err_fuz.m

The neuro-fuzzy software for identification and data analysis has been implemented in the MATLAB lan

function [errors,Jacobian]=err_fuz(inputs,centers,bases,par,bias,output)

%ERR_FUZ
%
%  [errors,Jacobian]=err_fuz(inputs,centers,bases,par,bias,output)
%
%
%	errors[no_data,1]   	
%	Jacobian[no_data,2*no_rules*no_var]	Jacobian matrix of the 
%						derivatives of each error
%						to each premise parameter
%					
%	inputs[no_data,no_var]
%	centers[no_rules,no_var]    	centers of the membership functions
%	bases[no_rules,no_var]	     	bases   of the membership functions
%	par[no_rules,no_par]	     	parameters of the consequents
%	bias[1,1]
%	output[no_data,1]
%                                                                                              
%	The following global variable are required:                     
%		memb_fun:	'gaussian'/'triangular'                
% 		arch:		'weigthed'/'comb'                      
%		format_out:	'linear'/'constant'                       

%_______________________________________________________October 17 1996___

global memb_fun;
global arch;
global format_out;

[no_data,no_var]=size(inputs);
[no_rules,no_var]=size(centers);
[no_rules,no_par]=size(par);


H_temp=zeros(2*no_rules*no_var,2*no_rules*no_var);
grad_temp=zeros(2*no_rules*no_var,1);
J_temp=0;
errors=zeros(no_data,1);
Jacobian=zeros(no_data,2*no_rules*no_var);



%__________________________________________________________


for n=1:no_data
	
				
	if strcmp(format_out,'linear')
		yi=par*[inputs(n,:),1]';
	
	elseif strcmp(format_out,'constant')
		yi=par;
	end

		
	if strcmp(memb_fun,'gaussian')
		distances=ones(no_rules,1)*inputs(n,:)-centers;
		wij=exp(-(distances.^2)./bases);
		der_wij_centers=2*(distances./bases).*wij;
		der_wij_bases=((distances./bases).^2).*wij;
	
	elseif strcmp(memb_fun,'triangular')
		distances=ones(no_rules,1)*inputs(n,:)-centers;
		wij=max(0,ones(no_rules,no_var)-2*abs(distances./bases));	
		der_wij_centers=(2*sign(distances)./bases).*(wij>0);
		der_wij_bases=(2*abs(distances)./(bases).^2).*(wij>0);
	end



	if (no_var>1)
		wi = prod ( wij')';
	else
		wi=wij;
	end				% wi [no_rules,1]
	
	Sum_w_y= yi'*wi;		% yi [no_rules,1]

	Sum_w= sum(wi);

	if (Sum_w==0)	
		Sum_w=1;  
	end

	
	if strcmp(arch,'comb')
		y=Sum_w_y;
		der_y_wi=yi;
	
	elseif strcmp(arch,'weigthed')
		y=Sum_w_y / Sum_w;
		der_y_wi=(yi*Sum_w - Sum_w_y) / (Sum_w ^2);
	end
				% der_y_wi[no_rules,1]
				%is the derivative of the output
				%wrt the degree of match of each rule
	
	errors(n,1)=y+bias-output(n);

	der_wi_wij=(wi*ones(1,no_var))./(wij+(wij==0));
					% der_wi_wij[no_rules,no_var]

	der_wi_centers= der_wi_wij .* der_wij_centers;
	der_wi_bases= der_wi_wij .* der_wij_bases;


	der_y_centers= (der_y_wi*ones(1,no_var)).* der_wi_centers;
	der_y_bases= (der_y_wi *ones(1,no_var)).* der_wi_bases;

	Jacobian(n,:)=[der_y_centers(:);der_y_bases(:)]';
	
end