kornia--kornia/tests/geometry/test_conversions.py

# LICENSE HEADER MANAGED BY add-license-header
#
# Copyright 2018 Kornia Team
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#

import sys
from functools import partial

import numpy as np
import pytest
import torch

import kornia
from kornia.core._compat import torch_version
from kornia.core.ops import eye_like
from kornia.geometry.conversions import (
    ARKitQTVecs_to_ColmapQTVecs,
    Rt_to_matrix4x4,
    axis_angle_to_rotation_matrix,
    camtoworld_graphics_to_vision_4x4,
    camtoworld_graphics_to_vision_Rt,
    camtoworld_to_worldtocam_Rt,
    camtoworld_vision_to_graphics_4x4,
    camtoworld_vision_to_graphics_Rt,
    euler_from_quaternion,
    matrix4x4_to_Rt,
    quaternion_from_euler,
    worldtocam_to_camtoworld_Rt,
)
from kornia.geometry.quaternion import Quaternion

from testing.base import BaseTester, assert_close


@pytest.fixture()
def atol(device, dtype):
    """Lower tolerance for cuda-float16 only."""
    if "cuda" in device.type and dtype == torch.float16:
        return 1.0e-3
    return 1.0e-4


@pytest.fixture()
def rtol(device, dtype):
    """Lower tolerance for cuda-float16 only."""
    if "cuda" in device.type and dtype == torch.float16:
        return 1.0e-3
    return 1.0e-4


class TestAngleAxisToQuaternion(BaseTester):
    # based on:
    # https://github.com/ceres-solver/ceres-solver/blob/master/internal/ceres/rotation_test.cc#L271

    def test_smoke(self, device, dtype):
        axis_angle = torch.zeros(3, dtype=dtype, device=device)
        quaternion = kornia.geometry.conversions.axis_angle_to_quaternion(axis_angle)
        assert quaternion.shape == (4,)

    @pytest.mark.parametrize("batch_size", (1, 3, 8))
    def test_smoke_batch(self, batch_size, device, dtype):
        axis_angle = torch.zeros(batch_size, 3, device=device, dtype=dtype)
        quaternion = kornia.geometry.conversions.axis_angle_to_quaternion(axis_angle)
        assert quaternion.shape == (batch_size, 4)

    def test_zero_angle(self, device, dtype, atol, rtol):
        axis_angle = torch.tensor((0.0, 0.0, 0.0), device=device, dtype=dtype)
        expected = torch.tensor((1.0, 0.0, 0.0, 0.0), device=device, dtype=dtype)
        quaternion = kornia.geometry.conversions.axis_angle_to_quaternion(axis_angle)
        self.assert_close(quaternion, expected, atol=atol, rtol=rtol)

    def test_small_angle_x(self, device, dtype, atol, rtol):
        theta = 1.0e-2
        axis_angle = torch.tensor((theta, 0.0, 0.0), device=device, dtype=dtype)
        expected = torch.tensor((np.cos(theta / 2.0), np.sin(theta / 2.0), 0.0, 0.0), device=device, dtype=dtype)
        quaternion = kornia.geometry.conversions.axis_angle_to_quaternion(axis_angle)
        self.assert_close(quaternion, expected, atol=atol, rtol=rtol)

    def test_small_angle_y(self, device, dtype, atol, rtol):
        theta = 1.0e-2
        axis_angle = torch.tensor((0.0, theta, 0.0), device=device, dtype=dtype)
        expected = torch.tensor((np.cos(theta / 2.0), 0.0, np.sin(theta / 2.0), 0.0), device=device, dtype=dtype)
        quaternion = kornia.geometry.conversions.axis_angle_to_quaternion(axis_angle)
        self.assert_close(quaternion, expected, atol=atol, rtol=rtol)

    def test_small_angle_z(self, device, dtype, atol, rtol):
        theta = 1.0e-2
        axis_angle = torch.tensor((0.0, 0.0, theta), device=device, dtype=dtype)
        expected = torch.tensor((np.cos(theta / 2.0), 0.0, 0.0, np.sin(theta / 2.0)), device=device, dtype=dtype)
        quaternion = kornia.geometry.conversions.axis_angle_to_quaternion(axis_angle)
        self.assert_close(quaternion, expected, atol=atol, rtol=rtol)

    def test_x_rotation(self, device, dtype, atol, rtol):
        half_sqrt2 = 0.5 * np.sqrt(2.0)
        axis_angle = torch.tensor((kornia.pi / 2.0, 0.0, 0.0), device=device, dtype=dtype)
        expected = torch.tensor((half_sqrt2, half_sqrt2, 0.0, 0.0), device=device, dtype=dtype)
        quaternion = kornia.geometry.conversions.axis_angle_to_quaternion(axis_angle)
        self.assert_close(quaternion, expected, atol=atol, rtol=rtol)

    def test_y_rotation(self, device, dtype, atol, rtol):
        half_sqrt2 = 0.5 * np.sqrt(2.0)
        axis_angle = torch.tensor((0.0, kornia.pi / 2.0, 0.0), device=device, dtype=dtype)
        expected = torch.tensor((half_sqrt2, 0.0, half_sqrt2, 0.0), device=device, dtype=dtype)
        quaternion = kornia.geometry.conversions.axis_angle_to_quaternion(axis_angle)
        self.assert_close(quaternion, expected, atol=atol, rtol=rtol)

