os2ref.m

Optimized scaling算法 可以用来优化选择

function[RMSEC,RMSEP]=os2ref(Xcal,ycal,Xval,yval);

% [RMSEC,RMSEP]=os2ref(Xcal,ycal,Xval,yval);
% 
% Optimized scaling 2, T. V. Karstang, R. Manne, Chemolab 14 (1992) 165-173
% y=(x*b)./(x*c), b-regression coefficient, c-scaling coefficient
% 
% Testing through all the objects for detection of best reference. RMSEC/RMSEP values for every score is obtained.
% Use bar(RMSEC) and bar(RMSEP)
% Xcal: scores for calibration set: [T,P]=apca(X), 
% Xval: scores for val.set: Tv=X*P
% 
% L. Stordrange 02.03.01, Uppdated 27.06.01

[i,j]=size(Xcal);
[v,w]=size(Xval);
RMSEC=zeros(i,j);
RMSEP=zeros(i,j);

for t=1:j
   for k=1:i
      xnull=Xcal(k,1:t); 
      ynull=ycal(k);
      Z=diag(ycal)*Xcal(:,1:t);
      Z(k,:)=zeros(1,t);
      ZX=[Z Xcal(:,1:t)];
      xnull0=[xnull,zeros(1,t)];
      
      % The final system of linear equations is denoted A*p=q
      A=[ZX'*ZX,xnull0';xnull0,0];
      q=[zeros(t,1);-ynull*xnull';1];
      p=A\q; % 
      
      c=p(1:t);
      b=-p(t+1:2*t);
      %lamda=-p(2*j+1);
      
      yc=(Xcal(:,1:t)*b)./(Xcal(:,1:t)*c);
      ec=yc-ycal;
      RMSEC(k,t)=sqrt((ec'*ec)/i);
      
      yv=(Xval(:,1:t)*b)./(Xval(:,1:t)*c);
      ev=yv-yval;
      RMSEP(k,t)=sqrt((ev'*ev)/v);
   end
end