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if (m > 1) { PetscBLASInt ione = 1, lda2 = (PetscBLASInt)lda; // the cast is safe since we've screened out those lda > PETSC_BLAS_INT_MAX above PetscScalar one = 1, zero = 0; PetscCallBLAS("BLASgemv", BLASgemv_(trans, &n, &m,
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<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 (m > 1) {</div><div> PetscBLASInt ione = 1, lda2 = (PetscBLASInt)lda; // the cast is safe since we've screened out those lda > PETSC_BLAS_INT_MAX above</div><div> PetscScalar one = 1, zero = 0;</div><div><br></div><div> PetscCallBLAS("BLASgemv", BLASgemv_(trans, &n, &m, &one, yarray, &lda2, xarray, &ione, &zero, z + i, &ione));</div><div> PetscCall(PetscLogFlops(PetscMax(m * (2.0 * n - 1), 0.0)));</div><div><br></div><div>The call to BLAS above is where it uses MKL.</div><div><br></div><div><br></div><div><br><blockquote type="cite"><div>On Jun 26, 2024, at 6:59 PM, Yongzhong Li <yongzhong.li@mail.utoronto.ca> 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: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">Hi Barry, I am looking into the source codes of VecMultiDot_Seq_GEMV</span><span lang="EN-US"><span class="Apple-converted-space"> </span></span><span lang="EN-US" style="font-size: 11pt;"><a href="https://urldefense.us/v3/__https://petsc.org/release/src/vec/vec/impls/seq/dvec2.c.html*VecMDot_Seq__;Iw!!G_uCfscf7eWS!YkdYdhSYNaujYHcsb6DHTn7qi2Cae0dZHw3sO7KUE55VZiuUPyXmKFJlSwNe0xr-uRcAZMgRLinheQIZsXxDJ9c$" style="color: purple; text-decoration: underline;">https://petsc.org/release/src/vec/vec/impls/seq/dvec2.c.html#VecMDot_Seq</a><br>Can I ask which lines of codes suggest the use of intel mkl?<br><br>Thanks,<o:p></o:p></span></div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">Yongzhong<o:p></o:p></span></div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"><o:p> </o:p></span></div><div id="mail-editor-reference-message-container"><div><div style="border-width: 1pt medium medium; border-style: solid none none; border-color: rgb(181, 196, 223) currentcolor currentcolor; border-image: none; padding: 3pt 0cm 0cm;"><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 12pt; font-family: Aptos, sans-serif;"><b><span style="">From:<span class="Apple-converted-space"> </span></span></b><span style="">Barry Smith <<a href="mailto:bsmith@petsc.dev" style="color: purple; text-decoration: underline;">bsmith@petsc.dev</a>><br><b>Date:<span class="Apple-converted-space"> </span></b>Wednesday, June 26, 2024 at 10:30</span><span style="font-family: Arial, sans-serif;"> </span><span style="">AM<br><b>To:<span class="Apple-converted-space"> </span></b>Yongzhong Li <<a href="mailto:yongzhong.li@mail.utoronto.ca" style="color: purple; text-decoration: underline;">yongzhong.li@mail.utoronto.ca</a>><br><b>Cc:<span class="Apple-converted-space"> </span></b><a href="mailto:petsc-users@mcs.anl.gov" style="color: purple; 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: purple; text-decoration: underline;">petsc-users@mcs.anl.gov</a>><br><b>Subject:<span class="Apple-converted-space"> </span></b>Re: [petsc-users] [petsc-maint] Assistance Needed with PETSc KSPSolve Performance Issue<o:p></o:p></span></p></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><o:p> </o:p></div></div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> In a debug version of PETSc run your application in a debugger and put a break point in VecMultiDot_Seq_GEMV. Then next through the code from that point to see what decision it makes about using dgemv() to see why it is not getting into the Intel code.<o:p></o:p></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><o:p> </o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><o:p> </o:p></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><br><br><o:p></o:p></div><blockquote style="margin-top: 5pt; margin-bottom: 5pt;"><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">On Jun 25, 2024, at 11:19<span style="font-family: Arial, sans-serif;"> </span>PM, Yongzhong Li <<a href="mailto:yongzhong.li@mail.utoronto.ca" style="color: purple; text-decoration: underline;">yongzhong.li@mail.utoronto.ca</a>> wrote:<o:p></o:p></div></div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><o:p> </o:p></div><div><div id="pfptBannerqgdldcn"><div id="pfptBannerqgdldcn"><div id="pfptBannerqgdldcn"><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-family: Arial, sans-serif;">This Message Is From an External Sender<o:p></o:p></span></div></div><div id="pfptBannerqgdldcn"><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-family: Arial, sans-serif;">This message came from outside your organization.<o:p></o:p></span></div></div></div></div><div><div><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">Hi Junchao, thank you for your help for these benchmarking test!<br><br>I check out to petsc/main and did a few things to verify from my side,<br><br>1. I ran the microbenchmark (vec/vec/tests/ex2k.c) test on my compute node. The results are as follow,</span><o:p></o:p></p></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">$ MKL_NUM_THREADS=64 ./ex2k -n 15 -m 4<br>Vector(N) VecMDot-1 VecMDot-3 VecMDot-8 VecMDot-30 (us)</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">--------------------------------------------------------------------------</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 128 14.5 1.2 1.8 5.2</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 256 1.5 0.9 1.6 4.7</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 512 2.7 2.8 6.1 13.2</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 1024 4.0 4.0 9.3 16.4</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 2048 7.4 7.3 11.3 39.3</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 4096 14.2 13.9 19.1 93.4</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 8192 28.8 26.3 25.4 31.3</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 16384 54.1 25.8 26.7 33.8</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 32768 109.8 25.7 24.2 56.0</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 65536 220.2 24.4 26.5 89.0</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 131072 424.1 31.5 36.1 149.6</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 262144 898.1 37.1 53.9 286.1</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 524288 1754.6 48.7 100.3 1122.2</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 1048576 3645.8 86.5 347.9 2950.4</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 2097152 7371.4 308.7 1440.6 6874.9</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">$ MKL_NUM_THREADS=1 ./ex2k -n 15 -m 4</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">Vector(N) VecMDot-1 VecMDot-3 VecMDot-8 VecMDot-30 (us)</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">--------------------------------------------------------------------------</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 128 14.9 1.2 1.9 5.2</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 256 1.5 1.0 1.7 4.7</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 512 2.7 2.8 6.1 12.0</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 1024 3.9 4.0 9.3 16.8</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 2048 7.4 7.3 10.4 41.3</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 4096 14.0 13.8 18.6 84.2</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 8192 27.0 21.3 43.8 177.5</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 16384 54.1 34.1 89.1 330.4</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 32768 110.4 82.1 203.5 781.1</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 65536 213.0 191.8 423.9 1696.4</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 131072 428.7 360.2 934.0 4080.0</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 262144 883.4 723.2 1745.6 10120.7</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 524288 1817.5 1466.1 4751.4 23217.2</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 1048576 3611.0 3796.5 11814.9 48687.7</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> 2097152 7401.9 10592.0 27543.2 106565.4</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"><br>I can see the speed up brought by more MKL threads, and if I set NKL_VERBOSE to 1, I can see something like</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><i><span lang="EN-US" style="font-size: 11pt;">MKL_VERBOSE ZGEMV(C,262144,8,0x7ffd375d6470,0x2ac76e7fb010,262144,0x16d0f40,1,0x7ffd375d6480,0x16435d0,1) 32.70us CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:6 ca<br><br></span></i><span lang="EN-US" style="font-size: 11pt;">From my understanding, the VecMDot()/VecMAXPY() can benefit from more MKL threads in my compute node and is using ZGEMV MKL BLAS.<br><br>However, when I ran my own program and set MKL_VERBOSE to 1, it is very strange that I still can’t find any MKL outputs, though I can see from the PETSc log that VecMDot and VecMAXPY() are called.</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"><br>I am wondering are VecMDot and VecMAXPY in KSPGMRESOrthog optimized in a way that is similar to ex2k test? Should I expect to see MKL outputs for whatever linear system I solve with KSPGMRES? Does it relate to if it is dense matrix or sparse matrix, although I am not really understand why VecMDot/MAXPY() have something to do with dense matrix-vector multiplication.<br><br>Thank you,</span><o:p></o:p></div></div><div><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">Yongzhong</span><o:p></o:p></p></div><div style="border-width: 1pt medium medium; border-style: solid none none; border-image: none; padding: 3pt 0cm 0cm; border-color: currentcolor;"><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 12pt; font-family: Aptos, sans-serif;"><b>From:<span class="apple-converted-space"> </span></b>Junchao Zhang <<a href="mailto:junchao.zhang@gmail.com" style="color: purple; text-decoration: underline;">junchao.zhang@gmail.com</a>><br><b>Date:<span class="apple-converted-space"> </span></b>Tuesday, June 25, 2024 at 6:34<span style="font-family: Arial, sans-serif;"> </span>PM<br><b>To:<span class="apple-converted-space"> </span></b>Matthew Knepley <<a href="mailto:knepley@gmail.com" style="color: purple; text-decoration: underline;">knepley@gmail.com</a>><br><b>Cc:<span class="apple-converted-space"> </span></b>Yongzhong Li <<a href="mailto:yongzhong.li@mail.utoronto.ca" style="color: purple; text-decoration: underline;">yongzhong.li@mail.utoronto.ca</a>>, Pierre Jolivet <<a href="mailto:pierre@joliv.et" style="color: purple; text-decoration: underline;">pierre@joliv.et</a>>,<span class="apple-converted-space"> </span><a href="mailto:petsc-users@mcs.anl.gov" style="color: purple; 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: purple; text-decoration: underline;">petsc-users@mcs.anl.gov</a>><br><b>Subject:<span class="apple-converted-space"> </span></b>Re: [petsc-users] [petsc-maint] Assistance Needed with PETSc KSPSolve Performance Issue<o:p></o:p></p></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">Hi, Yongzhong,<o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> Since the two kernels of KSPGMRESOrthog are VecMDot and VecMAXPY, if we can speed up the two with OpenMP threads, then we can speed up KSPGMRESOrthog. We recently added an optimization to do VecMDot/MAXPY() in dense matrix-vector multiplication (i.e., BLAS2 GEMV, with tall-and-skinny matrices ). So with MKL_VERBOSE=1, you should see something like "MKL_VERBOSE ZGEMV ..." in output. If not, could you try again with petsc/main?