I have in mind to to use getrf and getrs from the cuSolver package and to solve AB=X with B=I.
Is this the most best way to solve this problem?
If so, what is the best way to create the col-major identity matrix B in device memory? It can be done trivially using a for loop but this would 1. take up a lot of memory and 2. be quite slow. Is there a faster way?
Note that cuSolver does not provide getri unfortunately. Therefore I must to use getrs.
Until CUDA provides the LAPACK API getri, I think getrf and getrs is the best choice for large matrix inversion.
The matrix B is of the same size as A, so I don't think allocating B makes this task consume much larger memory than its input/output data does.
The complexity of getrf and getrs are O(n^3) and O(n^2), respectively, while setting B=I is of O(n^2) + O(n). I don't think it should be a bottleneck of the whole procedure. You may share your implementation, so we could check where the problem could be.