| Title: | Test Functions for Simulation Experiments and Evaluating Optimization and Emulation Algorithms |
|---|---|
| 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. |
| Authors: | Collin Erickson [aut, cre] |
| Maintainer: | Collin Erickson <[email protected]> |
| License: | GPL-3 |
| Version: | 0.2.2.9000 |
| Built: | 2025-02-12 03:25:45 UTC |
| Source: | https://github.com/collinerickson/testfunctions |
add_linear_terms: Add linear terms to another function. Allows you to easily change an existing function to include linear terms.
add_linear_terms(func, coeffs)add_linear_terms(func, coeffs)
func |
Function to add linear terms to |
coeffs |
Linear coefficients, should have same length as function has dimensions |
Function with added linear terms
banana(c(.1,.2)) add_linear_terms(banana, coeffs=c(10,1000))(c(.1,.2))banana(c(.1,.2)) add_linear_terms(banana, coeffs=c(10,1000))(c(.1,.2))
add_noise: Adds noise to any function
add_noise(func, noise = 0, noise_type = "Gauss")add_noise(func, noise = 0, noise_type = "Gauss")
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. |
A function that has noise
tf <- add_noise(function(x)sin(2*x*pi));curve(tf) tf <- add_noise(function(x)sin(2*x*pi), noise=.1);curve(tf)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.
add_null_dims(func, nactive)add_null_dims(func, nactive)
func |
Function to add null dimensions to |
nactive |
Number of active dimensions in func |
Function that can take any dimensional input
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))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
add_zoom(func, scale_low, scale_high)add_zoom(func, scale_low, scale_high)
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 |
Function with added linear terms
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)))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)))
branin: A function. 2 dimensional function.
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, ...)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, ...)
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 |
Function values at x
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.
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)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)
Gives details about how linear it is.
funcprofile(func, d, n = 1000 * d, bins = 30)funcprofile(func, d, n = 1000 * d, bins = 30)
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. |
Nothing, prints and plots
funcprofile(ackley, 2)funcprofile(ackley, 2)
nsin: Block wave
nsin(xx) vsin(xx)nsin(xx) vsin(xx)
xx |
Input values |
nsin evaluated at nsin
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)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
numGrad(func, ...)numGrad(func, ...)
func |
Function to get gradient of. |
... |
Arguments passed to numDeriv::grad(). |
A gradient function
numGrad(sin)numGrad(sin)
Create function calculating the numerical hessian
numHessian(func, ...)numHessian(func, ...)
func |
Function to get hessian of |
... |
Arguments passed to numDeriv::hessian(). |
A hessian function
numHessian(sin)numHessian(sin)
Evaluate an RFF (random wave function) at given input
RFF(x, freq, mag, dirr, offset, wave = sin, noise = 0)RFF(x, freq, mag, dirr, offset, wave = sin, noise = 0)
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 |
Output of RFF evaluated at x
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)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
RFF_get(D = 2, M = 30, wave = sin, noise = 0, seed = NULL)RFF_get(D = 2, M = 30, wave = sin, noise = 0, seed = NULL)
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 |
A random wave function
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))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))
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.
standard_test_func( func, scale_it_ = F, scale_low_ = NULL, scale_high_ = NULL, noise_ = 0, ... )standard_test_func( func, scale_it_ = F, scale_low_ = NULL, scale_high_ = NULL, noise_ = 0, ... )
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. |
A test function created using the standard_test_func template.
.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))).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)))
This returns a new function which a linear model has an r-squared of 0.
subtractlm(func, d, n = d * 100)subtractlm(func, d, n = d * 100)
func |
A function |
d |
Number of input dimensions |
n |
Number of points to use for the linear model |
A new function
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)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
test_func_applyMO( func, x, numoutdim, scale_it, scale_low, scale_high, noise = 0, ... )test_func_applyMO( func, x, numoutdim, scale_it, scale_low, scale_high, noise = 0, ... )
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 |
Function values at x
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)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)
TF_ackley: Ackley function for evaluating a single point.
TF_ackley(x, a = 20, b = 0.2, c = 2 * pi)TF_ackley(x, a = 20, b = 0.2, c = 2 * pi)
x |
Input vector at which to evaluate. |
a |
A constant for ackley() |
b |
A constant for ackley() |
c |
A constant for ackley() |
Function output evaluated at x.
