def test_backmap():
t = Tiling(
obstructions=(
GriddedPerm(Perm((0, )), ((0, 0), )),
GriddedPerm(Perm((0, 1)), ((0, 1), (0, 1))),
GriddedPerm(Perm((0, 1)), ((0, 2), (0, 2))),
GriddedPerm(Perm((0, 1)), ((0, 2), (1, 2))),
GriddedPerm(Perm((0, 1)), ((1, 0), (1, 2))),
GriddedPerm(Perm((0, 1)), ((1, 1), (1, 2))),
GriddedPerm(Perm((0, 1)), ((1, 2), (1, 2))),
GriddedPerm(Perm((1, 0)), ((0, 2), (1, 2))),
GriddedPerm(Perm((1, 0)), ((1, 1), (1, 1))),
GriddedPerm(Perm((1, 0)), ((1, 2), (1, 2))),
GriddedPerm(Perm((0, 2, 1)), ((0, 1), (0, 2), (0, 2))),
GriddedPerm(Perm((0, 2, 1)), ((1, 0), (1, 0), (1, 0))),
GriddedPerm(Perm((0, 2, 1)), ((1, 0), (1, 1), (1, 0))),
GriddedPerm(Perm((1, 2, 0)), ((0, 1), (0, 2), (1, 1))),
GriddedPerm(Perm((1, 2, 0)), ((0, 1), (1, 2), (1, 1))),
GriddedPerm(Perm((1, 2, 0)), ((1, 0), (1, 0), (1, 0))),
GriddedPerm(Perm((2, 0, 1)), ((0, 2), (0, 1), (0, 2))),
GriddedPerm(Perm((2, 0, 1)), ((1, 1), (1, 0), (1, 0))),
GriddedPerm(Perm((2, 0, 1)), ((1, 2), (1, 0), (1, 0))),
GriddedPerm(Perm((2, 1, 0)), ((0, 1), (1, 1), (1, 0))),
GriddedPerm(Perm((2, 1, 0)), ((0, 2), (1, 1), (1, 0))),
GriddedPerm(Perm((2, 1, 0)), ((1, 2), (1, 1), (1, 0))),
GriddedPerm(Perm((2, 3, 0, 1)), ((0, 1), (0, 2), (1, 0), (1, 0))),
),
requirements=((GriddedPerm(Perm((0, )), ((1, 2), )), ), ),
assumptions=(),
)
cellmap1 = {
(0, 1): (0, 1),
(1, 0): (2, 0),
(1, 1): (2, 1),
(1, 2): (1, 2),
}
cellmap2 = {
(0, 1): (0, 1),
(1, 2): (1, 3),
(2, 0): (2, 0),
(2, 1): (3, 2),
}
final_cell_map = {
(0, 1): (0, 1),
(1, 0): (2, 0),
(1, 1): (3, 2),
(1, 2): (1, 3),
}
rcs1 = _RowColSeparationSingleApplication(t)
t1 = rcs1.separated_tiling()
assert rcs1.get_cell_map() == cellmap1
rcs2 = _RowColSeparationSingleApplication(t1)
t2 = rcs2.separated_tiling()
assert rcs2.get_cell_map() == cellmap2
rcs = RowColSeparation(t)
assert rcs.separated_tiling() == t2
assert RowColSeparation(t).get_cell_map() == final_cell_map
def test_all_separation():
t = Tiling(obstructions=[
GriddedPerm(Perm((0, 1)), ((0, 0), ) * 2),
GriddedPerm(Perm((0, 1)), ((1, 0), ) * 2),
GriddedPerm(Perm((0, 1)), ((0, 0), (1, 0))),
GriddedPerm(Perm((1, 0)), ((0, 0), (1, 0))),
])
assert len(
list(
_RowColSeparationSingleApplication(t).all_separated_tiling())) == 2
assert (len(
list(
_RowColSeparationSingleApplication(t).all_separated_tiling(
only_max=False))) == 2)
def test_all_order():
t = Tiling(obstructions=[GriddedPerm(Perm((0, 1)), ((0, 0), (1, 0)))])
