def random_uniform(self, n_samples=1, bound=0.5):
"""
Sample in the Hypersphere with the uniform distribution.
Parameters
----------
n_samples : int, optional
bound: float, optional
Returns
-------
point : array-like, shape=[n_samples, dimension + 1]
"""
size = (n_samples, self.dimension)
if bound is None:
spherical_coord = gs.random.rand(*size) * gs.pi
spherical_coord[:, -1] *= 2
point = gs.zeros((n_samples, self.dimension + 1))
for i in range(self.dimension):
point[:,
i] = (gs.prod(gs.sin(spherical_coord[:, :i]), axis=1) *
gs.cos(spherical_coord[:, i]))
point[:, -1] = gs.prod(gs.sin(spherical_coord), axis=1)
else:
assert bound <= 0.5
point = bound * (2 * gs.random.rand(*size) - 1)
point = self.intrinsic_to_extrinsic_coords(point)
return point
def random_uniform(self, n_samples=1, bound=0.5):
"""
Sample in the Hypersphere with the uniform distribution.
"""
size = (n_samples, self.dimension)
if bound is None:
spherical_coord = gs.random.rand(*size) * gs.pi
spherical_coord[:, -1] *= 2
point = gs.zeros((n_samples, self.dimension+1))
for i in range(self.dimension):
point[:, i] = gs.prod(gs.sin(spherical_coord[:, :i]), axis=1)\
* gs.cos(spherical_coord[:, i])
point[:, -1] = gs.prod(gs.sin(spherical_coord), axis=1)
else:
point = bound * (2*gs.random.rand(*size) - 1)
point = self.intrinsic_to_extrinsic_coords(point)
return point
def corr(self, x):
"""Compute the correlation matrix of the topology with edge weights ``weights``.
Parameters
----------
x : array-like
Takes a vector of length 'number of total splits' of the structure.
Returns
-------
corr : array-like, shape=[n, n]
Returns the corresponding correlation matrix.
"""
corr = gs.zeros((self.n_labels, self.n_labels))
for path_dict in self.paths:
for (u, v), path in path_dict.items():
corr[u][v] = gs.prod([1 - x[self.where[split]] for split in path])
corr[v][u] = corr[u][v]
corr = gs.array(corr)
return corr + gs.eye(corr.shape[0])
def test_prod(self):
vec = gs.random.rand(10)
result = gs.prod(vec)
expected = gs.cumprod(vec)[-1]
self.assertAllClose(result, expected)
def __init__(self, shape, **kwargs):
if "dim" not in kwargs.keys():
kwargs["dim"] = int(gs.prod(gs.array(shape)))
super(VectorSpace, self).__init__(shape=shape, **kwargs)
self.shape = shape
def __init__(self, shape, default_point_type='vector', **kwargs):
if 'dim' not in kwargs.keys():
kwargs['dim'] = int(gs.prod(gs.array(shape)))
super(VectorSpace,
self).__init__(default_point_type=default_point_type, **kwargs)
self.shape = shape
def __init__(self, shape, **kwargs):
kwargs.setdefault("dim", int(gs.prod(gs.array(shape))))
super(VectorSpace, self).__init__(shape=shape, **kwargs)
self.shape = shape
self._basis = None
