<p>In <a href="https://github.com/mlpack/mlpack/pull/726#discussion_r74999041">src/mlpack/core/tree/binary_space_tree/rp_tree_mean_split_impl.hpp</a>:</p>
<pre style='color:#555'>&gt; +{
&gt; +  ElemType dist = 0;
&gt; +
&gt; +  for (size_t i = 0; i &lt; samples.n_elem; i++)
&gt; +    for (size_t j = i + 1; j &lt; samples.n_elem; j++)
&gt; +      dist += metric::SquaredEuclideanDistance::Evaluate(data.col(samples[i]),
&gt; +          data.col(samples[j]));
&gt; +
&gt; +  dist /= (samples.n_elem * (samples.n_elem - 1) / 2);
&gt; +
&gt; +  return dist;
&gt; +}
&gt; +
&gt; +template&lt;typename BoundType, typename MatType&gt;
&gt; +void RPTreeMeanSplit&lt;BoundType, MatType&gt;::GetRandomDirection(
&gt; +    arma::Col&lt;ElemType&gt;&amp; direction)
</pre>
<p>Ah actually, the function is already there!  <code>math::RandVector()</code>.  Maybe it would be useful to add an overload with a parameter that allows you to select the number of dimensions.  Note that selecting a random vector by uniformly sampling and then normalizing as you've done here actually causes bias, because you want to uniformly sample from the surface of a sphere.  I believe the implementation Nishant wrote many years ago uses the Box-Muller transform:</p>

<p><a href="https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform">https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform</a></p>

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