JuliaDiff / JuliaDiff/ChainRulesCore.jl

Projection for `x:: AbstractRange`

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ProjectTo
Dominant language
Julia
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Forks
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Description

If we want something like https://github.com/JuliaArrays/FillArrays.jl/pull/153 to project the gradient of a Fill onto a one-dimensional subspace, then I think we probably want something similar for the gradient of a range, but projecting onto a two-dimensional space, parameterised by the endpoints. Before I lose the bit of scrap paper I wrote this on, I think this would look as follows:

ProjectTo(x::AbstractRange) = ProjectTo{AbstractRange}()

function (project::ProjectTo{AbstractRange})(dx::AbstractVector)
    L = length(dx)
    μ = mean(dx)
    # δ = -sum(diff(dx))/2
    δ = sum(Base.splat(-), zip(dx, @view dx[2:end]))/2
    return LinRange(μ + δ, μ - δ, L)
end

(project::ProjectTo{AbstractRange})(dx::AbstractRange) = dx

Using LinRange allows for zero slope (e.g. for constant dx) and skips the high-precision machinery which StepRangeLen uses to hit endpoints exactly, as I don't think we're concerned about the last digit here. This isn't yet careful about element types etc.

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Research direction

Start by reviewing the ProjectTo entry point for AbstractRange and the proposed vector and range methods in the issue. Determine the intended projection onto endpoint-parameterized ranges, including element-type handling and constant gradients, then establish tests for vector inputs and unchanged range inputs before considering the work complete.

Written by the indexing model from the issue text.

Assessment

Tech stack
julia
Domain
backend-api-design
Issue type
Feature
Difficulty
5/5
Estimated time
Over a week
Activity status
Stale
Clarity
Mostly clear
Newbie friendliness
25/100

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