Right hand side derivative

[MaAl13]

Hello, i am trying to use your amazing software for my ODE system. However if i end up using it i get the error that a derivative was detected on the right hand side. My original system is not rational, so i followed advice from you for an old Issue here on github: #219 . This resulted in the following code:

using StructuralIdentifiability
using OrderedCollections

# Define the ODE model with variables and parameters 
ode = @ODEmodel begin
    # Define the state derivatives
    a'(t) = p_a * s_0 * nb(t) - d_a * pa1(t),
    b'(t) = p_b * pa2(t) - d_b * pb(t),
    nb'(t) = -nb(t) * n_ba * ((p_b * pa2(t) - d_b * pb(t)) / b(t)) * (1 - nb(t)),
    pa1'(t) = pa1(t) * n_a * ((p_a * s_0 * nb(t) - d_a * pa1(t)) / a(t)) * (1 - pa1(t)),
    pa2'(t) = pa2(t) * n_ab * ((p_a * s_0 * nb(t) - d_a * pa1(t)) / a(t)) * (1 - pa2(t)),
    pb'(t) = pb(t) * n_b * ((p_b * pa2(t) - d_b * pb(t)) / b(t)) * (1 - pb(t)),
    
    # Define the outputs
    y1(t) = a(t),  # First measurable output
    y2(t) = b(t)   # Second measurable output
end

# Specify the known initial conditions with variables 
known_initial_conditions = [a, b]

global_identifiability_results = assess_identifiability(
    ode,
    known_ic = known_initial_conditions
)

# Display the identifiability results
println("\nGlobal Identifiability Assessment Results:")
println("----------------------------------------")
for (key, value) in global_identifiability_results
    println("$key => $value")
end

And here is the error:
ERROR: LoadError: ArgumentError: Derivative are not allowed in the right-hand side
Stacktrace:
[1] (::StructuralIdentifiability.var"#676#677"{Bool, Symbol, Set{Any}, Set{Any}, Set{Symbol}})(x::Expr)
@ StructuralIdentifiability ~/.julia/packages/StructuralIdentifiability/rZ9cm/src/input_macro.jl:7
[2] walk
@ ~/.julia/packages/MacroTools/Cf2ok/src/utils.jl:135 [inlined]
[3] postwalk
@ ~/.julia/packages/MacroTools/Cf2ok/src/utils.jl:145 [inlined]
[4] (::MacroTools.var"#25#26"{StructuralIdentifiability.var"#676#677"{Bool, Symbol, Set{Any}, Set{Any}, Set{Symbol}}})(x::Expr)
@ MacroTools ~/.julia/packages/MacroTools/Cf2ok/src/utils.jl:145
[5] iterate(::Base.Generator{Vector{Any}, MacroTools.var"#25#26"{StructuralIdentifiability.var"#676#677"{Bool, Symbol, Set{Any}, Set{Any}, Set{Symbol}}}})
@ Base ./generator.jl:47
[6] _collect(c::Vector{Any}, itr::Base.Generator{Vector{Any}, MacroTools.var"#25#26"{StructuralIdentifiability.var"#676#677"{Bool, Symbol, Set{Any}, Set{Any}, Set{Symbol}}}}, ::Base.EltypeUnknown, isz::Base.HasShape{1})
@ Base ./array.jl:854
[7] collect_similar(cont::Vector{Any}, itr::Base.Generator{Vector{Any}, MacroTools.var"#25#26"{StructuralIdentifiability.var"#676#677"{Bool, Symbol, Set{Any}, Set{Any}, Set{Symbol}}}})
@ Base ./array.jl:763
[8] map(f::Function, A::Vector{Any})
@ Base ./abstractarray.jl:3285
[9] walk
@ ~/.julia/packages/MacroTools/Cf2ok/src/utils.jl:135 [inlined]
[10] postwalk
@ ~/.julia/packages/MacroTools/Cf2ok/src/utils.jl:145 [inlined]
[11] (::MacroTools.var"#25#26"{StructuralIdentifiability.var"#676#677"{Bool, Symbol, Set{Any}, Set{Any}, Set{Symbol}}})(x::Expr)
@ MacroTools ~/.julia/packages/MacroTools/Cf2ok/src/utils.jl:145
[12] iterate
@ ./generator.jl:47 [inlined]
[13] collect_to!(dest::Vector{LineNumberNode}, itr::Base.Generator{Vector{Any}, MacroTools.var"#25#26"{StructuralIdentifiability.var"#676#677"{Bool, Symbol, Set{Any}, Set{Any}, Set{Symbol}}}}, offs::Int64, st::Int64)
@ Base ./array.jl:892
[14] collect_to_with_first!(dest::Vector{LineNumberNode}, v1::LineNumberNode, itr::Base.Generator{Vector{Any}, MacroTools.var"#25#26"{StructuralIdentifiability.var"#676#677"{Bool, Symbol, Set{Any}, Set{Any}, Set{Symbol}}}}, st::Int64)
@ Base ./array.jl:870
[15] _collect(c::Vector{Any}, itr::Base.Generator{Vector{Any}, MacroTools.var"#25#26"{StructuralIdentifiability.var"#676#677"{Bool, Symbol, Set{Any}, Set{Any}, Set{Symbol}}}}, ::Base.EltypeUnknown, isz::Base.HasShape{1})
@ Base ./array.jl:864
[16] collect_similar(cont::Vector{Any}, itr::Base.Generator{Vector{Any}, MacroTools.var"#25#26"{StructuralIdentifiability.var"#676#677"{Bool, Symbol, Set{Any}, Set{Any}, Set{Symbol}}}})
@ Base ./array.jl:763
[17] map(f::Function, A::Vector{Any})
@ Base ./abstractarray.jl:3285
[18] walk
@ ~/.julia/packages/MacroTools/Cf2ok/src/utils.jl:135 [inlined]
[19] postwalk
@ ~/.julia/packages/MacroTools/Cf2ok/src/utils.jl:145 [inlined]
[20] _extract_aux!(funcs::Set{Any}, all_symb::Set{Any}, eq::Expr; ders_ok::Bool, type::Symbol)
@ StructuralIdentifiability ~/.julia/packages/StructuralIdentifiability/rZ9cm/src/input_macro.jl:3
[21] _extract_aux!
@ ~/.julia/packages/StructuralIdentifiability/rZ9cm/src/input_macro.jl:1 [inlined]
[22] macrohelper_extract_vars(equations::Vector{Expr}, type::Symbol)
@ StructuralIdentifiability ~/.julia/packages/StructuralIdentifiability/rZ9cm/src/input_macro.jl:67
[23] generate_model_code(::Symbol, ::Expr, ::Vararg{Expr})
@ StructuralIdentifiability ~/.julia/packages/StructuralIdentifiability/rZ9cm/src/input_macro.jl:105
[24] var"@ODEmodel"(source::LineNumberNode, module::Module, ex::Vararg{Expr})
@ StructuralIdentifiability ~/.julia/packages/StructuralIdentifiability/rZ9cm/src/input_macro.jl:270
in expression starting at /Users/malmansto/Documents/Timer/Structural_id.jl:49
in expression starting at /Users/malmansto/Documents/Timer/Structural_id.jl:49

