visualize/ca_body/utils/quaternion.py

"""
Copyright (c) Meta Platforms, Inc. and affiliates.
All rights reserved.
This source code is licensed under the license found in the
LICENSE file in the root directory of this source tree.
"""

import numpy as np
import torch as th

import torch.nn as nn
import torch.nn.functional as F


class Quaternion:
    """Torch Tensor based Quaternion class"""

    @staticmethod
    def identity(dtype=th.double):
        """
        Create identity quaternion
        """
        return th.tensor([0.0, 0.0, 0.0, 1.0], dtype=dtype)

    @staticmethod
    def mul(q, r):
        """
        mul two quaternions, expects those to be double tesnors of length 4
        """
        return th.stack(
            [
                (q * th.tensor([1.0, 1.0, -1.0, 1.0], dtype=q.dtype)).dot(r[[3, 2, 1, 0]]),
                (q * th.tensor([-1.0, 1.0, 1.0, 1.0], dtype=q.dtype)).dot(r[[2, 3, 0, 1]]),
                (q * th.tensor([1.0, -1.0, 1.0, 1.0], dtype=q.dtype)).dot(r[[1, 0, 3, 2]]),
                (q * th.tensor([-1.0, -1.0, -1.0, 1.0], dtype=q.dtype)).dot(r[[0, 1, 2, 3]]),
            ]
        )

    @staticmethod
    def rot(q, v):
        """
        Rotate 3d-vector v given with quaternion q
        """
        axis = q[:3]
        av = th.cross(axis, v)
        aav = th.cross(axis, av)
        return v + 2 * (av * q[3] + aav)

    @staticmethod
    def invert(q):
        """
        Get the inverse of quaternion q
        """
        return q * th.tensor([-1.0, -1.0, -1.0, 1.0], dtype=q.dtype) * (1.0 / q.dot(q))

    @staticmethod
    def fromAxisAngle(axis, angle):
        """
        Generate a quaternion representing a rotation around axis by angle
        """
        s = th.sin(angle * 0.5)
        c = th.cos(angle * 0.5).view([1])
        return th.cat((axis * s, c), 0)

    @staticmethod
    def fromXYZ(angles):
        """
        Generate a quaternion representing a rotation defined by a XYZ-Euler
        rotation.
        This is faster than creating three separate quaternions and muling
        them.
        """
        rc = th.cos(
            angles * th.tensor([-0.5, 0.5, 0.5], dtype=angles.dtype, device=angles.device)
        )
        rs = th.sin(
            angles * th.tensor([-0.5, 0.5, 0.5], dtype=angles.dtype, device=angles.device)
        )

        return th.stack(
            [
                -rs[0] * rc[1] * rc[2] - rc[0] * rs[1] * rs[2],
                rc[0] * rs[1] * rc[2] - rs[0] * rc[1] * rs[2],
                rc[0] * rc[1] * rs[2] + rs[0] * rs[1] * rc[2],
                rc[0] * rc[1] * rc[2] - rs[0] * rs[1] * rs[2],
            ]
        )

    @staticmethod
    def toMatrix(q):
        """
        Convert quaternion q to 3x3 rotation matrix
        """
        result = th.empty([3, 3], dtype=q.dtype)

        tx = q[0] * 2.0
        ty = q[1] * 2.0
        tz = q[2] * 2.0
        twx = tx * q[3]
        twy = ty * q[3]
        twz = tz * q[3]
        txx = tx * q[0]
        txy = ty * q[0]
        txz = tz * q[0]
        tyy = ty * q[1]
        tyz = tz * q[1]
        tzz = tz * q[2]

        result[0, 0] = 1.0 - (tyy + tzz)
        result[0, 1] = txy - twz
        result[0, 2] = txz + twy
        result[1, 0] = txy + twz
        result[1, 1] = 1.0 - (txx + tzz)
        result[1, 2] = tyz - twx
        result[2, 0] = txz - twy
        result[2, 1] = tyz + twx
        result[2, 2] = 1.0 - (txx + tyy)

        return result

    @staticmethod
    def toMatrixBatch(q):
        tx = q[..., 0] * 2.0
        ty = q[..., 1] * 2.0
        tz = q[..., 2] * 2.0
        twx = tx * q[..., 3]
        twy = ty * q[..., 3]
        twz = tz * q[..., 3]
        txx = tx * q[..., 0]
        txy = ty * q[..., 0]
        txz = tz * q[..., 0]
        tyy = ty * q[..., 1]
        tyz = tz * q[..., 1]
        tzz = tz * q[..., 2]

        return th.stack(
            (
                th.stack((1.0 - (tyy + tzz), txy + twz, txz - twy), dim=2),
                th.stack((txy - twz, 1.0 - (txx + tzz), tyz + twx), dim=2),
                th.stack((txz + twy, tyz - twx, 1.0 - (txx + tyy)), dim=2),
            ),
            dim=3,
        )

