import torch

def merge_tensors_fft2(v0: torch.Tensor, v1: torch.Tensor, t: float) -> torch.Tensor:
    """
    Merges two tensors using 2D Fourier transform interpolation.
    
    Parameters:
    - v0 (torch.Tensor): The first input tensor.
    - v1 (torch.Tensor): The second input tensor.
    - t (float): Interpolation parameter (0 <= t <= 1).
    
    Returns:
    - torch.Tensor: The tensor resulting from the interpolated inverse FFT.
    """
    # Ensure the input tensors are on the same device and dtype
    v0 = v0.to("cuda:0")
    v1 = v1.to("cuda:0")

    if len(v0.shape) == 1:
        fft_v0 = torch.fft.fft(v0)
        fft_v1 = torch.fft.fft(v1)
        result_fft = torch.zeros_like(fft_v0)
        
        real_v0 = fft_v0.real
        real_v1 = fft_v1.real
        abs_real_v0 = real_v0.abs() 
        abs_real_v1 = real_v1.abs() 

        sign_mask = real_v0.sign() == real_v1.sign()
        larger_values_mask = abs_real_v0 > abs_real_v1

        result_fft.real[sign_mask] = torch.max(real_v0[sign_mask], real_v1[sign_mask])
        result_fft.real[~sign_mask] = torch.where(larger_values_mask[~sign_mask], real_v0[~sign_mask], real_v1[~sign_mask])

        imag_v0 = fft_v0.imag
        imag_v1 = fft_v1.imag
        abs_imag_v0 = imag_v0.abs()
        abs_imag_v1 = imag_v1.abs()
        larger_values_mask_imag = abs_imag_v0 > abs_imag_v1

        result_fft.imag[sign_mask] = (1 - t) * imag_v0[sign_mask] + t * imag_v1[sign_mask]
        result_fft.imag[~sign_mask] = torch.where(larger_values_mask_imag[~sign_mask], imag_v0[~sign_mask], imag_v1[~sign_mask])

        merged_tensor = torch.fft.ifft(result_fft).real  # Taking the real part
        del v0, v1, fft_v0, fft_v1, result_fft
        return merged_tensor

    # Perform the 2D FFT on both tensors
    fft_v0 = torch.fft.fftn(v0, dim=(-2, -1))
    fft_v1 = torch.fft.fftn(v1, dim=(-2, -1))
    
    # Initialize the result FFT tensor
    result_fft = torch.zeros_like(fft_v0)
    
    # Compare real parts of the coefficients
    real_v0 = fft_v0.real
    real_v1 = fft_v1.real
    abs_real_v0 = real_v0.abs()
    abs_real_v1 = real_v1.abs()
    
    # Create masks for where signs match and where they do not
    sign_mask = real_v0.sign() == real_v1.sign()
    larger_values_mask = abs_real_v0 > abs_real_v1
    
    # Where signs match, interpolate; where signs do not match, take the larger by magnitude
    result_fft.real[sign_mask] = torch.max(real_v0[sign_mask], real_v1[sign_mask])
    result_fft.real[~sign_mask] = torch.where(larger_values_mask[~sign_mask], real_v0[~sign_mask], real_v1[~sign_mask])
    
    # Assuming the imaginary part should be treated similarly, adjust this if not
    imag_v0 = fft_v0.imag
    imag_v1 = fft_v1.imag
    abs_imag_v0 = imag_v0.abs()
    abs_imag_v1 = imag_v1.abs()
    larger_values_mask_imag = abs_imag_v0 > abs_imag_v1
    
    result_fft.imag[sign_mask] = (1 - t) * imag_v0[sign_mask] + t * imag_v1[sign_mask]
    result_fft.imag[~sign_mask] = torch.where(larger_values_mask_imag[~sign_mask], imag_v0[~sign_mask], imag_v1[~sign_mask])
    
    # Perform the inverse FFT to go back to the spatial domain
    merged_tensor = torch.fft.ifftn(result_fft, dim=(-2, -1)).real  # Taking the real part
    
    return merged_tensor

def merge_tensors_fft_shell(v0: torch.Tensor, v1: torch.Tensor) -> torch.Tensor:
    """
    Merges two tensors using 2D Fourier transform interpolation.
    
