logit.hessian {Bhat} R Documentation

## Hessian (curvature matrix)

### Description

Numerical evaluation of the Hessian of a real function f: R^n  \rightarrow R on a generalized logit scale, i.e. using transformed parameters according to x'=log((x-xl)/(xu-x))), with xl < x < xu.

### Usage

logit.hessian(
x = x,
f = f,
del = rep(0.002, length(x\$est)),
dapprox = FALSE,
nfcn = 0
)


### Arguments

 x a list with components 'label' (of mode character), 'est' (the parameter vector with the initial guess), 'low' (vector with lower bounds), and 'upp' (vector with upper bounds) f the function for which the Hessian is to be computed at point x del step size on logit scale (numeric) dapprox logical variable. If TRUE the off-diagonal elements are set to zero. If FALSE (default) the full Hessian is computed nfcn number of function calls

### Details

This version uses a symmetric grid for the numerical evaluation computation of first and second derivatives.

### Value

returns list with

 df first derivatives (logit scale) ddf Hessian (logit scale) nfcn number of function calls eigen eigen values (logit scale)

### Note

This function is part of the Bhat exploration tool

### Author(s)

E. Georg Luebeck (FHCRC)

dfp, newton, ftrf, btrf, dqstep

### Examples


## Rosenbrock Banana function
fr <- function(x) {
x1 <- x[1]
x2 <- x[2]
100 * (x2 - x1 * x1)^2 + (1 - x1)^2
}
## define
x <- list(label=c("a","b"),est=c(1,1),low=c(-100,-100),upp=c(100,100))
logit.hessian(x,f=fr,del=dqstep(x,f=fr,sens=0.01))
## shows the differences in curvature at the minimum of the Banana
## function along principal axis (in a logit-transformed coordinate system)



[Package Bhat version 0.9-12 Index]