dot-rxDiscreteAdjointGrad: Discrete adjoint gradient of a trajectory objective
In rxode2: Facilities for Simulating from ODE-Based Models

.rxDiscreteAdjointGrad

R Documentation

Discrete adjoint gradient of a trajectory objective

Description

Given the RK4 stages from .rxDiscreteForwardSens() and, per observation step, the objective covector ⁠c_n = dG/dX_{step_n}⁠, computes dG/dtheta by reverse-mode differentiation through the RK4 steps – equal to ⁠sum_n c_n^T S_{step_n}⁠ to machine precision, in one backward pass.

Usage

.rxDiscreteAdjointGrad(
  build,
  stages,
  params,
  h,
  obsSteps,
  cov,
  doses = NULL,
  lam0Cov = NULL
)

Arguments

`build`	object from `.rxDiscreteAdjointBuild()`.
`stages`	RK4 stage list from `.rxDiscreteForwardSens()`.
`params`	named numeric parameter vector.
`h`	fixed step size (same as the forward solve).
`obsSteps`	integer step indices at which observation covectors apply.
`cov`	list of covector vectors (length `ns`), aligned with `obsSteps`.
`doses`	optional list of additive-bolus dose specs (same format as `.rxDiscreteForwardSens()`); the exact transpose of the forward dose jump is applied, contributing `amt * dF/dtheta * lambda_c` to `dG/dtheta`.
`lam0Cov`	optional initial-condition sensitivity `dX0/dtheta` (`⁠ns x np⁠`) to add the terminal transversality `⁠lambda(t0)^T dX0/dtheta⁠`; default none.