Is it possible to use Linearmaps on custom data types? I have a struct data type v and wish to construct a function wrapped linear map A that can act on v like A*v. Would love to know how I could do this! Thanks in advance

I believe I somewhat understand how LinearMaps is working, but I’m not sure if I understand your question correctly. Therefore let us start with a simple example using LinearMaps A = rand(2, 2) fA!(y, x) = y .= A * x LA = LinearMap{Float64}(fA!, 2, 2) v = rand(2) @assert LA * v ≈ A * v Is that similar to what you are looking for? Edit: if v is a struct of your own making, you could either support converting it to a vector or add a Base.*(LinearMap, YourStruct) method

[image] goerch: Edit: if v is a struct of your own making, you could either support converting it to a vector or add a Base.*(LinearMap, YourStruct) method You can also make the struct a subtype of AbstractVector and implement the interface for Arrays. But probably adding Base.*(LinearMap, YourStruct) is easier/better.

[image] suavesito: You can also make the struct a subtype of AbstractVector and implement the interface for Arrays . Correct, this would most probably be the way to go if OP 's struct is part of a public API.

Maybe using ComponentArrays is faster than implementing the AbstractVector yourself? [image] Matrix free GMRES with structs? General Usage Maybe use https://github.com/jonniedie/ComponentArrays.jl ?

Thanks, yes that is what I am looking for. Are you suggesting that I define the action of the linearmap inside Base.*(LinearMap, struct)? I already have a function based linearmap(like the fA!+LA in your example) that takes in the struct and defines the action of the function/linearmap. Since I have already defined the action of the linearmap / * here I am not exactly sure what to define under Base. *(). Thoughts?

[image] Srikumar: Thanks, yes that is what I am looking for. I’m still not sure;) But then the natural continuation is something like using LinearMaps using StaticArrays A = rand(2, 2) fA!(y, x) = y .= A * x LA = LinearMap{Float64}(fA!, 2, 2) v = rand(2) @assert LA * v ≈ A * v struct SpecialVector v1::Float64 v2::Float64 end import Base.* function *(l::LinearMap{Float64}, v::SpecialVector) l * [v.v1, v.v2] end v = rand(2) sv = SpecialVector(v...) @assert LA * sv ≈ A * v Does this help?

Yeah I now get it, thanks a lot!

LinearMaps.jl

General Usage

gdalle April 13, 2022, 6:06am 5

Maybe using ComponentArrays is faster than implementing the AbstractVector yourself?

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LinearMaps.jl

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