JuliaArrays / JuliaArrays/StaticArrays.jl

Special case for 2x3 matrix solve

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Description

I'm doing some coordinate transformation stuff that requires the solution of a 2 by 3 system. Right now, all rectangular SMatrix systems are done by LinearAlgebra and the allocations mean I can't run this on the GPU. I coded this version which seems to be working and non-allocating.

@inline function (\)(a::SMatrix{2,3}, b::SVector{2})
    # columns of a'
    a1,a2 = a[1,:],a[2,:]
    
    # Q,R decomposition
    r11 = norm(a1)
    q1 = a1/r11
    r12 = q1'*a2
    p = a2-r12*q1
    r22 = norm(p) < eps(r11) ? one(r11) : norm(p)
    q2 = p/r22

    # forward substitution to solve R'v = b
    v1 = b[1]/r11
    v2 = (b[2]-r12*v1)/r22

    # return solution x = Qv 
    return q1*v1+q2*v2
end

I'm happy to add this to solve.jl and do a PR if it would be helpful.

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Research direction

Start in solve.jl and inspect how rectangular SMatrix systems are currently delegated to LinearAlgebra. Compare the proposed specialized 2x3 solve with the surrounding methods, then verify that the resulting path is non-allocating and suitable for GPU use. Done means the special case is integrated consistently with the existing solve behavior.

Written by the indexing model from the issue text.

Assessment

Tech stack
julia
Domain
backend
Issue type
Feature
Difficulty
3/5
Estimated time
1-2 days
Activity status
Stale
Clarity
Clearly specified
Newbie friendliness
45/100

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