def test_factoradics():
for i in range(100):
assert from_factoradic(to_factoradic(i)) == i
assert tuple(map(to_factoradic, range(10))) == (
(0,), (1, 0,), (1, 0, 0), (1, 1, 0), (2, 0, 0), (2, 1, 0),
(1, 0, 0, 0), (1, 0, 1, 0), (1, 1, 0, 0), (1, 1, 1, 0)
)
def index(self, perm):
'''Get the index number of permutation `perm` in this space.'''
if not isinstance(perm, collections.abc.Iterable):
raise ValueError
perm = sequence_tools.ensure_iterable_is_immutable_sequence(perm)
perm_set = set(perm) if not isinstance(perm, UnrecurrentedPerm) \
else set(perm._perm_sequence)
if not (perm_set <= set(self.sequence)):
raise ValueError
if sequence_tools.get_length(perm) != self.n_elements:
raise ValueError
if not isinstance(perm, self.perm_type):
perm = self.perm_type(perm, self)
if self.sequence != perm.nominal_perm_space.sequence:
# (This also covers `self.rapplied != perm.rapplied`)
raise ValueError
if self.domain != perm.domain:
# (This also covers `self.dapplied != perm.dapplied`)
raise ValueError
if self.is_degreed and (perm.degree not in self.degrees):
raise ValueError
# At this point we know the permutation contains the correct items, and
# has the correct degree.
if perm.is_dapplied:
return self.undapplied.index(perm.undapplied)
#######################################################################
elif self.is_degreed:
if perm.is_rapplied: return self.unrapplied.index(perm.unrapplied)
wip_perm_number = 0
wip_perm_sequence_dict = dict(self.fixed_map)
unused_values = list(self.free_values)
for i, value in enumerate(perm._perm_sequence):
if i in self.fixed_indices:
continue
unused_values.remove(value)
lower_values = [j for j in unused_values if j < value]
for lower_value in lower_values:
temp_fixed_map = dict(wip_perm_sequence_dict)
temp_fixed_map[i] = lower_value
wip_perm_number += PermSpace(
self.sequence_length,
degrees=self.degrees,
fixed_map=temp_fixed_map).length
wip_perm_sequence_dict[self.domain[i]] = value
perm_number = wip_perm_number
#######################################################################
elif self.is_recurrent:
assert not self.is_degreed and not self.is_dapplied
wip_perm_number = 0
unused_values = list(self.sequence)
reserved_values = list(self.fixed_map.values())
perm_sequence_list = list(perm._perm_sequence)
shit_set = set()
for i, value in enumerate(perm._perm_sequence):
if i in self.fixed_map:
if self.fixed_map[i] == value:
unused_values.remove(value)
reserved_values.remove(value)
continue
else:
raise ValueError
lower_values = [
thing
for thing in nifty_collections.OrderedSet(unused_values)
if (thing not in reserved_values or unused_values.count(
thing) > reserved_values.count(thing))
and unused_values.index(thing) < unused_values.index(value)
and thing not in shit_set
]
unused_values.remove(value)
for lower_value in lower_values:
temp_fixed_map = dict(
enumerate(perm_sequence_list[:i] + [lower_value]))
temp_fixed_map.update(self.fixed_map)
candidate_sub_perm_space = \
PermSpace._create_with_cut_prefix(
self.sequence,
n_elements=self.n_elements,
fixed_map=temp_fixed_map,
is_combination=self.is_combination,
shit_set=shit_set, perm_type=self.perm_type
)
wip_perm_number += candidate_sub_perm_space.length
if self.is_combination:
shit_set.add(lower_value)
perm_number = wip_perm_number
#######################################################################
elif self.is_fixed:
assert not self.is_degreed and not self.is_recurrent
free_values_perm_sequence = []
for i, perm_item in zip(self.domain, perm._perm_sequence):
if i in self.fixed_map:
if self.fixed_map[i] != perm_item:
raise ValueError
else:
free_values_perm_sequence.append(perm_item)
# At this point we know all the items that should be fixed are
# fixed.
perm_number = self._free_values_unsliced_perm_space.index(
free_values_perm_sequence)
#######################################################################
elif self.is_combination:
if perm.is_rapplied:
return self.unrapplied.index(perm.unrapplied)
assert not self.is_rapplied and not self.is_recurrent and \
not self.is_dapplied and not self.is_fixed and \
not self.is_degreed
if not cute_iter_tools.is_sorted(perm._perm_sequence):
raise ValueError
processed_perm_sequence = tuple(
self.sequence_length - 1 - item
for item in perm._perm_sequence[::-1])
perm_number = self.unsliced.length - 1 - sum(
(math_tools.binomial(item, i)
for i, item in enumerate(processed_perm_sequence, start=1)),
0)
#######################################################################
else:
factoradic_number = []
unused_values = list(self.sequence)
for i, value in enumerate(perm._perm_sequence):
index_of_current_number = unused_values.index(value)
factoradic_number.append(index_of_current_number)
unused_values.remove(value)
perm_number = math_tools.from_factoradic(
factoradic_number +
[0] * self.n_unused_elements) // math.factorial(
self.n_unused_elements)
#######################################################################
if perm_number not in self.canonical_slice:
raise ValueError
return perm_number - self.canonical_slice.start
def index(self, perm):
'''Get the index number of permutation `perm` in this space.'''
