From 5047864f82ed18ff9eb7e5b0f0eef6918e165c6d Mon Sep 17 00:00:00 2001
From: Nathanael Bosch <nathanael.bosch@uni-tuebingen.de>
Date: Wed, 1 Nov 2023 18:14:47 +0100
Subject: [PATCH] Towards a more modular state init by adding more options

This commit adss back a ForwardDiff.jl-based state initialization that was used
in a much earlier version of this package. And in almost all cases, this is not
very performant! But the initialization should ideally be more modular, the
choice being "exact" vs "inexact", and the actual autodiff implementation in the
exact case should also be easy to swap, e.g. when we'll use TaylorDiff.jl.
Therefore we try to refactor this a bit.
---
 src/initialization/taylormode.jl | 25 +++++++++++++++++++++++++
 1 file changed, 25 insertions(+)

diff --git a/src/initialization/taylormode.jl b/src/initialization/taylormode.jl
index 57e873453..8e0d4c228 100644
--- a/src/initialization/taylormode.jl
+++ b/src/initialization/taylormode.jl
@@ -59,5 +59,30 @@ function taylormode_get_derivatives(u, f::SciMLBase.AbstractODEFunction{true}, p
     duT = zero(uT)
     uauxT = similar(uT)
     TaylorIntegration.jetcoeffs!(f, tT, uT, duT, uauxT, p)
+    # return hcat([evaluate.(differentiate.(uT, i)) for i in 0:q]...)'
     return [evaluate.(differentiate.(uT, i)) for i in 0:q]
 end
+
+
+
+function forwarddiff_get_derivatives!(out, u, f::SciMLBase.AbstractODEFunction{true}, p, t, q)
+    _f(du, u) = f(du, u, p, t)
+    d = length(u0)
+    f_n = _f
+    out[1:d] .= u0
+    @views _f(out[d+1:2d], u0)
+    for o in 2:ndiffs
+        f_n = forwarddiff_vectorfield_derivative_iteration(f_n, _f)
+        @views f_n(out[o*d+1:(o+1)*d], u0)
+    end
+    return out
+end
+
+function forwarddiff_vectorfield_derivative_iteration(f_n, f_0)
+    function df(du, u)
+        J = ForwardDiff.jacobian(f_n, du, u)
+        f_0(du, u)
+        _matmul!(du, J, du)
+    end
+    return df
+end