def batched_dense_vec_jagged_2d_mul_ref(
    vectors: torch.Tensor,  # [B, H, N]
    matrices: torch.Tensor,  # [sum_B(N_B), H, D]
    offsets: torch.Tensor,  # [B + 1]
):
    """
    Reference function for fbgemm batched_dense_vec_jagged_2d_mul.
    https://pytorch.org/FBGEMM/python-api/jagged_tensor_ops.html#torch.ops.fbgemm.batched_dense_vec_jagged_2d_mul

    Parameters
    ----------
    vecrors: torch.Tensor
        Batch of vectors of the shape [B, H, N]. N is the maximum
        sequence length in the jagged Tensor `matrices`. Each vector
        in the batch is N-sized. The effective batch size is B * H.
    matrices: torch.Tensor
        Batch of jagged matrices (in a jagged Tensor) of the shape
        [sum_B(N_B), H, D]. The first dimension encodes the batch
        B of sequneces of variable length: from 0 to N. The matrices
        have variable number of rows (determined by the variable
        sequence lengths) and fixed number of columns: D. H is a
        factor of the effective batch size, just pulled to the
        right of the sum_B(N_B) dimension.
    offsets: torch.Tensor
        Rank-1 offsets Tensor describing the single jagged dimension
        (from 0 to N) in the jagged `matrices`.

    Returns
    -------
    torch.Tensor
        Batch of vectors resulting from the batched vector x jagged
        matrix multiplication. Shape: [B, H, D] (as N in the `vectors`
        is contracted with the variable sequence length encoded in the
        sum_B(N_B) dimension of the `matrices`).
    """
    assert vectors.dim() == 3
    B, H, N = vectors.size()

    assert matrices.dim() == 3
    assert matrices.size(1) == H
    D = matrices.size(2)

    assert offsets.dim() == 1
    assert offsets.size(0) == B + 1

    # pad the jagged matrices with zeros
    padded_matrices = jagged_to_dense(
        jagged=matrices,
        offsets_list=[offsets],
        dense_shape=[B, N, H, D],
        padding_value=0.0,
    )  # [B, N, H, D]

    return torch.matmul(
        vectors.unsqueeze(dim=2),  # [B, H, 1, N]
        padded_matrices.permute([0, 2, 1, 3]),  # [B, H, N, D]
    ).squeeze(dim=2)  # [B, H, D]
Reference function for fbgemm batched_dense_vec_jagged_2d_mul.
https://pytorch.org/FBGEMM/python-api/jagged_tensor_ops.html#torch.ops.fbgemm.batched_dense_vec_jagged_2d_mul

Parameters
----------
vecrors: torch.Tensor
Batch of vectors of the shape [B, H, N]. N is the maximum
sequence length in the jagged Tensor `matrices`. Each vector
in the batch is N-sized. The effective batch size is B * H.
matrices: torch.Tensor
Batch of jagged matrices (in a jagged Tensor) of the shape
[sum_B(N_B), H, D]. The first dimension encodes the batch
B of sequneces of variable length: from 0 to N. The matrices
have variable number of rows (determined by the variable
sequence lengths) and fixed number of columns: D. H is a
factor of the effective batch size, just pulled to the
right of the sum_B(N_B) dimension.
offsets: torch.Tensor
Rank-1 offsets Tensor describing the single jagged dimension
(from 0 to N) in the jagged `matrices`.

Returns
-------
torch.Tensor
Batch of vectors resulting from the batched vector x jagged
matrix multiplication. Shape: [B, H, D] (as N in the `vectors`
is contracted with the variable sequence length encoded in the
sum_B(N_B) dimension of the `matrices`).
python/aitemplate/testing/jagged_utils.py