Add ReverseDiff extension with analytical pullbacks

[Copilot]

Adds ReverseDiff.jl support using the analytical pullbacks already defined via ChainRulesCore rrules. Since @grad_from_chainrules doesn't support keyword arguments, implements custom SpecialInstruction types that record operations on ReverseDiff's tape and execute analytical gradients during the reverse pass.

Supported functions

• solve_lyapunov_equation / solve_sylvester_equation - all tracked/untracked input combinations
• calculate_jacobian, calculate_hessian, calculate_third_order_derivatives
• get_NSSS_and_parameters - with proper zero-gradient handling for failed solutions

Usage

using MacroModelling, ReverseDiff

@model RBC begin
    # ... model equations
end
@parameters RBC begin
    # ... parameters
end

function objective(params)
    SS, _ = MacroModelling.get_NSSS_and_parameters(RBC, params)
    return sum(SS)
end

grad = ReverseDiff.gradient(objective, param_values)

Implementation

• New ext/ReverseDiffExt.jl with SpecialInstruction dispatch types
• special_forward_exec! / special_reverse_exec! methods for each function
• Pullback formulas match existing rrules (e.g., Lyapunov: ∂A = ∂C * A * P' + ∂C' * A * P)

Original prompt

write an extension for reversediff.jl that uses @grad_from_chainrules on the rrules already written in the package. make sure they are compatible with reversediff.jl otherwise copy them over to the extension and modify them

---

💬 We'd love your input! Share your thoughts on Copilot coding agent in our 2 minute survey.