<o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> petsc has a microbenchmark (vec/vec/tests/ex2k.c) to test them. I ran VecMDot with multithreaded oneMKL (via setting MKL_NUM_THREADS), it was strange to see no speedup. I then configured petsc with openblas, I did see better performance with more threads<o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-family: "Courier New";">$ OMP_PROC_BIND=spread OMP_NUM_THREADS=1 ./ex2k -n 15 -m 4<br>Vector(N) VecMDot-3 VecMDot-8 VecMDot-30 (us)<br>--------------------------------------------------------------------------<br> 128 2.0 2.5 6.1<span class="apple-converted-space"> </span><br> 256 1.8 2.7 7.0<span class="apple-converted-space"> </span><br> 512 2.1 3.1 8.6<span class="apple-converted-space"> </span><br> 1024 2.7 4.0 12.3<span class="apple-converted-space"> </span><br> 2048 3.8 6.3 28.0<span class="apple-converted-space"> </span><br> 4096 6.1 10.6 42.4<span class="apple-converted-space"> </span><br> 8192 10.9 21.8 79.5<span class="apple-converted-space"> </span><br> 16384 21.2 39.4 149.6<span class="apple-converted-space"> </span><br> 32768 45.9 75.7 224.6<span class="apple-converted-space"> </span><br> 65536 142.2 215.8 732.1<span class="apple-converted-space"> </span><br> 131072 169.1 233.2 1729.4<span class="apple-converted-space"> </span><br> 262144 367.5 830.0 4159.2<span class="apple-converted-space"> </span><br> 524288 999.2 1718.1 8538.5<span class="apple-converted-space"> </span><br> 1048576 2113.5 4082.1 18274.8<span class="apple-converted-space"> </span><br> 2097152 5392.6 10273.4 43273.4 </span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-family: "Courier New";">$ OMP_PROC_BIND=spread OMP_NUM_THREADS=8 ./ex2k -n 15 -m 4<br>Vector(N) VecMDot-3 VecMDot-8 VecMDot-30 (us)<br>--------------------------------------------------------------------------<br> 128 2.0 2.5 6.0<span class="apple-converted-space"> </span><br> 256 1.8 2.7 15.0<span class="apple-converted-space"> </span><br> 512 2.1 9.0 16.6<span class="apple-converted-space"> </span><br> 1024 2.6 8.7 16.1<span class="apple-converted-space"> </span><br> 2048 7.7 10.3 20.5<span class="apple-converted-space"> </span><br> 4096 9.9 11.4 25.9<span class="apple-converted-space"> </span><br> 8192 14.5 22.1 39.6<span class="apple-converted-space"> </span><br> 16384 25.1 27.8 67.8<span class="apple-converted-space"> </span><br> 32768 44.7 95.7 91.5<span class="apple-converted-space"> </span><br> 65536 82.1 156.8 165.1<span class="apple-converted-space"> </span><br> 131072 194.0 335.1 341.5<span class="apple-converted-space"> </span><br> 262144 388.5 380.8 612.9<span class="apple-converted-space"> </span><br> 524288 1046.7 967.1 1653.3<span class="apple-converted-space"> </span><br> 1048576 1997.4 2169.0 4034.4<span class="apple-converted-space"> </span><br> 2097152 5502.9 5787.3 12608.1</span><o:p></o:p></div></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">The tall-and-skinny matrices in KSPGMRESOrthog vary in width. The average speedup depends on components. So I suggest you run ex2k to see in your environment whether oneMKL can speedup the kernels. <o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">--Junchao Zhang<o:p></o:p></div></div></div></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">On Mon, Jun 24, 2024 at 11:35<span style="font-family: Arial, sans-serif;"> </span>AM Junchao Zhang <<a href="mailto:junchao.zhang@gmail.com" style="color: purple; text-decoration: underline;">junchao.zhang@gmail.com</a>> wrote:<o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">Let me run some examples on our end to see whether the code calls expected functions. <o:p></o:p></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><br clear="all"><o:p></o:p></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">--Junchao Zhang<o:p></o:p></div></div></div></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">On Mon, Jun 24, 2024 at 10:46<span style="font-family: Arial, sans-serif;"> </span>AM Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank" style="color: purple; text-decoration: underline;">knepley@gmail.com</a>> wrote:<o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; color: white;">On Mon, Jun 24, 2024 at 11:</span><span style="font-size: 1pt; font-family: Arial, sans-serif; color: white;"> </span><span style="font-size: 1pt; color: white;">21 AM Yongzhong Li <yongzhong.</span><span style="font-size: 1pt; font-family: Arial, sans-serif; color: white;"> </span><span style="font-size: 1pt; color: white;">li@</span><span style="font-size: 1pt; font-family: Arial, sans-serif; color: white;"> </span><span style="font-size: 1pt; color: white;">mail.</span><span style="font-size: 1pt; font-family: Arial, sans-serif; color: white;"> </span><span style="font-size: 1pt; color: white;">utoronto.</span><span style="font-size: 1pt; font-family: Arial, sans-serif; color: white;"> </span><span style="font-size: 1pt; color: white;">ca> wrote: Thank you Pierre for your information. Do we have a conclusion for my original question about the parallelization efficiency for different stages of</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; color: white;">ZjQcmQRYFpfptBannerStart</span><o:p></o:p></div></div></div><div id="m_-7305460844614688919m_2643581689528628203pfptBanner0gnzkk2" style="border-width: 3pt medium medium; border-style: solid none none; border-image: none; padding: 6pt 0cm 0cm; margin-top: 12pt; margin-bottom: 12pt; border-color: currentcolor; border-radius: 4px; min-width: 200px;"><div id="m_-7305460844614688919m_2643581689528628203pfptBanner0gnzkk2" style="margin-bottom: 0.75pt; float: left;"><div id="m_-7305460844614688919m_2643581689528628203pfptBanner0gnzkk2"><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif; line-height: 13.5pt; background: rgb(208, 216, 220);"><b><span style="font-size: 10.5pt; font-family: Arial, sans-serif;">This Message Is From an External Sender</span></b><o:p></o:p></div></div></div><div id="m_-7305460844614688919m_2643581689528628203pfptBanner0gnzkk2" style="margin-top: 1.5pt;"><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif; line-height: 13.5pt; background: rgb(208, 216, 220);"><span style="font-size: 9pt; font-family: Arial, sans-serif;">This message came from outside your organization.</span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif; background: rgb(208, 216, 220);"><span style="font-size: 1pt;"> </span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; color: white;">ZjQcmQRYFpfptBannerEnd</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">On Mon, Jun 24, 2024 at 11:21<span style="font-family: Arial, sans-serif;"> </span>AM Yongzhong Li <<a href="mailto:yongzhong.li@mail.utoronto.ca" target="_blank" style="color: purple; text-decoration: underline;">yongzhong.li@mail.utoronto.ca</a>> wrote:<o:p></o:p></div></div></div><div><blockquote style="border-width: medium medium medium 1pt; border-style: none none none solid; border-image: none; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt; border-color: currentcolor currentcolor currentcolor rgb(204, 204, 204);"><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; color: white;">Thank you Pierre for your information. Do we have a conclusion for my original question about the parallelization efficiency for different stages of KSP Solve? Do we need to do more testing to figure out the issues? Thank you, Yongzhong From:</span><span style="font-size: 1pt; font-family: Arial, sans-serif; color: white;"> </span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; color: white;">ZjQcmQRYFpfptBannerStart</span><o:p></o:p></div></div></div><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261pfptBanner7d6k4n9" style="border-width: 3pt medium medium; border-style: solid none none; border-image: none; padding: 6pt 0cm 0cm; margin-top: 12pt; margin-bottom: 12pt; border-color: currentcolor; border-radius: 4px; min-width: 200px;"><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261pfptBanner7d6k4n9" style="margin-bottom: 0.75pt; float: left;"><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261pfptBanner7d6k4n9"><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif; line-height: 13.5pt; background: rgb(208, 216, 220);"><b><span style="font-size: 10.5pt; font-family: Arial, sans-serif;">This Message Is From an External Sender</span></b><o:p></o:p></div></div></div><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261pfptBanner7d6k4n9" style="margin-top: 1.5pt;"><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif; line-height: 13.5pt; background: rgb(208, 216, 220);"><span style="font-size: 9pt; font-family: Arial, sans-serif;">This message came from outside your organization.</span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif; background: rgb(208, 216, 220);"><span style="font-size: 1pt;"> </span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; color: white;">ZjQcmQRYFpfptBannerEnd</span><o:p></o:p></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">Thank you Pierre for your information. Do we have a conclusion for my original question about the parallelization efficiency for different stages of KSP Solve? Do we need to do more testing to figure out the issues?</span><o:p></o:p></div></div></div></div></div></blockquote><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">We have an extended discussion of this here: <a href="https://urldefense.us/v3/__https://petsc.org/release/faq/*what-kind-of-parallel-computers-or-clusters-are-needed-to-use-petsc-or-why-do-i-get-little-speedup__;Iw!!G_uCfscf7eWS!aQJpmm5W6l6FUiumnIPmkouzwzNUfx-Dyq04i1O2KS_InQGk6qjI7wUir0Hx6QEUQE2AMiJDsez3x4zRO7V_$" target="_blank" style="color: purple; text-decoration: underline;">https://petsc.org/release/faq/#what-kind-of-parallel-computers-or-clusters-are-needed-to-use-petsc-or-why-do-i-get-little-speedup</a><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">The kinds of operations you are talking about (SpMV, VecDot, VecAXPY, etc) are memory bandwidth limited. If there is no more bandwidth to be marshalled on your board, then adding more processes does nothing at all. This is why people were asking about how many "nodes" you are running on, because that is the unit of memory bandwidth, not "cores" which make little difference.