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function [AHCPfitAddiOutput]=parafac2(XFConstraintsOptionsAHCP);
% ___________________________________________________
%
% THE PARAFAC2 MODEL
% ___________________________________________________
%
%
%
% Algorithm to fit the PARAFAC2 model which is an advanced variant of the
% normal PARAFAC1 model. It handles slab-wise deviations between components
% in one mode as long as the cross-product of the components stays
% reasonably fixed. This can be utilized for modeling chromatographic
% data with retention time shifts modeling certain batch data of
% varying length etc. See Bro Kiers & Andersson Journal of Chemometrics
% 1999 13 295-309 for details on application and Kiers ten Berge &
% Bro Journal of Chemometrics 1999 13 275-294 for details on the algorithm
%
%
% The PARAFAC2 model is given
%
% Xk = A*Dk*(Pk*H)‘ + Ek k = 1 .. K
%
% Xk is a slab of data (I x J) in which J may actually vary with K. K
% is the number of slabs. A (I x F) are the scores or first-mode loadings. Dk
% is a diagonal matrix that holds the k‘th row of C in its diagonal. C
% (K x F) is the third mode loadings H is an F x F matrix and Pk is a
% J x F orthogonal matrix (J may actually vary from k to k. The output here
% is given as a cell array of size J x F x K. Thus to get e.g. the second P
% write P(::2) and to get the estimate of the second mode loadings at this
% second frontal slab (k = 2) write P(::2)*H. The matrix Ek holds the residuals.
%
% INPUT
%
% X
% Holds the data.
% If all slabs have similar size X is an array:
% X(::1) = X1; X(::2) = X2; etc.
% If the slabs have different size X is a cell array (type <>)
% X{1} = X1; X{2} = X2; etc.
% If you have your data in an ‘unfolded‘ two-way array of size
% I x JK (the three-way array is I x J x K) then simply type
% X = reshape(X[I J K]); to convert it to an array.
%
% F
% The number of components to extract
%
% Constraints
% Vector of length 2. The first element defines constraints
% imposed in the first mode the second defines contraints in
% third mode (the second mode is not included because constraints
% are not easily imposed in this mode)
%
% If Constraints = [a b] the following holds. If
% a = 0 => no constraints in the first mode
% a = 1 => nonnegativity in the first mode
% a = 2 => orthogonality in the first mode
% a = 3 => unimodality (and nonnegativity) in the first mode
% same holds for b for the third mode
%
% Options
% An optional vector of length 3
% Options(1) Convergence criterion
% 1e-7 if not given or given as zero
% Options(2) Maximal iterations
% default 2000 if not given or given as zero
% Options(3) Initialization method
% A rather slow initialization method is used per default
% but it pays to investigate in avoiding local minima.
%
属性 大小 日期 时间 名称
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文件 33001 2010-08-02 11:05 parafac2.m
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33001 1
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