CUSOLVER for linalg routines

[guillochon]

As the CULA library is effectively abandonware for the Mac (the free version links are broken and haven't been updated in 4 years), it is critical to have CUSOLVER working for all functions in order for skcuda to be useful on OS X.

Here's a running list of functions that should have the CUSOLVER option available within linalg that I believe currently don't:

• cho_solve
• inv
• qr
• eig (partially implemented)
• dmd

[lebedov]

svd and pinv already have cusolver support in the latest GitHub revision. eig has cusolver support when the input is symmetric/Hermitian.

[guillochon]

Ah, should the svd and pinv tests be enabled then for cusolver?

[lebedov]

There already are unit tests in place for svd/pinv cusolver support, e.g., here and here.

[lebedov]

cho_factor contains cusolver support.

[guillochon]

Oh great! For me at least, the one remaining function that would be great to have is cho_solve. Also inv seems like it should be higher priority.

[lebedov]

cho_solve now contains cusolver support.

[lebedov]

inv now contains cusolver support.

[lebedov]

qr now contains cusolver support.

[botev]

@lebedov Hi, does there exist any interface of cusolver for solving the linear system Ax=b where A is already upper or lower triangular (e.g. does not need the be factored). That is if we want to solve the system A^{-1/2} x = b and we already have L=A^{1/2} is there any interface to directly solve the system without going to factor L further?

[lebedov]

@botev, the cusolver*potrs and cusolver*getrs functions can be used to solve systems that have already been factorized with Cholesky or LU decomposition, respectively (the former is utilized in the cho_solve function, while the latter is used in the inv function). LAPACK does have a function for solving triangular systems (*tptrs), but I'm not aware of an equivalent in CUSOLVER.