CUDA Toolkit 12.4 (latest up to March 2024) doesn't provide xgetri function which is used in LAPACK for matrix inversion, in their cuSolver collection of LAPACK functions for dense matrices. I really don't know why they have not included xgetri in CUDA Toolkit, but if I want to implement matrix inversion using xgetrf+xgetrs, then I need to compose an identity matrix as right-hand-side which has leading dimension like the coefficient matrix and just fill its diagonal with one and leave large part of the memory on the device i.e., graphic card as zeros. This is not optimal from memory point of view, so I am wondering if anyone has any suggestion to do this task efficiently? I was also wondering if right-hand-side matrix (identity matrix in this case) can be stored in sparse format, but the library doesn't support it.
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