test_func_apply: bananagramacy2Dexp: bananagramacy2Dexp function 6 dimensional...

In TestFunctions: Test Functions for Simulation Experiments and Evaluating Optimization and Emulation Algorithms

bananagramacy2Dexp: bananagramacy2Dexp function 6 dimensional function. First two dimensions are banana function, next two are the gramacy2Dexp function, last two are null dimensions

Description

branin: A function. 2 dimensional function.

Usage

bananagramacy2Dexp(
  x,
  scale_it = T,
  scale_low = 0,
  scale_high = 1,
  noise = 0,
  ...
)

bananatimesgramacy2Dexp(
  x,
  scale_it = T,
  scale_low = 0,
  scale_high = 1,
  noise = 0,
  ...
)

gramacy2Dexp(x, scale_it = T, scale_low = -2, scale_high = 6, noise = 0, ...)

gramacy2Dexp3hole(
  x,
  scale_it = T,
  scale_low = 0,
  scale_high = 1,
  noise = 0,
  ...
)

gramacy6D(x, scale_it = T, scale_low = 0, scale_high = 1, noise = 0, ...)

branin(
  x,
  scale_it = T,
  scale_low = c(-5, 0),
  scale_high = c(10, 15),
  noise = 0
)

borehole(
  x,
  scale_it = T,
  scale_low = c(0.05, 100, 63070, 990, 63.1, 700, 1120, 9855),
  scale_high = c(0.15, 50000, 115600, 1110, 116, 820, 1680, 12045),
  noise = 0
)

franke(x, scale_it = F, scale_low = c(0, 0), scale_high = c(1, 1), noise = 0)

zhou1998(x, scale_it = F, scale_low = c(0, 0), scale_high = c(1, 1), noise = 0)

currin1991(
  x,
  scale_it = F,
  scale_low = c(0, 0),
  scale_high = c(1, 1),
  noise = 0
)

currin1991b(
  x,
  scale_it = F,
  scale_low = c(0, 0),
  scale_high = c(1, 1),
  noise = 0
)

limpoly(x, scale_it = F, scale_low = c(0, 0), scale_high = c(1, 1), noise = 0)

limnonpoly(
  x,
  scale_it = F,
  scale_low = c(0, 0),
  scale_high = c(1, 1),
  noise = 0
)

banana(
  x,
  scale_it = T,
  scale_low = c(-20, -10),
  scale_high = c(20, 5),
  noise = 0
)

banana_grad(
  x,
  scale_it = T,
  scale_low = c(-20, -10),
  scale_high = c(20, 5),
  noise = 0
)

gaussian1(
  x,
  scale_it = F,
  scale_low = c(0, 0),
  scale_high = c(1, 1),
  noise = 0
)

sinumoid(x, scale_it = F, scale_low = c(0, 0), scale_high = c(1, 1), noise = 0)

waterfall(
  x,
  scale_it = F,
  scale_low = c(0, 0),
  scale_high = c(1, 1),
  noise = 0
)

sqrtsin(
  x,
  scale_it = F,
  scale_low = c(0, 0),
  scale_high = c(1, 1),
  noise = 0,
  freq = 2 * pi
)

powsin(
  x,
  scale_it = F,
  scale_low = c(0, 0),
  scale_high = c(1, 1),
  noise = 0,
  freq = 2 * pi,
  pow = 0.7
)

OTL_Circuit(
  x,
  scale_it = T,
  scale_low = c(50, 25, 0.5, 1.2, 0.25, 50),
  scale_high = c(150, 70, 3, 2.5, 1.2, 300),
  noise = 0
)

GoldsteinPrice(
  x,
  scale_it = T,
  scale_low = c(-2, -2),
  scale_high = c(2, 2),
  noise = 0
)

GoldsteinPriceLog(
  x,
  scale_it = T,
  scale_low = c(-2, -2),
  scale_high = c(2, 2),
  noise = 0
)

ackley(
  x,
  scale_it = T,
  scale_low = -32.768,
  scale_high = 32.768,
  noise = 0,
  a = 20,
  b = 0.2,
  c = 2 * pi
)

piston(
  x,
  scale_it = T,
  scale_low = c(30, 0.005, 0.002, 1000, 90000, 290, 340),
  scale_high = c(60, 0.02, 0.01, 5000, 110000, 296, 360),
  noise = 0
)

wingweight(
  x,
  scale_it = T,
  scale_low = c(150, 220, 6, -10, 16, 0.5, 0.08, 2.5, 1700, 0.025),
  scale_high = c(200, 300, 10, 10, 45, 1, 0.18, 6, 2500, 0.08),
  noise = 0
)

welch(x, scale_it = T, scale_low = c(-0.5), scale_high = c(0.5), noise = 0)

robotarm(
  x,
  scale_it = T,
  scale_low = rep(0, 8),
  scale_high = c(rep(2 * pi, 4), rep(1, 4)),
  noise = 0
)

