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.
%??

?屬性????????????大小?????日期????時間???名稱
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?????文件??????33001??2010-08-02?11:05??parafac2.m

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????????????????33001????????????????????1