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