Source code for example_simulator_functions.agawal09

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"""Agawal09 function.

[1]: Agarwal, N., & Aluru, N. R. (2009). A domain adaptive stochastic
collocation approach for analysis of MEMS under uncertainties. Journal
of Computational Physics, 228(20), 7662?7688.
http://doi.org/10.1016/j.jcp.2009.07.014
"""

import numpy as np




def agawal09a(x1, x2, a1=0.5, a2=0.5):
    r"""Compute the Agawal09a function.

    Two dimensional benchmark function for UQ approaches proposed in [1].

    The function is defined as follows:

    .. math::
       f({\bf x}) = \begin{cases}
            0  & \textrm{if } x_1 > \alpha_1 \textrm{ or } x_2 > \alpha_2 \\
            \sin(\pi x_1 )\sin(\pi x_2 ) &  \textrm{otherwise}
            \end{cases}



    Distribution of the input random variables is probably uniform on [0,1].

    Args:
        x1 (float): First input parameter
        x2 (float): Second input parameter
        a1 (float): Coefficient (optional), with default value 0.5
        a2 (float): Coefficient (optional), with default value 0.5

    Returns:
        float: Value of `agawal09a` function
    """
    if x1 > a1 or x2 > a2:
        y = 0
    else:
        y = np.sin(np.pi * x1) * np.sin(np.pi * x2)

    return y