<o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> Thanks,<o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> Matt<o:p></o:p></div></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div><blockquote style="border-width: medium medium medium 1pt; border-style: none none none solid; border-image: none; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt; border-color: currentcolor currentcolor currentcolor rgb(204, 204, 204);"><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">Thank you,</span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">Yongzhong</span><o:p></o:p></div></div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261mail-editor-reference-message-container"><div><div style="border-width: 1pt medium medium; border-style: solid none none; border-image: none; padding: 3pt 0cm 0cm; border-color: currentcolor;"><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 12pt; font-family: Aptos, sans-serif;"><b>From:<span class="apple-converted-space"> </span></b>Pierre Jolivet <<a href="mailto:pierre@joliv.et" target="_blank" style="color: purple; text-decoration: underline;">pierre@joliv.et</a>><br><b>Date:<span class="apple-converted-space"> </span></b>Sunday, June 23, 2024 at 12:41<span style="font-family: Arial, sans-serif;"> </span>AM<br><b>To:<span class="apple-converted-space"> </span></b>Yongzhong Li <<a href="mailto:yongzhong.li@mail.utoronto.ca" target="_blank" style="color: purple; text-decoration: underline;">yongzhong.li@mail.utoronto.ca</a>><br><b>Cc:<span class="apple-converted-space"> </span></b><a href="mailto:petsc-users@mcs.anl.gov" target="_blank" style="color: purple; text-decoration: underline;">petsc-users@mcs.anl.gov</a><span class="apple-converted-space"> </span><<a href="mailto:petsc-users@mcs.anl.gov" target="_blank" style="color: purple; text-decoration: underline;">petsc-users@mcs.anl.gov</a>><br><b>Subject:<span class="apple-converted-space"> </span></b>Re: [petsc-users] [petsc-maint] Assistance Needed with PETSc KSPSolve Performance Issue<o:p></o:p></p></div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div><div><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></p><blockquote style="margin-top: 5pt; margin-bottom: 5pt;"><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">On 23 Jun 2024, at 4:07<span style="font-family: Arial, sans-serif;"> </span>AM, Yongzhong Li <<a href="mailto:yongzhong.li@mail.utoronto.ca" target="_blank" style="color: purple; text-decoration: underline;">yongzhong.li@mail.utoronto.ca</a>> wrote:<o:p></o:p></div></div></div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div><div><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261pfptBannerfa2qtuo"><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261pfptBannerfa2qtuo"><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261pfptBannerfa2qtuo"><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-family: Arial, sans-serif;">This Message Is From an External Sender</span><o:p></o:p></div></div></div><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261pfptBannerfa2qtuo"><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-family: Arial, sans-serif;">This message came from outside your organization.</span><o:p></o:p></div></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">Yeah, I ran my program again using -mat_view::ascii_info and set MKL_VERBOSE to be 1, then I noticed the outputs suggested that the matrix to be seqaijmkl type (I’ve attached a few as below)<br><br>--> Setting up matrix-vector products...</span><o:p></o:p></div></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">Mat Object: 1 MPI process</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> type: seqaijmkl</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> rows=16490, cols=35937</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> total: nonzeros=128496, allocated nonzeros=128496</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> total number of mallocs used during MatSetValues calls=0</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> not using I-node routines</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">Mat Object: 1 MPI process</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> type: seqaijmkl</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> rows=16490, cols=35937</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> total: nonzeros=128496, allocated nonzeros=128496</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> total number of mallocs used during MatSetValues calls=0</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> not using I-node routines</span><o:p></o:p></div></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">--> Solving the system...</span><o:p></o:p></div></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">Excitation 1 of 1...</span><o:p></o:p></div></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">================================================</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">Iterative solve completed in 7435 ms.</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">CONVERGED: rtol.</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">Iterations: 72</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">Final relative residual norm: 9.22287e-07</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">================================================</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">[CPU TIME] System solution: 2.27160000e+02 s.</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">[WALL TIME] System solution: 7.44387218e+00 s.<br><br>However, it seems to me that there were still no MKL outputs even I set MKL_VERBOSE to be 1. Although, I think it should be many spmv operations when doing KSPSolve(). Do you see the possible reasons?</span><o:p></o:p></div></div></div></div></div></blockquote><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">SPMV are not reported with MKL_VERBOSE (last I checked), only dense BLAS is.<o:p></o:p></div></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">Thanks,<o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">Pierre<o:p></o:p></div></div></div><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></p><blockquote style="margin-top: 5pt; margin-bottom: 5pt;"><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">Thanks,</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">Yongzhong</span><o:p></o:p></div></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> </span><o:p></o:p></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261mail-editor-reference-message-container"><div><div><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 12pt; font-family: Aptos, sans-serif;"><b>From: </b>Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank" style="color: purple; text-decoration: underline;">knepley@gmail.com</a>><br><b>Date: </b>Saturday, June 22, 2024 at 5:56<span style="font-family: Arial, sans-serif;"> </span>PM<br><b>To: </b>Yongzhong Li <<a href="mailto:yongzhong.li@mail.utoronto.ca" target="_blank" style="color: purple; text-decoration: underline;">yongzhong.li@mail.utoronto.ca</a>><br><b>Cc: </b>Junchao Zhang <<a href="mailto:junchao.zhang@gmail.com" target="_blank" style="color: purple; text-decoration: underline;">junchao.zhang@gmail.com</a>>, Pierre Jolivet <<a href="mailto:pierre@joliv.et" target="_blank" style="color: purple; text-decoration: underline;">pierre@joliv.et</a>>, <a href="mailto:petsc-users@mcs.anl.gov" target="_blank" style="color: purple; text-decoration: underline;">petsc-users@mcs.anl.gov</a> <<a href="mailto:petsc-users@mcs.anl.gov" target="_blank" style="color: purple; text-decoration: underline;">petsc-users@mcs.anl.gov</a>><br><b>Subject: </b>Re: [petsc-users] [petsc-maint] Assistance Needed with PETSc KSPSolve Performance Issue<o:p></o:p></p></div><table class="MsoNormalTable" border="0" cellspacing="0" cellpadding="0" align="left" width="100%" style="width: 967.609375px; display: table; float: none;"><tbody><tr><td style="background: rgb(166, 166, 166); padding: 5.25pt 1.5pt;"></td><td width="100%" style="width: 933.609375px; background: rgb(234, 234, 234); padding: 5.25pt 3.75pt 5.25pt 11.25pt;"><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="ZH-CN" style="font-size: 9pt; font-family: DengXian; color: rgb(33, 33, 33);">你通常不会收到来自</span><span style="font-size: 9pt; font-family: "Segoe UI", sans-serif; color: rgb(33, 33, 33);"> </span><span style=""><a href="mailto:knepley@gmail.com" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: "Segoe UI", sans-serif;">knepley@gmail.com</span></a></span><span style="font-size: 9pt; font-family: "Segoe UI", sans-serif; color: rgb(33, 33, 33);"> </span><span lang="ZH-CN" style="font-size: 9pt; font-family: DengXian; color: rgb(33, 33, 33);">的电子邮件。</span><span style=""><a href="https://urldefense.us/v3/__https://aka.ms/LearnAboutSenderIdentification__;!!G_uCfscf7eWS!fVvbGldqcUV5ju4jpu5oGmt-VjITi5JpCJzhHxpbgsERLVYZzglpxKOOyrBRGxjRxp7vWHwt3SnINFOQErR1Z8kcDcf3qwbYRxM$" target="_blank" style="color: purple; text-decoration: underline;"><span lang="ZH-CN" style="font-size: 9pt; font-family: DengXian;">了解这一点为什么很重要</span></a></span><o:p></o:p></div></div></div></div></td><td width="75" style="width: 56.25pt; background: rgb(234, 234, 234); padding: 5.25pt 3.75pt;"></td></tr></tbody></table><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">On Sat, Jun 22, 2024 at 5:03<span style="font-family: Arial, sans-serif;"> </span>PM Yongzhong Li <<a href="mailto:yongzhong.li@mail.utoronto.ca" target="_blank" style="color: purple; text-decoration: underline;">yongzhong.li@mail.utoronto.ca</a>> wrote:<o:p></o:p></div></div></div></div><div><blockquote style="border-width: medium medium medium 1pt; border-style: none none none solid; border-image: none; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt; border-color: currentcolor currentcolor currentcolor rgb(204, 204, 204);"><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; color: white;">MKL_VERBOSE=1 ./ex1 matrix nonzeros = 100, allocated nonzeros = 100 MKL_VERBOSE Intel(R) MKL 2019.