My definition is lacking how.. I mean, there are more functions and word types, these are just examples.
The point I was trying to make is that 'up' is certainly a preposition, but thinking in groups of meaning, as when you assign syntax within a clause, 'threw up' constitutes one, and further analysis does nothing to improve ones understanding, in fact the opposite is the case.
In the grammar I learned long ago one could call it a prepositional clause or a verb clause post modified by a preposition, but a descriptive language like grammatical analysis often forces conclusions that are irrelevant.