基于MATLAB实现共轭梯度法

%conjugategradientmethods%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)ifnargin6error('输入参数必须为6');endn=length(G);ifn==2formatlonge%ratsymsx1x2f=1/2*[x1,x2]*G*[x1;x2]+b'*[x1;x2]+c;g=[diff(f,x1);diff(f,x2)];g1=subs(subs(g,x1,X(1,1)),x2,X(2,1));d=-g1;a=-(d'*g1)/(d'*G*d);%a=-((X(:,1)'*G*d+b'*d)/(d'*G*d));a=g1(:,1)'*g1(:,1)/(d(:,1)'*G*d(:,1));X(:,2)=X(:,1)+a*d;g1=[g1subs(subs(g,x1,X(1,2)),x2,X(2,2))];m1=norm(g1(:,1));m=norm(g1(:,2));i=2;k=zeros(1);switchmethodcase'FR'whilem=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(:,i)'*G*d(:,i));X(:,i+1)=X(:,i)+a(i)*d(:,i);g1=[g1subs(subs(g,x1,X(1,i+1)),x2,X(2,i+1))];m1=m;m=norm(g1(:,i+1));i=i+1;endcase'PRP'whilem=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=[g1subs(subs(g,x1,X(1,i+1)),x2,X(2,i+1))];m=norm(g1(:,i+1));i=i+1;endcase'HS'whilem=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=[g1subs(subs(g,x1,X(1,i+1)),x2,X(2,i+1))];m=norm(g1(:,i+1));i=i+1;endcase'DY'whilem=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=[g1subs(subs(g,x1,X(1,i+1)),x2,X(2,i+1))];m=norm(g1(:,i+1));i=i+1;endcase'LS'whilem=ek(i-1)=g1(:,i)'*(g1(:,i)-g1(:,i-1))/(d(:,i-1)'*(-g1(:,i-1)));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(:,i))/(d(:,i)'*G*d(:,i)));X(:,i+1)=X(:,i)+a(i)*d(:,i);g1=[g1subs(subs(g,x1,X(1,i+1)),x2,X(2,i+1))];m=norm(g1(:,i+1));i=i+1;endcase'CD'whilem=ek(i-1)=g1(:,i)'*g1(:,i)/(d(:,i-1)'*(-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=[g1subs(subs(g,x1,X(1,i+1)),x2,X(2,i+1))];m=norm(g1(:,i+1));i=i+1;endcase'WYL'whilem=ek(i-1)=g1(:,i)'*(g1(:,i)-(m/m1)*g1(:,i-1))/(m1^2);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(:,i))/(d(:,i)'*G*d(:,i)));X(:,i+1)=X(:,i)+a(i)*d(:,i);g1=[g1subs(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;endend[px,py]=gradient(z,.2,.2);contour(v1,v2,z),holdon,quiver(v1,v2,px,py)[C,h]=contour(x,y,z);set(h,'ShowText','on','TextStep',get(h,'LevelStep')*2)x1=X(1,:);y1=X(2,:);plot(x1,y1,'r*:');