def norm(t):
"""
Computes the :math:`L^2` (Frobenius) norm of a tensor.
:param t: a :class:`Tensor`
:return: a scalar :math:`\ge 0`
"""
return torch.sqrt(torch.clamp(tn.normsq(t), min=0))
def var(t):
"""
Computes the variance of a :class:`Tensor`.
:param t: a :class:`Tensor`
:return: a scalar :math:`\ge 0`
"""
return tn.normsq(t - tn.mean(t)) / t.numel()
def r_squared(gt, approx):
"""
Computes the :math:`R^2` score between two tensors (torch or tntorch).
:param gt: a torch or tntorch tensor
:param approx: a torch or tntorch tensor
:return: a scalar <= 1
"""
gt, approx = _process(gt, approx)
if isinstance(gt, torch.Tensor) and isinstance(approx, torch.Tensor):
return 1 - torch.dist(gt, approx)**2 / torch.dist(gt, torch.mean(gt))**2
return 1 - tn.dist(gt, approx)**2 / tn.normsq(gt-tn.mean(gt))
def var(t, marginals=None):
"""
Computes the variance of a :class:`Tensor`.
:param t: a :class:`Tensor`
:param marginals: an optional list of vectors
:return: a scalar :math:`\ge 0`
"""
if marginals is not None:
assert len(marginals) == t.dim()
tcentered = t - tn.mean(t, marginals=marginals)
pdf = tn.Tensor(
[marg[None, :, None] / marg.sum() for marg in marginals])
return tn.dot(tcentered * pdf, tcentered)
return tn.normsq(t - tn.mean(t)) / t.numel()
def normsq(self, **kwargs):
"""
See :func:`metrics.normsq()`.
"""
return tn.normsq(self, **kwargs)