os2m.m

Optimized scaling算法 可以用来优化选择

function[RMSEC,ypcal,RMSEP,ypval,b,c]=os2m(Tcal,y,noll,Tval,yval,disp);

% [RMSEC,ypcal,RMSEP,ypval,b,c]=os2m(Tcal,y,noll,Tval,yval,disp);
% 
% Optimized scaling 2, T. V. Karstang, R. Manne, Chemolab 14 (1992) 165-173
% Uses scores T from pca, non sentered, instead of matrix X
%
% Input: 
% T(scores) 	- calibration set
% y(response) 	- calibration set
% noll(scalar)	- reference spectra 
% Tval=Xval*P	- scores validation set
% yval			- response validation set
% if plot then the result is displayed
%
% Prediction of new samples: ypred=(T*b)./(T*c);
%
%
% M-file given by R. Manne. Modified by L. Stordrange 06.06.01

[i,j]=size(Tcal);
m=size(Tval,1);

T=Tcal;
xnull=T(noll,:); 
ynull=y(noll);
Z=diag(y)*T;
Z(noll,:)=zeros(1,j);
ZX=[Z T];
xnull0=[xnull,zeros(1,j)];

% The final system of linear equations is denoted A*p=q
A=[ZX'*ZX,xnull0';xnull0,0];
q=[zeros(j,1);-ynull*xnull';1];
p=A\q; 

c=p(1:j);
b=-p(j+1:2*j);
%lamda=-p(2*j+1);
ypcal=(T*b)./(T*c);
e=y-ypcal;
RMSEC=sqrt((e'*e)/i);

po=polyfit(y,ypcal,1);

if nargin>5
   xi=linspace(min(y)*0.8,max(y)*1.2,4);
   z=polyval(po,xi);
   subplot(1,2,1)
   plot(y,ypcal,'.',xi,z),xlabel('y measured'),ylabel('y predicted')
   subplot(1,2,2)
   bar(e),xlabel('object #'),ylabel('residual')
end

% Predikerer valideringspr鴙er
ypval=(Tval*b)./(Tval*c);
e=yval-ypval;
RMSEP=sqrt((e'*e)/m);

figure
po=polyfit(yval,ypval,1);

if nargin>5
   xi=linspace(min(y)*0.8,max(yval)*1.2,4);
   z=polyval(po,xi);
   subplot(1,2,1)
   plot(yval,ypval,'.',xi,z),xlabel('y measured'),ylabel('y predicted')
   subplot(1,2,2)
   bar(e),xlabel('object #'),ylabel('residual')
end