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: euclideanfactory.m
    path of file: ./repos/lrslibrary/libs/manopt/manopt/manifolds/euclidean
    
    the code of the file until where you have to start completion: function M = euclideanfactory(m, n)
% Returns a manifold struct to optimize over m-by-n matrices.
%
% function M = euclideanfactory(m, n)
%
% Returns M, a structure describing the Euclidean space of m-by-n matrices
% equipped with the standard Frobenius distance and associated trace inner
% product as a manifold for Manopt.

% This file is part of Manopt: www.manopt.org.
% Original author: Nicolas Boumal, Dec. 30, 2012.
% Contributors: 
% Change log: 
%  July 5, 2013 (NB): added egred2rgrad, ehess2rhess, mat, vec, tangent.


    
function M = euclideanfactory(m, n)
% Returns a manifold struct to optimize over m-by-n matrices.
%
% function M = euclideanfactory(m, n)
%
% Returns M, a structure describing the Euclidean space of m-by-n matrices
% equipped with the standard Frobenius distance and associated trace inner
% product as a manifold for Manopt.

% This file is part of Manopt: www.manopt.org.
% Original author: Nicolas Boumal, Dec. 30, 2012.
% Contributors: 
% Change log: 
%  July 5, 2013 (NB): added egred2rgrad, ehess2rhess, mat, vec, tangent.

    
    if ~exist('n', 'var') || isempty(n)
        n = 1;
    end