    def test_z_rotation(self, device, dtype, atol, rtol):
        half_sqrt2 = 0.5 * np.sqrt(2.0)
        axis_angle = torch.tensor((0.0, 0.0, kornia.pi / 2.0), device=device, dtype=dtype)
        expected = torch.tensor((half_sqrt2, 0.0, 0.0, half_sqrt2), device=device, dtype=dtype)
        quaternion = kornia.geometry.conversions.axis_angle_to_quaternion(axis_angle)
        self.assert_close(quaternion, expected, atol=atol, rtol=rtol)

    def test_gradcheck(self, device):
        dtype = torch.float64
        eps = torch.finfo(dtype).eps
        axis_angle = torch.tensor((0.0, 0.0, 0.0), device=device, dtype=dtype) + eps
        # evaluate function gradient
        self.gradcheck(partial(kornia.geometry.conversions.axis_angle_to_quaternion), (axis_angle,))


class TestQuaternionToAngleAxis(BaseTester):
    def test_smoke(self, device, dtype):
        quaternion = torch.zeros(4, device=device, dtype=dtype)
        axis_angle = kornia.geometry.conversions.quaternion_to_axis_angle(quaternion)
        assert axis_angle.shape == (3,)

    @pytest.mark.parametrize("batch_size", (1, 3, 8))
    def test_smoke_batch(self, batch_size, device, dtype):
        quaternion = torch.zeros(batch_size, 4, device=device, dtype=dtype)
        axis_angle = kornia.geometry.conversions.quaternion_to_axis_angle(quaternion)
        assert axis_angle.shape == (batch_size, 3)

    def test_unit_quaternion(self, device, dtype, atol, rtol):
        quaternion = torch.tensor((1.0, 0.0, 0.0, 0.0), device=device, dtype=dtype)
        expected = torch.tensor((0.0, 0.0, 0.0), device=device, dtype=dtype)
        axis_angle = kornia.geometry.conversions.quaternion_to_axis_angle(quaternion)
        self.assert_close(axis_angle, expected, atol=atol, rtol=rtol)

    def test_x_rotation(self, device, dtype, atol, rtol):
        quaternion = torch.tensor((0.0, 1.0, 0.0, 0.0), device=device, dtype=dtype)
        expected = torch.tensor((kornia.pi, 0.0, 0.0), device=device, dtype=dtype)
        axis_angle = kornia.geometry.conversions.quaternion_to_axis_angle(quaternion)
        self.assert_close(axis_angle, expected, atol=atol, rtol=rtol)

    def test_y_rotation(self, device, dtype, atol, rtol):
        quaternion = torch.tensor((0.0, 0.0, 1.0, 0.0), device=device, dtype=dtype)
        expected = torch.tensor((0.0, kornia.pi, 0.0), device=device, dtype=dtype)
        axis_angle = kornia.geometry.conversions.quaternion_to_axis_angle(quaternion)
        self.assert_close(axis_angle, expected, atol=atol, rtol=rtol)

    def test_z_rotation(self, device, dtype, atol, rtol):
        quaternion = torch.tensor((np.sqrt(3.0) / 2.0, 0.0, 0.0, 0.5), device=device, dtype=dtype)
        expected = torch.tensor((0.0, 0.0, kornia.pi / 3.0), device=device, dtype=dtype)
        axis_angle = kornia.geometry.conversions.quaternion_to_axis_angle(quaternion)
        self.assert_close(axis_angle, expected, atol=atol, rtol=rtol)

    def test_small_angle_x(self, device, dtype, atol, rtol):
        theta = 1.0e-2
        quaternion = torch.tensor((np.cos(theta / 2.0), np.sin(theta / 2.0), 0.0, 0.0), device=device, dtype=dtype)
        expected = torch.tensor((theta, 0.0, 0.0), device=device, dtype=dtype)
        axis_angle = kornia.geometry.conversions.quaternion_to_axis_angle(quaternion)
        self.assert_close(axis_angle, expected, atol=atol, rtol=rtol)

    def test_small_angle_y(self, device, dtype, atol, rtol):
        theta = 1.0e-2
        quaternion = torch.tensor((np.cos(theta / 2), 0.0, np.sin(theta / 2), 0.0), device=device, dtype=dtype)
        expected = torch.tensor((0.0, theta, 0.0), device=device, dtype=dtype)
        axis_angle = kornia.geometry.conversions.quaternion_to_axis_angle(quaternion)
        self.assert_close(axis_angle, expected, atol=atol, rtol=rtol)

    def test_small_angle_z(self, device, dtype, atol, rtol):
        theta = 1.0e-2
        quaternion = torch.tensor((np.cos(theta / 2), 0.0, 0.0, np.sin(theta / 2)), device=device, dtype=dtype)
        expected = torch.tensor((0.0, 0.0, theta), device=device, dtype=dtype)
        axis_angle = kornia.geometry.conversions.quaternion_to_axis_angle(quaternion)
        self.assert_close(axis_angle, expected, atol=atol, rtol=rtol)

    def test_gradcheck(self, device):
        dtype = torch.float64
        eps = torch.finfo(dtype).eps
        quaternion = torch.tensor((1.0, 0.0, 0.0, 0.0), device=device, dtype=dtype) + eps
        # evaluate function gradient
        self.gradcheck(partial(kornia.geometry.conversions.quaternion_to_axis_angle), (quaternion,))


