// test_gauleg.java

public class test_gauleg
{
  public test_gauleg()
  {
    double area;
    double a = 1.0;
    double b = 2.0;
    int n = 8;
    int m;
    double x[] = new double[n+1];
    double w[] = new double[n+1];

    System.out.println("test gauleg.java integrate fm(p)=p^m from a=1 to b=2");
    for(m=2; m<=4; m++)
    {
      System.out.println("f2 on "+m+" points");
      new gaulegf(a, b, x, w, m);
      System.out.print("x="+x[1]+" "+x[2]);
      for(int j=3; j<=m; j++) System.out.print(" "+x[j]);
      System.out.println(" ");
      System.out.print("w="+w[1]+" "+w[2]);
      for(int j=3; j<=m; j++) System.out.print(" "+w[j]);
      System.out.println(" ");

      area = 0.0;
      for(int i=1; i<=m; i++)
      {
        area += w[i]*f2(x[i]);
      }
      System.out.println("f2 exact area=7/3 computed area = "+area);
      System.out.println("error= "+(area-7.0/3.0));
      System.out.println(" ");
    } // end m on f2
    for(m=2; m<=4; m++)
    {
      System.out.println("f3 on "+m+" points");
      new gaulegf(a, b, x, w, m);
      area = 0.0;
      for(int i=1; i<=m; i++)
      {
        area += w[i]*f3(x[i]);
      }
      System.out.println("f3 exact area=15/4 computed area = "+area);
      System.out.println("error= "+(area-15.0/4.0));
      System.out.println(" ");
    } // end m on f3

    for(m=2; m<=4; m++)
    {
      System.out.println("f4 on "+m+" points");
      new gaulegf(a, b, x, w, m);
      area = 0.0;
      for(int i=1; i<=m; i++)
      {
        area += w[i]*f4(x[i]);
      }
      System.out.println("f4 exact area=31/5 computed area = "+area);
      System.out.println("error= "+(area-31.0/5.0));
      System.out.println(" ");
    } // end m on f4

    for(m=2; m<=4; m++)
    {
      System.out.println("f5 on "+m+" points");
      new gaulegf(a, b, x, w, m);
      area = 0.0;
      for(int i=1; i<=m; i++)
      {
        area += w[i]*f5(x[i]);
      }
      System.out.println("f5 exact area=63/6 computed area = "+area);
      System.out.println("error= "+(area-63.0/6.0));
      System.out.println(" ");
    } // end m on f5

    for(m=2; m<=4; m++)
    {
      System.out.println("f6 on "+m+" points");
      new gaulegf(a, b, x, w, m);
      area = 0.0;
      for(int i=1; i<=m; i++)
      {
        area += w[i]*f6(x[i]);
      }
      System.out.println("f6 exact area=127/7 computed area = "+area);
      System.out.println("error= "+(area-127.0/7.0));
      System.out.println(" ");
    } // end m on f6

  }

  double f2(double p) // function to integrate
  {
    return p*p;
  }

  double f3(double p) // function to integrate
  {
    return p*p*p;
  }

  double f4(double p) // function to integrate
  {
    return p*p*p*p;
  }

  double f5(double p) // function to integrate
  {
    return p*p*p*p*p;
  }

  double f6(double p) // function to integrate
  {
    return p*p*p*p*p*p;
  }

  public static void main (String[] args)
  {
    new test_gauleg();
  }
} // end test_gauleg.java