cragglvy.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

//C
//C      EXTENDED CRAGG AND LEVY FUNCTION  STANDARD INITIAL POINT (1, 2,2,2,1,2,2,2,---,1,2,2,2)
//C
#include<iostream.h>
#define N 2
#include<math.h>
void CALF(int n,double X[N],double &F){
	F=0.0;
	int M=n/4;
	double A,B,C,D;
	for(int I=0;I<M;I++){
	A=(exp(X[4*I-3])-X[4*I-2])*(exp(X[4*I-3])-X[4*I-2]);
	B=10.0*(X[4*I-2]-X[4*I-1])*(X[4*I-2]-X[4*I-1])*(X[4*I-2]-X[4*I-1]);
	C=tan(X[4*I-1]-X[4*I])*(X[4*I-1]-X[4*I]);
	D=(X[4*I]-1.0);
	F=F+0.50*(A*A+B*B+C*C+D*D);
	}
} 
//C
//C
//C
void CALG(int n,double X[N],double G[N]){
	int M=n/4;
	double A,B,C,D;
	for(int I=0;I<M;I++){
      A=(exp(X[4*I-3])-X[4*I-2]);
	B=(X[4*I-2]-X[4*I-1]);
	C=tan(X[4*I-1]-X[4*I]);
	D=(X[4*I]-1.0);
	G[4*I-3]=2.0*A*A*A;
	G[4*I-2]=-2.0*A*A*A+300.0*B*B*B*B*B;
	G[4*I-1]=-300.0*B*B*B*B*B+2.0*C*C*C/((cos(X[4*I-1]-X[4*I]))*(cos(X[4*I-1]-X[4*I])));
	G[4*I]=-2.0*C*C*C/((cos(X[4*I-1]-X[4*I]))*(cos(X[4*I-1]-X[4*I])))+(X[4*I]-1.0);
	}
}


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%4==0)x[i]=1;
			else x[i]=2;
    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';

}