Unlike stats::optimHess which assumes the gradient is accurate, nlmixrHess does not make as strong an assumption that the gradient is accurate but takes more function evaluations to calculate the Hessian. In addition, this procedures optimizes the forward difference interval by nlmixrGill83

nlmixrHess(par, fn, ..., envir = parent.frame())

Arguments

par Initial values for the parameters to be optimized over. A function to be minimized (or maximized), with first argument the vector of parameters over which minimization is to take place. It should return a scalar result. Extra arguments sent to nlmixrGill83 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.

Value

Hessian matrix based on Gill83

Details

If you have an analytical gradient function, you should use stats::optimHess

References

https://v8doc.sas.com/sashtml/ormp/chap5/sect28.htm

nlmixrGill83, optimHess

Matthew Fidler

Examples

 func0 <- function(x){ sum(sin(x))  }
x <- (0:10)*2*pi/10
nlmixrHess(x, func0)
#>
#>               [,1]        [,2]        [,3]        [,4]        [,5]       [,6]
#>  [1,] 143438578824           0           0           0           0          0
#>  [2,]            0 54098751870           0           0           0          0
#>  [3,]            0           0 28167126506           0           0          0
#>  [4,]            0           0           0 17234064451           0          0
#>  [5,]            0           0           0           0 11620957271          0
#>  [6,]            0           0           0           0           0 8362405349
#>  [7,]            0           0           0           0           0          0
#>  [8,]            0           0           0           0           0          0
#>  [9,]            0           0           0           0           0          0
#> [10,]            0           0           0           0           0          0
#> [11,]            0           0           0           0           0          0
#>               [,7]         [,8]         [,9]        [,10]    [,11]
#>  [1,]            0            0            0            0     0.00
#>  [2,]            0            0            0            0     0.00
#>  [3,]            0            0            0            0     0.00
#>  [4,]            0            0            0            0     0.00
#>  [5,]            0            0            0            0     0.00
#>  [6,]            0            0            0            0     0.00
#>  [7,] 337177531807            0            0            0     0.00
#>  [8,]            0 546113920621            0            0     0.00
#>  [9,]            0            0 545713835656            0     0.00
#> [10,]            0            0            0 337491323869     0.00
#> [11,]            0            0            0            0 26296.35

fr <- function(x) {   ## Rosenbrock Banana function
x1 <- x[1]
x2 <- x[2]
100 * (x2 - x1 * x1)^2 + (1 - x1)^2
}
grr <- function(x) { ## Gradient of 'fr'
x1 <- x[1]
x2 <- x[2]
c(-400 * x1 * (x2 - x1 * x1) - 2 * (1 - x1),
200 *      (x2 - x1 * x1))
}

h1 <- optimHess(c(1.2,1.2), fr, grr)

h2 <- optimHess(c(1.2,1.2), fr)

## in this case h3 is closer to h1 where the gradient is known

h3 <- nlmixrHess(c(1.2,1.2), fr)
#>