SIAM test functions {adagio}

Trefethen and Wagon Test Functions

Description

Test functions for global optimization posed for the SIAM 100-digit challenge in 2002 by Nick Trefethen, Oxford University, UK.

Usage

fnTrefethen(p2)
fnWagon(p3)

Arguments

p2

Numerical vector of length 2.

p3

Numerical vector of length 3.

Details

These are highly nonlinear and oscillating functions in two and three dimensions with thousands of local mimima inside the unit square resp. cube (i.e., [-1, 1] x [-1, 1] or [-1, 1] x [-1, 1] x [-1, 1]).

Value

Function value is a single real number.

Author(s)

HwB <[e-mail]>

References

F. Bornemann, D. Laurie, S. Wagon, and J. Waldvogel (2004). The SIAM 100-Digit Challenge: A Study in High-Accuracy Numerical Computing. Society for Industrial and Applied Mathematics.

Examples

  x <- 2*runif(5) - 1
  fnTrefethen(x)
  fnWagon(x)

  ## Not run: 
  T <- matrix(NA, nrow=1001, ncol=1001)
  for (i in 1:1001) {
    for (j in 1:1001) {
        T[i, j] <- fnTrefethen(c(x[i], y[j]))
    }
  }
  image(x, y, T)
  contour(x, y, T, add=TRUE)
  
## End(Not run)