function [V, U, T, E] = Yf_FPCMC1_Step(X, V, c, m, eta)
%Yf_FPCMC1_Step One step in fuzzy-possibilistic c-mean clustering.
%
%   See Yf_FPCMC1.m  
%
%   Mahdi Amiri, June 20, 2003
%   http://yashil.20m.com/

n = size (X, 1);
p = size (X, 2);

dist = Yf_EuDistArrayOfVectors1 (V, X); % fill the distance matrix

% calculate new U, suppose m != 1
tmp = dist.^(-2/(m-1));      
U = tmp./(ones(c, 1)*sum(tmp));

% Correct the situation of "singularity" (one of the data points is
% exactly the same as one of the cluster centers).
si = find (tmp == Inf);
U(si) = 1;
if (size (si, 1) ~= 0)
    display ('FPCMC, Warning: Singularity occured and corrected.');
end

% calculate new T, suppose eta != 1
tmp = dist.^(-2/(eta-1));      
T = tmp./((sum(tmp')') * ones(1,n));

% Correct the situation of "singularity" (one of the data points is
% exactly the same as one of the cluster centers).
T(si) = 1; % Do more later

% Check constraint
tmp = find ((sum (T') - ones (1, c)) > 0.0001);
if (size(tmp,2) ~= 0)
    display ('FPCMC, Warning: Constraint for T is not hold.');
end

% Scale T
%maxU =  max(max(U));
%maxT =  max(max(T));
%if maxT < .5
%    ScF = .5 / maxT;
%    T = T * ScF;
%end

V_old = V;
Us = U.^m;
Ts = T.^eta;
V = ((Us+Ts)*X) ./ ((ones(p, 1)*sum((Us+Ts)'))'); % new center

E = norm (V - V_old, 1);