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"""Currin functions."""
import numpy as np
[docs]
def currin88_lofi(x1, x2):
r"""Low-fidelity version of the Currin88 benchmark function.
Simple two-dimensional example which appears several
times in the literature, see e.g. [1]-[3].
The low-fidelity version is defined as follows [3]:
:math:`f_{lofi}({\bf x}) = \frac{1}{4} \left[f_{hifi}(x_1+0.05,x_2+0.05) +
f_{hifi}(x_1+0.05,max(0,x_2-0.05)) \right] + \frac{1}{4} \left[f_{hifi}(x_1-0.05,x_2+0.05)
+ f_{hifi}(x_1-0.05,max(0,x_2-0.05)) \right]`
Args:
x1 (float): Input parameter 1 in [0,1]
x2 (float): Input parameter 2 in [0,1]
Returns:
float: Value of the *currin88* function
References:
[1] Currin, C., Mitchell, T., Morris, M., & Ylvisaker, D. (1988).
A Bayesian approach to the design and analysis of computer
experiments. Technical Report 6498. Oak Ridge National Laboratory.
[2] 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.
[3] Xiong, S., Qian, P. Z., & Wu, C. J. (2013). Sequential design and
analysis of high-accuracy and low-accuracy computer codes.
Technometrics, 55(1), 37-46.
"""
# maxarg = np.maximum(np.zeros((1,len(x2)),dtype = float), x2-1/20)
maxarg = np.maximum(np.zeros((1, 1), dtype=float), x2 - 1 / 20)
yh1 = currin88_hifi(x1 + 1 / 20, x2 + 1 / 20)
yh2 = currin88_hifi(x1 + 1 / 20, maxarg)
yh3 = currin88_hifi(x1 - 1 / 20, x2 + 1 / 20)
yh4 = currin88_hifi(x1 - 1 / 20, maxarg)
y = (yh1 + yh2 + yh3 + yh4) / 4
return y
[docs]
def currin88_hifi(x1, x2):
r"""High-fidelity version of the Currin88 benchmark function.
Simple two-dimensional example which appears several
times in the literature, see, e.g., [1]-[3].
The high-fidelity version is defined as follows:
:math:`f_{hifi}({\bf x}) = \left[1 - \exp(\frac{1}{2 x_2}) \right] \frac{2300x_1^3 +
1900 x_1^2 + 2092x_1 +60}{100x_1^3 + 500x_1^2 +4 x_1+20}`
[3] proposed the following low-fidelity version of the function:
:math:`f_{lofi}({\bf x}) = \frac{1}{4}[f_{hifi}(x_1+0.05,x_2+0.05) +
f_{hifi}(x_1+0.05,max(0,x_2-0.05))] + \frac{1}{4}[f_{hifi}(x_1-0.05,x_2+0.05)
+ f_{hifi}(x_1-0.05,max(0,x_2-0.05))]`
Args:
x1 (float): Input parameter 1 in [0,1]
x2 (float): Input parameter 2 in [0,1]
Returns:
float: Value of the *currin88* function
References:
[1] Currin, C., Mitchell, T., Morris, M., & Ylvisaker, D. (1988).
A Bayesian approach to the design and analysis of computer
experiments. Technical Report 6498. Oak Ridge National Laboratory.
[2] 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.
[3] Xiong, S., Qian, P. Z., & Wu, C. J. (2013). Sequential design and
analysis of high-accuracy and low-accuracy computer codes.
Technometrics, 55
"""
fact1 = 1 - np.exp(-1 / (2 * x2))
fact2 = 2300 * x1**3 + 1900 * x1**2 + 2092 * x1 + 60
fact3 = 100 * x1**3 + 500 * x1**2 + 4 * x1 + 20
y = fact1 * fact2 / fact3
return y
