The Dynamic Mode Decomposition (DMD) is a versatile and increasingly popular method for data driven analysis of dynamical systems that arise in a variety of applications in, e.g., computational fluid dynamics, robotics or machine learning. In the framework of numerical linear algebra, it is a data driven Rayleigh-Ritz procedure applied to a DMD matrix that is derived from the supplied data. In some applications, the physics of the underlying problem implies hermiticity of the DMD matrix, so the general DMD procedure is not computationally optimal. Furthermore, it does not guarantee important structural properties of the Hermitian eigenvalue problem and may return non-physical solutions. This paper proposes a software solution to the Hermitian (including the real symmetric) DMD matrices, accompanied with a numerical analysis that contains several fine and instructive numerical details. The eigenpairs are computed together with their residuals, and perturbation theory provides error bounds for the eigenvalues and eigenvectors. The software is developed and tested using the LAPACK package.

动态模式分解 (DMD) 是一种通用且日益流行的动态系统数据驱动分析方法，出现在计算流体动力学、机器人或机器学习等各种应用中。在数值线性代数的框架中，它是一种数据驱动的 Rayleigh-Ritz 过程，应用于从所提供的数据导出的 DMD 矩阵。在某些应用中，潜在问题的物理性质意味着 DMD 矩阵的厄尔米特性，因此一般的 DMD 过程在计算上并不是最优的。此外，它不能保证埃尔米特特征值问题的重要结构特性，并且可能返回非物理解。本文提出了 Hermitian（包括实对称）DMD 矩阵的软件解决方案，并附带包含几个精细且有启发性的数值细节的数值分析。特征对及其残差一起计算，微扰理论提供特征值和特征向量的误差界限。该软件是使用以下软件开发和测试的拉帕克包裹。