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: basicexample.m
    path of file: ./repos/lrslibrary/libs/manopt/checkinstall
    
    the code of the file until where you have to start completion: function basicexample
    
    % Verify that Manopt was indeed added to the Matlab path.

    
function basicexample
    
    % Verify that Manopt was indeed added to the Matlab path.
    if isempty(which('spherefactory'))
        error(['You should first add Manopt to the Matlab path.\n' ...
		       'Please run importmanopt first.']);
    end
    
    % Generate the problem data.
    n = 1000;
    A = randn(n);
    A = .5*(A+A');
    
    % Create the problem structure.
    manifold = spherefactory(n);
    problem.M = manifold;
    
    % Define the problem cost function and its gradient.
    problem.cost = @(x) -x'*(A*x);
    problem.grad = @(x) manifold.egrad2rgrad(x, -2*A*x);
    
    % Numerically check gradient consistency.
    checkgradient(problem);
 
    % Solve.
    % The trust-regions algorithm requires the Hessian. Since we do not
    % provide it, it will go for a standard approximation of it. The first
    % instruction tells Manopt not to issue a warning when this happens.
    warning('off', 'manopt:getHessian:approx');
    [x xcost info] = trustregions(problem); %#ok<ASGLU>
    
    % Display some statistics.
    figure;
    semilogy([info.iter], [info.gradnorm], '.-');
    xlabel('Iteration #');
    ylabel('Gradient norm');
    title('Convergence of the trust-regions algorithm on the sphere');
    
end