import java.applet.*;
import java.awt.*;
public class Example5_15 extends Applet
{
 public double espl3(double[] x,double[] y,double[] dy,double[] ddy,double[] t,double[] z,double[] dz,double[] ddz)
 {int i,j,n=x.length;
  double[] a=new double[n-1];
  double[] b=new double[n-1];
  double[] c=new double[n-1];
  double[] u=new double[n];
  double[] v=new double[n];
  double alpha=0,alpha1=0,beta=0,beta1=0,h,h1,h2;
  a[0]=0;b[0]=1;c[1]=0;
  alpha1=(x[n-1]-x[n-2])/(x[n-1]-x[n-2]+x[1]-x[0]);
  beta1=3*((1-alpha1)*(y[n-1]-y[n-2])/(x[n-1]-x[n-2])+alpha1*(y[1]-y[0])/(x[1]-x[0]));
  for(i=1;i<n-1;i++)
  {h1=x[i]-x[i-1];h2=x[i+1]-x[i];alpha=h1/(h1+h2);;
   beta=3*((1-alpha)*(y[i]-y[i-1])/h1+alpha*(y[i+1]-y[i])/h2);
   h=2+(1-alpha1)*a[i-1];
   a[i]=-alpha1/h;b[i]=-(1-alpha1)*b[i-1]/h;c[i]=(beta1-(1-alpha1)*c[i-1])/h;
   alpha1=alpha;beta1=beta;}
   u[n-1]=1;v[n-1]=0;
  for(i=n-2;i>0;i--){u[i]=a[i]*u[i+1]+b[i];v[i]=a[i]*v[i+1]+c[i];}
  dy[n-2]=(beta-alpha*v[1]-(1-alpha)*v[n-2])/(2+alpha*u[1]+(1-alpha)*u[n-2]);
  for(i=0;i<n-2;i++)dy[i]=u[i+1]*dy[n-2]+v[i+1];
  dy[n-1]=dy[0];
  for(i=0;i<n-1;i++)ddy[i]=(6*(y[i+1]-y[i])/(x[i+1]-x[i])-2*(2*dy[i]+dy[i+1]))/(x[i+1]-x[i]);
  ddy[n-1]=ddy[0];

  for(j=0;j<t.length;j++)
  {for(i=0;i<n-1;i++)if(t[j]<x[i+1])break;
   h=x[i+1]-x[i];h1=x[i+1]-t[j];h2=t[j]-x[i];
   z[j]=0;z[j]+=(3-2*h1/h)*h1*h1*y[i]/h/h;z[j]+=(3-2*h2/h)*h2*h2*y[i+1]/h/h;
   z[j]+=(1-h1/h)*h1*h1*dy[i]/h;z[j]-=(1-h2/h)*h2*h2*dy[i+1]/h;
   dz[j]=0;dz[j]+=6*(h1/h-1)*h1*y[i]/h/h;dz[j]-=6*(h2/h-1)*h2*y[i+1]/h/h;
   dz[j]+=(3*h1/h-2)*h1/h*dy[i];dz[j]+=(3*h2/h-2)*h2/h*dy[i+1];
   ddz[j]=0;ddz[j]+=6*(1-2*h1/h)*y[i]/h/h;ddz[j]+=6*(1-2*h2/h)*y[i+1]/h/h;
   ddz[j]+=(2-6*h1/h)*dy[i]/h;ddz[j]-=(2-6*h2/h)*dy[i+1]/h;
  }
  alpha=0;beta=0;
  for(i=0;i<n-1;i++)
  {h=x[i+1]-x[i];alpha+=h*(y[i]+y[i+1]);beta=h*h*h*(ddy[i]+ddy[i+1]);}
return (alpha/2-beta/24);
}

 public void paint(Graphics g)
 {double[] x=new double[37];
  double[] y=new double[37];
  double[] dy=new double[37];
  double[] ddy=new double[37];
  double[] t=new double[9];
  double[] z=new double[9];
  double[] dz=new double[9];
  double[] ddz=new double[9];
  double f=0;
  int i;
  for(i=0;i<37;i++){x[i]=i*Math.PI/18.0;y[i]=Math.sin(x[i]);}
  for(i=0;i<9;i++)t[i]=(2*i+1)*Math.PI/36.0;
  f=espl3(x,y,dy,ddy,t,z,dz,ddz);
  g.drawString("x(單位：度)       y                              y'                              y''",10,10);
  for(i=0;i<37;i++)
  g.drawString(""+(10*i)+"  "+y[i]+"  "+dy[i]+"  "+ddy[i],10,20+10*i);
  g.drawString("近似積分值為"+f,10,390);
  g.drawString("t(單位：度)       f(t)                           f'(t)                           f''(t)",10,400);
  for(i=0;i<9;i++)
  g.drawString(""+(5+10*i)+"  "+z[i]+"  "+dz[i]+"  "+ddz[i],10,410+10*i);

 }
}