Cherry is a decent belly wood, but it chrysalles easily. You have to tiller it perfectly, but if you do, it makes an excellent bow. Best to keep it wider and flat. I usually back it, but not with an over powering material (like bamboo). Maple works good.
Purpleheart? Don't know, but I use it a lot as a mid-lam in tri-lam ELBs. It works excellent in that application.