class TestRotationMatrixToQuaternion(BaseTester):
    @pytest.mark.parametrize("batch_size", (1, 3, 8))
    def test_smoke_batch(self, batch_size, device, dtype):
        matrix = torch.zeros(batch_size, 3, 3, device=device, dtype=dtype)
        quaternion = kornia.geometry.conversions.rotation_matrix_to_quaternion(matrix)
        assert quaternion.shape == (batch_size, 4)

    def test_identity(self, device, dtype, atol, rtol):
        matrix = torch.tensor(((1.0, 0.0, 0.0), (0.0, 1.0, 0.0), (0.0, 0.0, 1.0)), device=device, dtype=dtype)
        expected = torch.tensor((1.0, 0.0, 0.0, 0.0), device=device, dtype=dtype)
        quaternion = kornia.geometry.conversions.rotation_matrix_to_quaternion(matrix)
        self.assert_close(quaternion, expected, atol=atol, rtol=rtol)

    def test_rot_x_45(self, device, dtype, atol, rtol):
        matrix = torch.tensor(((1.0, 0.0, 0.0), (0.0, 0.0, -1.0), (0.0, 1.0, 0.0)), device=device, dtype=dtype)
        pi_half2 = torch.cos(kornia.pi / 4.0).to(device=device, dtype=dtype)
        expected = torch.tensor((pi_half2, pi_half2, 0.0, 0.0), device=device, dtype=dtype)
        quaternion = kornia.geometry.conversions.rotation_matrix_to_quaternion(matrix)
        self.assert_close(quaternion, expected, atol=atol, rtol=rtol)

    def test_back_and_forth(self, device, dtype, atol, rtol):
        eps = torch.finfo(dtype).eps
        matrix = torch.tensor(((1.0, 0.0, 0.0), (0.0, 0.0, -1.0), (0.0, 1.0, 0.0)), device=device, dtype=dtype)
        quaternion = kornia.geometry.conversions.rotation_matrix_to_quaternion(matrix, eps=eps)
        matrix_hat = kornia.geometry.conversions.quaternion_to_rotation_matrix(quaternion)
        self.assert_close(matrix, matrix_hat, atol=atol, rtol=rtol)

    def test_corner_case(self, device, dtype, atol, rtol):
        eps = torch.finfo(dtype).eps
        matrix = torch.tensor(
            (
                (-0.7799533010, -0.5432914495, 0.3106555045),
                (0.0492402576, -0.5481169224, -0.8349509239),
                (0.6238971353, -0.6359263659, 0.4542570710),
            ),
            device=device,
            dtype=dtype,
        )
        quaternion_true = torch.tensor(
            (0.177614107728004, 0.280136495828629, -0.440902262926102, 0.834015488624573), device=device, dtype=dtype
        )
        quaternion = kornia.geometry.conversions.rotation_matrix_to_quaternion(matrix, eps=eps)
        torch.set_printoptions(precision=10)
        self.assert_close(quaternion_true, quaternion, atol=atol, rtol=rtol)

    def test_cond1_180_rot_x(self, device, dtype, atol, rtol):
        # 180° rotation around X: trace < 0, m00 > m11 and m00 > m22 → activates cond_1 branch.
        # R_x(π) = diag(1, -1, -1); expected quaternion (w,x,y,z) = (0, 1, 0, 0).
        eps = torch.finfo(dtype).eps
        matrix = torch.tensor(((1.0, 0.0, 0.0), (0.0, -1.0, 0.0), (0.0, 0.0, -1.0)), device=device, dtype=dtype)
        expected = torch.tensor((0.0, 1.0, 0.0, 0.0), device=device, dtype=dtype)
        quaternion = kornia.geometry.conversions.rotation_matrix_to_quaternion(matrix, eps=eps)
        self.assert_close(quaternion.abs(), expected.abs(), atol=atol, rtol=rtol)
        # Round-trip: convert back and verify the rotation matrix is recovered.
        mat_back = kornia.geometry.conversions.quaternion_to_rotation_matrix(quaternion)
        self.assert_close(mat_back, matrix, atol=atol, rtol=rtol)

    def test_cond2_180_rot_y(self, device, dtype, atol, rtol):
        # 180° rotation around Y: trace < 0, m11 > m22 and m00 not dominant → activates cond_2 branch.
        # R_y(π) = diag(-1, 1, -1); expected quaternion (w,x,y,z) = (0, 0, 1, 0).
        eps = torch.finfo(dtype).eps
        matrix = torch.tensor(((-1.0, 0.0, 0.0), (0.0, 1.0, 0.0), (0.0, 0.0, -1.0)), device=device, dtype=dtype)
        expected = torch.tensor((0.0, 0.0, 1.0, 0.0), device=device, dtype=dtype)
        quaternion = kornia.geometry.conversions.rotation_matrix_to_quaternion(matrix, eps=eps)
        self.assert_close(quaternion.abs(), expected.abs(), atol=atol, rtol=rtol)
        mat_back = kornia.geometry.conversions.quaternion_to_rotation_matrix(quaternion)
        self.assert_close(mat_back, matrix, atol=atol, rtol=rtol)