rcs = _RowColSeparationSingleApplication(t)
assert list(rcs._all_order(rcs.row_ineq_graph())) == [[{(1, 0)}, {(0, 0)}]]
assert list(rcs._all_order(rcs.col_ineq_graph())) == [[{(0, 0)}, {(1, 0)}]]
t = Tiling(obstructions=[
GriddedPerm(Perm((0, 1)), ((0, 0), (1, 0))),
GriddedPerm(Perm((1, 0)), ((0, 0), (1, 0))),
])
rcs = _RowColSeparationSingleApplication(t)
assert sorted(rcs._all_order(rcs.row_ineq_graph())) == [
[{(1, 0)}, {(0, 0)}],
[{(0, 0)}, {(1, 0)}],
]
assert list(rcs._all_order(rcs.col_ineq_graph())) == [[{(0, 0)}, {(1, 0)}]]
def test_complete_inequalities_matrices(separable_tiling2):
rcs = _RowColSeparationSingleApplication(separable_tiling2)
row_m, col_m = rcs._complete_ineq_matrices()
# Row basic matrix
ob_ineq = [
((1, 0), (0, 0)),
((2, 0), (0, 0)),
((3, 0), (0, 0)),
((1, 1), (0, 1)),
((2, 1), (0, 1)),
((2, 0), (1, 0)),
((2, 1), (1, 1)),
((3, 0), (2, 0)),
]
for c1, c2 in product(separable_tiling2.active_cells, repeat=2):
if c1[1] < c2[1] or (c1, c2) in ob_ineq:
print(1, c1, c2)
assert_matrix_entry_is(rcs, row_m, c1, c2, 1)
else:
print(0, c1, c2)
assert_matrix_entry_is(rcs, row_m, c1, c2, 0)
assert rcs._ineq_matrices == (row_m, col_m)
# Column basic matrix
ob_ineq = [((0, 1), (0, 0))]
for c1, c2 in product(separable_tiling2.active_cells, repeat=2):
if c1[0] < c2[0] or (c1, c2) in ob_ineq:
assert_matrix_entry_is(rcs, col_m, c1, c2, 1)
else:
assert_matrix_entry_is(rcs, col_m, c1, c2, 0)
def test_backmap3():
t = Tiling(
obstructions=(
GriddedPerm(Perm((0, 1)), ((0, 0), (0, 0))),
GriddedPerm(Perm((0, 1)), ((0, 0), (0, 1))),
GriddedPerm(Perm((0, 1)), ((0, 0), (0, 2))),
GriddedPerm(Perm((0, 1)), ((0, 0), (1, 1))),
GriddedPerm(Perm((0, 1)), ((0, 0), (2, 0))),
GriddedPerm(Perm((0, 1)), ((0, 0), (2, 2))),
GriddedPerm(Perm((0, 1)), ((0, 1), (0, 2))),
GriddedPerm(Perm((0, 1)), ((0, 1), (1, 1))),
GriddedPerm(Perm((0, 1)), ((0, 2), (0, 2))),
GriddedPerm(Perm((0, 1)), ((1, 1), (1, 1))),
GriddedPerm(Perm((0, 1)), ((1, 1), (2, 1))),
GriddedPerm(Perm((0, 1)), ((2, 0), (2, 0))),
GriddedPerm(Perm((1, 0)), ((0, 0), (2, 0))),
GriddedPerm(Perm((1, 0)), ((0, 1), (0, 0))),
GriddedPerm(Perm((1, 0)), ((0, 1), (2, 1))),
GriddedPerm(Perm((1, 0)), ((0, 2), (0, 0))),
GriddedPerm(Perm((1, 0)), ((0, 2), (0, 1))),
GriddedPerm(Perm((1, 0)), ((1, 1), (2, 1))),
GriddedPerm(Perm((1, 0)), ((2, 1), (2, 0))),
GriddedPerm(Perm((1, 0)), ((2, 1), (2, 1))),
GriddedPerm(Perm((1, 0)), ((2, 2), (2, 1))),