    Parameters:
    - v0 (torch.Tensor): The first input tensor.
    - v1 (torch.Tensor): The second input tensor.
    
    Returns:
    - torch.Tensor: The tensor resulting from the maximal interpolated inverse FFT.
    """
    # Ensure the input tensors are on the same device and dtype
    v0 = v0.to("cuda:0")
    v1 = v1.to("cuda:0")

    if len(v0.shape) == 1:
        fft_v0 = torch.fft.fft(v0)
        fft_v1 = torch.fft.fft(v1)
        result_fft = torch.zeros_like(fft_v0)
        
        real_v0 = fft_v0.real
        real_v1 = fft_v1.real
        abs_real_v0 = real_v0.abs() 
        abs_real_v1 = real_v1.abs() 

        sign_mask = real_v0.sign() == real_v1.sign()
        larger_values_mask = abs_real_v0 > abs_real_v1

        result_fft.real[sign_mask] = torch.max(real_v0[sign_mask], real_v1[sign_mask])
        result_fft.real[~sign_mask] = torch.where(larger_values_mask[~sign_mask], real_v0[~sign_mask], real_v1[~sign_mask])

        imag_v0 = fft_v0.imag
        imag_v1 = fft_v1.imag
        abs_imag_v0 = imag_v0.abs()
        abs_imag_v1 = imag_v1.abs()
        larger_values_mask_imag = abs_imag_v0 > abs_imag_v1

        result_fft.imag[sign_mask] = torch.max(imag_v0[sign_mask], imag_v1[sign_mask])
        result_fft.imag[~sign_mask] = torch.where(larger_values_mask_imag[~sign_mask], imag_v0[~sign_mask], imag_v1[~sign_mask])

        merged_tensor = torch.fft.ifft(result_fft).real  # Taking the real part
        del v0, v1, fft_v0, fft_v1, result_fft
        return merged_tensor

    # Perform the 2D FFT on both tensors
    fft_v0 = torch.fft.fftn(v0, dim=(-2, -1))
    fft_v1 = torch.fft.fftn(v1, dim=(-2, -1))
    
    # Initialize the result FFT tensor
    result_fft = torch.zeros_like(fft_v0)
    
    # Compare real parts of the coefficients
    real_v0 = fft_v0.real
    real_v1 = fft_v1.real
    abs_real_v0 = real_v0.abs()
    abs_real_v1 = real_v1.abs()
    
    # Create masks for where signs match and where they do not
    sign_mask = real_v0.sign() == real_v1.sign()
    larger_values_mask = abs_real_v0 > abs_real_v1
    
    # Where signs match, interpolate; where signs do not match, take the larger by magnitude
    result_fft.real[sign_mask] = torch.max(real_v0[sign_mask], real_v1[sign_mask])
    result_fft.real[~sign_mask] = torch.where(larger_values_mask[~sign_mask], real_v0[~sign_mask], real_v1[~sign_mask])
    
    # Assuming the imaginary part should be treated similarly, adjust this if not
    imag_v0 = fft_v0.imag
    imag_v1 = fft_v1.imag
    abs_imag_v0 = imag_v0.abs()
    abs_imag_v1 = imag_v1.abs()
    larger_values_mask_imag = abs_imag_v0 > abs_imag_v1
    
    result_fft.imag[sign_mask] = torch.max(imag_v0[sign_mask], imag_v1[sign_mask])
    result_fft.imag[~sign_mask] = torch.where(larger_values_mask_imag[~sign_mask], imag_v0[~sign_mask], imag_v1[~sign_mask])
    
    # Perform the inverse FFT to go back to the spatial domain
    merged_tensor = torch.fft.ifftn(result_fft, dim=(-2, -1)).real  # Taking the real part
    
    return merged_tensor