function [Out1, Out2, Out3] = fastica(mixedsig, varargin)%FASTICA - Fast Independent Component Analysis%% FastICA for Matlab 6.x% Version 2.3, July 27 2004% Copyright (c) Jarmo Hurri, Hugo G鋠ert, Jaakko S鋜el? and Aapo Hyv鋜inen.%% FASTICA(mixedsig) estimates the independent components from given% multidimensional signals. Each row of matrix mixedsig is one% observed signal.  FASTICA uses Hyvarinen's fixed-point algorithm,% see http://www.cis.hut.fi/projects/ica/fastica/. Output from the% function depends on the number output arguments:%% [icasig] = FASTICA (mixedsig); the rows of icasig contain the% estimated independent components.%% [icasig, A, W] = FASTICA (mixedsig); outputs the estimated separating% matrix W and the corresponding mixing matrix A.%% [A, W] = FASTICA (mixedsig); gives only the estimated mixing matrix% A and the separating matrix W.%% Some optional arguments induce other output formats, see below.%% A graphical user interface for FASTICA can be launched by the% command FASTICAG%% FASTICA can be called with numerous optional arguments. Optional% arguments are given in parameter pairs, so that first argument is% the name of the parameter and the next argument is the value for% that parameter. Optional parameter pairs can be given in any order.%% OPTIONAL PARAMETERS:%% Parameter name        Values and description%%======================================================================% --Basic parameters in fixed-point algorithm:%% 'approach'            (string) The decorrelation approach used. Can be%                       symmetric ('symm'), i.e. estimate all the并行地計算獨立成分%                       independent component in parallel, or%                       deflation ('defl'), i.e. estimate independent%                       component one-by-one like in projection%                       pursuit.串行地計算獨立成分%                       Default is 'defl'.%% 'numOfIC'             (integer) Number of independent components to%                       be estimated. Default equals the dimension of%                       data.需要估計的獨立成分的個數，默認為數據維數%%======================================================================% --Choosing the nonlinearity:%% 'g'                   (string) Chooses the nonlinearity g used in %                       the fixed-point algorithm. Possible values:%%                       Value of 'g':      Nonlinearity used:%                       'pow3' (default)   g(u)=u^3%                       'tanh'             g(u)=tanh(a1*u)%                       'gauss             g(u)=u*exp(-a2*u^2/2)%                       'skew'             g(u)=u^2% % 'finetune'		(string) Chooses the nonlinearity g used when %                       fine-tuning. In addition to same values%                       as for 'g', the possible value 'finetune' is:%                       'off'              fine-tuning is disabled.%% 'a1'                  (number) Parameter a1 used when g='tanh'.%                       Default is 1.% 'a2'                  (number) Parameter a2 used when g='gaus'.%                       Default is 1.%% 'mu'			(number) Step size. Default is 1.%                       If the value of mu is other than 1, then the%                       program will use the stabilized version of the%                       algorithm (see also parameter 'stabilization').%%% 'stabilization'       (string) Values 'on' or 'off'. Default 'off'. %                       This parameter controls wether the program uses%                       the stabilized version of the algorithm or%                       not. If the stabilization is on, then the value%                       of mu can momentarily be halved if the program%                       senses that the algorithm is stuck between two%                       points (this is called a stroke). Also if there%                       is no convergence before half of the maximum%                       number of iterations has been reached then mu%                       will be halved for the rest of the rounds.% %======================================================================% --Controlling convergence:%% 'epsilon'             (number) Stopping criterion. Default is 0.0001.%% 'maxNumIterations'    (integer) Maximum number of iterations.%                       Default is 1000.%% 'maxFinetune'         (integer) Maximum number of iterations in %                       fine-tuning. Default 100.%% 'sampleSize'          (number) [0 - 1] Percentage of samples used in%                       one iteration. Samples are chosen in random.%                       Default is 1 (all samples).%% 'initGuess'           (matrix) Initial guess for A. Default is random.%                       You can now do a "one more" like this: %                       [ica, A, W] = fastica(mix, 'numOfIC',3);%                       [ica2, A2, W2] = fastica(mix, 'initGuess', A, 'numOfIC', 4);%%======================================================================% --Graphics and text output:%% 'verbose'             (string) Either 'on' or 'off'. Default is%                       'on': report progress of algorithm in text format.%% 'displayMode'         (string) Plot running estimates of independent%                       components: 'signals', 'basis', 'filters' or%                       'off'. Default is 'off'.