[petsc-users] Matvecs and KSPSolves with multiple vectors

[Barry Smith]

> 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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