def fnc(ra, *args):
    """
    Function used in the minimisation problem.

    :param ra:
        Semi-axis of the ellipses used in the Yu et al.
    :returns:
        The absolute difference between the epicentral distance and the
        adjusted distance
    """
    #
    # epicentral distance
    repi = args[0]
    #
    # azimuth
    theta = args[1]
    #
    # magnitude
    mag = args[2]
    #
    # coefficients
    coeff = args[3]
    #
    # compute the difference between epicentral distances
    rb = rbf(ra, coeff, mag)
    t1 = ra**2 * (np.sin(np.radians(theta)))**2
    t2 = rb**2 * (np.cos(np.radians(theta)))**2
    xx = ra * rb / (t1+t2)**0.5
    return xx-repi
def fnc ( ra , * args ) : repi = args [ 0 ] theta = args [ 1 ] mag = args [ 2 ] coeff = args [ 3 ] rb = rbf ( ra , coeff , mag ) t1 = ra ** 2 * ( np . sin ( np . radians ( theta ) ) ) ** 2 t2 = rb ** 2 * ( np . cos ( np . radians ( theta ) ) ) ** 2 xx = ra * rb / ( t1 + t2 ) ** 0.5 return xx - repi
Function used in the minimisation problem.

    :param ra:
        Semi-axis of the ellipses used in the Yu et al.
    :returns:
        The absolute difference between the epicentral distance and the
        adjusted distance