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# fmt: off
import numpy as np
from numpy.testing import assert_allclose
from ase.cell import Cell
from ase.lattice import all_variants
def test_standard_form():
TOL = 1E-10
for lat in all_variants():
cell0 = lat.tocell()
for sign in [-1, 1]:
cell = Cell(sign * cell0)
# lower triangular form
rcell, Q = cell.standard_form(form='lower')
assert_allclose(rcell @ Q, cell, atol=TOL)
assert_allclose(np.linalg.det(rcell), np.linalg.det(cell))
assert_allclose(rcell.ravel()[[1, 2, 5]], 0, atol=TOL)
# upper triangular form
rcell, Q = cell.standard_form(form='upper')
assert_allclose(rcell @ Q, cell, atol=TOL)
assert_allclose(np.linalg.det(rcell), np.linalg.det(cell))
assert_allclose(rcell.ravel()[[3, 6, 7]], 0, atol=TOL)
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