newton_raph: Multivariate Newton-Raphson fitting method

In ohines/plmed: Causal Mediation Effects For Partially Linear Models

Description

newton_raph provides an environment for performing iterated Newton Raphson root finding of multivariate functions with an optional Backtracking line search, For more on line search see: http://cosmos.phy.tufts.edu/~danilo/AST16/Material/RootFinding.pdf page479

Usage

newton_raph(
  vec_J,
  par0,
  ...,
  LSearch = FALSE,
  w = rep.int(1, length(par0)),
  Max.it = 2000,
  prec = 1e-05,
  step.scale = 1
)

Arguments

vec_J	a function which returns newton-raphson steps via $step and the functions via $vec
par0	Initial values for the parameters to be optimized over.
...	Further arguments to be passed to vec_J
LSearch	Option to perform the Backtracking line search algorithm. Defaults to FALSE
w	Weights for Backtracking algorithm. Must be non-negative with length equal to length(par0)
Max.it	Maximum number of iterations (Function calls)
prec	Parameter precision tolerance. Iteration will stop when the step is smaller than the precision for all parameters.
step.scale	Optional scaling step to perform damped Newton Raphson.

Value

A list containing the par estimates and an evaluation of the vec_J function at these parameters.

Examples

#Optimisation of the function f(x,y) = (x*exp(y) - 1, -1-x^2 + y)
vec_J <- function(par){
    x=par[1]
    y=par[2]
    f = c(x*exp(y) - 1, -1-x^2 + y)
    fdash = matrix(c(exp(y),-2*x,x*exp(y),1),ncol=2)
    step = solve(fdash,f)
    return(list(step=step, vec=f))
}

newton_raph(vec_J,par0=c(0,0))

ohines/plmed documentation built on Jan. 9, 2021, 11:59 a.m.