Just pushed an update so that the below is possible, for automatically
approximating a function with a singularity. This seems like the same vein
as what you were suggesting.
Fun(x->exp(x)/sqrt(1-x.^2),JacobiWeightSpace(-.5,-.5))
On Monday, September 15, 2014 8:11:18 PM UTC+10, Gabriel Mitchell wrote:
>
> >Here’s a partial list of features in Chebfun not in ApproxFun:
> > 1) Automatic edge detection and domain splitting
>
> The automatic splitting capability of chebfun is definitely really cool,
> but it always seemed to me to be a bit more then one would need for most
> use cases. That is, if I am defining some function like
>
> f = Fun(g::Function,[-1,1])
>
> where g is composed of things like absolute values and step functions I
> might need to do something sophisticated to figure out how to break up the
> domain, but if I instead pass something like
>
> f = Fun(g::PiecewiseFunction,[-1,1])
>
> which has some g that has been annotated by the user in some obvious way
> (or semiautomatically, given some basic rules for composing PiecewiseFunction
> types under standard operations) I might have a much easier time. In
> practice, when setting up problems in the first place one is often paying
> attention to where discontinuities are anyway, so providing such a
> mechanism might even be a natural way to help someone set up their problem.
>
> Maybe this kind of thing is incompatible with ApproxFun (sorry, I didn't
> look in detail yet). But at any rate, super cool work! If there are any
> plans to start a gallery of examples ala chebfun I would be happy to
> contribute some from population dynamics.
>
> On Friday, September 12, 2014 1:43:27 AM UTC+2, 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 <[email protected]>
>> wrote:
>>
>> > This is great!
>> >
>> > At this point, what are the major differences in functionality between
>> ApproxFun and Chebfun?
>>
>>
