<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body style="overflow-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;"><div><br></div><div> If you switch to use the main branch of petsc <a href="https://petsc.org/release/install/download/#advanced-obtain-petsc-development-version-with-git">https://petsc.org/release/install/download/#advanced-obtain-petsc-development-version-with-git</a> you will not have the problem below (previously we required that a row exist before we zeroed it but now we allow the row to initially have no entries and still be zeroed.</div><div><br></div><div> Barry</div><div><br></div> <br><div><blockquote type="cite"><div>On Feb 3, 2023, at 1:04 PM, Karthikeyan Chockalingam - STFC UKRI <karthikeyan.chockalingam@stfc.ac.uk> wrote:</div><br class="Apple-interchange-newline"><div><meta charset="UTF-8"><div class="WordSection1" style="page: WordSection1; caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;"><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Thank you. The entire error output was an attachment in my previous email. I am pasting here for your reference.<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"><o:p> </o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"><o:p> </o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"><o:p> </o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">[1;31m[0]PETSC ERROR: --------------------- Error Message --------------------------------------------------------------<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">[0;39m[0;49m[0]PETSC ERROR: Object is in wrong state<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">[0]PETSC ERROR: Matrix is missing diagonal entry in row 0 (65792)<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">[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!<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">[0]PETSC ERROR: Option left: name:-options_left (no value)<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">[0]PETSC ERROR: See<span class="Apple-converted-space"> </span><a href="https://petsc.org/release/faq/" style="color: blue; text-decoration: underline;">https://petsc.org/release/faq/</a><span class="Apple-converted-space"> </span>for trouble shooting.<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">[0]PETSC ERROR: Petsc Development GIT revision: v3.18.1-127-ga207d08eda GIT Date: 2022-10-30 11:03:25 -0500<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">[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<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">[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<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">[0]PETSC ERROR: #1 MatZeroRowsColumns_SeqAIJ() at /Users/karthikeyan.chockalingam/AMReX/SRC_PKG/petsc/src/mat/impls/aij/seq/aij.c:2218<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">[0]PETSC ERROR: #2 MatZeroRowsColumns() at /Users/karthikeyan.chockalingam/AMReX/SRC_PKG/petsc/src/mat/interface/matrix.c:6085<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">[0]PETSC ERROR: #3 MatZeroRowsColumns_MPIAIJ() at /Users/karthikeyan.chockalingam/AMReX/SRC_PKG/petsc/src/mat/impls/aij/mpi/mpiaij.c:879<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">[0]PETSC ERROR: #4 MatZeroRowsColumns() at /Users/karthikeyan.chockalingam/AMReX/SRC_PKG/petsc/src/mat/interface/matrix.c:6085<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">[0]PETSC ERROR: #5 MatZeroRowsColumnsIS() at /Users/karthikeyan.chockalingam/AMReX/SRC_PKG/petsc/src/mat/interface/matrix.c:6124<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">[0]PETSC ERROR: #6 localAssembly() at /Users/karthikeyan.chockalingam/AMReX/amrFEM/src/FENodalPoisson.cpp:435<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> Residual norms for redistribute_ solve.<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> 0 KSP preconditioned resid norm 5.182603110407e+00 true resid norm 1.382027496109e+01 ||r(i)||/||b|| 1.000000000000e+00<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> 1 KSP preconditioned resid norm 1.862430383976e+00 true resid norm 4.966481023937e+00 ||r(i)||/||b|| 3.593619546588e-01<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> 2 KSP preconditioned resid norm 2.132803507689e-01 true resid norm 5.687476020503e-01 ||r(i)||/||b|| 4.115313216645e-02<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> 3 KSP preconditioned resid norm 5.499797533437e-02 true resid norm 1.466612675583e-01 ||r(i)||/||b|| 1.061203687852e-02<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> 4 KSP preconditioned resid norm 2.829814271435e-02 true resid norm 7.546171390493e-02 ||r(i)||/||b|| 5.460217985345e-03<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> 5 KSP preconditioned resid norm 7.431048995318e-03 true resid norm 1.981613065418e-02 ||r(i)||/||b|| 1.433844891652e-03<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> 6 KSP preconditioned resid norm 3.182040728972e-03 true resid norm 8.485441943932e-03 ||r(i)||/||b|| 6.139850305312e-04<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> 7 KSP preconditioned resid norm 1.030867020459e-03 true resid norm 2.748978721225e-03 ||r(i)||/||b|| 1.989091193167e-04<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> 8 KSP preconditioned resid norm 4.469429300003e-04 true resid norm 1.191847813335e-03 ||r(i)||/||b|| 8.623908111021e-05<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> 9 KSP preconditioned resid norm 1.237303313796e-04 true resid norm 3.299475503456e-04 ||r(i)||/||b|| 2.387416685085e-05<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> 