Create noneigen discretization of the equispaced local state spaces

noneigen.m

function [MF, bins ] = noneigen( X, xx );
%% 
% X :: values to be binned
% xx :: cellarray for the local state space

dims = cumprod(cellfun(@(x)numel(x),xx));
%%
MF = zeros( size(X,1), ...
                dims(end) );

for ii = 1 : numel( dims );
    dx = mean( diff(xx{ii}))
    D = 1 - abs(bsxfun(@minus, X(:,ii), xx{ii})./dx);
    D(:) = ( D>=0 & D<=1 ) .* D;
    if ii == 1
        bins = xx{ii}';
        MF( :, 1 : dims(ii)) = D;
    else
        bins = [repmat(bins,numel(xx{ii}),1), reshape( ...
                                                    repmat(xx{ii}(:)' , size(bins, 1) ,1), dims(ii), 1) ];
        MF(:, 1 : dims(ii) ) = reshape( ...
                                bsxfun( @times, MF(:, 1 :  dims(ii-1) ) , permute( D, [ 1 3 2] ) ), ...
                                size(X,1),[])
    end
    
end


%% Check
% V = zeros( size(X,1), numel(xx));
% for jj = 1 : size(bins,2)
%     V(:,jj) = sum( bsxfun( @times, MF,  bins(:,jj)'), 2 );
% end

sample.m

% Sample points
X = rand(10,3);

% Three axes in the local state space
xx{1} = linspace(0,1,11);
xx{2} = linspace(0,1,5);
xx{3} = linspace(0,1,4);

[MF, bins ] = noneigen( X, xx );