%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)

if nargin<6

error('输入参数必须为6');

end

n=length(G);

if n==2

format long e %rat

syms x1 x2

f=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=[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 method

case 'FR'

while m>=e

k(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=[g1 subs(subs(g,x1,X(1,i+1)),x2,X(2,i+1))];

m1=m;

m=norm(g1(:,i+1));

i=i+1;

end

case 'PRP'

while m>=e

k(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,X(1,i+1)),x2,X(2,i+1))];

m=norm(g1(:,i+1));

i=i+1;

end

case 'HS'

while m>=e

k(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;

end

case 'DY'

while m>=e

k(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;

end

case 'LS'

while m>=e

k(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=[g1 subs(subs(g,x1,X(1,i+1)),x2,X(2,i+1))];

m=norm(g1(:,i+1));

i=i+1;

end

case 'CD'

while m>=e

k(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,i+1))];

m=norm(g1(:,i+1));

i=i+1;

end

case 'WYL'

while m>=e

k(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=[g1 subs(subs(g,x1,X(1,i+1)),x2,X(2,i+1))];

m1=m;

m=norm(g1(:,i+1));

i=i+1;

end

end

fv=subs(subs(f,x1,X(1,i)),x2,X(2,i));

end

l1=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));

for i=1:s(1)

for j=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;

end

end

[px,py] = gradient(z,.2,.2);

contour(v1,v2,z), hold on, 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*:');