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POMatlab slow performance using closures
 

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  1. POMatlab slow performance using closures
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    <p>I'm coding a solution for Poisson equation on a 2d rectangle using finite elements. In order to simplify the code I store handles to the basis functions in an array and then loop over these basis functions to create my matrix and right hand side. The problem with this is that even for very coarse grids it is prohibitively slow. For a 9x9 grid (using Dirichlet BC, there are 49 nodes to solve for) it takes around 20 seconds. Using the profile I've noticed that around half the time is spent accessing (not executing) my basis functions. </p> <p>The profiler says <code>matrix_assembly&gt;@(x,y)bilinearBasisFunction(x,y,xc(k-1),xc(k),xc(k+1),yc(j-1),yc(j),yc(j+1)) (156800 calls, 11.558 sec)</code>, the self time (not executing the bilinear basis code) is over 9 seconds. Any ideas as to why this might be so slow?</p> <p>Here's some of the code, I can post more if needed:</p> <pre><code>%% setting up the basis functions, storing them in cell array basisFunctions = cell(nu, 1); %nu is #unknowns i = 1; for j = 2:length(yc) - 1 for k = 2:length(xc) - 1 basisFunctions{i} = @(x,y) bilinearBasisFunction(x,y, xc(k-1), xc(k),... xc(k+1), yc(j-1), yc(j), yc(j+1)); %my code for bilinear basis functions i = i+1; end end %% Assemble matrices and RHS M = zeros(nu,nu); S = zeros(nu,nu); F = zeros(nu, 1); for iE = 1:ne for iBF = 1:nu [z1, dx1, dy1] = basisFunctions{iBF}(qx(iE), qy(iE)); F(iBF) = F(iBF) + z1*forcing_handle(qx(iE),qy(iE))/ae(iE); for jBF = 1:nu [z2, dx2, dy2] = basisFunctions{jBF}(qx(iE), qy(iE)); %M(iBF,jBF) = M(iBF,jBF) + z1*z2/ae(iE); S(iBF,jBF) = S(iBF, jBF) + (dx1*dx2 + dy1*dy2)/ae(iE); end end end </code></pre>
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    1. USLukas Bystricky
    1. USLukas Bystricky
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    1. COFor a start, you're calling that line 156,800 times (creating that many anonymous functions) in a double `for` loop and changing the parameter values using indexing each time! And are you sure `nu` is equal to `(length(xc)-2)*(length(yc)-2)` to avoid reallocation in the cell `basisFunctions` array?
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      1. POMatlab slow performance using closures
      1. UShorchler
    2. COIs there any reason to have 156800 functions instead of one function with the parameters `(jBF,qx(iE), qy(iE))`?
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      1. POMatlab slow performance using closures
      1. USDaniel
    3. CO@DanielR : there's only 49 functions, each with slightly different parameters. There are other ways to do this of course, but the way I did it here has the advantage of being very readable, and I don't see why it should be so much slower.
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      1. POMatlab slow performance using closures
      1. USLukas Bystricky
 

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