// peval.java Horners method for evaluating a polynomial 
//            eval is function that computes Horners method

public class peval
{
  public peval()
  {
    double y;
    double c[] = new double[11];
    double r[] = new double[11];

    System.out.println("peval.java running");
    // test peval by generation roots of a polynomial, 
    // then generating the polynomial, then evaluating 
    for(int n=3; n<11; n++) // n is degree of polynomial 
    {
      System.out.println(" ");
      System.out.println("y = c[0] + c[1]*x + c[2]*x^2 +...+ c[n]*x^n, for n="
                         +n);
      System.out.println("roots are:");
      r[0] = 0.1;
      System.out.println("r[0]="+r[0]);
      r[1] = 2.5;
      System.out.println("r[1]="+r[1]);
      for(int i=2; i<n; i++)
      {
        r[i] = r[i-1]+r[i-2];
        System.out.println("r["+i+"]="+r[i]);
      }
      // generate polynomial coefficients 
      c[0] = r[0]*r[1];
      c[1] = -(r[0]+r[1]);
      c[2] = 1.0;
      for(int j=2; j<n; j++)
      {
        for(int i=j+1; i>0; i--) c[i] = c[i-1];
        c[0] = 0.0;
        for(int i=0; i<=j; i++) c[i] = c[i] - r[j]*c[i+1];
      }
      System.out.println("polynomial coefficients are:");
      for(int i=0; i<=n; i++) System.out.println("c["+i+"]="+c[i]);
      System.out.println("polynomial evaluated at each root:");
      for(int i=0; i<n; i++)
      {
        y = eval(n, r[i], c);
        System.out.println("r["+i+"]="+r[i]+", eval("+n+"+,r["+i+"],c)="+y);
      }
    }
  } // end peval 

  double eval(int n, double x, double c[])
  { // Horners method for evaluating a polynomial   
    // an nth order polynomial has n+1 coefficients 
    // stored in c[0] through c[n]                  
    // y = c[0] + c[1]*x + c[2]*x^2 +...+ c[n]*x^n  
    
    double y = c[n]*x;
    if(n<=0) return c[0];
    for(int i=n-1; i>0; i--) y = (c[i]+y)*x;
    return y+c[0];
  } // end eval 

  public static void main (String[] args)
  {
    new peval();
  }
}