Divide-by-zero error thrown during vector initialization

Describe the bug 🐞

Using a custom Number type that throws an error when it is divided by zero (as opposed to returning Inf as Float64 does), an error is thrown during the initialization of the derivatives vector for non-fsal integrators (e.g. Vern integrators).

This is caused by line 51 in src/initdt.jl, i.e.:

f₀ = zero.(u0 ./ t)

and can be overcome by replacing the above with:

f₀ = zero.(u0 ./ oneunit(t))

or oneunit_tType I guess.

Expected behavior

The derivatives vector is initialized with the correct size and data type.

Minimal Reproducible Example 👇

using OrdinaryDiffEq
using DACE

function kepler_ode!(du, u, p, t)
    du[1:3] .= u[4:6]
    du[4:6] .= -u[1:3] * p ./ sum(u[1:3].^2)^(3/2)
end

DACE.init(2,6)
xs = [1.0, 0.0, 0.0, 0.0, 1.0, 0.0] .+ [DA(i,1.0) for i in 1:6]

prob = ODEProblem(kepler_ode!, xs, [0.0, 2π], p=1.0)
sol = solve(prob, Vern7(), abstol=1e-12, reltol=1e-12)

Error & Stacktrace ⚠️

ERROR: daceDivideDouble:  (ID: 641)
Stacktrace:
  [1] /(arg1::DACE.DAAllocated, arg2::Float64)
    @ DACE /workspace/programs/julia/packages/CxxWrap/HG6cm/src/CxxWrap.jl:663
  [2] _broadcast_getindex_evalf
    @ ./broadcast.jl:709 [inlined]
  [3] _broadcast_getindex
    @ ./broadcast.jl:682 [inlined]
  [4] _getindex
    @ ./broadcast.jl:706 [inlined]
  [5] _broadcast_getindex
    @ ./broadcast.jl:681 [inlined]
  [6] getindex
    @ ./broadcast.jl:636 [inlined]
  [7] macro expansion
    @ ./broadcast.jl:1004 [inlined]
  [8] macro expansion
    @ ./simdloop.jl:77 [inlined]
  [9] copyto!
    @ ./broadcast.jl:1003 [inlined]
 [10] copyto!
    @ ./broadcast.jl:956 [inlined]
 [11] copy
    @ ./broadcast.jl:928 [inlined]
 [12] materialize
    @ ./broadcast.jl:903 [inlined]
 [13] ode_determine_initdt(u0::Vector{…}, t::Float64, tdir::Float64, dtmax::Float64, abstol::Float64, reltol::Float64, internalnorm::typeof(DiffEqBase.ODE_DEFAULT_NORM), prob::ODEProblem{…}, integrator::OrdinaryDiffEq.ODEIntegrator{…})
    @ OrdinaryDiffEq /workspace/programs/julia/packages/OrdinaryDiffEq/ZbQoo/src/initdt.jl:51
 [14] auto_dt_reset!
    @ /workspace/programs/julia/packages/OrdinaryDiffEq/ZbQoo/src/integrators/integrator_interface.jl:453 [inlined]
 [15] handle_dt!(integrator::OrdinaryDiffEq.ODEIntegrator{…})
    @ OrdinaryDiffEq /workspace/programs/julia/packages/OrdinaryDiffEq/ZbQoo/src/solve.jl:571
 [16] __init(prob::ODEProblem{…}, alg::Vern7{…}, timeseries_init::Tuple{}, ts_init::Tuple{}, ks_init::Tuple{}, recompile::Type{…}; saveat::Tuple{}, tstops::Tuple{}, d_discontinuities::Tuple{}, save_idxs::Nothing, save_everystep::Bool, save_on::Bool, save_start::Bool, save_end::Nothing, callback::Nothing, dense::Bool, calck::Bool, dt::Float64, dtmin::Float64, dtmax::Float64, force_dtmin::Bool, adaptive::Bool, gamma::Rational{…}, abstol::Float64, reltol::Float64, qmin::Rational{…}, qmax::Int64, qsteady_min::Int64, qsteady_max::Int64, beta1::Nothing, beta2::Nothing, qoldinit::Rational{…}, controller::Nothing, fullnormalize::Bool, failfactor::Int64, maxiters::Int64, internalnorm::typeof(DiffEqBase.ODE_DEFAULT_NORM), internalopnorm::typeof(LinearAlgebra.opnorm), isoutofdomain::typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), unstable_check::typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), verbose::Bool, timeseries_errors::Bool, dense_errors::Bool, advance_to_tstop::Bool, stop_at_next_tstop::Bool, initialize_save::Bool, progress::Bool, progress_steps::Int64, progress_name::String, progress_message::typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), progress_id::Symbol, userdata::Nothing, allow_extrapolation::Bool, initialize_integrator::Bool, alias_u0::Bool, alias_du0::Bool, initializealg::OrdinaryDiffEq.DefaultInit, kwargs::@Kwargs{…})
    @ OrdinaryDiffEq /workspace/programs/julia/packages/OrdinaryDiffEq/ZbQoo/src/solve.jl:533
 [17] __init (repeats 5 times)
    @ /workspace/programs/julia/packages/OrdinaryDiffEq/ZbQoo/src/solve.jl:11 [inlined]
 [18] __solve(::ODEProblem{…}, ::Vern7{…}; kwargs::@Kwargs{…})
    @ OrdinaryDiffEq /workspace/programs/julia/packages/OrdinaryDiffEq/ZbQoo/src/solve.jl:6
 [19] __solve
    @ /workspace/programs/julia/packages/OrdinaryDiffEq/ZbQoo/src/solve.jl:1 [inlined]
 [20] solve_call(_prob::ODEProblem{…}, args::Vern7{…}; merge_callbacks::Bool, kwargshandle::Nothing, kwargs::@Kwargs{…})
    @ DiffEqBase /workspace/programs/julia/packages/DiffEqBase/NaUtB/src/solve.jl:612
 [21] solve_call
    @ /workspace/programs/julia/packages/DiffEqBase/NaUtB/src/solve.jl:569 [inlined]
 [22] #solve_up#53
    @ /workspace/programs/julia/packages/DiffEqBase/NaUtB/src/solve.jl:1080 [inlined]
 [23] solve_up
    @ /workspace/programs/julia/packages/DiffEqBase/NaUtB/src/solve.jl:1066 [inlined]
 [24] #solve#51
    @ /workspace/programs/julia/packages/DiffEqBase/NaUtB/src/solve.jl:1003 [inlined]
 [25] top-level scope
    @ /workspace/programs/julia/dev/DACE/examples/mre.jl:13
Some type information was truncated. Use `show(err)` to see complete types.