    @staticmethod
    def toMatrixBatchDim1(q):
        tx = q[..., 0] * 2.0
        ty = q[..., 1] * 2.0
        tz = q[..., 2] * 2.0
        twx = tx * q[..., 3]
        twy = ty * q[..., 3]
        twz = tz * q[..., 3]
        txx = tx * q[..., 0]
        txy = ty * q[..., 0]
        txz = tz * q[..., 0]
        tyy = ty * q[..., 1]
        tyz = tz * q[..., 1]
        tzz = tz * q[..., 2]

        return th.stack(
            (
                th.stack((1.0 - (tyy + tzz), txy + twz, txz - twy), dim=1),
                th.stack((txy - twz, 1.0 - (txx + tzz), tyz + twx), dim=1),
                th.stack((txz + twy, tyz - twx, 1.0 - (txx + tyy)), dim=1),
            ),
            dim=2,
        )


    @staticmethod
    def batchMul(q, r):
        """
        mul two quaternions, expects those to be double tesnors of length 4

        Args:
            q: N x K x 4 quaternions
            r: N x K x 4 quaternions

        Returns:
            N x K x 4 multiplied quaternions
        """
        return th.stack(
            [
                th.sum(
                    th.mul(
                        th.mul(
                            q,
                            th.tensor(
                                [[[1.0, 1.0, -1.0, 1.0]]],
                                dtype=q.dtype,
                                device=q.device,
                            ),
                        ),
                        r[:, :, (3, 2, 1, 0)],
                    ),
                    dim=-1,
                ),
                th.sum(
                    th.mul(
                        th.mul(
                            q,
                            th.tensor(
                                [[[-1.0, 1.0, 1.0, 1.0]]],
                                dtype=q.dtype,
                                device=q.device,
                            ),
                        ),
                        r[:, :, (2, 3, 0, 1)],
                    ),
                    dim=-1,
                ),
                th.sum(
                    th.mul(
                        th.mul(
                            q,
                            th.tensor(
                                [[[1.0, -1.0, 1.0, 1.0]]],
                                dtype=q.dtype,
                                device=q.device,
                            ),
                        ),
                        r[:, :, (1, 0, 3, 2)],
                    ),
                    dim=-1,
                ),
                th.sum(
                    th.mul(
                        th.mul(
                            q,
                            th.tensor(
                                [[[-1.0, -1.0, -1.0, 1.0]]],
                                dtype=q.dtype,
                                device=q.device,
                            ),
                        ),
                        r[:, :, (0, 1, 2, 3)],
                    ),
                    dim=-1,
                ),
            ],
            dim=2,
        )

    @staticmethod
    def batchRot(q, v):
        """
        Rotate 3d-vector v given with quaternion q

        Args:
            q: N x K x 4 quaternions
            v: N x K x 3 vectors

        Returns:
            N x K x 3 rotated vectors
        """
        av = th.cross(q[:, :, :3], v, dim=2)
        aav = th.cross(q[:, :, :3], av, dim=2)
        return th.add(v, 2 * th.add(th.mul(av, q[:, :, 3].unsqueeze(2)), aav))

    
    @staticmethod
    def batchInvert(q):
        """
        Get the inverse of quaternion q

        Args:
            q: N x K x 4 quaternions

        Returns:
            N x K x 4 inverted quaternions
        """
        return (
            q
            * th.tensor([-1.0, -1.0, -1.0, 1.0], dtype=q.dtype, device=q.device)
            * (th.reciprocal(th.sum(q * q, dim=2).unsqueeze(2)))
        )

    @staticmethod
    def batchFromXYZ(r):
        """
        Generate a quaternion representing a rotation defined by a XYZ-Euler
        rotation.

