krons.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 Y = krons(U,i,m)
%KRONS   Assembles U++ for use in the Bilinear Identification Toolbox.
%
%   KRONS(U,i,m) returns U^{++}_{i-1|0}. U should be a block Hankel matrix,
%   i>0 an integer and m the number of inputs of the system.
%
%   See also BILINID, BLOCIOBI, BLOCPLBI, BLOCHANK, KHATRI.
%
% 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.

% Old code

%ColU = size(U,2);
%Y = zeros(m*(m+1)/2,ColU);
%for k=1:m
%  Y((k-1)*m+1:(k-1)*m+m-k+1,:) = khatri(U(k,:),U(k:m,:));
%end	
%
%if i > 1
%  for j = 1:i-1
%	Yp = khatri(U(j*m+1:(j+1)*m,:),Y);
%	Y = [Y; Yp];
%  end
%end

% More efficient code - avoids unneccesary dynamic memory allocation. See
% the Matlab User's Guide on efficient memory management.

Y = zeros(m/2*(m+1)^i,size(U,2)); % preallocate just enough memory

p = 1; % set counter
for k=1:m
  q = m-k+1; % number of rows in khatri(U(k,:),U(k:m,:))
  Y(p:p+q-1,:) =  khatri(U(k,:),U(k:m,:));
  p = p+q; % update counter
end	

if i > 1
  A = zeros(m/2*(m+1)^(i-1),size(U,2)); % preallocate just enough memory
  for j = 1:i-1
	A(1:p-1,:) = Y(1:p-1,:); % avoid dynamic memory allocation
	q = m*(p-1); % number of rows in khatri(U(j*m+1:(j+1)*m,:),A(1:p-1,:))
	Y(p:p+q-1,:) = khatri(U(j*m+1:(j+1)*m,:),A(1:p-1,:));
	p = p+q; % update counter
  end
end

% *** last line of krons.m  ***