%--------------------------------------------------------------------------
%      Exp_Reg is function developped by J.C. COMTE  comtejc@gmail.com
%                              CNC  UMR CNRS 5229.
%                          Last Release  July. 2007
%         This work is protected by the CeCILL-C Licence (see below).
%
%
%  x and y are two unidimensional vector.
%  c is a caracter indicating the expential direction.
%  p or P -> Growing, n or N -> Decreasing.
%  
%  a, b, L are the coefficients of the exponential relation y=A+B e^(L x)
%  x and Y returns the data fitting.
%
%
%  
% This software is governed by the [CeCILL|CeCILL-B|CeCILL-C] license under
%French law and
% abiding by the rules of distribution of free software.  You can  use, 
% modify and/ or redistribute the software under the terms of the 
%[CeCILL|CeCILL-B|CeCILL-C]
% license as circulated by CEA, CNRS and INRIA at the following URL
% "http://www.cecill.info". 
% 
% As a counterpart to the access to the source code and  rights to copy,
% modify and redistribute granted by the license, users are provided only
% with a limited warranty  and the software's author,  the holder of the
% economic rights,  and the successive licensors  have only  limited
% liability. 
% 
% In this respect, the user's attention is drawn to the risks associated
% with loading,  using,  modifying and/or developing or reproducing the
% software by the user in light of its specific status of free software,
% that may mean  that it is complicated to manipulate,  and  that  also
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%--------------------------------------------------------------------------


function [A B L x Y]=Exp_Reg(x,y,c)

if (c=='n'|| c=='N')
  ordr=8;
elseif (c=='p'||c=='P')
 ordr=5;
end;

[P,X,Y]=Poly_Reg(x,y,ordr);

L=2*P(ordr-1)/P(ordr);
B=P(ordr)/L;
A=P(ordr+1)-B;

if (c=='n'|| c=='N')
n=int32(size(X,2)/2);
X=X(1,1:n);
Y=Y(1,1:n);
elseif (c=='p'||c=='P')
n=int32(size(X,2));
X=X(1,n/2:n);
Y=Y(1,n/2:n);
end;
    

Y=log(Y-A);
[L b]=Lin_Reg(X,Y);

B=real(exp(b));
L=real(L);
Y=real(A+B*exp(L*x));