I've been using a variation of quickselect to find median rows of a matrix at certain columns.

There's a problem with quickselect: while it will find the median, it doesn't properly pivot the median around itself if the median occurs multiple times. So you could end up with the median sprinkled around both sides, which may or may not be a problem (it was for me).

One way to solve this is to take a second pass over the data to pivot -- which is essentially the core of QS where you nibble from both ends and swap low/high values.

Another nice property of QS is that it'll be approximately sorted, with values generally growing closer to the median towards the middle. This helps if you need to do repeated sub-selections on the partitions.