%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%     COPYRIGHT: 
%     Paul Harrison, Laurent Badel, Mark Wall and Magnus JE Richardson
%     (2014)
%     
%     This code 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 version 3. 
% 
%     This program 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.
% 
%     See <http://www.gnu.org/licenses/> for the GNU General Public License
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


function [ Data_gen_class,Variables ] = Generate_EIF( N )
%GENERATEEIF Generate populations of EIF neuron models of layer 2/3, 4,
%slender-tufted layer 5, and thick-tufted layer 5 pyramidal cells. Requires
%MATLAB Statistics toolbox. 
%   Input:
%       N = number of cells to generate. 4x1 vector consisting of the
%       number required for each class in the order stated above. If the
%       same number from each class are required just input a single
%       number.
%   Output:
%       Data_gen_class = 4x1 cell array where each element corresponds to 
%       the cell classes in the order stated above (Data_gen_class{1} are 
%       layer 2/3 cells etc.). Each element in the cell array is an N(k)*5
%       array of parameter values. Rows correspond to to model neurons and
%       columns are parameters [C,tau,E,VT,DT].
%       Variables = Cell array of variable names.

nClass=4;%Number of cell classes
if numel(N)==1
    N=N*ones(nClass,1);
end

%% Distribution Parameters
Variables={'C';'tau';'E';'VT';'DT'};
DistName={'logn';'logn';'norm';'norm';'logn'};
nVar=numel(DistName);%Number of EIF parameters
mu=[4.87 4.86 4.86 5.61;...%C
    2.67 2.82 2.88 2.9;...%tau
    -79.3 -71.8 -69.9 -68.5;...%E
    -49.5 -48.7 -49.7 -52.7;...%VT
    .227 .213 .235 .0836];%DT
sig=[.258 .289 .251 .273;...%C
    .171 .24 .255 .229;...%tau
    4.27 4.2 4.18 3.98;...%E
    3.81 3.53 3.56 3.59;...VT
    .359 .266 .361 .364];%DT

Rho{1}=...
   [1.0000 -0.2721  0.0042 -0.5636 -0.1307;
   -0.2721  1.0000 -0.1357  0.4244 -0.4509;
    0.0042 -0.1357  1.0000  0.4765 -0.0464;
   -0.5636  0.4244  0.4765  1.0000 -0.3097;
   -0.1307 -0.4509 -0.0464 -0.3097  1.0000];
Rho{2}=...
   [1.0000  0.1124  0.2056 -0.2430 -0.1318;
    0.1124  1.0000  0.2773 -0.0053 -0.1034;
    0.2056  0.2773  1.0000  0.3427 -0.3416;
   -0.2430 -0.0053  0.3427  1.0000 -0.4020;
   -0.1318 -0.1034 -0.3416 -0.4020  1.0000];
Rho{3}=...
   [1.0000  0.3380  0.4681 -0.1710 -0.2218;
    0.3380  1.0000  0.2582 -0.0344 -0.2067;
    0.4681  0.2582  1.0000  0.3974 -0.4300;
   -0.1710 -0.0344  0.3974  1.0000 -0.1410;
   -0.2218 -0.2067 -0.4300 -0.1410  1.0000];
Rho{4}=...
   [1.0000  0.0639  0.1435 -0.2865 -0.2151;
    0.0639  1.0000  0.0773 -0.0066 -0.2062;
    0.1435  0.0773  1.0000  0.3730  0.1508;
   -0.2865 -0.0066  0.3730  1.0000  0.1949;
   -0.2151 -0.2062  0.1508  0.1949  1.0000];

%% Generate Random Sample
Data_copula_gen=cell(nClass,1);
Data_gen_class=cell(nClass,1);
for k=1:nClass
    %Allocate memory
    Data_copula_gen{k}=zeros(N(k),nVar);
    Data_gen_class{k}=zeros(N(k),nVar);
        
    %Generate a random sample from the t copula
    Data_copula_gen{k}=copularnd('Gaussian',Rho{k},N(k));
    
    %Transform the random sample back to the original scale of the data
    for j=1:nVar
        Data_gen_class{k}(:,j)=icdf(DistName{j},Data_copula_gen{k}(:,j),...
            mu(j,k),sig(j,k));
    end
end

end