exthsv.m

剑桥大学用于线性和双线性动力学系统辨识的工具箱

function s = exthsv(t,method)
%EXTHSV   Extract distinct Hankel singular values from a set of estimates.
%
%   S = EXTHSV(T,METHOD) extracts Hankel singular values from the estimates
%   T and outputs them in S, bearing in mind which METHOD will be used to
%   identify the system. The algorithm guarantees that each of the singular
%   values are strictly positive and distinct, arranged from largest S(1) to
%   smallest S(end). If METHOD is 'ncf' or 'pr', then the singular values
%   are also strictly less than 1.
%
%   See also CONHSV.
%
% CUED System Identification Toolbox.
% Cambridge University Engineering Department.
% Copyright (C) 1998-2002. All Rights Reserved.

% Version 1.00, Date: 01/06/2002
% Created by H. Chen and E.C. Kerrigan.

n = length(t);
  
if strcmp(method,'sb') | strcmp(method,'mp')

  % This operation is the reverse of
  %     t = s;
  %     for i=1:n-1
  %       t(i) = s(i) - s(i+1);
  %     end
  %     t = log(t); 
  
  t = exp(t); 
  
  s = t(:); 
  
  for i=n-1:-1:1
	s(i) = t(i) + s(i+1); 
  end  

elseif strcmp(method,'ncf') | strcmp(method,'pr')

  % This operation is the reverse of
  %     t = s;
  %     t(1) = log(s(1)/(1-s(1)));
  %     for i=2:n
  %       t(i) = log(s(i)/(s(i-1)-s(i)));
  %     end
  
  s = t(:);
  
  s(1) = exp(t(1))/(1+exp(t(1)));
  for i=2:n
	s(i) = s(i-1) * exp(t(i))/(1+exp(t(i)));
  end
  
else
  error('EXTHSV: Unknown METHOD.')
end