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# Copyright The PyTorch Lightning team.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import torch
from torch import Tensor
from torchmetrics.utilities.checks import _check_same_shape
from torchmetrics.utilities.exceptions import TorchMetricsUserError
def _minkowski_distance_update(preds: Tensor, targets: Tensor, p: float) -> Tensor:
"""Update and return variables required to compute Minkowski distance.
Checks for same shape of input tensors.
Args:
preds: Predicted tensor
targets: Ground truth tensor
p: Non-negative number acting as the p to the errors
"""
_check_same_shape(preds, targets)
if not (isinstance(p, (float, int)) and p >= 1):
raise TorchMetricsUserError(f"Argument ``p`` must be a float or int greater than 1, but got {p}")
difference = torch.abs(preds - targets)
return torch.sum(torch.pow(difference, p))
def _minkowski_distance_compute(distance: Tensor, p: float) -> Tensor:
"""Compute Minkowski Distance.
Args:
distance: Sum of the p-th powers of errors over all observations
p: The non-negative numeric power the errors are to be raised to
Example:
>>> preds = torch.tensor([0., 1, 2, 3])
>>> target = torch.tensor([0., 2, 3, 1])
>>> distance_p_sum = _minkowski_distance_update(preds, target, 5)
>>> _minkowski_distance_compute(distance_p_sum, 5)
tensor(2.0244)
"""
return torch.pow(distance, 1.0 / p)
def minkowski_distance(preds: Tensor, targets: Tensor, p: float) -> Tensor:
r"""Compute the `Minkowski distance`_.
.. math:: d_{\text{Minkowski}} = \\sum_{i}^N (| y_i - \\hat{y_i} |^p)^\frac{1}{p}
This metric can be seen as generalized version of the standard euclidean distance which corresponds to minkowski
distance with p=2.
Args:
preds: estimated labels of type Tensor
targets: ground truth labels of type Tensor
p: int or float larger than 1, exponent to which the difference between preds and target is to be raised
Return:
Tensor with the Minkowski distance
Example:
>>> from torchmetrics.functional.regression import minkowski_distance
>>> x = torch.tensor([1.0, 2.8, 3.5, 4.5])
>>> y = torch.tensor([6.1, 2.11, 3.1, 5.6])
>>> minkowski_distance(x, y, p=3)
tensor(5.1220)
"""
minkowski_dist_sum = _minkowski_distance_update(preds, targets, p)
return _minkowski_distance_compute(minkowski_dist_sum, p)
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