// test2_Cnuderiv.java  needs Complex.java  Cnuderiv.java compiled  
//          order 1  independent points 2-6   Ux ... on first degree
//          order 2  independent points 3-6   Uxx ... on second degree
//          order 3  independent points 4-7   Uxxx ... on third degree
//          order 4  independent points 5-8   Uxxxx ... on fourth degree
class test2_Cnuderiv
{
  Complex Czero = new Complex(0.0,0.0);
  Complex Cone = new Complex(1.0,0.0);

  test2_Cnuderiv()
  {
    int debug = 0;
    int order, nx;
    Complex xmin = new Complex(-0.5, -0.5);
    Complex xmax = new Complex(0.5, 0.5);

    Complex xg[] = new Complex[10];
    Complex U[] = new Complex[10];
    Complex cx[] = new Complex[10];
    Complex cxx[] = new Complex[10];
    Complex cxxx[] = new Complex[10];
    Complex cxxxx[] = new Complex[10];
    Complex est, actual, hx;
    double err, maxerr=0.0;

    System.out.println("test2_Cnuderiv.java running, testing:");

    System.out.println("f(x):= sin(x)");
    System.out.println(" ");
    System.out.println("xg are grid coordinates where derivative computed");
    System.out.println("cx, cxx, cxxx, cxxxx are first, second, third, fourth derivative coefficients");
    System.out.println("derivative is computed at xg[i] ");
    System.out.println("  new Cnuderiv(order, nx, i, xg, cx);");
    System.out.println("  est = 0.0; derivative");
    System.out.println("  for(int j=0; j<nx; j++"); 
    System.out.println("    est += cx[j]*f(xg[j])");
    System.out.println(" ");

    order = 1;
    for(nx=2; nx<=6; nx++)
    {
      maxerr = 0.0;
      hx = (xmax.subtract(xmin)).divide(new Complex((double)(nx-1),0.0));
      for(int i=0; i<nx; i++)
      {
	xg[i] = xmin.add(new Complex((double)i,0.0).multiply(hx));
        U[i] = xg[i].sin();
        System.out.println("xg["+i+"]="+xg[i]+", U="+U[i]);
        hx = hx.add(new Complex(0.005,-0.004)); // non uniform
      }
      for(int point=0; point<nx; point++)
      {
        new Cnuderiv(order, nx, point, xg, cx);
        for(int j=0; j<nx; j++)
          System.out.println("cx["+j+"]="+cx[j]);
        est = Czero;
        for(int j=0; j<nx; j++)
	  est = est.add(cx[j].multiply(U[j]));
        actual = xg[point].cos();
        err = (actual.subtract(est)).abs();
        System.out.println("point="+point+", est="+est+", actual="+actual+", err="+err);
        System.out.println(" ");
        maxerr = Math.max(maxerr, err);
      } // point
      System.out.println("order="+order+", nx="+nx+", maxerr="+maxerr);
      System.out.println(" ");
      System.out.println(" ");
    } // end nx for order 1

    order = 2;
    for(nx=3; nx<=6; nx++)
    {
      maxerr = 0.0;
      hx = (xmax.subtract(xmin)).divide(new Complex((double)(nx-1),0.0));
      for(int i=0; i<nx; i++)
      {
	xg[i] = xmin.add(new Complex((double)i,0.0).multiply(hx));
        U[i] = xg[i].sin();
        if(nx==6) System.out.println("xg["+i+"]="+xg[i]+", U="+U[i]);
        hx = hx.add(new Complex(0.005,-0.004)); // non uniform
      }
      for(int point=0; point<nx; point++)
      {
        new Cnuderiv(order, nx, point, xg, cxx);
        for(int j=0; j<nx; j++)
          System.out.println("cxx["+j+"]="+cxx[j]);
        est = Czero;
        for(int j=0; j<nx; j++)
	  est = est.add(cxx[j].multiply(U[j]));
        actual = (xg[point].sin()).negate();
        err = (actual.subtract(est)).abs();
        if(nx==6) System.out.println("point="+point+", est="+est+", actual="+actual+", err="+err);
        if(nx==6) System.out.println(" ");
        maxerr = Math.max(maxerr, err);
      } // point
      System.out.println("order="+order+", nx="+nx+", maxerr="+maxerr);
      System.out.println(" ");
      System.out.println(" ");
    } // end nx for order 2

    order = 3;
    for(nx=4; nx<=8; nx++)
    {
      maxerr = 0.0;
      hx = (xmax.subtract(xmin)).divide(new Complex((double)(nx-1),0.0));
      for(int i=0; i<nx; i++)
      {
	xg[i] = xmin.add(new Complex((double)i,0.0).multiply(hx));
        U[i] = xg[i].sin();
        if(nx==8) System.out.println("xg["+i+"]="+xg[i]+", U="+U[i]);
        hx = hx.add(new Complex(0.005,-0.004)); // non uniform
      }
      for(int point=0; point<nx; point++)
      {
        new Cnuderiv(order, nx, point, xg, cxxx);
        for(int j=0; j<nx; j++)
          System.out.println("cxxx["+j+"]="+cxxx[j]);
        est = Czero;
        for(int j=0; j<nx; j++)
	  est = est.add(cxxx[j].multiply(U[j]));
        actual = (xg[point].cos()).negate();
        err = (actual.subtract(est)).abs();
        if(nx==8) System.out.println("point="+point+", est="+est+", actual="+actual+", err="+err);
        if(nx==8) System.out.println(" ");
        maxerr = Math.max(maxerr, err);
      } // point
      System.out.println("order="+order+", nx="+nx+", maxerr="+maxerr);
      System.out.println(" ");
      System.out.println(" ");
    } // end nx for order 3

    order = 4;
    for(nx=4; nx<=9; nx++)
    {
      maxerr = 0.0;
      hx = (xmax.subtract(xmin)).divide(new Complex((double)(nx-1),0.0));
      for(int i=0; i<nx; i++)
      {
	xg[i] = xmin.add(new Complex((double)i,0.0).multiply(hx));
        U[i] = xg[i].sin();
        if(nx==9) System.out.println("xg["+i+"]="+xg[i]+", U="+U[i]);
        hx = hx.add(new Complex(0.005,-0.004)); // non uniform
      }
      for(int point=0; point<nx; point++)
      {
        new Cnuderiv(order, nx, point, xg, cxxx);
        for(int j=0; j<nx; j++)
          System.out.println("cxxx["+j+"]="+cxxx[j]);
        est = Czero;
        for(int j=0; j<nx; j++)
	  est = est.add(cxxx[j].multiply(U[j]));
        actual = xg[point].sin();
        err = (actual.subtract(est)).abs();
        if(nx==9) System.out.println("point="+point+", est="+est+", actual="+actual+", err="+err);
        if(nx==9) System.out.println(" ");
        maxerr = Math.max(maxerr, err);
      } // point
      System.out.println("order="+order+", nx="+nx+", maxerr="+maxerr);
      System.out.println(" ");
      System.out.println(" ");
    } // end nx for order 4

  } // end test2_Cnuderiv

  public static void main (String[] args)
  {
    new test2_Cnuderiv();
  }
} // end  class test2_Cnuderiv