请问有人知道共轭梯度法的FR,PRP,HS三个算法的Matlab程序吗?

%共轭梯度法 FR

% G为对称正定矩阵，X是初始点，e为精度

%a是精确线搜索步长

function [m2,a,d,X,g1,f1] = conjgrad(G,b,c,X,e)

n=length(G)

if n==2

format long e %rat

syms x1 x2

f=1/2*[x1,x2]*G*[x1x2]+b'*[x1x2]+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))m2=norm(g1(:,2))

k=(m2/m1)^2

i=2

while m2>=e

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=m2m2=norm(g1(:,i+1))

k(i)=(m2/m1)^2

i=i+1

end

f1=subs(subs(f,x1,X(1,i)),x2,X(2,i))

elseif n==3

format long

syms x1 x2 x3

f=1/2*[x1,x2,x3]*G*[x1x2x3]+b'*[x1x2x3]+c

g=[diff(f,x1)diff(f,x2)diff(f,x3)]

g1=subs(subs(subs(g,x1,X(1,1)),x2,X(2,1)),x3,X(3,1))

d=-g1

a=-((X(:,1)'*G*d+b'*d)/(d'*G*d))

X(:,2)=X(:,1)+a*d

g1=[g1 subs(subs(subs(g,x1,X(1,2)),x2,X(2,2)),x3,X(3,2))]

k=(norm(g1(:,2))/norm(g1(:,1)))^2

m=norm(g1(:,2))

i=2

while m>=e

d(:,i)=-g1(:,i)+k*d(:,i-1)

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(subs(g,x1,X(1,i+1)),x2,X(2,i+1)),x3,X(3,i+1))]

k=(norm(g1(:,i+1))/norm(g1(:,i)))^2

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

i=i+1

end

f1=subs(subs(subs(f,x1,X(1,i)),x2,X(2,i)),x3,X(3,i))

end

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