TF_ackley(c(0, 0)) # minimum of zero, hard to solveTF_ackley(c(0, 0)) # minimum of zero, hard to solve
TF_bananagramacy2Dexp: bananagramacy2Dexp function for evaluating a single point.
TF_bananagramacy2Dexp(x)TF_bananagramacy2Dexp(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
TF_bananagramacy2Dexp(rep(0,6)) TF_bananagramacy2Dexp(rep(1,6))TF_bananagramacy2Dexp(rep(0,6)) TF_bananagramacy2Dexp(rep(1,6))
TF_bananatimesgramacy2Dexp: bananatimesgramacy2Dexp function for evaluating a single point.
TF_bananatimesgramacy2Dexp(x)TF_bananatimesgramacy2Dexp(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
TF_bananatimesgramacy2Dexp(rep(0,6)) TF_bananatimesgramacy2Dexp(rep(1,6))TF_bananatimesgramacy2Dexp(rep(0,6)) TF_bananatimesgramacy2Dexp(rep(1,6))
TF_beale: Beale function for evaluating a single point.
TF_beale(x)TF_beale(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
TF_beale(rep(0,2)) TF_beale(rep(1,2))TF_beale(rep(0,2)) TF_beale(rep(1,2))
TF_beambending: beambending function for evaluating a single point.
TF_beambending(x)TF_beambending(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
TF_beambending(rep(0,3)) TF_beambending(rep(1,3))TF_beambending(rep(0,3)) TF_beambending(rep(1,3))
TF_branin: A function taking in a single vector. 2 dimensional function. See corresponding function with "TF_" for more details.
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)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)
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. |
Function output evaluated at x.
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.
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_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.
TF_chengsandu(x)TF_chengsandu(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
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.
TF_chengsandu(rep(0,2)) TF_chengsandu(rep(1,2))TF_chengsandu(rep(0,2)) TF_chengsandu(rep(1,2))
TF_detpep8d: detpep8d function for evaluating a single point.
TF_detpep8d(x)TF_detpep8d(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
TF_detpep8d(rep(0,2)) TF_detpep8d(rep(1,2))TF_detpep8d(rep(0,2)) TF_detpep8d(rep(1,2))
TF_easom: Easom function for evaluating a single point.
TF_easom(x)TF_easom(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
TF_easom(rep(0,2)) TF_easom(rep(1,2))TF_easom(rep(0,2)) TF_easom(rep(1,2))
TF_Gfunction: G-function for evaluating a single point.
TF_Gfunction(x, a = (1:length(x) - 1)/2)TF_Gfunction(x, a = (1:length(x) - 1)/2)
x |
Input vector at which to evaluate. |
a |
Parameter for Gfunction |
Function output evaluated at x.
TF_Gfunction(rep(0,8)) TF_Gfunction(rep(1,8))TF_Gfunction(rep(0,8)) TF_Gfunction(rep(1,8))
TF_GoldsteinPrice: Goldstein Price function for evaluating a single point
TF_GoldsteinPrice(x)TF_GoldsteinPrice(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
TF_GoldsteinPrice(c(0, -1)) # minimumTF_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.
TF_GoldsteinPriceLog(x)TF_GoldsteinPriceLog(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
TF_GoldsteinPriceLog(c(0, -1)) # minimumTF_GoldsteinPriceLog(c(0, -1)) # minimum
TF_gramacy2Dexp: gramacy2Dexp function for evaluating a single point.
TF_gramacy2Dexp(x)TF_gramacy2Dexp(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
Gramacy, Robert B., and Herbert KH Lee. "Adaptive design and analysis of supercomputer experiments." Technometrics 51.2 (2009): 130-145.
TF_gramacy2Dexp(rep(0,2)) TF_gramacy2Dexp(rep(1,2))TF_gramacy2Dexp(rep(0,2)) TF_gramacy2Dexp(rep(1,2))
TF_gramacy2Dexp3hole: gramacy2Dexp3hole function for evaluating a single point.
TF_gramacy2Dexp3hole(x)TF_gramacy2Dexp3hole(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
Gramacy, Robert B., and Herbert KH Lee. "Adaptive design and analysis of supercomputer experiments." Technometrics 51.2 (2009): 130-145.
