All Available Functions

All Available Functions#

The table below lists all the test functions available in UQTestFuns from the uncertainty quantification (UQ) literature, regardless of their typical applications.

Name	Input Dimension	Constructor
Ackley	M	`Ackley()`
Alemazkoor & Meidani (2018) 2D	2	`Alemazkoor2D()`
Alemazkoor & Meidani (2018) 20D	20	`Alemazkoor20D()`
Borehole	8	`Borehole()`
Bratley et al. (1992) A	M	`Bratley1992a()`
Bratley et al. (1992) B	M	`Bratley1992b()`
Bratley et al. (1992) C	M	`Bratley1992c()`
Bratley et al. (1992) D	M	`Bratley1992d()`
Cantilever Beam (2D)	2	`CantileverBeam2D`
Cheng and Sandu (2010) 2D	2	`Cheng2D`
Circular Pipe Crack	2	`CircularPipeCrack()`
Coffee Cup Model	2	`CoffeeCup()`
Currin et al. (1988) Sine	1	`CurrinSine()`
Convex Failure Domain	2	`ConvexFailDomain()`
Damped Cosine	1	`DampedCosine()`
Damped Oscillator	7	`DampedOscillator()`
Damped Oscillator Reliability	8	`DampedOscillatorReliability()`
Dette & Pepelyshev (2010) 8D	3	`Dette8D()`
Dette & Pepelyshev (2010) Curved	3	`DetteCurved()`
Dette & Pepelyshev (2010) Exponential	3	`DetteExp()`
Flood	8	`Flood()`
Forrester et al. (2008)	1	`Forrester2008()`
Four-branch	2	`FourBranch()`
(1st) Franke	2	`Franke1()`
(2nd) Franke	2	`Franke2()`
(3rd) Franke	2	`Franke3()`
(4th) Franke	2	`Franke4()`
(5th) Franke	2	`Franke5()`
(6th) Franke	2	`Franke6()`
Friedman (6D)	6	`Friedman6D()`
Friedman (10D)	10	`Friedman10D()`
Gayton Hat	2	`GaytonHat()`
Genz (Continuous)	M	`GenzContinuous()`
Genz (Corner Peak)	M	`GenzCornerPeak()`
Genz (Discontinuous)	M	`GenzDiscontinuous()`
Genz (Gaussian)	M	`GenzGaussian()`
Genz (Oscillatory)	M	`GenzOscillatory()`
Genz (Product Peak)	M	`GenzProductPeak()`
Gramacy (2007) Sine	1	`GramacySine()`
Higdon (2002) Sine	1	`HigdonSine()`
Holsclaw et al. (2013) Sine	1	`HolsclawSine()`
Hyper-sphere Bound	2	`HyperSphere()`
Ishigami	3	`Ishigami()`
Lim et al. (2002) Non-Polynomial	2	`LimNonPoly()`
Lim et al. (2002) Polynomial	2	`LimPoly()`
Linkletter et al. (2006) Decreasing Coefficients	10	`LinkletterDecCoeffs()`
Linkletter et al. (2006) Inert	10	`LinkletterInert()`
Linkletter et al. (2006) Linear	10	`LinkletterLinear()`
Linkletter et al. (2006) Sine	10	`LinkletterSine()`
McLain S1	2	`McLainS1()`
McLain S2	2	`McLainS2()`
McLain S3	2	`McLainS3()`
McLain S4	2	`McLainS4()`
McLain S5	2	`McLainS5()`
Moon (2010) 3D	3	`Moon3D()`
Morris et al. (2006)	M	`Morris2006()`
Oakley & O’Hagan (2002) 1D	1	`Oakley1D()`
OTL Circuit	6 / 20	`OTLCircuit()`
Piston Simulation	7 / 20	`Piston()`
Simple Portfolio Model	3	`Portfolio3D()`
Robot Arm	8	`RobotArm()`
Rosenbrock	M	`Rosenbrock()`
RS - Circular Bar	2	`RSCircularBar()`
RS - Quadratic	2	`RSQuadratic()`
SaltelliLinear	M	`SaltelliLinear()`
Sobol’-G	M	`SobolG()`
Sobol’-G*	M	`SobolGStar()`
Sobol’-Levitan	M	`SobolLevitan()`
Solar Cell Model	5	`SolarCell()`
Speed Reducer Shaft	5	`SpeedReducerShaft()`
Sulfur	9	`Sulfur()`
Undamped Oscillator	6	`UndampedOscillator()`
Webster et al. (1996) 2D	2	`Webster2D()`
Welch et al. (1992)	20	`Welch1992()`
Wing Weight	10	`WingWeight()`

