import torch
import numpy as np
from torch.nn import functional as F
from einops.einops import rearrange


def cam2pixel(cam_coord, f, c):
    x = cam_coord[:, 0] / cam_coord[:, 2] * f[0] + c[0]
    y = cam_coord[:, 1] / cam_coord[:, 2] * f[1] + c[1]
    z = cam_coord[:, 2]
    return np.stack((x, y, z), 1)


def pixel2cam(pixel_coord, f, c):
    x = (pixel_coord[:, 0] - c[0]) / f[0] * pixel_coord[:, 2]
    y = (pixel_coord[:, 1] - c[1]) / f[1] * pixel_coord[:, 2]
    z = pixel_coord[:, 2]
    return np.stack((x, y, z), 1)


def world2cam(world_coord, R, t):
    cam_coord = np.dot(R, world_coord.transpose(1, 0)).transpose(1, 0) + t.reshape(1, 3)
    return cam_coord


def cam2world(cam_coord, R, t):
    world_coord = np.dot(np.linalg.inv(R), (cam_coord - t.reshape(1, 3)).transpose(1, 0)).transpose(1, 0)
    return world_coord


def rigid_transform_3D(A, B):
    n, dim = A.shape
    centroid_A = np.mean(A, axis=0)
    centroid_B = np.mean(B, axis=0)
    H = np.dot(np.transpose(A - centroid_A), B - centroid_B) / n
    U, s, V = np.linalg.svd(H)
    R = np.dot(np.transpose(V), np.transpose(U))
    if np.linalg.det(R) < 0:
        s[-1] = -s[-1]
        V[2] = -V[2]
        R = np.dot(np.transpose(V), np.transpose(U))

    varP = np.var(A, axis=0).sum()
    c = 1 / varP * np.sum(s)

    t = -np.dot(c * R, np.transpose(centroid_A)) + np.transpose(centroid_B)
    return c, R, t


def rigid_align(A, B):
    c, R, t = rigid_transform_3D(A, B)
    A2 = np.transpose(np.dot(c * R, np.transpose(A))) + t
    return A2


def transform_joint_to_other_db(src_joint, src_name, dst_name):
    src_joint_num = len(src_name)
    dst_joint_num = len(dst_name)

    new_joint = np.zeros(((dst_joint_num,) + src_joint.shape[1:]), dtype=np.float32)
    for src_idx in range(len(src_name)):
        name = src_name[src_idx]
        if name in dst_name:
            dst_idx = dst_name.index(name)
            new_joint[dst_idx] = src_joint[src_idx]

    return new_joint


def rotation_matrix_to_angle_axis(rotation_matrix):
    """Convert 3x4 rotation matrix to Rodrigues vector

    Args:
        rotation_matrix (Tensor): rotation matrix.

    Returns:
        Tensor: Rodrigues vector transformation.

    Shape:
        - Input: :math:`(N, 3, 4)`
        - Output: :math:`(N, 3)`

    Example:
        >>> input = torch.rand(2, 3, 4)  # Nx4x4
        >>> output = tgm.rotation_matrix_to_angle_axis(input)  # Nx3
    """
    # todo add check that matrix is a valid rotation matrix
    quaternion = rotation_matrix_to_quaternion(rotation_matrix)
    return quaternion_to_angle_axis(quaternion)

def quaternion_to_angle_axis(quaternion: torch.Tensor) -> torch.Tensor:
    """Convert quaternion vector to angle axis of rotation.

    Adapted from ceres C++ library: ceres-solver/include/ceres/rotation.h

    Args:
        quaternion (torch.Tensor): tensor with quaternions.

    Return:
        torch.Tensor: tensor with angle axis of rotation.

