grosen.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>
#define N 2
/*---subroutine calf(n,x,f)---*/
void CALF(int n,double x[],double &f){
	int i;
	double c=100.0;
	f=0.0;
	for(i=0;i<n-1;i++)
        f=f+c*(x[i+1]-x[i]*x[i])*(x[i+1]-x[i]*x[i])+(1.0-x[i])*(1.0-x[i]);
}//calf
/*------Gradient subroutine calg(n,x,g)--------*/
void CALG(int n,double x[],double g[]){
	int i;
	double c=100.0;
	g[0]=-4.0*c*x[0]*(x[1]-x[0]*x[0])-2.0*(1.0-x[0]);
	for(i=1;i<n-1;i++)
        g[i]=2.0*c*(x[i]-x[i-1]*x[i-1])-4.0*c*x[i]*(x[i+1]-x[i]*x[i])-2.0*(1.0-x[i]);
	g[n-1]=2.0*c*(x[n-1]-x[n-2]*x[n-2]);
}//calg
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],g[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]=0;
			else x[i]=0;
   CALG(N,x,G);
   for(i=0;i<N;i++)
	   g[i]=G[i];
	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';

}