def random_normal(self, *size, mean=0, std=1):
"""
Create a point on the manifold, measure is induced by Normal distribution on the tangent space of zero.
Parameters
----------
size : shape
the desired shape
mean : float|tensor
mean value for the Normal distribution
std : float|tensor
std value for the Normal distribution
Returns
-------
ManifoldTensor
random point on the PoincareBall manifold
Notes
-----
The device and dtype will match the device and dtype of the Manifold
"""
self._assert_check_shape(size2shape(*size), "x")
tens = torch.randn(*size, device=self.c.device, dtype=self.c.dtype) * std + mean
return ManifoldTensor(self.expmap0(tens), manifold=self)
def random_normal(self, *size, mean=0.0, std=1.0, device=None, dtype=None):
"""
Create a point on the manifold, measure is induced by Normal distribution.
Parameters
----------
size : shape
the desired shape
mean : float|tensor
mean value for the Normal distribution
std : float|tensor
std value for the Normal distribution
device : torch.device
the desired device
dtype : torch.dtype
the desired dtype
Returns
-------
ManifoldTensor
random point on the manifold
"""
self._assert_check_shape(size2shape(*size), "x")
mean = torch.as_tensor(mean, device=device, dtype=dtype)
std = torch.as_tensor(std, device=device, dtype=dtype)
tens = std.new_empty(*size).normal_() * std + mean
return tensor.ManifoldTensor(tens, manifold=self)
def random_normal(self,
*size,
mean=0,
std=1,
dtype=None,
device=None) -> "geoopt.ManifoldTensor":
"""
Create a point on the manifold, measure is induced by Normal distribution on the tangent space of zero.
Parameters
----------
size : shape
the desired shape
mean : float|tensor
mean value for the Normal distribution
std : float|tensor
std value for the Normal distribution
dtype: torch.dtype
target dtype for sample, if not None, should match Manifold dtype
device: torch.device
target device for sample, if not None, should match Manifold device
Returns
-------
ManifoldTensor
random point on the PoincareBall manifold
Notes
-----
The device and dtype will match the device and dtype of the Manifold
"""
size = size2shape(*size)
self._assert_check_shape(size, "x")
if device is not None and device != self.c.device:
raise ValueError(
"`device` does not match the manifold `device`, set the `device` argument to None"
)
if dtype is not None and dtype != self.c.dtype:
raise ValueError(
"`dtype` does not match the manifold `dtype`, set the `dtype` argument to None"
)
tens = (torch.randn(size, device=self.c.device, dtype=self.c.dtype) *
std / size[-1]**0.5 + mean)
return geoopt.ManifoldTensor(self.expmap0(tens), manifold=self)
def random_uniform(self, *size, dtype=None, device=None):
"""
Uniform random measure on Sphere manifold.
Parameters
----------
size : shape
the desired output shape
dtype : torch.dtype
desired dtype
device : torch.device
desired device
Returns
-------
ManifoldTensor
random point on Sphere manifold
Notes
-----
In case of projector on the manifold, dtype and device are set automatically and shouldn't be provided.
If you provide them, they are checked to match the projector device and dtype
"""
self._assert_check_shape(size2shape(*size), "x")
if self.projector is None:
tens = torch.randn(*size, device=device, dtype=dtype)
else:
if device is not None and device != self.projector.device:
raise ValueError(
"`device` does not match the projector `device`, set the `device` argument to None"
)
if dtype is not None and dtype != self.projector.dtype:
raise ValueError(
"`dtype` does not match the projector `dtype`, set the `dtype` arguement to None"
)
tens = torch.randn(*size,
device=self.projector.device,
dtype=self.projector.dtype)
return ManifoldTensor(self.projx(tens), manifold=self)
def random_naive(self, *size, dtype=None, device=None):
"""
Naive approach to get random matrix on Stiefel manifold.
A helper function to sample a random point on the Stiefel manifold.
The measure is non-uniform for this method, but fast to compute.
Parameters
----------
size : shape
the desired output shape
dtype : torch.dtype
desired dtype
device : torch.device
desired device
Returns
-------
ManifoldTensor
random point on Stiefel manifold
"""
self._assert_check_shape(size2shape(*size), "x")
tens = torch.randn(*size, device=device, dtype=dtype)
return ManifoldTensor(linalg.qr(tens)[0], manifold=self)