[petsc-users] Eliminating rows and columns which are zeros
Karthikeyan Chockalingam - STFC UKRI
karthikeyan.chockalingam at stfc.ac.uk
Fri Feb 3 17:21:44 CST 2023
Thanks Matt for your response.
I can confirm, I have the right size allocation for matrix. The linear system converges to the right solution.
But I do know, for a fact many rows in my matrix diagonal entrees are zeros (because I intentionally don’t assign anything).
Is that what is causing the problem? In other words do all diagonals have to be assigned a value (at least zero)?
Back to my first thread, I looking to do something like the below (and I assumed that all entrees in a matrix has an initial value of zero by creation)
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
Best,
Karthik.
From: Matthew Knepley <knepley at gmail.com>
Date: Friday, 3 February 2023 at 18:35
To: Chockalingam, Karthikeyan (STFC,DL,HC) <karthikeyan.chockalingam at stfc.ac.uk>
Cc: Barry Smith <bsmith at petsc.dev>, petsc-users at mcs.anl.gov <petsc-users at mcs.anl.gov>
Subject: Re: [petsc-users] Eliminating rows and columns which are zeros
On Fri, Feb 3, 2023 at 1:05 PM Karthikeyan Chockalingam - STFC UKRI via petsc-users <petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>> wrote:
Thank you. The entire error output was an attachment in my previous email. I am pasting here for your reference.
The options "-options_left" does not take effect until PetscFinalize(), but your program crashed before that ran, so it comes up as
not used in the error message, but then it runs and it is used.
The main problem is that you have not preallocated the matrix to match your input.
Thanks,
Matt
[1;31m[0]PETSC ERROR: --------------------- Error Message --------------------------------------------------------------
[0;39m[0;49m[0]PETSC ERROR: Object is in wrong state
[0]PETSC ERROR: Matrix is missing diagonal entry in row 0 (65792)
[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)
[0]PETSC ERROR: See https://petsc.org/release/faq/ for trouble shooting.
[0]PETSC ERROR: Petsc Development GIT revision: v3.18.1-127-ga207d08eda GIT Date: 2022-10-30 11:03:25 -0500
[0]PETSC ERROR: /Users/karthikeyan.chockalingam/AMReX/amrFEM/build/Debug/amrFEM on a named HC20210312 by karthikeyan.chockalingam Fri Feb 3 11:10:01 2023
[0]PETSC ERROR: Configure options --with-debugging=0 --prefix=/Users/karthikeyan.chockalingam/AMReX/petsc --download-fblaslapack=yes --download-scalapack=yes --download-mumps=yes --with-hypre-dir=/Users/karthikeyan.chockalingam/AMReX/hypre/src/hypre
[0]PETSC ERROR: #1 MatZeroRowsColumns_SeqAIJ() at /Users/karthikeyan.chockalingam/AMReX/SRC_PKG/petsc/src/mat/impls/aij/seq/aij.c:2218
[0]PETSC ERROR: #2 MatZeroRowsColumns() at /Users/karthikeyan.chockalingam/AMReX/SRC_PKG/petsc/src/mat/interface/matrix.c:6085
[0]PETSC ERROR: #3 MatZeroRowsColumns_MPIAIJ() at /Users/karthikeyan.chockalingam/AMReX/SRC_PKG/petsc/src/mat/impls/aij/mpi/mpiaij.c:879
[0]PETSC ERROR: #4 MatZeroRowsColumns() at /Users/karthikeyan.chockalingam/AMReX/SRC_PKG/petsc/src/mat/interface/matrix.c:6085
[0]PETSC ERROR: #5 MatZeroRowsColumnsIS() at /Users/karthikeyan.chockalingam/AMReX/SRC_PKG/petsc/src/mat/interface/matrix.c:6124
[0]PETSC ERROR: #6 localAssembly() at /Users/karthikeyan.chockalingam/AMReX/amrFEM/src/FENodalPoisson.cpp:435
Residual norms for redistribute_ solve.
0 KSP preconditioned resid norm 5.182603110407e+00 true resid norm 1.382027496109e+01 ||r(i)||/||b|| 1.000000000000e+00
1 KSP preconditioned resid norm 1.862430383976e+00 true resid norm 4.966481023937e+00 ||r(i)||/||b|| 3.593619546588e-01
2 KSP preconditioned resid norm 2.132803507689e-01 true resid norm 5.687476020503e-01 ||r(i)||/||b|| 4.115313216645e-02
3 KSP preconditioned resid norm 5.499797533437e-02 true resid norm 1.466612675583e-01 ||r(i)||/||b|| 1.061203687852e-02
4 KSP preconditioned resid norm 2.829814271435e-02 true resid norm 7.546171390493e-02 ||r(i)||/||b|| 5.460217985345e-03
5 KSP preconditioned resid norm 7.431048995318e-03 true resid norm 1.981613065418e-02 ||r(i)||/||b|| 1.433844891652e-03
6 KSP preconditioned resid norm 3.182040728972e-03 true resid norm 8.485441943932e-03 ||r(i)||/||b|| 6.139850305312e-04
7 KSP preconditioned resid norm 1.030867020459e-03 true resid norm 2.748978721225e-03 ||r(i)||/||b|| 1.989091193167e-04
8 KSP preconditioned resid norm 4.469429300003e-04 true resid norm 1.191847813335e-03 ||r(i)||/||b|| 8.623908111021e-05
9 KSP preconditioned resid norm 1.237303313796e-04 true resid norm 3.299475503456e-04 ||r(i)||/||b|| 2.387416685085e-05
10 KSP preconditioned resid norm 5.822094326756e-05 true resid norm 1.552558487134e-04 ||r(i)||/||b|| 1.123391894522e-05
11 KSP preconditioned resid norm 1.735776150969e-05 true resid norm 4.628736402585e-05 ||r(i)||/||b|| 3.349236115503e-06
Linear redistribute_ solve converged due to CONVERGED_RTOL iterations 11
KSP Object: (redistribute_) 1 MPI process
type: cg
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
left preconditioning
using PRECONDITIONED norm type for convergence test
PC Object: (redistribute_) 1 MPI process
type: jacobi
type DIAGONAL
linear system matrix = precond matrix:
Mat Object: 1 MPI process
type: mpiaij
rows=48896, cols=48896
total: nonzeros=307976, allocated nonzeros=307976
total number of mallocs used during MatSetValues calls=0
not using I-node (on process 0) routines
End of program
solve time 0.564714744 seconds
Starting max value is: 0
Min value of level 0 is: 0
Interpolated min value is: 741.978761
Unused ParmParse Variables:
[TOP]::model.type(nvals = 1) :: [3]
[TOP]::ref_ratio(nvals = 1) :: [2]
AMReX (22.10-20-g3082028e4287) finalized
#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
Best,
Karthik.
From: Barry Smith <bsmith at petsc.dev<mailto:bsmith at petsc.dev>>
Date: Friday, 3 February 2023 at 17:41
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
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<mailto: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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https://www.cse.buffalo.edu/~knepley/<http://www.cse.buffalo.edu/~knepley/>
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