    def test_all_four_branches_in_batch(self, device, dtype, atol, rtol):
        # Batch of 4 rotation matrices that each activate a different internal branch.
        # Verify consistency via round-trip: R → q → R must recover the original rotation.
        eps = torch.finfo(dtype).eps
        identity = torch.eye(3, device=device, dtype=dtype)  # trace > 0 → trace_positive_cond
        rot_x_180 = torch.tensor(((1.0, 0.0, 0.0), (0.0, -1.0, 0.0), (0.0, 0.0, -1.0)), device=device, dtype=dtype)
        rot_y_180 = torch.tensor(((-1.0, 0.0, 0.0), (0.0, 1.0, 0.0), (0.0, 0.0, -1.0)), device=device, dtype=dtype)
        rot_z_180 = torch.tensor(((-1.0, 0.0, 0.0), (0.0, -1.0, 0.0), (0.0, 0.0, 1.0)), device=device, dtype=dtype)
        batch = torch.stack([identity, rot_x_180, rot_y_180, rot_z_180])  # (4, 3, 3)
        quaternions = kornia.geometry.conversions.rotation_matrix_to_quaternion(batch, eps=eps)
        mats_back = kornia.geometry.conversions.quaternion_to_rotation_matrix(quaternions)
        self.assert_close(mats_back, batch, atol=atol, rtol=rtol)

    def test_gradcheck(self, device):
        dtype = torch.float64
        eps = torch.finfo(dtype).eps
        matrix = torch.eye(3, device=device, dtype=dtype)
        # evaluate function gradient
        self.gradcheck(partial(kornia.geometry.conversions.rotation_matrix_to_quaternion, eps=eps), (matrix,))

    def test_dynamo(self, device, dtype, torch_optimizer):
        quaternion = torch.tensor((0.0, 0.0, 1.0), device=device, dtype=dtype)
        op = kornia.geometry.conversions.quaternion_log_to_exp
        op_optimized = torch_optimizer(op)

        actual = op_optimized(quaternion)
        expected = op(quaternion)

        self.assert_close(actual, expected)


class TestQuaternionToRotationMatrix(BaseTester):
    @pytest.mark.parametrize("batch_dims", ((), (1,), (3,), (8,), (1, 1), (5, 6)))
    def test_smoke_batch(self, batch_dims, device, dtype):
        quaternion = torch.zeros(*batch_dims, 4, device=device, dtype=dtype)
        matrix = kornia.geometry.conversions.quaternion_to_rotation_matrix(quaternion)
        assert matrix.shape == (*batch_dims, 3, 3)

    def test_unit_quaternion(self, device, dtype, atol, rtol):
        quaternion = torch.tensor((1.0, 0.0, 0.0, 0.0), device=device, dtype=dtype)
        expected = torch.tensor(((1.0, 0.0, 0.0), (0.0, 1.0, 0.0), (0.0, 0.0, 1.0)), device=device, dtype=dtype)
        matrix = kornia.geometry.conversions.quaternion_to_rotation_matrix(quaternion)
        self.assert_close(matrix, expected, atol=atol, rtol=rtol)

    def test_x_rotation(self, device, dtype, atol, rtol):
        quaternion = torch.tensor((0.0, 1.0, 0.0, 0.0), device=device, dtype=dtype)
        expected = torch.tensor(((1.0, 0.0, 0.0), (0.0, -1.0, 0.0), (0.0, 0.0, -1.0)), device=device, dtype=dtype)
        matrix = kornia.geometry.conversions.quaternion_to_rotation_matrix(quaternion)
        self.assert_close(matrix, expected, atol=atol, rtol=rtol)

    def test_y_rotation(self, device, dtype, atol, rtol):
        quaternion = torch.tensor((0.0, 0.0, 1.0, 0.0), device=device, dtype=dtype)
        expected = torch.tensor(((-1.0, 0.0, 0.0), (0.0, 1.0, 0.0), (0.0, 0.0, -1.0)), device=device, dtype=dtype)
        matrix = kornia.geometry.conversions.quaternion_to_rotation_matrix(quaternion)
        self.assert_close(matrix, expected, atol=atol, rtol=rtol)

    def test_z_rotation(self, device, dtype, atol, rtol):
        quaternion = torch.tensor((0.0, 0.0, 0.0, 1.0), device=device, dtype=dtype)
        expected = torch.tensor(((-1.0, 0.0, 0.0), (0.0, -1.0, 0.0), (0.0, 0.0, 1.0)), device=device, dtype=dtype)
        matrix = kornia.geometry.conversions.quaternion_to_rotation_matrix(quaternion)
        self.assert_close(matrix, expected, atol=atol, rtol=rtol)

    def test_gradcheck(self, device):
        quaternion = torch.tensor((0.0, 0.0, 0.0, 1.0), device=device, dtype=torch.float64)
        # evaluate function gradient
        self.gradcheck(partial(kornia.geometry.conversions.quaternion_to_rotation_matrix), (quaternion,))

    def test_dynamo(self, device, dtype, torch_optimizer):
        quaternion = torch.tensor((0.0, 0.0, 1.0, 0.0), device=device, dtype=dtype)
        op = kornia.geometry.conversions.quaternion_to_rotation_matrix
        op_optimized = torch_optimizer(op)

        actual = op_optimized(quaternion)
        expected = op(quaternion)

        self.assert_close(actual, expected)


