function [Xc,Z]= airPLS(X,lambda,order,wep,p,itermax)
% Baseline correction using adaptive iteratively reweighted Penalized Least Squares;
% Input
% X:row matrix of spectra or chromatogram (size m*n, m is sample and n is variable)
% lambda: lambda is an adjustable parameter, it can be adjusted by user. The larger lambda is, the smoother z will be
% order: an integer indicating the order of the difference of penalties
% wep: weight exception proportion at both the start and end
% p: asymmetry parameter for the start and end
% itermax: maximum iteration times
% Output
% Xc: the corrected spectra or chromatogram vector (size m*n)
% Z: the fitted vector (size m*n)
% Examples:
% Xc=airPLS(X);
% [Xc,Z]=airPLS(X,10e9,2,0.1,0.5,20);
% Reference:
% (1) Eilers, P. H. C., A perfect smoother. Analytical Chemistry 75 (14), 3631 (2003).
% (2) Eilers, P. H. C., Baseline Correction with Asymmetric Least
% Squares Smoothing, http://www.science.uva.nl/~hboelens/publications/draftpub/Eilers_2005.pdf
% (3) Gan, Feng, Ruan, Guihua, and Mo, Jinyuan, Baseline correction by improved iterative polynomial fitting with automatic threshold. Chemometrics and Intelligent Laboratory Systems 82 (1-2), 59 (2006).
%
% zhimin zhang @ central south university on Mar 30,2011
if nargin < 6
itermax=20;
if nargin < 5
p=0.05;
if nargin < 4
wep=0.1;
if nargin < 3
order=2;
if nargin < 2
lambda=10e7;
if nargin < 1
error('airPLS:NotEnoughInputs','Not enough input arguments. See airPLS.');
end
end
end
end
end
end
[m,n]=size(X);
wi = [1:ceil(n*wep) floor(n-n*wep):n];
D = diff(speye(n), order);
DD = lambda*D'*D;
for i=1:m
w=ones(n,1);
x=X(i,:);
for j=1:itermax
W=spdiags(w, 0, n, n);
C = chol(W + DD);
z = (C\(C'\(w .* x')))';
d = x-z;
dssn= abs(sum(d(d<0)));
if(dssn<0.001*sum(abs(x)))
break;
end
w(d>=0) = 0;
w(wi) = p;
w(d<0) = j*exp(abs(d(d<0))/dssn);
end
Z(i,:)=z;
end
Xc=X-Z;
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