text: # 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, Sequence, Tuple
  
  import torch
  from torch import Tensor
  from torch.nn import functional as F
  
  from torchmetrics.utilities.checks import _check_same_shape
  from torchmetrics.utilities.distributed import reduce
  
  
  def _gaussian(kernel_size: int, sigma: float, dtype: torch.dtype, device: torch.device) -> Tensor:
      """Computes 1D gaussian kernel.
  
      Args:
          kernel_size: size of the gaussian kernel
          sigma: Standard deviation of the gaussian kernel
          dtype: data type of the output tensor
          device: device of the output tensor
  
      Example:
          >>> _gaussian(3, 1, torch.float, 'cpu')
          tensor([[0.2741, 0.4519, 0.2741]])
      """
      dist = torch.arange(start=(1 - kernel_size) / 2, end=(1 + kernel_size) / 2, step=1, dtype=dtype, device=device)
      gauss = torch.exp(-torch.pow(dist / sigma, 2) / 2)
      return (gauss / gauss.sum()).unsqueeze(dim=0)  # (1, kernel_size)
  
  
  def _gaussian_kernel(
      channel: int, kernel_size: Sequence[int], sigma: Sequence[float], dtype: torch.dtype, device: torch.device
  ) -> Tensor:
      """Computes 2D gaussian kernel.
  
      Args:
          channel: number of channels in the image
          kernel_size: size of the gaussian kernel as a tuple (h, w)
          sigma: Standard deviation of the gaussian kernel
          dtype: data type of the output tensor
          device: device of the output tensor
  
      Example:
          >>> _gaussian_kernel(1, (5,5), (1,1), torch.float, "cpu")
          tensor([[[[0.0030, 0.0133, 0.0219, 0.0133, 0.0030],
                    [0.0133, 0.0596, 0.0983, 0.0596, 0.0133],
                    [0.0219, 0.0983, 0.1621, 0.0983, 0.0219],
                    [0.0133, 0.0596, 0.0983, 0.0596, 0.0133],
                    [0.0030, 0.0133, 0.0219, 0.0133, 0.0030]]]])
      """
  
      gaussian_kernel_x = _gaussian(kernel_size[0], sigma[0], dtype, device)
      gaussian_kernel_y = _gaussian(kernel_size[1], sigma[1], dtype, device)
      kernel = torch.matmul(gaussian_kernel_x.t(), gaussian_kernel_y)  # (kernel_size, 1) * (1, kernel_size)
  
      return kernel.expand(channel, 1, kernel_size[0], kernel_size[1])
  
  
  def _ssim_update(preds: Tensor, target: Tensor) -> Tuple[Tensor, Tensor]:
      """Updates and returns variables required to compute Structural Similarity Index Measure. Checks for same shape
      and type of the input tensors.
  
      Args:
          preds: Predicted tensor
          target: Ground truth tensor
      """
  
      if preds.dtype != target.dtype:
          raise TypeError(
              "Expected `preds` and `target` to have the same data type."
              f" Got preds: {preds.dtype} and target: {target.dtype}."
          )
      _check_same_shape(preds, target)
      if len(preds.shape) != 4:
          raise ValueError(
              "Expected `preds` and `target` to have BxCxHxW shape."
              f" Got preds: {preds.shape} and target: {target.shape}."
          )
      return preds, target
  
  
  def _ssim_compute(
      preds: Tensor,
      target: Tensor,
      kernel_size: Sequence[int] = (11, 11),
      sigma: Sequence[float] = (1.5, 1.5),
      reduction: str = "elementwise_mean",
      data_range: Optional[float] = None,
      k1: float = 0.01,
      k2: float = 0.03,
  ) -> Tensor:
      """Computes Structual Similarity Index Measure.
  
      Args:
          preds: estimated image
          target: ground truth image
          kernel_size: size of the gaussian kernel (default: (11, 11))
          sigma: Standard deviation of the gaussian kernel (default: (1.5, 1.5))
          reduction: a method to reduce metric score over labels.
  
