Flux.jl/src/tracker/numeric.jl

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function gradient(f, xs::AbstractArray...)
xs = track.(xs)
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back!(f(xs...))
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grad.(xs)
end
function ngradient(f, xs::AbstractArray...)
y = f(xs...)
grads = zeros.(xs)
for (x, Δ) in zip(xs, grads)
for i in 1:length(x)
δ = sqrt(eps())
tmp, x[i] = x[i], x[i]+δ
y = f(xs...)
x[i] = tmp
Δ[i] = (y-y)/δ
end
end
return grads
end
gradcheck(f, xs...) = all(isapprox.(ngradient(f, xs...), gradient(f, xs...), rtol = 1e-6))