import torch


def slerp(v1, v2, t, DOT_THR=0.9995, to_cpu=False, zdim=-1):
    """SLERP for pytorch tensors interpolating `v1` to `v2` with scale of `t`.

    `DOT_THR` determines when the vectors are too close to parallel.
        If they are too close, then a regular linear interpolation is used.

    `to_cpu` is a flag that optionally computes SLERP on the CPU.
        If the input tensors were on a GPU, it moves them back after the computation.  

    `zdim` is the feature dimension over which to compute norms and find angles.
        For example: if a sequence of 5 vectors is input with shape [5, 768]
        Then `zdim = 1` or `zdim = -1` computes SLERP along the feature dim of 768.

    Theory Reference:
    https://splines.readthedocs.io/en/latest/rotation/slerp.html
    PyTorch reference:
    https://discuss.pytorch.org/t/help-regarding-slerp-function-for-generative-model-sampling/32475/3
    Numpy reference: 
    https://gist.github.com/dvschultz/3af50c40df002da3b751efab1daddf2c
    """

    # check if we need to move to the cpu
    if to_cpu:
        orig_device = v1.device
        v1, v2 = v1.to('cpu'), v2.to('cpu')

    # take the dot product between normalized vectors
    v1_norm = v1 / torch.norm(v1, dim=zdim, keepdim=True)
    v2_norm = v2 / torch.norm(v2, dim=zdim, keepdim=True)
    dot = (v1_norm * v2_norm).sum(zdim)

    for _ in range(len(dot.shape), len(v1.shape)):
        dot = dot[..., None]

    # if the vectors are too close, return a simple linear interpolation
    if (torch.abs(dot) > DOT_THR).any():
        res = (1 - t) * v1 + t * v2
    else:
        # compute the angle terms we need
        theta = torch.acos(dot)
        theta_t = theta * t
        sin_theta = torch.sin(theta)
        sin_theta_t = torch.sin(theta_t)

        # compute the sine scaling terms for the vectors
        s1 = torch.sin(theta - theta_t) / sin_theta
        s2 = sin_theta_t / sin_theta

        # interpolate the vectors
        res = s1 * v1 + s2 * v2

    # check if we need to move them back to the original device
    if to_cpu:
        res.to(orig_device)

    return res