%% 'displayInterval'     Number of iterations between plots.%                       Default is 1 (plot after every iteration).%%======================================================================% --Controlling reduction of dimension and whitening:%% Reduction of dimension is controlled by 'firstEig' and 'lastEig', or% alternatively by 'interactivePCA'. %% 'firstEig'            (integer) This and 'lastEig' specify the range for%                       eigenvalues that are retained, 'firstEig' is%                       the index of largest eigenvalue to be%                       retained. Default is 1.%% 'lastEig'             (integer) This is the index of the last (smallest)%                       eigenvalue to be retained. Default equals the%                       dimension of data.%% 'interactivePCA'      (string) Either 'on' or 'off'. When set 'on', the%                       eigenvalues are shown to the user and the%                       range can be specified interactively. Default%                       is 'off'. Can also be set to 'gui'. Then the user%                       can use the same GUI that's in FASTICAG.%% If you already know the eigenvalue decomposition of the covariance% matrix, you can avoid computing it again by giving it with the% following options:%% 'pcaE'                (matrix) Eigenvectors% 'pcaD'                (matrix) Eigenvalues%% If you already know the whitened data, you can give it directly to% the algorithm using the following options:%% 'whiteSig'            (matrix) Whitened signal% 'whiteMat'            (matrix) Whitening matrix% 'dewhiteMat'          (matrix) dewhitening matrix%% If values for all the 'whiteSig', 'whiteSig' and 'dewhiteMat' are% suplied, they will be used in computing the ICA. PCA and whitening% are not performed. Though 'mixedsig' is not used in the main% algorithm it still must be entered - some values are still% calculated from it.%% Performing preprocessing only is possible by the option:%% 'only'                (string) Compute only PCA i.e. reduction of%                       dimension ('pca') or only PCA plus whitening%                       ('white'). Default is 'all': do ICA estimation%                       as well.  This option changes the output%                       format accordingly. For example: %%                       [whitesig, WM, DWM] = FASTICA(mixedsig, %                       'only', 'white') %                       returns the whitened signals, the whitening matrix%                       (WM) and the dewhitening matrix (DWM). (See also%                       WHITENV.) In FastICA the whitening matrix performs%                       whitening and the reduction of dimension. Dewhitening%                       matrix is the pseudoinverse of whitening matrix.%                        %                       [E, D] = FASTICA(mixedsig, 'only', 'pca') %                       returns the eigenvector (E) and diagonal %                       eigenvalue (D) matrices  containing the %                       selected subspaces. %%======================================================================% EXAMPLES%%       [icasig] = FASTICA (mixedsig, 'approach', 'symm', 'g', 'tanh');%               Do ICA with tanh nonlinearity and in parallel (like%               maximum likelihood estimation for supergaussian data).%%       [icasig] = FASTICA (mixedsig, 'lastEig', 10, 'numOfIC', 3);%               Reduce dimension to 10, and estimate only 3%               independent components.%%       [icasig] = FASTICA (mixedsig, 'verbose', 'off', 'displayMode', 'off');%               Don't output convergence reports and don't plot%               independent components.%%% A graphical user interface for FASTICA can be launched by the% command FASTICAG%%   See also FASTICAG% @(#)$Id: fastica.m,v 1.11 2004/07/27 11:46:46 jarmo Exp $%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Check some basic requirements of the dataif nargin == 0,  error ('You must supply the mixed data as input argument.');endif length (size (mixedsig)) > 2,  error ('Input data can not have more than two dimensions.');endif any (any (isnan (mixedsig))),  error ('Input data contains NaN''s.');endif ~isa (mixedsig, 'double')  fprintf ('Warning: converting input data into regular (double) precision.\n');  mixedsig = double (mixedsig);end%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Remove the mean and check the data[mixedsig, mixedmean] = remmean(mixedsig);[Dim, NumOfSampl] = size(mixedsig);%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Default values for optional parameters% Allverbose           = 'on';% Default values for 'pcamat' parametersfirstEig          = 1;lastEig           = Dim;interactivePCA    = 'off';% Default values for 'fpica' parametersapproach          = 'defl';numOfIC           = Dim;g                 = 'pow3';finetune          = 'off';a1                = 1;a2                = 1;myy               = 1;stabilization     = 'off';epsilon           = 0.0001;maxNumIterations  = 1000;maxFinetune       = 5;initState         = 'rand';guess             = 0;sampleSize        = 1;displayMode       = 'off';