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forcibly zero the memory
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test/downstream/default_linsolve_structure.jl

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using LinearAlgebra, OrdinaryDiffEq, Test
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f = (du,u,p,t) -> du .= u ./ t
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jac = (J,u,p,t) -> (J[1,1] = 1/t; J[2,2] = 1/t; J)
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jac = (J,u,p,t) -> (J[1,1] = 1/t; J[2,2] = 1/t; J[1,2] = 0; J[2,1] = 0)
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jp_diag = Diagonal(zeros(2))
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fun = ODEFunction(f; jac=jac, jac_prototype=jp_diag)

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