Re: [julia-users] Re: ANN: ApproxFun v0.0.3 with general linear PDE solving on rectangles
I'll add to the partial list, just in case it is useful: a) Algorithm for the convolution of Chebyshev series b) Bivariate rootfinding c) Linearity detection of operators (closely related to (5)) d) Automatic (though a little rough) approximation of functions with singularities e) Remez, cf, least squares, pade polynomial approximation f) Vector calculus g) Field of values algorithm It may be good to have 3), 4), 6), 7), b). Not sure if Julia offers any advantage for 2), 5), 8), c). On Thursday, 11 September 2014 19:43:27 UTC-4, Sheehan Olver wrote: Chebfun is a lot more full featured, and ApproxFun is _very_ rough around the edges. ApproxFun will probably end up a very different animal than chebfun: right now the goal is to tackle PDEs on a broader class of domains, something I think is beyond the scope of Chebfun due to issues with Matlab's speed, memory management, etc. Here’s a partial list of features in Chebfun not in ApproxFun: 1)Automatic edge detection and domain splitting 2)Support for delta functions 3)Built-in time stepping (pde15s) 4)Eigenvalue problems 5)Automatic nonlinear ODE solver 6)Operator exponential 7)Smarter constructor for determining convergence 8)Automatic differentiation I have no concrete plans at the moment of adding these features, though eigenvalue problems and operator exponentials will likely find their way in at some point. Sheehan On 12 Sep 2014, at 12:14 am, Steven G. Johnson steve...@gmail.com javascript: wrote: This is great! At this point, what are the major differences in functionality between ApproxFun and Chebfun?
[julia-users] Re: FastGauss.jl: fast computation of Gauss quadrature rules
Jason Merrill, Thank you for your speed up suggestions. Managed to get close to a factor of 2 speed up out of GaussLegendre. I quickly looked at GaussJacobi too and also got a significant speed up there... still more to do on that code. Alex On Tuesday, 2 September 2014 20:52:28 UTC-4, Alex Townsend wrote: Both those tools look great. Trying them now. Thanks a bunch. Alex On Tuesday, 2 September 2014 19:16:36 UTC-4, Jason Merrill wrote: On Tuesday, September 2, 2014 5:57:43 AM UTC-7, Alex Townsend wrote: On Tuesday, 2 September 2014 03:00:10 UTC-4, Jason Merrill wrote: On Monday, September 1, 2014 2:33:31 PM UTC-7, Alex Townsend wrote: I have written a package FastGauss.jl available here: https://github.com/ajt60gaibb/FastGauss.jl I am a Julia beginner (only been learning for 2 weeks) so I am assuming the code can be improved in a million and one ways. Please tell me if I've done something that Julia does not like. I am not sure if it is appropriate to make this an official package. One thing to look out for is making sure your functions have consistent return types. E.g. in https://github.com/ajt60gaibb/FastGauss.jl/blob/91e2ac656b856876563d5aacf7b5a405e068b3da/src/GaussLobatto.jl#L4 you have Thanks! I tried to get the return types consistent, but obviously missed a few. I've been trying to use @code_typed to tell me this information, but reading the output is a little difficult (at the moment). I think the community as a whole would like to see better tooling around finding and fixing this kind of soft bug. You might check out https://github.com/tonyhffong/Lint.jl, and https://github.com/astrieanna/TypeCheck.jl. I haven't tried either of them myself yet, but I've heard people say good things about both of them.
