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// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) 2000 - INRIA - Carlos Klimann
//
// This file must be used under the terms of the CeCILL.
// This source file is licensed as described in the file COPYING, which
// you should have received as part of this distribution. The terms
// are also available at
// http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
//
function [facpr,comprinc,lambda,tsquare]=princomp(x,eco)
//
//This function performs several computations known as
//"principal component analysis".
//The idea behind this method is to represent in an
//approximative manner a cluster of n individuals in a
//smaller dimensional subspace. In order to do that it
//projects the cluster onto a subspace. The choice of the
//k-dimensional projection subspace is made in such a way
//that the distances in the projection have a minimal
//deformation: we are looking for a k-dimensional subspace
//such that the squares of the distances in the projection
//is as big as possible (in fact in a projection,
//distances can only stretch). In other words, inertia of
//the projection onto the k dimensional subspace must be
//maximal.
//
//References: Saporta, Gilbert, Probabilites, Analyse des
//Donnees et Statistique, Editions Technip, Paris, 1990.
//
//derived from pca,
// author: carlos klimann
//
if argn(2)<2 then eco=%f,end
if type(eco)<>4 then
error(msprintf(_("%s: Wrong type for input argument #%d: Boolean expected."),"princomp",2))
end
if x==[] then
facpr=[];
comprinc=[];
lambda=[];
tsquare=[];
return;
end
[rowx,colx]=size(x)
//center data
y=center(x,1)
//compute eigenvectors of y'*y using svd
if eco then
[U,lambda,facpr]=svd(y,"e");
else
[U,lambda,facpr]=svd(y);
end
lambda=diag(lambda).^2/(rowx-1);//normalize
comprinc=y*facpr
if rowx <= colx then
if eco then
lambda(rowx)=[]
facpr(:,rowx)=[];
comprinc(:,rowx) = [];
else
lambda(rowx:$)=[]
comprinc(:,rowx:$) = [];
end
end
q=find(lambda<=max(rowx,colx)*%eps*lambda(1),1)
if q==[] then q=size(lambda,'*'),end
tsquare=(rowx-1)*sum(U(:,1:q).^2,2)
endfunction
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