</span><span style="font-size: 1pt; font-family: Arial, sans-serif; color: white;"> </span><span style="font-size: 1pt; color: white;">0 Update 4 Product build 20190411 for Intel(R) 64 architecture Intel(R) Advanced Vector Extensions 512 (Intel(R) AVX-512) with support of Vector</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; color: white;">ZjQcmQRYFpfptBannerStart</span><o:p></o:p></div></div></div></div><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322pfptBanner3e1hrxr" style="margin-top: 12pt; margin-bottom: 12pt; border-color: currentcolor; border-radius: 4px; min-width: 200px;"><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322pfptBanner3e1hrxr" style="margin-bottom: 0.75pt; float: left;"><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322pfptBanner3e1hrxr"><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif; line-height: 13.5pt; background: rgb(208, 216, 220);"><b><span style="font-size: 10.5pt; font-family: Arial, sans-serif;">This Message Is From an External Sender</span></b><o:p></o:p></div></div></div></div><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322pfptBanner3e1hrxr" style="margin-top: 1.5pt;"><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif; line-height: 13.5pt; background: rgb(208, 216, 220);"><span style="font-size: 9pt; font-family: Arial, sans-serif;">This message came from outside your organization.</span><o:p></o:p></div></div></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif; background: rgb(208, 216, 220);"><span style="font-size: 1pt;"> </span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; color: white;">ZjQcmQRYFpfptBannerEnd</span><o:p></o:p></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-family: "Courier New";">MKL_VERBOSE=1 ./ex1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"><br></span><span style="font-size: 11pt;">matrix nonzeros = 100, allocated nonzeros = 100</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE Intel(R) MKL 2019.0 Update 4 Product build 20190411 for Intel(R) 64 architecture Intel(R) Advanced Vector Extensions 512 (Intel(R) AVX-512) with support of Vector Neural Network Instructions enabled processors, Lnx 2.50GHz lp64 gnu_thread</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZGEMV(N,10,10,0x7ffd9d7078f0,0x187eb20,10,0x187f7c0,1,0x7ffd9d707900,0x187ff70,1) 167.34ms CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZSYTRF(L,10,0x1894b50,10,0x1893df0,0x7ffd9d7078c0,-1,0) 77.19ms CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZSYTRF(L,10,0x1894b50,10,0x1893df0,0x1894490,10,0) 83.97ms CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZSYTRS(L,10,1,0x1894b50,10,0x1893df0,0x1880720,10,0) 44.94ms CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZAXPY(10,0x7ffd9d7078f0,0x187f7c0,1,0x1880720,1) 20.72us CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZSYTRS(L,10,2,0x1894b50,10,0x1893df0,0x187d2a0,10,0) 4.22us CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZGEMM(N,N,10,2,10,0x7ffd9d707790,0x187eb20,10,0x187d2a0,10,0x7ffd9d7077a0,0x1896a70,10) 1.41ms CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZAXPY(20,0x7ffd9d7078a0,0x1896a70,1,0x187b650,1) 381ns CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZSYTRF(L,10,0x1894b50,10,0x1893df0,0x7ffd9d707840,-1,0) 742ns CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZSYTRF(L,10,0x1894b50,10,0x1893df0,0x18951a0,10,0) 4.20us CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZSYTRS(L,10,1,0x1894b50,10,0x1893df0,0x1880720,10,0) 2.94us CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZAXPY(10,0x7ffd9d7078f0,0x187f7c0,1,0x1880720,1) 292ns CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZGEMV(N,10,10,0x7ffd9d7078f0,0x187eb20,10,0x187f7c0,1,0x7ffd9d707900,0x187ff70,1) 1.17us CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZGETRF(10,10,0x1894b50,10,0x1893df0,0) 202.48ms CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZGETRS(N,10,1,0x1894b50,10,0x1893df0,0x1880720,10,0) 20.78ms CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZAXPY(10,0x7ffd9d7078f0,0x187f7c0,1,0x1880720,1) 954ns CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZGETRS(N,10,2,0x1894b50,10,0x1893df0,0x187d2a0,10,0) 30.74ms CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZGEMM(N,N,10,2,10,0x7ffd9d707790,0x187eb20,10,0x187d2a0,10,0x7ffd9d7077a0,0x18969c0,10) 3.95us CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZAXPY(20,0x7ffd9d7078a0,0x18969c0,1,0x187b650,1) 995ns CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZGETRF(10,10,0x1894b50,10,0x1893df0,0) 4.09us CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZGETRS(N,10,1,0x1894b50,10,0x1893df0,0x1880720,10,0) 3.92us CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZAXPY(10,0x7ffd9d7078f0,0x187f7c0,1,0x1880720,1) 274ns CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZGEMV(N,15,10,0x7ffd9d7078f0,0x187ec70,15,0x187fc30,1,0x7ffd9d707900,0x1880400,1) 1.59us CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZGEQRF(15,10,0x1894b40,15,0x1894550,0x7ffd9d707900,-1,0) 47.07us CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZGEQRF(15,10,0x1894b40,15,0x1894550,0x1895cb0,10,0) 26.62us CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZUNMQR(L,C,15,1,10,0x1894b40,15,0x1894550,0x1895b00,15,0x7ffd9d7078b0,-1,0) 35.32us CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZUNMQR(L,C,15,1,10,0x1894b40,15,0x1894550,0x1895b00,15,0x1895cb0,10,0) 42.33ms CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZTRTRS(U,N,N,10,1,0x1894b40,15,0x1895b00,15,0) 16.11us CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZAXPY(10,0x7ffd9d7078f0,0x187fc30,1,0x1880c70,1) 395ns CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZGEMM(N,N,15,2,10,0x7ffd9d707790,0x187ec70,15,0x187d310,10,0x7ffd9d7077a0,0x187b5b0,15) 3.22us CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZUNMQR(L,C,15,2,10,0x1894b40,15,0x1894550,0x1897760,15,0x7ffd9d7078c0,-1,0) 730ns CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZUNMQR(L,C,15,2,10,0x1894b40,15,0x1894550,0x1897760,15,0x1895cb0,10,0) 4.42us CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZTRTRS(U,N,N,10,2,0x1894b40,15,0x1897760,15,0) 5.96us CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZAXPY(20,0x7ffd9d7078a0,0x187d310,1,0x1897610,1) 222ns CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZGEQRF(15,10,0x1894b40,15,0x18954b0,0x7ffd9d707820,-1,0) 685ns CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZGEQRF(15,10,0x1894b40,15,0x18954b0,0x1895d60,10,0) 6.11us CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZUNMQR(L,C,15,1,10,0x1894b40,15,0x18954b0,0x1895bb0,15,0x7ffd9d7078b0,-1,0) 390ns CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZUNMQR(L,C,15,1,10,0x1894b40,15,0x18954b0,0x1895bb0,15,0x1895d60,10,0) 3.09us CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZTRTRS(U,N,N,10,1,0x1894b40,15,0x1895bb0,15,0) 1.05us CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">MKL_VERBOSE ZAXPY(10,0x7ffd9d7078f0,0x187fc30,1,0x1880c70,1) 257ns CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1</span><span lang="EN-US" style="font-size: 11pt;"><br><br>Yes, for petsc example, there are MKL outputs, but for my own program. All I did is to change the matrix type from MATAIJ to MATAIJMKL to get optimized performance for spmv from MKL. Should I expect to see any MKL outputs in this case?</span><o:p></o:p></div></div></div></div></div></div></blockquote><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">Are you sure that the type changed? You can MatView() the matrix with format ascii_info to see.<o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> Thanks,<o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> Matt<o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div></div><blockquote style="border-width: medium medium medium 1pt; border-style: none none none solid; border-image: none; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt; border-color: currentcolor currentcolor currentcolor rgb(204, 204, 204);"><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">Thanks,</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">Yongzhong</span><o:p></o:p></div></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;"> </span><o:p></o:p></div></div><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322mail-editor-reference-message-container"><div><div><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 12pt; font-family: Aptos, sans-serif;"><b>From: </b>Junchao Zhang <<a href="mailto:junchao.zhang@gmail.com" target="_blank" style="color: purple; text-decoration: underline;">junchao.zhang@gmail.com</a>><br><b>Date: </b>Saturday, June 22, 2024 at 9:40<span style="font-family: Arial, sans-serif;"> </span>AM<br><b>To: </b>Yongzhong Li <<a href="mailto:yongzhong.li@mail.utoronto.ca" target="_blank" style="color: purple; text-decoration: underline;">yongzhong.li@mail.utoronto.ca</a>><br><b>Cc: </b>Pierre Jolivet <<a href="mailto:pierre@joliv.et" target="_blank" style="color: purple; text-decoration: underline;">pierre@joliv.et</a>>, <a href="mailto:petsc-users@mcs.anl.gov" target="_blank" style="color: purple; text-decoration: underline;">petsc-users@mcs.anl.gov</a> <<a href="mailto:petsc-users@mcs.anl.gov" target="_blank" style="color: purple; text-decoration: underline;">petsc-users@mcs.anl.gov</a>><br><b>Subject: </b>Re: [petsc-users] [petsc-maint] Assistance Needed with PETSc KSPSolve Performance Issue<o:p></o:p></p></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">No, you don't. It is strange. Perhaps you can you run a petsc example first and see if MKL is really used<o:p></o:p></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-family: "Courier New";">$ cd src/mat/tests</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-family: "Courier New";">$ make ex1</span><o:p></o:p></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-family: "Courier New";">$ MKL_VERBOSE=1 ./ex1</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><br clear="all"><o:p></o:p></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">--Junchao Zhang<o:p></o:p></div></div></div></div></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">On Fri, Jun 21, 2024 at 4:03<span style="font-family: Arial, sans-serif;"> </span>PM Yongzhong Li <<a href="mailto:yongzhong.li@mail.utoronto.ca" target="_blank" style="color: purple; text-decoration: underline;">yongzhong.li@mail.utoronto.ca</a>> wrote:<o:p></o:p></div></div></div></div><blockquote style="border-width: medium medium medium 1pt; border-style: none none none solid; border-image: none; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt; border-color: currentcolor currentcolor currentcolor rgb(204, 204, 204);"><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">I am using<br><br>export MKL_VERBOSE=1</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">./xx<br><br>in the bash file, do I have to use -</span><span lang="EN-US"> </span>ksp_converged_reason<span lang="EN-US">?