if not isinstance(perm, collections.Iterable):
raise ValueError
try:
perm = sequence_tools.ensure_iterable_is_immutable_sequence(
perm,
allow_unordered=False
)
except sequence_tools.UnorderedIterableException:
raise ValueError('An unordered iterable is never contained in a '
'`PermSpace`. Try an ordered one.')
perm_set = set(perm) if not isinstance(perm, UnrecurrentedPerm) \
else set(perm._perm_sequence)
if not (perm_set <= set(self.sequence)):
raise ValueError
if sequence_tools.get_length(perm) != self.n_elements:
raise ValueError
if not isinstance(perm, self.perm_type):
perm = self.perm_type(perm, self)
if self.sequence != perm.nominal_perm_space.sequence:
# (This also covers `self.rapplied != perm.rapplied`)
raise ValueError
if self.domain != perm.domain:
# (This also covers `self.dapplied != perm.dapplied`)
raise ValueError
if self.is_degreed and (perm.degree not in self.degrees):
raise ValueError
# At this point we know the permutation contains the correct items, and
# has the correct degree.
if perm.is_dapplied: return self.undapplied.index(perm.undapplied)
#######################################################################
elif self.is_degreed:
if perm.is_rapplied: return self.unrapplied.index(perm.unrapplied)
wip_perm_number = 0
wip_perm_sequence_dict = dict(self.fixed_map)
unused_values = list(self.free_values)
for i, value in enumerate(perm._perm_sequence):
if i in self.fixed_indices:
continue
unused_values.remove(value)
lower_values = [j for j in unused_values if j < value]
for lower_value in lower_values:
temp_fixed_map = dict(wip_perm_sequence_dict)
temp_fixed_map[i] = lower_value
wip_perm_number += PermSpace(
self.sequence_length, degrees=self.degrees,
fixed_map=temp_fixed_map
).length
wip_perm_sequence_dict[self.domain[i]] = value
perm_number = wip_perm_number
#######################################################################
elif self.is_recurrent:
assert not self.is_degreed and not self.is_dapplied
wip_perm_number = 0
unused_values = list(self.sequence)
reserved_values = list(self.fixed_map.values())
perm_sequence_list = list(perm._perm_sequence)
shit_set = set()
for i, value in enumerate(perm._perm_sequence):
if i in self.fixed_map:
if self.fixed_map[i] == value:
unused_values.remove(value)
reserved_values.remove(value)
continue
else:
raise ValueError
lower_values = [
thing for thing in
nifty_collections.OrderedSet(unused_values) if
(thing not in reserved_values or unused_values.count(thing)
> reserved_values.count(thing)) and
unused_values.index(thing) < unused_values.index(value) and
thing not in shit_set
]
unused_values.remove(value)
for lower_value in lower_values:
temp_fixed_map = dict(
enumerate(perm_sequence_list[:i] + [lower_value])
)
temp_fixed_map.update(self.fixed_map)
candidate_sub_perm_space = \
PermSpace._create_with_cut_prefix(
self.sequence,
n_elements=self.n_elements,
fixed_map=temp_fixed_map,
is_combination=self.is_combination,
shit_set=shit_set, perm_type=self.perm_type
)
wip_perm_number += candidate_sub_perm_space.length
if self.is_combination:
shit_set.add(lower_value)
perm_number = wip_perm_number
#######################################################################
elif self.is_fixed:
assert not self.is_degreed and not self.is_recurrent
free_values_perm_sequence = []
for i, perm_item in zip(self.domain, perm._perm_sequence):
if i in self.fixed_map:
if self.fixed_map[i] != perm_item:
raise ValueError
else:
free_values_perm_sequence.append(perm_item)
# At this point we know all the items that should be fixed are
# fixed.
perm_number = self._free_values_unsliced_perm_space.index(
free_values_perm_sequence
)
#######################################################################
elif self.is_combination:
if perm.is_rapplied:
return self.unrapplied.index(perm.unrapplied)
assert not self.is_rapplied and not self.is_recurrent and \
not self.is_dapplied and not self.is_fixed and \
not self.is_degreed
if not cute_iter_tools.is_sorted(perm._perm_sequence):
raise ValueError
processed_perm_sequence = tuple(
self.sequence_length - 1 -
item for item in perm._perm_sequence[::-1]
)
perm_number = self.unsliced.length - 1 - sum(
(math_tools.binomial(item, i) for i, item in
enumerate(processed_perm_sequence, start=1)),
0
)
#######################################################################
else:
factoradic_number = []
unused_values = list(self.sequence)
for i, value in enumerate(perm._perm_sequence):
index_of_current_number = unused_values.index(value)
factoradic_number.append(index_of_current_number)
unused_values.remove(value)
perm_number = math_tools.from_factoradic(
factoradic_number +
[0] * self.n_unused_elements
) // math.factorial(self.n_unused_elements)
#######################################################################
if perm_number not in self.canonical_slice:
raise ValueError
return perm_number - self.canonical_slice.start
