feat: add default_target_function

Create a default target function as described in Eq. 3 from the QN paper
(https://doi.org/10.1186/1752-0509-1-4).

Author: ReubenJ

src/GraphDynamicalSystems.jl

@@ -23,6 +23,7 @@ export QualitativeNetwork,
     get_domain,
     target_functions,
     interpret,
-    create_qn_system
+    create_qn_system,
+    default_target_function
 
 end

src/qualitative_networks.jl

@@ -158,6 +158,57 @@ function build_qn_grammar(
     return g
 end
 
+"""
+    $TYPEDSIGNATURES
+
+Construct a default target function for an entity in a QN from a list of
+`activators` and `inhibitors`.
+
+Follows the definition given in Eq. 3 of ["Qualitative networks: a symbolic
+approach to analyze biological signaling
+networks"](https://doi.org/10.1186/1752-0509-1-4).
+
+## Examples
+
+Say we have a component `X` and it has an lower bound on its state value of 0,
+an upper bound of 4, activators `A`, `B`, `C`, and inhibitors `D`, `E`, `F`,
+then the following example constructs an expression for its default target
+function.
+
+```jldoctest
+julia> default_target_function(0, 4, [:A, :B, :C], [:D, :E, :F])
+:(max(0, (A + B + C) / 3 - (D + E + F) / 3))
+```
+
+"""
+function default_target_function(
+    lower_bound::Integer,
+    upper_bound::Integer,
+    activators::AbstractVector = [],
+    inhibitors::AbstractVector = [],
+)
+    sum_only_or_nothing = x -> if length(x) == 0
+        nothing
+    elseif length(x) == 1
+        :($(only(x)))
+    elseif length(x) > 1
+        :($(Expr(:call, :+, x...)) / $(length(x)))
+    end
+
+    expr_activators = sum_only_or_nothing(activators)
+    expr_inhibitors = sum_only_or_nothing(inhibitors)
+
+    if isnothing(expr_activators) && isnothing(expr_inhibitors)
+        error("Constructing a default target function for a QN with no \
+              activators or inhibitors.")
+    elseif isnothing(expr_activators) # no activators, special case mentioned in paper
+        return :($upper_bound - $expr_inhibitors)
+    elseif isnothing(expr_inhibitors)
+        return :($expr_activators)
+    else
+        return :(max($lower_bound, $expr_activators - $expr_inhibitors))
+    end
+end
 
 struct Entity{I}
     target_function::Any

test/qn_test.jl

@@ -112,3 +112,32 @@ end
 
     basins = basins_of_attraction(mapper, grid)
 end
+
+@testitem "Construct default target functions" begin
+    lower_bound = 0
+    upper_bound = 4
+    activators = [:A, :B, :C]
+    inhibitors = [:D, :E, :F]
+
+    @test default_target_function(lower_bound, upper_bound, activators, inhibitors) ==
+          :(max($lower_bound, (A + B + C) / 3 - (D + E + F) / 3))
+
+    activators = [:A, :B]
+    inhibitors = [:D]
+
+    @test default_target_function(lower_bound, upper_bound, activators, inhibitors) ==
+          :(max($lower_bound, (A + B) / 2 - D))
+
+    activators = []
+    inhibitors = [:D]
+
+    @test default_target_function(lower_bound, upper_bound, activators, inhibitors) ==
+          :($upper_bound - D)
+
+    activators = [:A]
+    inhibitors = []
+
+    @test default_target_function(lower_bound, upper_bound, activators, inhibitors) == :(A)
+
+    @test_throws r"no activators or inhibitors" default_target_function(0, 4)
+end