import numpy as np


# --------------------------------------------------------
# 3D sine-cosine position embedding
# References:
# MVD: https://github.com/ruiwang2021/mvd/blob/main/modeling_finetune.py
# --------------------------------------------------------
def get_3d_sincos_pos_embed(embed_dim, grid_size, t_size, cls_token=False):
    """
    grid_size: int of the grid height and width
    t_size: int of the temporal size
    return:
    pos_embed: [t_size*grid_size*grid_size, embed_dim] or [1+t_size*grid_size*grid_size, embed_dim] (w/ or w/o cls_token)
    """
    assert embed_dim % 4 == 0
    embed_dim_spatial = embed_dim // 4 * 3
    embed_dim_temporal = embed_dim // 4

    # spatial
    grid_h = np.arange(grid_size, dtype=np.float32)
    grid_w = np.arange(grid_size, dtype=np.float32)
    grid = np.meshgrid(grid_w, grid_h)  # here w goes first
    grid = np.stack(grid, axis=0)

    grid = grid.reshape([2, 1, grid_size, grid_size])
    pos_embed_spatial = get_2d_sincos_pos_embed_from_grid(
        embed_dim_spatial, grid
    )

    # temporal
    grid_t = np.arange(t_size, dtype=np.float32)
    pos_embed_temporal = get_1d_sincos_pos_embed_from_grid(
        embed_dim_temporal, grid_t
    )

    # concate: [T, H, W] order
    pos_embed_temporal = pos_embed_temporal[:, np.newaxis, :]
    pos_embed_temporal = np.repeat(
        pos_embed_temporal, grid_size**2, axis=1
    )  # [T, H*W, D // 4]
    pos_embed_spatial = pos_embed_spatial[np.newaxis, :, :]
    pos_embed_spatial = np.repeat(
        pos_embed_spatial, t_size, axis=0
    )  # [T, H*W, D // 4 * 3]

    pos_embed = np.concatenate([pos_embed_temporal, pos_embed_spatial], axis=-1)
    pos_embed = pos_embed.reshape([-1, embed_dim])  # [T*H*W, D]

    if cls_token:
        pos_embed = np.concatenate(
            [np.zeros([1, embed_dim]), pos_embed], axis=0
        )
    return pos_embed


# --------------------------------------------------------
# 2D sine-cosine position embedding
# References:
# Transformer: https://github.com/tensorflow/models/blob/master/official/nlp/transformer/model_utils.py
# MoCo v3: https://github.com/facebookresearch/moco-v3
# --------------------------------------------------------
def get_2d_sincos_pos_embed(embed_dim, grid_size, cls_token=False):
    """
    grid_size: int of the grid height and width
    return:
    pos_embed: [grid_size*grid_size, embed_dim] or [1+grid_size*grid_size, embed_dim] (w/ or w/o cls_token)
    """
    grid_h = np.arange(grid_size, dtype=np.float32)
    grid_w = np.arange(grid_size, dtype=np.float32)
    grid = np.meshgrid(grid_w, grid_h)  # here w goes first
    grid = np.stack(grid, axis=0)

    grid = grid.reshape([2, 1, grid_size, grid_size])
    pos_embed = get_2d_sincos_pos_embed_from_grid(embed_dim, grid)
    if cls_token:
        pos_embed = np.concatenate(
            [np.zeros([1, embed_dim]), pos_embed], axis=0
        )
    return pos_embed


def get_1d_sincos_pos_embed(embed_dim, t_size, cls_token=False):
    """
    t_size: int of the temporal size
    return:
    pos_embed: [t_size, embed_dim] or [1+t_size, embed_dim] (w/ or w/o cls_token)
    """
    grid_t = np.arange(t_size, dtype=np.float32)
    pos_embed = get_1d_sincos_pos_embed_from_grid(embed_dim, grid_t)
    if cls_token:
        pos_embed = np.concatenate(
            [np.zeros([1, embed_dim]), pos_embed], axis=0
        )
    return pos_embed


def get_2d_sincos_pos_embed_from_grid(embed_dim, grid):
    assert embed_dim % 2 == 0

    # use half of dimensions to encode grid_h
    emb_h = get_1d_sincos_pos_embed_from_grid(
        embed_dim // 2, grid[0]
    )  # (H*W, D/2)
    emb_w = get_1d_sincos_pos_embed_from_grid(
        embed_dim // 2, grid[1]
    )  # (H*W, D/2)

    emb = np.concatenate([emb_h, emb_w], axis=1)  # (H*W, D)
    return emb


def get_1d_sincos_pos_embed_from_grid(embed_dim, pos):
    """
    embed_dim: output dimension for each position
    pos: a list of positions to be encoded: size (M,)
    out: (M, D)
    """
    assert embed_dim % 2 == 0
    omega = np.arange(embed_dim // 2, dtype=np.float32)
    omega /= embed_dim / 2.0
    omega = 1.0 / 10000**omega  # (D/2,)

    pos = pos.reshape(-1)  # (M,)
    out = np.einsum("m,d->md", pos, omega)  # (M, D/2), outer product

    emb_sin = np.sin(out)  # (M, D/2)
    emb_cos = np.cos(out)  # (M, D/2)

    emb = np.concatenate([emb_sin, emb_cos], axis=1)  # (M, D)
    return emb