# TypeError: non-boolean (Term{Bool}) used in boolean context when trying to modelingtoolkitize a DifferentialEquations.jl SDEProblem

**URL:** https://discourse.julialang.org/t/typeerror-non-boolean-term-bool-used-in-boolean-context-when-trying-to-modelingtoolkitize-a-differentialequations-jl-sdeproblem/51130
**Category:** Optimization (Mathematical)
**Tags:** question, diffeq, optimization, modelingtoolkit
**Created:** [December 2, 2020, 5:06pm UTC](https://discourse.julialang.org/t/typeerror-non-boolean-term-bool-used-in-boolean-context-when-trying-to-modelingtoolkitize-a-differentialequations-jl-sdeproblem/51130 "2020-12-02T17:06:16Z")
**Posts on this page:** 4
**Page:** 1

<div class="post-metadata">

### Author: ![claudio20497](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/claudio20497/32/36602_2.png) [@claudio20497](https://discourse.julialang.org/u/claudio20497)
#### Post date: [December 2, 2020, 5:06pm UTC](https://discourse.julialang.org/t/typeerror-non-boolean-term-bool-used-in-boolean-context-when-trying-to-modelingtoolkitize-a-differentialequations-jl-sdeproblem/51130/1 "2020-12-02T17:06:16Z")

</div>

Hello,

This issue is maybe related to [this one](https://discourse.julialang.org/t/boundserror-attempt-to-access-float64-using-modelingtoolkit-jl-and-autooptimize-jl-to-optimize-a-differentialequations-jl-model/51000) although the solution could be totally different. If this is the wrong place to post it, please tell me and I’ll be happy to move it.

So the goal would be to optimize a DifferentialEquations.jl `EnsembleProblem` simulation built upon an `SDEProblem` with noise produced by distributions taken from Distributions.jl.  
Here is a simplified version of the model:

```julia
using DifferentialEquations, Distributions, DiffEqBayes, AutoOptimize

# Model parameters

β = 0.01# infection rate
λ_R = 0.05 # inverse of transition time from infected to recovered
λ_D = 0.83 # inverse of transition time from infected to dead
σ_β = 0.01 
σ_R = 0.01 
σ_D = 0.01 

𝒫 = vcat([β, λ_R, λ_D,σ_β,σ_R, σ_D]...)

# regional contact matrix and regional population

## regional contact matrix
regional_all_contact_matrix = [3.45536 0.485314 0.506389 0.123002 ; 0.597721 2.11738 0.911374 0.323385 ; 0.906231 1.35041 1.60756 0.67411 ; 0.237902 0.432631 0.726488 0.979258] # 4x4 contact matrix

## regional population stratified by age
N= [723208 , 874150, 1330993, 1411928] # array of 4 elements, each of which representing the absolute amount of population in the corresponding age class.

# Initial conditions 
i₀ = 0.075 # fraction of initial infected people in every age class
I₀ = repeat([i₀],4)
S₀ = N.-I₀
R₀ = [0.0 for n in 1:length(N)]
D₀ = [0.0 for n in 1:length(N)]
D_tot₀ = [0.0 for n in 1:length(N)]
ℬ = vcat([S₀, I₀, R₀, D₀, D_tot₀]...) 

# Time 
final_time = 20
𝒯 = (1.0,final_time); 

function SIRD_ac!(du,u,p,t)  
    # Parameters to be calibrated
    β, λ_R, λ_D, _,_,_ = p

    # initialize this parameter (death probability stratified by age, taken from literature)
    
    δ₁, δ₂, δ₃, δ₄ = [0.003/100, 0.004/100, (0.015+0.030+0.064+0.213+0.718)/(5*100), (2.384+8.466+12.497+1.117)/(4*100)]
    δ = vcat(repeat([δ₁],1),repeat([δ₂],1),repeat([δ₃],1),repeat([δ₄],4-1-1-1))

    C = regional_all_contact_matrix 

    
    # State variables
    S = @view u[4*0+1:4*1]
    I = @view u[4*1+1:4*2]
    R = @view u[4*2+1:4*3]
    D = @view u[4*3+1:4*4]
    D_tot = @view u[4*4+1:4*5]

    # Differentials
    dS = @view du[4*0+1:4*1]
    dI = @view du[4*1+1:4*2]
    dR = @view du[4*2+1:4*3]
    dD = @view du[4*3+1:4*4]
    dD_tot = @view du[4*4+1:4*5]
    
    # Force of infection
    Λ = β*[sum([C[i,j]*I[j]/N[j] for j in 1:size(C)[1]]) for i in 1:size(C)[2]] 
    
    # System of equations
    @. dS = -Λ*S
    @. dI = Λ*S - ((1-δ)*λ_R + δ*λ_D)*I
    @. dR = λ_R*(1-δ)*I 
    @. dD = λ_D*δ*I
    @. dD_tot = dD[1]+dD[2]+dD[3]+dD[4]
    

end;

# define noise
function SIRD_ac_noise!(du,u,p,t)  
    # Parameters to be calibrated
    _,_,_, σ_β, σ_R, σ_D = p

    # initialize this parameter (death probability stratified by age, taken from literature)
    
    δ₁, δ₂, δ₃, δ₄ = [0.003/100, 0.004/100, (0.015+0.030+0.064+0.213+0.718)/(5*100), (2.384+8.466+12.497+1.117)/(4*100)]
    δ = vcat(repeat([δ₁],1),repeat([δ₂],1),repeat([δ₃],1),repeat([δ₄],4-1-1-1))

    C = regional_all_contact_matrix 
    
    

    
    # State variables
    S = @view u[4*0+1:4*1]
    I = @view u[4*1+1:4*2]
    R = @view u[4*2+1:4*3]
    D = @view u[4*3+1:4*4]
    D_tot = @view u[4*4+1:4*5]

    # Differentials
    dS = @view du[4*0+1:4*1]
    dI = @view du[4*1+1:4*2]
    dR = @view du[4*2+1:4*3]
    dD = @view du[4*3+1:4*4]
    dD_tot = @view du[4*4+1:4*5]
    
    # Force of infection
    Λ = rand(Normal(0.0, σ_β))*[sum([C[i,j]*I[j]/N[j] for j in 1:size(C)[1]]) for i in 1:size(C)[2]] 
    
    # System of equations
    @. dS = -Λ*S
    @. dI = Λ*S - ((1-δ)*rand(Normal( 0.0,σ_R)) + δ*rand(Normal( 0.0,σ_D)))*I
    @. dR = rand(Normal( 0.0,σ_R))*(1-δ)*I 
    @. dD = rand(Normal( 0.0,σ_D))*δ*I
    @. dD_tot = dD[1]+dD[2]+dD[3]+dD[4]
    

end;

# create problem and check it works
sde_problem = SDEProblem(SIRD_ac!,SIRD_ac_noise!,ℬ, 𝒯, 𝒫 )
solution = @time solve(sde_problem, saveat = 1:final_time);