    Shape:
        - Input: :math:`(*, 4)` where `*` means, any number of dimensions
        - Output: :math:`(*, 3)`

    Example:
        >>> quaternion = torch.rand(2, 4)  # Nx4
        >>> angle_axis = tgm.quaternion_to_angle_axis(quaternion)  # Nx3
    """
    if not torch.is_tensor(quaternion):
        raise TypeError("Input type is not a torch.Tensor. Got {}".format(
            type(quaternion)))

    if not quaternion.shape[-1] == 4:
        raise ValueError("Input must be a tensor of shape Nx4 or 4. Got {}"
                         .format(quaternion.shape))
    # unpack input and compute conversion
    q1: torch.Tensor = quaternion[..., 1]
    q2: torch.Tensor = quaternion[..., 2]
    q3: torch.Tensor = quaternion[..., 3]
    sin_squared_theta: torch.Tensor = q1 * q1 + q2 * q2 + q3 * q3

    sin_theta: torch.Tensor = torch.sqrt(sin_squared_theta)
    cos_theta: torch.Tensor = quaternion[..., 0]
    two_theta: torch.Tensor = 2.0 * torch.where(
        cos_theta < 0.0,
        torch.atan2(-sin_theta, -cos_theta),
        torch.atan2(sin_theta, cos_theta))

    k_pos: torch.Tensor = two_theta / sin_theta
    k_neg: torch.Tensor = 2.0 * torch.ones_like(sin_theta)
    k: torch.Tensor = torch.where(sin_squared_theta > 0.0, k_pos, k_neg)

    angle_axis: torch.Tensor = torch.zeros_like(quaternion)[..., :3]
    angle_axis[..., 0] += q1 * k
    angle_axis[..., 1] += q2 * k
    angle_axis[..., 2] += q3 * k
    return angle_axis

def rotation_matrix_to_quaternion(rotation_matrix, eps=1e-6):
    """Convert 3x4 rotation matrix to 4d quaternion vector

    This algorithm is based on algorithm described in
    https://github.com/KieranWynn/pyquaternion/blob/master/pyquaternion/quaternion.py#L201

    Args:
        rotation_matrix (Tensor): the rotation matrix to convert.

    Return:
        Tensor: the rotation in quaternion

    Shape:
        - Input: :math:`(N, 3, 4)`
        - Output: :math:`(N, 4)`

    Example:
        >>> input = torch.rand(4, 3, 4)  # Nx3x4
        >>> output = tgm.rotation_matrix_to_quaternion(input)  # Nx4
    """
    if not torch.is_tensor(rotation_matrix):
        raise TypeError("Input type is not a torch.Tensor. Got {}".format(
            type(rotation_matrix)))

    input_shape = rotation_matrix.shape
    if len(input_shape) == 2:
        rotation_matrix = rotation_matrix.unsqueeze(0)

    if len(rotation_matrix.shape) > 3:
        raise ValueError(
            "Input size must be a three dimensional tensor. Got {}".format(
                rotation_matrix.shape))
    if not rotation_matrix.shape[-2:] == (3, 4):
        raise ValueError(
            "Input size must be a N x 3 x 4  tensor. Got {}".format(
                rotation_matrix.shape))

    rmat_t = torch.transpose(rotation_matrix, 1, 2)

    mask_d2 = rmat_t[:, 2, 2] < eps

    mask_d0_d1 = rmat_t[:, 0, 0] > rmat_t[:, 1, 1]
    mask_d0_nd1 = rmat_t[:, 0, 0] < -rmat_t[:, 1, 1]

    t0 = 1 + rmat_t[:, 0, 0] - rmat_t[:, 1, 1] - rmat_t[:, 2, 2]
    q0 = torch.stack([rmat_t[:, 1, 2] - rmat_t[:, 2, 1],
                      t0, rmat_t[:, 0, 1] + rmat_t[:, 1, 0],
                      rmat_t[:, 2, 0] + rmat_t[:, 0, 2]], -1)
    t0_rep = t0.repeat(4, 1).t()

    t1 = 1 - rmat_t[:, 0, 0] + rmat_t[:, 1, 1] - rmat_t[:, 2, 2]
    q1 = torch.stack([rmat_t[:, 2, 0] - rmat_t[:, 0, 2],
                      rmat_t[:, 0, 1] + rmat_t[:, 1, 0],
                      t1, rmat_t[:, 1, 2] + rmat_t[:, 2, 1]], -1)
    t1_rep = t1.repeat(4, 1).t()

    t2 = 1 - rmat_t[:, 0, 0] - rmat_t[:, 1, 1] + rmat_t[:, 2, 2]
    q2 = torch.stack([rmat_t[:, 0, 1] - rmat_t[:, 1, 0],
                      rmat_t[:, 2, 0] + rmat_t[:, 0, 2],
                      rmat_t[:, 1, 2] + rmat_t[:, 2, 1], t2], -1)
    t2_rep = t2.repeat(4, 1).t()

