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Avoid divide the first element for type check in normalize #1458

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Avoid divide the first element for type check in normalize #1458

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2 changes: 1 addition & 1 deletion src/generic.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -2109,7 +2109,7 @@ NaN
function normalize(a::AbstractArray, p::Real = 2)
nrm = norm(a, p)
if !isempty(a)
aa = copymutable_oftype(a, typeof(first(a)/nrm))
aa = copymutable_oftype(a, float(Base.promote_eltype(a, nrm)))
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This won't work for arrays of arrays:

julia> a = [[1,2], [3,4]]; nrm = norm(a)
5.477225575051661

julia> Base.promote_eltype(a, nrm)
Any

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Maybe instead of calling __normalize!, which requires us to compute the type of the array, we should just call map, which does the type computation for us. Something like:

function normalize(a::AbstractArray, p::Real = 2)
    nrm = norm(a, p)
    # duplicate logic from __normalize!, but applied to map:
    δ = inv(prevfloat(typemax(nrm)))
    if nrm ≥ δ # Safe to multiply with inverse
        return map(Base.Fix2(*, inv(nrm)), a)
    else # scale elements to avoid overflow
        εδ = eps(one(nrm))/δ
        result = map(Base.Fix2(*, εδ), a)
        return rmul!(result, inv(nrm*εδ))
    end
end

This duplicates the logic in __normalize!, but that seems easier than duplicating the logic in map?

return __normalize!(aa, nrm)
else
T = typeof(zero(eltype(a))/nrm)
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