import torch


# batch*n
def normalize_vector(v):
    batch = v.shape[0]
    v_mag = torch.sqrt(v.pow(2).sum(1))  # batch
    eps = torch.tensor(1e-8, device=v.device)
    v_mag = torch.max(v_mag, eps)
    v_mag = v_mag.view(batch, 1).expand(batch, v.shape[1])
    v = v / v_mag
    return v


# u, v batch*n
def cross_product(u, v):
    batch = u.shape[0]
    # print (u.shape)
    # print (v.shape)
    i = u[:, 1] * v[:, 2] - u[:, 2] * v[:, 1]
    j = u[:, 2] * v[:, 0] - u[:, 0] * v[:, 2]
    k = u[:, 0] * v[:, 1] - u[:, 1] * v[:, 0]

    out = torch.cat((i.view(batch, 1), j.view(batch, 1), k.view(batch, 1)), 1)  # batch*3

    return out


# poses batch*6
# poses
def compute_rotation_matrix_from_ortho6d(poses):
    x_raw = poses[:, 0:3]  # batch*3
    y_raw = poses[:, 3:6]  # batch*3

    x = normalize_vector(x_raw)  # batch*3
    z = cross_product(x, y_raw)  # batch*3
    z = normalize_vector(z)  # batch*3
    y = cross_product(z, x)  # batch*3

    x = x.view(-1, 3, 1)
    y = y.view(-1, 3, 1)
    z = z.view(-1, 3, 1)
    matrix = torch.cat((x, y, z), 2)  # batch*3*3
    return matrix


# input batch*4*4 or batch*3*3
# output torch batch*3 x, y, z in radiant
# the rotation is in the sequence of x,y,z
def compute_euler_angles_from_rotation_matrices(rotation_matrices):
    batch = rotation_matrices.shape[0]
    R = rotation_matrices
    sy = torch.sqrt(R[:, 0, 0] * R[:, 0, 0] + R[:, 1, 0] * R[:, 1, 0])
    singular = sy < 1e-6
    singular = singular.float()

    x = torch.atan2(R[:, 2, 1], R[:, 2, 2])
    y = torch.atan2(-R[:, 2, 0], sy)
    z = torch.atan2(R[:, 1, 0], R[:, 0, 0])

    xs = torch.atan2(-R[:, 1, 2], R[:, 1, 1])
    ys = torch.atan2(-R[:, 2, 0], sy)
    zs = R[:, 1, 0] * 0

    out_euler = torch.zeros(batch, 3, device=rotation_matrices.device)

    out_euler[:, 0] = x * (1 - singular) + xs * singular
    out_euler[:, 1] = y * (1 - singular) + ys * singular
    out_euler[:, 2] = z * (1 - singular) + zs * singular

    return out_euler


def get_R(x, y, z):
    """Get rotation matrix from three rotation angles (radians). right-handed.
    Args:
        x: rotation angle around x-axis
        y: rotation angle around y-axis
        z: rotation angle around z-axis
    Returns:
        R: [3, 3]. rotation matrix.
    """
    # x
    Rx = torch.tensor(
        [[1, 0, 0], [0, torch.cos(x), -torch.sin(x)], [0, torch.sin(x), torch.cos(x)]],
        device=x.device,
    )
    # y
    Ry = torch.tensor(
        [[torch.cos(y), 0, torch.sin(y)], [0, 1, 0], [-torch.sin(y), 0, torch.cos(y)]],
        device=y.device,
    )
    # z
    Rz = torch.tensor(
        [[torch.cos(z), -torch.sin(z), 0], [torch.sin(z), torch.cos(z), 0], [0, 0, 1]],
        device=z.device,
    )

    R = torch.mm(Rz, torch.mm(Ry, Rx))
    return R