[petsc-users] Matvecs and KSPSolves with multiple vectors

[Pierre Jolivet]

To expand on Barry’s answer, we have observed repeatedly that MatMatMult with MatAIJ performs better than MatMult with MatMAIJ, you can reproduce this on your own with https://petsc.org/release/src/mat/tests/ex237.c.html.
Also, I’m guessing you are using some sort of preconditioner within your KSP.
Not all are “KSPMatSolve-ready”, i.e., they may treat blocks of right-hand sides column by column, which is very inefficient.
You could run your code with -info dump and send us dump.0 to see what needs to be done on our end to make things more efficient, should you not be satisfied with the current performance of the code.

Thanks,
Pierre

> On 7 Dec 2023, at 8:34 PM, Barry Smith <bsmith at petsc.dev> wrote:
> 
> 
> 
>> On Dec 7, 2023, at 1:17 PM, Sreeram R Venkat <srvenkat at utexas.edu> wrote:
>> 
>> I have 2 sequential matrices M and R (both MATSEQAIJCUSPARSE of size n x n) and a vector v of size n*m. v = [v_1 , v_2 ,... , v_m] where v_i has size n. The data for v can be stored either in column-major or row-major order.  Now, I want to do 2 types of operations:
>> 
>> 1. Matvecs of the form M*v_i = w_i, for i = 1..m. 
>> 2. KSPSolves of the form R*x_i = v_i, for i = 1..m.
>> 
>> From what I have read on the documentation, I can think of 2 approaches. 
>> 
>> 1. Get the pointer to the data in v (column-major) and use it to create a dense matrix V. Then do a MatMatMult with M*V = W, and take the data pointer of W to create the vector w. For KSPSolves, use KSPMatSolve with R and V.
>> 
>> 2. Create a MATMAIJ using M/R and use that for matvecs directly with the vector v. I don't know if KSPSolve with the MATMAIJ will know that it is a multiple RHS system and act accordingly.
>> 
>> Which would be the more efficient option?
> 
> Use 1. 
>> 
>> As a side-note, I am also wondering if there is a way to use row-major storage of the vector v.
> 
> No
> 
>> The reason is that this could allow for more coalesced memory access when doing matvecs.
> 
>   PETSc matrix-vector products use BLAS GMEV matrix-vector products for the computation so in theory they should already be well-optimized
> 
>> 
>> Thanks,
>> Sreeram

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