Trefethen and Wagon Test Functions
Test functions for global optimization posed for the SIAM 100-digit challenge in 2002 by Nick Trefethen, Oxford University, UK.
fnTrefethen(p2) fnWagon(p3)
p2 |
Numerical vector of length 2. |
p3 |
Numerical vector of length 3. |
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]).
Function value is a single real number.
HwB <hwborchers@googlemail.com>
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.
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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.