You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: productExact.m
    path of file: ./repos/Image-Harmonization-Dataset-iHarmony4/Lalonde and Efros/utils/3rd_party/@kde
    
    the code of the file until where you have to start completion: function dens = productExact(npd_placeholder, npdensities , analyticFns, analyticParams)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% productExact(kde,{kdes} [,{analyticFns},{analyticParams}]);
%          generate the exact density for the product of the input densities
%          this produces an N1xN2xN3x... particle density
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    
function dens = productExact(npd_placeholder, npdensities , analyticFns, analyticParams)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% productExact(kde,{kdes} [,{analyticFns},{analyticParams}]);
%          generate the exact density for the product of the input densities
%          this produces an N1xN2xN3x... particle density
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Copyright (C) 2003 Alexander Ihler; distributable under GPL -- see README.txt

  for i=1:length(npdensities)
    if (npdensities{i}.type ~= 0) error('Sorry! Product only works for Gaussian densities.'); end