def std(t):
"""
Computes the standard deviation of a :class:`Tensor`.
:param t: a :class:`Tensor`
:return: a scalar :math:`\ge 0`
"""
return torch.sqrt(tn.var(t))
def normalized_moment(t, k, eps=1e-12):
"""
Compute a normalized central moment :math:`\\mathbb{E}[(t - \\mathbb{E}[t])^k] / \\sigma^k'.
:param t: input :class:`Tensor`
:param k: the desired moment order (integer :math:`\ge 1`)
:param eps: relative error for rounding (default is 1e-12)
:return: the :math:`k`-th order normalized moment of `t`
"""
return raw_moment(t - tn.mean(t), k=k,
eps=eps) / tn.var(t)**(k / 2.) / t.numel()
def normalized_moment(t, k, marginals=None, eps=1e-12, algorithm='eig'):
"""
Compute a normalized central moment :math:`\\mathbb{E}[(t - \\mathbb{E}[t])^k] / \\sigma^k'.
:param t: input :class:`Tensor`
:param k: the desired moment order (integer :math:`\ge 1`)
:param marginals: an optional list of vectors
:param eps: relative error for rounding (default is 1e-12)
:return: the :math:`k`-th order normalized moment of `t`
"""
return raw_moment(t - tn.mean(t, marginals=marginals),
k=k,
marginals=marginals,
eps=eps,
algorithm=algorithm) / tn.var(t, marginals=marginals)**(
k / 2.) # / t.numel()
def var(self, **kwargs):
"""
See :func:`metrics.var()`.
"""
return tn.var(self, **kwargs)
def check():
x = t.torch()
assert tn.relative_error(tn.mean(t), torch.mean(x)) <= 1e-3
assert tn.relative_error(tn.var(t), torch.var(x)) <= 1e-3
assert tn.relative_error(tn.norm(t), torch.norm(x)) <= 1e-3
