emukit.test_functions.sensitivity package

Submodules

class emukit.test_functions.sensitivity.ishigami.Ishigami(a, b)

Bases: object

Ishigami function was first introduced in ‘Ishigami and T. Homma, An importance quantification technique in uncertainty analysis for computer 556 models, in Uncertainty Modeling and Analysis, 1990. Proceedings., First International Symposium 557 on, IEEE, 1990, pp. 398–403’. This class contains: the elements of the Sobol decomposition of the Ishigami function, three low fidelity approximations, and the values of the main effects of the Sobol components:

\[f(x_1,x_2,x_3) = \sum f_i(x_i) + \sum f_{ij}(x_i,x_j) + f(x_1,x_2,x_3)\]
fidelity1(x)

Highest fidelity

\[\sin(x_1) + a \sin(x_2)^2 + b x_3 ^ 4 \sin(x_1)\]
Parameters

x (ndarray) – (n_points x 3) numpy array containing inputs to function

Return type

ndarray

fidelity2(x)

Low fidelity approximation

\[\sin(x_1) + a \sin(x_2) + b x_3 ^ 4 \sin(x_1)\]
Parameters

x (ndarray) – (n_points x 3) numpy array containing inputs to function

Return type

ndarray

fidelity3(x)

Low fidelity approximation

\[\sin(x_1) + 0.95 a \sin(x_2)^2 + b x_3 ^ 4 \sin(x_1)\]
Parameters

x (ndarray) – (n_points x 3) numpy array containing inputs to function

Return type

ndarray

fidelity4(x)

Low fidelity approximation

\[\sin(x_1) + 0.6 a \sin(x_2)^2 + 9 b x_3 ^ 4 \sin(x_1)\]
Parameters

x (ndarray) – (n_points x 3) numpy array containing inputs to function

Return type

ndarray

f0()

Constant effect of high fidelity function

Return type

float

f1(x1)

First order effect of x_1 on high fidelity function

Return type

ndarray

f2(x2)

First order effect of x_2 on high fidelity function

Return type

ndarray

f3(x3)

First order effect of x_3 on high fidelity function

Return type

ndarray

f12(x12)

Second order effect of x_1 and x_2 on high fidelity function

Return type

ndarray

f13(x13)

Second order effect of x_1 and x_3 on high fidelity function

Return type

ndarray

f23(x23)

Second order effect of x_2 and x_3 on high fidelity function

Return type

ndarray

f123(x123)

Third order effect of all inputs on high fidelity function

Return type

ndarray

Module contents