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import numpy as np
from scipy.integrate import trapezoid
from ase.dft.dos import DOS
from ase.dft.kpoints import monkhorst_pack
__all__ = ['DOS', 'monkhorst_pack']
def get_distribution_moment(x, y, order=0):
"""Return the moment of nth order of distribution.
1st and 2nd order moments of a band correspond to the band's
center and width respectively.
For integration, the trapezoid rule is used.
"""
x = np.asarray(x)
y = np.asarray(y)
if order == 0:
return trapezoid(y, x)
elif isinstance(order, int):
return trapezoid(x**order * y, x) / trapezoid(y, x)
elif hasattr(order, '__iter__'):
return [get_distribution_moment(x, y, n) for n in order]
else:
raise ValueError(f'Illegal order: {order}')
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