import torch

def convert_flow_to_deformation(flow):
    r"""convert flow fields to deformations.

    Args:
        flow (tensor): Flow field obtained by the model
    Returns:
        deformation (tensor): The deformation used for warping
    """
    b,c,h,w = flow.shape
    flow_norm = 2 * torch.cat([flow[:,:1,...]/(w-1),flow[:,1:,...]/(h-1)], 1)
    grid = make_coordinate_grid(flow)
    deformation = grid + flow_norm.permute(0,2,3,1)
    return deformation

def make_coordinate_grid(flow):
    r"""obtain coordinate grid with the same size as the flow filed.

    Args:
        flow (tensor): Flow field obtained by the model
    Returns:
        grid (tensor): The grid with the same size as the input flow
    """    
    b,c,h,w = flow.shape

    x = torch.arange(w).to(flow)
    y = torch.arange(h).to(flow)

    x = (2 * (x / (w - 1)) - 1)
    y = (2 * (y / (h - 1)) - 1)

    yy = y.view(-1, 1).repeat(1, w)
    xx = x.view(1, -1).repeat(h, 1)

    meshed = torch.cat([xx.unsqueeze_(2), yy.unsqueeze_(2)], 2)
    meshed = meshed.expand(b, -1, -1, -1)
    return meshed    

    
def warp_image(source_image, deformation):
    r"""warp the input image according to the deformation

    Args:
        source_image (tensor): source images to be warped
        deformation (tensor): deformations used to warp the images; value in range (-1, 1)
    Returns:
        output (tensor): the warped images
    """ 
    _, h_old, w_old, _ = deformation.shape
    _, _, h, w = source_image.shape
    if h_old != h or w_old != w:
        deformation = deformation.permute(0, 3, 1, 2)
        deformation = torch.nn.functional.interpolate(deformation, size=(h, w), mode='bilinear')
        deformation = deformation.permute(0, 2, 3, 1)
    return torch.nn.functional.grid_sample(source_image, deformation)