The Dynamic Mode Decomposition (DMD) is a method for computational analysis of nonlinear dynamical systems in data driven scenarios. Based on high fidelity numerical simulations or experimental data, the DMD can be used to reveal the latent structures in the dynamics or as a forecasting or a model order reduction tool. The theoretical underpinning of the DMD is the Koopman operator on a Hilbert space of observables of the dynamics under study. This paper describes a numerically robust and versatile variant of the DMD and its implementation using the state-of-the-art dense numerical linear algebra software package LAPACK. The features of the proposed software solution include residual bounds for the computed eigenpairs of the DMD matrix, eigenvectors refinements and computation of the eigenvectors of the Exact DMD, compressed DMD for efficient analysis of high dimensional problems that can be easily adapted for fast updates in a streaming DMD. Numerical analysis is the bedrock of numerical robustness and reliability of the software, that is tested following the highest standards and practices of LAPACK. Important numerical topics are discussed in detail and illustrated using numerous numerical examples.

动态模式分解 (DMD) 是一种在数据驱动场景中对非线性动力系统进行计算分析的方法。基于高保真度数值模​​拟或实验数据，DMD 可用于揭示动力学中的潜在结构或作为预测或模型降阶工具。DMD 的理论基础是所研究的动力学可观测量希尔伯特空间上的库普曼算子。本文描述了 DMD 的数值鲁棒性和通用性变体及其使用最先进的密集数值线性代数软件包的实现拉帕克。所提出的软件解决方案的功能包括计算 DMD 矩阵特征对的残差边界、特征向量细化和精确 DMD 特征向量的计算、压缩 DMD，用于有效分析高维问题，可以轻松适应快速更新流式 DMD。数值分析是软件数值稳健性和可靠性的基石，按照最高标准和实践进行测试拉帕克。详细讨论了重要的数字主题，并使用大量数字示例进行了说明。