/* test_laphi.c  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       */
 
#include <stdio.h>
#include "laphi.h"

int main(int argc, char *argv[])
{
  int N = 5;
  int j, k, n;
  double h, hf;
  double xg[7];
  double x, y, yp, ypp, yppp, ypppp;
  double xmin = 0.0; /* xg[0] */
  double xmax = 1.0; /* xg[n] */

  printf("test_laphi.c running on 0<x<1 for N=%d \n", N);
  printf(" L_order,point  order is highest power of x, point 0..n \n");
  printf("      L_n,j(x) = product i=0,n i!=j (x-x_i)/(x_j-x_i)  \n");
  printf("      for points x_0, x_1, ... , x_n \n");
  printf("      generate L_n,j(x) for n=1,5  j=0,n and derivatives to 4th \n");

  for(n=1; n<=N; n++) /* points go 0 to n */
  {
    h = (xmax-xmin)/n;
    for(j=0; j<=n; j++)
    {
      xg[j]=xmin+j*h;
      printf("xg[%d]=%g \n", 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 = phi(x, j, n, xg);

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

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

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

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

        printf("L_%d,%d(%7.4f)=%7.4f, yp=%7.3f, ypp=%7.2f, yppp=%7.1f, ypppp=%8.1f\n",
                n, j, x, y, yp, ypp, yppp, ypppp);
      } /* end loop on k,x */
      printf("\n");
    } /* end loop on j */
    printf("\n");
  } /* end loop on n */


  printf("end test_laphi.c \n");
  return 0;
} /* end test_laphi.c */