Hi, I have been experimenting with various finite difference algorithms for computing derivatives and I found and implemented a general algorithm for computing arbitrarily high derivative to arbitrarily high order [1]. So for anyone interested in playing with it I wrapped it up in a small package.
I would also like to ask for your an advice on how to improve the performance of the function fdd, so far for a first derivative on a three point stencil (on a non-uniformly spaced mesh) it takes ten times as much time to compute the derivative, when compared to a hand crafted implementation of the same function. For a comparison you can call using FiniteDifferenceDerivatives x=linspace(0,1,1000) f=sin(x) df=copy(x) @elapsed for i = 1:1000; fdd(1,3,x,f); end # general function => ~0.5 s @elapsed for i = 1:1000; fdd13(x,f); end # hand crafted => ~0.05 s Obviously, most of the time is spent inside fddcoeffs. One way I could increase the performance is to cache the results of fddcoeffs (its result depends only on the mesh). In my use case however, the mesh changes often and fddcoeffs has to be called every time fdd is called. I also tried to replace x[i1:i1+order-1] with view(x,i1:i1+order-1) in the call to fddcoeffs (with view from ArrayViews), but it didn't result in much of an improvement. I also played with swapping the indexing order of c in fddcoeffs, but to no avail (maybe because the typical size of the matrix c is small (3x3 or similar)). Maybe I should try to inline the fddcoeffs into the main body of fdd (I did this in my earlier version, and it actually resulted in an improvement, but it looked kind of less elegant)? Any advice (or pull requests) would be welcome. [1] https://github.com/pwl/FiniteDifferenceDerivatives.jl Cheers, Paweł
