共轭梯度法--MATLAB程序.docx

1、%conjugate gradient methods%method:FR,PRP,HS,DY,CD,WYL,LS%精确线搜索 , 梯度终止准则function m,k,d,a,X,g1,fv = conjgradme( G,b,c,X,e,method)ifnargin=ek(i-1)=(m/m1)2;d(:,i)=-g1(:,i)+k(i-1)*d(:,i-1);a(i)=-(d(:,i)*g1(:,i)/(d(:,i)*G*d(:,i);%a1(i)=-(X(:,i)*G*d(:,i)+b*d(:,i)/(d(:,i)*G*d(:, i);a(i)=g1(:,i)*g1(:,i)/(d(

2、:,i)*G*d(:,i);X(:,i+1)=X(:,i)+a(i)*d(:,i);g1=g1 subs(subs(g,x1,X(1,i+1),x2,X(2,i+1);m1=m;m=norm(g1(:,i+1);i=i+1;endcasePRPwhilem=ek(i-1)=g1(:,i)*(g1(:,i)-g1(:,i-1)/(norm(g1(:,i-1)2;d(:,i)=-g1(:,i)+k(i-1)*d(:,i-1);a(i)=-(d(:,i)*g1(:,i)/(d(:,i)*G*d(:,i);X(:,i+1)=X(:,i)+a(i)*d(:,i);g1=g1 subs(subs(g,x1

3、,X(1,i+1),x2,X(2,i+1);m=norm(g1(:,i+1);i=i+1;endcaseHSwhilem=ek(i-1)=g1(:,i)*(g1(:,i)-g1(:,i-1)/(d(:,i-1)*(g1(:,i)-g1(:,i-1);d(:,i)=-g1(:,i)+k(i-1)*d(:,i-1);a(i)=-(d(:,i)*g1(:,i)/(d(:,i)*G*d(:,i);X(:,i+1)=X(:,i)+a(i)*d(:,i);g1=g1 subs(subs(g,x1,X(1,i+1),x2,X(2,i+1);m=norm(g1(:,i+1);i=i+1;endcaseDYwh

4、ilem=ek(i-1)=g1(:,i)*g1(:,i)/(d(:,i-1)*(g1(:,i)-g1(:,i-1);d(:,i)=-g1(:,i)+k(i-1)*d(:,i-1);a(i)=-(d(:,i)*g1(:,i)/(d(:,i)*G*d(:,i);X(:,i+1)=X(:,i)+a(i)*d(:,i);g1=g1 subs(subs(g,x1,X(1,i+1),x2,X(2,i+1);m=norm(g1(:,i+1);i=i+1;endcaseLSwhilem=ek(i-1)=g1(:,i)*(g1(:,i)-g1(:,i-1)/(d(:,i-1)*(-g1(:,i-1);d(:,i

5、)=-g1(:,i)+k(i-1)*d(:,i-1);a(i)=-(d(:,i)*g1(:,i)/(d(:,i)*G*d(:,i); %a(i)=-(X(:,i)*G*d( :,i)+b*d(:,i)/(d(:,i)*G*d(:,i);X(:,i+1)=X(:,i)+a(i)*d(:,i);g1=g1 subs(subs(g,x1,X(1,i+1),x2,X(2,i+1);m=norm(g1(:,i+1);i=i+1;endcaseCDwhilem=ek(i-1)=g1(:,i)*g1(:,i)/(d(:,i-1)*(-g1(:,i-1);d(:,i)=-g1(:,i)+k(i-1)*d(:,

6、i-1);a(i)=-(d(:,i)*g1(:,i)/(d(:,i)*G*d(:,i);X(:,i+1)=X(:,i)+a(i)*d(:,i);g1=g1 subs(subs(g,x1,X(1,i+1),x2,X(2,i+1);m=norm(g1(:,i+1);i=i+1;endcaseWYLwhilem=ek(i-1)=g1(:,i)*(g1(:,i)-(m/m1)*g1(:,i-1)/(m12);d(:,i)=-g1(:,i)+k(i-1)*d(:,i-1);a(i)=-(d(:,i)*g1(:,i)/(d(:,i)*G*d(:,i);%a(i)=-(X(:,i)*G*d(:,i)+b*d

7、(:,i)/(d(:,i)*G*d(:,i);X(:,i+1)=X(:,i)+a(i)*d(:,i);g1=g1 subs(subs(g,x1,X(1,i+1),x2,X(2,i+1);m1=m;m=norm(g1(:,i+1);i=i+1;endendfv=subs(subs(f,x1,X(1,i),x2,X(2,i);endl1=X(1,i);l2=X(2,i);w1=X(1,1);w2=X(2,1);v1=min(l1,w1)-abs(l1-w1)/10:abs(l1-w1)/10:max(l1,w1)+abs(l1-w1)/10;v2=min(l2,w2)-abs(l2-w2)/10:abs(l2-w2)/10:max(l2,w2)+abs(l2-w2)/10;x,y=meshgrid(v1,v2);s=size(x);z=zeros(size(x);fori=1:s(1)forj=1:s(2)z(i,j)=1/2*x(i,j),y(i,j)*G*x(i,j);y(i,j)+b*x(i,j);y(i,j)+c;endendpx,py = gradient(z,.2,.2);contour(v1,v2,z), holdon , qui