I would love to see lots of improvements in the Calculus package. The interface is kind of wonky and there’s probably a lot of places where we’re getting less than ideal results.
But I currently own far too many of Julia’s packages at the moment. If other people want to take some of them over, it will radically improve my life. As things stand, it’s literally impossible for me to keep up with the workload that package maintenance would involve. — John On Jan 20, 2014, at 10:54 AM, Ivar Nesje <[email protected]> wrote: > The calculus package could definitely be much better if someone with knowhow > and time would improve it. Unfortunately it seems like @johnmyleswhite does > not maintain this package anymore, and nobody has taken up the ball. > > > kl. 19:40:28 UTC+1 mandag 20. januar 2014 skrev Hans W Borchers følgende: > I looked into the Calculus package and its derivative functions. First, I got > errors when running examples from the README file: > > julia> second_derivative(x -> sin(x), pi) > ERROR: no method eps(DataType,) > in finite_difference at > /Users/HwB/.julia/Calculus/src/finite_difference.jl:27 > in second_derivative at /Users/HwB/.julia/Calculus/src/derivative.jl:67 > > Then I was a bit astonished to see not too accurate results such as > > julia> abs(second_derivative(sin, 1.0) + sin(1.0)) > 6.647716624952338e-7 > > while, when applying the standard central formula for second derivatives, > (f(x+h) - 2*f(x) + f(x-h)) / h^2 with the (by theory) suggested step length > eps^0.25 (for second derivatives) will result in a much better value: > > julia> h = eps()^0.25; > > julia> f = sin; x = 1.0; > > julia> df = (sin(x+h) - 2*sin(x) + sin(x-h)) / h^2 > -0.8414709866046906 > > julia> abs(df + sin(1.0)) > 1.7967940468821553e-9 > > The functions for numerical differentiation in Calculus look quite involved, > maybe it would be preferable to apply known approaches derived from Taylor > series. Even the fourth order derivative will in this case lead to an > absolute error below 1e-05!