    t3 = 1 + rmat_t[:, 0, 0] + rmat_t[:, 1, 1] + rmat_t[:, 2, 2]
    q3 = torch.stack([t3, rmat_t[:, 1, 2] - rmat_t[:, 2, 1],
                      rmat_t[:, 2, 0] - rmat_t[:, 0, 2],
                      rmat_t[:, 0, 1] - rmat_t[:, 1, 0]], -1)
    t3_rep = t3.repeat(4, 1).t()

    mask_c0 = mask_d2.float() * mask_d0_d1.float()
    mask_c1 = mask_d2.float() * (1 - mask_d0_d1.float())
    mask_c2 = (1 - mask_d2.float()) * mask_d0_nd1.float()
    mask_c3 = (1 - mask_d2.float()) * (1 - mask_d0_nd1.float())
    mask_c0 = mask_c0.view(-1, 1).type_as(q0)
    mask_c1 = mask_c1.view(-1, 1).type_as(q1)
    mask_c2 = mask_c2.view(-1, 1).type_as(q2)
    mask_c3 = mask_c3.view(-1, 1).type_as(q3)

    q = q0 * mask_c0 + q1 * mask_c1 + q2 * mask_c2 + q3 * mask_c3
    q /= torch.sqrt(t0_rep * mask_c0 + t1_rep * mask_c1 +  # noqa
                    t2_rep * mask_c2 + t3_rep * mask_c3)
    q *= 0.5

    if len(input_shape) == 2:
        q = q.squeeze(0)
    return q

def rot6d_to_axis_angle(x):
    batch_size = x.shape[0]

    x = x.view(-1, 3, 2)
    a1 = x[:, :, 0]
    a2 = x[:, :, 1]
    b1 = F.normalize(a1)
    b2 = F.normalize(a2 - torch.einsum('bi,bi->b', b1, a2).unsqueeze(-1) * b1)
    b3 = torch.cross(b1, b2)
    rot_mat = torch.stack((b1, b2, b3), dim=-1)  # 3x3 rotation matrix

    rot_mat = torch.cat([rot_mat, torch.zeros((batch_size, 3, 1)).cuda().float()], 2)  # 3x4 rotation matrix
    axis_angle = rotation_matrix_to_angle_axis(rot_mat).reshape(-1, 3)  # axis-angle 
    axis_angle[torch.isnan(axis_angle)] = 0.0
    return axis_angle

def rot6d_to_rotmat(x):
    """Convert 6D rotation representation to 3x3 rotation matrix.
    Based on Zhou et al., "On the Continuity of Rotation Representations in Neural Networks", CVPR 2019
    Input:
        (B,6) Batch of 6-D rotation representations
    Output:
        (B,3,3) Batch of corresponding rotation matrices
    """
    if x.shape[-1] == 6:
        batch_size = x.shape[0]
        if len(x.shape) == 3:
            num = x.shape[1]
            x = rearrange(x, 'b n d -> (b n) d', d=6)
        else:
            num = 1
        x = rearrange(x, 'b (k l) -> b k l', k=3, l=2)
        # x = x.view(-1,3,2)
        a1 = x[:, :, 0]
        a2 = x[:, :, 1]
        b1 = F.normalize(a1)
        b2 = F.normalize(a2 - torch.einsum('bi,bi->b', b1, a2).unsqueeze(-1) * b1)
        b3 = torch.cross(b1, b2, dim=-1)

        mat = torch.stack((b1, b2, b3), dim=-1)
        if num > 1:
            mat = rearrange(mat, '(b n) h w-> b n h w', b=batch_size, n=num, h=3, w=3)
    else:
        x = x.view(-1,3,2)
        a1 = x[:, :, 0]
        a2 = x[:, :, 1]
        b1 = F.normalize(a1)
        b2 = F.normalize(a2 - torch.einsum('bi,bi->b', b1, a2).unsqueeze(-1) * b1)
        b3 = torch.cross(b1, b2, dim=-1)
        mat = torch.stack((b1, b2, b3), dim=-1)
    return mat