[julia-users] Re: FastGauss.jl: fast computation of Gauss quadrature rules
On Tuesday, 2 September 2014 03:00:10 UTC-4, Jason Merrill wrote: On Monday, September 1, 2014 2:33:31 PM UTC-7, Alex Townsend wrote: I have written a package FastGauss.jl available here: https://github.com/ajt60gaibb/FastGauss.jl I am a Julia beginner (only been learning for 2 weeks) so I am assuming the code can be improved in a million and one ways. Please tell me if I've done something that Julia does not like. I am not sure if it is appropriate to make this an official package. One thing to look out for is making sure your functions have consistent return types. E.g. in https://github.com/ajt60gaibb/FastGauss.jl/blob/91e2ac656b856876563d5aacf7b5a405e068b3da/src/GaussLobatto.jl#L4 you have Thanks! I tried to get the return types consistent, but obviously missed a few. I've been trying to use @code_typed to tell me this information, but reading the output is a little difficult (at the moment). if ( n == 1 ) error(Lobatto undefined for n = 1.) elseif ( n == 2 ) x = ([-1.0,1.0],[1.0,1.0]) elseif ( n == 3 ) x = ([-1, 0, 1], [1.0, 4.0, 1.0]/3) # ... In the n==2 case, you're returning a tuple of two float vectors, but in the n==3 case, you're returning a tuple with one Int vector and one float vector. This issue crops up in a few other places, including sometimes returning a number and other times returning a vector. Another thing you might want to consider is devectorizing compound operations on vectors to avoid allocating containers to store intermediate results (either using https://github.com/lindahua/Devectorize.jl or manually). To pick one random place where this might be relevant: https://github.com/ajt60gaibb/FastGauss.jl/blob/5e3a8a2f9a7e327622bdd43f69bb712afcb16743/src/GaussJacobi.jl#L36 Good point. This makes a _huge_ difference in speed. Thank you. I had heard that devectorize was a good thing in Julia, but I'm from MATLAB where it's the opposite. I'll go through the code and update. I'm not 100% sure whether this will be relevant to your API, but many high performance Julia libs expose mutating versions of functions (marked with an ! at the end) that normally return arrays, allowing the caller to instead pass in a preallocated array for the result to be stored in that could potentially be reused from call to call. OK. I'll have a closer look at some commands with the ! suffix. If a quadrature rule may in some cases be used only once, it might be nice if there were a way to apply the quadrature method to a function on the fly without ever generating the entire node and weight vector. Thank you very much Jason.
[julia-users] Re: FastGauss.jl: fast computation of Gauss quadrature rules
Both those tools look great. Trying them now. Thanks a bunch. Alex On Tuesday, 2 September 2014 19:16:36 UTC-4, Jason Merrill wrote: On Tuesday, September 2, 2014 5:57:43 AM UTC-7, Alex Townsend wrote: On Tuesday, 2 September 2014 03:00:10 UTC-4, Jason Merrill wrote: On Monday, September 1, 2014 2:33:31 PM UTC-7, Alex Townsend wrote: I have written a package FastGauss.jl available here: https://github.com/ajt60gaibb/FastGauss.jl I am a Julia beginner (only been learning for 2 weeks) so I am assuming the code can be improved in a million and one ways. Please tell me if I've done something that Julia does not like. I am not sure if it is appropriate to make this an official package. One thing to look out for is making sure your functions have consistent return types. E.g. in https://github.com/ajt60gaibb/FastGauss.jl/blob/91e2ac656b856876563d5aacf7b5a405e068b3da/src/GaussLobatto.jl#L4 you have Thanks! I tried to get the return types consistent, but obviously missed a few. I've been trying to use @code_typed to tell me this information, but reading the output is a little difficult (at the moment). I think the community as a whole would like to see better tooling around finding and fixing this kind of soft bug. You might check out https://github.com/tonyhffong/Lint.jl, and https://github.com/astrieanna/TypeCheck.jl. I haven't tried either of them myself yet, but I've heard people say good things about both of them.
[julia-users] FastGauss.jl: fast computation of Gauss quadrature rules
I have written a package FastGauss.jl available here: https://github.com/ajt60gaibb/FastGauss.jl to compute Gauss quadrature rules to 16-digit precision (so far Legendre, Jacobi, Lobatto, Radau), aiming to be the fastest implementation in Julia. For example, this is how long it takes to compute 1,000,000 Gauss-Legendre nodes and weights: tic(), GaussLegendre( 100 ); toc() elapsed time: 0.336489122 seconds In my comparisons, GaussLegendre() is faster than Base.gauss() for n60 (nothing in it for small n), but my implementation right now does not allow for higher precision. I couldn't find a Gauss-Jacobi code in Base. I am a Julia beginner (only been learning for 2 weeks) so I am assuming the code can be improved in a million and one ways. Please tell me if I've done something that Julia does not like. I am not sure if it is appropriate to make this an official package.