[pogudingleb]

Hi Marius,

Thanks for reporting! I think that the reason for this behaviour is that @ODEmodel macro has slightly different syntax, it expects parenthesis afterwards, not begin ... end. So if you replace

ode = @ODEmodel begin
    # Define the state derivatives
    a'(t) = p_a * s_0 * nb(t) - d_a * pa1(t),
    b'(t) = p_b * pa2(t) - d_b * pb(t),
    nb'(t) = -nb(t) * n_ba * ((p_b * pa2(t) - d_b * pb(t)) / b(t)) * (1 - nb(t)),
    pa1'(t) = pa1(t) * n_a * ((p_a * s_0 * nb(t) - d_a * pa1(t)) / a(t)) * (1 - pa1(t)),
    pa2'(t) = pa2(t) * n_ab * ((p_a * s_0 * nb(t) - d_a * pa1(t)) / a(t)) * (1 - pa2(t)),
    pb'(t) = pb(t) * n_b * ((p_b * pa2(t) - d_b * pb(t)) / b(t)) * (1 - pb(t)),
    
    # Define the outputs
    y1(t) = a(t),  # First measurable output
    y2(t) = b(t)   # Second measurable output
end

with

ode = @ODEmodel(
    # Define the state derivatives
    a'(t) = p_a * s_0 * nb(t) - d_a * pa1(t),
    b'(t) = p_b * pa2(t) - d_b * pb(t),
    nb'(t) = -nb(t) * n_ba * ((p_b * pa2(t) - d_b * pb(t)) / b(t)) * (1 - nb(t)),
    pa1'(t) = pa1(t) * n_a * ((p_a * s_0 * nb(t) - d_a * pa1(t)) / a(t)) * (1 - pa1(t)),
    pa2'(t) = pa2(t) * n_ab * ((p_a * s_0 * nb(t) - d_a * pa1(t)) / a(t)) * (1 - pa2(t)),
    pb'(t) = pb(t) * n_b * ((p_b * pa2(t) - d_b * pb(t)) / b(t)) * (1 - pb(t)),
    
    # Define the outputs
    y1(t) = a(t),  # First measurable output
    y2(t) = b(t)   # Second measurable output
)

everything will work.

[MaAl13]

Thank you very much for the solution! It indeed works now :)
I have one more question, is it possible to define known parameters?

[sumiya11]

Hi! Appending an output for a known parameter should work. For example,

ode = @ODEmodel(
    # Define the state derivatives
    a'(t) = p_a * s_0 * nb(t) - d_a * pa1(t),
    b'(t) = p_b * pa2(t) - d_b * pb(t),
    nb'(t) = -nb(t) * n_ba * ((p_b * pa2(t) - d_b * pb(t)) / b(t)) * (1 - nb(t)),
    pa1'(t) = pa1(t) * n_a * ((p_a * s_0 * nb(t) - d_a * pa1(t)) / a(t)) * (1 - pa1(t)),
    pa2'(t) = pa2(t) * n_ab * ((p_a * s_0 * nb(t) - d_a * pa1(t)) / a(t)) * (1 - pa2(t)),
    pb'(t) = pb(t) * n_b * ((p_b * pa2(t) - d_b * pb(t)) / b(t)) * (1 - pb(t)),
    
    # Define the outputs
    y1(t) = a(t),  # First measurable output
    y2(t) = b(t),   # Second measurable output
    y3(t) = p_a
)

[MaAl13]

Thank you very much, awesome!