RoosArnold(x, scale_it = F, scale_low = 0, scale_high = 1, noise = 0)

Gfunction(x, scale_it = F, scale_low = 0, scale_high = 1, noise = 0, ...)

beale(x, scale_it = T, scale_low = -4.5, scale_high = 4.5, noise = 0, ...)

easom(x, scale_it = T, scale_low = -4.5, scale_high = 4.5, noise = 0, ...)

griewank(x, scale_it = T, scale_low = -600, scale_high = 600, noise = 0, ...)

hump(x, scale_it = T, scale_low = -5, scale_high = 5, noise = 0, ...)

levy(x, scale_it = T, scale_low = -10, scale_high = 10, noise = 0, ...)

levytilt(x, scale_it = T, scale_low = 0, scale_high = 1, noise = 0, ...)

michalewicz(x, scale_it = T, scale_low = 0, scale_high = pi, noise = 0, ...)

rastrigin(
  x,
  scale_it = T,
  scale_low = -5.12,
  scale_high = 5.12,
  noise = 0,
  ...
)

moon_high(x, scale_it = F, scale_low = 0, scale_high = 1, noise = 0, ...)

linkletter_nosignal(
  x,
  scale_it = F,
  scale_low = 0,
  scale_high = 1,
  noise = 0,
  ...
)

morris(x, scale_it = T, scale_low = 0, scale_high = 1, noise = 0, ...)

detpep8d(x, scale_it = T, scale_low = 0, scale_high = 1, noise = 0, ...)

hartmann(x, scale_it = F, scale_low = 0, scale_high = 1, noise = 0, ...)

quad_peaks(x, scale_it = T, scale_low = 0, scale_high = 1, noise = 0, ...)

quad_peaks_slant(
  x,
  scale_it = T,
  scale_low = 0,
  scale_high = 1,
  noise = 0,
  ...
)

SWNExpCos(x, scale_it = T, scale_low = 0, scale_high = 1, noise = 0, ...)

logistic(x, scale_it = T, scale_low = 0, scale_high = 1, noise = 0, ...)

logistic15(x, scale_it = T, scale_low = 0, scale_high = 1, noise = 0, ...)

logistic_plateau(
  x,
  scale_it = T,
  scale_low = 0,
  scale_high = 1,
  noise = 0,
  ...
)

vertigrad(x, scale_it = T, scale_low = 0, scale_high = 1, noise = 0, ...)

vertigrad_grad(x, scale_it = T, scale_low = 0, scale_high = 1, noise = 0, ...)

beambending(
  x,
  scale_it = T,
  scale_low = c(10, 1, 0.1),
  scale_high = c(20, 2, 0.2),
  noise = 0,
  ...
)

chengsandu(x, scale_it = T, scale_low = 0, scale_high = 1, noise = 0, ...)

steelcolumnstress(
  x,
  scale_it = T,
  scale_low = c(330, 4e+05, 420000, 420000, 200, 10, 100, 10, 12600),
  scale_high = c(470, 6e+05, 780000, 780000, 400, 30, 500, 50, 29400),
  noise = 0,
  ...
)

winkel(x, scale_it = T, scale_low = 0, scale_high = 1, noise = 0, ...)

boreholeMV(
  x,
  NOD = 51,
  scale_it = T,
  scale_low = c(0.05, 100, 63070, 990, 63.1, 700, 1120, 9855),
  scale_high = c(0.15, 50000, 115600, 1110, 116, 820, 1680, 12045),
  noise = 0
)

test_func_apply(func, x, scale_it, scale_low, scale_high, noise = 0, ...)

Arguments

x	Input value, either a matrix whose rows are points or a vector for a single point. Be careful with 1-D functions.
scale_it	Should the data be scaled from [0, 1]^D to [scale_low, scale_high]? This means the input data is confined to be in [0, 1]^D, but the function isn't.
scale_low	Lower bound for each variable
scale_high	Upper bound for each variable
noise	If white noise should be added, specify the standard deviation for normal noise
...	Additional parameters for func
freq	Wave frequency for sqrtsin and powsin
pow	Power for powsin
a	A constant for ackley()
b	A constant for ackley()
c	A constant for ackley()
NOD	number of output dimensions
func	A function to evaluate

Value

Function values at x

References

Gramacy, Robert B., and Herbert KH Lee. "Adaptive design and analysis of supercomputer experiments." Technometrics 51.2 (2009): 130-145.

Gramacy, Robert B., and Herbert KH Lee. "Adaptive design and analysis of supercomputer experiments." Technometrics 51.2 (2009): 130-145.

