def testIsotypePartition(tensor):
"""Test that the components of tensor add up to tensor,
that projecting them again the same way leaves them unchanged,
and that projecting them differently leaves them zero"""
#print("---")
total = np.zeros_like(tensor, dtype="float64")
for pp in partitions(tensor.ndim):
p = IntegerPartition(pp).partition
t=project(tensor, p)
#print (p)
#print(";")
#print(t)
#print(t-project(t,p))
#print(project(t,p))
assert np.allclose(t,project(t,p))
#print(tensor,total,t)
total += t
for qq in partitions(tensor.ndim):
q=IntegerPartition(qq).partition
if q!=p:
#print(p,q)
#print(project(t,q))
assert np.allclose(0,project(t,q))
#print(".")
#print(tensor)
#print(total)
assert np.allclose(tensor,total)
print("test ok")
def _get_all_partitions_tuples(n) -> List[IntTuple]:
partition = IntegerPartition([1] * n)
end_result = IntegerPartition([n])
result = [tuple(partition.partition)]
while partition != end_result:
partition = partition.next_lex()
result.append(tuple(partition.partition))
return result
def get_all_partitions(self) -> List[Partition]:
partition = IntegerPartition([1] * self.n)
end_result = IntegerPartition([self.n])
result = [Partition(partition.partition)]
while partition != end_result:
partition = partition.next_lex()
result.append(Partition(partition.partition))
return result
def test_integer_partition():
# no zeros in partition
raises(ValueError, lambda: IntegerPartition(list(range(3))))
# check fails since 1 + 2 != 100
raises(ValueError, lambda: IntegerPartition(100, list(range(1, 3))))
a = IntegerPartition(8, [1, 3, 4])
b = a.next_lex()
c = IntegerPartition([1, 3, 4])
d = IntegerPartition(8, {1: 3, 3: 1, 2: 1})
assert a == c
assert a.integer == d.integer
assert a.conjugate == [3, 2, 2, 1]
assert (a == b) is False
assert a <= b
assert (a > b) is False
assert a != b
for i in range(1, 11):
next = set()
prev = set()
a = IntegerPartition([i])
ans = set([IntegerPartition(p) for p in partitions(i)])
n = len(ans)
for j in range(n):
next.add(a)
a = a.next_lex()
IntegerPartition(i, a.partition) # check it by giving i
for j in range(n):
prev.add(a)
a = a.prev_lex()
IntegerPartition(i, a.partition) # check it by giving i
assert next == ans
assert prev == ans
assert IntegerPartition([1, 2, 3]).as_ferrers() == '###\n##\n#'
assert IntegerPartition([1, 1, 3]).as_ferrers('o') == 'ooo\no\no'
assert str(IntegerPartition([1, 1, 3])) == '[3, 1, 1]'
assert IntegerPartition([1, 1, 3]).partition == [3, 1, 1]
raises(ValueError, lambda: random_integer_partition(-1))
assert random_integer_partition(1) == [1]
assert random_integer_partition(10, seed=[1, 3, 2, 1, 5, 1]
) == [5, 2, 1, 1, 1]
def test_integer_partition():
# no zeros in partition
raises(ValueError, lambda: IntegerPartition(list(range(3))))
# check fails since 1 + 2 != 100
raises(ValueError, lambda: IntegerPartition(100, list(range(1, 3))))
a = IntegerPartition(8, [1, 3, 4])
b = a.next_lex()
c = IntegerPartition([1, 3, 4])
d = IntegerPartition(8, {1: 3, 3: 1, 2: 1})
assert a == c
assert a.integer == d.integer
assert a.conjugate == [3, 2, 2, 1]
assert (a == b) is False
assert a <= b
assert (a > b) is False
assert a != b
for i in range(1, 11):
next = set()
prev = set()
a = IntegerPartition([i])
ans = set([IntegerPartition(p) for p in partitions(i)])
n = len(ans)
for j in range(n):
next.add(a)
a = a.next_lex()
IntegerPartition(i, a.partition) # check it by giving i
for j in range(n):
prev.add(a)
a = a.prev_lex()
IntegerPartition(i, a.partition) # check it by giving i
assert next == ans
assert prev == ans
assert IntegerPartition([1, 2, 3]).as_ferrers() == '###\n##\n#'
assert IntegerPartition([1, 1, 3]).as_ferrers('o') == 'ooo\no\no'
assert str(IntegerPartition([1, 1, 3])) == '[3, 1, 1]'
assert IntegerPartition([1, 1, 3]).partition == [3, 1, 1]
raises(ValueError, lambda: random_integer_partition(-1))
assert random_integer_partition(1) == [1]
assert random_integer_partition(10, seed=[1, 3, 2, 1, 5,
1]) == [5, 2, 1, 1, 1]