def batch_rodrigues(theta):
    """Convert axis-angle representation to rotation matrix.
    Args:
        theta: size = [B, 3]
    Returns:
        Rotation matrix corresponding to the quaternion -- size = [B, 3, 3]
    """
    l1norm = torch.norm(theta + 1e-8, p = 2, dim = 1)
    angle = torch.unsqueeze(l1norm, -1)
    normalized = torch.div(theta, angle)
    angle = angle * 0.5
    v_cos = torch.cos(angle)
    v_sin = torch.sin(angle)
    quat = torch.cat([v_cos, v_sin * normalized], dim = 1)
    return quat_to_rotmat(quat)

def quat_to_rotmat(quat):
    """Convert quaternion coefficients to rotation matrix.
    Args:
        quat: size = [B, 4] 4 <===>(w, x, y, z)
    Returns:
        Rotation matrix corresponding to the quaternion -- size = [B, 3, 3]
    """ 
    norm_quat = quat
    norm_quat = norm_quat/norm_quat.norm(p=2, dim=1, keepdim=True)
    w, x, y, z = norm_quat[:,0], norm_quat[:,1], norm_quat[:,2], norm_quat[:,3]

    B = quat.size(0)

    w2, x2, y2, z2 = w.pow(2), x.pow(2), y.pow(2), z.pow(2)
    wx, wy, wz = w*x, w*y, w*z
    xy, xz, yz = x*y, x*z, y*z

    rotMat = torch.stack([w2 + x2 - y2 - z2, 2*xy - 2*wz, 2*wy + 2*xz,
                          2*wz + 2*xy, w2 - x2 + y2 - z2, 2*yz - 2*wx,
                          2*xz - 2*wy, 2*wx + 2*yz, w2 - x2 - y2 + z2], dim=1).view(B, 3, 3)
    return rotMat   

def sample_joint_features(img_feat, joint_xy):
    height, width = img_feat.shape[2:]
    x = joint_xy[:, :, 0] / (width - 1) * 2 - 1
    y = joint_xy[:, :, 1] / (height - 1) * 2 - 1
    grid = torch.stack((x, y), 2)[:, :, None, :]
    img_feat = F.grid_sample(img_feat, grid, align_corners=True)[:, :, :, 0]  # batch_size, channel_dim, joint_num
    img_feat = img_feat.permute(0, 2, 1).contiguous()  # batch_size, joint_num, channel_dim
    return img_feat


def soft_argmax_2d(heatmap2d):
    batch_size = heatmap2d.shape[0]
    height, width = heatmap2d.shape[2:]
    heatmap2d = heatmap2d.reshape((batch_size, -1, height * width))
    heatmap2d = F.softmax(heatmap2d, 2)
    heatmap2d = heatmap2d.reshape((batch_size, -1, height, width))

    accu_x = heatmap2d.sum(dim=(2))
    accu_y = heatmap2d.sum(dim=(3))

    accu_x = accu_x * torch.arange(width).float().cuda()[None, None, :]
    accu_y = accu_y * torch.arange(height).float().cuda()[None, None, :]

    accu_x = accu_x.sum(dim=2, keepdim=True)
    accu_y = accu_y.sum(dim=2, keepdim=True)

    coord_out = torch.cat((accu_x, accu_y), dim=2)
    return coord_out


def soft_argmax_3d(heatmap3d):
    batch_size = heatmap3d.shape[0]
    depth, height, width = heatmap3d.shape[2:]
    heatmap3d = heatmap3d.reshape((batch_size, -1, depth * height * width))
    heatmap3d = F.softmax(heatmap3d, 2)
    heatmap3d = heatmap3d.reshape((batch_size, -1, depth, height, width))

    accu_x = heatmap3d.sum(dim=(2, 3))
    accu_y = heatmap3d.sum(dim=(2, 4))
    accu_z = heatmap3d.sum(dim=(3, 4))

    accu_x = accu_x * torch.arange(width).float().cuda()[None, None, :]
    accu_y = accu_y * torch.arange(height).float().cuda()[None, None, :]
    accu_z = accu_z * torch.arange(depth).float().cuda()[None, None, :]

    accu_x = accu_x.sum(dim=2, keepdim=True)
    accu_y = accu_y.sum(dim=2, keepdim=True)
    accu_z = accu_z.sum(dim=2, keepdim=True)

    coord_out = torch.cat((accu_x, accu_y, accu_z), dim=2)
    return coord_out