daniele@160: function varargout = Spark(obj)
daniele@160: % Calculates the minimum number of linearly dependent atoms in the matrix A
daniele@160: % WARNING: this function computes a combinatorial function, use only if the
daniele@160: % size of the problem is small (i.e. <20)
daniele@160: if nargout <= 1
daniele@160:     A = obj.phi;
daniele@160:     k = size(A,2);
daniele@160:     if k>20
daniele@160:         warning('This function computes a combinatorial function, use only if thesize of the problem is small (i.e. <20).');
daniele@160:         choice = input('The calculation of spark will take a long time... do you wish to continue anyway (y/n)','s');
daniele@160:         if strcmpi( choice,'n')
daniele@160:             return
daniele@160:         end
daniele@160:     end
daniele@160:     sigma = 2;
daniele@160:     while true
daniele@160:         P = nchoosek(1:k,sigma);
daniele@160:         for i=1:size(P,1)
daniele@160:             r = rank(A(:,P(i,:)));
daniele@160:             if r<sigma
daniele@160:                 varargout{1} = sigma;
daniele@160:                 return
daniele@160:             end
daniele@160:         end
daniele@160:         sigma = sigma + 1;
daniele@160:         if sigma==k
daniele@160:             varargout{1} = inf;
daniele@160:             return
daniele@160:         end
daniele@160:     end
daniele@160: else
daniele@160:     %% TODO: calculate lower and upper bounds on the spark
daniele@160:     varargout{1} = 2;
daniele@160:     varargout{2} = inf;
daniele@160: end