Sheehan Olver

`A_mul_B!` for transforms

6

See DifferentialEquations.jl gitter discussion with @ChrisRackauckas FFTW exposes this: https://github.com/JuliaMath/FFTW.jl/blob/8302e8730150ed999d58e371edfe8db2a979af71/src/fft.jl#L635-L639

Error out of adaptiveqr if bandrange is too large

1

Just had a case where a bug was giving huge Funs (181k coefficients), so \ just went on forever. It would probably be ideal to put a default upper limit...

Right now it uses a Mobius transformations, but this breaks down as t -> π

```julia Z = ApproxFun.ZeroOperator(ApproxFun.SequenceSpace(), ApproxFun.ConstantSpace(Float64)) [1 Z] |>ApproxFun.bandinds. # returns (0,-719) which is wrong, should be (0,0) ```

Make `points` lazy

5

That is, return an `AbstractVector`. This has the benefit that we can do fast transforms like: ```julia x = points(Chebyshev(),100) # Returns `ChebyshevPoints` f = Fun(exp) f.(x) # use transform,...

`[Chebyshev() ; Chebyshev()]` should probably return an `ArraySpace(Chebyshev(),2)`

The idea is to support, for example: ```julia f = Fun(Chebyshev(), Array{Float64}(1_000_000)) x = Fun() f .= cos.(1_000_000.*x) # no allocation ``` this is useful for time-stepping, for example. To...

Composing of functions and funs

38

Code like `x->abs(f(x))` in `abs(f::Fun)` doesn't benefit from the fact that `f` can be evaluated fast at the grid. Perhaps we need to override `∘(f, ::Fun)` to return `ComposeFun`, that...

Cosine clenshaw should work in angle variables

4

Right now it calls cos, which introduces inaccuracy

at the moment `[Fun(),1]` will promote `1` to be ` Fun(Chebyshev(Interval(NaN,NaN)),[1.0])`. But now that we can use `[Fun();1]` and get out a `Fun`, the existing promotion seems unnecessary. We should...