def _get_clones(module, n):
    return nn.ModuleList([copy.deepcopy(module) for _ in range(n)])

def bias_init_with_prob(prior_prob=0.01):
    """initialize conv/fc bias value according to a given probability value."""
    return float(-np.log((1 - prior_prob) / prior_prob))  # return bias_init

def linear_init_(module):
    bound = 1 / math.sqrt(module.weight.shape[0])
    uniform_(module.weight, -bound, bound)
    if hasattr(module, 'bias') and module.bias is not None:
        uniform_(module.bias, -bound, bound)

def inverse_sigmoid(x, eps=1e-5):
    x = x.clamp(min=0, max=1)
    x1 = x.clamp(min=eps)
    x2 = (1 - x).clamp(min=eps)
    return torch.log(x1 / x2)

def multi_scale_deformable_attn_pytorch(value: torch.Tensor, value_spatial_shapes: torch.Tensor,
                                        sampling_locations: torch.Tensor,
                                        attention_weights: torch.Tensor) -> torch.Tensor:
    """
    Multi-scale deformable attention.
    https://github.com/IDEA-Research/detrex/blob/main/detrex/layers/multi_scale_deform_attn.py
    """

    bs, _, num_heads, embed_dims = value.shape
    _, num_queries, num_heads, num_levels, num_points, _ = sampling_locations.shape
    value_list = value.split([H_ * W_ for H_, W_ in value_spatial_shapes], dim=1)
    sampling_grids = 2 * sampling_locations - 1
    sampling_value_list = []
    for level, (H_, W_) in enumerate(value_spatial_shapes):
        # bs, H_*W_, num_heads, embed_dims ->
        # bs, H_*W_, num_heads*embed_dims ->
        # bs, num_heads*embed_dims, H_*W_ ->
        # bs*num_heads, embed_dims, H_, W_
        value_l_ = (value_list[level].flatten(2).transpose(1, 2).reshape(bs * num_heads, embed_dims, H_, W_))
        # bs, num_queries, num_heads, num_points, 2 ->
        # bs, num_heads, num_queries, num_points, 2 ->
        # bs*num_heads, num_queries, num_points, 2
        sampling_grid_l_ = sampling_grids[:, :, :, level].transpose(1, 2).flatten(0, 1)
        # bs*num_heads, embed_dims, num_queries, num_points
        sampling_value_l_ = F.grid_sample(value_l_,
                                          sampling_grid_l_,
                                          mode='bilinear',
                                          padding_mode='zeros',
                                          align_corners=False)
        sampling_value_list.append(sampling_value_l_)
    # (bs, num_queries, num_heads, num_levels, num_points) ->
    # (bs, num_heads, num_queries, num_levels, num_points) ->
    # (bs, num_heads, 1, num_queries, num_levels*num_points)
    attention_weights = attention_weights.transpose(1, 2).reshape(bs * num_heads, 1, num_queries,
                                                                  num_levels * num_points)
    output = ((torch.stack(sampling_value_list, dim=-2).flatten(-2) * attention_weights).sum(-1).view(
        bs, num_heads * embed_dims, num_queries))
    return output.transpose(1, 2).contiguous()