topic dcsrilut routine parameter in Intel® oneAPI Math Kernel Library

dcsrilut routine parameter

lke — Wed, 22 Jan 2025 12:41:51 GMT

Hi,

I'm trying to use dcsrilut to create a ilut preconditioner for a sparse iterative solver.

But it seems that the parameter maxfil doesn't mean the number of extra calculated entries in addition to the original non-zeros in the rows of LU factors. According to the explanation in the manual " Maximum fill-in, which is half of the preconditioner bandwidth. The number of non-zero elements in the rows of the preconditioner cannot exceed (2*maxfil+1).", this is the number of total entries per row in LU factors.

Could anyone please clarify this? Do I misunderstand it, or is it different from the common meaning of maxfil for ilut? Thanks in advance.

Regards,

Re:dcsrilut routine parameter

Aleksandra_K — Mon, 10 Feb 2025 11:47:07 GMT

Hi,

I think the misunderstanding comes from the variety of definitions of the matrix bandwidth in the literature (it can be defined as a sum, sum+1 or max of upper and lower bandwidths). Using this terminology, the maxfil parameter corresponds to the maximum of lower and upper bandwidths of the preconditioner, thus the number of non-zero elements in the rows of the preconditioner is no bigger than 2*maxfil +1.

Could you provide a reference for the other (which you referred to as common) meaning of maxfil to help me further investigate the issue?

Regards,

Aleksandra

Re: Re:dcsrilut routine parameter

lke — Mon, 10 Feb 2025 13:14:14 GMT

Hi Aleksandra,

Thanks for your reply. I don't recall any specific reference, but some other iterative solvers adopt the following definition: numberofNonzero = 2*mafill+nL(i)+nU(i)+1, where nL and nU are the number of nonzero in the L and U parts of the i-th row of A, respectively.

But I don't think other solvers' implementation matters. What you have clarified is the only important thing to use correctly dcsrilut routine. Thanks for it.

Regards,