86 lines
1.7 KiB
Julia
86 lines
1.7 KiB
Julia
compute_f = x -> [x[1]^2; x[2]^2 + x[3]; -x[3]^2 + x[4] + x[5]^3]
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compute_Jf = x -> [
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2x[1] 0 0 0 0;
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0 2x[2] 1 0 0;
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0 0 -2x[3] 1 3*x[5]^2
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]
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function compute_Hf(x)
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Hf = zeros(3, 5, 5)
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Hf[1, 1, 1] = 2
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Hf[2, 2, 2] = 2
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Hf[3, 3, 3] = -2
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Hf[3, 5, 5] = 6 * x[5]
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return Hf
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end
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@testset "Tensors" begin
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m, n = 3, 5
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x = 2rand(n) .- 0.5
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@test TaylorTest.check(compute_f, compute_Jf, x)
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@test TaylorTest.check(compute_Jf, compute_Hf, x)
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end
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TP = TO.tensorproduct
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function prod(A, B)
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return TP([1, 2, 3], A, [1, 2], B, [3])
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end
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function revprod(A, B)
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return TP([1, 3, 2], B, [3], A, [1, 2])
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end
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function symprod(A, B)
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return prod(A, B) + revprod(A, B)
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end
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@testset "Product of scalar and vector functions" begin
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v = x -> [exp(2 * x[1]), cos(x[1] * x[2]), 1.0]
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Jv = x -> [
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2*exp(2 * x[1]) 0;
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-x[2]*sin(x[1] * x[2]) -x[1]*sin(x[1] * x[2]);
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0 0
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]
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Hv = x -> begin
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h = zeros(3, 2, 2)
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h[1, :, :] = [
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4*exp(2 * x[1]) 0;
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0 0
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]
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h[2, :, :] = [
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-x[2]^2*cos(x[1] * x[2]) -sin(x[1] * x[2])-x[1]*x[2]*cos(x[1] * x[2]);
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-sin(x[1] * x[2])-x[1]*x[2]*cos(x[1] * x[2]) -x[1]^2*cos(x[1] * x[2])
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]
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h
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end
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φ = x -> x[1] * x[2]^2
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∇φ = x -> [x[2]^2; 2x[1] * x[2]]
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Hφ = x -> [
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0 2x[2];
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2x[2] 2*x[1]
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]
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f = x -> v(x) * φ(x)
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Jf = x -> φ(x) * Jv(x) + v(x) * ∇φ(x)'
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Hf = x -> φ(x) * Hv(x) + symprod(Jv(x), ∇φ(x)) + TP(v(x), [1], Hφ(x), [2, 3])
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x = 2rand(2) .- 0.5
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@test TaylorTest.check(v, Jv, x)
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@test TaylorTest.check(Jv, Hv, x)
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@test TaylorTest.check(φ, ∇φ, x)
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@test TaylorTest.check(∇φ, Hφ, x)
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@test TaylorTest.check(f, Jf, x)
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@test TaylorTest.check(Jf, Hf, x)
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end
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