        Args:
            r: N x K x 3 rotation vectors

        Returns:
            N x K x 4 quaternions
        """
        rm = r * th.tensor([[[-0.5, 0.5, 0.5]]], dtype=r.dtype, device=r.device)
        rc = th.cos(rm)
        rs = th.sin(rm)

        return th.stack(
            [
                th.sub(
                    th.mul(th.neg(rs[:, :, 0]), th.mul(rc[:, :, 1], rc[:, :, 2])),
                    th.mul(rc[:, :, 0], th.mul(rs[:, :, 1], rs[:, :, 2])),
                ),
                th.sub(
                    th.mul(rc[:, :, 0], th.mul(rs[:, :, 1], rc[:, :, 2])),
                    th.mul(rs[:, :, 0], th.mul(rc[:, :, 1], rs[:, :, 2])),
                ),
                th.add(
                    th.mul(rc[:, :, 0], th.mul(rc[:, :, 1], rs[:, :, 2])),
                    th.mul(rs[:, :, 0], th.mul(rs[:, :, 1], rc[:, :, 2])),
                ),
                th.sub(
                    th.mul(rc[:, :, 0], th.mul(rc[:, :, 1], rc[:, :, 2])),
                    th.mul(rs[:, :, 0], th.mul(rs[:, :, 1], rs[:, :, 2])),
                ),
            ],
            dim=2,
        )

    @staticmethod
    def batchMatrixFromXYZ(r):
        """
        Generate a matrix representing a rotation defined by a XYZ-Euler
        rotation.

        Args:
            r: N x 3 rotation vectors

        Returns:
            N x 3 x 3 rotation matrices
        """
        rc = th.cos(r)
        rs = th.sin(r)
        cx = rc[:, 0]
        cy = rc[:, 1]
        cz = rc[:, 2]
        sx = rs[:, 0]
        sy = rs[:, 1]
        sz = rs[:, 2]

        result = th.stack(
            (
                cy * cz,
                -cx * sz + sx * sy * cz,
                sx * sz + cx * sy * cz,
                cy * sz,
                cx * cz + sx * sy * sz,
                -sx * cz + cx * sy * sz,
                -sy,
                sx * cy,
                cx * cy,
            ),
            dim=1,
        ).view(-1, 3, 3)
        return result

    @staticmethod
    def batchQuatFromMatrix(m):
        """
        :param m: B*3*3
        :return: B*4, order xyzw
        """
        assert len(m.shape) == 3
        b, j, k = m.shape
        assert j == 3
        assert k == 3
        result = th.zeros((b, 4), dtype=th.float32).to(m.device)
        S = th.zeros((b,), dtype=th.float32).to(m.device)

        m00 = m[:, 0, 0]
        m01 = m[:, 0, 1]
        m02 = m[:, 0, 2]
        m10 = m[:, 1, 0]
        m11 = m[:, 1, 1]
        m12 = m[:, 1, 2]
        m20 = m[:, 2, 0]
        m21 = m[:, 2, 1]
        m22 = m[:, 2, 2]

        tr = m00 + m11 + m22
        flag = tr > 0
        S[flag] = 2 * th.sqrt(1 + tr[flag])
        result[flag, 0] = (m21 - m12)[flag] / S[flag]
        result[flag, 1] = (m02 - m20)[flag] / S[flag]
        result[flag, 2] = (m10 - m01)[flag] / S[flag]
        result[flag, 3] = 0.25 * S[flag]

        flag = ~flag & (m00 > m11) & (m00 > m22)
        S[flag] = 2 * th.sqrt(1.0 + m00[flag] - m11[flag] - m22[flag])
        result[flag, 0] = 0.25 * S[flag]
        result[flag, 1] = (m01 + m10)[flag] / S[flag]
        result[flag, 2] = (m02 + m20)[flag] / S[flag]
        result[flag, 3] = (m21 - m12)[flag] / S[flag]

        flag = ~flag & (m11 > m22)
        S[flag] = 2 * th.sqrt(1.0 + m11[flag] - m00[flag] - m22[flag])
        result[flag, 0] = (m01 + m10)[flag] / S[flag]
        result[flag, 1] = 0.25 * S[flag]
        result[flag, 2] = (m12 + m21)[flag] / S[flag]
        result[flag, 3] = (m02 - m20)[flag] / S[flag]

