%  Copyright (C) 2015, 2016   Fernando Pujaico Rivera
%
%  This file is a part of the Bio Speckle Laser Tool Library (BSLTL) package.
%
%  This BSLTL computer package is free software; you can redistribute it
%  and/or modify it under the terms of the GNU General Public License as
%  published by the Free Software Foundation; either version 3 of the
%  License, or (at your option) any later version.
%
%  This BSLTL computer package is distributed hoping that it could be
%  useful, but WITHOUT ANY WARRANTY; without even the implied warranty of
%  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
%  GNU General Public License for more details.
%
%  You should have received a copy of the GNU General Public License
%  along with this program; if not, please download it from
%  <http://www.gnu.org/licenses>.

function [Skew varargout] = graphskew(DATA,varargin)
%
%  This function calculates the temporal speckle skewness matrix (S). Use as
%  input data a 3D matrix created grouping NTIMES intensity matrices I(k)
%  1<=k<=NTIMES
%
%  I(k)=DATA(:,:,k)
%
%  $MU = \frac{1}{NTIMES} \sum\limits_{k=1}^{NTIMES} I(k) \approx E[I(k)]$
%
%  $SIGMA = \sqrt{ \frac{1}{NTIMES} \sum\limits_{k=1}^{NTIMES} (I(k)-MU)^2}$
%
%  $S \approx E[\left(\frac{I(k)-MU}{SIGMA}\right)^3]$
%
%  The function additionally returns the temporal standard deviation matrix 
%  and temporal expected matrix.
%
%
%  After starting the main routine just type the following command at the
%  prompt:
%  S       = graphskew(DATA);
%  [S D]   = graphskew(DATA);
%  [S D E] = graphskew(DATA);
%    
%  Input:
%  DATA is the speckle data pack. Where DATA is a 3D matrix created grouping NTIMES 
%       intensity matrices with NLIN lines and NCOL columns. When N=size(DATA), then
%       N(1,1) represents NLIN and
%       N(1,2) represents NCOL and
%       N(1,3) represents NTIMES.
%  SHOW [Optional] If SHOW is equal to string 'off', then the result will
%  not be plotted.
%
%  Output:
%  K    returns the temporal speckle skewness matrix of image Data Pack.
%  D    [Optional] returns the temporal standard deviation matrix of image Data Pack.
%  E    [Optional] returns the temporal expected matrix of image Data Pack.
%
%
%  For help, bug reports and feature suggestions, please visit:
%  http://nongnu.org/bsltl
%

%  Code developed by:  Fernando Pujaico Rivera <fernando.pujaico.rivera@gmail.com>
%  Code documented by: Fernando Pujaico Rivera <fernando.pujaico.rivera@gmail.com>
%  Code reviweed by: Roberto A Braga Jr <robertobraga@deg.ufla.br>
%
%  Date: 16 of July of 2015.
%  Review: 22 of July of 2015.
%  Review: 23 of March of 2016.
%
    NSIZE = size(DATA);
	NLIN  = NSIZE(1,1);
	NCOL  = NSIZE(1,2);
	NTIMES= NSIZE(1,3);
    
    if (NTIMES<2)
        error('Number of frames used are not enough.');
    end
    
    
    SIGMA = zeros(NLIN,NCOL);
    ED    = zeros(NLIN,NCOL);
	Skew  = zeros(NLIN,NCOL);

            
	for k = 1:NTIMES                
        ED = ED+ DATA(:,:,k) ;
    end
	ED=ED/NTIMES;
	%disp('Mean matrix calculated');

    for k = 1:NTIMES 
                     
        SIGMA =  SIGMA + (DATA(:,:,k)-ED).^2;
    end
    

    SIGMA = sqrt(SIGMA/NTIMES) ;

	%disp('Deviation matrix calculated');
	
	for k = 1:NTIMES 
		Skew=Skew+((DATA(:,:,k)-ED)./SIGMA).^3;
    end

	Skew=Skew/NTIMES;

	%disp('Skewness matrix calculated');

	if(nargout>=2)
		varargout{1}=SIGMA;
	end

	if(nargout>=3)
		varargout{2}=ED;
	end

	SHOW='';
	if(nargin>=2)
		if(ischar(varargin{1}))
			SHOW=varargin{1};
		end
	end

    if ( ~strcmp(SHOW,'off'))     
		figure   
	    imagesc(ED); colorbar;
	    title('Images: Speckle Mean');   
		daspect ([1 1 1]);   
    
		figure   
	    imagesc(SIGMA); colorbar;
	    title('Images: Speckle Standard Deviation');      
		daspect ([1 1 1]);

		figure   
	    imagesc(Skew); colorbar;
	    title('Images: Speckle Skewness');    
		daspect ([1 1 1]);
	end       
 
