tridia.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

//
//cF45                            TRIDIA                               
//*
//*                     Initial point x0=[1,1,...,1]. 
//*
//*
#include<iostream.h>
#include<math.h>
#define N 5     
void  CALF(int n,double x[],double &f)
{
      double alpha, beta, gamma, delta;
                
      alpha=2.0;
      beta=1.0;
      gamma=1.0;
      delta=1.0;
        
      f=gamma*pow((delta*x[0]-1.0),2);
      
	  for(int i=1;i<n;i++)
	  {
        f = f + float(i+1)*pow((alpha*x[i]-beta*x[i-1]),2);
	  }
}
//*-- Gradient
void CALG(int n,double x[],double g[])
{
     double alpha, beta, gamma, delta;
                
      alpha=2.0;
      beta=1.0;
      gamma=1.0;
      delta=1.0;
      g[0] = 2.0*gamma*(delta*x[0]-1.0)*delta-4.0*(alpha*x[1]-beta*x[1])*beta;
     
    for(int i=1;i<n-1;i++)
	  {
        g[i] = 2.0*float(i+1)*(alpha*x[i]-beta*x[i-1])*alpha -2.0*float(i+2)*(alpha*x[i+1]-beta*x[i])*beta;
	  }       

      g[n-1] = 2.0*float(n)*(alpha*x[n-1]-beta*x[n-2])*alpha;

}

//*********************************************************************************
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;
			else x[i]=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';

}