| Type: | Package |
| Title: | Test Functions for Simulation Experiments and Evaluating Optimization and Emulation Algorithms |
| Version: | 0.2.2 |
| Maintainer: | Collin Erickson <collinberickson@gmail.com> |
| Description: | Test functions are often used to test computer code. They are used in optimization to test algorithms and in metamodeling to evaluate model predictions. This package provides test functions that can be used for any purpose. |
| License: | GPL-3 |
| RoxygenNote: | 7.3.1 |
| Encoding: | UTF-8 |
| Depends: | ContourFunctions, numDeriv, rmarkdown |
| Suggests: | knitr, covr, ggplot2, testthat |
| VignetteBuilder: | knitr |
| NeedsCompilation: | no |
| Packaged: | 2024-09-14 04:20:38 UTC; colli |
| Author: | Collin Erickson [aut, cre] |
| Repository: | CRAN |
| Date/Publication: | 2024-09-15 04:10:08 UTC |
Evaluate an RFF (random wave function) at given input
Description
Evaluate an RFF (random wave function) at given input
Usage
RFF(x, freq, mag, dirr, offset, wave = sin, noise = 0)
Arguments
x |
Matrix whose rows are points to evaluate or a vector representing a single point. In 1 dimension you must use a matrix for multiple points, not a vector. |
freq |
Vector of wave frequencies |
mag |
Vector of wave magnitudes |
dirr |
Matrix of wave directions |
offset |
Vector of wave offsets |
wave |
Type of wave |
noise |
Standard deviation of random normal noise to add |
Value
Output of RFF evaluated at x
Examples
curve(RFF(matrix(x,ncol=1),3,1,1,0))
curve(RFF(matrix(x,ncol=1),3,1,1,0, noise=.1), n=1e3, type='p', pch=19)
curve(RFF(matrix(x,ncol=1),c(3,20),c(1,.1),c(1,1),c(0,0)), n=1e3)
Create a new RFF function
Description
Create a new RFF function
Usage
RFF_get(D = 2, M = 30, wave = sin, noise = 0, seed = NULL)
Arguments
D |
Number of dimensions |
M |
Number of random waves |
wave |
Type of wave |
noise |
Standard deviation of random normal noise to add |
seed |
Seed to set before randomly selecting function |
Value
A random wave function
Examples
func <- RFF_get(D=1)
curve(func)
f <- RFF_get(D=1, noise=.1)
curve(f(matrix(x,ncol=1)))
for(i in 1:100) curve(f(matrix(x,ncol=1)), add=TRUE, col=sample(2:8,1))
TF_Gfunction: G-function for evaluating a single point.
Description
TF_Gfunction: G-function for evaluating a single point.
Usage
TF_Gfunction(x, a = (1:length(x) - 1)/2)
Arguments
x |
Input vector at which to evaluate. |
a |
Parameter for Gfunction |
Value
Function output evaluated at x.
Examples
TF_Gfunction(rep(0,8))
TF_Gfunction(rep(1,8))
TF_GoldsteinPrice: Goldstein Price function for evaluating a single point
Description
TF_GoldsteinPrice: Goldstein Price function for evaluating a single point
Usage
TF_GoldsteinPrice(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
Examples
TF_GoldsteinPrice(c(0, -1)) # minimum
TF_GoldsteinPrice: Goldstein Price function for evaluating a single point on a log scale, normalized to have mean 0 and variance 1.
Description
TF_GoldsteinPrice: Goldstein Price function for evaluating a single point on a log scale, normalized to have mean 0 and variance 1.
Usage
TF_GoldsteinPriceLog(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
Examples
TF_GoldsteinPriceLog(c(0, -1)) # minimum
TF_RoosArnold: Roos & Arnold (1963) function for evaluating a single point.
Description
TF_RoosArnold: Roos & Arnold (1963) function for evaluating a single point.
Usage
TF_RoosArnold(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
Examples
TF_RoosArnold(rep(0,8))
TF_RoosArnold(rep(1,8))
TF_SWNExpCos: SWNExpCos function for evaluating a single point.
