Comparing two functions on a discretized grid

The fingerprint introduced in doi:10.1038/s41597-022-01754-z can be used to compare two functions in a flexible and efficient way.

How to create a grid

The generation of grids is described in more detail here. As an example we create two discretized axis and combine them into a DiscretizedGrid object:

[1]:

from aim2dat.fct import DiscretizedAxis
from aim2dat.fct.fingerprint import FunctionDiscretizationFingerprint
import numpy as np
import matplotlib.pyplot as plt
import yaml

axis = DiscretizedAxis(axis_type="x", max=20, min=0, min_step=0.2, max_num_steps=1)
axis.discretization_method = "uniform"
axis.discretize_axis()

axis2 = DiscretizedAxis(axis_type="y", max=0.3, min=0, min_step=0.003, max_num_steps=1)
axis2.discretization_method = "uniform"
axis2.discretize_axis()

[1]:

DiscretizedAxis
        axis_type: y
        max: 0.3
        min: 0
        min_step: 0.003
        max_num_steps: 1
        precision: 6
        discretization_method: _uniform_discretization

<aim2dat.fct.discretization.DiscretizedAxis object at 0x7f78e689f130>

[2]:

grid = axis + axis2
grid

[2]:

<aim2dat.fct.discretization.DiscretizedGrid at 0x7f79284ba8c0>

[3]:

grid.create_grid()

(1, 101)
(101, 101)

[3]:

<aim2dat.fct.discretization.DiscretizedGrid at 0x7f79284ba8c0>

[4]:

grid.plot_grid()

[4]:
../_images/examples_fct-fingerprint_comparison_4_0.png

Apply the fringerprint

First, show the example data. This DOS plot will be transferred to a discrete representation.

[5]:

path = "files/function_analysis/"
with open(path + "example_energy_dos.yaml") as file:
    example_dos_energy, example_dos = np.array(yaml.safe_load(file))


plt.plot(example_dos_energy, example_dos)

[5]:

[<matplotlib.lines.Line2D at 0x7f78dd555990>]
../_images/examples_fct-fingerprint_comparison_6_1.png

Create an instance of the FunctionDiscretizationFingerprint class

The class expects the grid as an input.

[6]:

spectra_fp = FunctionDiscretizationFingerprint(grid=grid)

Calculate the fingerprint. The fingerprint will be stored in an internal dictionary in case a label is provided. The label is needed for the comparison of fingerprints.

[7]:

fp = spectra_fp.calculate_fingerprint(example_dos_energy, example_dos, label="test")
fp

[7]:

array([0., 0., 0., ..., 1., 1., 1.])

The fingerprint and grid can be visualized using the following method.

[8]:

spectra_fp.plot_fingerprint(example_dos_energy, example_dos)

[8]:
../_images/examples_fct-fingerprint_comparison_12_0.png

Shift the DOS as an example for a comparison.

[9]:

spectra_fp.plot_fingerprint(example_dos_energy, example_dos + 0.5)

[9]:
../_images/examples_fct-fingerprint_comparison_14_0.png 
[10]:

fp_shifted = spectra_fp.calculate_fingerprint(
    example_dos_energy, example_dos + 0.5, label="test_shifted"
)

Compare the two fingerprints. The return value measures the similarity. A value of 1 indicates the highest similarity, 0 the lowest.

[11]:

spectra_fp.compare_fingerprints("test", "test_shifted")

[11]:

0.254196