def sample(self, size=100, random_state=None):
""" Draw a permutation uniformly at random and record the descents i.e. indices where :math:`\\sigma(i+1) < \\sigma(i)` and something else...
:param size:
size of the permutation i.e. degree :math:`N` of :math:`\\mathfrak{S}_N`.
:type size:
int
.. seealso::
- :cite:`Kam18`, Sec ??
.. todo::
ask @kammmoun to complete the docsting and Section in see also
"""
rng = check_random_state(random_state)
self.size = size
sigma = uniform_permutation(self.size + 1, random_state=rng)
X = sigma[:-1] > sigma[1:] # Record the descents in permutation
Y = rng.binomial(n=2, p=self.x_0, size=self.size + 1) != 1
descent = [
i for i in range(self.size)
if (~Y[i] and Y[i + 1]) or (~Y[i] and ~Y[i + 1] and X[i])
]
self.list_of_samples.append(descent)
def sample(self):
""" Sample from the Poissonized Plancherel measure.
"""
N = np.random.poisson(self.theta)
sigma = uniform_permutation(N)
P, _ = RSK(sigma)
# young_diag = [len(row) for row in P]
young_diag = np.fromiter(map(len, P), dtype=int)
self.list_of_young_diag.append(young_diag)
# sampl = [len(row) - i + 0.5 for i, row in enumerate(P, start=1)]
sampl = young_diag - np.arange(0.5, young_diag.size)
self.list_of_samples.append(sampl.tolist())
def sample(self, size=100):
""" Draw a permutation :math:`\sigma \in \mathfrak{S}_N` uniformly at random and record the descents i.e. :math:`\{ i ~;~ \sigma_i > \sigma_{i+1} \}`.
:param size:
size of the permutation i.e. degree :math:`N` of :math:`\mathfrak{S}_N`.
:type size:
int
"""
self.size = size
sigma = uniform_permutation(self.size)
descent = 1 + np.where(sigma[:-1] > sigma[1:])[0]
self.list_of_samples.append(descent.tolist())
def sample(self, size=100, random_state=None):
""" Draw a permutation :math:`\\sigma \\in \\mathfrak{S}_N` uniformly at random and record the descents i.e. :math:`\\{ i ~;~ \\sigma_i > \\sigma_{i+1} \\}`.
:param size:
size of the permutation i.e. degree :math:`N` of :math:`\\mathfrak{S}_N`.
:type size:
int
"""
rng = check_random_state(random_state)
self.size = size
sigma = uniform_permutation(self.size, random_state=rng)
descent = 1 + np.where(sigma[:-1] > sigma[1:])[0]
self.list_of_samples.append(descent.tolist())
def sample(self, random_state=None):
""" Sample from the Poissonized Plancherel measure.
:param random_state:
:type random_state:
None, np.random, int, np.random.RandomState
"""
rng = check_random_state(random_state)
N = rng.poisson(self.theta)
sigma = uniform_permutation(N, random_state=rng)
P, _ = RSK(sigma)
# young_diag = [len(row) for row in P]
young_diag = np.fromiter(map(len, P), dtype=int)
self.list_of_young_diag.append(young_diag)
# sampl = [len(row) - i + 0.5 for i, row in enumerate(P, start=1)]
sampl = young_diag - np.arange(0.5, young_diag.size)
self.list_of_samples.append(sampl.tolist())
def test_uniform_permutation_sampler(self):
"""
"""
samples = [uniform_permutation(self.N) for _ in range(self.nb_samples)]
self.assertTrue(self.uniformity_adequation(samples))