Fermi Contours#

PyPI Status Python Version License

Read the documentation at https://fermi-contours.readthedocs.io/ Tests Codecov

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Reference#

Code adapted from

Perez-Piskunow, Pablo M, Bovenzi, Nicandro, Akhmerov, Anton R, & Breitkreiz, Maxim. (2021). Code and data associated with the paper “Chiral Anomaly Trapped in Weyl Metals: Nonequilibrium Valley Polarization at Zero Magnetic Field” (1.0.1). Zenodo. https://doi.org/10.5281/zenodo.4704325

and extended to take into account periodic boundaries and other edge-cases.

Requirements#

  • Python >=3.9

Installation#

You can install Fermi Contours via pip from PyPI:

$ pip install fermi-contours

Usage#

Please see the Command-line Reference for details.

Contributing#

Contributions are very welcome. To learn more, see the Contributor Guide.

License#

Distributed under the terms of the MIT license, Fermi Contours is free and open source software.

Issues#

If you encounter any problems, please file an issue along with a detailed description.

Credits#

This project was generated from @cjolowicz’s Hypermodern Python Cookiecutter template.

Python API#

class fermi_contours.marching_squares.MarchingSquares(grid_values=None, func=None, bounds=None, res=None, open_contours=True, periodic=False)#

Bases: object

Marching square class.

Parameters:

  • grid_values (ndarray of floats with shape (n, m), optional) – Values of the function on a 2-dimensional coordinates grid.

  • func (callable) – Function that returns floats for each point in a 2-dimensional coordinates space. If grid_values is provided, func is used to resolve saddle points. If grid_values is not provided, then func, bounds and res must be provided. The grid_values is obtained using a 2-dimensional coordinates grid.

  • bounds (ndarray-like of shape (2, 2)) – Bounds in the x- and y-axis ((x_min, x_max), (y_min, y_max)), optional. If not provided, the bounds are assumed to be ((0, n), (0, m)).

  • res (int, optional) – Number of linear points to subdivide each of the axis intervals. If bounds is not provided, res is not used, and the shape of the grid_values is used instead.

  • open_contours (bool) – Wheather to allow open contours or raise an error when contours do not close on themselves.

  • periodic (bool, default to 'False') – If ‘True’, the 2-dimensional coordinates grid has periodic boundaries. Thus, the point (n, j) is equivalent to (0, j), and (i, m) equivalent to (i, 0). If bounds are provided, then x_max should be mapped to x_min, and y_max to y_min.

__call__(level=0)#

Calcualte the Fermi contours for a Fermi level.

Sets values for the attributes defined below.

Parameters:

level (float, default to '0') – Isolevel.

Returns:

contour_paths – Each list has numerical interpolated points along the path.

Return type:

list of lists of pairs of floats.

Tutorial#

Computing contours of a custom function#

The function defines a 3d surface, for which we will compute its contours.

We start by importing our library and some plotting functions.

[1]:

import numpy as np

from fermi_contours import marching_squares as ms

from matplotlib import pyplot as plt
from matplotlib import colors
from mpl_toolkits.axes_grid1 import make_axes_locatable

[2]:

def plot_contours(squares, levels, contours, cmap=None, background_cmap="Blues"):
    if cmap is None:
        cmap = plt.cm.Oranges

    fig = plt.figure(figsize=plt.figaspect(2))
    ax1 = fig.add_subplot(2, 1, 1)
    ax2 = fig.add_subplot(2, 1, 2, projection='3d', computed_zorder=False)

    # 2d axis

    n = len(levels)
    color_list = cmap(np.linspace(0, 1, n))
    norm = colors.Normalize(vmin=min(levels), vmax=max(levels))

    divider = make_axes_locatable(ax1)
    cax1 = divider.new_horizontal(size="5%", pad=0.2)
    fig.add_axes(cax1)
    fig.colorbar(plt.cm.ScalarMappable(norm=norm, cmap=cmap), cax=cax1)
    X, Y = np.meshgrid(*squares.grid_points)
    ax1.pcolormesh(X, Y, squares.grid_values.T, cmap=background_cmap);



    for i, contours_per_level in enumerate(contours):
        for contour in contours_per_level:

            ax1.plot(*np.array(contour).T, color=color_list[i])



    # 3d axis
    X, Y = np.meshgrid(*squares.grid_points)
    ax2.plot_surface(X, Y, squares.grid_values.T, alpha=1, cmap=background_cmap)
    ax2.view_init(azim=-80, elev=20)


    for i, (level, contours_per_level) in enumerate(zip(levels, contours)):
        for contour in contours_per_level:
            if len(contour) > 0:
                _x, _y = np.array(contour)[None, :].T
                _z = np.ones(len(_x))[:, None] * level
                ax2.plot(_x, _y, _z, color=color_list[i])

    return fig, ax1, ax2

The custom function can be anything that takes two floats and returns another float. If the function is expensive to compute in a serial way, consider computing the grid_values elsewhere, and provide the values instead of the function.

