// test_laphi.java  family of Lagrange functions and derivatives  
//             L_n,j(x) = product i=0,n i!=j (x-x_i)/(x_j-x_i) 
//             for points x_0, x_1, ... , x_n                  
//  generate L_n,j(x) for n=1,5  j=0,n and derivatives to 4th  
//  should be same results as produced by lagrange_fem.c
 
// needs laphi.class

public class test_laphi 
{
  laphi L = new laphi();
  test_laphi()
  {
    System.out.println("test_laphi.java running");

    int N = 5;
    int j, k, n;
    double h, hf;
    double xg[] = new double[N+1]; // points go 1 to N
    double x, y, yp, ypp, yppp, ypppp;
    double xmin = 0.0; // xg[0] 
    double xmax = 1.0; // xg[n] 

    System.out.println("test_laphi.java running on 0<x<1 for N="+ N);
    System.out.println(" L_order,point  order is highest power of x, point 0..n ");
    System.out.println("      L_n,j(x) = product i=0,n i!=j (x-x_i)/(x_j-x_i)  ");
    System.out.println("      for points x_0, x_1, ... , x_n ");
    System.out.println("      generate L_n,j(x) for n=1,5  j=0,n and derivatives to 4th ");
    System.out.println(" check against lagrange_fem_c.out ");
    for(n=1; n<=N; n++) // points go 1 to N
    {
      h = (xmax-xmin)/n;
      for(j=0; j<=n; j++)
      {
        xg[j]=xmin+j*h;
        System.out.println("xg["+j+"]="+ xg[j]);
      }
      hf = h/4.0;
      for(j=0; j<=n; j++)
      {
        for(k=0; k<=4*n; k++)
        {
          x = xmin+k*hf;

          // evaluate function, n,j,x,xg,denom 
          y = L.phi(x, j, n, xg);

          // evaluate first derivative of function, n,j,x,xg,denom 
          yp = L.phip(x, j, n, xg);

          // evaluate second derivative of function, n,j,x,xg,denom 
          ypp = L.phipp(x, j, n, xg);

          // evaluate third derivative of function, n,j,x,xg,denom 
          yppp = L.phippp(x, j, n, xg);

          // evaluate fourth derivative of function, n,j,x,xg,denom 
          ypppp = L.phipppp(x, j, n, xg);

          System.out.println("L_"+n+","+j+"("+x+")y="+y+", yp="+yp);
          System.out.println("ypp="+ypp+", yppp="+yppp);
          System.out.println("ypppp="+ypppp);
        } // end loop on k,x 
        System.out.println("");
      } // end loop on j 
      System.out.println("");
    } // end loop on n 
    System.out.println("end test_laphi.java ");
  }

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

} // end test_laphi.java