Generalized regular k-point grid generation on the fly

In the DFT community, it is common practice to use regular k-point grids (Monkhorst-Pack, MP) for Brillioun zone integration. Recently Wisesa et al. (2016) and Morgan et al. (2018) demonstrated that generalized regular (GR) grids offer an advantage over traditional MP grids. The difference is simple but effective. At the same k-point density, GR grids have greater symmetry and 60% fewer irreducible k-points. GR grids have not been widely adopted because one must search through a large number of candidate grids; in many cases, a brute force search could take hours. This work describes an algorithm that can quickly search over GR grids for those that have the most uniform distribution of points and the best symmetry reduction. The grids are ∼60% more efficient, on average, than MP grids and can now be generated on the fly in seconds.