[3]:

def surface(x, y):
    return x ** 2 + y ** 2

To instantiate our MarchingSquares class, we need to provide the bounds of the grid. These bounds will be used to scale the position of the contours.

[4]:

squares = ms.MarchingSquares(
    func=surface,
    res=[20, 10],
    bounds=[[-2,2], [-1, 1]],
)

At this point, the squares instance has extracted the grid_points and their grid_values. If these are not provided, the grid_points are computed them using the res and bounds parameters, and the grid_values are the evaluations of func on those points.

[5]:

X, Y = np.meshgrid(*squares.grid_points)
plt.pcolormesh(X, Y, squares.grid_values.T, cmap="Blues");
_images/tutorial_10_0.png
Computing contours#

Now, we just call our instance with the values of the levels for which we want to compute the contour.

[6]:

levels = np.linspace(0, 1, 21)
levels

[6]:

array([0.  , 0.05, 0.1 , 0.15, 0.2 , 0.25, 0.3 , 0.35, 0.4 , 0.45, 0.5 ,
       0.55, 0.6 , 0.65, 0.7 , 0.75, 0.8 , 0.85, 0.9 , 0.95, 1.  ])

[7]:

contours = [squares(l) for l in levels]

To visualize the contours, we can plot the grid_values in blue, and the set of contours in orange.

[8]:

plot_contours(squares, levels=levels, contours=contours)

[8]:

(<Figure size 400x800 with 3 Axes>, <Axes: >, <Axes3D: >)
_images/tutorial_15_1.png

Special cases#

Open contours#

It may happen that our contour is not closed, or at least not within the bounds that we want. In this case, we can set the parameter open_contours=True to allow this behaviour. This can also lead to more than one contour per level

[9]:

levels_open = np.linspace(0, 5, 21)
levels_open

[9]:

array([0.  , 0.25, 0.5 , 0.75, 1.  , 1.25, 1.5 , 1.75, 2.  , 2.25, 2.5 ,
       2.75, 3.  , 3.25, 3.5 , 3.75, 4.  , 4.25, 4.5 , 4.75, 5.  ])

[10]:

contours_open = [squares(l) for l in levels_open]

To visualize the contours, we can plot the grid_values in blue, and the set of contours in orange.

[11]:

plot_contours(squares, levels=levels_open, contours=contours_open)

[11]:

(<Figure size 400x800 with 3 Axes>, <Axes: >, <Axes3D: >)
_images/tutorial_20_1.png
Periodic boundaries#

If we want that contours wrap around the edges of our grid, we can set the parameter periodic=True.

To make use of this functionality, let’s define a periodic function and plot the contours.

[12]:

def surface_periodic(x, y):
    period = np.pi
    return np.sin(period * x / 2) + np.sin(period * y )

[13]:

squares_periodic = ms.MarchingSquares(
    func=surface_periodic,
    res=[20, 10],
    bounds=[[-2,2], [-1, 1]],
    periodic=False,
)

[14]:

levels_periodic = np.linspace(-2, 2, 21)
levels_periodic

[14]:

array([-2. , -1.8, -1.6, -1.4, -1.2, -1. , -0.8, -0.6, -0.4, -0.2,  0. ,
        0.2,  0.4,  0.6,  0.8,  1. ,  1.2,  1.4,  1.6,  1.8,  2. ])

[15]:

contours_periodic = [squares_periodic(l) for l in levels_periodic]

[16]:

plot_contours(squares_periodic, levels=levels_periodic, contours=contours_periodic, cmap=plt.cm.PuOr)

[16]:

(<Figure size 400x800 with 3 Axes>, <Axes: >, <Axes3D: >)
_images/tutorial_26_1.png

Usage#

Command line interface#

fermi-contours#

Fermi Contours.

fermi-contours [OPTIONS]

Options

--version#

Show the version and exit.

Contributor Guide#

Thank you for your interest in improving this project. This project is open-source under the [MIT license] and welcomes contributions in the form of bug reports, feature requests, and pull requests.

Here is a list of important resources for contributors:

How to report a bug#

Report bugs on the Issue Tracker.

When filing an issue, make sure to answer these questions:

  • Which operating system and Python version are you using?

  • Which version of this project are you using?

  • What did you do?

  • What did you expect to see?

  • What did you see instead?

The best way to get your bug fixed is to provide a test case, and/or steps to reproduce the issue.

How to request a feature#

Request features on the Issue Tracker.

How to set up your development environment#

You need Python 3.7+ and the following tools:

Install the package with development requirements:

$ poetry install

You can now run an interactive Python session, or the command-line interface:

$ poetry run python
$ poetry run fermi-contours

How to test the project#

Run the full test suite:

$ nox

List the available Nox sessions:

$ nox --list-sessions

You can also run a specific Nox session. For example, invoke the unit test suite like this:

$ nox --session=tests

Unit tests are located in the tests directory, and are written using the pytest testing framework.