```

Attempting to directly `auto_optimize` the `EnsembleProblem` using AutoOprimize.jl seems not supported:

```julia
ens_problem = EnsembleProblem(sde_problem)

```

```julia
MethodError: no method matching auto_optimize(::EnsembleProblem{SDEProblem{Array{Float64,1},Tuple{Float64,Float64},true,Array{Float64,1},Nothing,SDEFunction{true,typeof(SIRD_ac!),typeof(SIRD_ac_noise!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},typeof(SIRD_ac_noise!),Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}},Nothing},typeof(DiffEqBase.DEFAULT_PROB_FUNC),typeof(DiffEqBase.DEFAULT_OUTPUT_FUNC),typeof(DiffEqBase.DEFAULT_REDUCTION),Nothing})
Closest candidates are:
  auto_optimize(!Matched::ODEProblem) at C:\Users\claud\.julia\packages\AutoOptimize\29daN\src\AutoOptimize.jl:29
  auto_optimize(!Matched::ODEProblem, !Matched::Any; verbose, stiff, mtkify, sparsify, gpuify, static, gpup) at C:\Users\claud\.julia\packages\AutoOptimize\29daN\src\AutoOptimize.jl:29

Stacktrace:
 [1] top-level scope at In[4]:1
 [2] include_string(::Function, ::Module, ::String, ::String) at .\loading.jl:1091

```

So hoping to still ger some benefit at `ens_problem` simulation time, I tried to `auto_optimize` the `sde_problem` before building the `ens_problem` upon it, but this too seems not to be implemented:

```julia
auto_sde_problem = auto_optimize(sde_problem)

```

```julia
MethodError: no method matching auto_optimize(::SDEProblem{Array{Float64,1},Tuple{Float64,Float64},true,Array{Float64,1},Nothing,SDEFunction{true,typeof(SIRD_ac!),typeof(SIRD_ac_noise!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},typeof(SIRD_ac_noise!),Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}},Nothing})
Closest candidates are:
  auto_optimize(!Matched::ODEProblem) at C:\Users\claud\.julia\packages\AutoOptimize\29daN\src\AutoOptimize.jl:29
  auto_optimize(!Matched::ODEProblem, !Matched::Any; verbose, stiff, mtkify, sparsify, gpuify, static, gpup) at C:\Users\claud\.julia\packages\AutoOptimize\29daN\src\AutoOptimize.jl:29

Stacktrace:
 [1] top-level scope at In[5]:1
 [2] include_string(::Function, ::Module, ::String, ::String) at .\loading.jl:1091

