# Rodas5 and ModelingToolkit much slower than Sundials' IDA on large systems

**URL:** https://discourse.julialang.org/t/rodas5-and-modelingtoolkit-much-slower-than-sundials-ida-on-large-systems/60712
**Category:** Modelling & Simulations
**Tags:** modelingtoolkit
**Created:** [May 7, 2021, 1:15pm UTC](https://discourse.julialang.org/t/rodas5-and-modelingtoolkit-much-slower-than-sundials-ida-on-large-systems/60712 "2021-05-07T13:15:33Z")
**Posts on this page:** 1
**Showing post:** 3

<div class="post-metadata">

### Author: ![bmetherall](https://avatars.discourse-cdn.com/v4/letter/b/b38774/32.png) [@bmetherall](https://discourse.julialang.org/u/bmetherall)
#### Post date: [May 7, 2021, 3:42pm UTC](https://discourse.julialang.org/t/rodas5-and-modelingtoolkit-much-slower-than-sundials-ida-on-large-systems/60712/3 "2021-05-07T15:42:42Z")

</div>

Thanks for the comments, I guess IDA is the way to go. Is there a way to define a DAEProblem in MTK to use with Sundials (I can’t really find any documentation about this)? When I naively try

```julia
	prob = DAEProblem(DAEFunction(sys), ICs, tspan, param_values)
	
	@time sol = solve(prob, IDA(), reltol = 1e-10, abstol = 1e-6);

```

I get the error `ERROR: LoadError: MethodError: no method matching size(::Tuple{Float64, Float64})`.

> **Full Trace**
>
> ```julia
> ERROR: LoadError: MethodError: no method matching size(::Tuple{Float64, Float64})
> Closest candidates are:
> size(::Tuple, ::Integer) at tuple.jl:27
> size(::Union{LinearAlgebra.QR, LinearAlgebra.QRCompactWY, LinearAlgebra.QRPivoted}) at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.6/LinearAlgebra/src/qr.jl:524
> size(::Union{LinearAlgebra.QR, LinearAlgebra.QRCompactWY, LinearAlgebra.QRPivoted}, ::Integer) at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.6/LinearAlgebra/src/qr.jl:523
> ...
> Stacktrace:
> [1] (DAEProblem{true, duType, tType, isinplace, P, F, K, D} where {duType, tType, isinplace, P, F, K, D})(f::DAEFunction{true, ModelingToolkit.var"#f#160"{RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(Symbol("##arg#576"), Symbol("##arg#577"), Symbol("##arg#578"), :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x77493f90, 0x4499b563, 0xe171eec5, 0xf4ea53b4, 0x48cc079b)}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(Symbol("##out#579"), Symbol("##arg#576"), Symbol("##arg#577"), Symbol("##arg#578"), :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x3967f6b7, 0xd19b559f, 0xc7f890a0, 0xde6739f5, 0x3c2fea5e)}}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Vector{Symbol}, Nothing}, du0::Vector{Float64}, u0::Tuple{Float64, Float64}, tspan::Vector{Float64}, p::SciMLBase.NullParameters; differential_vars::Nothing, kwargs::Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
> @ SciMLBase ~/.julia/packages/SciMLBase/9EjAY/src/problems/dae_problems.jl:18
> [2] (DAEProblem{true, duType, tType, isinplace, P, F, K, D} where {duType, tType, isinplace, P, F, K, D})(f::DAEFunction{true, ModelingToolkit.var"#f#160"{RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(Symbol("##arg#576"), Symbol("##arg#577"), Symbol("##arg#578"), :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x77493f90, 0x4499b563, 0xe171eec5, 0xf4ea53b4, 0x48cc079b)}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(Symbol("##out#579"), Symbol("##arg#576"), Symbol("##arg#577"), Symbol("##arg#578"), :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x3967f6b7, 0xd19b559f, 0xc7f890a0, 0xde6739f5, 0x3c2fea5e)}}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Vector{Symbol}, Nothing}, du0::Vector{Float64}, u0::Tuple{Float64, Float64}, tspan::Vector{Float64}, p::SciMLBase.NullParameters)
> @ SciMLBase ~/.julia/packages/SciMLBase/9EjAY/src/problems/dae_problems.jl:18
> [3] DAEProblem(f::DAEFunction{true, ModelingToolkit.var"#f#160"{RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(Symbol("##arg#576"), Symbol("##arg#577"), Symbol("##arg#578"), :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x77493f90, 0x4499b563, 0xe171eec5, 0xf4ea53b4, 0x48cc079b)}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(Symbol("##out#579"), Symbol("##arg#576"), Symbol("##arg#577"), Symbol("##arg#578"), :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x3967f6b7, 0xd19b559f, 0xc7f890a0, 0xde6739f5, 0x3c2fea5e)}}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Vector{Symbol}, Nothing}, du0::Vector{Float64}, u0::Tuple{Float64, Float64}, tspan::Vector{Float64}, p::SciMLBase.NullParameters; kwargs::Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
> @ SciMLBase ~/.julia/packages/SciMLBase/9EjAY/src/problems/dae_problems.jl:37
> [4] DAEProblem(f::DAEFunction{true, ModelingToolkit.var"#f#160"{RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(Symbol("##arg#576"), Symbol("##arg#577"), Symbol("##arg#578"), :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x77493f90, 0x4499b563, 0xe171eec5, 0xf4ea53b4, 0x48cc079b)}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(Symbol("##out#579"), Symbol("##arg#576"), Symbol("##arg#577"), Symbol("##arg#578"), :t), ModelingToolkit.var"#_RGF_ModTag", ModelingToolkit.var"#_RGF_ModTag", (0x3967f6b7, 0xd19b559f, 0xc7f890a0, 0xde6739f5, 0x3c2fea5e)}}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Vector{Symbol}, Nothing}, du0::Vector{Float64}, u0::Tuple{Float64, Float64}, tspan::Vector{Float64}, p::SciMLBase.NullParameters) (repeats 2 times)
> @ SciMLBase ~/.julia/packages/SciMLBase/9EjAY/src/problems/dae_problems.jl:37
> [5] solve_system(sys::ODESystem; tspan::Tuple{Float64, Float64}, param_values::Vector{Float64})
> @ Main ~/Desktop/Silicon_Processes/Numerics/Example.jl:67
> [6] solve_system(sys::ODESystem)
> @ Main ~/Desktop/Silicon_Processes/Numerics/Example.jl:61
> [7] top-level scope
> @ ~/Desktop/Silicon_Processes/Numerics/Example.jl:78
> [8] include(fname::String)
> @ Base.MainInclude ./client.jl:444
> [9] top-level scope
> @ REPL[25]:1
> in expression starting at /home/brady/Desktop/Silicon_Processes/Numerics/Example.jl:78
> 
> ```

If not, would following something like  
[https://discourse.julialang.org/t/error-evaluating-sparse-analytical-jacobian-from-modelingtoolkit-in-dae-system/45764/2](https://discourse.julialang.org/t/error-evaluating-sparse-analytical-jacobian-from-modelingtoolkit-in-dae-system/45764/2)  
be best for optimizing the Jacobian calculation and exploiting the sparsity?

---

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