        flag = ~flag
        S[flag] = 2 * th.sqrt(1.0 + m22[flag] - m00[flag] - m11[flag])
        result[flag, 0] = (m02 + m20)[flag] / S[flag]
        result[flag, 1] = (m12 + m21)[flag] / S[flag]
        result[flag, 2] = 0.25 * S[flag]
        result[flag, 3] = (m10 - m01)[flag] / S[flag]

        return result


class RodriguesVecBatch(nn.Module):
    def __init__(self):
        super(RodriguesVecBatch, self).__init__()
        self.register_buffer("eye", (th.eye(3)))
        self.register_buffer(
            "zero",
            (
                th.zeros(
                    1,
                )
            ),
        )
        # mat = th.zeros((nbat,3,3),dtype=th.float32,device=r.device,requires_grad=True)

    def forward(
        self, v0, v1
    ):  # assuming v0 and v1 are already normalized, compute matrix aligning v0 to v1
        nbat = v0.size(0)
        cosn = (v0 * v1).sum(dim=1, keepdim=True).unsqueeze(2)
        # r = v0.cross(v1,dim=1)
        r = v1.cross(v0, dim=1)
        sinn = r.pow(2).sum(1, keepdim=True).sqrt().unsqueeze(2)
        rn = r.unsqueeze(2) / (sinn + 1e-10)
        R = cosn * self.eye.unsqueeze(0).expand(nbat, 3, 3)
        R = R + (1.0 - cosn) * rn.bmm(rn.permute(0, 2, 1))
        R[:, 0, 1] = R[:, 0, 1] + rn[:, 2, 0] * sinn[:, 0, 0]
        R[:, 1, 0] = R[:, 0, 1] - rn[:, 2, 0] * sinn[:, 0, 0]
        R[:, 0, 2] = R[:, 0, 2] - rn[:, 1, 0] * sinn[:, 0, 0]
        R[:, 2, 0] = R[:, 2, 0] + rn[:, 1, 0] * sinn[:, 0, 0]
        R[:, 1, 2] = R[:, 1, 2] + rn[:, 0, 0] * sinn[:, 0, 0]
        R[:, 2, 1] = R[:, 2, 1] - rn[:, 0, 0] * sinn[:, 0, 0]
        return R


class RodriguesBatch(nn.Module):
    def __init__(self):
        super(RodriguesBatch, self).__init__()
        self.register_buffer("eye", (th.eye(3)))
        self.register_buffer(
            "zero",
            (
                th.zeros(
                    1,
                )
            ),
        )

    def forward(self, r):
        # pdb.set_trace()
        nbat = r.size(0)
        n = ((r * r).sum(dim=1, keepdim=True) + 1e-10).sqrt()
        rn = th.div(r, n).unsqueeze(2)

        cosn = th.cos(n).unsqueeze(2)
        sinn = th.sin(n).unsqueeze(2)
        R = cosn * self.eye.unsqueeze(0).expand(nbat, 3, 3)
        R = R + (1.0 - cosn) * rn.bmm(rn.permute(0, 2, 1))

        R[:, 0, 1] = R[:, 0, 1] + rn[:, 2, 0] * sinn[:, 0, 0]
        R[:, 1, 0] = R[:, 0, 1] - rn[:, 2, 0] * sinn[:, 0, 0]
        R[:, 0, 2] = R[:, 0, 2] - rn[:, 1, 0] * sinn[:, 0, 0]
        R[:, 2, 0] = R[:, 2, 0] + rn[:, 1, 0] * sinn[:, 0, 0]
        R[:, 1, 2] = R[:, 1, 2] + rn[:, 0, 0] * sinn[:, 0, 0]
        R[:, 2, 1] = R[:, 2, 1] - rn[:, 0, 0] * sinn[:, 0, 0]
        return R


class NormalComputer(nn.Module):
    def __init__(self, height, width, maskin=None):
        super(NormalComputer, self).__init__()
        # self.register_buffer('eye', (th.eye(3)))
        # self.register_buffer('zero', (th.zeros(1,)))

        patchttnum = 5  # neighbor + self
        patchmatch_uvpos = np.zeros((height, width, patchttnum, 2), dtype=np.int32)
        vec_standuv = (
            np.indices((height, width))
            .swapaxes(0, 2)
            .swapaxes(0, 1)
            .astype(np.int32)
            .reshape(height, width, 1, 2)
        )
        patchmatch_uvpos = patchmatch_uvpos + vec_standuv
        localpatchcoord = np.zeros((patchttnum, 2), dtype=np.int32)
        localpatchcoord = np.array([[-1, 0], [0, 1], [1, 0], [0, -1], [0, 0]]).astype(np.int32)

        patchmatch_uvpos = patchmatch_uvpos + localpatchcoord.reshape(1, 1, patchttnum, 2)
        patchmatch_uvpos[..., 0] = np.clip(patchmatch_uvpos[..., 0], 0, height - 1)
        patchmatch_uvpos[..., 1] = np.clip(patchmatch_uvpos[..., 1], 0, width - 1)