Description
TF_SWNExpCos: SWNExpCos function for evaluating a single point.
Usage
TF_SWNExpCos(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
References
Santner, T. J., Williams, B. J., & Notz, W. (2003). The Design and Analysis of Computer Experiments. Springer Science & Business Media.
Examples
TF_SWNExpCos(rep(0,2))
TF_SWNExpCos(rep(1,2))
TF_ackley: Ackley function for evaluating a single point.
Description
TF_ackley: Ackley function for evaluating a single point.
Usage
TF_ackley(x, a = 20, b = 0.2, c = 2 * pi)
Arguments
x |
Input vector at which to evaluate. |
a |
A constant for ackley() |
b |
A constant for ackley() |
c |
A constant for ackley() |
Value
Function output evaluated at x.
Examples
TF_ackley(c(0, 0)) # minimum of zero, hard to solve
TF_bananagramacy2Dexp: bananagramacy2Dexp function for evaluating a single point.
Description
TF_bananagramacy2Dexp: bananagramacy2Dexp function for evaluating a single point.
Usage
TF_bananagramacy2Dexp(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
Examples
TF_bananagramacy2Dexp(rep(0,6))
TF_bananagramacy2Dexp(rep(1,6))
TF_bananatimesgramacy2Dexp: bananatimesgramacy2Dexp function for evaluating a single point.
Description
TF_bananatimesgramacy2Dexp: bananatimesgramacy2Dexp function for evaluating a single point.
Usage
TF_bananatimesgramacy2Dexp(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
Examples
TF_bananatimesgramacy2Dexp(rep(0,6))
TF_bananatimesgramacy2Dexp(rep(1,6))
TF_beale: Beale function for evaluating a single point.
Description
TF_beale: Beale function for evaluating a single point.
Usage
TF_beale(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
Examples
TF_beale(rep(0,2))
TF_beale(rep(1,2))
TF_beambending: beambending function for evaluating a single point.
Description
TF_beambending: beambending function for evaluating a single point.
Usage
TF_beambending(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
Examples
TF_beambending(rep(0,3))
TF_beambending(rep(1,3))
Base test function.
Description
TF_branin: A function taking in a single vector. 2 dimensional function. See corresponding function with "TF_" for more details.
Usage
TF_branin(
x,
a = 1,
b = 5.1/(4 * pi^2),
cc = 5/pi,
r = 6,
s = 10,
tt = 1/(8 * pi)
)
TF_borehole(x)
TF_franke(x)
TF_zhou1998(x)
TF_currin1991(x)
TF_currin1991b(x)
TF_limpoly(x)
TF_limnonpoly(x)
TF_banana(x)
TF_banana_grad(x, v1, v2)
TF_gaussian1(x, center = 0.5, s2 = 0.01)
TF_sinumoid(x)
TF_sqrtsin(x, freq = 2 * pi)
TF_powsin(x, freq = 2 * pi, pow = 0.7)
TF_OTL_Circuit(x)
TF_boreholeMV(x, NOD = 51)
Arguments
x |
Input vector at which to evaluate. |
a |
Parameter for TF_branin |
b |
Parameter for TF_branin |
cc |
Parameter for TF_branin |
r |
Parameter for TF_branin |
s |
Parameter for TF_branin |
tt |
Parameter for TF_branin |
v1 |
Scale parameter for first dimension |
v2 |
Scale parameter for second dimension |
center |
Where to center the function, a vector. |
s2 |
Variance of the Gaussian. |
freq |
Wave frequency for TF_sqrtsin and TF_powsin |
pow |
Power to raise wave to for TF_powsin. |
NOD |
number of output dimensions. |
Value
Function output evaluated at x.
References
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.
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.
