inv_li.m

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

function [SSE,par,bias]=inv_li(inputs,centers,bases,output)

%INV_LI		Inversion on the consequents for linear output models
%
%  [SSE,par,bias]=inv_li(inputs,centers,bases,output)
%
%	SSE[1,1]			Sum of the squeared errors
%	par[no_rules,no_var+1]		Parameters of the consequents
%	bias[1,1]			Shifts up or down all the
%					consequents 
%
%	inputs[no_data,no_var]
%	centers[no_rules,no_var]
%	bases[no_rules,no_var]
%	output[no_data,1]
%
%	The following global variable are required:                     
%		memb_fun:	'gaussian'/'triangular'                
% 		arch:		'weigthed'/'comb'                      
%		format_out:	'linear'/'constant'                       
%		model_bias:	'bias'/'no_bias'

%_______________________________________________________9 April 1996____


global memb_fun;
global arch;
global format_out;
global model_bias;

[no_data,no_var]=size(inputs);
[no_rules,no_var]=size(centers);
no_par=no_var+1;


w=ones(no_data,no_rules);	%Matrix of the degree of match of each
				%datum to the premise of each rule
Sum_w=zeros(no_data,1);

for i=1:no_rules
	for j=1:no_var
		if strcmp(memb_fun,'gaussian')
			match=exp(-((inputs(:,j)-centers(i,j)).^2)/bases(i,j));
		end

		if strcmp(memb_fun,'triangular')
			match=max(0,ones(no_data,1)-2*abs(inputs(:,j)-centers(i,j))/bases(i,j));
		end

		w(:,i)=w(:,i).*match;
	end

	Sum_w=Sum_w + w(:,i);
end

Sum_w=Sum_w+(Sum_w==0);

X=zeros(no_data,no_par*no_rules);

if strcmp(arch,'comb')
	in_ext=[inputs,ones(size(inputs,1),1)];
	for i=1:no_rules
		for j=1:no_par
			X(:,(i-1)*no_par+j)=w(:,i).*in_ext(:,j);
		end
	end
end

if strcmp(arch,'weigthed')
	in_ext=[inputs,ones(size(inputs,1),1)];
	for i=1:no_rules
		for j=1:no_par
			X(:,(i-1)*no_par+j)=(w(:,i)./Sum_w).*in_ext(:,j);
		end
	end
end




if strcmp(model_bias,'bias')
	A=[X,ones(no_data,1)];
	tol=1e-9;

	P_and_bias=pinv(A,tol)*output;

	P=P_and_bias(1:no_par*no_rules,:);
	bias=P_and_bias(no_par*no_rules+1,:);
end



if strcmp(model_bias,'no_bias')
	A=X;
	tol=1e-9;

	P=pinv(A,tol)*output;
	bias=0;
end



SSE=sumsqr(output-X*P-bias);

par=(reshape(P,no_par,no_rules))';