API reference

Index

Docstrings

ImplicitDifferentiation.ImplicitFunctionType
ImplicitFunction{F,C,L}

Differentiable wrapper for an implicit function x -> ŷ(x) whose output is defined by explicit conditions F(x,ŷ(x)) = 0.

We can obtain the Jacobian of with the implicit function theorem:

∂₁F(x,ŷ(x)) + ∂₂F(x,ŷ(x)) * ∂ŷ(x) = 0

If x ∈ ℝⁿ, y ∈ ℝᵐ and F(x,y) ∈ ℝᶜ, this amounts to solving the linear system A * J = B, where A ∈ ℝᶜᵐ, B ∈ ℝᶜⁿ and J ∈ ℝᵐⁿ.

Fields:

  • forward::F: callable of the form x -> ŷ(x)
  • conditions::C: callable of the form (x,y) -> F(x,y)
  • linear_solver::L: callable of the form (A,b) -> u such that A * u = b
source