AutoDiff

AbstractStack{VT}

Abstract variable storing the inputs and the intermediate values in the expression tree.

AbstractExpression

Abstract type for differentiable function $f(x)$. Any AbstractExpression implements two functions: a forward mode to evaluate $f(x)$, and an adjoint to evaluate $∂f(x)$.

Forward mode

The direct evaluation of the function $f$ is implemented as

(expr::AbstractExpression)(output::VT, stack::AbstractStack{VT}) where VT<:AbstractArray

the input being specified in stack, the results being stored in the array output.

Reverse mode

The adjoint of the function is specified by the function adjoint!, with the signature:

adjoint!(expr::AbstractExpression, ∂stack::AbstractStack{VT}, stack::AbstractStack{VT}, ̄v::VT) where VT<:AbstractArray

The variable stack stores the result of the direct evaluation, and is not modified in adjoint!. The results are stored inside the adjoint stack ∂stack.

adjoint!(expr::AbstractExpression, ∂stack::AbstractStack{VT}, stack::AbstractStack{VT}, ̄v::VT) where VT<:AbstractArray

Compute the adjoint of the AbstractExpression expr with relation to the adjoint vector ̄v. The results are stored in the adjoint stack ∂stack. The variable stack stores the result of a previous direct evaluation, and is not modified in adjoint!.

AbstractJacobian

Automatic differentiation for the compressed Jacobian of any nonlinear constraint $h(x)$.

AbstractHessianProd

Returns the adjoint-Hessian-vector product $λ^⊤ H v$ of any nonlinear constraint $h(x)$.

AbstractHessianProd

Full sparse Hessian $H$ of any nonlinear constraint $h(x)$.

seed!(
    H::AbstractHessianProd,
    v::AbstractVector{T},
) where {T}

Seed the duals with v to compute the Hessian vector product $λ^⊤ H v$.

seed_coloring!(
    M::Union{AbstractJacobian, AbstractFullHessian}
    coloring::AbstractVector,
)

Seed the duals with the coloring based seeds to compute the Jacobian or Hessian $M$.

partials!(jac::AbstractJacobian)

Extract partials from Jacobian jac in jac.J.

partials!(hess::AbstractFullHessian)

Extract partials from Hessian hess into hess.H.

set_value!(
    jac,
    primals::AbstractVector{T}
) where {T}

Set values of ForwardDiff.Dual numbers in jac to primals.