The problem isn't that a particular library is AMD or NVIDIA only in terms of computation, but NVIDIA or AMD only in terms of performance. GPU implementations are usually optimised for a specific architecture, which is then the "supported" architecture.

On occasion, such implementations do use vendor specific tools (such as CUDA), but there are a plethora of tools such as OpenCL, SyCL etc that provide portability - but not always performance portability, meaning that they will still be tuned to a specific architecture.

For performance portability, the LIFT project (http://www.lift-project.org/) provides a partial solution. Our approach relies on a high level model of computation (think or something like a functional, or pattern based programming language) coupled with a rewrite-based compiler that explores the space of OpenCL programs with which to implement a computation.

That lets us "optimise" a given implementation to a specific architecture, entirely automatically, in a way that many other low level approaches simply aren't able to, as they contain too many implementation (rather than computation) details.