<br><br>Thanks,</span><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US">Yongzhong</span><o:p></o:p></div></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580mail-editor-reference-message-container"><div><div><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 12pt; font-family: Aptos, sans-serif;"><b>From: </b>Pierre Jolivet <<a href="mailto:pierre@joliv.et" target="_blank" style="color: purple; text-decoration: underline;">pierre@joliv.et</a>><br><b>Date: </b>Friday, June 21, 2024 at 1:47<span style="font-family: Arial, sans-serif;"> </span>PM<br><b>To: </b>Yongzhong Li <<a href="mailto:yongzhong.li@mail.utoronto.ca" target="_blank" style="color: purple; text-decoration: underline;">yongzhong.li@mail.utoronto.ca</a>><br><b>Cc: </b>Junchao Zhang <<a href="mailto:junchao.zhang@gmail.com" target="_blank" style="color: purple; text-decoration: underline;">junchao.zhang@gmail.com</a>>, <a href="mailto:petsc-users@mcs.anl.gov" target="_blank" style="color: purple; text-decoration: underline;">petsc-users@mcs.anl.gov</a> <<a href="mailto:petsc-users@mcs.anl.gov" target="_blank" style="color: purple; text-decoration: underline;">petsc-users@mcs.anl.gov</a>><br><b>Subject: </b>Re: [petsc-users] [petsc-maint] Assistance Needed with PETSc KSPSolve Performance Issue<o:p></o:p></p></div><table class="MsoNormalTable" border="0" cellspacing="0" cellpadding="0" align="left" width="100%" style="width: 936.828125px; display: table; float: none;"><tbody><tr><td style="background: rgb(166, 166, 166); padding: 5.25pt 1.5pt;"></td><td width="100%" style="width: 902.828125px; background: rgb(234, 234, 234); padding: 5.25pt 3.75pt 5.25pt 11.25pt;"><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="ZH-CN" style="font-size: 9pt; font-family: DengXian; color: rgb(33, 33, 33);">你通常不会收到来自</span><span style="font-size: 9pt; font-family: "Segoe UI", sans-serif; color: rgb(33, 33, 33);"> </span><span style=""><a href="mailto:pierre@joliv.et" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: "Segoe UI", sans-serif;">pierre@joliv.et</span></a></span><span style="font-size: 9pt; font-family: "Segoe UI", sans-serif; color: rgb(33, 33, 33);"> </span><span lang="ZH-CN" style="font-size: 9pt; font-family: DengXian; color: rgb(33, 33, 33);">的电子邮件。</span><span style=""><a href="https://urldefense.us/v3/__https://aka.ms/LearnAboutSenderIdentification__;!!G_uCfscf7eWS!flsZMI97ne0yyxHhLda3hROB9qsgstuZS-jPinxGIzFCCSdn1ujdoMR8dyz-5_kVqqMM-12Lt0dTdjKrx3wXhHZmBhNydvFQeSY$" target="_blank" style="color: purple; text-decoration: underline;"><span lang="ZH-CN" style="font-size: 9pt; font-family: DengXian;">了解这一点为什么很重要</span></a></span><o:p></o:p></div></div></div></div></td><td width="75" style="width: 56.25pt; background: rgb(234, 234, 234); padding: 5.25pt 3.75pt;"></td></tr></tbody></table><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">How do you set the variable?<o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">$ MKL_VERBOSE=1 ./ex1 -ksp_converged_reason<o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">MKL_VERBOSE oneMKL 2024.0 Update 1 Product build 20240215 for Intel(R) 64 architecture Intel(R) Advanced Vector Extensions 2 (Intel(R) AVX2) enabled processors, Lnx 2.80GHz lp64 intel_thread<o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">MKL_VERBOSE DDOT(10,0x22127c0,1,0x22127c0,1) 2.02ms CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1<o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">MKL_VERBOSE DSCAL(10,0x7ffc9fb4ff08,0x22127c0,1) 12.67us CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1<o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">MKL_VERBOSE DDOT(10,0x22127c0,1,0x2212840,1) 1.52us CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1<o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">MKL_VERBOSE DDOT(10,0x2212840,1,0x2212840,1) 167ns CNR:OFF Dyn:1 FastMM:1 TID:0 NThr:1<o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">[...]<o:p></o:p></div></div></div></div><div><div style="margin-bottom: 12pt;"><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div><blockquote style="margin-top: 5pt; margin-bottom: 5pt;"><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">On 21 Jun 2024, at 7:37<span style="font-family: Arial, sans-serif;"> </span>PM, Yongzhong Li <<a href="mailto:yongzhong.li@mail.utoronto.ca" target="_blank" style="color: purple; text-decoration: underline;">yongzhong.li@mail.utoronto.ca</a>> wrote:<o:p></o:p></div></div></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div><div><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580pfptBannermu5fqka"><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580pfptBannermu5fqka"><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580pfptBannermu5fqka"><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-family: Arial, sans-serif;">This Message Is From an External Sender </span><o:p></o:p></div></div></div></div><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580pfptBannermu5fqka"><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-family: Arial, sans-serif;">This message came from outside your organization.</span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">Hello all,<br><br>I set MKL_VERBOSE = 1, but observed no print output specific to the use of MKL. Does PETSc enable this verbose output?<br><br>Best,</span><o:p></o:p></div></div></div></div><div><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt;">Yongzhong</span><o:p></o:p></p></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></div></div></div><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580mail-editor-reference-message-container"><div><div><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 12pt; font-family: Aptos, sans-serif;"><b>From: </b>Pierre Jolivet <<a href="mailto:pierre@joliv.et" target="_blank" style="color: purple; text-decoration: underline;">pierre@joliv.et</a>><br><b>Date: </b>Friday, June 21, 2024 at 1:36<span style="font-family: Arial, sans-serif;"> </span>AM<br><b>To: </b>Junchao Zhang <<a href="mailto:junchao.zhang@gmail.com" target="_blank" style="color: purple; text-decoration: underline;">junchao.zhang@gmail.com</a>><br><b>Cc: </b>Yongzhong Li <<a href="mailto:yongzhong.li@mail.utoronto.ca" target="_blank" style="color: purple; text-decoration: underline;">yongzhong.li@mail.utoronto.ca</a>>, <a href="mailto:petsc-users@mcs.anl.gov" target="_blank" style="color: purple; text-decoration: underline;">petsc-users@mcs.anl.gov</a> <<a href="mailto:petsc-users@mcs.anl.gov" target="_blank" style="color: purple; text-decoration: underline;">petsc-users@mcs.anl.gov</a>><br><b>Subject: </b>Re: [petsc-users] [petsc-maint] Assistance Needed with PETSc KSPSolve Performance Issue<o:p></o:p></p></div><table class="MsoNormalTable" border="0" cellspacing="0" cellpadding="0" align="left" width="100%" style="width: 856.828125px; display: table; float: none;"><tbody><tr><td style="background: rgb(166, 166, 166); padding: 5.25pt 1.5pt;"></td><td width="100%" style="width: 822.828125px; background: rgb(234, 234, 234); padding: 5.25pt 3.75pt 5.25pt 11.25pt;"><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="ZH-CN" style="font-size: 9pt; font-family: DengXian; color: rgb(33, 33, 33);">你通常不会收到来自</span><span style="font-size: 9pt; font-family: "Segoe UI", sans-serif; color: rgb(33, 33, 33);"> </span><span style=""><a href="mailto:pierre@joliv.et" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: "Segoe UI", sans-serif;">pierre@joliv.et</span></a></span><span style="font-size: 9pt; font-family: "Segoe UI", sans-serif; color: rgb(33, 33, 33);"> </span><span lang="ZH-CN" style="font-size: 9pt; font-family: DengXian; color: rgb(33, 33, 33);">的电子邮件。</span><span style=""><a href="https://urldefense.us/v3/__https://aka.ms/LearnAboutSenderIdentification__;!!G_uCfscf7eWS!eXBeeIXo9Yqgp2nypqwKYimLnGBZXnF4dXxgLM1UoOIO6n8nt3XlfgjVWLPWJh4UOa5NNpx-nrJb_H828XRQKUREfR2m69oCbxI$" target="_blank" style="color: purple; text-decoration: underline;"><span lang="ZH-CN" style="font-size: 9pt; font-family: DengXian;">了解这一点为什么很重要</span></a></span><o:p></o:p></div></div></div></div></div></td><td width="75" style="width: 56.25pt; background: rgb(234, 234, 234); padding: 5.25pt 3.75pt;"></td></tr></tbody></table><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><div><div><div style="margin-bottom: 12pt;"><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><blockquote style="margin-top: 5pt; margin-bottom: 5pt;"><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">On 21 Jun 2024, at 6:42<span style="font-family: Arial, sans-serif;"> </span>AM, Junchao Zhang <<a href="mailto:junchao.zhang@gmail.com" target="_blank" style="color: purple; text-decoration: underline;">junchao.zhang@gmail.com</a>> wrote:<o:p></o:p></div></div></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><div><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580pfptBanners71iuax"><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580pfptBanners71iuax"><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580pfptBanners71iuax"><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-family: Arial, sans-serif;">This Message Is From an External Sender</span><o:p></o:p></div></div></div></div></div><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580pfptBanners71iuax"><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-family: Arial, sans-serif;">This message came from outside your organization.</span><o:p></o:p></div></div></div></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">I remember there are some MKL env vars to print MKL routines called. </span><o:p></o:p></div></div></div></div></div></div></blockquote><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">The environment variable is MKL_VERBOSE<o:p></o:p></div></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">Thanks,<o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">Pierre<o:p></o:p></div></div></div></div></div><div><div style="margin-bottom: 12pt;"><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><blockquote style="margin-top: 5pt; margin-bottom: 5pt;"><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">Maybe we can try it to see what MKL routines are really used and then we can understand why some petsc functions did not speed up </span><o:p></o:p></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"><br clear="all"></span><o:p></o:p></div></div></div></div><div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">--Junchao Zhang</span><o:p></o:p></div></div></div></div></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">On Thu, Jun 20, 2024 at 10:39 PM Yongzhong Li <</span><a href="mailto:yongzhong.li@mail.utoronto.ca" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">yongzhong.li@mail.utoronto.ca</span></a><span style="font-size: 9pt; font-family: Helvetica;">> wrote:</span><o:p></o:p></div></div></div></div></div><blockquote style="border-width: medium medium medium 1pt; border-style: none none none solid; border-image: none; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt; border-color: currentcolor currentcolor currentcolor rgb(204, 204, 204);"><div><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580m_-4861803116733450987pfptBannerqdehbik" style="margin-top: 12pt; margin-bottom: 12pt; border-width: initial; border-style: initial; border-color: currentcolor; border-radius: 4px; min-width: 200px;"><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580m_-4861803116733450987pfptBannerqdehbik" style="margin-bottom: 0.75pt; float: left;"><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580m_-4861803116733450987pfptBannerqdehbik"><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif; line-height: 13.5pt; background: rgb(208, 216, 220);"><b><span style="font-size: 10.5pt; font-family: Arial, sans-serif;">This Message Is From an External Sender</span></b><o:p></o:p></div></div></div></div></div><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580m_-4861803116733450987pfptBannerqdehbik" style="margin-top: 1.5pt;"><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif; line-height: 13.5pt; background: rgb(208, 216, 220);"><span style="font-size: 9pt; font-family: Arial, sans-serif;">This message came from outside your organization.