def exercise_gruber_1973_example():
start = ucgmx((4, 136, 76, -155, -31, 44))
assert start.is_similar_to(
uctbx.unit_cell(
(2, 11.66, 8.718, 139 + 40 / 60., 152 + 45 / 60., 19 + 24 / 60.)))
buerger = ucgmx((4, 16, 16, -16, -1, -3))
assert buerger.is_similar_to(
uctbx.unit_cell((2, 4, 4, 120, 93.5833, 100.807)))
niggli = ucgmx((4, 16, 16, 16, 3, 4))
assert niggli.is_similar_to(
uctbx.unit_cell((2, 4, 4, 60, 79.1931, 75.5225)))
red = reduction_base.gruber_parameterization(start)
assert not red.is_buerger_cell()
assert approx_equal(red.as_gruber_matrix(), (4, 136, 76, -155, -31, 44))
assert approx_equal(red.as_niggli_matrix(),
(4, 136, 76, -155 / 2., -31 / 2., 44 / 2.))
assert approx_equal(red.as_sym_mat3(),
(4, 136, 76, 44 / 2., -31 / 2., -155 / 2.))
assert red.as_unit_cell().is_similar_to(start)
red = reduction_base.gruber_parameterization(buerger)
assert red.is_buerger_cell()
assert not red.is_niggli_cell()
red = reduction_base.gruber_parameterization(niggli)
assert red.is_niggli_cell()
red = reduce(start)
assert red.as_unit_cell().is_similar_to(niggli)
assert red.r_inv().elems == (-1, 5, 9, 0, -1, -1, 0, 0, 1)
assert red.n_iterations() == 29
red = reduce(buerger)
assert red.as_unit_cell().is_similar_to(niggli)
assert red.r_inv().elems == (-1, 0, 0, 0, 1, 1, 0, 1, 0)
assert red.n_iterations() == 4
red = reduce(niggli)
assert red.as_unit_cell().is_similar_to(niggli)
assert red.r_inv().elems == (1, 0, 0, 0, 1, 0, 0, 0, 1)
assert red.n_iterations() == 1
try:
red = krivy_gruber_1976.reduction(buerger, iteration_limit=1)
except krivy_gruber_1976.iteration_limit_exceeded:
pass
else:
raise Exception_expected
assert not start.is_buerger_cell()
assert not start.is_niggli_cell()
assert buerger.is_buerger_cell()
assert not buerger.is_niggli_cell()
assert niggli.is_buerger_cell()
assert niggli.is_niggli_cell()
red = start.niggli_reduction()
assert red.n_iterations() == 29
assert start.niggli_cell().is_similar_to(niggli)
def exercise_gruber_1973_example():
start = ucgmx((4,136,76,-155,-31,44))
assert start.is_similar_to(uctbx.unit_cell(
(2, 11.66, 8.718, 139+40/60., 152+45/60., 19+24/60.)))
buerger = ucgmx((4,16,16,-16,-1,-3))
assert buerger.is_similar_to(uctbx.unit_cell(
(2, 4, 4, 120, 93.5833, 100.807)))
niggli = ucgmx((4,16,16,16,3,4))
assert niggli.is_similar_to(uctbx.unit_cell(
(2, 4, 4, 60, 79.1931, 75.5225)))
red = reduction_base.gruber_parameterization(start)
assert not red.is_buerger_cell()
assert approx_equal(red.as_gruber_matrix(), (4,136,76,-155,-31,44))
assert approx_equal(red.as_niggli_matrix(), (4,136,76,-155/2.,-31/2.,44/2.))
assert approx_equal(red.as_sym_mat3(), (4,136,76,44/2.,-31/2.,-155/2.))
