# -*- coding: utf-8 -*-
import numpy
from itertools import product
from sagar.toolkit.mathtool import binomialCoeff
[文档]def remove_redundant(mol_positions, sites, perms, e_num=None, method='jshash'):
if method == 'jshash':
for i in remove_redundant_by_hash(mol_positions, sites, perms, e_num):
yield i
if method == 'ccsort':
pass
[文档]def remove_redundant_by_hash(mol_positions, sites, perms, e_num):
"""
输入一个分子坐标`mol_positions`
和每个坐标位点上的可能取代情况`sites`
母体结构所有的置换操作`perms`
options:
位点上元素的比例`e_num`
"""
# perms = self._get_perms_from_rots_and_trans(rots, trans)
# TODO: 加入一个机制，来清晰的设定位点上无序的状态
sites = numpy.array(sites)
arg_sites = [len(i) for i in sites]
# redundant configurations do not want see again
# 用于记录在操作作用后已经存在的构型排列，而无序每次都再次对每个结构作用所有操作
redundant = set()
# deg_total = 0
# loop over configurations
for atoms_mark in _atoms_gen(arg_sites, e_num):
arr_atoms_mark = numpy.array(atoms_mark)
ahash = _hash_atoms(atoms_mark)
if ahash in redundant:
continue
else:
list_all_transmuted = []
for p in perms:
atoms_transmuted = arr_atoms_mark[p]
redundant.add(_hash_atoms(atoms_transmuted))
# degeneracy
list_all_transmuted.append(atoms_transmuted)
arr_all_transmuted = numpy.array(list_all_transmuted)
deg = numpy.unique(arr_all_transmuted, axis=0).shape[0]
atoms = _mark_to_atoms(arr_atoms_mark, sites)
# 返回一个包含不重复位置和原子类别的tuple
# TODO: 合并成为一个独特的类？？
m = (mol_positions, atoms)
yield (m, deg)
def _mark_to_atoms(arr_mark, sites):
num_of_site_groups = len(sites)
arr_atoms = arr_mark.reshape(num_of_site_groups, -1)
# import pdb; pdb.set_trace()
atoms = numpy.zeros_like(arr_atoms)
for i, row in enumerate(arr_atoms):
for j, v in enumerate(row):
atoms[i][j] = sites[i][v]
return atoms.flatten().tolist()
def _atoms_gen(args, e_num=None):
"""
parameter:
args: list, represent number of atoms of each site.
e_num: None or tuple, concentration of element in disorderd sites,
default=None, for all configurations
给定每个位点原子无序的数目，产生所有可能的原子排列，共k^n种。
TODO: 在这里加入浓度比？
"""
if e_num is None:
p = []
for i in args:
p.append(range(i))
return product(*p)
else:
# import pdb; pdb.set_trace()
disorder_site = [s for s in args if s > 1]
num_disorder_site = len(disorder_site)
if num_disorder_site != sum(e_num):
raise ValueError("concentration given error, wanted sum {:d}, got {:d}".format(
num_disorder_site, sum(e_num)))
arr_arrange = _serial_int_to_arrangement(e_num)
# 若该位点只有一个元素，则在arr_arrange中加入指定列
for col, n in enumerate(args):
if n == 1:
arr_arrange = numpy.insert(arr_arrange, col, 0, axis=1)
return arr_arrange
def _hash_atoms(atoms):
"""
给出一个atoms排列，返回一个string代表该排列。可用于hash表。
"""
return ''.join(str(i) for i in atoms)
def _serial_int_to_arrangement(e_num):
"""
Algorithm From:
Hart, G. L. W., Nelson, L. J., & Forcade, R. W. (2012).
Generating derivative structures at a fixed concentration, 59, 101–107.
Corrections:
Some error in paper: fig. 5 --- loop over site: should be t = t - 1
"""
slots_total = _slots_total = sum(e_num)
comb = []
max = 1
for v in e_num:
bino = binomialCoeff(_slots_total, v)
comb.append(bino)
max *= bino
_slots_total -= v
max = int(max)
arr_arrangement = numpy.full((max, slots_total), -1)
for i in range(max):
open_slots = slots_total
for e in range(len(e_num)):
y, x = divmod(i, comb[e])
a = e_num[e]
n_color = a
m = open_slots
for idx, value in enumerate(arr_arrangement[i]):
if value != -1:
# 该slot已经放置原子
continue
else:
b = binomialCoeff(m - 1, a - 1)
if b <= x:
x -= b
else:
a -= 1
arr_arrangement[i][idx] = e
m -= 1
open_slots -= n_color
return arr_arrangement