extrigon.cpp

共轭梯度的几种方法对标准函数的测试结果比较 附比较结果

//cF2                          Extended Trigonometric Function
//*
//*                          Initial Point: [1/n,-----1/n].
#include<iostream.h>
#include<math.h>
#define N 2
void CALF(int n,double x[N],double &f){

      double s, temp[11000]; 
      s=float(n);
      for(int i=0;i<n;i++)
        s=s-cos(x[i]);  
      for(i=0;i<n;i++)
        temp[i]=s+float(i+1)*(1.0-cos(x[i]))-sin(x[i]);
      f=0.0;
      for(i=0;i<n;i++)
        f=f+temp[i]*temp[i];
}



//* Gradient
void CALG(int n,double x[N],double g[N]){
      double s, temp[11000];
      s=float(n);
      for(int i=0;i<n;i++)
        s=s-cos(x[i]); 
      for(i=0;i<n;i++)
        temp[i]=s+float(i+1)*(1.0-cos(x[i]))-sin(x[i]);
      s=0.0;
      for(i=0;i<n;i++)
        s=s+temp[i];
      
      for(i=0;i<n;i++)
        g[i]=2.0*s*sin(x[i])+2.0*temp[i]*(float(i+1)*sin(x[i])-cos(x[i]));  
}
 
    
//**************************************************************

double DOIT(double m1[N],double m2[N]){
	double sum=0;
	for(int i=0;i<N;i++)
		sum+=m1[i]*m2[i];
	return sum;
}//DOIT
int wolf1(double x[],double work[],double g[],double alpha,double c1,double c2){
	double f1,f2;
	double temp[N];
	CALF(N,x,f1);
	for(int i=0;i<N;i++)
		temp[i]=x[i]+alpha*work[i];
	CALF(N,temp,f2);
	double temp1=DOIT(g,work);
	double temp2=-c1*alpha*temp1;
	if((f1-f2)>=temp2)return 1;
	else return 0;
}//wolf1
int wolf2(double x[],double work[],double g[],double alpha,double c1,double c2){
	double ng[N];
	double temp[N];
	for(int i=0;i<N;i++)
		temp[i]=x[i]+alpha*work[i];
	CALG(N,temp,ng);
	double temp1=DOIT(ng,work);
	double temp2=c2*DOIT(g,work);
	if(temp1>=temp2)return 1;
	else return 0;
}//wolf2
void main()
{	
	double x[N],G[N],work[N];
	double c1=0.1,c2=0.5;
	double alpha=1;
	double a=0,b=1000;
	int k=0;
	for(int i=0;i<N;i++)
		if(i%2==0)x[i]=1/N;
			else x[i]=1/N;
   CALG(N,x,G);
	for(i=0;i<N;i++)
		work[i]=-G[i];
	wolf1(x,work,G,alpha,c1,c2);
step2:
	if(wolf1(x,work,G,alpha,c1,c2)&&wolf2(x,work,G,alpha,c1,c2)){
	for(i=0;i<N;i++)
		   x[i]=x[i]+alpha*work[i];
	goto step5;}
	if(wolf1(x,work,G,alpha,c1,c2)==0){
		k++;
		goto step3;}
	if(wolf2(x,work,G,alpha,c1,c2)==0){
		k++;
		goto step4;}
step3:
	b=alpha;
	alpha=(a+alpha)/2;
	goto step2;
step4:
	a=alpha; 
	alpha=(2*alpha)>(alpha+b)/2?(alpha+b)/2:(2*alpha);
	goto step2;
step5:
	cout<<"迭带步数"<<k<<'\n';
	cout<<"alpha:"<<alpha<<'\n';

}