Purgatory starts on the right side of the large roof. Thrash your way up the mossy, ferny offwidth to some dirty finger locks and then a good jug. From here traverse up and left in a very thin crack, to under the roof. There are at least two options for pulling over the roof and onto the cracked slab above.
On the left side of the Pearly Gates crag, to the right of Pearly Gates and the large roof.
Trad rack including very thin gear for the finger traverse, and a #4 Camalot makes the beginning feel much safer. Anchor is bolted and a 60m rope is long enough to TR.