c++求積分算法

//c++ 作業：用兩重菜單顯示 積分函數和積分方法

#include<iostream>
#include<cmath>
using namespace std;
class Function{
public:
virtual double operator()(double x) const=0; 
};
class Function1:public Function{
public:
double operator()(double x) const;
};
double Function1::operator()(double x) const{
return  log(1.0+x)/(1.0+x*x);
}
class Function2:public Function{
public:
       double operator()(double x) const;
 };
double Function2::operator()(double x) const{
        return  x*x;


}
class Function3:public Function{
public:
       double operator()(double x) const;
 };
double Function3::operator()(double x) const{
        return  sin(x);


}
class Function4:public Function{
public:
       double operator()(double x) const;
 };
double Function4::operator()(double x) const{
        return  cos(x);


}


class Integration
{
public:
    virtual double operator()(double a,double b,double eps)=0;
    virtual  ~Integration(){}
};


class Trapz1:public Integration
{
private:
    Function &f;
public:
    Trapz1(Function &fun):f(fun){}
    double operator()(double a,double b,double eps)
    {
        int n=200;
        double h=(b-a)/n;
        double sum=0,tmp;
        for(int i=1;i<n;i++)
        {
            tmp=2*f(a+i*h);
            sum+=tmp;
        }
        sum=(sum+f(a)+f(b))*h/2;
        return sum;
    }


};//梯形法求積分


class Trapz2:public Integration
{
private:
    Function &f;
public:
    Trapz2(Function &fun):f(fun){}
    double operator()(double a,double b,double eps)
    {
        bool done=false;
        int n=1;
        double h=(b-a);
        double tn=h*(f(a)+f(b))/2;
        double t2n;
        do
        {
            double sum=0;
            for(int k=0;k<n;k++)
            {
                double  x=a+(k+0.5)*h;
                sum+=f(x);
            }
            t2n=(tn+h*sum)/2.0;
            if(fabs(tn-t2n)<eps)
                done=true;
            else
            {
                n=n*2;
                h=h/2;
                tn=t2n;
            }
        }while(!done);
    return t2n;
    }
};//變步長求積分


class Simpson:public Integration
{
private:
    Function &f;
public:
    Simpson(Function &fun):f(fun){}
    virtual double operator()(double a,double b,double eps)
    {
        int n=400;
        double h=(b-a)/(2*n);
        double sum=0;
        for(int i=1;i<=(2*n-1);i=i+2)
        {
            double tmp=4*f(a+i*h);
            sum=sum+tmp;
        }
        for(int i=2;i<=(2*n-2);i=i+2)
        {
            double tmp=2*f(a+i*h);
            sum=sum+tmp;
        }
        sum=(sum+f(a)+f(b))*h/3;
        return sum;
    }
};//辛普生法求積分


class Rectangle:public Integration
{
private:
    Function &f;
public:
    Rectangle(Function &fun):f(fun){}
    virtual double operator()(double a,double b,double eps)
    {
        double sum=0;
        int n=400;
        double h=(b-a)/n;
        for(int i=1;i<n;i++)
        {
            double tmp=h*f(a+i*h+h/2);
            sum=sum+tmp;
        }
        return sum;
    }
};//矩形法求積分


void mune1();
void mune2();

Function *fp;

Integration *tp;

int main(){
	mune1();
	return 0;
}
void mune1(){

int choice;

cout<<"****************************"<<endl;

cout<<"*  1.y=log(1.0+x)/(1.0+x*x)*"<<endl;

cout<<"*  2.y=x^2                 *"<<endl;

cout<<"*  3.y=sin(x)              *"<<endl;

cout<<"*  4.y=cos(x)              *"<<endl;

cout<<"*  0.退出系統              *"<<endl;

cout<<"****************************"<<endl;

cout<<"****請選折要積分的函數******"<<endl;

cin>>choice;

switch(choice){

    case 1:

        fp=new Function1;

	mune2();

    break;

    case 2:

	fp=new Function2;

	mune2();

    break;

    case 3:

	fp=new Function3;

	mune2();

    break;

    case 4:

	fp=new Function3;

	mune2();

    break;

   case 0:

   break;

   default:

	cout<<"輸入錯誤請重新輸入！"<<endl;

}

}
void mune2(){

int flag=1,choice;

double x,y,exp;

cout<<"請輸入積分區間（x，y）和精度"<<endl;

         cin>>x>>y>>exp;

while(flag){

cout<<"**********************"<<endl;

cout<<"*  1.變步長求積分    *"<<endl;

cout<<"*  2.梯形法求積分    *"<<endl;

cout<<"*  3.辛普生法求積分  *"<<endl;

cout<<"*  4.矩形法求積分    *"<<endl;

cout<<"*  5.重新輸入積分區間*"<<endl;

cout<<"*  0.返回上級菜單    *"<<endl;

cout<<"**********************"<<endl;

cout<<"****請選折求積分方法**"<<endl;

cin>>choice;

switch(choice){

case 1:

	tp=new Trapz2(*fp);

	flag=1;

break;

case 2:

	tp=new Trapz1(*fp);

	flag=1;

break;

	case 3:

	tp=new Simpson(*fp);

	flag=1;

break;

case 4:

	tp=new Rectangle(*fp);

	flag=1;

break;

case 5:

       cout<<"請輸入積分區間（x，y）和精度"<<endl;

       cin>>x>>y>>exp;

	flag=2;

break;

case 0:

	flag=0;

break;

default:

	cout<<"輸入錯誤請重新輸入"<<endl;

	flag=2;

}

if(flag==1){

		cout<<"積分結果："<<(*tp)(x,y,exp)<<endl;

  	}

}
	mune1();
}