add segbuf to quadgkjl

[lxvm]

Sometimes quadgk is used in the inner loop of a larger calculation (such as a nested integral) and it is desirable to reduce the number of allocations it makes. This pr adds a segbuf field to the QuadGKJL algorithm to allow the user to pass in a segment buffer that reduces the amount of memory allocated by the routine when reused across calls with compatible domain, integral, and error types.

julia> using Integrals, QuadGK

julia> g(x, (k,)) = sin(k*x)
g (generic function with 1 method)

julia> alg = QuadGKJL(; segbuf=QuadGK.alloc_segbuf(Float64, Float64, Float64))
QuadGKJL{typeof(LinearAlgebra.norm), Vector{QuadGK.Segment{Float64, Float64, Float64}}}(7, LinearAlgebra.norm, QuadGK.Segment{Float64, Float64, Float64}[QuadGK.Segment{Float64, Float64, Float64}(0.0, 0.0, 0.0, 0.0)])

julia> solve(IntegralProblem(g, 0, 1, 80.0), QuadGKJL(; segbuf=QuadGK.alloc_segbuf(Float64, Float64, Float64)))^C

julia> @allocated solve(IntegralProblem(g, 0, 1, 80.0))
2800

julia> @allocated solve(IntegralProblem(g, 0, 1, 80.0), alg)
1072

[ChrisRackauckas]

I would think this would be best to do at init time?

[lxvm]

I don't follow what you mean by init time: is it when init.jl load extensions?
In #135 it seemed like it would be a good idea to add solver keywords to the algorithm structs.

Perhaps an issue holding back this pr is that the QuadGK.jl version is restricted to 2.1 in the Project.toml, while segbufs aren't added to QuadGK.jl until version 2.6 by JuliaMath/QuadGK.jl#59

Is the idea to define QuadGKJL in init.jl because the segbuf keyword may or may not exist depending on the QuadGK.jl version? So something like:

@static if isdefined(QuadGK, :alloc_segbuf)
# define QuadGKJL with segbuf
else
# define current version of QuadGKJL
end

[ArnoStrouwen]

Need to add the keyword to the docstring.

[ArnoStrouwen]

I think this is what is meant by init:
https://docs.sciml.ai/SciMLBase/stable/interfaces/Init_Solve/#init-and-the-Iterator-Interface
Currently this is not set up properly in Integrals.jl, but should be added.

[lxvm]

Thank you for the link. I see how it would be a good idea to cache the quadrature rule, or at least allocate memory for it. It's hard to predict how general-purpose a caching interface for quadratures can be, since there are quadratures tailored to all sorts of problems, but if we set up the init interface then at least each algorithm could have a corresponding cache.

It seems like I could close this pr and open a new one for properly providing the init interface as soon as I have some time for it

[ChrisRackauckas]

It seems like I could close this pr and open a new one for properly providing the init interface as soon as I have some time for it

Yeah I think this is probably the right direction here. In the end, we really just need the init part of the interface in this package, and then need to just cache everything.