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
TF_branin(runif(2))
TF_borehole(runif(8))
TF_franke(runif(2))
TF_zhou1998(runif(2))
TF_currin1991(runif(2))
TF_currin1991b(runif(2))
TF_limpoly(runif(2))
TF_limnonpoly(runif(2))
TF_banana(runif(2))
TF_banana_grad(runif(2), v1=40, v2=15)
TF_gaussian1(runif(2))
TF_sinumoid(runif(2))
TF_sqrtsin(runif(2))
TF_powsin(runif(2))
TF_OTL_Circuit(c(50,25,0.5,1.2,0.25,50))
TF_boreholeMV(runif(8))
TF_chengsandu: chengsandu function for evaluating a single point.
Description
TF_chengsandu: chengsandu function for evaluating a single point.
Usage
TF_chengsandu(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
References
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.
Examples
TF_chengsandu(rep(0,2))
TF_chengsandu(rep(1,2))
TF_detpep8d: detpep8d function for evaluating a single point.
Description
TF_detpep8d: detpep8d function for evaluating a single point.
Usage
TF_detpep8d(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
Examples
TF_detpep8d(rep(0,2))
TF_detpep8d(rep(1,2))
TF_easom: Easom function for evaluating a single point.
Description
TF_easom: Easom function for evaluating a single point.
Usage
TF_easom(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
Examples
TF_easom(rep(0,2))
TF_easom(rep(1,2))
TF_gramacy2Dexp: gramacy2Dexp function for evaluating a single point.
Description
TF_gramacy2Dexp: gramacy2Dexp function for evaluating a single point.
Usage
TF_gramacy2Dexp(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
References
Gramacy, Robert B., and Herbert KH Lee. "Adaptive design and analysis of supercomputer experiments." Technometrics 51.2 (2009): 130-145.
Examples
TF_gramacy2Dexp(rep(0,2))
TF_gramacy2Dexp(rep(1,2))
TF_gramacy2Dexp3hole: gramacy2Dexp3hole function for evaluating a single point.
Description
TF_gramacy2Dexp3hole: gramacy2Dexp3hole function for evaluating a single point.
Usage
TF_gramacy2Dexp3hole(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
References
Gramacy, Robert B., and Herbert KH Lee. "Adaptive design and analysis of supercomputer experiments." Technometrics 51.2 (2009): 130-145.
Examples
TF_gramacy2Dexp3hole(rep(0,2))
TF_gramacy2Dexp3hole(rep(1,2))
TF_gramacy6D: gramacy6D function for evaluating a single point.
Description
From Gramacy and Lee (2009).
Usage
TF_gramacy6D(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
References
Gramacy, Robert B., and Herbert KH Lee. "Adaptive design and analysis of supercomputer experiments." Technometrics 51.2 (2009): 130-145.
Examples
TF_gramacy6D(rep(0,6))
TF_gramacy6D(rep(1,6))
TF_griewank: Griewank function for evaluating a single point.
Description
TF_griewank: Griewank function for evaluating a single point.
Usage
TF_griewank(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
Examples
TF_griewank(rep(0,2))
TF_griewank(rep(1,2))
TF_hartmann: hartmann function for evaluating a single point.
Description
TF_hartmann: hartmann function for evaluating a single point.
Usage
TF_hartmann(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
Examples
TF_hartmann(rep(0,6))
TF_hartmann(rep(1,6))
TF_hartmann(c(.20169, .150011, .476874, .275332, .311652, .6573)) # Global minimum of -3.322368
TF_hump: Hump function for evaluating a single point.
Description
TF_hump: Hump function for evaluating a single point.
Usage
TF_hump(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
Examples
TF_hump(rep(0,2))
TF_hump(rep(1,2))
TF_levy: Levy function for evaluating a single point.
Description
TF_levy: Levy function for evaluating a single point.
Usage
TF_levy(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
Examples
TF_levy(rep(0,2))
TF_levy(rep(1,2))
TF_levytilt: Levy function with a tilt for evaluating a single point.
Description
TF_levytilt: Levy function with a tilt for evaluating a single point.
Usage
TF_levytilt(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
Examples
TF_levytilt(rep(0,2))
TF_levytilt(rep(1,2))
TF_linkletter_nosignal: Linkletter (2006) no signal function for evaluating a single point.
