# exp2d.rand

##### Random 2-d Exponential Data

A Random subsample of `data(exp2d)`

, or
Latin Hypercube sampled data evaluated with `exp2d.Z`

##### Usage

`exp2d.rand(n1 = 50, n2 = 30, lh = NULL, dopt = 1)`

##### Arguments

- n1
Number of samples from the first, interesting, quadrant

- n2
Number of samples from the other three, uninteresting, quadrants

- lh
If

`!is.null(lh)`

then Latin Hypercube (LH) sampling (`lhs`

) is used instead of subsampling from`data(exp2d)`

;`lh`

should be a single nonnegative integer specifying the desired number of predictive locations,`XX`

; or, it should be a vector of length 4, specifying the number of predictive locations desired from each of the four quadrants (interesting quadrant first, then counter-clockwise)- dopt
If

`dopt >= 2`

then d-optimal subsampling from LH candidates of the multiple indicated by the value of`dopt`

will be used. This argument only makes sense when`!is.null(lh)`

##### Details

When `is.null(lh)`

, data is subsampled without replacement from
`data(exp2d)`

. Of the `n1 + n2 <= 441`

input/response pairs `X,Z`

, there are `n1`

are taken from the
first quadrant, i.e., where the response is interesting,
and the remaining `n2`

are taken from the other three
quadrants. The remaining `441 - (n1 + n2)`

are treated as
predictive locations

Otherwise, when `!is.null(lh)`

, Latin Hypercube Sampling
(`lhs`

) is used

If `dopt >= 2`

then `n1*dopt`

LH candidates are used
for to get a D-optimal subsample of size `n1`

from the
first (interesting) quadrant. Similarly `n2*dopt`

in the
rest of the un-interesting region.
A total of `lh*dopt`

candidates will be used for sequential D-optimal
subsampling for predictive locations `XX`

in all four
quadrants assuming the already-sampled `X`

locations will
be in the design.

In all three cases, the response is evaluated as
$$Z(X)=x_1 * \exp(x_1^2-x_2^2).$$
thus creating the outputs `Ztrue`

and `ZZtrue`

.
Zero-mean normal noise with `sd=0.001`

is added to the
responses `Z`

and `ZZ`

##### Value

Output is a `list`

with entries:

2-d `data.frame`

with `n1 + n2`

input locations

Numeric vector describing the responses (with noise) at the
`X`

input locations

Numeric vector describing the true responses (without
noise) at the `X`

input locations

2-d `data.frame`

containing the remaining
`441 - (n1 + n2)`

input locations

Numeric vector describing the responses (with noise) at
the `XX`

predictive locations

Numeric vector describing the responses (without
noise) at the `XX`

predictive locations

##### References

Gramacy, R. B. (2007). *tgp: An R Package for Bayesian
Nonstationary, Semiparametric Nonlinear Regression and Design by
Treed Gaussian Process Models.*
Journal of Statistical Software, **19**(9).
https://www.jstatsoft.org/v19/i09

Gramacy, R. B., Lee, H. K. H. (2008).
*Bayesian treed Gaussian process models with an application
to computer modeling*. Journal of the American Statistical Association,
103(483), pp. 1119-1130. Also available as ArXiv article 0710.4536
https://arxiv.org/abs/0710.4536

##### See Also

##### Examples

```
# NOT RUN {
## randomly subsampled data
## ------------------------
eds <- exp2d.rand()
# higher span = 0.5 required because the data is sparse
# and was generated randomly
eds.g <- interp.loess(eds$X[,1], eds$X[,2], eds$Z, span=0.5)
# perspective plot, and plot of the input (X & XX) locations
par(mfrow=c(1,2), bty="n")
persp(eds.g, main="loess surface", theta=-30, phi=20,
xlab="X[,1]", ylab="X[,2]", zlab="Z")
plot(eds$X, main="Randomly Subsampled Inputs")
points(eds$XX, pch=19, cex=0.5)
## Latin Hypercube sampled data
## ----------------------------
edlh <- exp2d.rand(lh=c(20, 15, 10, 5))
# higher span = 0.5 required because the data is sparse
# and was generated randomly
edlh.g <- interp.loess(edlh$X[,1], edlh$X[,2], edlh$Z, span=0.5)
# perspective plot, and plot of the input (X & XX) locations
par(mfrow=c(1,2), bty="n")
persp(edlh.g, main="loess surface", theta=-30, phi=20,
xlab="X[,1]", ylab="X[,2]", zlab="Z")
plot(edlh$X, main="Latin Hypercube Sampled Inputs")
points(edlh$XX, pch=19, cex=0.5)
# show the quadrants
abline(h=2, col=2, lty=2, lwd=2)
abline(v=2, col=2, lty=2, lwd=2)
# }
# NOT RUN {
## D-optimal subsample with a factor of 10 (more) candidates
## ---------------------------------------------------------
edlhd <- exp2d.rand(lh=c(20, 15, 10, 5), dopt=10)
# higher span = 0.5 required because the data is sparse
# and was generated randomly
edlhd.g <- interp.loess(edlhd$X[,1], edlhd$X[,2], edlhd$Z, span=0.5)
# perspective plot, and plot of the input (X & XX) locations
par(mfrow=c(1,2), bty="n")
persp(edlhd.g, main="loess surface", theta=-30, phi=20,
xlab="X[,1]", ylab="X[,2]", zlab="Z")
plot(edlhd$X, main="D-optimally Sampled Inputs")
points(edlhd$XX, pch=19, cex=0.5)
# show the quadrants
abline(h=2, col=2, lty=2, lwd=2)
abline(v=2, col=2, lty=2, lwd=2)
# }
```

*Documentation reproduced from package tgp, version 2.4-17, License: LGPL*