fttuckp1.m

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

function [Ypred,R]=fttuckp1(Xcal,r1,r2,r3,W1,W2,W3,Xpred,Ycal,CenMode);
%function [Ypred,R]=fttuckp1(Xcal,r1,r2,r3,W1,W2,W3,Xpred,Ycal,CenMode);
%
%This particular procedure (fttuckp1) calculates the regression
%coefficients of the modelling of Y from A*R=Y. A is calculated
%from the solution to the TUCKER3 model.
%NOTE:This predictor is build to, and should ONLY be used with,
%solutions from FTTUCK01.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,W2,W3 : Number of factors along each way.
% 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 (W1 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 Gcal]=fttuck01(Xcal,r1,r2,r3,W1,W2,W3,1,0);

%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);
tmp2=zeros(W1,r3*r2);
for k=1:r3,
  tmp1=Ccal(k,1)*Gcal(:,1:W2)*Bcal';
  for l=2:W3,
    tmp1=tmp1+Ccal(k,l)*Gcal(:,(l-1)*W2+1:l*W2)*Bcal';
  end;
  tmp2(1:W1,(k-1)*r2+1:k*r2)=tmp1;
end;
Apred=Xpred*tmp2'/(tmp2*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('FTTUCKP1: Execution ended.')