Ah my apologies - Haskell is my main language and I am used to being told that
I have missed an argument and I still haven’t got my head round Julia’s type
system.
> julia> typeof(Fun)
> DataType
> julia> help(Fun)
> DataType : ApproxFun.Fun{S<:ApproxFun.FunctionSpace{T,D},T<:Number}
> supertype: Any
> fields : [:coefficients,:space]
It would be nice if julia told you what arguments a function required. Perhaps
it does and I just don’t know how to ask it nicely.
Anyway the good news is that I get a very accurate answer (since I know the
answer analytically in this case). Thanks for your help and for a great package.
Dominic Steinitz
[email protected]
http://idontgetoutmuch.wordpress.com
On 22 Mar 2015, at 09:25, Sheehan Olver <[email protected]> wrote:
> You can do the following
>
> d = Interval(0,1)
> f1 = Fun(x->0,d)
> f2 = Fun(x->1 / ((1 + x)^2 + 1),d)
> f3 = Fun(y->y / (1 + y^2),d)
> f4 = Fun(y->y / (4 + y^2),d)
>
> u = [dirichlet(d^2),lap(d^2)]\[f1,f2,f3,f4]
>
>
>
>> On 22 Mar 2015, at 7:35 pm, Dominic Steinitz <[email protected]> wrote:
>>
>> Ah thanks - that produces an answer. However I want the boundary conditions
>> to be on [0,1]^2. I tried
>>
>>> dd = (domain(Fun(identity,[0.0,1.0])))^2
>>
>>
>>> u = [dirichlet(dd),lap(dd)]\[f1,f2,f3,f4]
>>
>>
>> but this gives me
>>
>>> julia> u = [dirichlet(dd),lap(dd)]\[f1,f2,f3,f4]
>>> WARNING: [a,b] concatenation is deprecated; use [a;b] instead
>>> in depwarn at
>>> /Applications/Julia-0.4.0-dev-5587ca352f.app/Contents/Resources/julia/lib/julia/sys.dylib
>>> in oldstyle_vcat_warning at
>>> /Applications/Julia-0.4.0-dev-5587ca352f.app/Contents/Resources/julia/lib/julia/sys.dylib
>>> in vect at abstractarray.jl:35
>>> ERROR: AssertionError: domainscompatible(a,b)
>>> in conversion_rule at
>>> /Users/dom/.julia/v0.4/ApproxFun/src/Spaces/Ultraspherical/UltrasphericalOperators.jl:313
>>> in conversion_type at
>>> /Users/dom/.julia/v0.4/ApproxFun/src/Fun/FunctionSpace.jl:146
>>> in coefficients at
>>> /Users/dom/.julia/v0.4/ApproxFun/src/Fun/FunctionSpace.jl:233
>>> in * at /Users/dom/.julia/v0.4/ApproxFun/src/Operators/algebra.jl:398
>>> in cont_reduce_dofs! at
>>> /Users/dom/.julia/v0.4/ApproxFun/src/PDE/cont_lyap.jl:20
>>> in cont_reduce_dofs! at
>>> /Users/dom/.julia/v0.4/ApproxFun/src/PDE/cont_lyap.jl:64
>>> in cont_constrained_lyap at
>>> /Users/dom/.julia/v0.4/ApproxFun/src/PDE/cont_lyap.jl:297
>>> in pdesolve at /Users/dom/.julia/v0.4/ApproxFun/src/PDE/pdesolve.jl:127
>>> in pdesolve at /Users/dom/.julia/v0.4/ApproxFun/src/PDE/pdesolve.jl:126
>>> in pdesolve at /Users/dom/.julia/v0.4/ApproxFun/src/PDE/pdesolve.jl:101
>>> in \ at /Users/dom/.julia/v0.4/ApproxFun/src/PDE/pdesolve.jl:138
>>
>>
>> I am not clear which domains are incompatible.
>>
>> Dominic Steinitz
>> [email protected]
>> http://idontgetoutmuch.wordpress.com
>>
>> On 22 Mar 2015, at 02:25, Sheehan Olver <[email protected]> wrote:
>>
>>>
>>> It's expanding f1-f4 as bivariate functions on [-1,1]^2, but instead you
>>> want to expand them as univariate functions on [-1,1]:
>>>
>>> d = Interval()^2
>>>
>>> f1 = Fun(x->0)
>>> f2 = Fun(x->1 / ((1 + x)^2 + 1))
>>> f3 = Fun(y->y / (1 + y^2))
>>> f4 = Fun(y->y / (4 + y^2))
>>>
>>> u = [dirichlet(d),lap(d)]\[f1,f2,f3,f4]
>>>
>>>
>>>
>>> On Sunday, March 22, 2015 at 8:02:45 AM UTC+11, idontgetoutmuch wrote:
>>>
>>>
>>> I am trying to solve Laplace's equation using ApproxFun with the following
>>> boundary conditions
>>>
>>> {
>>> \phi(x, 0) &= 0 \\
>>> \phi(x, 1) &= \frac{1}{(1 + x)^2 + 1} \\
>>> \phi(0, y) &= \frac{y}{1 + y^2} \\
>>> \phi(1, y) &= \frac{y}{4 + y^2}
>>> \end{aligned}
>>> }
>>>
>>> I'm not clear how to express these. I've tried
>>>
>>> {
>>> d = Interval()^2
>>>
>>> f1 = Fun((x,y)->0)
>>> f2 = Fun((x,y)->1 / ((1 + x)^2 + 1))
>>> f3 = Fun((x,y)->y / (1 + y^2))
>>> f4 = Fun((x,y)->y / (4 + y^2))
>>>
>>> u = [dirichlet(d),lap(d)]\[f1,f2,f3,f4]
>>> }
>>>
>>> and
>>>
>>> {
>>> u = [dirichlet(d),lap(d)]\[zeros(1),f2,f3,f4]
>>> }
>>>
>>> but in both cases I get errors (which I can attach).
>>>
>>> I can see ldirichlet and rdirichlet exist but I need to specify the top and
>>> bottom as well.
>>
>