In a Python terminal, you can list all the available functions along with the corresponding constructor using list_functions() (shown below in the HTML format):

import uqtestfuns as uqtf

uqtf.list_functions(tablefmt="html")

No.	Constructor	# Input	# Output	Param.	Application	Description
1	Ackley()	M	1	True	optimization, metamodeling	Optimization test function from Ackley (1987)
2	Alemazkoor20D()	20	1	False	metamodeling	High-dimensional low-degree polynomial from Alemazkoor & Meidani (2018)
3	Alemazkoor2D()	2	1	False	metamodeling	Low-dimensional high-degree polynomial from Alemazkoor & Meidani (2018)
4	Borehole()	8	1	False	metamodeling, sensitivity	Borehole function from Harper and Gupta (1983)
5	Bratley1992a()	M	1	False	integration, sensitivity	Integration test function #1 from Bratley et al. (1992)
6	Bratley1992b()	M	1	False	integration, sensitivity	Integration test function #2 from Bratley et al. (1992)
7	Bratley1992c()	M	1	False	integration, sensitivity	Integration test function #3 from Bratley et al. (1992)
8	Bratley1992d()	M	1	False	integration, sensitivity	Integration test function #4 from Bratley et al. (1992)
9	CantileverBeam2D()	2	1	True	reliability	Cantilever beam reliability problem from Rajashekhar and Ellington (1993)
10	Cheng2D()	2	1	False	metamodeling	Two-dimensional test function from Cheng and Sandu (2010)
11	CircularPipeCrack()	2	1	True	reliability	Circular pipe under bending moment from Verma et al. (2015)
12	CoffeeCup()	2	150	True	metamodeling	Cooling coffee cup model from Tennøe et al. (2018)
13	ConvexFailDomain()	2	1	False	reliability	Convex failure domain problem from Borri and Speranzini (1997)
14	CurrinSine()	1	1	False	metamodeling	Sine function from Currin et al. (1988)
15	DampedCosine()	1	1	False	metamodeling	One-dimensional damped cosine from Santner et al. (2018)
16	DampedOscillator()	7	1	False	metamodeling, sensitivity	Damped oscillator model from Igusa and Der Kiureghian (1985)
17	DampedOscillatorReliability()	8	1	True	reliability	Performance function from Der Kiureghian and De Stefano (1990)
18	Dette8D()	8	1	False	metamodeling	8D function from Dette and Pepelyshev (2010)
19	DetteCurved()	3	1	False	metamodeling	Curved function from Dette and Pepelyshev (2010)
20	DetteExp()	3	1	False	metamodeling	Exponential function from Dette and Pepelyshev (2010)
21	Flood()	8	1	False	metamodeling, sensitivity	Flood model from Iooss and Lemaître (2015)
22	Forrester2008()	1	1	False	optimization, metamodeling	One-dimensional function from Forrester et al. (2008)
23	FourBranch()	2	1	True	reliability	Series system reliability from Katsuki and Frangopol (1994)
24	Franke1()	2	1	False	metamodeling	(1st) Franke function from Franke (1979)
25	Franke2()	2	1	False	metamodeling	(2nd) Franke function from Franke (1979)
26	Franke3()	2	1	False	metamodeling	(3rd) Franke function from Franke (1979)
27	Franke4()	2	1	False	metamodeling	(4th) Franke function from Franke (1979)
28	Franke5()	2	1	False	metamodeling	(5th) Franke function from Franke (1979)
29	Franke6()	2	1	False	metamodeling	(6th) Franke function from Franke (1979)
30	Friedman10D()	10	1	False	metamodeling	Ten-dimensional function from Friedman (1991)
31	Friedman6D()	6	1	False	metamodeling, sensitivity	Six-dimensional function from Friedman et al. (1983)
32	GaytonHat()	2	1	False	reliability	Two-Dimensional Gayton Hat function from Echard et al. (2013)
33	GenzContinuous()	M	1	True	integration	Continuous (but non- differentiable) integrand from Genz (1984)
34	GenzCornerPeak()	M	1	True	integration, metamodeling, sensitivity	Corner peak integrand from Genz (1984)
35	GenzDiscontinuous()	M	1	True	integration, sensitivity	Discontinuous integrand from Genz (1984)
36	GenzGaussian()	M	1	True	integration	Gaussian integrand from Genz (1984)
