feat: add isInitial

docs/src/tutorials/initialization.md

@@ -536,3 +536,14 @@ sol[α * x - β * x * y]
 ```@example init
 plot(sol)
 ```
+
+## Summary of Initialization API
+
+```@docs; canonical=false
+Initial
+isinitial
+generate_initializesystem
+initialization_equations
+guesses
+defaults
+```

src/ModelingToolkit.jl

@@ -286,7 +286,7 @@ export toexpr, get_variables
 export simplify, substitute
 export build_function
 export modelingtoolkitize
-export generate_initializesystem, Initial
+export generate_initializesystem, Initial, isinitial
 
 export alg_equations, diff_equations, has_alg_equations, has_diff_equations
 export get_alg_eqs, get_diff_eqs, has_alg_eqs, has_diff_eqs

src/systems/abstractsystem.jl

@@ -622,7 +622,7 @@
 """
     Initial(x)
 
 The `Initial` operator. Used by initializaton to store constant constraints on variables
 of a system. See the documentation section on initialization for more information.
 """
 struct Initial <: Symbolics.Operator end
@@ -717,6 +717,22 @@
     return sys
 end
 
+"""
+Returns true if the parameter `p` is of the form `Initial(x)`.
+"""
+function isinitial(p)
+    p = unwrap(p)
+    if iscall(p)
+        operation(p) isa Initial && return true
+        if operation(p) === getindex
+            operation(arguments(p)[1]) isa Initial && return true
+        end
+    else
+        return false
+    end
+    return false
+end
+
 """
 $(TYPEDSIGNATURES)
 

test/variable_utils.jl

@@ -145,3 +145,16 @@ end
         @test isequal(parse_variable(sys, str), var)
     end
 end
+
+@testset "isinitial" begin
+    t = ModelingToolkit.t_nounits
+    @variables x(t) z(t)[1:5]
+    @parameters a b c[1:4]
+    @test isinitial(Initial(z))
+    @test isinitial(Initial(x))
+    @test isinitial(Initial(a))
+    @test isinitial(Initial(z[1]))
+    @test isinitial(Initial(c[4]))
+    @test !isinitial(c)
+    @test !isinitial(x)
+end