# Eigenvalues problem in ApproxFun
**URL:** https://discourse.julialang.org/t/eigenvalues-problem-in-approxfun/580
**Category:** Numerics
**Created:** [November 26, 2016, 3:37pm UTC](https://discourse.julialang.org/t/eigenvalues-problem-in-approxfun/580 "2016-11-26T15:37:45Z")
**Posts on this page:** 12
**Page:** 1
### Author:  [@mzaffalon](https://discourse.julialang.org/u/mzaffalon)
#### Post date: [November 26, 2016, 3:37pm UTC](https://discourse.julialang.org/t/eigenvalues-problem-in-approxfun/580/1 "2016-11-26T15:37:45Z")
Is ApproxFun able to compute the eigenstates of a 1dimensional linear differential operator in the way Chebfun does? I assume not yet.
I am interested in the Schroedinger equation.
michele
---
### Author:  [@dlfivefifty](https://discourse.julialang.org/u/dlfivefifty)
#### Post date: [November 27, 2016, 12:19am UTC](https://discourse.julialang.org/t/eigenvalues-problem-in-approxfun/580/2 "2016-11-27T00:19:48Z")
There’s some very basic support:
```julia
using ApproxFun
S = Chebyshev()
B = dirichlet()
D = Derivative(S)
x = Fun()
λ,V=eigs([B;D^2 + x^2],200)
```
Here, `n=200` is a discretization size, and the eigenvalues/vectors are pruned to only return those which have converged.
Here all but the last operator is interpreted as a boundary condition. This syntax will likely be changed, and I’m hoping in the future to replace `eigs` built out of discrete matrices with a simultaneous inverse iteration (built on top of \).
---
### Author:  [@mzaffalon](https://discourse.julialang.org/u/mzaffalon)
#### Post date: [November 27, 2016, 10:00am UTC](https://discourse.julialang.org/t/eigenvalues-problem-in-approxfun/580/3 "2016-11-27T10:00:17Z")
Thank you so much! Here are the first three states of the harmonic oscillator
computed with the following code:
```julia
S = Chebyshev(Interval(-5,5))
B = dirichlet()
D = Derivative(S)
x = Fun(identity, Interval(-5, 5))
λ, V = eigs([B;-D^2/2 + x^2/2], 200)
p = sortperm(λ)
plot(V[p[1]])
plot!(V[p[2]])
plot!(V[p[3]])
```
and their energies (they should be 1/2, 3/2 and 5/2)
```julia
(0.500000000076718,1.5000000036715844,2.500000084018815)
```
(The eigenstates are not normalized, but you are surely aware of this.)
---
### Author:  [@Mason](https://discourse.julialang.org/u/Mason)
#### Post date: [March 15, 2018, 7:46pm UTC](https://discourse.julialang.org/t/eigenvalues-problem-in-approxfun/580/4 "2018-03-15T19:46:19Z")
Sorry to revive this old conversation but I’m trying to do somrthing similar to @mzaffalon but I guess something has changed with ApproxFun so the code used above doesn’t seem to work anymore. Trivially, `dirichlet()` is now `Dirichlet`, but even with that fixed, I am getting an error message I don’t quite understand when trying to recreate these results.
```julia
using ApproxFun
S = Chebyshev(Interval(-5,5))
B = Dirichlet()
D = Derivative(S)
x = Fun(identity, Interval(-5, 5))
λ, V = eigs([B;-D^2/2 + x^2/2], 200)
```
produces the error
```julia
Implement Conversion from ApproxFun.Chebyshev{ApproxFun.Segment{Float64},Float64} to ApproxFun.ArraySpace{ApproxFun.Space,1,ApproxFun.Point{Float64},Any}
defaultConversion(::ApproxFun.Chebyshev{ApproxFun.Segment{Float64},Float64}, ::ApproxFun.ArraySpace{ApproxFun.Space,1,ApproxFun.Point{Float64},Any}) at Conversion.jl:35
#eigs#725 at eigs.jl:11 [inlined]
eigs(::ApproxFun.InterlaceOperator{Float64,1,ApproxFun.Chebyshev{ApproxFun.Segment{Float64},Float64},ApproxFun.ArraySpace{ApproxFun.Space,1,ApproxFun.Point{Float64},Any},ApproxFun.CachedIterator{Tuple{Int64,Int64},ApproxFun.BlockInterlacer{Tuple{ApproxFun.Repeated{Bool}}},Tuple{Int64,Int64,Tuple{Void},Tuple{Int64}}},ApproxFun.CachedIterator{Tuple{Int64,Int64},ApproxFun.BlockInterlacer{Tuple{Array{Int64,1},ApproxFun.Repeated{Bool}}},Tuple{Int64,Int64,Tuple{Int64,Void},Tuple{Int64,Int64}}},Tuple{ApproxFun.Infinity{Bool},ApproxFun.Infinity{Bool}}}, ::Int64) at eigs.jl:8
include_string(::String, ::String) at loading.jl:522
include_string(::String, ::String, ::Int64) at eval.jl:30
include_string(::Module, ::String, ::String, ::Int64, ::Vararg{Int64,N} where N) at eval.jl:34
(::Atom.##100#105{String,Int64,String})() at eval.jl:75
withpath(::Atom.##100#105{String,Int64,String}, ::String) at utils.jl:30
withpath(::Function, ::String) at eval.jl:38
hideprompt(::Atom.##99#104{String,Int64,String}) at repl.jl:66
macro expansion at eval.jl:73 [inlined]
(::Atom.##98#103{Dict{String,Any}})() at task.jl:80
```
Does anyone have any ideas on how to do this with the current version of `ApproxFun`?