Gramacy, Robert B., and Herbert KH Lee. "Adaptive design and analysis of supercomputer experiments." Technometrics 51.2 (2009): 130-145.

Dixon, L. C. W. (1978). The global optimization problem: an introduction. Towards Global Optimiation 2, 1-15.

Morris, M. D., Mitchell, T. J., & Ylvisaker, D. (1993). Bayesian design and analysis of computer experiments: use of derivatives in surface prediction. Technometrics, 35(3), 243-255.

Worley, Brian A. Deterministic uncertainty analysis. No. ORNL-6428. Oak Ridge National Lab., TN (USA), 1987.

Franke, R. (1979). A critical comparison of some methods for interpolation of scattered data. Monterey, California: Naval Postgraduate School. Page 13.

An, J., & Owen, A. (2001). Quasi-regression. Journal of complexity, 17(4), 588-607.

Currin, C., Mitchell, T., Morris, M., & Ylvisaker, D. (1991). Bayesian prediction of deterministic functions, with applications to the design and analysis of computer experiments. Journal of the American Statistical Association, 86(416), 953-963.

Currin, C., Mitchell, T., Morris, M., & Ylvisaker, D. (1991). Bayesian prediction of deterministic functions, with applications to the design and analysis of computer experiments. Journal of the American Statistical Association, 86(416), 953-963.

Lim, Yong B., Jerome Sacks, W. J. Studden, and William J. Welch. "Design and analysis of computer experiments when the output is highly correlated over the input space." Canadian Journal of Statistics 30, no. 1 (2002): 109-126.

Lim, Yong B., Jerome Sacks, W. J. Studden, and William J. Welch. "Design and analysis of computer experiments when the output is highly correlated over the input space." Canadian Journal of Statistics 30, no. 1 (2002): 109-126.

Haario, H., Saksman, E., & Tamminen, J. (1999). Adaptive proposal distribution for random walk Metropolis algorithm. Computational Statistics, 14(3), 375-396.

Joseph, V. R., Dasgupta, T., Tuo, R., & Wu, C. J. (2015). Sequential exploration of complex surfaces using minimum energy designs. Technometrics, 57(1), 64-74.

Ben-Ari, Einat Neumann, and David M. Steinberg. "Modeling data from computer experiments: an empirical comparison of kriging with MARS and projection pursuit regression." Quality Engineering 19.4 (2007): 327-338.

Kenett, Ron S., Shelemyahu Zacks, and Daniele Amberti. Modern Industrial Statistics: with applications in R, MINITAB and JMP. John Wiley & Sons, 2013.

Forrester, A., & Keane, A. (2008). Engineering design via surrogate modelling: a practical guide. John Wiley & Sons.

http://www.abe.ufl.edu/jjones/ABE_5646/2010/Morris.1991

http://www.tandfonline.com/doi/pdf/10.1198/TECH.2010.09157?needAccess=true

Santner, T. J., Williams, B. J., & Notz, W. (2003). The Design and Analysis of Computer Experiments. Springer Science & Business Media.

Cheng, Haiyan, and Adrian Sandu. "Collocation least-squares polynomial chaos method." In Proceedings of the 2010 Spring Simulation Multiconference, p. 80. Society for Computer Simulation International, 2010.

Kuschel, Norbert, and Rudiger Rackwitz. "Two basic problems in reliability-based structural optimization." Mathematical Methods of Operations Research 46, no. 3 (1997): 309-333.

Prikhodko, Pavel, and Nikita Kotlyarov. "Calibration of Sobol indices estimates in case of noisy output." arXiv preprint arXiv:1804.00766 (2018).

Winkel, Munir A., Jonathan W. Stallings, Curt B. Storlie, and Brian J. Reich. "Sequential Optimization in Locally Important Dimensions." arXiv preprint arXiv:1804.10671 (2018).

Morris, M. D., Mitchell, T. J., & Ylvisaker, D. (1993). Bayesian design and analysis of computer experiments: use of derivatives in surface prediction. Technometrics, 35(3), 243-255.

Worley, Brian A. Deterministic uncertainty analysis. No. ORNL-6428. Oak Ridge National Lab., TN (USA), 1987.

