# branin: Branin-Hoo 2-dimensional test function In smint: Smooth Multivariate Interpolation for Gridded and Scattered Data

## Description

Branin-Hoo 2-dimensional test function.

## Usage

 `1` ```branin(x) ```

## Arguments

 `x` Numeric vector with length 2.

## 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 at (nearly) : x1 = c(0.96, 0.15), x2 = c(0.12, 0.82) and x3 = c(0.54, 0.15).

## Value

The Branin-Hoo function's value.

## Author(s)

David Ginsbourger

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28``` ```GD <- Grid(nlevels = c("x" = 20, "y" = 20)) x <- levels(GD)[[1]]; y <- levels(GD)[[2]] f <- apply_Grid(GD, branin) dim(f) <- nlevels(GD) contour(x = x, y = y, z = f, nlevels = 40) nOut <- 100; Xout2 <- array(runif(nOut * 2), dim = c(nOut, 2)) colnames(Xout2) <- c("x", "y") ## interpolate using default method (Lagrange) GIL <- interp_Grid(X = GD, Y = f, Xout = Xout2) ## interpolate using a natural spline GIS <- interp_Grid(X = GD, Y = f, Xout = Xout2, cardinalBasis1d = function(x, xout) { cardinalBasis_natSpline(x = x, xout = xout)\$CB }) F <- apply(Xout2, 1, branin) mat <- cbind(Xout2, fTrue = F, fIntL = GIL, errorLag = F - GIL, fIntS = GIS, errorSpline = F - GIS) apply(mat[ , c("errorLag", "errorSpline")], 2, function(x) mean(abs(x))) ## Not run: ## for the users of the "rgl" package only... library(rgl) persp3d(x = x, y = y, z = f, aspect = c(1, 1, 0.5), col = "lightblue", alpha = 0.8) spheres3d(Xout2[ , 1], Xout2[ , 2], GIS, col = "orangered", radius = 2) ## End(Not run) ```

smint documentation built on April 14, 2017, 1:49 p.m.