class TestQuaternionLogToExp(BaseTester):
    @pytest.mark.parametrize("batch_size", (1, 3, 8))
    def test_smoke_batch(self, batch_size, device, dtype):
        quaternion_log = torch.zeros(batch_size, 3, device=device, dtype=dtype)
        quaternion_exp = kornia.geometry.conversions.quaternion_log_to_exp(quaternion_log)
        assert quaternion_exp.shape == (batch_size, 4)

    def test_unit_quaternion(self, device, dtype, atol, rtol):
        eps = torch.finfo(dtype).eps
        quaternion_log = torch.tensor((0.0, 0.0, 0.0), device=device, dtype=dtype)
        expected = torch.tensor((1.0, 0.0, 0.0, 0.0), device=device, dtype=dtype)
        quaternion_exp = kornia.geometry.conversions.quaternion_log_to_exp(quaternion_log, eps=eps)
        self.assert_close(quaternion_exp, expected, atol=atol, rtol=rtol)

    def test_pi_quaternion_x(self, device, dtype, atol, rtol):
        eps = torch.finfo(dtype).eps
        one = torch.tensor(1.0, device=device, dtype=dtype)
        quaternion_log = torch.tensor((1.0, 0.0, 0.0), device=device, dtype=dtype)
        expected = torch.tensor((torch.cos(one), torch.sin(one), 0.0, 0.0), device=device, dtype=dtype)
        quaternion_exp = kornia.geometry.conversions.quaternion_log_to_exp(quaternion_log, eps=eps)
        self.assert_close(quaternion_exp, expected, atol=atol, rtol=rtol)

    def test_pi_quaternion_y(self, device, dtype, atol, rtol):
        eps = torch.finfo(dtype).eps
        one = torch.tensor(1.0, device=device, dtype=dtype)
        quaternion_log = torch.tensor((0.0, 1.0, 0.0), device=device, dtype=dtype)
        expected = torch.tensor((torch.cos(one), 0.0, torch.sin(one), 0.0), device=device, dtype=dtype)
        quaternion_exp = kornia.geometry.conversions.quaternion_log_to_exp(quaternion_log, eps=eps)
        self.assert_close(quaternion_exp, expected, atol=atol, rtol=rtol)

    def test_pi_quaternion_z(self, device, dtype, atol, rtol):
        eps = torch.finfo(dtype).eps
        one = torch.tensor(1.0, device=device, dtype=dtype)
        quaternion_log = torch.tensor((0.0, 0.0, 1.0), device=device, dtype=dtype)
        expected = torch.tensor((torch.cos(one), 0.0, 0.0, torch.sin(one)), device=device, dtype=dtype)
        quaternion_exp = kornia.geometry.conversions.quaternion_log_to_exp(quaternion_log, eps=eps)
        self.assert_close(quaternion_exp, expected, atol=atol, rtol=rtol)

    def test_back_and_forth(self, device, dtype, atol, rtol):
        eps = torch.finfo(dtype).eps
        quaternion_log = torch.tensor((1.0, 0.0, 0.0), device=device, dtype=dtype)

        quaternion_exp = kornia.geometry.conversions.quaternion_log_to_exp(quaternion_log, eps=eps)
        quaternion_log_hat = kornia.geometry.conversions.quaternion_exp_to_log(quaternion_exp, eps=eps)
        self.assert_close(quaternion_log, quaternion_log_hat, atol=atol, rtol=rtol)

    def test_gradcheck(self, device):
        dtype = torch.float64
        eps = torch.finfo(dtype).eps
        quaternion = torch.tensor((0.0, 0.0, 1.0), device=device, dtype=dtype)
        # evaluate function gradient
        self.gradcheck(partial(kornia.geometry.conversions.quaternion_log_to_exp, eps=eps), (quaternion,))

    def test_dynamo(self, device, dtype, torch_optimizer):
        quaternion = torch.tensor((0.0, 0.0, 1.0), device=device, dtype=dtype)
        op = kornia.geometry.conversions.quaternion_log_to_exp
        op_optimized = torch_optimizer(op)

        actual = op_optimized(quaternion)
        expected = op(quaternion)

        self.assert_close(actual, expected)


class TestQuaternionExpToLog(BaseTester):
    @pytest.mark.parametrize("batch_size", (1, 3, 8))
    def test_smoke_batch(self, batch_size, device, dtype):
        eps = torch.finfo(dtype).eps
        quaternion_exp = torch.zeros(batch_size, 4, device=device, dtype=dtype)
        quaternion_log = kornia.geometry.conversions.quaternion_exp_to_log(quaternion_exp, eps=eps)
        assert quaternion_log.shape == (batch_size, 3)

    def test_unit_quaternion(self, device, dtype, atol, rtol):
        eps = torch.finfo(dtype).eps
        quaternion_exp = torch.tensor((1.0, 0.0, 0.0, 0.0), device=device, dtype=dtype)
        expected = torch.tensor((0.0, 0.0, 0.0), device=device, dtype=dtype)
        quaternion_log = kornia.geometry.conversions.quaternion_exp_to_log(quaternion_exp, eps=eps)
        self.assert_close(quaternion_log, expected, atol=atol, rtol=rtol)

    def test_pi_quaternion_x(self, device, dtype, atol, rtol):
        eps = torch.finfo(dtype).eps
        quaternion_exp = torch.tensor((0.0, 1.0, 0.0, 0.0), device=device, dtype=dtype)
        expected = torch.tensor((kornia.pi / 2.0, 0.0, 0.0), device=device, dtype=dtype)
        quaternion_log = kornia.geometry.conversions.quaternion_exp_to_log(quaternion_exp, eps=eps)
        self.assert_close(quaternion_log, expected, atol=atol, rtol=rtol)

