def total_variation_loss(input: torch.Tensor,
exponent: float = 2.0,
reduction: str = "mean") -> torch.Tensor:
r"""Calculates the total variation loss. See
:class:`pystiche.ops.TotalVariationOperator` for details.
Args:
input: Input image
exponent: Parameter :math:`\beta` . A higher value leads to more smoothed
results. Defaults to ``2.0``.
reduction: Reduction method of the output passed to
:func:`pystiche.misc.reduce`. Defaults to ``"mean"``.
Examples:
>>> import pystiche.loss.functional as F
>>> input = torch.rand(2, 3, 256, 256)
>>> score = F.total_variation_loss(input)
"""
# this ignores the last row and column of the image
grad_vert = input[:, :, :-1, :-1] - input[:, :, 1:, :-1]
grad_horz = input[:, :, :-1, :-1] - input[:, :, :-1, 1:]
grad = pystiche.nonnegsqrt(grad_vert**2.0 + grad_horz**2.0)
loss = grad**exponent
return reduce(loss, reduction)
def test_nonnegsqrt():
vals = (-1.0, 0.0, 1.0, 2.0)
desireds = (0.0, 0.0, 1.0, sqrt(2.0))
for val, desired in zip(vals, desireds):
x = torch.tensor(val, requires_grad=True)
y = pystiche.nonnegsqrt(x)
assert y == ptu.approx(desired)
def test_main(self):
vals = (-1.0, 0.0, 1.0, 2.0)
desireds = (0.0, 0.0, 1.0, sqrt(2.0))
for val, desired in zip(vals, desireds):
x = torch.tensor(val)
y = pystiche.nonnegsqrt(x)
assert y == ptu.approx(desired)
def test_nonnegsqrt_grad():
vals = (-1.0, 0.0, 1.0, 2.0)
desireds = (0.0, 0.0, 1.0 / 2.0, 1.0 / (2.0 * sqrt(2.0)))
for val, desired in zip(vals, desireds):
x = torch.tensor(val, requires_grad=True)
y = pystiche.nonnegsqrt(x)
y.backward()
assert x.grad == ptu.approx(desired)
def test_nonnegsqrt(self):
vals = (-1.0, 0.0, 1.0, 2.0)
desireds = (0.0, 0.0, 1.0, sqrt(2.0))
for val, desired in zip(vals, desireds):
x = torch.tensor(val, requires_grad=True)
y = pystiche.nonnegsqrt(x)
actual = y.item()
self.assertAlmostEqual(actual, desired)