Description
TF_linkletter_nosignal: Linkletter (2006) no signal function for evaluating a single point.
Usage
TF_linkletter_nosignal(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
Examples
TF_linkletter_nosignal(rep(0,2))
TF_linkletter_nosignal(rep(1,2))
TF_logistic: logistic function for evaluating a single point.
Description
TF_logistic: logistic function for evaluating a single point.
Usage
TF_logistic(x, offset = 0, scl = 1)
Arguments
x |
Input vector at which to evaluate. |
offset |
Amount it should be offset |
scl |
Scale parameter |
Value
Function output evaluated at x.
Examples
TF_logistic(0)
TF_logistic(1)
TF_logistic15: logistic15 function for evaluating a single point. Same as logistic except adjusted to be reasonable from 0 to 1.
Description
TF_logistic15: logistic15 function for evaluating a single point. Same as logistic except adjusted to be reasonable from 0 to 1.
Usage
TF_logistic15(x, offset = 0.5, scl = 15)
Arguments
x |
Input vector at which to evaluate. |
offset |
Amount it should be offset |
scl |
Scale parameter |
Value
Function output evaluated at x.
Examples
TF_logistic15(0)
TF_logistic15(1)
curve(Vectorize(TF_logistic15)(x))
TF_logistic_plateau: logistic_plateau function for evaluating a single point.
Description
TF_logistic_plateau: logistic_plateau function for evaluating a single point.
Usage
TF_logistic_plateau(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
Examples
TF_logistic_plateau(0)
TF_logistic_plateau(.5)
TF_michalewicz: Michalewicz function for evaluating a single point.
Description
TF_michalewicz: Michalewicz function for evaluating a single point.
Usage
TF_michalewicz(x, m = 10)
Arguments
x |
Input vector at which to evaluate. |
m |
Parameter for the michalewicz function |
Value
Function output evaluated at x.
Examples
TF_michalewicz(rep(0,2))
TF_michalewicz(rep(1,2))
TF_moon_high: Moon (2010) high-dimensional function for evaluating a single point.
Description
TF_moon_high: Moon (2010) high-dimensional function for evaluating a single point.
Usage
TF_moon_high(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
Examples
TF_moon_high(rep(0,20))
TF_moon_high(rep(1,20))
TF_morris: morris function for evaluating a single point.
Description
TF_morris: morris function for evaluating a single point.
Usage
TF_morris(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
References
http://www.abe.ufl.edu/jjones/ABE_5646/2010/Morris.1991
Examples
TF_morris(rep(0,20))
TF_morris(rep(1,20))
TF_piston: Piston simulation function for evaluating a single point.
Description
TF_piston: Piston simulation function for evaluating a single point.
Usage
TF_piston(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
Examples
TF_piston(c(30,.005,.002,1e3,9e4,290,340)) # minimum of zero, hard to solve
TF_quad_peaks: quad_peaks function for evaluating a single point.
Description
TF_quad_peaks: quad_peaks function for evaluating a single point.
Usage
TF_quad_peaks(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
Examples
TF_quad_peaks(rep(0,2))
TF_quad_peaks(rep(1,2))
TF_quad_peaks_slant: quad_peaks_slant function for evaluating a single point.
Description
TF_quad_peaks_slant: quad_peaks_slant function for evaluating a single point.
Usage
TF_quad_peaks_slant(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
Examples
TF_quad_peaks_slant(rep(0,2))
TF_quad_peaks_slant(rep(1,2))
TF_rastrigin: Rastrigin function for evaluating a single point.
Description
TF_rastrigin: Rastrigin function for evaluating a single point.
Usage
TF_rastrigin(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
Examples
TF_rastrigin(rep(0,2))
TF_rastrigin(rep(1,2))
TF_robotarm: Robot arm function for evaluating a single point.
Description
TF_robotarm: Robot arm function for evaluating a single point.
Usage
TF_robotarm(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
Examples
TF_robotarm(rep(0,8))
TF_robotarm(rep(1,8))
TF_steelcolumnstress: steelcolumnstress function for evaluating a single point.
