DFT_M
本仓库包含 DFT_M 项目相关的代码文件。所有代码均使用 Python、MATLAB 等编程语言编写，旨在为相关领域的研究和应用提供工具和参考实现。
This repository contains code files related to the DFT_M project. All code is written in programming languages such as Python and MATLAB, aiming to provide tools and reference implementations for research and applications in related fields.
作者（Author）希望代码能够被免费、公开地使用、修改和分发。 如果您有任何问题、建议或改进意见，欢迎通过以下方式联系：
The author intends the code to be used, modified, and distributed freely and openly. If you have any questions, suggestions, or improvements, please feel free to contact via:
邮箱/Email: [email protected]
微信/WeChat: hn_87165
微信公众号/WeChat Official Account: DFT计算杂谈
重要提醒 / Important Notice
环境适配 / Environment Adaptation
下载后请仔细阅读代码：每个脚本和函数都包含了必要的注释和说明。在使用前，请务必理解代码的功能和逻辑。
Please read the code carefully after downloading: Each script and function contains necessary comments and instructions. Before using, please ensure you understand the functionality and logic of the code.
适配您的代码环境：本仓库中的代码可能在特定的软件版本、操作系统或硬件配置下开发和测试。在运行前，请确保您的环境满足以下要求，并根据需要进行调整：
Adapt to your code environment: The code in this repository may have been developed and tested under specific software versions, operating systems, or hardware configurations. Before running, please ensure your environment meets the following requirements and make adjustments as needed:
Python: 检查并安装所需的第三方库（如 NumPy、SciPy、Matplotlib 等）。建议使用虚拟环境。
Python: Check and install required third-party libraries (e.g., NumPy, SciPy, Matplotlib, etc.). Using a virtual environment is recommended.
MATLAB: 确保您拥有合适的许可证，并安装了必要的工具箱。
MATLAB: Ensure you have a valid license and have installed the necessary toolboxes.
其他依赖：部分代码可能依赖特定的外部工具或数据文件，请根据代码注释进行准备。
Other dependencies: Some code may rely on specific external tools or data files. Please prepare them according to the code comments.
执行前测试：建议先在小型或示例数据集上运行代码，验证其正确性和性能，再应用于您的实际数据或生产环境。
Test before execution: It is recommended to run the code on small or sample datasets first to verify its correctness and performance before applying it to your actual data or production environment.
安全性 / Security
作为用户，您有责任在使用前审查代码的安全性。请勿直接在不了解代码行为的环境中运行从互联网下载的脚本。
As a user, you are responsible for reviewing the security of the code before use. Do not directly run scripts downloaded from the internet in environments where you do not understand their behavior.
如果代码会处理您的敏感或私有数据，请确保在隔离和安全的环境中运行，并考虑进行数据脱敏。
If the code will process your sensitive or private data, please ensure it runs in an isolated and secure environment, and consider data anonymization.
**免责声明：**作者对代码的适用性、准确性或安全性不作任何明示或暗示的保证。使用本代码产生的任何风险由使用者自行承担。
Disclaimer: The author makes no warranties, express or implied, regarding the suitability, accuracy, or security of the code. Any risks arising from the use of this code are borne by the user.
问题与反馈 / Issues and Feedback
我们欢迎并感谢任何形式的反馈，包括但不限于：
We welcome and appreciate any form of feedback, including but not limited to:
错误报告：如果您在使用中发现任何错误或异常行为，请告知我们。
Bug reports: If you find any bugs or abnormal behavior while using the code, please let us know.
改进建议：如果您有改进代码性能、可读性、功能或文档的建议，我们非常乐意听取。
Improvement suggestions: If you have suggestions for improving code performance, readability, functionality, or documentation, we would be happy to hear them.
使用问题：如果您在配置环境或理解代码逻辑时遇到困难，可以联系我们寻求帮助（但请注意，我们可能无法提供实时或详细的个别支持）。
Usage questions: If you encounter difficulties in configuring the environment or understanding the code logic, you can contact us for help (but please note that we may not be able to provide real-time or detailed individual support).
许可证 / License
本项目采用 Apache License 2.0 开源许可证。详情请参阅项目根目录下的 LICENSE 文件。
This project is licensed under the Apache License 2.0. For details, please refer to the LICENSE file in the root directory of the project.
感谢您对 DFT_M 项目的关注与支持！
Thank you for your interest and support in the DFT_M project!