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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.
from typing import Optional
import torch
from torch import Tensor
from typing_extensions import Literal
from torchmetrics.functional.pairwise.helpers import _check_input, _reduce_distance_matrix
from torchmetrics.utilities.exceptions import TorchMetricsUserError
def _pairwise_minkowski_distance_update(
x: Tensor, y: Optional[Tensor] = None, exponent: float = 2, zero_diagonal: Optional[bool] = None
) -> Tensor:
"""Calculate the pairwise minkowski distance matrix.
Args:
x: tensor of shape ``[N,d]``
y: tensor of shape ``[M,d]``
exponent: int or float larger than 1, exponent to which the difference between preds and target is to be raised
zero_diagonal: determines if the diagonal of the distance matrix should be set to zero
"""
x, y, zero_diagonal = _check_input(x, y, zero_diagonal)
if not (isinstance(exponent, (float, int)) and exponent >= 1):
raise TorchMetricsUserError(f"Argument ``p`` must be a float or int greater than 1, but got {exponent}")
# upcast to float64 to prevent precision issues
_orig_dtype = x.dtype
x = x.to(torch.float64)
y = y.to(torch.float64)
distance = (x.unsqueeze(1) - y.unsqueeze(0)).abs().pow(exponent).sum(-1).pow(1.0 / exponent)
if zero_diagonal:
distance.fill_diagonal_(0)
return distance.to(_orig_dtype)
def pairwise_minkowski_distance(
x: Tensor,
y: Optional[Tensor] = None,
exponent: float = 2,
reduction: Literal["mean", "sum", "none", None] = None,
zero_diagonal: Optional[bool] = None,
) -> Tensor:
r"""Calculate pairwise minkowski distances.
.. math::
d_{minkowski}(x,y,p) = ||x - y||_p = \sqrt[p]{\sum_{d=1}^D (x_d - y_d)^p}
If both :math:`x` and :math:`y` are passed in, the calculation will be performed pairwise between the rows of
:math:`x` and :math:`y`. If only :math:`x` is passed in, the calculation will be performed between the rows
of :math:`x`.
Args:
x: Tensor with shape ``[N, d]``
y: Tensor with shape ``[M, d]``, optional
exponent: int or float larger than 1, exponent to which the difference between preds and target is to be raised
reduction: reduction to apply along the last dimension. Choose between `'mean'`, `'sum'`
(applied along column dimension) or `'none'`, `None` for no reduction
zero_diagonal: if the diagonal of the distance matrix should be set to 0. If only `x` is given
this defaults to `True` else if `y` is also given it defaults to `False`
Returns:
A ``[N,N]`` matrix of distances if only ``x`` is given, else a ``[N,M]`` matrix
Example:
>>> import torch
>>> from torchmetrics.functional.pairwise import pairwise_minkowski_distance
>>> x = torch.tensor([[2, 3], [3, 5], [5, 8]], dtype=torch.float32)
>>> y = torch.tensor([[1, 0], [2, 1]], dtype=torch.float32)
>>> pairwise_minkowski_distance(x, y, exponent=4)
tensor([[3.0092, 2.0000],
[5.0317, 4.0039],
[8.1222, 7.0583]])
>>> pairwise_minkowski_distance(x, exponent=4)
tensor([[0.0000, 2.0305, 5.1547],
[2.0305, 0.0000, 3.1383],
[5.1547, 3.1383, 0.0000]])
"""
distance = _pairwise_minkowski_distance_update(x, y, exponent, zero_diagonal)
return _reduce_distance_matrix(distance, reduction)
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