Description
TF_steelcolumnstress: steelcolumnstress function for evaluating a single point.
Usage
TF_steelcolumnstress(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
References
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).
Examples
TF_steelcolumnstress(rep(0,8))
TF_steelcolumnstress(rep(1,8))
TF_vertigrad: vertigrad function for evaluating a single point.
Description
TF_vertigrad: vertigrad function for evaluating a single point.
Usage
TF_vertigrad(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
Examples
TF_vertigrad(rep(0,2))
TF_vertigrad(rep(1,2))
TF_vertigrad_grad: vertigrad_grad function for evaluating a single point.
Description
TF_vertigrad_grad: vertigrad_grad function for evaluating a single point.
Usage
TF_vertigrad_grad(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
References
Forrester, A., & Keane, A. (2008). Engineering design via surrogate modelling: a practical guide. John Wiley & Sons.
Examples
TF_vertigrad_grad(rep(0,2))
TF_vertigrad_grad(rep(1,2))
TF_welch: Welch function for evaluating a single point.
Description
TF_welch: Welch function for evaluating a single point.
Usage
TF_welch(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
Examples
TF_welch(rep(0,20)) # minimum of zero, hard to solve
TF_wingweight: Wing weight function for evaluating a single point.
Description
TF_wingweight: Wing weight function for evaluating a single point.
Usage
TF_wingweight(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
References
Forrester, A., & Keane, A. (2008). Engineering design via surrogate modelling: a practical guide. John Wiley & Sons.
Examples
TF_wingweight(c(150,220,6,-10,16,.5,.08,2.5,1700,.025)) # minimum of zero, hard to solve
TF_winkel: winkel function for evaluating a single point.
Description
TF_winkel: winkel function for evaluating a single point.
Usage
TF_winkel(x)
Arguments
x |
Input vector at which to evaluate. |
Value
Function output evaluated at x.
References
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).
Examples
TF_winkel(rep(0,2))
TF_winkel(rep(1,2))
add_linear_terms: Add linear terms to another function. Allows you to easily change an existing function to include linear terms.
Description
add_linear_terms: Add linear terms to another function. Allows you to easily change an existing function to include linear terms.
Usage
add_linear_terms(func, coeffs)
Arguments
func |
Function to add linear terms to |
coeffs |
Linear coefficients, should have same length as function has dimensions |
Value
Function with added linear terms
Examples
banana(c(.1,.2))
add_linear_terms(banana, coeffs=c(10,1000))(c(.1,.2))
add_noise: Adds noise to any function
Description
add_noise: Adds noise to any function
Usage
add_noise(func, noise = 0, noise_type = "Gauss")
Arguments
func |
Function to add noise to. |
noise |
Standard deviation of Gaussian noise |
noise_type |
Type of noise, only option now is "Gauss" for Gaussian noise. |
Value
A function that has noise
Examples
tf <- add_noise(function(x)sin(2*x*pi));curve(tf)
tf <- add_noise(function(x)sin(2*x*pi), noise=.1);curve(tf)
add_null_dims: Add null dimensions to another function. Allows you to pass in input data with any number of dimensions and it will only keep the first nactive.
Description
add_null_dims: Add null dimensions to another function. Allows you to pass in input data with any number of dimensions and it will only keep the first nactive.
Usage
add_null_dims(func, nactive)
Arguments
func |
Function to add null dimensions to |
nactive |
Number of active dimensions in func |
Value
Function that can take any dimensional input
Examples
banana(c(.1,.2))
# banana(c(.1,.2,.4,.5,.6,.7,.8)) # gives warning
add_null_dims(banana, nact=2)(c(.1,.2,.4,.5,.6,.7,.8))
add_zoom: Zoom in on region of another function. Allows you to easily change an existing function so that [0,1]^n refers to a subregion of the original function
Description
add_zoom: Zoom in on region of another function. Allows you to easily change an existing function so that [0,1]^n refers to a subregion of the original function
Usage
add_zoom(func, scale_low, scale_high)
Arguments
func |
Function to add linear terms to |
scale_low |
Vector of low end of scale values for each dimension |
scale_high |
Vector of high end of scale values for each dimension |
Value
Function with added linear terms
Examples
banana(c(.5,.85))
add_zoom(banana, c(0,.5), c(1,1))(c(.5,.7))
add_zoom(banana, c(.2,.5), c(.8,1))(matrix(c(.5,.7),ncol=2))
ContourFunctions::cf(banana)
ContourFunctions::cf(add_zoom(banana, c(0,.5), c(1,1)))
ContourFunctions::cf(add_zoom(banana, c(.2,.5), c(.8,1)))
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)
Profile a function
Description
Gives details about how linear it is.
