function [p,mu,vc,ev] = projectpca(data,nr_or_mu,vc,ev)% projectpca : project data matrix on first nr eigenvectors%  After the call, p will have a unit covariance matrix (changed from previous version!)% two syntaxes:%   [p,mu,vc,ev] = projectpca(data,nr)%	  data - d*n data matrix%	  nr   - on how many eigenvectors will we project ?% OR, if pca is aleady available:%   [p,mu,vc,ev] = projectpca(data,mu,vc,ev)%	  data - d*n data matrix%     mu   - d*1  mean of the data%	  vc   - d*nr first nr eigenvectors (optional)%	  ev   - 1*nr first nr eigenvalues  (optional)% output in both cases:%	p	- nr*n resulting projection%   mu  - d*1  mean of the data%	vc	- d*nr first nr eigenvectors%	ev	- 1*nr first nr eigenvalues% Copyright (c) 1995-2001 Frank Dellaert% All rights Reserved%% historical note%  Rather than using chemometrics copyrighted pca:%   [eigenvectors,eigenvalues] = pca(x,nr);%   vc = eigenvectors(:,1:nr);%   ev = eigenvalues(1:nr);%  We now use MATLAB built-in svds.%  Also, we now multiply by diag(ev.^-0.5*sqrt(n)) to get whitened data.[d,n] = size(data);switch nargincase 2   nr=nr_or_mu;   mu = mean(data,2);   [vc,S,dummy] = svds(cov(data',1),nr);   ev=diag(S);case 4   mu=nr_or_mu;otherwise   error('incorrect number of arguments');endx = data - repmat(mu,1,n);p = diag(ev.^-0.5) * vc' * x;