Cluster analysis

This example demonstrates how to analyze a cluster space and to extract the number of orbits, clusters, and parameters as a function of the cutoff radii for each order. Such an analysis is particularly useful in preparation of a compressive sensing optimization run.


Number of orbits, clusters, and parameters as a function of cutoff radius for FCC Al.

Source code

The complete source code is available in

Basic example showing how to carry out an analysis of the ClusterSpace

Runs in approximately 4 minutes on an Intel Core i5-4670K CPU.
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from import bulk
from hiphive import ClusterSpace

tol = 1e-4

# setup
max_cutoffs = [10, 10, 7]
atoms = bulk('Al', 'fcc', a=4.05)
cs = ClusterSpace(atoms, max_cutoffs, acoustic_sum_rules=False)

# get data
df = pd.DataFrame(cs.orbit_data)

# collect number of orbits, clusters and parameters
parameter_data = {}
for order in cs.cutoffs.orders:
    parameter_data[order] = []
    cutoffs = sorted(set(df.loc[df.order == order, 'maximum_distance']))
    for cutoff in cutoffs:
        selection = 'maximum_distance < {} and order == {}'.format(
            cutoff+tol, order)
        sub_orbits = df.query(selection)
        num_orbits = len(sub_orbits)
        num_clusters = sub_orbits.n_clusters.sum()
        num_params = sub_orbits.n_parameters.sum()
            [cutoff, num_orbits, num_clusters, num_params])
    parameter_data[order] = np.array(parameter_data[order])

# plot
fs = 14
lw = 2
ms = 9
fig = plt.figure(figsize=(14, 4))
ax1 = fig.add_subplot(1, 3, 1)
ax2 = fig.add_subplot(1, 3, 2)
ax3 = fig.add_subplot(1, 3, 3)
for i, ax in enumerate([ax1, ax2, ax3], start=1):
    for order, data in parameter_data.items():
        ax.semilogy(data[:, 0], data[:, i], '-o', ms=ms, lw=lw, label=order)
    ax.legend(loc=2,  title='Order', fontsize=fs)
    ax.set_xlim([0.0, np.max(max_cutoffs)])
    ax.set_xlabel('Cutoff (A)', fontsize=fs)

ax1.set_ylabel('Number of orbits', fontsize=fs)
ax2.set_ylabel('Number of clusters', fontsize=fs)
ax3.set_ylabel('Number of parameters', fontsize=fs)