10 KSP preconditioned resid norm 5.822094326756e-05 true resid norm 1.552558487134e-04 ||r(i)||/||b|| 1.123391894522e-05<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> 11 KSP preconditioned resid norm 1.735776150969e-05 true resid norm 4.628736402585e-05 ||r(i)||/||b|| 3.349236115503e-06<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> Linear redistribute_ solve converged due to CONVERGED_RTOL iterations 11<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">KSP Object: (redistribute_) 1 MPI process<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> type: cg<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> maximum iterations=10000, initial guess is zero<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> left preconditioning<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> using PRECONDITIONED norm type for convergence test<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">PC Object: (redistribute_) 1 MPI process<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> type: jacobi<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> type DIAGONAL<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> linear system matrix = precond matrix:<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> Mat Object: 1 MPI process<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> type: mpiaij<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> rows=48896, cols=48896<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> total: nonzeros=307976, allocated nonzeros=307976<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> total number of mallocs used during MatSetValues calls=0<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> not using I-node (on process 0) routines<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">End of program<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> solve time 0.564714744 seconds<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Starting max value is: 0<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Min value of level 0 is: 0<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Interpolated min value is: 741.978761<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Unused ParmParse Variables:<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> [TOP]::model.type(nvals = 1) :: [3]<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> [TOP]::ref_ratio(nvals = 1) :: [2]<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"><o:p> </o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">AMReX (22.10-20-g3082028e4287) finalized<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">#PETSc Option Table entries:<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">-ksp_type preonly<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">-options_left<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">-pc_type redistribute<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">-redistribute_ksp_converged_reason<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">-redistribute_ksp_monitor_true_residual<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">-redistribute_ksp_type cg<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">-redistribute_ksp_view<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">-redistribute_pc_type jacobi<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">#End of PETSc Option Table entries<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">There are no unused options.<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Program ended with exit code: 0<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"><o:p> </o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"><o:p> </o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Best,<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Karthik.<o:p></o:p></span></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"><o:p> </o:p></span></div><div style="border-style: solid none none; border-top-width: 1pt; border-top-color: rgb(181, 196, 223); padding: 3pt 0cm 0cm;"><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 10pt; font-family: Calibri, sans-serif;"><b><span style="font-size: 12pt;">From:<span class="Apple-converted-space"> </span></span></b><span style="font-size: 12pt;">Barry Smith <<a href="mailto:bsmith@petsc.dev" style="color: blue; text-decoration: underline;">bsmith@petsc.dev</a>><br><b>Date:<span class="Apple-converted-space"> </span></b>Friday, 3 February 2023 at 17:41<br><b>To:<span class="Apple-converted-space"> </span></b>Chockalingam, Karthikeyan (STFC,DL,HC) <<a href="mailto:karthikeyan.chockalingam@stfc.ac.uk" style="color: blue; text-decoration: underline;">karthikeyan.chockalingam@stfc.ac.uk</a>><br><b>Cc:<span class="Apple-converted-space"> </span></b><a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;">petsc-users@mcs.anl.gov</a><span class="Apple-converted-space"> </span><<a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;">petsc-users@mcs.anl.gov</a>><br><b>Subject:<span class="Apple-converted-space"> </span></b>Re: [petsc-users] Eliminating rows and columns which are zeros<o:p></o:p></span></p></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"><o:p> </o:p></span></div></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> We need all the error output for the errors you got below to understand why the errors are happening.<o:p></o:p></span></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"><br><br><o:p></o:p></span></div><blockquote style="margin-top: 5pt; margin-bottom: 5pt;"><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">On Feb 3, 2023, at 11:41 AM, Karthikeyan Chockalingam - STFC UKRI <<a href="mailto:karthikeyan.chockalingam@stfc.ac.uk" style="color: blue; text-decoration: underline;">karthikeyan.chockalingam@stfc.ac.uk</a>> wrote:<o:p></o:p></span></div></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"><o:p> </o:p></span></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Hello Barry,</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">I would like to better understand<span class="apple-converted-space"> </span>pc_type redistribute usage.<span class="apple-converted-space"> </span></span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">I am plan to use pc_type<span class="apple-converted-space"> </span><u>redistribute</u><span class="apple-converted-space"> </span>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.</span><o:p></o:p></div></div></div></blockquote><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"><o:p> </o:p></span></div></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> Indeed the linear solve will be more efficient if you use the redistribute solver. <o:p></o:p></span></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"><o:p> </o:p></span></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> 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).<br><br><o:p></o:p></span></div><blockquote style="margin-top: 5pt; margin-bottom: 5pt;"><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Question (1)</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">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<span class="apple-converted-space"><u> </u></span>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?<span class="apple-converted-space"><u> </u></span><u>Is this the correct usage?</u></span><o:p></o:p></div></div></div></blockquote><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"><o:p> </o:p></span></div></div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> See above<br><br><o:p></o:p></span></div><blockquote style="margin-top: 5pt; margin-bottom: 5pt;"><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Question (2)</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">I tried using pc_type redistribute for a two level system.</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">I have<span class="apple-converted-space"> </span><b><u>attached</u></b><span class="apple-converted-space"> </span>the output only for (level 1)</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">The solution converges to right solution but still petsc outputs some error messages.</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">[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!</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">[0]PETSC ERROR: Option left: name:-options_left (no value)</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">But the there were no unused options</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">#PETSc Option Table entries:</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">-ksp_type preonly</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">-options_left</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">-pc_type redistribute</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">-redistribute_ksp_converged_reason</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">-redistribute_ksp_monitor_true_residual</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">-redistribute_ksp_type cg</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">-redistribute_ksp_view</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">-redistribute_pc_type jacobi</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">#End of PETSc Option Table entries</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><b><span style="font-size: 11pt;">There are no unused options.</span></b><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Program ended with exit code: 0</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><o:p> </o:p></div></div></div></blockquote><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">I cannot explain this<br><br><o:p></o:p></span></div><blockquote style="margin-top: 5pt; margin-bottom: 5pt;"><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"><br>Question (2)</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif; background-color: white;"><span style="font-size: 11pt;">[0;39m[0;49m[0]PETSC ERROR: Object is in wrong state</span><span style="font-size: 8.5pt; font-family: Menlo;"><o:p></o:p></span></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif; background-color: white;"><span style="font-size: 11pt;">[0]PETSC ERROR: Matrix is missing diagonal entry in row 0 (65792)</span><span style="font-size: 8.5pt; font-family: Menlo;"><o:p></o:p></span></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">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.<span class="apple-converted-space"> </span><u>Is my understanding correct?</u></span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Question (3)<br><br><br></span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif; background-color: white;"><span style="font-size: 8.5pt; font-family: Menlo;">[0]PETSC ERROR: #5 MatZeroRowsColumnsIS() at /Users/karthikeyan.chockalingam/AMReX/SRC_PKG/petsc/src/mat/interface/matrix.c:6124</span><span style="font-size: 8.5pt; font-family: Menlo;"><o:p></o:p></span></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif; background-color: white;"><span style="font-size: 8.5pt; font-family: Menlo;"> </span><span style="font-size: 8.5pt; font-family: Menlo;"><o:p></o:p></span></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">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.</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Thank you for your help.</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Kind regards,</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Karthik.</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif; background-color: white;"><span style="font-size: 8.5pt; font-family: Menlo;"> </span><span style="font-size: 8.5pt; font-family: Menlo;"><o:p></o:p></span></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div style="border-style: solid none none; border-top-width: 1pt; border-top-color: rgb(181, 196, 223); padding: 3pt 0cm 0cm;"><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 10pt; font-family: Calibri, sans-serif;"><b><span style="font-size: 12pt;">From:<span class="apple-converted-space"> </span></span></b><span style="font-size: 12pt;">Barry Smith <<a href="mailto:bsmith@petsc.dev" style="color: blue; text-decoration: underline;">bsmith@petsc.dev</a>><br><b>Date:<span class="apple-converted-space"> </span></b>Tuesday, 10 January 2023 at 18:50<br><b>To:<span class="apple-converted-space"> </span></b>Chockalingam, Karthikeyan (STFC,DL,HC) <<a href="mailto:karthikeyan.chockalingam@stfc.ac.uk" style="color: blue; text-decoration: underline;">karthikeyan.chockalingam@stfc.ac.uk</a>><br><b>Cc:<span class="apple-converted-space"> </span></b><a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;">petsc-users@mcs.anl.gov</a><span class="apple-converted-space"> </span><<a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;">petsc-users@mcs.anl.gov</a>><br><b>Subject:<span class="apple-converted-space"> </span></b>Re: [petsc-users] Eliminating rows and columns which are zeros</span><o:p></o:p></p></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> 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.</span><o:p></o:p></div></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> Barry</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"><br><br><br></span><o:p></o:p></div></div><blockquote style="margin-top: 5pt; margin-bottom: 5pt;"><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">On Jan 10, 2023, at 11:25 AM, Karthikeyan Chockalingam - STFC UKRI <<a href="mailto:karthikeyan.chockalingam@stfc.ac.uk" style="color: blue; text-decoration: underline;">karthikeyan.chockalingam@stfc.ac.uk</a>> wrote:</span><o:p></o:p></div></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Thank you Barry. This is great!</span><o:p></o:p></div></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">I plan to solve using ‘-pc_type redistribute’ after applying the Dirichlet bc using</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif; background-color: white;"><span class="s1"><span style="font-size: 9pt; font-family: Menlo; color: rgb(108, 54, 169);">MatZeroRowsColumnsIS</span></span><span style="font-size: 9pt; font-family: Menlo;">(</span><span class="s2"><span style="font-size: 9pt; font-family: Menlo; color: rgb(50, 109, 116);">A</span></span><span style="font-size: 9pt; font-family: Menlo;">,<span class="apple-converted-space"> </span></span><span class="s2"><span style="font-size: 9pt; font-family: Menlo; color: rgb(50, 109, 116);">isout</span></span><span style="font-size: 9pt; font-family: Menlo;">,<span class="apple-converted-space"> </span></span><span class="s3"><span style="font-size: 9pt; font-family: Menlo; color: rgb(28, 0, 207);">1</span></span><span style="font-size: 9pt; font-family: Menlo;">,<span class="apple-converted-space"> </span></span><span class="s2"><span style="font-size: 9pt; font-family: Menlo; color: rgb(50, 109, 116);">x</span></span><span style="font-size: 9pt; font-family: Menlo;">,<span class="apple-converted-space"> </span></span><span class="s2"><span style="font-size: 9pt; font-family: Menlo; color: rgb(50, 109, 116);">b)</span></span><span style="font-size: 9pt; font-family: Menlo;">;<span class="apple-converted-space"> </span></span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif; background-color: white;"><span style="font-size: 9pt; font-family: Menlo;"> </span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">While I retrieve the solution data from x (after the solve) – can I index them using the original ordering (if I may say that)?</span><o:p></o:p></div></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Kind regards,</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Karthik.</span><o:p></o:p></div></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div style="border-style: solid none none; border-top-width: 1pt; border-top-color: rgb(181, 196, 223); padding: 3pt 0cm 0cm;"><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 10pt; font-family: Calibri, sans-serif;"><b><span style="font-size: 12pt;">From:<span class="apple-converted-space"> </span></span></b><span style="font-size: 12pt;">Barry Smith <</span><a href="mailto:bsmith@petsc.dev" style="color: blue; text-decoration: underline;"><span style="font-size: 12pt;">bsmith@petsc.dev</span></a><span style="font-size: 12pt;">><br><b>Date:<span class="apple-converted-space"> </span></b>Tuesday, 10 January 2023 at 16:04<br><b>To:<span class="apple-converted-space"> </span></b>Chockalingam, Karthikeyan (STFC,DL,HC) <</span><a href="mailto:karthikeyan.chockalingam@stfc.ac.uk" style="color: blue; text-decoration: underline;"><span style="font-size: 12pt;">karthikeyan.chockalingam@stfc.ac.uk</span></a><span style="font-size: 12pt;">><br><b>Cc:<span