# Source code for kornia.losses.divergence

```r"""Losses based on the divergence between probability distributions."""

import torch
import torch.nn.functional as F

def _kl_div_2d(p: torch.Tensor, q: torch.Tensor) -> torch.Tensor:
# D_KL(P || Q)
batch, chans, height, width = p.shape
unsummed_kl = F.kl_div(
q.reshape(batch * chans, height * width).log(), p.reshape(batch * chans, height * width), reduction='none'
)
kl_values = unsummed_kl.sum(-1).view(batch, chans)
return kl_values

def _js_div_2d(p: torch.Tensor, q: torch.Tensor) -> torch.Tensor:
# JSD(P || Q)
m = 0.5 * (p + q)
return 0.5 * _kl_div_2d(p, m) + 0.5 * _kl_div_2d(q, m)

# TODO: add this to the main module

def _reduce_loss(losses: torch.Tensor, reduction: str) -> torch.Tensor:
if reduction == 'none':
return losses
return torch.mean(losses) if reduction == 'mean' else torch.sum(losses)

[docs]def js_div_loss_2d(input: torch.Tensor, target: torch.Tensor, reduction: str = 'mean'):
r"""Calculate the Jensen-Shannon divergence loss between heatmaps.

Args:
input: the input tensor with shape :math:`(B, N, H, W)`.
target: the target tensor with shape :math:`(B, N, H, W)`.
reduction: Specifies the reduction to apply to the
output: ``'none'`` | ``'mean'`` | ``'sum'``. ``'none'``: no reduction
will be applied, ``'mean'``: the sum of the output will be divided by
the number of elements in the output, ``'sum'``: the output will be
summed.

Examples:
>>> input = torch.full((1, 1, 2, 4), 0.125)
>>> loss = js_div_loss_2d(input, input)
>>> loss.item()
0.0
"""
return _reduce_loss(_js_div_2d(target, input), reduction)

[docs]def kl_div_loss_2d(input: torch.Tensor, target: torch.Tensor, reduction: str = 'mean'):
r"""Calculate the Kullback-Leibler divergence loss between heatmaps.

Args:
input: the input tensor with shape :math:`(B, N, H, W)`.
target: the target tensor with shape :math:`(B, N, H, W)`.
reduction: Specifies the reduction to apply to the
output: ``'none'`` | ``'mean'`` | ``'sum'``. ``'none'``: no reduction
will be applied, ``'mean'``: the sum of the output will be divided by
the number of elements in the output, ``'sum'``: the output will be
summed.

Examples:
>>> input = torch.full((1, 1, 2, 4), 0.125)
>>> loss = js_div_loss_2d(input, input)
>>> loss.item()
0.0
"""
return _reduce_loss(_kl_div_2d(target, input), reduction)
```