    def test_pi_quaternion_y(self, device, dtype, atol, rtol):
        eps = torch.finfo(dtype).eps
        quaternion_exp = torch.tensor((0.0, 0.0, 1.0, 0.0), device=device, dtype=dtype)
        expected = torch.tensor((0.0, kornia.pi / 2.0, 0.0), device=device, dtype=dtype)
        quaternion_log = kornia.geometry.conversions.quaternion_exp_to_log(quaternion_exp, eps=eps)
        self.assert_close(quaternion_log, expected, atol=atol, rtol=rtol)

    def test_pi_quaternion_z(self, device, dtype, atol, rtol):
        eps = torch.finfo(dtype).eps
        quaternion_exp = torch.tensor((0.0, 0.0, 0.0, 1.0), device=device, dtype=dtype)
        expected = torch.tensor((0.0, 0.0, kornia.pi / 2.0), device=device, dtype=dtype)
        quaternion_log = kornia.geometry.conversions.quaternion_exp_to_log(quaternion_exp, eps=eps)
        self.assert_close(quaternion_log, expected, atol=atol, rtol=rtol)

    def test_back_and_forth(self, device, dtype, atol, rtol):
        eps = torch.finfo(dtype).eps
        quaternion_exp = torch.tensor((0.0, 1.0, 0.0, 0.0), device=device, dtype=dtype)
        quaternion_log = kornia.geometry.conversions.quaternion_exp_to_log(quaternion_exp, eps=eps)
        quaternion_exp_hat = kornia.geometry.conversions.quaternion_log_to_exp(quaternion_log, eps=eps)
        self.assert_close(quaternion_exp, quaternion_exp_hat, atol=atol, rtol=rtol)

    def test_gradcheck(self, device):
        dtype = torch.float64
        eps = torch.finfo(dtype).eps
        quaternion = torch.tensor((0.0, 1.0, 0.0, 0.0), device=device, dtype=dtype)
        # evaluate function gradient
        self.gradcheck(partial(kornia.geometry.conversions.quaternion_exp_to_log, eps=eps), (quaternion,))

    def test_dynamo(self, device, dtype, torch_optimizer):
        quaternion = torch.tensor((0.0, 0.0, 1.0, 0.0), device=device, dtype=dtype)
        op = kornia.geometry.conversions.quaternion_exp_to_log
        op_optimized = torch_optimizer(op)

        actual = op_optimized(quaternion)
        expected = op(quaternion)

        self.assert_close(actual, expected)


class TestAngleAxisToRotationMatrix(BaseTester):
    @pytest.mark.parametrize("batch_size", (1, 2, 5))
    def test_rand_axis_angle_gradcheck(self, batch_size, device, atol, rtol):
        dtype = torch.float64
        # generate input data
        axis_angle = torch.rand(batch_size, 3, device=device, dtype=dtype)
        eye_batch = eye_like(3, axis_angle)

        # apply transform
        rotation_matrix = kornia.geometry.conversions.axis_angle_to_rotation_matrix(axis_angle)

        rotation_matrix_eye = torch.matmul(rotation_matrix, rotation_matrix.transpose(-2, -1))
        self.assert_close(rotation_matrix_eye, eye_batch, atol=atol, rtol=rtol)

        # evaluate function gradient
        self.gradcheck(kornia.geometry.conversions.axis_angle_to_rotation_matrix, (axis_angle,))

    def test_axis_angle_to_rotation_matrix(self, device, dtype, atol, rtol):
        rmat_1 = torch.tensor(
            (
                (-0.30382753, -0.95095137, -0.05814062),
                (-0.71581715, 0.26812278, -0.64476041),
                (0.62872461, -0.15427791, -0.76217038),
            ),
            device=device,
            dtype=dtype,
        )
        rvec_1 = torch.tensor((1.50485376, -2.10737739, 0.7214174), device=device, dtype=dtype)

        rmat_2 = torch.tensor(
            (
                (0.6027768, -0.79275544, -0.09054801),
                (-0.67915707, -0.56931658, 0.46327563),
                (-0.41881476, -0.21775548, -0.88157628),
            ),
            device=device,
            dtype=dtype,
        )
        rvec_2 = torch.tensor((-2.44916812, 1.18053411, 0.4085298), device=device, dtype=dtype)
        rmat = torch.stack((rmat_2, rmat_1), dim=0)
        rvec = torch.stack((rvec_2, rvec_1), dim=0)

        self.assert_close(kornia.geometry.conversions.axis_angle_to_rotation_matrix(rvec), rmat, atol=atol, rtol=rtol)


class TestRotationMatrixToAngleAxis(BaseTester):
    @pytest.mark.parametrize("batch_size", (1, 2, 5))
    def test_rand_quaternion_gradcheck(self, batch_size, device, dtype, atol, rtol):
        # generate input data
        quaternion = torch.rand(batch_size, 4, device=device, dtype=dtype)
        quaternion = kornia.geometry.conversions.normalize_quaternion(quaternion + 1e-6)
        rotation_matrix = kornia.geometry.conversions.quaternion_to_rotation_matrix(quaternion=quaternion)

        eye_batch = eye_like(3, rotation_matrix)
        rotation_matrix_eye = torch.matmul(rotation_matrix, rotation_matrix.transpose(-2, -1))
        # This didn't pass with atol=0.001, rtol=0.001 for float16 Cuda 11.2 GeForce 1080 Ti
        self.assert_close(rotation_matrix_eye, eye_batch, atol=atol * 10.0, rtol=rtol * 10.0)

