[mlpack-git] [mlpack/mlpack] Universal B tree implementation (#746)

[Ryan Curtin]

> +void CellBound<MetricType, ElemType>::AddBound(
> +    const arma::Col<ElemType>& loCorner,
> +    const arma::Col<ElemType>& hiCorner)
> +{
> +  assert(numBounds < loBound.n_cols);
> +  assert(loBound.n_rows == dim);
> +  assert(loCorner.n_elem == dim);
> +  assert(hiCorner.n_elem == dim);
> +
> +  // If the subrectangle is not contained entirely in the outer rectangle,
> +  // we shrink it.
> +  for (size_t k = 0; k < dim; k++)
> +  {
> +    loBound(k, numBounds) = std::max(loCorner[k], bounds[k].Lo());
> +
> +    hiBound(k, numBounds) = std::min(bounds[k].Hi(), hiCorner[k]);

I believe what you are doing here is, if possible, shrinking one of the UB hyperrectangles down using the minimum point-enclosing hyperrectangle. But I believe you could get a tighter bound if you instead iterated over all points, using only those that fall into this UB hyperrectangle, in order to shrink the UB hyperrectangle.  I guess it is easier to demonstrate what I mean with code...

```
math::Range r(loCorner[k], hiCorner[k]);
for (size_t j = 0; j < data.n_cols; ++j)
{
  if (hyperrectangle contains data.col(j))
  {
    r.Lo() = std::max(r.Lo(), data(k, j));
    r.Hi() = std::min(r.Hi(), data(k, j));
  }
}
```

The handling will become a little more tricky for operator|=(), but I believe this should help make the bounds tighter and decrease runtime. Let me know if I can clarify what I mean.
    

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