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SciMLJacobianOperators.jl

This is a subpackage on NonlinearSolve providing a general purpose JacVec and VecJac operator built on top on DifferentiationInterface.jl.

import Pkg
Pkg.add("SciMLJacobianOperators")
import SciMLJacobianOperators

Jacobian API

SciMLJacobianOperators.JacobianOperator — Type
JacobianOperator{iip, T} <: AbstractJacobianOperator{T} <: AbstractSciMLOperator{T}

A Jacobian Operator Provides both JVP and VJP without materializing either (if possible).

Constructor

JacobianOperator(prob::AbstractNonlinearProblem, fu, u; jvp_autodiff = nothing,
    vjp_autodiff = nothing, skip_vjp::Val = Val(false), skip_jvp::Val = Val(false))

By default, the JacobianOperator will compute JVP. Use Base.adjoint or Base.transpose to switch to VJP.

Computing the VJP

Computing the VJP is done according to the following rules:

  • If f has a vjp method, then we use that.
  • If f has a jac method and no vjp_autodiff is provided, then we use jac * v.
  • If vjp_autodiff is provided we using DifferentiationInterface.jl to compute the VJP.

Computing the JVP

Computing the JVP is done according to the following rules:

  • If f has a jvp method, then we use that.
  • If f has a jac method and no jvp_autodiff is provided, then we use v * jac.
  • If jvp_autodiff is provided we using DifferentiationInterface.jl to compute the JVP.

Special Case (Number)

For Number inputs, VJP and JVP are not distinct. Hence, if either vjp or jvp is provided, then we use that. If neither is provided, then we use v * jac if jac is provided. Finally, we use the respective autodiff methods to compute the derivative using DifferentiationInterface.jl and multiply by v.

Methods Provided

Warning

Currently it is expected that p during problem construction is same as p during operator evaluation. This restriction will be lifted in the future.

  • (op::JacobianOperator)(v, u, p): Computes ∂f(u, p)/∂u * v or ∂f(u, p)/∂uᵀ * v.
  • (op::JacobianOperator)(res, v, u, p): Computes ∂f(u, p)/∂u * v or ∂f(u, p)/∂uᵀ * v and stores the result in res.

See also VecJacOperator and JacVecOperator.

source

Stateful Operators