NDIND (X, T, n, l)

%function [LogD, l] = NDIND (X, T, n, l)
%
%This function will calculate the n'th derivative of the indicator
%function. This values have a higher descriptive power of the system: it
%allows a better prediction of the optimal number of principal components.
%
%Syntax:
%   [LogD, l] = NDIND (X, T, n, l)
%   [LogD, l] = NDIND (X, T, n)
%   [LogD, l] = NDIND (Ind, n)
%
%Input parameters:
%   - X: your data-matrix
%   - T: the corresponding scores of the PCA-analysis
%   - n: type of differention: if:
%      2: log of second derivative: optimal value at first max
%      3: log of third derivative: optimal value at first min
%      rod: Ratio Of Derivatives: Optimal value at first max
%   - l: value calculated vfor the first l principal components, (optional
%      default all calculated principal components)
%   - Ind: (in case of third possible syntax): already calculated values of the
%      Indicator function
%
%Output parameters:
%    - LogD: the n'th derivative of the of the indicator function
%    - l: the corresponding PCS
%
%Literature:
%   1) Elbergali, A. et al. Analytica chimica acta, 379, 1999, 143-158
%
%See also:
%   help INDFunc
%

%The Biodata toolbox for MATLAB: a spectral database system for storing and
%processing spectra
%C 2005-2008, Kris De Gussem, Raman Spectroscopy Research Group, Department
%of analytical chemistry, Ghent University
%C 2009 Kris De Gussem
%
%This file is part of Biodata.
%
%Biodata 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.
%
%Biodata is distributed in the hope that it will 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 Biodata.  If not, see <http://www.gnu.org/licenses/>.

%Copyright (c) 2005-2009, Kris De Gussem
%All rights reserved.
%
%Redistribution and use in source and binary forms, with or without 
%modification, are permitted provided that the following conditions are 
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%
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function [LogD, l] = NDIND (X, T, n, l)
%check input parameters
if nargin == 2
    Ind = X;
    n = T;
    if n == 3
        l = 2:(size(Ind,1)-2);
    else
        l = 2:(size(Ind,1)-1);
    end
    
else
    switch nargin
        case 3
            if n == 3
                l = 2:(size (T,2)-2);
            else
                l = 2:(size (T,2)-1);
            end
        case 4
            
        otherwise
            error ('Biodata:msg', '3 or 4 input parameters required ...');
    end

    if size (X,1) ~= size (T,1)
        error ('Biodata:msg', 'Size of X and T do not correspond ...');
    end
    
    Ind = INDFunc (X,T);
end

switch n
    case 2
        LogD = log10 (Ind(l+1,1)) - 2 * log10 (Ind(l,1)) + log10 (Ind(l-1,1));
    case 3
        LogD = log10 (Ind(l+2,1)) - 3 * log10 (Ind(l+1,1)) + 3 * log(Ind(l,1)) - log (Ind(l-1,1));
    case 'rod'
        LogD = (Ind(l-1,1) - Ind(l,1)) ./ (Ind(l,1) - Ind (l+1,1));
end