[petsc-users] Eliminating rows and columns which are zeros

Barry Smith bsmith at petsc.dev
Fri Feb 3 11:40:44 CST 2023 

   We need all the error output for the errors you got below to understand why the errors are happening.

> On Feb 3, 2023, at 11:41 AM, Karthikeyan Chockalingam - STFC UKRI <karthikeyan.chockalingam at stfc.ac.uk> wrote:
> 
> Hello Barry,
>  
> I would like to better understand pc_type redistribute usage. 
>  
> I am plan to use pc_type redistribute in the context of adaptive mesh refinement on a structured grid in 2D. My base mesh (level 0) is indexed from 0 to N-1 elements and refined mesh (level 1) is indexed from 0 to 4(N-1) elements. When I construct system matrix A on (level 1); I probably only use 20% of 4(N-1)  elements, however the indexes are scattered in the range of 0 to 4(N-1). That leaves 80% of the rows and columns of the system matrix A on (level 1) to be zero. From your earlier response, I believe this would be a use case for petsc_type redistribute.

  Indeed the linear solve will be more efficient if you use the redistribute solver. 

  But I don't understand your plan. With adaptive refinement I would just create the two matrices, one for the initial grid on which you solve the system, this will be a smaller matrix and then create a new larger matrix for the refined grid (and discard the previous matrix).
>  
>  
> Question (1)
>  
>  
> If N is really large, I would have to allocate memory of size 4(N-1) for the system matrix A on (level 1). How does pc_type redistribute help? Because, I did end up allocating memory for a large system, where most of the rows and columns are zeros. Is most of the allotted memory not wasted? Is this the correct usage?

  See above
>  
>  
> Question (2)
>  
>  
> I tried using pc_type redistribute for a two level system.
> I have attached the output only for  (level 1)
> The solution converges to right solution but still petsc outputs some error messages.
>  
> [0]PETSC ERROR: WARNING! There are option(s) set that were not used! Could be the program crashed before they were used or a spelling mistake, etc!
> [0]PETSC ERROR: Option left: name:-options_left (no value)
>  
> But the there were no unused options
>  
> #PETSc Option Table entries:
> -ksp_type preonly
> -options_left
> -pc_type redistribute
> -redistribute_ksp_converged_reason
> -redistribute_ksp_monitor_true_residual
> -redistribute_ksp_type cg
> -redistribute_ksp_view
> -redistribute_pc_type jacobi
> #End of PETSc Option Table entries
> There are no unused options.
> Program ended with exit code: 0
> 
I cannot explain this
> 
> Question (2)
>  
> [0;39m[0;49m[0]PETSC ERROR: Object is in wrong state
> [0]PETSC ERROR: Matrix is missing diagonal entry in row 0 (65792)
>  
> What does this error message imply? Given I only use 20% of 4(N-1) indexes, I can imagine most of the diagonal entrees are zero. Is my understanding correct?
>  
>  
> Question (3)
> 
> [0]PETSC ERROR: #5 MatZeroRowsColumnsIS() at /Users/karthikeyan.chockalingam/AMReX/SRC_PKG/petsc/src/mat/interface/matrix.c:6124
>  
> I am using MatZeroRowsColumnsIS to set the homogenous Dirichelet boundary. I don’t follow why I get this error message as the linear system converges to the right solution.
>  
> Thank you for your help.
>  
> Kind regards,
> Karthik.
>  
>  
>  
> From: Barry Smith <bsmith at petsc.dev <mailto:bsmith at petsc.dev>>
> Date: Tuesday, 10 January 2023 at 18:50
> To: Chockalingam, Karthikeyan (STFC,DL,HC) <karthikeyan.chockalingam at stfc.ac.uk <mailto:karthikeyan.chockalingam at stfc.ac.uk>>
> Cc: petsc-users at mcs.anl.gov <mailto:petsc-users at mcs.anl.gov> <petsc-users at mcs.anl.gov <mailto:petsc-users at mcs.anl.gov>>
> Subject: Re: [petsc-users] Eliminating rows and columns which are zeros
> 
>  
>   Yes, after the solve the x will contain correct values for ALL the locations including the (zeroed out rows). You use case is exactly what redistribute it for.
>  
>   Barry
>  
> 
> 
> On Jan 10, 2023, at 11:25 AM, Karthikeyan Chockalingam - STFC UKRI <karthikeyan.chockalingam at stfc.ac.uk <mailto:karthikeyan.chockalingam at stfc.ac.uk>> wrote:
>  
> Thank you Barry. This is great!
>  
> I plan to solve using ‘-pc_type redistribute’ after applying the Dirichlet bc using
> MatZeroRowsColumnsIS(A, isout, 1, x, b); 
>  
> While I retrieve the solution data from x (after the solve) – can I index them using the original ordering (if I may say that)?
>  
> Kind regards,
> Karthik.
>  
> From: Barry Smith <bsmith at petsc.dev <mailto:bsmith at petsc.dev>>
> Date: Tuesday, 10 January 2023 at 16:04
> To: Chockalingam, Karthikeyan (STFC,DL,HC) <karthikeyan.chockalingam at stfc.ac.uk <mailto:karthikeyan.chockalingam at stfc.ac.uk>>
> Cc: petsc-users at mcs.anl.gov <mailto:petsc-users at mcs.anl.gov> <petsc-users at mcs.anl.gov <mailto:petsc-users at mcs.anl.gov>>
> Subject: Re: [petsc-users] Eliminating rows and columns which are zeros
> 
>  
> https://petsc.org/release/docs/manualpages/PC/PCREDISTRIBUTE/#pcredistribute   -pc_type redistribute
>  
>  
> It does everything for you. Note that if the right hand side for any of the "zero" rows is nonzero then the system is inconsistent and the system does not have a solution.
>  
> Barry
>  
> 
> 
> 
> On Jan 10, 2023, at 10:30 AM, Karthikeyan Chockalingam - STFC UKRI via petsc-users <petsc-users at mcs.anl.gov <mailto:petsc-users at mcs.anl.gov>> wrote:
>  
> Hello,
>  
> I am assembling a MATIJ of size N, where a very large number of rows (and corresponding columns), are zeros. I would like to potentially eliminate them before the solve.
>  
> For instance say N=7
>  
> 0 0  0  0 0 0 0
> 0 1 -1  0 0 0 0
> 0 -1 2  0 0 0 -1
> 0 0  0  0 0 0 0
> 0 0  0  0 0 0 0
> 0 0  0  0 0 0 0
> 0 0  -1 0 0 0 1
>  
> I would like to reduce it to a 3x3
>  
> 1 -1 0
> -1 2 -1
> 0 -1 1
>  
> I do know the size N.
>  
> Q1) How do I do it?
> Q2) Is it better to eliminate them as it would save a lot of memory?
> Q3) At the moment, I don’t know which rows (and columns) have the zero entries but with some effort I probably can find them. Should I know which rows (and columns) I am eliminating?
>  
> Thank you.
>  
> Karthik.
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>  
> <petsc_redistribute.txt>

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