assert red.as_unit_cell().is_similar_to(start)
red = reduction_base.gruber_parameterization(buerger)
assert red.is_buerger_cell()
assert not red.is_niggli_cell()
red = reduction_base.gruber_parameterization(niggli)
assert red.is_niggli_cell()
red = reduce(start)
assert red.as_unit_cell().is_similar_to(niggli)
assert red.r_inv().elems == (-1, 5, 9, 0, -1, -1, 0, 0, 1)
assert red.n_iterations() == 29
red = reduce(buerger)
assert red.as_unit_cell().is_similar_to(niggli)
assert red.r_inv().elems == (-1, 0, 0, 0, 1, 1, 0, 1, 0)
assert red.n_iterations() == 4
red = reduce(niggli)
assert red.as_unit_cell().is_similar_to(niggli)
assert red.r_inv().elems == (1, 0, 0, 0, 1, 0, 0, 0, 1)
assert red.n_iterations() == 1
try:
red = krivy_gruber_1976.reduction(buerger, iteration_limit=1)
except krivy_gruber_1976.iteration_limit_exceeded:
pass
else:
raise Exception_expected
assert not start.is_buerger_cell()
assert not start.is_niggli_cell()
assert buerger.is_buerger_cell()
assert not buerger.is_niggli_cell()
assert niggli.is_buerger_cell()
assert niggli.is_niggli_cell()
red = start.niggli_reduction()
assert red.n_iterations() == 29
assert start.niggli_cell().is_similar_to(niggli)
def exercise_krivy_gruber_1976_example():
start = ucgmx((9, 27, 4, -5, -4, -22))
assert start.is_similar_to(
uctbx.unit_cell(
(3, 5.196, 2, 103 + 55 / 60., 109 + 28 / 60., 134 + 53 / 60.)))
for gmx in ((4, 9, 9, -8, -1, -4), (4, 9, 9, 9, 1, 4)):
red = reduction_base.gruber_parameterization(ucgmx(gmx))
assert red.is_buerger_cell()
assert not red.is_niggli_cell()
niggli = ucgmx((4, 9, 9, 9, 3, 4))
assert niggli.is_similar_to(
uctbx.unit_cell((2, 3, 3, 60, 75 + 31 / 60., 70 + 32 / 60.)))
red = reduction_base.gruber_parameterization(niggli)
assert red.is_niggli_cell()
red = reduce(start)
assert red.as_unit_cell().is_similar_to(niggli)
assert red.r_inv().elems == (0, 1, 2, 0, 0, 1, 1, 1, 2)
assert red.n_iterations() == 11
def exercise_krivy_gruber_1976_example():
start = ucgmx((9,27,4,-5,-4,-22))
assert start.is_similar_to(uctbx.unit_cell(
(3, 5.196, 2, 103+55/60., 109+28/60., 134+53/60.)))
for gmx in ((4,9,9,-8,-1,-4),
(4,9,9,9,1,4)):
red = reduction_base.gruber_parameterization(ucgmx(gmx))
assert red.is_buerger_cell()
assert not red.is_niggli_cell()
niggli = ucgmx((4,9,9,9,3,4))
assert niggli.is_similar_to(uctbx.unit_cell(
(2, 3, 3, 60, 75+31/60., 70+32/60.)))
red = reduction_base.gruber_parameterization(niggli)
assert red.is_niggli_cell()
red = reduce(start)
assert red.as_unit_cell().is_similar_to(niggli)
assert red.r_inv().elems == (0, 1, 2, 0, 0, 1, 1, 1, 2)
assert red.n_iterations() == 11
def is_niggli_cell(self, relative_epsilon=None): from cctbx.uctbx.reduction_base import gruber_parameterization return gruber_parameterization(self, relative_epsilon).is_niggli_cell()
def is_niggli_cell(self, relative_epsilon=None): from cctbx.uctbx.reduction_base import gruber_parameterization return gruber_parameterization(self, relative_epsilon).is_niggli_cell()
def exercise_gruber_types(n_trials_per_type, dump=0, verbose=0):
mk2_sets = gruber_1973_table_1.get_mk2_sets()
type_conditions = gruber_1973_table_1.get_type_conditions()
random_unimodular = random_unimodular_integer_matrix_generator()
have_errors = False
for k in range(1, 29):
set = mk2_sets[k]
tc = type_conditions[k]
if (0 or verbose):
print(" ", tc.ck_types, tc.defks)
n_errors = 0
for i_trial in range(n_trials_per_type):
gruber_matrix = random_gruber_matrix(tc)
type_cell = ucgmx(gruber_matrix)
if (0 or verbose):
print(" ", gruber_matrix)
print(" ", type_cell)
red = reduction_base.gruber_parameterization(type_cell)
assert red.is_niggli_cell()
n_different_cells = 0
for m in set:
other_cell = type_cell.change_basis(
m.inverse().transpose().elems, 1)
if (0 or verbose):
print(" ", m.elems, m.determinant())
print(" ", other_cell)
red = reduction_base.gruber_parameterization(other_cell)
if (not red.is_buerger_cell()):
print(" Error: Transformed cell is not a Buerger cell.")
