What is the fastest way of appending an element to an array?

Question

This is a follow-up question to How to append an element to an array in MATLAB? That question addressed how to append an element to an array. Two approaches are discussed there:

A = [A elem]  % for a row array
A = [A; elem] % for a column array

and

A(end+1) = elem;

The second approach has the obvious advantage of being compatible with both row and column arrays.

However, this question is: which of the two approaches is fastest? My intuition tells me that the second one is, but I'd like some evidence for or against that. Any idea?

Answer 1

The second approach (A(end+1) = elem) is faster

According to the benchmarks below (run with the timeit benchmarking function from File Exchange), the second approach (A(end+1) = elem) is faster and should therefore be preferred.

Interestingly, though, the performance gap between the two approaches is much narrower in older versions of MATLAB than it is in more recent versions.

R2008a

R2013a

Benchmark code

function benchmark

    n = logspace(2, 5, 40);
    % n = logspace(2, 4, 40); 
    tf = zeros(size(n));
    tg = tf;

    for k = 1 : numel(n)
        x = rand(round(n(k)), 1);

        f = @() append(x);
        tf(k) = timeit(f);

        g = @() addtoend(x);
        tg(k) = timeit(g);
    end

    figure
    hold on
    plot(n, tf, 'bo')
    plot(n, tg, 'ro')
    hold off
    xlabel('input size')
    ylabel('time (s)')
    leg = legend('y = [y, x(k)]', 'y(end + 1) = x(k)');
    set(leg, 'Location', 'NorthWest');
end

% Approach 1: y = [y, x(k)];
function y = append(x)
    y = [];
    for k = 1 : numel(x);
        y = [y, x(k)];
    end
end

% Approach 2: y(end + 1) = x(k);
function y = addtoend(x)
    y = [];
    for k = 1 : numel(x);
        y(end + 1) = x(k);
    end
end