How to submit changes#

Open a pull request to submit changes to this project.

Your pull request needs to meet the following guidelines for acceptance:

  • The Nox test suite must pass without errors and warnings.

  • Include unit tests. This project maintains 100% code coverage.

  • If your changes add functionality, update the documentation accordingly.

Feel free to submit early, though—we can always iterate on this.

To run linting and code formatting checks before committing your change, you can install pre-commit as a Git hook by running the following command:

$ nox --session=pre-commit -- install

It is recommended to open an issue before starting work on anything. This will allow a chance to talk it over with the owners and validate your approach.

Contributor Covenant Code of Conduct#

Our Pledge#

We as members, contributors, and leaders pledge to make participation in our community a harassment-free experience for everyone, regardless of age, body size, visible or invisible disability, ethnicity, sex characteristics, gender identity and expression, level of experience, education, socio-economic status, nationality, personal appearance, race, caste, color, religion, or sexual identity and orientation.

We pledge to act and interact in ways that contribute to an open, welcoming, diverse, inclusive, and healthy community.

Our Standards#

Examples of behavior that contributes to a positive environment for our community include:

  • Demonstrating empathy and kindness toward other people

  • Being respectful of differing opinions, viewpoints, and experiences

  • Giving and gracefully accepting constructive feedback

  • Accepting responsibility and apologizing to those affected by our mistakes, and learning from the experience

  • Focusing on what is best not just for us as individuals, but for the overall community

Examples of unacceptable behavior include:

  • The use of sexualized language or imagery, and sexual attention or advances of any kind

  • Trolling, insulting or derogatory comments, and personal or political attacks

  • Public or private harassment

  • Publishing others’ private information, such as a physical or email address, without their explicit permission

  • Other conduct which could reasonably be considered inappropriate in a professional setting

Enforcement Responsibilities#

Community leaders are responsible for clarifying and enforcing our standards of acceptable behavior and will take appropriate and fair corrective action in response to any behavior that they deem inappropriate, threatening, offensive, or harmful.

Community leaders have the right and responsibility to remove, edit, or reject comments, commits, code, wiki edits, issues, and other contributions that are not aligned to this Code of Conduct, and will communicate reasons for moderation decisions when appropriate.

Scope#

This Code of Conduct applies within all community spaces, and also applies when an individual is officially representing the community in public spaces. Examples of representing our community include using an official e-mail address, posting via an official social media account, or acting as an appointed representative at an online or offline event.

Enforcement#

Instances of abusive, harassing, or otherwise unacceptable behavior may be reported to the community leaders responsible for enforcement at pablo@piskunow.com. All complaints will be reviewed and investigated promptly and fairly.

All community leaders are obligated to respect the privacy and security of the reporter of any incident.

Enforcement Guidelines#

Community leaders will follow these Community Impact Guidelines in determining the consequences for any action they deem in violation of this Code of Conduct:

1. Correction#

Community Impact: Use of inappropriate language or other behavior deemed unprofessional or unwelcome in the community.

Consequence: A private, written warning from community leaders, providing clarity around the nature of the violation and an explanation of why the behavior was inappropriate. A public apology may be requested.

2. Warning#

Community Impact: A violation through a single incident or series of actions.

Consequence: A warning with consequences for continued behavior. No interaction with the people involved, including unsolicited interaction with those enforcing the Code of Conduct, for a specified period of time. This includes avoiding interactions in community spaces as well as external channels like social media. Violating these terms may lead to a temporary or permanent ban.

3. Temporary Ban#

Community Impact: A serious violation of community standards, including sustained inappropriate behavior.

Consequence: A temporary ban from any sort of interaction or public communication with the community for a specified period of time. No public or private interaction with the people involved, including unsolicited interaction with those enforcing the Code of Conduct, is allowed during this period. Violating these terms may lead to a permanent ban.

4. Permanent Ban#

Community Impact: Demonstrating a pattern of violation of community standards, including sustained inappropriate behavior, harassment of an individual, or aggression toward or disparagement of classes of individuals.

Consequence: A permanent ban from any sort of public interaction within the community.

Attribution#

This Code of Conduct is adapted from the Contributor Covenant, version 2.1, available at https://www.contributor-covenant.org/version/2/1/code_of_conduct.html.

Community Impact Guidelines were inspired by Mozilla’s code of conduct enforcement ladder.

For answers to common questions about this code of conduct, see the FAQ at https://www.contributor-covenant.org/faq. Translations are available at https://www.contributor-covenant.org/translations.

License#

BSD-2-Clause License

Copyright (c) 2022, Pablo Perez Piskunow
All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this
   list of conditions and the following disclaimer.

2. Redistributions in binary form must reproduce the above copyright notice,
   this list of conditions and the following disclaimer in the documentation
   and/or other materials provided with the distribution.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.