ftparap1.m

Tucker, PARAFAC, GRAM, RAFA and misc. 2nd order models with a test data set (old version now covered

function [Ypred,R]=ftparap1(Xcal,r1,r2,r3,W,Xpred,Ycal,CenMode);
%function [Ypred,R]=ftparap1(Xcal,r1,r2,r3,W,Xpred,Ycal,CenMode);
%
%This particular procedure (ftparap1) calculates the regression
%coefficients of the modelling of Y from A*R=Y. A is calculated
%from the solution to the PARAFAC model.
%NOTE:This predictor is build to, and should ONLY be used with,
%solutions from FTPARA01.M or FTPARA02.M
%(same scheme for updating A)
%
% Xcal     : Supermatrix (r1 x r2穜3) from cube (r1 x r2 x r3).
%            This supermatrix contains the EEM's for which the
%            concentration will be determined.
% r1,r2,r3 : Number of observations along each way.
% W1       : Number of factors.
% Xpred    : Supermatrix (rp x r2穜3) with objects whose
%            Y-values must be estimated.
% Ycal     : Y values to use for calibration, must have same 
%            number of rows as Xcal. Ycal (r1 x ry)
% CenMode  : If CenMode=0 no centering else centering.
% Ypred    : Ypred (rp x ry) Predicted values for the objects
%            contained in Xpred.
% R        : Regression coefficients. R (W x ry)            
% Author   : Claus A. Andersson, May 1995 
% Copyright: Food Technology,
%            Royal Veterinary & Agricultural University
%            Copenhagen, Denmark
% E-mail   : [e-mail]

%Centers X
if CenMode==1,
  st=ones(size(Xcal,1),1);
  Xcen=mean(Xcal);
  Xcal=Xcal-st*Xcen;
end;

%Calculates the scores of the calibration matrix
[Acal Bcal Ccal]=ftpara01(Xcal,r1,r2,r3,W,1,0);

%Centers Y
if CenMode==1,
  st=ones(size(Ycal,1),1);
  Ycen=mean(Ycal);
  Ycal=Ycal-st*Ycen;
end;

%Calculates the regression coefficients in R
R=(Acal'*Acal)\Acal'*Ycal;

%Centers Xpred
if CenMode==1,
  st=ones(size(Xpred,1),1);
  Xpred=Xpred-st*Xcen;
end;

%Determines scores of the new material in Xnew
rpred1=size(Xpred,1);
Dtcal=diag(Ccal(1,:));
tmp1=Xpred(1:rpred1,1:r2)*Bcal*Dtcal;
tmp2=Dtcal*Bcal'*Bcal*Dtcal;
for t=2:r3,
  Dtcal=diag(Ccal(t,:));
  tmp1=tmp1+Xpred(1:rpred1,(t-1)*r2+1:t*r2)*Bcal*Dtcal;
  tmp2=tmp2+Dtcal*Bcal'*Bcal*Dtcal;
end;
Apred=tmp1/tmp2;

%Predicts Y from new score
Ypred=Apred*R;

%Adds from centering
if CenMode==1,
  st=ones(size(Ypred,1),1);
  Ypred=Ypred+st*Ycen;
end;

disp('FTPARAP1: Execution ended.')