS 1.0e-14 
double complex f(double complex z);  /* f(z) */
double complex df(double complex z);  /* f'(z) */

int main(void)
{
  int n;
  double absfz; 
  double complex z,u,fz,dfz;

  z = -1.0 + 1.0 * I; /* 初期値(-1+i) */
  n = 0;
  absfz = cabs(f(z));
  printf("%2s %20s %19s %10s\n","n","Re(z_n)  ","Im(z_n)  ","|f(z_n)|");
  printf("%2d %20.15f %19.15f %10.3e\n",n,creal(z),cimag(z),absfz); 
 
  while(absfz > EPS && n < NMAX)
    {
      fz = f(z);
      dfz = df(z);
      u = fz/dfz;
      z = z - u;
      n++;
      absfz=cabs(f(z));
      printf("%2d %20.15f %19.15f %10.3e\n",n,creal(z),cimag(z),absfz); 
    }
  
  return 0;
}

double complex f(double complex z)
{
  double complex w;

  w = (z * z - 2.0) * z - 5.0;

  return w;
}


double complex df(double complex z)
{
  double complex w;

  w = 3.0 * z * z - 2.0;

  return w;
}