Cool! Let me know if you want any functionality added to make it useful.
Sent from my iPhone
> On Jun 20, 2014, at 11:11 PM, 'Stéphane Laurent' via julia-users
> <julia-users@googlegroups.com> wrote:
>
> Thank you, it works !!
>
> NB: I'm Stéphane and not Stéphanie :-)
>
>
> Le vendredi 20 juin 2014 00:13:08 UTC+2, Sheehan Olver a écrit :
>>
>> Hi Stephanie,
>>
>> Are you on the latest GitHub version? You can get on it with
>>
>> Pkg.checkout("ApproxFun")
>>
>> Sent from my iPad
>>
>>> On 20 Jun 2014, at 3:19 am, 'Stéphane Laurent' via julia-users
>>> <julia...@googlegroups.com> wrote:
>>>
>>> Hello Sheehan,
>>>
>>> I get this error when I run your code:
>>>
>>> julia> for k=1:5
>>> u=u-[B,L+gp(u)]\[0.,0.,L*u+g(u)-1.];
>>> end
>>> ERROR: Reducing over an empty array is not allowed.
>>> in _mapreduce at reduce.jl:151
>>> in mapreduce at reduce.jl:173
>>> in old_addentries! at
>>> /home/sdl/.julia/v0.3/ApproxFun/src/Operators/OperatorAlgebra.jl:106
>>> in addentries! at
>>> /home/sdl/.julia/v0.3/ApproxFun/src/Operators/OperatorAlgebra.jl:141
>>> in ShiftArray at
>>> /home/sdl/.julia/v0.3/ApproxFun/src/Operators/ShiftArray.jl:16
>>> in BandedArray at
>>> /home/sdl/.julia/v0.3/ApproxFun/src/Operators/ShiftArray.jl:110
>>> in getindex at /home/sdl/.julia/v0.3/ApproxFun/src/Operators/Operator.jl:46
>>> in getindex at
>>> /home/sdl/.julia/v0.3/ApproxFun/src/Operators/AlmostBandedOperator.jl:133
>>> in backsubstitution! at
>>> /home/sdl/.julia/v0.3/ApproxFun/src/Operators/adaptiveqr.jl:78
>>> in ultraiconversion at
>>> /home/sdl/.julia/v0.3/ApproxFun/src/Operators/Operator.jl:71
>>> in * at /home/sdl/.julia/v0.3/ApproxFun/src/Operators/Operator.jl:97
>>> in anonymous at no file:2
>>>
>>>
>>> Le mercredi 11 juin 2014 23:27:52 UTC+2, Sheehan Olver a écrit :
>>>>
>>>> Hi Stèphane,
>>>>
>>>> Nonlinear is not built in, but it’s easy enough to do by hand with
>>>> Newton iteration in function space. Let me know if there is any confusion
>>>> with the code below. I suppose I could just add a “nonlinsolve” routine
>>>> that bundles this up.
>>>>
>>>> (I am on the latest branch so this may or may not work on the 0.0.1
>>>> tag.)
>>>>
>>>>
>>>> Cheers,
>>>>
>>>> Sheehan
>>>>
>>>>
>>>>
>>>> x=Fun(identity,[-1.,1.])
>>>> d=x.domain
>>>> B=dirichlet(d)
>>>> D=diff(d)
>>>>
>>>> # Sets up L and g for equation in the form Lu + g(u)-1==0
>>>>
>>>> L=D^2 + 2(1-x.^2)*D
>>>> g=u->u.^2;gp=u->2u
>>>>
>>>> u=0.x # initial guess for the solution is zero
>>>>
>>>> for k=1:5
>>>> u=u-[B,L+gp(u)]\[0.,0.,L*u+g(u)-1.];
>>>> end
>>>>
>>>> norm(diff(u,2) + 2(1-x.^2).*diff(u) + g(u) -1) # This equals 0.0
>>>>
>>>>
>>>>> On 12 Jun 2014, at 1:02 am, 'Stéphane Laurent' via julia-users
>>>>> <julia...@googlegroups.com> wrote:
>>>>>
>>>>> Hello Sheehan,
>>>>>
>>>>> I have unsuccessfully tried to understand how works the differential
>>>>> equation solver (I do not understand the Airy example).
>>>>>
>>>>> It would be nice to have an example of code for a simple BVP such as :
>>>>>
>>>>> u" + 2(1-x^2)u + u^2 = 1 , u(-1) = u(1) = 0
>>>>>
>>>>> Regards,
>>>>> Stéphane
>>>>>
>>>>> Le lundi 24 mars 2014 02:04:25 UTC+1, Sheehan Olver a écrit :
>>>>>>
>>>>>>
>>>>>> I tagged a new release for ApproxFun
>>>>>> (https://github.com/dlfivefifty/ApproxFun) with major new features that
>>>>>> might interest people. Below are ODE solving and random number sampling
>>>>>> examples, find more in ApproxFun/examples. The code is meant as alpha
>>>>>> quality, so don't expect too much beyond the examples. There is
>>>>>> rudimentary support for PDE solving (e.g. Helmholtz in a square), but
>>>>>> it's reliability is limited without a better Lyapanov solver
>>>>>> (https://github.com/JuliaLang/julia/issues/5814).
>>>>>>
>>>>>> Cheers,
>>>>>>
>>>>>> Sheehan
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>> Pkg.add("ApproxFun")
>>>>>> using ApproxFun
>>>>>>
>>>>>> ODE Solving: solve the Airy equation on [-1000,10]
>>>>>>
>>>>>> x=Fun(identity,[-2000.,10.])
>>>>>> d=x.domain
>>>>>> D=diff(d)
>>>>>> ai=[dirichlet(d),D^2 - x]\[airyai(-2000.),0.]
>>>>>> plot(ai)
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>> Random number sampling: Sample a 2D Cauchy distribution on (-∞,∞)^2
>>>>>>
>>>>>> f = Fun2D((x,y)->1./(2π.*(x.^2 .+ y.^2 .+ 1).^(3/2)),Line(),Line())
>>>>>> r = sample(f,100)
>>>>
