共軛梯度法MATLAB程序

1、%conjugate gradient methods%method:FR,PRP,HS,DY,CD,WYL,LS%精確線搜索,梯度終止準(zhǔn)則function m,k,d,a,X,g1,fv = conjgradme( G,b,c,X,e,methodif nargin<6error('輸入?yún)?shù)必須為6'endn=length(G;if n=2format long e%ratsyms x1x2f=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

2、=-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=g1 subs(subs(g,x1,X(1,2,x2,X(2,2;m1=norm(g1(:,1;m=norm(g1(:,2;i=2;k=zeros(1;switch methodcase'FR'while m>=ek(i-1=(m/m12;d(:,i=-g1(:,i+k(i-1*d(:,i-1;a(i=-(d

3、(:,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=g1 subs(subs(g,x1,X(1,i+1,x2,X(2,i+1;m1=m;m=norm(g1(:,i+1;i=i+1;endcase'PRP'while m>=ek(i-1=g1(:,i'*(g1(:,i-g1(:,i-1/(

4、norm(g1(:,i-12;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;endcase'HS'while m>=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;

5、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;endcase'DY'while m>=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(

6、:,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;endcase'LS'while m>=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

7、;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;endcase'CD'while m>=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=g1 subs(subs(g,x1,X(1,i+1,x2,X(2

8、,i+1;m=norm(g1(:,i+1;i=i+1;endcase'WYL'while m>=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(:,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

9、+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-w1/1 0;v2=min(l2,w2-abs(l2-w2/10:abs(l2-w2/10:max(l2,w2+abs(l2-w2/1 0;x,y=meshgrid(v1,v2;s=size(x;z=zeros(size(x;for i=1:s(1for j=1:s(2z(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, hold on, quiver(v1,v2,px,