DiceKriging (version 1.6.0)

branin: 2D test function

Description

Branin-Hoo 2-dimensional test function.

Usage

branin(x)

Arguments

x

a 2-dimensional vector specifying the location where the function is to be evaluated.

Value

A real number equal to the Branin-Hoo function values at x

Details

The Branin-Hoo function is defined here over [0,1] x [0,1], instead of [-5,0] x [10,15] as usual. It has 3 global minima : x1 = c(0.9616520, 0.15); x2 = c(0.1238946, 0.8166644); x3 = c(0.5427730, 0.15)

Examples

# NOT RUN {
n.grid <- 20
x.grid <- y.grid <- seq(0,1,length=n.grid)
design.grid <- expand.grid(x.grid, y.grid)
response.grid <- apply(design.grid, 1, branin)
z.grid <- matrix(response.grid, n.grid, n.grid)
contour(x.grid,y.grid,z.grid,40)
x1 = c(0.9616520, 0.15); x2 = c(0.1238946, 0.8166644); x3 = c(0.5427730, 0.15)
points(rbind(t(x1), t(x2), t(x3)), pch=19, col="red")
title("Fonction de Branin")
# }