TF_gramacy2Dexp3hole(rep(0,2)) TF_gramacy2Dexp3hole(rep(1,2))TF_gramacy2Dexp3hole(rep(0,2)) TF_gramacy2Dexp3hole(rep(1,2))
From Gramacy and Lee (2009).
TF_gramacy6D(x)TF_gramacy6D(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
Gramacy, Robert B., and Herbert KH Lee. "Adaptive design and analysis of supercomputer experiments." Technometrics 51.2 (2009): 130-145.
TF_gramacy6D(rep(0,6)) TF_gramacy6D(rep(1,6))TF_gramacy6D(rep(0,6)) TF_gramacy6D(rep(1,6))
TF_griewank: Griewank function for evaluating a single point.
TF_griewank(x)TF_griewank(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
TF_griewank(rep(0,2)) TF_griewank(rep(1,2))TF_griewank(rep(0,2)) TF_griewank(rep(1,2))
TF_hartmann: hartmann function for evaluating a single point.
TF_hartmann(x)TF_hartmann(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
TF_hartmann(rep(0,6)) TF_hartmann(rep(1,6)) TF_hartmann(c(.20169, .150011, .476874, .275332, .311652, .6573)) # Global minimum of -3.322368TF_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.
TF_hump(x)TF_hump(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
TF_hump(rep(0,2)) TF_hump(rep(1,2))TF_hump(rep(0,2)) TF_hump(rep(1,2))
TF_levy: Levy function for evaluating a single point.
TF_levy(x)TF_levy(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
TF_levy(rep(0,2)) TF_levy(rep(1,2))TF_levy(rep(0,2)) TF_levy(rep(1,2))
TF_levytilt: Levy function with a tilt for evaluating a single point.
TF_levytilt(x)TF_levytilt(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
TF_levytilt(rep(0,2)) TF_levytilt(rep(1,2))TF_levytilt(rep(0,2)) TF_levytilt(rep(1,2))
TF_linkletter_nosignal: Linkletter (2006) no signal function for evaluating a single point.
TF_linkletter_nosignal(x)TF_linkletter_nosignal(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
TF_linkletter_nosignal(rep(0,2)) TF_linkletter_nosignal(rep(1,2))TF_linkletter_nosignal(rep(0,2)) TF_linkletter_nosignal(rep(1,2))
TF_logistic: logistic function for evaluating a single point.
TF_logistic(x, offset = 0, scl = 1)TF_logistic(x, offset = 0, scl = 1)
x |
Input vector at which to evaluate. |
offset |
Amount it should be offset |
scl |
Scale parameter |
Function output evaluated at x.
TF_logistic(0) TF_logistic(1)TF_logistic(0) TF_logistic(1)
TF_logistic_plateau: logistic_plateau function for evaluating a single point.
TF_logistic_plateau(x)TF_logistic_plateau(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
TF_logistic_plateau(0) TF_logistic_plateau(.5)TF_logistic_plateau(0) TF_logistic_plateau(.5)
TF_logistic15: logistic15 function for evaluating a single point. Same as logistic except adjusted to be reasonable from 0 to 1.
TF_logistic15(x, offset = 0.5, scl = 15)TF_logistic15(x, offset = 0.5, scl = 15)
x |
Input vector at which to evaluate. |
offset |
Amount it should be offset |
scl |
Scale parameter |
Function output evaluated at x.
TF_logistic15(0) TF_logistic15(1) curve(Vectorize(TF_logistic15)(x))TF_logistic15(0) TF_logistic15(1) curve(Vectorize(TF_logistic15)(x))
TF_michalewicz: Michalewicz function for evaluating a single point.
TF_michalewicz(x, m = 10)TF_michalewicz(x, m = 10)
x |
Input vector at which to evaluate. |
m |
Parameter for the michalewicz function |
Function output evaluated at x.
TF_michalewicz(rep(0,2)) TF_michalewicz(rep(1,2))TF_michalewicz(rep(0,2)) TF_michalewicz(rep(1,2))
TF_moon_high: Moon (2010) high-dimensional function for evaluating a single point.
TF_moon_high(x)TF_moon_high(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
TF_moon_high(rep(0,20)) TF_moon_high(rep(1,20))TF_moon_high(rep(0,20)) TF_moon_high(rep(1,20))
TF_morris: morris function for evaluating a single point.