Environment (please complete the following information):

Output of using Pkg; Pkg.status()

Project DACE v0.1.0
Status `/workspace/programs/julia/dev/DACE/Project.toml`
  [1f15a43c] CxxWrap v0.15.0
  [2b5f629d] DiffEqBase v6.149.1
  [1dea7af3] OrdinaryDiffEq v6.74.1
  [40de70a5] DACE_jll v0.0.11+0 `/workspace/programs/julia/dev/DACE_jll`

The DACE package is obtained from https://github.com/a-ev/DACE.jl

Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)

Project DACE v0.1.0
Status `/workspace/programs/julia/dev/DACE/Manifest.toml`
⌅ [47edcb42] ADTypes v0.2.7
  [7d9f7c33] Accessors v0.1.36
  [79e6a3ab] Adapt v4.0.4
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.10.0
  [4c555306] ArrayLayouts v1.9.2
  [62783981] BitTwiddlingConvenienceFunctions v0.1.5
  [2a0fbf3d] CPUSummary v0.2.4
  [d360d2e6] ChainRulesCore v1.23.0
  [fb6a15b2] CloseOpenIntervals v0.1.12
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.0
  [34da2185] Compat v4.14.0
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [187b0558] ConstructionBase v1.5.5
  [adafc99b] CpuId v0.3.1
  [1f15a43c] CxxWrap v0.15.0
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.20
  [e2d170a0] DataValueInterfaces v1.0.0
  [2b5f629d] DiffEqBase v6.149.1
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [ffbed154] DocStringExtensions v0.9.3
  [4e289a0a] EnumX v1.0.4
⌃ [f151be2c] EnzymeCore v0.6.6
  [d4d017d3] ExponentialUtilities v1.26.1
  [e2ba6199] ExprTools v0.1.10
  [7034ab61] FastBroadcast v0.2.8
  [9aa1b823] FastClosures v0.3.2
  [29a986be] FastLapackInterface v2.0.2
⌃ [1a297f60] FillArrays v1.10.0
  [6a86dc24] FiniteDiff v2.23.1
  [f6369f11] ForwardDiff v0.10.36
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [46192b85] GPUArraysCore v0.1.6
  [c145ed77] GenericSchur v0.5.4
  [86223c79] Graphs v1.10.0
  [3e5b6fbb] HostCPUFeatures v0.1.16
  [615f187c] IfElse v0.1.1
  [d25df0c9] Inflate v0.1.4
  [3587e190] InverseFunctions v0.1.13
  [92d709cd] IrrationalConstants v0.2.2
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.5.0
  [ef3ab10e] KLU v0.6.0
  [ba0b0d4f] Krylov v0.9.5
  [10f19ff3] LayoutPointers v0.1.15
  [5078a376] LazyArrays v1.10.0
  [d3d80556] LineSearches v7.2.0
  [7ed4a6bd] LinearSolve v2.28.0
  [2ab3a3ac] LogExpFunctions v0.3.27
  [bdcacae8] LoopVectorization v0.12.169
  [1914dd2f] MacroTools v0.5.13
  [d125e4d3] ManualMemory v0.1.8
  [a3b82374] MatrixFactorizations v2.2.0
  [bb5d69b7] MaybeInplace v0.1.2
  [46d2c3a1] MuladdMacro v0.2.4
  [d41bc354] NLSolversBase v7.8.3
  [77ba4419] NaNMath v1.0.2
  [8913a72c] NonlinearSolve v3.10.0
  [6fe1bfb0] OffsetArrays v1.14.0
  [bac558e1] OrderedCollections v1.6.3
  [1dea7af3] OrdinaryDiffEq v6.74.1
  [65ce6f38] PackageExtensionCompat v1.0.2
  [d96e819e] Parameters v0.12.3
  [f517fe37] Polyester v0.7.13
  [1d0040c9] PolyesterWeave v0.2.1