    @pytest.mark.parametrize("batch_size", [4])
    def test_gradcheck(self, batch_size, device):
        dtype = torch.float64
        quaternion = torch.rand(batch_size, 4, device=device, dtype=dtype)
        quaternion = kornia.geometry.conversions.normalize_quaternion(quaternion + 1e-6)
        rotation_matrix = kornia.geometry.conversions.quaternion_to_rotation_matrix(quaternion=quaternion)
        # evaluate function gradient
        self.gradcheck(kornia.geometry.conversions.rotation_matrix_to_axis_angle, (rotation_matrix,))

    def test_rotation_matrix_to_axis_angle(self, device, dtype, atol, rtol):
        rmat_1 = torch.tensor(
            (
                (-0.30382753, -0.95095137, -0.05814062),
                (-0.71581715, 0.26812278, -0.64476041),
                (0.62872461, -0.15427791, -0.76217038),
            ),
            device=device,
            dtype=dtype,
        )
        rvec_1 = torch.tensor((1.50485376, -2.10737739, 0.7214174), device=device, dtype=dtype)

        rmat_2 = torch.tensor(
            (
                (0.6027768, -0.79275544, -0.09054801),
                (-0.67915707, -0.56931658, 0.46327563),
                (-0.41881476, -0.21775548, -0.88157628),
            ),
            device=device,
            dtype=dtype,
        )
        rvec_2 = torch.tensor((-2.44916812, 1.18053411, 0.4085298), device=device, dtype=dtype)
        rmat = torch.stack((rmat_2, rmat_1), dim=0)
        rvec = torch.stack((rvec_2, rvec_1), dim=0)

        self.assert_close(kornia.geometry.conversions.rotation_matrix_to_axis_angle(rmat), rvec, atol=atol, rtol=rtol)


class TestRadDegConversions(BaseTester):
    def test_pi(self):
        self.assert_close(kornia.constants.pi.item(), 3.141592)

    @pytest.mark.parametrize("batch_shape", [(2, 3), (1, 2, 3), (2, 3, 3), (5, 5, 3)])
    def test_rad2deg(self, batch_shape, device, dtype):
        # generate input data
        x_rad = kornia.constants.pi * torch.rand(batch_shape, device=device, dtype=dtype)

        # convert radians/degrees
        x_deg = kornia.geometry.conversions.rad2deg(x_rad)
        x_deg_to_rad = kornia.geometry.conversions.deg2rad(x_deg)

        # compute error
        self.assert_close(x_rad, x_deg_to_rad)

    @pytest.mark.parametrize("batch_shape", [(2, 3), (1, 2, 3), (2, 3, 3), (5, 5, 3)])
    def test_rad2deg_gradcheck(self, batch_shape, device):
        dtype = torch.float64
        x_rad = torch.rand(batch_shape, device=device, dtype=dtype)
        # evaluate function gradient
        self.gradcheck(kornia.geometry.conversions.rad2deg, (x_rad,))

    @pytest.mark.parametrize("batch_shape", [(2, 3), (1, 2, 3), (2, 3, 3), (5, 5, 3)])
    def test_deg2rad(self, batch_shape, device, dtype, atol, rtol):
        # generate input data
        x_deg = 180.0 * torch.rand(batch_shape, device=device, dtype=dtype)

        # convert radians/degrees
        x_rad = kornia.geometry.conversions.deg2rad(x_deg)
        x_rad_to_deg = kornia.geometry.conversions.rad2deg(x_rad)

        self.assert_close(x_deg, x_rad_to_deg, atol=atol, rtol=rtol)

    @pytest.mark.parametrize("batch_shape", [(2, 3), (1, 2, 3), (2, 3, 3), (5, 5, 3)])
    def test_deg2rad_gradcheck(self, batch_shape, device):
        x_deg = 180.0 * torch.rand(batch_shape, device=device, dtype=torch.float64)
        self.gradcheck(kornia.geometry.conversions.deg2rad, (x_deg,))


class TestPolCartConversions(BaseTester):
    def test_smoke(self, device, dtype):
        x = torch.ones(1, 1, 1, 1, device=device, dtype=dtype)
        assert kornia.geometry.conversions.pol2cart(x, x) is not None
        assert kornia.geometry.conversions.cart2pol(x, x) is not None

    @pytest.mark.parametrize("batch_shape", [(2, 3), (1, 2, 3), (2, 3, 3), (5, 5, 3)])
    def test_pol2cart(self, batch_shape, device, dtype):
        # generate input data
        rho = torch.rand(batch_shape, dtype=dtype)
        phi = kornia.constants.pi * torch.rand(batch_shape, dtype=dtype)
        rho = rho.to(device)
        phi = phi.to(device)

        # convert pol/cart
        x_pol2cart, y_pol2cart = kornia.geometry.conversions.pol2cart(rho, phi)
        rho_pol2cart, phi_pol2cart = kornia.geometry.conversions.cart2pol(x_pol2cart, y_pol2cart, 0)

        self.assert_close(rho, rho_pol2cart)
        self.assert_close(phi, phi_pol2cart)

