57 lines
1.5 KiB
Julia
57 lines
1.5 KiB
Julia
function gauss(p::Vector{Float64}; x::Float64=0.0)
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λ, μ, σ = p
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return λ / sqrt(2π * σ^2) * exp(-(x - μ)^2/2σ^2)
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end
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function J_gauss(p::Vector{Float64}; x::Float64=0.0)
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λ, μ, σ = p
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c = [(1/λ) ((x - μ) / σ^2) ((x - μ)^2 - σ^2)/σ^3]
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return c .* gauss(p; x=x)
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end
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function H_gauss(p::Vector{Float64}; x::Float64=0.0)
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λ, μ, σ = p
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c = zeros(3, 3)
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# c[1,1] = 0
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c[1, 2] = c[2, 1] = (x-μ) / (λ * σ^2)
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c[1, 3] = c[3, 1] = -((μ + σ - x)*(-μ + σ + x))/(λ*σ^3)
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c[2, 2] = ((x - μ)^2 - σ^2) / σ^4
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c[2, 3] = c[3, 2] = -((μ - x)*((μ - x)^2 - 3σ^2))/σ^5
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c[3, 3] = (-5*σ^2*(μ - x)^2 + (μ - x)^4 + 2*σ^4)/σ^6
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return c .* gauss(p; x=x)
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end
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@testset "Gauss function" begin
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λ = 10 * rand()
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μ = 10 * (rand() - 0.5)
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σ = 10rand()
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p = [λ, μ, σ]
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x = σ * (2 * rand() - 1) + μ
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@assert abs(gauss(p; x=x)) > 1e-7 "gauss(p; x=x) is too small: $(gauss(p; x=x))"
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@test TaylorTest.check(gauss, J_gauss, p; x=x)
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@test TaylorTest.check(J_gauss, H_gauss, p; x=x)
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end
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@testset "Composed Gauss function" begin
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p = 1 .+ 5 * rand(6)
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x = p[3] + p[4] + 2p[5] + sqrt(p[6]) * (2rand() - 1)
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p_aux = _p -> [_p[1]/_p[2], _p[3] + _p[4] + 2_p[5], _p[6]]
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J_p_aux = _p -> [1/_p[2] -_p[1]/_p[2]^2 0 0 0 0;
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0 0 1 1 2 0;
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0 0 0 0 0 1]
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g = (_p; x=x) -> gauss(p_aux(_p); x=x)
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Jg = (_p; x=x) -> J_gauss(p_aux(_p); x=x) * J_p_aux(p)
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Hg = (_p; x=x) -> J_gauss(p_aux(_p); x=x) * J_p_aux(p)
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@test TaylorTest.check(g, Jg, p; x=x)
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end
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