Analysis of $Mo_{1-x}Re_xS_2$ images¶

Extract statistically significant information about effective interactions between Mo and Re atoms

Table of Contents¶

1. Images
2. Target and random histograms
3. Create and populate lattice

Notebook setup

In [4]:

%matplotlib inline

import os
import sys
import copy
import pickle
from collections import Counter
from itertools import product, combinations
import numpy as np
import matplotlib.pyplot as plt
import h5py
from scipy.stats import norm, chi2
from scipy.optimize import fmin

from subprocess import Popen, PIPE
import multiprocessing as mp

In [5]:

%load_ext autoreload
%autoreload 2

In [6]:

sys.path.append('../src/utils')
from utils import *

In [22]:

path_raw = '../data/raw'
path_tmp = "../data/tmp"

1. Images¶

Extract Mo and Re positions for each image

In [8]:

# select relevant atomic coordinates for further analysis
# different files store different atoms in centroids_1 and centroids_2 -> sort this out
names = ['re05', 're55', 're78', 're95'] # hdf5 file name roots

# Separate atoms to Mo and Re based on image-specific intensity threshold
intensity_thresh = [0.80, 0.45, 0.45, 0.45]  # intensity thresholds for each image
atom_pos, atom_ids, intensities = get_atom_positions(path_raw, names, intensity_thresh)

show_images(names, atom_pos, atom_ids, intensities)

No description has been provided for this image

In [27]:

# Save atom positions for further spatial analys
for i in range(len(names)):
    np.save(os.path.join(path_tmp, names[i] + "_pos.npy"), atom_pos[i])
    np.save(os.path.join(path_tmp, names[i] + "_ids.npy"), atom_ids[i])

Identify distinct local configurations and collect target histograms¶

In [6]:

distance_thresh = [45, 32, 30, 26]  # distance thresholds for each image
target_hist, num_samples = collect_target_histograms(names, atom_pos, atom_ids, distance_thresh)

cfg_types = sorted(set([c for h in target_hist.values() for c in h]))

# symmetry number for each configuration
conf_counts, conf_dict, trans_hist = config_symmetry_numbers(cfg_types)

#trans_hist = make_transform_matrix(cfg_types, conf_dict)

# probability of each symmetrized configuration for a given Re concentration
x_re = rhenium_concentration(target_hist)

# random - null hypothesis
prob_conf = random_config_proba(names, conf_counts, x_re)

# applies uninformative multinomial (Jeffrey's) prior to deal with low-sampling-caused zero counts
target_hist_adjusted = apply_prior(names, conf_counts, cfg_types, target_hist, prob_conf)

# get estimated probability distribution of the target for model optimization
gsv = get_probability_histogram(names, cfg_types, target_hist_adjusted)
#gsv = get_probability_histogram(names, cfg_types, target_hist)

2. Target and random histograms¶

Comparison of target (adjusted) and random (null) histograms of local configurations

In [7]:

plot_histograms(names, num_samples, target_hist, target_hist_adjusted, prob_conf, cfg_types, x_re)

3. Create and populate lattice¶

Define a hexagonal lattice by mapping from square lattice

In [ ]: