Jacobian Wrappers

AbstractNonlinearSolveJacobianCache{iip} <: Function

Abstract Type for all Jacobian Caches used in NonlinearSolve.jl.

JacobianCache(prob, alg, f::F, fu, u, p; autodiff = nothing,
    vjp_autodiff = nothing, jvp_autodiff = nothing, linsolve = missing) where {F}

Construct a cache for the Jacobian of f w.r.t. u.

Arguments

• prob: A NonlinearProblem or a NonlinearLeastSquaresProblem.
• alg: A AbstractNonlinearSolveAlgorithm. Used to check for concrete_jac.
• f: The function to compute the Jacobian of.
• fu: The evaluation of f(u, p) or f(_, u, p). Used to determine the size of the result cache and Jacobian.
• u: The current value of the state.
• p: The current value of the parameters.

Keyword Arguments

• autodiff: Automatic Differentiation or Finite Differencing backend for computing the jacobian. By default, selects a backend based on sparsity parameters, type of state, function properties, etc.
• vjp_autodiff: Automatic Differentiation or Finite Differencing backend for computing the vector-Jacobian product.
• jvp_autodiff: Automatic Differentiation or Finite Differencing backend for computing the Jacobian-vector product.
• linsolve: Linear Solver Algorithm used to determine if we need a concrete jacobian or if possible we can just use a NonlinearSolve.JacobianOperator instead.

jacobian_cache(ad, f, y, x, p) --> J, cache

Returns a Jacobian Matrix and a cache for the Jacobian computation.

value_and_jacobian(ad, f, y, x, p, cache; J = nothing)

Compute f(x), d/dx f(x) in the most efficient way based on ad. None of the arguments except cache (& J if not nothing) are mutated.