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julia> x =randn(5); P =plan_rfft(x);
julia>eltype(P)
Float64
julia> P * x
3-element Vector{ComplexF64}:-0.3514539021978911+0.0im-0.8023047651675712+1.243731722698685im2.8759555200391196-2.679171588261927im
If a "plan" is in some sense analogous to a matrix the eltype should be type of the output, in this case ComplexF64.