Examples

bananagramacy2Dexp(runif(6))
bananagramacy2Dexp(matrix(runif(6*20),ncol=6))
bananatimesgramacy2Dexp(runif(6))
bananatimesgramacy2Dexp(matrix(runif(6*20),ncol=6))
gramacy2Dexp(runif(2))
gramacy2Dexp(matrix(runif(2*20),ncol=2))
gramacy2Dexp3hole(runif(2))
gramacy2Dexp3hole(matrix(runif(2*20),ncol=2))
gramacy6D(runif(6))
gramacy6D(matrix(runif(6*20),ncol=6))
branin(runif(2))
branin(matrix(runif(20), ncol=2))
borehole(runif(8))
borehole(matrix(runif(80), ncol=8))
franke(runif(2))
zhou1998(runif(2))
currin1991(runif(2))
currin1991b(runif(2))
limpoly(runif(2))
limnonpoly(runif(2))
banana(runif(2))
x <- y <- seq(0, 1, len=100)
z <- outer(x, y, Vectorize(function(a, b){banana(c(a, b))}))
contour(x, y, z)
banana_grad(runif(2))
x <- y <- seq(0, 1, len=100)
z <- outer(x, y, Vectorize(function(a, b){sum(banana_grad(c(a, b))^2)}))
contour(x, y, z)
gaussian1(runif(2))
sinumoid(runif(2))
x <- y <- seq(0, 1, len=100)
z <- outer(x, y, Vectorize(function(a, b){sinumoid(c(a, b))}))
contour(x, y, z)
waterfall(runif(2))
sqrtsin(runif(1))
curve(sqrtsin(matrix(x,ncol=1)))
powsin(runif(1))#,pow=2)
OTL_Circuit(runif(6))
OTL_Circuit(matrix(runif(60),ncol=6))
GoldsteinPrice(runif(2))
GoldsteinPrice(matrix(runif(60),ncol=2))
GoldsteinPriceLog(runif(2))
GoldsteinPriceLog(matrix(runif(60),ncol=2))
ackley(runif(2))
ackley(matrix(runif(60),ncol=2))
piston(runif(7))
piston(matrix(runif(7*20),ncol=7))
wingweight(runif(10))
wingweight(matrix(runif(10*20),ncol=10))
welch(runif(20))
welch(matrix(runif(20*20),ncol=20))
robotarm(runif(8))
robotarm(matrix(runif(8*20),ncol=8))
RoosArnold(runif(8))
RoosArnold(matrix(runif(8*20),ncol=8))
Gfunction(runif(8))
Gfunction(matrix(runif(8*20),ncol=8))
beale(runif(2))
beale(matrix(runif(2*20),ncol=2))
easom(runif(2))
easom(matrix(runif(2*20),ncol=2))
griewank(runif(2))
griewank(matrix(runif(2*20),ncol=2))
hump(runif(2))
hump(matrix(runif(2*20),ncol=2))
levy(runif(2))
levy(matrix(runif(2*20),ncol=2))
levytilt(runif(2))
levytilt(matrix(runif(2*20),ncol=2))
michalewicz(runif(2))
michalewicz(matrix(runif(2*20),ncol=2))
rastrigin(runif(2))
rastrigin(matrix(runif(2*20),ncol=2))
moon_high(runif(20))
moon_high(matrix(runif(20*20),ncol=20))
linkletter_nosignal(runif(2))
linkletter_nosignal(matrix(runif(2*20),ncol=2))
morris(runif(20))
morris(matrix(runif(20*20),ncol=20))
detpep8d(runif(2))
detpep8d(matrix(runif(2*20),ncol=2))
hartmann(runif(2))
hartmann(matrix(runif(6*20),ncol=6))
quad_peaks(runif(2))
quad_peaks(matrix(runif(2*20),ncol=2))
quad_peaks_slant(runif(2))
quad_peaks_slant(matrix(runif(2*20),ncol=2))
SWNExpCos(runif(2))
SWNExpCos(matrix(runif(2*20),ncol=2))
curve(logistic, from=-5,to=5)
curve(logistic(x,offset=.5, scl=15))
logistic(matrix(runif(20),ncol=1))
curve(logistic15)
curve(logistic15(x,offset=.25))
logistic15(matrix(runif(20),ncol=1))
curve(logistic_plateau(matrix(x,ncol=1)))
logistic_plateau(matrix(runif(20),ncol=1))
vertigrad(runif(2))
vertigrad(matrix(runif(2*20),ncol=2))
vertigrad_grad(runif(2))
vertigrad_grad(matrix(runif(2*20),ncol=2))
beambending(runif(3))
beambending(matrix(runif(3*20),ncol=3))
chengsandu(runif(2))
chengsandu(matrix(runif(2*20),ncol=2))
steelcolumnstress(runif(8))
steelcolumnstress(matrix(runif(8*20),ncol=8))
winkel(runif(2))
winkel(matrix(runif(2*20),ncol=2))
boreholeMV(runif(8))
boreholeMV(matrix(runif(80), ncol=8))
x <- matrix(seq(0,1,length.out=10), ncol=1)
y <- test_func_apply(sin, x, TRUE, 0, 2*pi, .05)
plot(x,y)
curve(sin(2*pi*x), col=2, add=TRUE)

TestFunctions documentation built on Sept. 30, 2024, 9:31 a.m.