Usage
funcprofile(func, d, n = 1000 * d, bins = 30)
Arguments
func |
A function with a single output |
d |
The number of input dimensions for the function |
n |
The number of points to use for the linear model. |
bins |
Number of bins in histogram. |
Value
Nothing, prints and plots
Examples
funcprofile(ackley, 2)
Wave functions
Description
nsin: Block wave
Usage
nsin(xx)
vsin(xx)
Arguments
xx |
Input values |
Value
nsin evaluated at nsin
Examples
curve(nsin(2*pi*x), n = 1000)
curve(nsin(12*pi*x), n = 1000)
curve(vsin(2*pi*x), n = 1000)
curve(vsin(12*pi*x), n = 1000)
Create function calculating the numerical gradient
Description
Create function calculating the numerical gradient
Usage
numGrad(func, ...)
Arguments
func |
Function to get gradient of. |
... |
Arguments passed to numDeriv::grad(). |
Value
A gradient function
Examples
numGrad(sin)
Create function calculating the numerical hessian
Description
Create function calculating the numerical hessian
Usage
numHessian(func, ...)
Arguments
func |
Function to get hessian of |
... |
Arguments passed to numDeriv::hessian(). |
Value
A hessian function
Examples
numHessian(sin)
Create a standard test function.
Description
This makes it easier to create many functions that follow the same template. R CMD check doesn't like the ... if this command is used to create functions in the package, so it is not currently used.
Usage
standard_test_func(
func,
scale_it_ = F,
scale_low_ = NULL,
scale_high_ = NULL,
noise_ = 0,
...
)
Arguments
func |
A function that takes a vector representing a single point. |
scale_it_ |
Should the function scale the inputs from [0, 1]^D to [scale_low_, scale_high_] by default? This can be overridden when actually giving the output function points to evaluate. |
scale_low_ |
What is the default lower bound of the data? |
scale_high_ |
What is the default upper bound of the data? |
noise_ |
Should noise be added to the function by default? |
... |
Parameters passed to func when evaluating points. |
Value
A test function created using the standard_test_func template.
Examples
.gaussian1 <- function(x, center=.5, s2=.01) {
exp(-sum((x-center)^2/2/s2))
}
gaussian1 <- standard_test_func(.gaussian1, scale_it=FALSE, scale_low = c(0,0), scale_high = c(1,1))
curve(gaussian1(matrix(x,ncol=1)))
Subtract linear model from a function
Description
This returns a new function which a linear model has an r-squared of 0.
Usage
subtractlm(func, d, n = d * 100)
Arguments
func |
A function |
d |
Number of input dimensions |
n |
Number of points to use for the linear model |
Value
A new function
Examples
subtractlm(ackley, 2)
f <- function(x) {
if (is.matrix(x)) x[,1]^2
else x[1]^2
}
ContourFunctions::cf(f)
ContourFunctions::cf(subtractlm(f, 2), batchmax=Inf)
General function for evaluating a test function with multivariate output
Description
General function for evaluating a test function with multivariate output
Usage
test_func_applyMO(
func,
x,
numoutdim,
scale_it,
scale_low,
scale_high,
noise = 0,
...
)
Arguments
func |
A function to evaluate |
x |
Input value, either a matrix whose rows are points or a vector for a single point. Be careful with 1-D functions. |
numoutdim |
Number of output dimensions |
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 |
Value
Function values at x
Examples
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)