<div dir="ltr"><div class="gmail_extra"><div class="gmail_quote">On Thu, Jul 31, 2014 at 3:24 PM, Brian Yang <span dir="ltr"><<a href="mailto:jyang29@uh.edu" target="_blank">jyang29@uh.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div dir="ltr"><div><div><div><div><div><div><div><div><div><div>Hi all,<br><br></div>Here's an abstract of the problem,<br><br></div>I got src and rec, they are 3D images with the same size, say Z, X, Y.<br></div><br>
</div>We call one (Z, X) is a panel and then there's Y panels for both src and rec. BTW, they hold complex numbers.<br><br></div>For example, for the <b>first</b> panel (always process the same panel) of src and rec:<br>
<br></div>Take the first panel of src as our A (20x20),<br></div>take the first column of first panel of rec as our b (20x1),<br></div>solve the linear system and get x (20x1),<br></div>go to next column of the first panel of rec until finish this panel,<br>
</div><div>assemble all the solution x column by column (20x20).</div></div></blockquote><div><br></div><div>This is a fine conceptual explanation of the algorithm, however I do not think you</div><div>want to implement it this way. Since you are solving all these panels independently,</div>
<div>you can just construct the block matrix, with each panel as a block and solve it all</div><div>at once (they clearly fit into memory). This might not be optimal for multiple rhs.</div><div><br></div><div>If the matrices really are dense and you have multiple rhs, then you should look at</div>
<div>using Elemental. We have an interface to it, although I am not sure we have hooked up</div><div>the multiple rhs solves.</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div dir="ltr"><div>After finishing the first panel of src and rec, go to next... repeat.<br><br><br></div><div>Hope I explained well of my problem. I used SeqDense matrix for A and Seq vector for b.<br>
</div><div><br></div><div>Here's the flow,<br><br></div><div>- start<br></div><div>- all the nodes will share all the Y panels, each node will get part of them<br></div><div>- each node will read in its own part of src and rec images<br>
</div><div>- for each node, take a panel of src and rec<br></div><div><b>- create Mat and Vec, fill them<br></b></div><div><b>- create KSP and solve by lsqr<br></b></div><div><b>- get the solution<br></b></div><div><b>- destroy all the petsc object, A, b, x (destroying KSP will give me error here!)</b><br>
</div><div>- repeat for the next panel<br><br><br></div><div>Here's the time (seconds) output from node 2 (random choice):<br><br></div><div> <u><b>entire time for this panel</b></u> <u><i>solving time</i></u><br>
</div><div><br><blockquote style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex" class="gmail_quote"> processing panel 1 <u><b>time</b></u>= 3.2995000E-02 <u><i>solver</i></u>= 3.0995002E-02<br>
processing panel 2 time= 3.5994001E-02 solver= 3.4995001E-02<br> processing panel 3 time= 3.9994001E-02 solver= 3.8994007E-02<br> processing panel 4 time= 4.4993997E-02 solver= 4.3993995E-02<br>
processing panel 5 time= 4.8991993E-02 solver= 4.6992987E-02<br> processing panel 6 time= 5.4991007E-02 solver= 5.3991005E-02<br> processing panel 7 time= 5.8990985E-02 solver= 5.7990998E-02<br>
processing panel 8 time= 6.3990027E-02 solver= 6.1990023E-02<br> processing panel 9 time= 6.8989992E-02 solver= 6.6990018E-02<br> processing panel 10 time= 7.3989004E-02 solver= 7.1989000E-02<br>
processing panel 11 time= 7.7987969E-02 solver= 7.6987982E-02<br> processing panel 12 time= 8.1988037E-02 solver= 7.9988003E-02<br> processing panel 13 time= 8.8985980E-02 solver= 8.6987019E-02<br>
processing panel 14 time= 9.4985008E-02 solver= 9.2984974E-02<br> processing panel 15 time= 0.1009850 solver= 9.8985016E-02<br> processing panel 16 time= 0.1119831 solver= 0.1099830 <br>
processing panel 17 time= 0.1269809 solver= 0.1239820 <br> processing panel 18 time= 0.1469780 solver= 0.1439790 <br> processing panel 19 time= 0.1709731 solver= 0.1669741 <br>
