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
- 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