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Precompute mismatch scaling factor #60

@briochemc

Description

@briochemc

Specifically, refactor these to allow the user to provide transpose(o) * W * o instead of recalculating it every time:

## new functions for more generic obs packages
# TODO Add an optional function argument to transform the data before computingn the mismatch
# Example if for isotope tracers X where one ususally wants to minimize the mismatch in δ or ε.
function mismatch(x, grd::OceanGrid, obs; c=identity, W=I, M=interpolationmatrix(grd, obs.metadata), iwet=iswet(grd, obs))
o = view(obs, iwet)
δx = M * c(x) - o
return 0.5 * transpose(δx) * W * δx / (transpose(o) * W * o)
end
mismatch(x, grd::OceanGrid, ::Missing; kwargs...) = 0
function ∇mismatch(x, grd::OceanGrid, obs; c=identity, W=I, M=interpolationmatrix(grd, obs.metadata), iwet=iswet(grd, obs))
∇c = Diagonal(ForwardDiff.derivative(λ -> c(x .+ λ), 0.0))
o = view(obs, iwet)
δx = M * c(x) - o
return transpose(W * δx) * M * ∇c / (transpose(o) * W * o)
end
∇mismatch(x, grd::OceanGrid, ::Missing; kwargs...) = transpose(zeros(length(x)))
# In case the mismatch is not based on the tracer but on some function of it
function indirectmismatch(xs::Tuple, grd::OceanGrid, modify::Function, obs, i, M=interpolationmatrix(grd, obs[i].metadata), iwet=iswet(grd, obs[i]))
x2 = modify(xs...)
out = 0.0
M = interpolationmatrix(grd, obs[i].metadata)
iwet = iswet(grd, obs[i])
o = view(obs[i], iwet)
δx = M * x2[i] - o
return 0.5 * transpose(δx) * δx / (transpose(o) * o)
end
function ∇indirectmismatch(xs::Tuple, grd::OceanGrid, modify::Function, obs, i, M=interpolationmatrix(grd, obs[i].metadata), iwet=iswet(grd, obs[i]))
nt, nb = length(xs), length(iswet(grd))
x2 = modify(xs...)
o = view(obs[i], iwet)
δx = M * x2[i] - o
∇modᵢ = ∇modify(modify, xs, i)
return transpose(δx) * M * ∇modᵢ / (transpose(o) * o)
end

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