Minimum supercell problem

For all the q-vectors that fits in a given supercell, phonon can be computed from that same cell. However, to maximize the computational efficiency, we need to compute the q-vectors at the smallest supercell possible where that q-vector fits in. This leads us the the minimum supercell problem. More generically, at arbitrary order, we need to find the supercell that fits in all the q-vectors of a given Q of that order.

A brute-force search might gives us the answer relatively easily at most of the times, a mathematical approach can maximize the efficiency of this search as well.

The details of the algorithms are described in the paper Phys. Rev. B 100, 014303 (2019).

Here we simply shows how to use it.

In the new version, this feature will simply be a function that returns the supa provided Q, all the mathematical operations will be performed using smith_normal_form module.

from mincell import minCell

m = minCell("1/2 0 0")
print m.mult
print m.supa

2
[[2 0 0]
 [0 1 0]
 [0 0 1]]

m = minCell("1/2 1/2 0")
print m.mult
print m.supa

2
[[1 1 0]
 [0 2 0]
 [0 0 1]]

m = minCell("1/2 1/2 1/2")
print m.mult
print m.supa

2
[[1 0 1]
 [0 1 1]
 [0 0 2]]

m = minCell("1/2 1/2 0; 0 1/2 1/2")
print m.mult
print m.supa

4
[[1 1 1]
 [0 2 0]
 [0 0 2]]