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())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.
Hessian matrix based on Gill83
If you have an analytical gradient function, you should use `stats::optimHess`
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)
#>