ApproxFun.jl

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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...

dlfivefifty

`f = Fun(exp)` and `x = Fun()` is a very convenient as a debug tool, but the semantics are pretty horrible: why would asking to create a `Fun` to represent...

dlfivefifty

Support other abstract array backends

12

The proposal is to template out the coefficient storage ```Julia struct Fun{S,T,V} space::S coefficients::V end ``` this will allow, for example, `Fun{Chebyshev,Float64,GPUArray{Float64}}`. Also, it will allow views of coefficients and...

dlfivefifty

applying Multiplication operators in coefficient space is O(n^2) if you use clenshaw, that is, only ever multiply by J

dlfivefifty

Use Polynomials.roots instead of custom implementation for `complexroots`

6

The benefit is then you get a speed up from FastPolynomialRoots.jl. There may be a slowdown for the roots command. If the issue https://github.com/JuliaMath/Polynomials.jl/issues/130 goes forward, then this won't be...

dlfivefifty

It's possible to increment both alpha and beta with a banded operator with upper bandwidth 2. When `alpha == beta`, then the first band is identically zero with no rounding...

MikaelSlevinsky

Matrix functions

1

After Julia 1.0 (https://github.com/JuliaLang/julia/pull/23233), the following should "just work:" ```julia julia> using ApproxFun julia> Fun(exp)(rand(2,2)) ERROR: MethodError: no method matching isless(::Array{Float64,2}, ::Int64) Closest candidates are: isless(::ApproxFun.Infinity{Bool}, ::Number) at /Users/Mikael/.julia/v0.6/ApproxFun/src/LinearAlgebra/helper.jl:517 isless(::AbstractFloat,...

MikaelSlevinsky

when `p == Inf`, the p-norm calls `maximum(abs, f)`, (note that this changed from `maxabs(f)` in https://github.com/JuliaApproximation/ApproxFun.jl/commit/20de8e3d981071f2dcecf4350af5182885c844e0 due to deprecations. But `Base`'s `maximum(abs, f)` returns a piecewise `Fun` and behaves...

MikaelSlevinsky

Change a<b, max(a,b) to a.<b, max.(a,b)

4

The current usage is confusing as you'd expect `

dlfivefifty

There are too many templated variables in Operators, causing slow compiles without actual speed improvement, since `PlusOperator` works with generic operators anyways.

dlfivefifty