nlmixr2est (version 5.0.2)

nlmixr2Gill83: Get the optimal forward difference interval by Gill83 method

Description

Get the optimal forward difference interval by Gill83 method

Usage

nlmixr2Gill83(
  what,
  args,
  envir = parent.frame(),
  which,
  gillRtol = sqrt(.Machine$double.eps),
  gillK = 10L,
  gillStep = 2,
  gillFtol = 0
)

Value

A data frame with the following columns:

- info Gradient evaluation/forward difference information

- hf Forward difference final estimate

- df Derivative estimate

- df2 2nd Derivative Estimate

- err Error of the final estimate derivative

- aEps Absolute difference for forward numerical differences

- rEps Relative Difference for backward numerical differences

- aEpsC Absolute difference for central numerical differences

- rEpsC Relative difference for central numerical differences

The info returns one of the following:

- "Not Assessed" Gradient wasn't assessed

- "Good Success" in Estimating optimal forward difference interval

- "High Grad Error" Large error; Derivative estimate error fTol or more of the derivative

- "Constant Grad" Function constant or nearly constant for this parameter

- "Odd/Linear Grad" Function odd or nearly linear, df = K, df2 ~ 0

- "Grad changes quickly" df2 increases rapidly as h decreases

Arguments

what

either a function or a non-empty character string naming the function to be called.

args

a list of arguments to the function call. The names attribute of args gives the argument names.

envir

an environment within which to evaluate the call. This will be most useful if what is a character string and the arguments are symbols or quoted expressions.

which

Which parameters to calculate the forward difference and optimal forward difference interval

gillRtol

The relative tolerance used for Gill 1983 determination of optimal step size.

gillK

The total number of possible steps to determine the optimal forward/central difference step size per parameter (by the Gill 1983 method). If 0, no optimal step size is determined. Otherwise this is the optimal step size determined.

gillStep

When looking for the optimal forward difference step size, this is This is the step size to increase the initial estimate by. So each iteration the new step size = (prior step size)*gillStep

gillFtol

The gillFtol is the gradient error tolerance that is acceptable before issuing a warning/error about the gradient estimates.

Author

Matthew Fidler

Examples

## These are taken from the numDeriv::grad examples to show how
## simple gradients are assessed with nlmixr2Gill83

nlmixr2Gill83(sin, pi)

nlmixr2Gill83(sin, (0:10)*2*pi/10)

func0 <- function(x){ sum(sin(x))  }
nlmixr2Gill83(func0 , (0:10)*2*pi/10)

func1 <- function(x){ sin(10*x) - exp(-x) }
curve(func1,from=0,to=5)

x <- 2.04
numd1 <- nlmixr2Gill83(func1, x)
exact <- 10*cos(10*x) + exp(-x)
c(numd1$df, exact, (numd1$df - exact)/exact)

x <- c(1:10)
numd1 <- nlmixr2Gill83(func1, x)
exact <- 10*cos(10*x) + exp(-x)
cbind(numd1=numd1$df, exact, err=(numd1$df - exact)/exact)

sc2.f <- function(x){
  n <- length(x)
   sum((1:n) * (exp(x) - x)) / n
}

sc2.g <- function(x){
  n <- length(x)
  (1:n) * (exp(x) - 1) / n
}

x0 <- rnorm(100)
exact <- sc2.g(x0)

g <- nlmixr2Gill83(sc2.f, x0)

max(abs(exact - g$df)/(1 + abs(exact)))