cuSOLVER automatically parallelizes computation on many matrices?

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I have to make same computations (for example, get eigenvalues of A1, A2, ...) on many(>10^15) matrices, so I want use threads as many as possible.

But I couldn't find cuBLAS or cuSOLVER codes stating number of threads. Does cuSOLVER automatically distribute resources and parallelize computations if I write code with for loop and cuSOLVER functions?
Or is there any cuSOLVER or cuBLAS API that I can control the number of threads and parallelize functions? ......

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Does cuSOLVER automatically distribute resources and parallelize computations if I write code with for loop and cuSOLVER functions?

No.

Or is there any cuSOLVER or cuBLAS API that I can control the number of threads and parallelize functions?

No.

But, if you care to read the CUSOLVER documentation, you will see that there is a batched sparse QR factorization routine. This can be used to solve eigenvalue problems.