              - ``'elementwise_mean'``: takes the mean (default)
              - ``'sum'``: takes the sum
              - ``'none'``: no reduction will be applied
  
          data_range: Range of the image. If ``None``, it is determined from the image (max - min)
          k1: Parameter of SSIM. Default: 0.01
          k2: Parameter of SSIM. Default: 0.03
  
      Example:
          >>> preds = torch.rand([16, 1, 16, 16])
          >>> target = preds * 0.75
          >>> preds, target = _ssim_update(preds, target)
          >>> _ssim_compute(preds, target)
          tensor(0.9219)
      """
      if len(kernel_size) != 2 or len(sigma) != 2:
          raise ValueError(
              "Expected `kernel_size` and `sigma` to have the length of two."
              f" Got kernel_size: {len(kernel_size)} and sigma: {len(sigma)}."
          )
  
      if any(x % 2 == 0 or x <= 0 for x in kernel_size):
          raise ValueError(f"Expected `kernel_size` to have odd positive number. Got {kernel_size}.")
  
      if any(y <= 0 for y in sigma):
          raise ValueError(f"Expected `sigma` to have positive number. Got {sigma}.")
  
      if data_range is None:
          data_range = max(preds.max() - preds.min(), target.max() - target.min())
  
      c1 = pow(k1 * data_range, 2)
      c2 = pow(k2 * data_range, 2)
      device = preds.device
  
      channel = preds.size(1)
      dtype = preds.dtype
      kernel = _gaussian_kernel(channel, kernel_size, sigma, dtype, device)
      pad_h = (kernel_size[0] - 1) // 2
      pad_w = (kernel_size[1] - 1) // 2
  
      preds = F.pad(preds, (pad_h, pad_h, pad_w, pad_w), mode="reflect")
      target = F.pad(target, (pad_h, pad_h, pad_w, pad_w), mode="reflect")
  
      input_list = torch.cat((preds, target, preds * preds, target * target, preds * target))  # (5 * B, C, H, W)
      outputs = F.conv2d(input_list, kernel, groups=channel)
      output_list = [outputs[x * preds.size(0) : (x + 1) * preds.size(0)] for x in range(len(outputs))]
  
      mu_pred_sq = output_list[0].pow(2)
      mu_target_sq = output_list[1].pow(2)
      mu_pred_target = output_list[0] * output_list[1]
  
      sigma_pred_sq = output_list[2] - mu_pred_sq
      sigma_target_sq = output_list[3] - mu_target_sq
      sigma_pred_target = output_list[4] - mu_pred_target
  
      upper = 2 * sigma_pred_target + c2
      lower = sigma_pred_sq + sigma_target_sq + c2
  
      ssim_idx = ((2 * mu_pred_target + c1) * upper) / ((mu_pred_sq + mu_target_sq + c1) * lower)
      ssim_idx = ssim_idx[..., pad_h:-pad_h, pad_w:-pad_w]
  
      return reduce(ssim_idx, reduction)
  
  
  def ssim(
      preds: Tensor,
      target: Tensor,
      kernel_size: Sequence[int] = (11, 11),
      sigma: Sequence[float] = (1.5, 1.5),
      reduction: str = "elementwise_mean",
      data_range: Optional[float] = None,
      k1: float = 0.01,
      k2: float = 0.03,
  ) -> Tensor:
      """Computes Structual Similarity Index Measure.
  
      Args:
          preds: estimated image
          target: ground truth image
          kernel_size: size of the gaussian kernel (default: (11, 11))
          sigma: Standard deviation of the gaussian kernel (default: (1.5, 1.5))
          reduction: a method to reduce metric score over labels.
  
              - ``'elementwise_mean'``: takes the mean (default)
              - ``'sum'``: takes the sum
              - ``'none'``: no reduction will be applied
  
          data_range: Range of the image. If ``None``, it is determined from the image (max - min)
          k1: Parameter of SSIM. Default: 0.01
          k2: Parameter of SSIM. Default: 0.03
  
      Return:
          Tensor with SSIM score
  
      Raises:
          TypeError:
              If ``preds`` and ``target`` don't have the same data type.
          ValueError:
              If ``preds`` and ``target`` don't have ``BxCxHxW shape``.
          ValueError:
              If the length of ``kernel_size`` or ``sigma`` is not ``2``.
          ValueError:
              If one of the elements of ``kernel_size`` is not an ``odd positive number``.
          ValueError:
              If one of the elements of ``sigma`` is not a ``positive number``.
  
      Example:
          >>> from torchmetrics.functional import ssim
          >>> preds = torch.rand([16, 1, 16, 16])
          >>> target = preds * 0.75
          >>> ssim(preds, target)
          tensor(0.9219)
      """
      preds, target = _ssim_update(preds, target)
      return _ssim_compute(preds, target, kernel_size, sigma, reduction, data_range, k1, k2)
  