GriddedPerm(Perm((0, 1, 2)), ((0, 1), (0, 1), (2, 1))),
GriddedPerm(Perm((0, 1, 2)), ((0, 1), (2, 1), (2, 2))),
GriddedPerm(Perm((0, 2, 1)), ((0, 1), (0, 1), (0, 1))),
GriddedPerm(Perm((0, 2, 1)), ((0, 1), (2, 2), (2, 2))),
GriddedPerm(Perm((0, 2, 1)), ((2, 1), (2, 2), (2, 2))),
GriddedPerm(Perm((0, 2, 1)), ((2, 2), (2, 2), (2, 2))),
GriddedPerm(Perm((1, 0, 2)), ((2, 2), (2, 2), (2, 2))),
GriddedPerm(Perm((1, 2, 0)), ((0, 2), (2, 2), (2, 2))),
GriddedPerm(Perm((1, 2, 0)), ((2, 2), (2, 2), (2, 2))),
GriddedPerm(Perm((2, 0, 1)), ((0, 1), (0, 1), (0, 1))),
GriddedPerm(Perm((2, 0, 1)), ((2, 2), (2, 0), (2, 2))),
GriddedPerm(Perm((2, 0, 1)), ((2, 2), (2, 2), (2, 2))),
GriddedPerm(Perm((2, 1, 0)), ((0, 2), (2, 2), (2, 0))),
GriddedPerm(Perm((2, 1, 0)), ((0, 2), (2, 2), (2, 2))),
GriddedPerm(Perm((2, 1, 0)), ((2, 2), (2, 2), (2, 0))),
GriddedPerm(Perm((2, 1, 0)), ((2, 2), (2, 2), (2, 2))),
),
requirements=((GriddedPerm(Perm((0, )), ((2, 1), )), ), ),
)
cellmap1 = {
(0, 0): (2, 0),
(0, 1): (0, 2),
(0, 2): (1, 4),
(2, 0): (3, 1),
(2, 1): (3, 3),
(2, 2): (3, 4),
}
print(t)
rcs1 = _RowColSeparationSingleApplication(t)
t1 = rcs1.separated_tiling()
print(t1)
assert rcs1.get_cell_map() == cellmap1
rcs = RowColSeparation(t)
assert rcs.separated_tiling() == t1
assert rcs.get_cell_map() == cellmap1
def test_cell_order(separable_tiling1):
rcs = _RowColSeparationSingleApplication(separable_tiling1)
ob = GriddedPerm(Perm((0, 1)), ((0, 0), (0, 1)))
assert rcs._col_cell_order(ob) == ((0, 1), (0, 0))
ob = GriddedPerm(Perm((1, 0)), ((0, 1), (0, 0)))
assert rcs._col_cell_order(ob) == ((0, 0), (0, 1))
ob = GriddedPerm(Perm((0, 1)), ((0, 0), (1, 0)))
assert rcs._row_cell_order(ob) == ((1, 0), (0, 0))
ob = GriddedPerm(Perm((1, 0)), ((0, 0), (1, 0)))
assert rcs._row_cell_order(ob) == ((0, 0), (1, 0))
def test_map_gridded_perm(separable_tiling1):
rcs = _RowColSeparationSingleApplication(separable_tiling1)
ob = GriddedPerm(Perm((0, 1, 2)), ((0, 0), (1, 0), (1, 0)))
cell_map = {(0, 0): (0, 0), (1, 0): (1, 1)}
assert rcs._map_gridded_perm(cell_map,
ob) == GriddedPerm(Perm((0, 1, 2)),
((0, 0), (1, 1), (1, 1)))
ob = GriddedPerm(Perm((0, 1, 2)), ((0, 0), (1, 0), (1, 0)))
assert rcs._map_gridded_perm(cell_map,
ob) == GriddedPerm(Perm((0, 1, 2)),
((0, 0), (1, 1), (1, 1)))
def test_maximal_order():
t = Tiling(obstructions=[
GriddedPerm(Perm((0, 1)), ((0, 0), (1, 0))),
GriddedPerm(Perm((1, 0)), ((0, 0), (1, 0))),
])
rcs = _RowColSeparationSingleApplication(t)