---
### Author:  [@dlfivefifty](https://discourse.julialang.org/u/dlfivefifty)
#### Post date: [March 15, 2018, 10:53pm UTC](https://discourse.julialang.org/t/eigenvalues-problem-in-approxfun/580/5 "2018-03-15T22:53:38Z")
I think I changed the override to `eigs(Bcs, A, n)`, that is, give the bcs seperate from the operator. I’ll check it works in the morning.
---
### Author:  [@Mason](https://discourse.julialang.org/u/Mason)
#### Post date: [March 15, 2018, 10:58pm UTC](https://discourse.julialang.org/t/eigenvalues-problem-in-approxfun/580/6 "2018-03-15T22:58:28Z")
> [@dlfivefifty](#):
>
> I think I changed the override to eigs(Bcs, A, n), that is, give the bcs seperate from the operator. I’ll check it works in the morning.
Yes, `eigs` will accept arguments of that form. But in this case, it throws an error because `size(Dirichlet(),1) == ∞`.
---
### Author:  [@dlfivefifty](https://discourse.julialang.org/u/dlfivefifty)
#### Post date: [March 16, 2018, 7:43am UTC](https://discourse.julialang.org/t/eigenvalues-problem-in-approxfun/580/7 "2018-03-16T07:43:31Z")
A work around was posted here [https://github.com/JuliaApproximation/ApproxFun.jl/issues/564#issuecomment-373555416](https://github.com/JuliaApproximation/ApproxFun.jl/issues/564#issuecomment-373555416)
---
### Author:  [@Mason](https://discourse.julialang.org/u/Mason)
#### Post date: [March 16, 2018, 4:14pm UTC](https://discourse.julialang.org/t/eigenvalues-problem-in-approxfun/580/8 "2018-03-16T16:14:07Z")
> [@dlfivefifty](#):
>
> A work around was posted here [Problem with eigs · Issue #564 · JuliaApproximation/ApproxFun.jl · GitHub](https://github.com/JuliaApproximation/ApproxFun.jl/issues/564#issuecomment-373555416)
Thanks very much!
Sorry to pester you but I was looking at some [examples](http://www.chebfun.org/examples/ode-eig/Eigenstates.html) used in `chebfun` and it seems that they’re able to get eigenvalues for all sorts of funny potentials, most of which don’t seem to work for me with `ApproxFun`.
For instance, for the absolute value potential,
```julia
S = Chebyshev(Interval(-10,10))
B = Dirichlet(S)
D = Derivative(S)
V = Fun(x -> abs(x), Interval(-10, 10))
λ, ψ = eigs(B, -D^2/2 + V, 200)
```
returns _no_ eigenvalues or eigenvectors even though they must exist.
I also tried various ways of making `abs(x)` better behaved like
```julia
V = Fun(x -> sqrt(x^2), Interval(-10, 10))
```
and
```julia
V = Fun(x -> sqrt(x^2 +0.1), Interval(-10, 10))
```
but to no avail. Do you have any ideas about what could cause this?
---
### Author:  [@dlfivefifty](https://discourse.julialang.org/u/dlfivefifty)
#### Post date: [March 16, 2018, 4:49pm UTC](https://discourse.julialang.org/t/eigenvalues-problem-in-approxfun/580/9 "2018-03-16T16:49:33Z")
Don’t use the constructor for functions with singularities, and specify a tolerance for `eigs`. This works pretty well form me:
```julia
x = Fun(-20 .. 20)
V = abs(x)
D = Derivative()
S = space(V)
B = [Dirichlet(S); continuity(S,0:1)]
λ, v = eigs(B, -D^2 + V, 500,tolerance=1E-10)
p = plot(V; legend=false)
for k=1:20
plot!(real(v[k]/norm(v[k]) + λ[k]))
end
p
```
---
### Author:  [@Mason](https://discourse.julialang.org/u/Mason)
#### Post date: [March 16, 2018, 5:14pm UTC](https://discourse.julialang.org/t/eigenvalues-problem-in-approxfun/580/10 "2018-03-16T17:14:55Z")
Ah, I see! Maybe I’ll spend some time with this and shoot you a pull request to add something about this to the documentation.
---
### Author:  [@dlfivefifty](https://discourse.julialang.org/u/dlfivefifty)
#### Post date: [March 16, 2018, 6:15pm UTC](https://discourse.julialang.org/t/eigenvalues-problem-in-approxfun/580/11 "2018-03-16T18:15:51Z")
👍 also think about adding an example to [GitHub - JuliaApproximation/ApproxFunExamples: Examples for using ApproFun.jl](https://github.com/JuliaApproximation/ApproxFunExamples)
---
### Author:  [@Mason](https://discourse.julialang.org/u/Mason)
#### Post date: [March 16, 2018, 6:25pm UTC](https://discourse.julialang.org/t/eigenvalues-problem-in-approxfun/580/12 "2018-03-16T18:25:19Z")
Just an FYI, the above code doesn’t seem to work on the current tagged version of `Approxfun` but works fine on the `Master` branch.