function [PCs, err] = PCAspace ( data, N )

%
%  function [U, S, mn, err] = PCA ( dataTrain, dataTest, N )
%
%  Computes PCA and reconstruction error forsome test data.
%
%    data	[n x m]		input data points (column-wise)
%
%    N		scalar		first N principle components are retained
%
%    PCs.U	[n x N]		PCA basis
%
%    PCs.S	[n x 1]		singular values
%
%    PCs.mu	[n x 1]		mean data vector	 
%
%    err	[m' x 1]	reconstruction error (absolute value of
%				distance from PCA space
%
%  Markus Weber
%
%  (c) by California Institute of Technology
%
%  $Log$
%

M = size(data, 2);

PCs.mu = mean(data')';

phi = data - PCs.mu * ones(1, M);

[U S V] = svd(phi * phi');

PCs.S = diag(S);

PCs.U = U(:, 1:N);

%phiTest = dataTest - PCs.mu * ones(1, size(dataTest, 2));

%D = PCs.U * (PCs.U' * phiTest) - phiTest;

%err = sqrt(sum(D .^ 2))';