class="apple-converted-space"> </span></b></span><a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;"><span style="font-size: 12pt;">petsc-users@mcs.anl.gov</span></a><span class="apple-converted-space"><span style="font-size: 12pt;"> </span></span><span style="font-size: 12pt;"><</span><a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;"><span style="font-size: 12pt;">petsc-users@mcs.anl.gov</span></a><span style="font-size: 12pt;">><br><b>Subject:<span class="apple-converted-space"> </span></b>Re: [petsc-users] Eliminating rows and columns which are zeros</span><o:p></o:p></p></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><a href="https://petsc.org/release/docs/manualpages/PC/PCREDISTRIBUTE/#pcredistribute" style="color: blue; text-decoration: underline;"><span style="font-size: 11pt;">https://petsc.org/release/docs/manualpages/PC/PCREDISTRIBUTE/#pcredistribute</span></a><span style="font-size: 11pt;"> -pc_type redistribute</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div><div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">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.</span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div><div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Barry</span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div><div><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"><br><br></span><o:p></o:p></p></div></div><blockquote style="margin-top: 5pt; margin-bottom: 5pt;"><div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">On Jan 10, 2023, at 10:30 AM, Karthikeyan Chockalingam - STFC UKRI via petsc-users <</span><a href="mailto:petsc-users@mcs.anl.gov" style="color: blue; text-decoration: underline;"><span style="font-size: 11pt;">petsc-users@mcs.anl.gov</span></a><span style="font-size: 11pt;">> wrote:</span><o:p></o:p></div></div></div></div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Hello,</span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div><div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">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.</span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div><div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">For instance say N=7</span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div><div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif; background-color: white;"><span style="font-size: 9pt; font-family: Menlo; color: rgb(93, 108, 121);">0 0<span class="apple-converted-space"> </span>0<span class="apple-converted-space"> </span>0 0 0 0</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif; background-color: white;"><span style="font-size: 9pt; font-family: Menlo; color: rgb(93, 108, 121);">0 1 -1<span class="apple-converted-space"> </span>0 0 0 0</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif; background-color: white;"><span style="font-size: 9pt; font-family: Menlo; color: rgb(93, 108, 121);">0 -1 2<span class="apple-converted-space"> </span>0 0 0 -1</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif; background-color: white;"><span style="font-size: 9pt; font-family: Menlo; color: rgb(93, 108, 121);">0 0<span class="apple-converted-space"> </span>0<span class="apple-converted-space"> </span>0 0 0 0</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif; background-color: white;"><span style="font-size: 9pt; font-family: Menlo; color: rgb(93, 108, 121);">0 0<span class="apple-converted-space"> </span>0<span class="apple-converted-space"> </span>0 0 0 0</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif; background-color: white;"><span style="font-size: 9pt; font-family: Menlo; color: rgb(93, 108, 121);">0 0<span class="apple-converted-space"> </span>0<span class="apple-converted-space"> </span>0 0 0 0</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif; background-color: white;"><span style="font-size: 9pt; font-family: Menlo; color: rgb(93, 108, 121);">0 0<span class="apple-converted-space"> </span>-1 0 0 0 1</span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div><div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">I would like to reduce it to a 3x3</span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div><div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">1 -1 0</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">-1 2 -1</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">0 -1 1</span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div><div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">I do know the size N.</span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div><div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Q1) How do I do it?</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Q2) Is it better to eliminate them as it would save a lot of memory?</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">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?</span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div><div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Thank you.</span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div><div><div><div><div style="margin: 0cm; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;">Karthik.</span><o:p></o:p></div></div></div></div><p style="caret-color: rgb(0, 0, 0); font-variant-caps: normal; text-align: start; -webkit-text-stroke-width: 0px; word-spacing: 0px;"><span style="font-size: 6pt; font-family: Helvetica;">This email and any attachments are intended solely for the use of the named recipients. 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