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Args: x: An input tensor. Shape :math:`(N, C, H, W)`. y: A target tensor. Shape :math:`(N, C, H, W)`. kernel: 2D Gaussian kernel. data_range: Maximum value range of images (usually 1.0 or 255). k1: Algorithm parameter, K1 (small constant, see [1]). k2: Algorithm parameter, K2 (small constant, see [1]). Try a larger K2 constant (e.g. 0.4) if you get a negative or NaN results. Returns: Full Value of Structural Similarity (SSIM) index. rAKernel size can't be greater than actual input size. Input size: . Kernel size: r(r<rweightstridepaddinggroups@)rrrx)r ValueErrorrconv2dr|)r-r~rrrrc1c2 n_channelsZmu_xZmu_yZmu_xxZmu_yyZmu_xyZsigma_xxZsigma_yyZsigma_xycsssrrrrrs0(   rc$Csf|d}|d|dks|d|dkr'td|d||d}|d}|d} |d } |d} |d } tj| |dd |d } tj| |dd |d }tj| |dd |d }tj| |dd |d }| d|d}|d|d}| |||}| |||}d }| d| d}| d| d}| | | | }| | | | }tj||dd |d |}tj||dd |d |}tj||dd |d |}tj||dd |d |}tj||fdd }tj||fdd }|d|||d|d||} |d|||d|d||}!|!| }!|!jdd }"| jdd }#|"|#fS)aaCalculate Structural Similarity (SSIM) index for Complex X and Y per channel. Args: x: An input tensor. Shape :math:`(N, C, H, W, 2)`. y: A target tensor. Shape :math:`(N, C, H, W, 2)`. kernel: 2-D gauss kernel. data_range: Maximum value range of images (usually 1.0 or 255). k1: Algorithm parameter, K1 (small constant, see [1]). k2: Algorithm parameter, K2 (small constant, see [1]). Try a larger K2 constant (e.g. 0.4) if you get a negative or NaN results. Returns: Full Value of Complex Structural Similarity (SSIM) index. r<rrrrr().r).r<rrrrx)rr) rrrrpowr#stack unsqueezer|)$r-r~rrrrrrrx_realx_imagZy_realZy_imagZmu1_realZmu1_imagZmu2_realZmu2_imagZmu1_sqZmu2_sqZ mu1_mu2_realZ mu1_mu2_imagZ compensationx_sqy_sqZx_y_realZx_y_imagZ sigma1_sqZ sigma2_sqZ sigma12_realZ sigma12_imagZsigma12Zmu1_mu2rrrrrrrrsL ( ,,  rrsigmarrQcCsdtj|||d}||dd8}|d}|d|d d|d}||}|dS)aGReturns 2D Gaussian kernel N(0,`sigma`^2) Args: kernel_size: Size of the kernel sigma: Std of the distribution device: target device for kernel generation dtype: target data type for kernel generation Returns: gaussian_kernel: Tensor with shape (1, kernel_size, kernel_size) )rQrr<rr(r)r#arangerexpsum)rrrrQcoordsgrrrr1s  &  rr)FT)rrrrj)-r?r!rrznumpyr"inspectrrichrtypingrrrr#torch.nnnnZtorch.nn.functional functionalr%lightning.pytorch.utilities.rank_zerorrrrrintr'r.r/r2r:r6rOrnFunctionrIrrr*floatrrtyperrrrrs    ,,     '   9  H