orthproj.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 = orthproj(A,B)
%ORTHPROJ   Orthogonal projection onto a subspace.
%
%   ORTHPROJ(A,B) projects the row vectors of matrix A onto the subspace
%      spanned by the row vectors of matrix B. 
%
%   Usage:
%      Y = orthproj(A,B)
%
%   Inputs: 
%      A := Matrix with n rows and m columns.
%      B := Matrix with k rows and m columns.
%   
%   Outputs:  
%      Y := A*B'*pinv(B*B')*B. Matrix with n rows and m columns.
%   
%   See also COORPROJ, PINV.
%
% 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.
 
colA = size(A,2);
colB = size(B,2);

if colB ~= colA, 
 error('The column numbers of the two input matrices are not equal.')
end

%  find the bases of the row space of B
k = rank(B);
[s,v,d] = svd(B);
d = d';
B = d(1:k,:); clear d

%y = A*(B'/colB)*pinv(B*B'/colB)*B;
y = A*B'*pinv(B*B')*B;

% *** last line of orthproj.m ***