From 97c99198cee459eb19217413b0fe775f902b4e0b Mon Sep 17 00:00:00 2001
From: Michael Kraus <michael.kraus@ipp.mpg.de>
Date: Thu, 5 Dec 2024 12:15:39 +0100
Subject: [PATCH] Add LDAEProblem for degenerate Lagrangians.

---
 src/EulerLagrange.jl              |  4 +++-
 src/lagrangian_degenerate.jl      | 24 ++++++++++++++++++++++++
 test/lagrangian_lotka_volterra.jl |  4 +++-
 3 files changed, 30 insertions(+), 2 deletions(-)

diff --git a/src/EulerLagrange.jl b/src/EulerLagrange.jl
index 4291953..91ea543 100644
--- a/src/EulerLagrange.jl
+++ b/src/EulerLagrange.jl
@@ -8,15 +8,17 @@ module EulerLagrange
 
     import GeometricBase: equations, functions, parameters
     import GeometricEquations: HODE, HODEProblem
-    import GeometricEquations: LODE, LODEProblem
+    import GeometricEquations: LODE, LODEProblem, LDAE, LDAEProblem
     import GeometricEquations: ODE, ODEProblem
     import GeometricEquations: _lode_default_v̄
 
     RuntimeGeneratedFunctions.init(@__MODULE__)
 
 
+    export ODE, ODEProblem
     export HODE, HODEProblem
     export LODE, LODEProblem
+    export LDAE, LDAEProblem
 
     export equations, functions, parameters, variables
 
diff --git a/src/lagrangian_degenerate.jl b/src/lagrangian_degenerate.jl
index 6f3491e..2f495ce 100644
--- a/src/lagrangian_degenerate.jl
+++ b/src/lagrangian_degenerate.jl
@@ -155,3 +155,27 @@ function LODEProblem(lsys::DegenerateLagrangianSystem, tspan::Tuple, tstep::Real
     _λ₀ = AlgebraicVariable(λ₀)
     LODEProblem(lsys, tspan, tstep, _q₀, _p₀, _λ₀; kwargs...)
 end
+
+
+function LDAE(lsys::DegenerateLagrangianSystem; v̄ = functions(lsys).v, f̄ = functions(lsys).f, kwargs...)
+    eqs = functions(lsys)
+    LDAE(eqs.ϑ, eqs.f, eqs.u, eqs.g, eqs.ϕ, eqs.ū, eqs.ḡ, eqs.ψ, eqs.ω, eqs.L; v̄ = v̄, f̄ = f̄, invariants = (h = eqs.H,), kwargs...)
+end
+
+function LDAEProblem(lsys::DegenerateLagrangianSystem, tspan::Tuple, tstep::Real, ics::NamedTuple; v̄ = functions(lsys).v, f̄ = functions(lsys).f, kwargs...)
+    eqs = functions(lsys)
+    LDAEProblem(eqs.ϑ, eqs.f, eqs.u, eqs.g, eqs.ϕ, eqs.ū, eqs.ḡ, eqs.ψ, eqs.ω, eqs.L, tspan, tstep, ics; v̄ = v̄, f̄ = f̄, invariants = (h = eqs.H,), kwargs...)
+end
+
+function LDAEProblem(lsys::DegenerateLagrangianSystem, tspan::Tuple, tstep::Real, q₀::StateVariable, p₀::StateVariable, λ₀::AlgebraicVariable, μ₀::AlgebraicVariable; kwargs...)
+    ics = (q = q₀, p = p₀, λ = λ₀, μ = μ₀)
+    LDAEProblem(lsys, tspan, tstep, ics; kwargs...)
+end
+
+function LDAEProblem(lsys::DegenerateLagrangianSystem, tspan::Tuple, tstep::Real, q₀::AbstractArray, p₀::AbstractArray, λ₀::AbstractArray = zero(q₀), μ₀::AbstractArray = zero(λ₀); kwargs...)
+    _q₀ = StateVariable(q₀)
+    _p₀ = StateVariable(p₀)
+    _λ₀ = AlgebraicVariable(λ₀)
+    _μ₀ = AlgebraicVariable(μ₀)
+    LDAEProblem(lsys, tspan, tstep, _q₀, _p₀, _λ₀, _μ₀; kwargs...)
+end
diff --git a/test/lagrangian_lotka_volterra.jl b/test/lagrangian_lotka_volterra.jl
index cded987..b2fa610 100644
--- a/test/lagrangian_lotka_volterra.jl
+++ b/test/lagrangian_lotka_volterra.jl
@@ -1,5 +1,4 @@
 using EulerLagrange
-using GeometricEquations
 using LinearAlgebra
 using Test
 
@@ -119,3 +118,6 @@ f̃(ṗ₂, t₀, q₀, v₀, params)
 
 @test_nowarn LODE(deg_lag_sys)
 @test_nowarn LODEProblem(deg_lag_sys, tspan, tstep, q₀, v₀; parameters = params)
+
+@test_nowarn LDAE(deg_lag_sys)
+@test_nowarn LDAEProblem(deg_lag_sys, tspan, tstep, q₀, v₀; parameters = params)