        # geoemtry mask , apply simiilar to texture mask
        # mesh_mask_int = mesh_mask.reshape(height,width).astype(np.int32)
        if maskin is None:
            maskin = np.ones((height, width), dtype=np.int32)
        mesh_mask_int = maskin.reshape(height, width).astype(
            np.int32
        )  # using all pixel valid mask; can use a tailored mask
        patchmatch_mask = mesh_mask_int[patchmatch_uvpos[..., 0], patchmatch_uvpos[..., 1]].reshape(
            height, width, patchttnum, 1
        )
        patch_indicemap = patchmatch_uvpos * patchmatch_mask + (1 - patchmatch_mask) * vec_standuv

        tensor_patch_geoindicemap = th.from_numpy(patch_indicemap).long()
        tensor_patch_geoindicemap1d = (
            tensor_patch_geoindicemap[..., 0] * width + tensor_patch_geoindicemap[..., 1]
        )

        self.register_buffer("tensor_patch_geoindicemap1d", tensor_patch_geoindicemap1d)
        # tensor_patchmatch_uvpos = th.from_numpy(patchmatch_uvpos).long()
        # tensor_vec_standuv = th.from_numpy(vec_standuv).long()

    def forward(self, t_georecon):  # in: N 3 H W
        # pdb.set_trace()
        # Intergration switch it to index_select
        # geometry_in = index_selection_nd(
        #     t_georecon.view(t_georecon.size(0), t_georecon.size(1), -1),
        #     self.tensor_patch_geoindicemap1d,
        #     2,
        # ).permute(0, 2, 3, 4, 1)

        geometry_in = th.index_select(
            t_georecon.view(t_georecon.size(0), t_georecon.size(1), -1),
            self.tensor_patch_geoindicemap1d,
            2,
        ).permute(0, 2, 3, 4, 1)

        normal = (geometry_in[..., 0, :] - geometry_in[..., 4, :]).cross(
            geometry_in[..., 1, :] - geometry_in[..., 4, :], dim=3
        )
        normal = normal + (geometry_in[..., 1, :] - geometry_in[..., 4, :]).cross(
            geometry_in[..., 2, :] - geometry_in[..., 4, :], dim=3
        )
        normal = normal + (geometry_in[..., 2, :] - geometry_in[..., 4, :]).cross(
            geometry_in[..., 3, :] - geometry_in[..., 4, :], dim=3
        )
        normal = normal + (geometry_in[..., 3, :] - geometry_in[..., 4, :]).cross(
            geometry_in[..., 0, :] - geometry_in[..., 4, :], dim=3
        )
        normal = normal / th.clamp(normal.pow(2).sum(3, keepdim=True).sqrt(), min=1e-6)
        return normal.permute(0, 3, 1, 2)


def pointcloud_rigid_registration(src_pointcloud, dst_pointcloud, reduce_loss: bool = True):
    """
    Calculate RT and residual L2 loss for two pointclouds
    :param src_pointcloud: x (b, v, 3)
    :param dst_pointcloud: y (b, v, 3)
    :return: loss, R, t  s.t. ||Rx+t-y||_2^2 minimal.
    """
    if len(src_pointcloud.shape) == 2:
        src_pointcloud = src_pointcloud.unsqueeze(0)
    if len(dst_pointcloud.shape) == 2:
        dst_pointcloud = dst_pointcloud.unsqueeze(0)
    bn = src_pointcloud.shape[0]

    assert src_pointcloud.shape == dst_pointcloud.shape
    assert src_pointcloud.shape[2] == 3

    X = src_pointcloud - src_pointcloud.mean(dim=1, keepdim=True)
    Y = dst_pointcloud - dst_pointcloud.mean(dim=1, keepdim=True)

    XYT = th.einsum("nji,njk->nik", X, Y)
    muX = src_pointcloud.mean(dim=1)
    muY = dst_pointcloud.mean(dim=1)

