Going strictly by the numbers, Ipe is 10% stiffer than purple heart, and ~8% more flexible. Ipe is also nearly 20% more dense.
On that analysis, you should be able to make your Purple Heart bow 20% wider than you would for ipe, and roughly 10% thinner back to belly and you should be in the ballpark.
I have never used purple heart, but have used a lot of ipe, and I have successfully used wood database to estimate the dimensions for alternative belly woods based on my Ipe designs.
I will say though, Purple Heart has a reputation for being brittle, suffering from compression fractures, and being extremely difficult to work ... although Ipe is a bear to work also.