</span><o:p></o:p></div></div></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif; background: rgb(208, 216, 220);"><span style="font-size: 1pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Helvetica;">Hi Barry, sorry for my last results. I didn’t fully understand the stage profiling and logging in PETSc, now I only record KSPSolve() stage of my program. Some sample codes are as follow,<br><br> // Static variable to keep track of the stage counter</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Helvetica;"> static int stageCounter = 1;</span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Helvetica;"> // Generate a unique stage name</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Helvetica;"> std::ostringstream oss;</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Helvetica;"> oss << "Stage " << stageCounter << " of Code";</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Helvetica;"> std::string stageName = oss.str();</span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Helvetica;"> // Register the stage</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Helvetica;"> PetscLogStage stagenum;</span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Helvetica;"> PetscLogStageRegister(stageName.c_str(), &stagenum);</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Helvetica;"> PetscLogStagePush(stagenum);</span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Helvetica;"> <b>KSPSolve(*ksp_ptr, b, x);</b></span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Helvetica;"> PetscLogStagePop();</span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Helvetica;"> stageCounter++;<br><br>I have attached my new logging results, there are 1 main stage and 4 other stages where each one is KSPSolve() call.<br><br>To provide some additional backgrounds, if you recall, I have been trying to get efficient iterative solution using multithreading. I found out by compiling PETSc with Intel MKL library instead of OpenBLAS, I am able to perform sparse matrix-vector multiplication faster, I am using MATSEQAIJMKL. This makes the shell matrix vector product in each iteration scale well with the #of threads. However, I found out the total GMERS solve time (~KSPSolve() time) is not scaling well the #of threads.<br><br>From the logging results I learned that when performing KSPSolve(), there are some CPU overheads in PCApply() and KSPGMERSOrthog(). I ran my programs using different number of threads and plotted the time consumption for PCApply() and KSPGMERSOrthog() against #of thread. I found out these two operations are not scaling with the threads at all! My results are attached as the pdf to give you a clear view.<br><br>My questions is,<br><br>From my understanding, in PCApply, MatSolve() is involved, KSPGMERSOrthog() will have many vector operations, so why these two parts can’t scale well with the # of threads when the intel MKL library is linked?<br><br>Thank you,<br>Yongzhong</span><o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580m_-4861803116733450987mail-editor-reference-message-container"><div><div><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 12pt; font-family: Aptos, sans-serif;"><b><span style="font-size: 9pt; font-family: Helvetica;">From: </span></b><span style="font-size: 9pt; font-family: Helvetica;">Barry Smith <</span><a href="mailto:bsmith@petsc.dev" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">bsmith@petsc.dev</span></a><span style="font-size: 9pt; font-family: Helvetica;">><br><b>Date: </b>Friday, June 14, 2024 at 11:36</span><span style="font-size: 9pt; font-family: Arial, sans-serif;"> </span><span style="font-size: 9pt; font-family: Helvetica;">AM<br><b>To: </b>Yongzhong Li <</span><a href="mailto:yongzhong.li@mail.utoronto.ca" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">yongzhong.li@mail.utoronto.ca</span></a><span style="font-size: 9pt; font-family: Helvetica;">><br><b>Cc: </b></span><a href="mailto:petsc-users@mcs.anl.gov" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">petsc-users@mcs.anl.gov</span></a><span style="font-size: 9pt; font-family: Helvetica;"> <</span><a href="mailto:petsc-users@mcs.anl.gov" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">petsc-users@mcs.anl.gov</span></a><span style="font-size: 9pt; font-family: Helvetica;">>, </span><a href="mailto:petsc-maint@mcs.anl.gov" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">petsc-maint@mcs.anl.gov</span></a><span style="font-size: 9pt; font-family: Helvetica;"> <</span><a href="mailto:petsc-maint@mcs.anl.gov" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">petsc-maint@mcs.anl.gov</span></a><span style="font-size: 9pt; font-family: Helvetica;">>, Piero Triverio <</span><a href="mailto:piero.triverio@utoronto.ca" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">piero.triverio@utoronto.ca</span></a><span style="font-size: 9pt; font-family: Helvetica;">><br><b>Subject: </b>Re: [petsc-maint] Assistance Needed with PETSc KSPSolve Performance Issue</span><o:p></o:p></p></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> I am a bit confused. Without the initial guess computation, there are still a bunch of events I don't understand </span><o:p></o:p></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">MatTranspose 79 1.0 4.0598e+01 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 0 0 0 0 0 0 0 0 0 0 0</span><o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">MatMatMultSym 110 1.0 1.7419e+02 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 1 0 0 0 0 1 0 0 0 0 0</span><o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">MatMatMultNum 90 1.0 1.2640e+02 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 1 0 0 0 0 1 0 0 0 0 0</span><o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">MatMatMatMultSym 20 1.0 1.3049e+02 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 1 0 0 0 0 1 0 0 0 0 0</span><o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">MatRARtSym 25 1.0 1.2492e+02 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 1 0 0 0 0 1 0 0 0 0 0</span><o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">MatMatTrnMultSym 25 1.0 8.8265e+01 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 0 0 0 0 0 0 0 0 0 0 0</span><o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">MatMatTrnMultNum 25 1.0 2.4820e+02 1.0 6.83e+10 1.0 0.0e+00 0.0e+00 0.0e+00 1 0 0 0 0 1 0 0 0 0 275</span><o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">MatTrnMatMultSym 10 1.0 7.2984e-01 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 0 0 0 0 0 0 0 0 0 0 0</span><o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">MatTrnMatMultNum 10 1.0 9.3128e-01 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 0 0 0 0 0 0 0 0 0 0 0</span><o:p></o:p></div></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">in addition there are many more VecMAXPY then VecMDot (in GMRES they are each done the same number of times)</span><o:p></o:p></div></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">VecMDot 5588 1.0 1.7183e+03 1.0 2.06e+13 1.0 0.0e+00 0.0e+00 0.0e+00 8 10 0 0 0 8 10 0 0 0 12016</span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">VecMAXPY 22412 1.0 8.4898e+03 1.0 4.17e+13 1.0 0.0e+00 0.0e+00 0.0e+00 39 20 0 0 0 39 20 0 0 0 4913</span><o:p></o:p></div></div></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">Finally there are a huge number of </span><o:p></o:p></div></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">MatMultAdd 258048 1.0 1.4178e+03 1.0 6.10e+13 1.0 0.0e+00 0.0e+00 0.0e+00 7 29 0 0 0 7 29 0 0 0 43025</span><o:p></o:p></div></div></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">Are you making calls to all these routines? Are you doing this inside your MatMult() or before you call KSPSolve?</span><o:p></o:p></div></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">The reason I wanted you to make a simpler run without the initial guess code is that your events are far more complicated than would be produced by GMRES alone so it is not possible to understand the behavior you are seeing without fully understanding all the events happening in the code.</span><o:p></o:p></div></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> Barry</span><o:p></o:p></div></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div><div><div style="margin-bottom: 12pt;"><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div><blockquote style="margin-top: 5pt; margin-bottom: 5pt;"><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">On Jun 14, 2024, at 1:19</span><span style="font-size: 9pt; font-family: Arial, sans-serif;"> </span><span style="font-size: 9pt; font-family: Helvetica;">AM, Yongzhong Li <</span><a href="mailto:yongzhong.li@mail.utoronto.ca" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">yongzhong.li@mail.utoronto.ca</span></a><span style="font-size: 9pt; font-family: Helvetica;">> wrote:</span><o:p></o:p></div></div></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div><div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Helvetica;">Thanks, I have attached the results without using any KSPGuess. At low frequency, the iteration steps are quite close to the one with KSPGuess, specifically <br><br> KSPGuess Object: 1 MPI process</span><o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Helvetica;"> type: fischer</span><o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Helvetica;"> Model 1, size 200<br><br>However, I found at higher frequency, the # of iteration steps are significant higher than the one with KSPGuess, I have attahced both of the results for your reference.