print(" gruber_matrix:", gruber_matrix)
n_errors += 1
else:
n_different_cells += 1
if (red.is_niggli_cell()):
if (not other_cell.is_similar_to(type_cell)):
print(
" Error: Transformed cell is a Niggli cell.")
print(" gruber_matrix:", gruber_matrix)
n_errors += 1
else:
krivy_cell = reduce(type_cell).as_unit_cell()
assert krivy_cell.is_similar_to(type_cell)
krivy_cell = reduce(other_cell).as_unit_cell()
assert krivy_cell.is_similar_to(type_cell)
r_inv = random_unimodular.next().elems
random_cell = type_cell.change_basis(r_inv, 1)
if (0 or verbose):
print(" Random:", random_cell, r_inv)
red = reduce(random_cell)
krivy_cell = red.as_unit_cell()
if (dump):
print("type_cell:", type_cell)
print("random_cell:", random_cell)
print("krivy_cell:", krivy_cell)
print()
if (not krivy_cell.is_similar_to(type_cell)):
print(" Error: Random cell recovery.")
print(" gruber_matrix:", gruber_matrix)
print(" r_inv:", r_inv)
print(" red.as_gruber_matrix():",
red.as_gruber_matrix())
n_errors += 1
if (n_different_cells == 0):
print(
" Error: Transformation does not yield different cells.")
n_errors += 1
raise RuntimeError
if ((0 or verbose) and n_errors != 0):
print("Errors for type %d:" % k, n_errors)
if (n_errors != 0):
have_errors = True
assert not have_errors
def exercise_gruber_types(n_trials_per_type, dump=0, verbose=0):
mk2_sets = gruber_1973_table_1.get_mk2_sets()
type_conditions = gruber_1973_table_1.get_type_conditions()
random_unimodular = random_unimodular_integer_matrix_generator()
have_errors = False
for k in xrange(1,29):
set = mk2_sets[k]
tc = type_conditions[k]
if (0 or verbose):
print " ", tc.ck_types, tc.defks
n_errors = 0
for i_trial in xrange(n_trials_per_type):
gruber_matrix = random_gruber_matrix(tc)
type_cell = ucgmx(gruber_matrix)
if (0 or verbose):
print " ", gruber_matrix
print " ", type_cell
red = reduction_base.gruber_parameterization(type_cell)
assert red.is_niggli_cell()
n_different_cells = 0
for m in set:
other_cell = type_cell.change_basis(m.inverse().transpose().elems, 1)
if (0 or verbose):
print " ", m.elems, m.determinant()
print " ", other_cell
red = reduction_base.gruber_parameterization(other_cell)
if (not red.is_buerger_cell()):
print " Error: Transformed cell is not a Buerger cell."
print " gruber_matrix:", gruber_matrix
n_errors += 1
else:
n_different_cells += 1
if (red.is_niggli_cell()):
if (not other_cell.is_similar_to(type_cell)):
print " Error: Transformed cell is a Niggli cell."
print " gruber_matrix:", gruber_matrix
n_errors += 1
else:
krivy_cell = reduce(type_cell).as_unit_cell()
assert krivy_cell.is_similar_to(type_cell)
krivy_cell = reduce(other_cell).as_unit_cell()
assert krivy_cell.is_similar_to(type_cell)
r_inv = random_unimodular.next().elems
random_cell = type_cell.change_basis(r_inv, 1)
if (0 or verbose):
print " Random:", random_cell, r_inv
red = reduce(random_cell)
krivy_cell = red.as_unit_cell()
if (dump):
print "type_cell:", type_cell
print "random_cell:", random_cell
print "krivy_cell:", krivy_cell
print
if (not krivy_cell.is_similar_to(type_cell)):
print " Error: Random cell recovery."
print " gruber_matrix:", gruber_matrix
print " r_inv:", r_inv
print " red.as_gruber_matrix():", red.as_gruber_matrix()
n_errors += 1
if (n_different_cells == 0):
print " Error: Transformation does not yield different cells."
n_errors += 1
raise RuntimeError
if ((0 or verbose) and n_errors != 0):
print "Errors for type %d:" % k, n_errors
if (n_errors != 0):
have_errors = True
assert not have_errors