possible_order = [
[{(1, 0)}, {(0, 0)}],
[{(0, 0)}, {(1, 0)}],
]
assert sorted(rcs._maximal_order(rcs.row_ineq_graph())) in possible_order
assert rcs.max_row_order in possible_order
assert list(rcs._maximal_order(rcs.col_ineq_graph())) == [{(0, 0)},
{(1, 0)}]
assert rcs.max_col_order == [{(0, 0)}, {(1, 0)}]
def test_basic_matrix(separable_tiling2):
rcs = _RowColSeparationSingleApplication(separable_tiling2)
# Row basic matrix
m = rcs._basic_matrix(True)
for c1, c2 in product(separable_tiling2.active_cells, repeat=2):
if c1[1] < c2[1]:
assert_matrix_entry_is(rcs, m, c1, c2, 1)
else:
assert_matrix_entry_is(rcs, m, c1, c2, 0)
# Column basic matrix
m = rcs._basic_matrix(False)
for c1, c2 in product(separable_tiling2.active_cells, repeat=2):
if c1[0] < c2[0]:
assert_matrix_entry_is(rcs, m, c1, c2, 1)
else:
assert_matrix_entry_is(rcs, m, c1, c2, 0)
def test_separates_tiling():
t = Tiling(
obstructions=[
GriddedPerm(Perm((0, 1)), ((0, 0), (1, 0))),
GriddedPerm(Perm((2, 0, 1)), ((0, 0), (1, 0), (1, 0))),
GriddedPerm(Perm((2, 0, 1)), ((0, 0), (0, 0), (0, 0))),
GriddedPerm(Perm((2, 0, 1)), ((1, 0), (1, 0), (1, 0))),
],
requirements=[[GriddedPerm(Perm((0, )), ((1, 0), ))]],
)
print(t)
rcs = _RowColSeparationSingleApplication(t)
row_order = [{(1, 0)}, {(0, 0)}]
col_order = [{(0, 0)}, {(1, 0)}]
sep_t = rcs._separates_tiling(row_order, col_order)
print(sep_t)
assert sep_t == Tiling(
obstructions=[
GriddedPerm(Perm((2, 0, 1)), ((0, 1), (1, 0), (1, 0))),
GriddedPerm(Perm((2, 0, 1)), ((0, 1), (0, 1), (0, 1))),
GriddedPerm(Perm((2, 0, 1)), ((1, 0), (1, 0), (1, 0))),
],
requirements=[[GriddedPerm(Perm((0, )), ((1, 0), ))]],
)
def test_col_ineq_graph(separable_tiling2):
rcs = _RowColSeparationSingleApplication(separable_tiling2)
assert rcs.col_ineq_graph()._matrix == rcs._complete_ineq_matrices()[1]
def test_cell_at_idx(separable_tiling2):
rcs = _RowColSeparationSingleApplication(separable_tiling2)
for i in range(len(separable_tiling2.active_cells)):
assert i == rcs.cell_idx(rcs.cell_at_idx(i))
def test_cell_idx(separable_tiling2):
rcs = _RowColSeparationSingleApplication(separable_tiling2)
for c in separable_tiling2.active_cells:
assert c == rcs.cell_at_idx(rcs.cell_idx(c))
def test_init(separable_tiling2):
rcs = _RowColSeparationSingleApplication(separable_tiling2)
assert rcs._tiling == separable_tiling2
assert len(rcs._active_cells) == 7
assert (3, 1) not in rcs._active_cells