<br><br>Moreover, could I ask why the one without the KSPGuess options can be used for a baseline comparsion? What are we comparing here? How does it relate to the performance issue/bottleneck I found? “</span><b><span style="font-size: 9pt; font-family: Helvetica;">I have noticed that the time taken by </span></b><b><span style="font-size: 9pt; font-family: "Courier New";">KSPSolve</span></b><b><span style="font-size: 9pt; font-family: Helvetica;"> is </span></b><b><span lang="EN-US" style="font-size: 9pt; font-family: Helvetica;">almost two times </span></b><b><span style="font-size: 9pt; font-family: Helvetica;">greater than the CPU time for matrix-vector product multiplied by the number of iteration</span></b><span lang="EN-US" style="font-size: 11pt; font-family: Helvetica;">” <br><br>Thank you!<br>Yongzhong</span><o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div></div><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580m_-4861803116733450987mail-editor-reference-message-container"><div><div><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 12pt; font-family: Aptos, sans-serif;"><b><span style="font-size: 9pt; font-family: Helvetica;">From: </span></b><span style="font-size: 9pt; font-family: Helvetica;">Barry Smith <</span><a href="mailto:bsmith@petsc.dev" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">bsmith@petsc.dev</span></a><span style="font-size: 9pt; font-family: Helvetica;">><br><b>Date: </b>Thursday, June 13, 2024 at 2:14</span><span style="font-size: 9pt; font-family: Arial, sans-serif;"> </span><span style="font-size: 9pt; font-family: Helvetica;">PM<br><b>To: </b>Yongzhong Li <</span><a href="mailto:yongzhong.li@mail.utoronto.ca" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">yongzhong.li@mail.utoronto.ca</span></a><span style="font-size: 9pt; font-family: Helvetica;">><br><b>Cc: </b></span><a href="mailto:petsc-users@mcs.anl.gov" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">petsc-users@mcs.anl.gov</span></a><span style="font-size: 9pt; font-family: Helvetica;"> <</span><a href="mailto:petsc-users@mcs.anl.gov" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">petsc-users@mcs.anl.gov</span></a><span style="font-size: 9pt; font-family: Helvetica;">>, </span><a href="mailto:petsc-maint@mcs.anl.gov" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">petsc-maint@mcs.anl.gov</span></a><span style="font-size: 9pt; font-family: Helvetica;"> <</span><a href="mailto:petsc-maint@mcs.anl.gov" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">petsc-maint@mcs.anl.gov</span></a><span style="font-size: 9pt; font-family: Helvetica;">>, Piero Triverio <</span><a href="mailto:piero.triverio@utoronto.ca" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">piero.triverio@utoronto.ca</span></a><span style="font-size: 9pt; font-family: Helvetica;">><br><b>Subject: </b>Re: [petsc-maint] Assistance Needed with PETSc KSPSolve Performance Issue</span><o:p></o:p></p></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> Can you please run the same thing without the KSPGuess option(s) for a baseline comparison?</span><o:p></o:p></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> Thanks</span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> Barry</span><o:p></o:p></div></div></div></div></div></div><div><div><div><div style="margin-bottom: 12pt;"><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div><blockquote style="margin-top: 5pt; margin-bottom: 5pt;"><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">On Jun 13, 2024, at 1:27</span><span style="font-size: 9pt; font-family: Arial, sans-serif;"> </span><span style="font-size: 9pt; font-family: Helvetica;">PM, Yongzhong Li <</span><a href="mailto:yongzhong.li@mail.utoronto.ca" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">yongzhong.li@mail.utoronto.ca</span></a><span style="font-size: 9pt; font-family: Helvetica;">> wrote:</span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div></div><div><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580m_-4861803116733450987pfptBannerxs2204y"><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580m_-4861803116733450987pfptBannerxs2204y"><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580m_-4861803116733450987pfptBannerxs2204y"><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Arial, sans-serif;">This Message Is From an External Sender</span><o:p></o:p></div></div></div></div></div></div><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580m_-4861803116733450987pfptBannerxs2204y"><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Arial, sans-serif;">This message came from outside your organization.</span><o:p></o:p></div></div></div></div></div></div></div></div><div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Helvetica;">Hi Matt,<br><br>I have rerun the program with the keys you provided. The system output when performing ksp solve and the final petsc log output were stored in a .txt file attached for your reference.<br><br>Thanks!<br>Yongzhong</span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div></div></div><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580m_-4861803116733450987mail-editor-reference-message-container"><div><div><p class="MsoNormal" style="margin: 0cm 0cm 12pt; font-size: 12pt; font-family: Aptos, sans-serif;"><b><span style="font-size: 9pt; font-family: Helvetica;">From: </span></b><span style="font-size: 9pt; font-family: Helvetica;">Matthew Knepley <</span><a href="mailto:knepley@gmail.com" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">knepley@gmail.com</span></a><span style="font-size: 9pt; font-family: Helvetica;">><br><b>Date: </b>Wednesday, June 12, 2024 at 6:46</span><span style="font-size: 9pt; font-family: Arial, sans-serif;"> </span><span style="font-size: 9pt; font-family: Helvetica;">PM<br><b>To: </b>Yongzhong Li <</span><a href="mailto:yongzhong.li@mail.utoronto.ca" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">yongzhong.li@mail.utoronto.ca</span></a><span style="font-size: 9pt; font-family: Helvetica;">><br><b>Cc: </b></span><a href="mailto:petsc-users@mcs.anl.gov" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">petsc-users@mcs.anl.gov</span></a><span style="font-size: 9pt; font-family: Helvetica;"> <</span><a href="mailto:petsc-users@mcs.anl.gov" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">petsc-users@mcs.anl.gov</span></a><span style="font-size: 9pt; font-family: Helvetica;">>, </span><a href="mailto:petsc-maint@mcs.anl.gov" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">petsc-maint@mcs.anl.gov</span></a><span style="font-size: 9pt; font-family: Helvetica;"> <</span><a href="mailto:petsc-maint@mcs.anl.gov" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">petsc-maint@mcs.anl.gov</span></a><span style="font-size: 9pt; font-family: Helvetica;">>, Piero Triverio <</span><a href="mailto:piero.triverio@utoronto.ca" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">piero.triverio@utoronto.ca</span></a><span style="font-size: 9pt; font-family: Helvetica;">><br><b>Subject: </b>Re: [petsc-maint] Assistance Needed with PETSc KSPSolve Performance Issue</span><o:p></o:p></p></div><table class="MsoNormalTable" border="0" cellspacing="0" cellpadding="0" align="left" width="100%" style="width: 601.4375px; display: table; float: none;"><tbody><tr><td style="background: rgb(166, 166, 166); padding: 5.25pt 1.5pt;"></td><td width="100%" style="width: 567.4375px; background: rgb(234, 234, 234); padding: 5.25pt 3.75pt 5.25pt 11.25pt;"><div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="ZH-CN" style="font-size: 9pt; font-family: DengXian; color: rgb(33, 33, 33);">你通常不会收到来自</span><span style="font-size: 9pt; font-family: "Segoe UI", sans-serif; color: rgb(33, 33, 33);"> </span><span style=""><a href="mailto:knepley@gmail.com" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: "Segoe UI", sans-serif;">knepley@gmail.com</span></a></span><span style="font-size: 9pt; font-family: "Segoe UI", sans-serif; color: rgb(33, 33, 33);"> </span><span lang="ZH-CN" style="font-size: 9pt; font-family: DengXian; color: rgb(33, 33, 33);">的电子邮件。</span><span style=""><a href="https://urldefense.us/v3/__https://aka.ms/LearnAboutSenderIdentification__;!!G_uCfscf7eWS!djGfJnEhNJROfsMsBJy5u_KoRKbug55xZ64oHKUFnH2cWku_Th1hwt4TDdoMd8pWYVDzJeqJslMNZwpO3y0Et94d31qk-oCEwo4$" target="_blank" style="color: purple; text-decoration: underline;"><span lang="ZH-CN" style="font-size: 9pt; font-family: DengXian;">了解这一点为什么很重要</span></a></span><o:p></o:p></div></div></div></div></div></div></div></td><td width="75" style="width: 56.25pt; background: rgb(234, 234, 234); padding: 5.25pt 3.75pt;"></td></tr></tbody></table><div><div><div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">On Wed, Jun 12, 2024 at 6:36</span><span style="font-size: 9pt; font-family: Arial, sans-serif;"> </span><span style="font-size: 9pt; font-family: Helvetica;">PM Yongzhong Li <</span><a href="mailto:yongzhong.li@mail.utoronto.ca" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">yongzhong.li@mail.utoronto.ca</span></a><span style="font-size: 9pt; font-family: Helvetica;">> wrote:</span><o:p></o:p></div></div></div></div></div></div></div><div><blockquote style="border-width: medium medium medium 1pt; border-style: none none none solid; border-image: none; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt; border-color: currentcolor currentcolor currentcolor rgb(204, 204, 204);"><div><div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; font-family: Helvetica; color: white;">Dear PETSc’s developers, I hope this email finds you well. I am currently working on a project using PETSc and have encountered a performance issue with the KSPSolve function. Specifically, I have noticed that the time taken by KSPSolve is </span><o:p></o:p></div></div></div></div></div></div></div><div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; font-family: Helvetica; color: white;">ZjQcmQRYFpfptBannerStart</span><o:p></o:p></div></div></div></div></div></div></div><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580m_-4861803116733450987m_5223539340070699115pfptBannerpeukvww" style="margin-top: 12pt; margin-bottom: 12pt; border-width: initial; border-style: initial; border-color: currentcolor; border-radius: 4px; min-width: 200px;"><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580m_-4861803116733450987m_5223539340070699115pfptBannerpeukvww" style="margin-bottom: 0.75pt; float: left;"><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580m_-4861803116733450987m_5223539340070699115pfptBannerpeukvww"><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif; line-height: 13.5pt; background: rgb(208, 216, 220);"><b><span style="font-size: 10.5pt; font-family: Arial, sans-serif;">This Message Is From an External Sender</span></b><o:p></o:p></div></div></div></div></div></div></div><div id="m_-7305460844614688919m_2643581689528628203m_6159968039748304261m_1825240119000957322m_-6075196701903926580m_-4861803116733450987m_5223539340070699115pfptBannerpeukvww" style="margin-top: 1.5pt;"><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif; line-height: 13.5pt; background: rgb(208, 216, 220);"><span style="font-size: 9pt; font-family: Arial, sans-serif;">This message came from outside your organization.