  [d236fae5] PreallocationTools v0.4.21
  [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.13.0
  [f2c3362d] RecursiveFactorization v0.2.23
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.0
  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.42
  [0bca4576] SciMLBase v2.34.0
  [c0aeaf25] SciMLOperators v0.3.8
  [53ae85a6] SciMLStructures v1.1.0
  [efcf1570] Setfield v1.1.1
  [727e6d20] SimpleNonlinearSolve v1.7.0
  [699a6c99] SimpleTraits v0.9.4
  [ce78b400] SimpleUnPack v1.1.0
⌃ [47a9eef4] SparseDiffTools v2.18.0
  [e56a9233] Sparspak v0.3.9
  [276daf66] SpecialFunctions v2.3.1
  [aedffcd0] Static v0.8.10
  [0d7ed370] StaticArrayInterface v1.5.0
  [90137ffa] StaticArrays v1.9.3
  [1e83bf80] StaticArraysCore v1.4.2
  [7792a7ef] StrideArraysCore v0.5.5
  [2efcf032] SymbolicIndexingInterface v0.3.16
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.11.1
  [8290d209] ThreadingUtilities v0.5.2
  [a759f4b9] TimerOutputs v0.5.23
  [d5829a12] TriangularSolve v0.2.0
  [410a4b4d] Tricks v0.1.8
  [781d530d] TruncatedStacktraces v1.4.0
  [3a884ed6] UnPack v1.0.2
  [3d5dd08c] VectorizationBase v0.21.66
  [19fa3120] VertexSafeGraphs v0.2.0
  [40de70a5] DACE_jll v0.0.11+0 `/workspace/programs/julia/dev/DACE_jll`
  [1d5cc7b8] IntelOpenMP_jll v2024.1.0+0
  [856f044c] MKL_jll v2024.1.0+0
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [3eaa8342] libcxxwrap_julia_jll v0.12.2+0
  [1317d2d5] oneTBB_jll v2021.12.0+0
  [0dad84c5] ArgTools v1.1.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [8ba89e20] Distributed
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [4af54fe1] LazyArtifacts
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.10.0
  [de0858da] Printf
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays v1.10.0
  [10745b16] Statistics v1.10.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v1.1.0+0
  [deac9b47] LibCURL_jll v8.4.0+0
  [e37daf67] LibGit2_jll v1.6.4+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.2+1
  [14a3606d] MozillaCACerts_jll v2023.1.10
  [4536629a] OpenBLAS_jll v0.3.23+4
  [05823500] OpenLibm_jll v0.8.1+2
  [bea87d4a] SuiteSparse_jll v7.2.1+1
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.8.0+1
  [8e850ede] nghttp2_jll v1.52.0+1
  [3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`

Output of versioninfo()

Julia Version 1.10.2
Commit bd47eca2c8a (2024-03-01 10:14 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 24 × 13th Gen Intel(R) Core(TM) i7-13700
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, goldmont)
Threads: 1 default, 0 interactive, 1 GC (on 24 virtual cores)
Environment:
  JULIA_DEPOT_PATH = /workspace/programs/julia
  JULIA_EDITOR = code
  JULIA_NUM_THREADS =

SciML / OrdinaryDiffEq.jl

Divide-by-zero error thrown during vector initialization #2173