    R = th.zeros((bn, 3, 3), dtype=src_pointcloud.dtype).to(src_pointcloud.device)
    t = th.zeros((bn, 1, 3), dtype=src_pointcloud.dtype).to(src_pointcloud.device)
    loss = th.zeros((bn,), dtype=src_pointcloud.dtype).to(src_pointcloud.device)

    for i in range(bn):
        u_, s_, v_ = th.svd(XYT[i, :, :])
        detvut = th.det(v_.mm(u_.t()))
        diag_m = th.ones_like(s_)
        diag_m[-1] = detvut

        r_ = v_.mm(th.diag(diag_m)).mm(u_.t())
        t_ = muY[i, :] - r_.mm(muX[i, :, None])[:, 0]

        R[i, :, :] = r_
        t[i, 0, :] = t_
        loss[i] = (th.einsum("ij,nj->ni", r_, X[i]) - Y[i]).pow(2).sum(1).mean(0)

    loss = loss.mean(0) if reduce_loss else loss
    return loss, R, t


def pointcloud_rigid_registration_balanced(src_pointcloud, dst_pointcloud, weight):
    """
    Calculate RT and residual L2 loss for two pointclouds
    :param src_pointcloud: x (b, v, 3)
    :param dst_pointcloud: y (b, v, 3)
    :param weight:  (v, ), duplication of vertices
    :return: loss, R, t  s.t. ||w(Rx+t-y)||_2^2 minimal.
    """
    if len(src_pointcloud.shape) == 2:
        src_pointcloud = src_pointcloud.unsqueeze(0)
    if len(dst_pointcloud.shape) == 2:
        dst_pointcloud = dst_pointcloud.unsqueeze(0)
    bn = src_pointcloud.shape[0]

    assert src_pointcloud.shape == dst_pointcloud.shape
    assert src_pointcloud.shape[2] == 3
    assert src_pointcloud.shape[1] == weight.shape[0]
    assert len(weight.shape) == 1
    w = weight[None, :, None]

    def s1(a):
        return a.sum(dim=1, keepdim=True)

    w2 = w.pow(2)
    sw2 = s1(w2)
    X = src_pointcloud
    Y = dst_pointcloud

    wXYT = th.einsum("nji,njk->nik", w2 * (sw2 - w2) * X, Y)
    U, s, V = batch_svd(wXYT)
    UT = U.permute(0, 2, 1).contiguous()
    det = batch_det(V.bmm(UT))
    diag = th.ones_like(s).to(s.device)
    diag[:, -1] = det

    R = V.bmm(batch_diag(diag)).bmm(UT)
    RX = th.einsum("bij,bnj->bni", R, X)
    t = th.sum(w * (Y - RX), dim=1, keepdim=True) / sw2
    loss = w * (RX + t - Y)
    loss = F.mse_loss(loss, th.zeros_like(loss)) * 3

    return loss, R, t


def batch_dot(x, y):
    assert x.shape == y.shape
    assert len(x.shape) == 2
    return th.einsum("ni,ni->n", x, y)


def batch_svd(x):
    assert len(x.shape) == 3
    bn, m, n = x.shape
    U = th.zeros((bn, m, m), dtype=th.float32).to(x.device)
    s = th.zeros((bn, min(n, m)), dtype=th.float32).to(x.device)
    V = th.zeros((bn, n, n), dtype=th.float32).to(x.device)
    for i in range(bn):
        u_, s_, v_ = th.svd(x[i, :, :])
        U[i] = u_
        s[i] = s_
        V[i] = v_
    return U, s, V


def batch_diag(x):
    if len(x.shape) == 2:
        bn, n = x.shape
        res = th.zeros((bn, n, n), dtype=th.float32).to(x.device)
        res[:, range(n), range(n)] = x
        return res
    elif len(x.shape) == 3:
        assert x.shape[1] == x.shape[2]
        n = x.shape[1]
        return x[:, range(n), range(n)]
    else:
        raise ValueError("dim of batch_diag should be 2 or 3")


def batch_det(x):
    assert len(x.shape) == 3
    assert x.shape[1] == x.shape[2]
    bn, _, _ = x.shape
    res = th.zeros((bn,), dtype=th.float32).to(x.device)
    for i in range(bn):
        res[i] = th.det(x[i])
    return res