</span><o:p></o:p></div></div></div></div></div></div></div></div><div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif; background: rgb(208, 216, 220);"><span style="font-size: 1pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div></div></div></div></div><div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 1pt; font-family: Helvetica; color: white;">ZjQcmQRYFpfptBannerEnd</span><o:p></o:p></div></div></div></div></div></div></div><div><div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">Dear </span><span lang="EN-US" style="font-size: 9pt; font-family: Helvetica;">PETSc’s developers</span><span style="font-size: 9pt; font-family: Helvetica;">,</span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">I hope this email finds you well.</span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">I am currently working on a project using PETSc and have encountered a performance issue with the </span><span style="font-size: 9pt; font-family: "Courier New";">KSPSolve</span><span style="font-size: 9pt; font-family: Helvetica;"> function. Specifically, <b>I have noticed that the time taken by </b></span><b><span style="font-size: 9pt; font-family: "Courier New";">KSPSolve</span></b><b><span style="font-size: 9pt; font-family: Helvetica;"> is </span></b><b><span lang="EN-US" style="font-size: 9pt; font-family: Helvetica;">almost two times </span></b><b><span style="font-size: 9pt; font-family: Helvetica;">greater than the CPU time for matrix-vector product multiplied by the number of iteration steps</span></b><span style="font-size: 9pt; font-family: Helvetica;">. </span><span lang="EN-US" style="font-size: 9pt; font-family: Helvetica;">I use C++ chrono to record CPU time.</span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">For context, I am using a shell system matrix</span><span lang="EN-US" style="font-size: 9pt; font-family: Helvetica;"> A</span><span style="font-size: 9pt; font-family: Helvetica;">. Despite my efforts to </span><span lang="EN-US" style="font-size: 9pt; font-family: Helvetica;">parallelize</span><span style="font-size: 9pt; font-family: Helvetica;"> the matrix-vector product</span><span lang="EN-US" style="font-size: 9pt; font-family: Helvetica;"> (Ax)</span><span style="font-size: 9pt; font-family: Helvetica;">, the overall solve time remains higher</span><span lang="EN-US" style="font-size: 9pt; font-family: Helvetica;"> than the matrix vector product per iteration indicates when multiple threads were used</span><span style="font-size: 9pt; font-family: Helvetica;">. Here are a few details of my setup:</span><o:p></o:p></div></div></div></div></div></div><ul type="disc" style="margin-bottom: 0cm; margin-top: 0cm;"><li class="MsoNormal" style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><b><span style="font-size: 9pt; font-family: Helvetica;">Matrix Type</span></b><span style="font-size: 9pt; font-family: Helvetica;">: Shell system matrix</span><o:p></o:p></li><li class="MsoNormal" style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><b><span style="font-size: 9pt; font-family: Helvetica;">Preconditioner</span></b><span style="font-size: 9pt; font-family: Helvetica;">: </span><span lang="EN-US" style="font-size: 9pt; font-family: Helvetica;">Shell PC</span><o:p></o:p></li><li class="MsoNormal" style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><b><span style="font-size: 9pt; font-family: Helvetica;">Parallel Environment</span></b><span style="font-size: 9pt; font-family: Helvetica;">: </span><span lang="EN-US" style="font-size: 9pt; font-family: Helvetica;">Using Intel MKL as PETSc’s BLAS/LAPACK library, multithreading is enabled</span><o:p></o:p></li></ul><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 9pt; font-family: Helvetica;">I have considered several potential reasons, such as preconditioner setup, additional solver operations, and the inherent overhead of using a shell system matrix. <b>However, since KSPSolve is a high-level API, I have been unable to pinpoint the exact cause of the increased solve time.</b></span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 9pt; font-family: Helvetica;">Have you observed the same issue? </span><span style="font-size: 9pt; font-family: Helvetica;">Could you</span><span lang="EN-US" style="font-size: 9pt; font-family: Helvetica;"> please </span><span style="font-size: 9pt; font-family: Helvetica;">provide some </span><span lang="EN-US" style="font-size: 9pt; font-family: Helvetica;">experience </span><span style="font-size: 9pt; font-family: Helvetica;">on how to diagnose and address this performance discrepancy? Any insights or recommendations you could offer would be greatly appreciated.</span><o:p></o:p></div></div></div></div></div></div></div></div></div></blockquote><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">For any performance question like this, we need to see the output of your code run with</span><o:p></o:p></div></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> -ksp_view -ksp_monitor_true_residual -ksp_converged_reason -log_view</span><o:p></o:p></div></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> Thanks,</span><o:p></o:p></div></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> Matt</span><o:p></o:p></div></div></div></div></div></div></div><div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div></div></div></div><blockquote style="border-width: medium medium medium 1pt; border-style: none none none solid; border-image: none; padding: 0cm 0cm 0cm 6pt; margin: 5pt 0cm 5pt 4.8pt; border-color: currentcolor currentcolor currentcolor rgb(204, 204, 204);"><div><div><div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">Thank you for your time and assistance.</span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">Best</span><span lang="EN-US" style="font-size: 9pt; font-family: Helvetica;"> regards,</span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 9pt; font-family: Helvetica;">Yongzhong</span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif;">-----------------------------------------------------------</span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><b><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif;">Yongzhong Li</span></b><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif;">PhD student | Electromagnetics Group</span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif;">Department of Electrical & Computer Engineering</span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif;">University of Toronto</span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><a href="https://urldefense.us/v3/__http://www.modelics.org__;!!G_uCfscf7eWS!cuLttMJEcegaqu461Bt4QLsO4fASfLM5vjRbtyNhWJQiInbjgNwkGNdkFE1ebSbFjOUatYB0-jd2yQWMWzqkDFFjwMvNl3ZKAr8$" target="_blank" style="color: purple; text-decoration: underline;"><span lang="EN-US" style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(5, 99, 193);">http://www.modelics.org</span></a><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div></div></div></div></div></blockquote></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"><br clear="all"></span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">-- </span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div><div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;">What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener</span><o:p></o:p></div></div></div></div></div></div></div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div></div></div><div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><a href="https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!djGfJnEhNJROfsMsBJy5u_KoRKbug55xZ64oHKUFnH2cWku_Th1hwt4TDdoMd8pWYVDzJeqJslMNZwpO3y0Et94d31qkNOuenGA$" target="_blank" style="color: purple; text-decoration: underline;"><span style="font-size: 9pt; font-family: Helvetica;">https://www.cse.buffalo.edu/~knepley/</span></a><o:p></o:p></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"><ksp_petsc_log.txt></span><o:p></o:p></div></div></div></div></div></div></blockquote></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"> </span><o:p></o:p></div></div></div></div></div></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span style="font-size: 9pt; font-family: Helvetica;"><ksp_petsc_log.txt><ksp_petsc_log_noguess.txt></span><o:p></o:p></div></div></div></div></div></blockquote></div></div></div></div></div></div></div></blockquote></div></div></blockquote></div></div></div></div></div></div></blockquote></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div></div></div></div></div></div></div></blockquote></div></div></div></div></div></div></blockquote></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><br clear="all"><o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">-- <o:p></o:p></div></div></div><div><div><div><div><div><div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener<o:p></o:p></div></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><a href="https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!fVvbGldqcUV5ju4jpu5oGmt-VjITi5JpCJzhHxpbgsERLVYZzglpxKOOyrBRGxjRxp7vWHwt3SnINFOQErR1Z8kcDcf3cNeD9Gw$" target="_blank" style="color: purple; text-decoration: underline;">https://www.cse.buffalo.edu/~knepley/</a><o:p></o:p></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></blockquote></div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div></div></div></div></blockquote></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><br clear="all"><o:p></o:p></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><span class="gmailsignatureprefix">--</span><span class="apple-converted-space"> </span><o:p></o:p></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;">What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener<o:p></o:p></div></div></div><div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"> <o:p></o:p></div></div></div><div><div style="margin: 0cm; font-size: 12pt; font-family: Aptos, sans-serif;"><a href="https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!aQJpmm5W6l6FUiumnIPmkouzwzNUfx-Dyq04i1O2KS_InQGk6qjI7wUir0Hx6QEUQE2AMiJDsez3x2Os2C2d$" target="_blank" style="color: purple; text-decoration: underline;">https://www.cse.buffalo.edu/~knepley/</a></div></div></div></div></blockquote></div></div></div></div></div></div></blockquote></div><br></body></html>