37	GenzOscillatory()	M	1	True	integration	Oscillatory integrand from Genz (1984)
38	GenzProductPeak()	M	1	True	integration	Product peak integrand from Genz (1984)
39	GramacySine()	1	1	False	metamodeling	One-dimensional sine function from Gramacy (2007)
40	HigdonSine()	1	1	False	metamodeling	Sine function from Higdon (2002)
41	HolsclawSine()	1	1	False	metamodeling	Sine function from Holsclaw et al. (2013)
42	HyperSphere()	2	1	False	reliability	Hyper-sphere bound reliability problem from Li et al. (2018)
43	Ishigami()	3	1	True	sensitivity	Ishigami function from Ishigami and Homma (1991)
44	LimNonPoly()	2	1	False	metamodeling	Two-dimensional non-polynomial function from Lim et al. (2002)
45	LimPoly()	2	1	False	metamodeling	Two-dimensional polynomial function from Lim et al. (2002)
46	LinkletterDecCoeffs()	10	1	False	metamodeling, sensitivity	Linear function with decreasing coefficients (8 active inputs) from Linkletter et al. (2006)
47	LinkletterInert()	10	1	False	sensitivity	Inert function with 10 inactive inputs from Linkletter et al. (2006)
48	LinkletterLinear()	10	1	False	metamodeling, sensitivity	Linear function with 4 active inputs from Linkletter et al. (2006)
49	LinkletterSine()	10	1	False	metamodeling, sensitivity	Sine function with 2 active inputs from Linkletter et al. (2006)
50	McLainS1()	2	1	False	metamodeling	McLain S1 function from McLain (1974)
51	McLainS2()	2	1	False	metamodeling	McLain S2 function from McLain (1974)
52	McLainS3()	2	1	False	metamodeling	McLain S3 function from McLain (1974)
53	McLainS4()	2	1	False	metamodeling	McLain S4 function from McLain (1974)
54	McLainS5()	2	1	False	metamodeling	McLain S5 function from McLain (1974)
55	Moon3D()	3	1	False	sensitivity	Three-dimensional function from Moon (2010)
56	Morris2006()	M	1	True	sensitivity	Test function from Morris et al. (2006)
57	OTLCircuit()	6	1	False	metamodeling, sensitivity	Output transformerless (OTL) circuit model from Ben-Ari and Steinberg (2007)
58	Oakley1D()	1	1	False	metamodeling	One-dimensional function from Oakley and O'Hagan (2002)
59	Piston()	7	1	False	metamodeling, sensitivity	Piston simulation model from Ben-Ari and Steinberg (2007)
60	Portfolio3D()	3	1	True	sensitivity	Simple portfolio model from Saltelli et al. (2004)
61	RSCircularBar()	2	1	True	reliability	RS problem as a circular bar from Verma et al. (2016)
62	RSQuadratic()	2	1	False	reliability	RS problem w/ one quadratic term from Waarts (2000)
63	RobotArm()	8	1	False	metamodeling	Four-segment robot arm function from An and Owen (2001)
64	Rosenbrock()	M	1	True	optimization, metamodeling	Optimization test function from Rosenbrock (1960), also known as the banana function
65	SaltelliLinear()	M	1	False	sensitivity	Linear function from Saltelli et al. (2000)
66	SobolG()	M	1	True	sensitivity, integration	Sobol'-G function from Saltelli and Sobol' (1995)
67	SobolGStar()	M	1	True	sensitivity	Sobol'-G* function from Saltelli et al. (2010)
68	SobolLevitan()	M	1	True	sensitivity	Test function from Sobol' and Levitan (1999)
69	SolarCell()	5	1	True	metamodeling, sensitivity	Single-diode solar-cell model from Constantine et al. (2015)
70	SpeedReducerShaft()	5	1	False	reliability	Reliability of a shaft in a speed reducer from Du and Sudjianto (2004)
71	Sulfur()	9	1	False	metamodeling, sensitivity	Sulfur model from Charlson et al. (1992)
72	UndampedOscillator()	6	1	False	reliability, metamodeling	Undamped, non-linear, single DOF oscillator
73	Webster2D()	2	1	False	metamodeling	2D polynomial function from Webster et al. (1996).
74	Welch1992()	20	1	False	metamodeling, sensitivity, integration	20-Dimensional function from Welch et al. (1992)
75	WingWeight()	10	1	False	metamodeling, sensitivity	Wing weight model from Forrester et al. (2008)