48 lines
1.4 KiB
Julia
48 lines
1.4 KiB
Julia
module TaylorTest
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import LinearAlgebra: norm, dot
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import TensorOperations: @tensor
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function check(f, Jf, x, constant_components::Vector{Int}=Int[]; f_kwargs...)
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direction = 2 * (rand(size(x)...) .- 0.5)
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for cst in constant_components
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direction[cst] = 0
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end
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if direction isa Array
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direction ./= norm(direction)
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end
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ε_array = 10.0 .^ (-5:1:-1)
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n = size(ε_array)
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f_x = f(x; f_kwargs...)
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Jf_x = Jf(x; f_kwargs...)
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if ndims(f_x) == 0
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# if f is a scalar function, avoid potential ∇f vs Jac(f) by using dot
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error_array = [norm(f(x + ε * direction; f_kwargs...) - (f_x + ε * dot(Jf_x, direction))) for ε in ε_array]
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elseif ndims(f_x) == 1 || prod(size(f_x)) == maximum(size(f_x))
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# f is essentially a vector, potentially horizontal
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# f simply use matrix multiplication
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error_array = [norm(vec(f(x + ε * direction; f_kwargs...) - f_x) - ε * Jf_x * direction) for ε in ε_array]
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else
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@tensor begin
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Jf_x_direction[i,j] := Jf_x[i,j,k] * direction[k]
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end
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error_array = [norm(f(x + ε * direction; f_kwargs...) - f_x - ε * Jf_x_direction) for ε in ε_array]
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end
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m = maximum(error_array)
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if m < 1e-8
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@warn "f looks linear!"
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return true
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end
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order = trunc(([ones(n) log.(ε_array)]\log.(error_array))[2] - 1; digits=2)
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@info "Approximation order ~ $order"
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return isapprox(order, 1; atol=0.5)
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end
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end # module TaylorTest
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