TF_morris(x)TF_morris(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
http://www.abe.ufl.edu/jjones/ABE_5646/2010/Morris.1991
TF_morris(rep(0,20)) TF_morris(rep(1,20))TF_morris(rep(0,20)) TF_morris(rep(1,20))
TF_piston: Piston simulation function for evaluating a single point.
TF_piston(x)TF_piston(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
TF_piston(c(30,.005,.002,1e3,9e4,290,340)) # minimum of zero, hard to solveTF_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.
TF_quad_peaks(x)TF_quad_peaks(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
TF_quad_peaks(rep(0,2)) TF_quad_peaks(rep(1,2))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.
TF_quad_peaks_slant(x)TF_quad_peaks_slant(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
TF_quad_peaks_slant(rep(0,2)) TF_quad_peaks_slant(rep(1,2))TF_quad_peaks_slant(rep(0,2)) TF_quad_peaks_slant(rep(1,2))
TF_rastrigin: Rastrigin function for evaluating a single point.
TF_rastrigin(x)TF_rastrigin(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
TF_rastrigin(rep(0,2)) TF_rastrigin(rep(1,2))TF_rastrigin(rep(0,2)) TF_rastrigin(rep(1,2))
TF_robotarm: Robot arm function for evaluating a single point.
TF_robotarm(x)TF_robotarm(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
TF_robotarm(rep(0,8)) TF_robotarm(rep(1,8))TF_robotarm(rep(0,8)) TF_robotarm(rep(1,8))
TF_RoosArnold: Roos & Arnold (1963) function for evaluating a single point.
TF_RoosArnold(x)TF_RoosArnold(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
TF_RoosArnold(rep(0,8)) TF_RoosArnold(rep(1,8))TF_RoosArnold(rep(0,8)) TF_RoosArnold(rep(1,8))
TF_steelcolumnstress: steelcolumnstress function for evaluating a single point.
TF_steelcolumnstress(x)TF_steelcolumnstress(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
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).
TF_steelcolumnstress(rep(0,8)) TF_steelcolumnstress(rep(1,8))TF_steelcolumnstress(rep(0,8)) TF_steelcolumnstress(rep(1,8))
TF_SWNExpCos: SWNExpCos function for evaluating a single point.
TF_SWNExpCos(x)TF_SWNExpCos(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
Santner, T. J., Williams, B. J., & Notz, W. (2003). The Design and Analysis of Computer Experiments. Springer Science & Business Media.
TF_SWNExpCos(rep(0,2)) TF_SWNExpCos(rep(1,2))TF_SWNExpCos(rep(0,2)) TF_SWNExpCos(rep(1,2))
TF_vertigrad: vertigrad function for evaluating a single point.
TF_vertigrad(x)TF_vertigrad(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
TF_vertigrad(rep(0,2)) TF_vertigrad(rep(1,2))TF_vertigrad(rep(0,2)) TF_vertigrad(rep(1,2))
TF_vertigrad_grad: vertigrad_grad function for evaluating a single point.
TF_vertigrad_grad(x)TF_vertigrad_grad(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
Forrester, A., & Keane, A. (2008). Engineering design via surrogate modelling: a practical guide. John Wiley & Sons.
TF_vertigrad_grad(rep(0,2)) TF_vertigrad_grad(rep(1,2))TF_vertigrad_grad(rep(0,2)) TF_vertigrad_grad(rep(1,2))
TF_welch: Welch function for evaluating a single point.
TF_welch(x)TF_welch(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
TF_welch(rep(0,20)) # minimum of zero, hard to solveTF_welch(rep(0,20)) # minimum of zero, hard to solve
TF_wingweight: Wing weight function for evaluating a single point.
TF_wingweight(x)TF_wingweight(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
Forrester, A., & Keane, A. (2008). Engineering design via surrogate modelling: a practical guide. John Wiley & Sons.
TF_wingweight(c(150,220,6,-10,16,.5,.08,2.5,1700,.025)) # minimum of zero, hard to solveTF_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.
TF_winkel(x)TF_winkel(x)
x |
Input vector at which to evaluate. |
Function output evaluated at x.
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).
TF_winkel(rep(0,2)) TF_winkel(rep(1,2))TF_winkel(rep(0,2)) TF_winkel(rep(1,2))