Given indices and weights and an original embeddings
    initialize the positions of new points relative to the
    indices and weights (of their neighbors in the source data).

    Parameters
    ----------
    indices: array of shape (n_new_samples, n_neighbors)
        The indices of the neighbors of each new sample

    weights: array of shape (n_new_samples, n_neighbors)
        The membership strengths of associated 1-simplices
        for each of the new samples.

    embedding: array of shape (n_samples, dim)
        The original embedding of the source data.

    Returns
    -------
    new_embedding: array of shape (n_new_samples, dim)
        An initial embedding of the new sample points.

def init_transform(indices, weights, embedding):
    """Given indices and weights and an original embeddings
    initialize the positions of new points relative to the
    indices and weights (of their neighbors in the source data).

    Parameters
    ----------
    indices: array of shape (n_new_samples, n_neighbors)
        The indices of the neighbors of each new sample

    weights: array of shape (n_new_samples, n_neighbors)
        The membership strengths of associated 1-simplices
        for each of the new samples.

    embedding: array of shape (n_samples, dim)
        The original embedding of the source data.

    Returns
    -------
    new_embedding: array of shape (n_new_samples, dim)
        An initial embedding of the new sample points.
    """
    result = np.zeros((indices.shape[0], embedding.shape[1]), dtype=np.float32)

    for i in range(indices.shape[0]):
        for j in range(indices.shape[1]):
            for d in range(embedding.shape[1]):
                result[i, d] += weights[i, j] * embedding[indices[i, j], d]

    return result