Source code for

# -*- coding: utf-8 -*-

# (c) 2019, Microsoft Research
# Author: Dominik Gresch <>
Defines a function to align two bandstructures in such a way
that their difference is minimized.

from collections import namedtuple

import numpy as np
from scipy.optimize import minimize

from fsc.export import export

from .difference import calculate as calculate_diff

AlignResult = namedtuple(
    ['shift', 'eigenvals1_shifted', 'eigenvals2_shifted', 'difference']

[docs]@export def calculate(eigenvals1, eigenvals2, *, symmetric_shift=False, **kwargs): """ Shift the two sets of eigenvalues such that their difference is minimized. :param eigenvals1: The first set of eigenvalues. :type eigenvals1: EigenvalsData :param eigenvals2: The second set of eigenvalues. :type eigenvals2: EigenvalsData :param symmetric_shift: If `True`, the two sets of eigenvalues are shifted by equal and opposite values. Otherwise, only the second set of eigenvalues is shifted. :type symmetric_shift: bool :param kwargs: Keyword arguments passed on to :func:`.difference.calculate`. :type kwargs: dict """ def _do_shift(shift_delta): if symmetric_shift: return ( eigenvals1.shift(-shift_delta / 2), eigenvals2.shift(shift_delta / 2) ) return eigenvals1, eigenvals2.shift(shift_delta) def opt_func(delta): shift_delta, = delta ev1, ev2 = _do_shift(shift_delta=shift_delta) return calculate_diff(eigenvals1=ev1, eigenvals2=ev2, **kwargs) res = minimize(fun=opt_func, x0=np.array([0])) shift, = res.x ev1, ev2 = _do_shift(shift_delta=shift) difference = return AlignResult( shift=shift, eigenvals1_shifted=ev1, eigenvals2_shifted=ev2, difference=difference )