processing panel 20 time= 0.1909720 solver= 0.1869720 <br> processing panel 21 time= 0.2019690 solver= 0.1979700 <br> processing panel 22 time= 0.2239659 solver= 0.2199659 <br>
processing panel 23 time= 0.2369640 solver= 0.2319648 <br> processing panel 24 time= 0.2499621 solver= 0.2449629 <br> processing panel 25 time= 0.2709589 solver= 0.2659600 <br>
processing panel 26 time= 0.2869561 solver= 0.2829571 <br> processing panel 27 time= 0.3129530 solver= 0.3059540 <br> processing panel 28 time= 0.3389480 solver= 0.3329499 <br>
processing panel 29 time= 0.3719430 solver= 0.3649440 <br> processing panel 30 time= 0.3949399 solver= 0.3879409 <br> processing panel 31 time= 0.4249353 solver= 0.4169374 <br>
processing panel 32 time= 0.4549308 solver= 0.4469318 <br> processing panel 33 time= 0.4859262 solver= 0.4759283 <br> processing panel 34 time= 0.5119228 solver= 0.5019240 <br>
processing panel 35 time= 0.5449171 solver= 0.5349178 <br> processing panel 36 time= 0.5689130 solver= 0.5579152 <br> processing panel 37 time= 0.5959096 solver= 0.5849104 <br>
processing panel 38 time= 0.6199055 solver= 0.6079073<br></blockquote><div><br></div><div>You could see the time for solving the panels are increasing all the time. The panel number here is the local one. If I start to solve from panel 40 (random choice):<br>
</div></div></div></blockquote><div><br></div><div>It certainly looks like you have a growing memory footprint. It is likely to have happened</div><div>when you extracted/replaced parts of the matrix, which I think is unnecessary as I said above.</div>
<div><br></div><div> Thanks,</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div><div><blockquote style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex" class="gmail_quote">
processing panel 40 time= 5.5992007E-02 solver= 5.1991999E-02<br> processing panel 41 time= 9.1986001E-02 solver= 9.0986013E-02<br>
processing panel 42 time= 0.1309800 solver= 0.1299810 <br> processing panel 43 time= 0.1719730 solver= 0.1709740 <br> processing panel 44 time= 0.2119681 solver= 0.2109680 <br>
processing panel 45 time= 0.2529620 solver= 0.2519621 <br> processing panel 46 time= 0.2919550 solver= 0.2909551 <br> processing panel 47 time= 0.3319499 solver= 0.3309500 <br>
processing panel 48 time= 0.3719430 solver= 0.3709428 <br> processing panel 49 time= 0.4129372 solver= 0.4109371 <br> processing panel 50 time= 0.4529319 solver= 0.4509320 <br>
processing panel 51 time= 0.4929240 solver= 0.4909239 <br> processing panel 52 time= 0.5339203 solver= 0.5319204 <br> processing panel 53 time= 0.5779119 solver= 0.5759130 <br>
processing panel 54 time= 0.6199059 solver= 0.6179061 <br> processing panel 55 time= 0.6648979 solver= 0.6628990 <br> processing panel 56 time= 0.7248902 solver= 0.7218900 <br>
processing panel 57 time= 0.7938790 solver= 0.7908792 <br> processing panel 58 time= 0.8728676 solver= 0.8698678 <br> processing panel 59 time= 0.9778509 solver= 0.9748516 <br>
processing panel 60 time= 1.125830 solver= 1.122829 <br> processing panel 61 time= 1.273806 solver= 1.268806 <br> processing panel 62 time= 1.448780 solver= 1.444779 <br>
processing panel 63 time= 1.647749 solver= 1.643749 <br> processing panel 64 time= 1.901712 solver= 1.896712 <br> processing panel 65 time= 2.143673 solver= 2.138674 <br>
processing panel 66 time= 2.437630 solver= 2.431629 <br> processing panel 67 time= 2.744583 solver= 2.736586 <br> processing panel 68 time= 3.041536 solver= 3.035538<br>
</blockquote><div><br></div><div>The trend is the same, the time is increasing and also starts from a very quick one. <br><br><br></div><div>Since I have thousands of panels for src and rec, the execution time is unbearable as it goes.<br>
</div><div>So I am wondering whether I used the right method? or there's memory issue?<br><br></div><div>Thanks.<br></div></div></div></div>
</blockquote></div><br><br clear="all"><div><br></div>-- <br>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
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