function [R,lam2,x2]=decorder(A,lambda,V)
% 利用相似变换对矩阵A进行降阶，从而可用幂法求次大特征值和特征向量

%  NUMERICAL METHODS: Matlab Programs
% (c) 2007 by Xie Liling
%  Complementary Software to accompany the textbook:
%  Information and Computing Science: A Laboratory Course

[n,n]=size(A);

% 选主元
[m,p]=max(abs(V));

% 构造排列阵Ip
Ip=eye(n);
Ip(1,1)=0; Ip(1,p)=1;  Ip(p,1)=1; Ip(p,p)=0;

Y=Ip*V;
L=eye(n);
for i=2:n
    L(i,1)=-Y(i)/Y(1);
end

S=L*Ip;
R=S*A*inv(S); % R为分块矩阵

% 对R右下块阵（降阶）求按模最大特征值和特征向量
A2=R(2:n,2:n);
V0=ones(n-1,1);
[lam2,Y2,k2]= powerm(A2,V0,1e-12,100);

alpha=-R(1,2:n)*Y2/(lambda(end)-lam2(end));
z2=[alpha;Y2];
x2=inv(S)*z2;

% 对特征向量规范化
c=max(abs(x2));
x2=x2/c;