We present two open-source implementations of the locally optimal block preconditioned conjugate gradient (lobpcg) algorithm to find a few eigenvalues and eigenvectors of large, possibly sparse matrices. We then test lobpcg for various quantum chemistry problems, encompassing medium to large, dense to sparse, well-behaved to ill-conditioned ones, where the standard method typically used is Davidson’s diagonalization. Numerical tests show that while Davidson’s method remains the best choice for most applications in quantum chemistry, LOBPCG represents a competitive alternative, especially when memory is an issue, and can even outperform Davidson for ill-conditioned, non-diagonally dominant problems.

我们提出了局部最优块预条件共轭梯度 ( lobpcg ) 算法的两种开源实现，以查找大型且可能稀疏矩阵的一些特征值和特征向量。然后，我们测试lobpcg的各种量子化学问题，包括中型到大型、密集到稀疏、良好行为到不良条件问题，其中通常使用的标准方法是戴维森对角化。数值测试表明，虽然戴维森方法仍然是量子化学中大多数应用的最佳选择，但 LOBPCG 代表了一种有竞争力的替代方案，特别是当内存成为问题时，甚至可以在病态、非对角占优问题上优于戴维森方法。