fletchbv3.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

#include<iostream.h>
#include<math.h>
#define N 10



//cF41                              FLETCBV3  
//*
//*                Initial Point: [1/(n+1),2/(n+1).,...,n/(n+1)].
//*
      void CALF(int n,double x[],double &f)
	  { 
		  double kappa, objscale,p,h, c1,c2;
		  kappa = 1.0;
		  objscale = 100000000.0;
		  h = 1.0/(float(n)+1.0);
		  p = 1.0/objscale;                                 
		  
		  c1 = p*(h*h+2.0)/(h*h);
		  c2 = kappa*p/(h*h);                
                       
		  f=0.50*p*(x[0]*x[0]+x[n-1]*x[n-1]);
      
		  for(int i=0;i<n-1;i++)
			  f = f+0.50*p*pow((x[i]-x[i+1]),2);
      
		  for(i=0;i<n;i++)
			  f = f-c1*x[i]-c2*cos(x[i]);
      }

//*-- Gradient
      void CALG(int n,double x[],double g[])
	  { 
     
		  double kappa, objscale,p,h, c1,c2;
      
		  kappa = 1.0;
		  objscale = 100000000.0;
		  h = 1.0/(float(n)+1.0);
		  p = 1.0/objscale;                                
		  
		  c1 = p*(h*h+2.0)/(h*h);
		  c2 = kappa*p/(h*h);
		  
      g[0] = 2.0*p*x[0] - p*x[1] - c1 + c2*sin(x[0]);
      
     for(int i=1;i<n-1;i++)
        g[i] = -p*(x[i-1]-x[i]) + p*(x[i]-x[i+1]) - c1 + c2*sin(x[i]);

      
      g[n-1] = 2.0*p*x[n-1] - p*x[n-2] - c1 + c2*sin(x[n-1]);            
                                       
	  }
//*
//****************************************************************

//************************************************************          
                                                                       



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*fabs(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;
	double temp,temp1,temp2,temp3,temp_x[N],temp_g[N];
	int k=0;
	for(int i=0;i<N;i++)
		if(i%2==0)x[i]=1/(N+1);
			else x[i]=1/(N+1);
    CALG(N,x,G);
	for(i=0;i<N;i++)
		work[i]=-G[i];
	CALF(N,x,temp1);
	temp2=DOIT(G,work);
step2:
    for(i=0;i<N;i++)
		   temp_x[i]=x[i]+alpha*work[i];
	CALF(N,temp_x,temp);
	if(wolf1(x,work,G,alpha,c1,c2))
		goto step3;
	else{
		b=alpha;
		alpha=a+(alpha-a)/(2*(1+(temp1-temp)/((alpha-a)*temp2)));
		k++;
		goto step2;
	}
step3:
	for(i=0;i<N;i++)
		   temp_x[i]=x[i]+alpha*work[i];
	CALG(N,temp_x,temp_g);
	temp3=DOIT(temp_g,work);
	if(wolf2(x,work,G,alpha,c1,c2))
		goto step4;
	else{
		 a=alpha;
		 alpha=alpha+((alpha-a)*temp3)/(temp2-temp3);
		 temp1=temp;
		 temp2=temp3;
		 k++;
		 goto step2;
		
	}
step4:
	cout<<"迭带步数"<<k<<'\n';
	cout<<"alpha:"<<alpha<<'\n';

}