# DifferentialEquations.jl and systems with heterogenous units

**URL:** <https://discourse.julialang.org/t/differentialequations-jl-and-systems-with-heterogenous-units/2952>\
**Category:** Numerics\
**Tags:** diffeq, unitful\
**Created:** [March 29, 2017, 5:28pm UTC](https://discourse.julialang.org/t/differentialequations-jl-and-systems-with-heterogenous-units/2952 "2017-03-29T17:28:02Z")\
**Posts on this page:** 1\
**Showing post:** 4

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [March 30, 2017, 4:26am UTC](https://discourse.julialang.org/t/differentialequations-jl-and-systems-with-heterogenous-units/2952/4 "2017-03-30T04:26:45Z")

</div>

I you don’t care too much about performance, and easier way to do this would be to just not have a strictly typed array.

```julia
    rv0 = Vector{Number}()
    r0 = [1131.340, -2282.343, 6672.423]u"km"
    v0 = [-5.64305, 4.30333, 2.42879]u"km/s"
    append!(rv0,r0); append!(rv0,v0)

```

But I noticed that

```nohighlight
     Δt = 86400.0*365u"s"
    mu = 398600.4418u"km^3/s^2"
    prob = ODEProblem((t, y, dy) -> newton!(t, y, dy, mu), rv0, (0.0u"s", Δt))
    solve(prob, Vern8())[end]

```

this errors.

```julia
ERROR: DimensionError: 1//1000000 and 1.13134 km are not dimensionally compatible.
 in .+(::Rational{Int64}, ::Unitful.Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Length}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Meter,Unitful.Dimensions{(Unitful.Dimension{:Length}(1//1),)}}(3,1//1),),Unitful.Dimensions{(Unitful.Dimension{:Length}(1//1),)}}}) at .\operators.jl:152
 in collect(::Base.Generator{Array{Unitful.Quantity{Float64,D,U},1},Base.##143#145{Rational{Int64}}}) at .\array.jl:307
 in .+(::Rational{Int64}, ::Array{Unitful.Quantity{Float64,D,U},1}) at .\arraymath.jl:90
 in +(::Rational{Int64}, ::Array{Unitful.Quantity{Float64,D,U},1}) at .\arraymath.jl:130
 in ode_determine_initdt(::Array{Number,1}, ::Unitful.Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0,1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}}, ::Float64, ::Unitful.Quantity{Float64,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)},Unitful.FreeUnits{(Unitful.Unit{:Second,Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}(0,1//1),),Unitful.Dimensions{(Unitful.Dimension{:Time}(1//1),)}}}, ::Rational{Int64}, ::Float64, ::OrdinaryDiffEq.#ODE_DEFAULT_NORM, ::DiffEqBase.ODEProblem{Array{Number,1},Quantity{Float64, Dimensions:{�}, Units:{s}},true,##3#4}, ::Int64) at C:\Users\Chris\.julia\v0.5\OrdinaryDiffEq\src\initdt.jl:5

```

This makes me think that the previous solution won’t work either. This isn’t going to work because it doesn’t know what to type some of the internal constants, and it usually types them using `eltype(u0)`. In this case, `eltype(u0)` is not concrete, so it dies. To handle this case, the solvers will need to generalize how it does the typing.

Would you mind opening an issue? It’ll take some work to make heterogenous arrays like this work. And I think that with a proper broadcast (making them an iterator in the right), they can even work well. But it’ll take some work.

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