```

Then trying to `modelingtoolkitize` the problem (as before hoping that doing it before building the `ens_problem` upon it returns a faster EnsembleProblem that building it directly on `sde_problem` would), I get:

```julia
sys = modelingtoolkitize(sde_problem)

```

```julia
TypeError: non-boolean (Term{Bool}) used in boolean context

Stacktrace:
 [1] macro expansion at C:\Users\claud\.julia\packages\Distributions\xT124\src\utils.jl:5 [inlined]
 [2] Normal(::Num, ::Num; check_args::Bool) at C:\Users\claud\.julia\packages\Distributions\xT124\src\univariate\continuous\normal.jl:37
 [3] Normal at C:\Users\claud\.julia\packages\Distributions\xT124\src\univariate\continuous\normal.jl:37 [inlined]
 [4] Normal at C:\Users\claud\.julia\packages\Distributions\xT124\src\univariate\continuous\normal.jl:42 [inlined]
 [5] SIRD_ac_noise!(::Array{Any,1}, ::Array{Num,1}, ::Array{Num,1}, ::Num) at .\In[1]:111
 [6] modelingtoolkitize(::SDEProblem{Array{Float64,1},Tuple{Float64,Float64},true,Array{Float64,1},Nothing,SDEFunction{true,typeof(SIRD_ac!),typeof(SIRD_ac_noise!),LinearAlgebra.UniformScaling{Bool},Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing,Nothing},typeof(SIRD_ac_noise!),Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}},Nothing}) at C:\Users\claud\.julia\packages\ModelingToolkit\HTjKG\src\systems\diffeqs\modelingtoolkitize.jl:71
 [7] top-level scope at In[2]:1
 [8] include_string(::Function, ::Module, ::String, ::String) at .\loading.jl:1091

```

I’m particularly puzzled by this last error, since ModelingToolkit [seems to support SDEs](https://mtk.sciml.ai/stable/systems/SDESystem/).

So what am I missing?

environment:

```julia
(computationalEpi) pkg> st
Status `E:\IlMIoDrive\magistrale\2anno\primo_periodo\computationalEpi\Project.toml`
  [ff3c4d4f] AutoOptimize v0.1.0 `https://github.com/SciML/AutoOptimize.jl#master`
  [8f4d0f93] Conda v1.5.0
  [071ae1c0] DiffEqGPU v1.8.0
  [0c46a032] DifferentialEquations v6.15.0
  [7073ff75] IJulia v1.23.1
  [961ee093] ModelingToolkit v4.0.8
  [d330b81b] PyPlot v2.9.0

```

Thank you very much

---

<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: [December 12, 2020, 4:26am UTC](https://discourse.julialang.org/t/typeerror-non-boolean-term-bool-used-in-boolean-context-when-trying-to-modelingtoolkitize-a-differentialequations-jl-sdeproblem/51130/2 "2020-12-12T04:26:09Z")

</div>

Duplicate of [https://github.com/SciML/ModelingToolkit.jl/issues/685](https://github.com/SciML/ModelingToolkit.jl/issues/685)

---

<div class="post-metadata">

### Author: ![claudio20497](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/claudio20497/32/36602_2.png) [@claudio20497](https://discourse.julialang.org/u/claudio20497)
#### Post date: [December 22, 2020, 2:09pm UTC](https://discourse.julialang.org/t/typeerror-non-boolean-term-bool-used-in-boolean-context-when-trying-to-modelingtoolkitize-a-differentialequations-jl-sdeproblem/51130/3 "2020-12-22T14:09:55Z")

</div>

Hello @ChrisRackauckas ,

Thanks, now the code above runs correctly. Anyway, if i change whichever `Normal` distribution to `LogNormal`, i get the same error again. I can of course do , as you suggested [here](https://github.com/SciML/ModelingToolkit.jl/issues/685):

```julia
ModelingToolkit.@register LogNormal(mu,sigma)
ModelingToolkit.@register Base.rand(x)

```

And in that case it works.

---

<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: [December 22, 2020, 2:16pm UTC](https://discourse.julialang.org/t/typeerror-non-boolean-term-bool-used-in-boolean-context-when-trying-to-modelingtoolkitize-a-differentialequations-jl-sdeproblem/51130/4 "2020-12-22T14:16:37Z")

</div>

And it also just works on the latest version of ModelingToolkit which adds these registrations by default.