    @pytest.mark.parametrize("batch_shape", [(2, 3)])
    def test_gradcheck(self, batch_shape, device):
        rho = torch.rand(batch_shape, dtype=torch.float64, device=device)
        phi = kornia.constants.pi * torch.rand(batch_shape, dtype=torch.float64, device=device)
        self.gradcheck(kornia.geometry.conversions.pol2cart, (rho, phi))
        self.gradcheck(kornia.geometry.conversions.cart2pol, (rho, phi))

    @pytest.mark.parametrize("batch_shape", [(2, 3), (1, 2, 3), (2, 3, 3), (5, 5, 3)])
    def test_cart2pol(self, batch_shape, device, dtype):
        # generate input data
        x = torch.rand(batch_shape, dtype=dtype)
        y = torch.rand(batch_shape, dtype=dtype)
        x = x.to(device)
        y = y.to(device)

        # convert cart/pol
        rho_cart2pol, phi_cart2pol = kornia.geometry.conversions.cart2pol(x, y, 0)
        x_cart2pol, y_cart2pol = kornia.geometry.conversions.pol2cart(rho_cart2pol, phi_cart2pol)

        self.assert_close(x, x_cart2pol)
        self.assert_close(y, y_cart2pol)


class TestConvertPointsToHomogeneous(BaseTester):
    def test_convert_points(self, device, dtype):
        # generate input data
        points_h = torch.tensor(
            [[1.0, 2.0, 1.0], [0.0, 1.0, 2.0], [2.0, 1.0, 0.0], [-1.0, -2.0, -1.0], [0.0, 1.0, -2.0]],
            device=device,
            dtype=dtype,
        )

        expected = torch.tensor(
            [
                [1.0, 2.0, 1.0, 1.0],
                [0.0, 1.0, 2.0, 1.0],
                [2.0, 1.0, 0.0, 1.0],
                [-1.0, -2.0, -1.0, 1.0],
                [0.0, 1.0, -2.0, 1.0],
            ],
            device=device,
            dtype=dtype,
        )

        # to euclidean
        points = kornia.geometry.conversions.convert_points_to_homogeneous(points_h)
        self.assert_close(points, expected, atol=1e-4, rtol=1e-4)

    def test_convert_points_batch(self, device, dtype):
        # generate input data
        points_h = torch.tensor([[[2.0, 1.0, 0.0]], [[0.0, 1.0, 2.0]], [[0.0, 1.0, -2.0]]], device=device, dtype=dtype)

        expected = torch.tensor(
            [[[2.0, 1.0, 0.0, 1.0]], [[0.0, 1.0, 2.0, 1.0]], [[0.0, 1.0, -2.0, 1.0]]], device=device, dtype=dtype
        )

        # to euclidean
        points = kornia.geometry.conversions.convert_points_to_homogeneous(points_h)
        self.assert_close(points, expected, atol=1e-4, rtol=1e-4)

    @pytest.mark.parametrize("batch_shape", [(2, 3), (1, 2, 3), (2, 3, 3), (5, 5, 3)])
    def test_gradcheck(self, batch_shape, device):
        points_h = torch.rand(batch_shape, device=device, dtype=torch.float64)

        # evaluate function gradient
        self.gradcheck(kornia.geometry.conversions.convert_points_to_homogeneous, (points_h,))

    def test_dynamo(self, device, dtype, torch_optimizer):
        points_h = torch.zeros(1, 2, 3, device=device, dtype=dtype)

        op = kornia.geometry.conversions.convert_points_to_homogeneous
        op_optimized = torch_optimizer(op)

        actual = op_optimized(points_h)
        expected = op(points_h)

        self.assert_close(actual, expected)


class TestConvertAtoH(BaseTester):
    def test_convert_points(self, device, dtype):
        # generate input data
        A = torch.tensor([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0]], device=device, dtype=dtype).view(1, 2, 3)

        expected = torch.tensor([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], device=device, dtype=dtype).view(
            1, 3, 3
        )

        # to euclidean
        H = kornia.geometry.conversions.convert_affinematrix_to_homography(A)
        self.assert_close(H, expected)

    @pytest.mark.parametrize("batch_shape", [(10, 2, 3), (16, 2, 3)])
    def test_gradcheck(self, batch_shape, device):
        points_h = torch.rand(batch_shape, device=device, dtype=torch.float64)

        # evaluate function gradient
        self.gradcheck(kornia.geometry.conversions.convert_affinematrix_to_homography, (points_h,))

    def test_dynamo(self, device, dtype, torch_optimizer):
        points_h = torch.zeros(1, 2, 3, device=device, dtype=dtype)

        op = kornia.geometry.conversions.convert_affinematrix_to_homography
        op_optimized = torch_optimizer(op)

        actual = op_optimized(points_h)
        expected = op(points_h)

        self.assert_close(actual, expected)


class TestConvertPointsFromHomogeneous(BaseTester):
    @pytest.mark.parametrize("batch_shape", [(2, 3), (1, 2, 3), (2, 3, 3), (5, 5, 3)])
    def test_cardinality(self, device, dtype, batch_shape):
        points_h = torch.rand(batch_shape, device=device, dtype=dtype)
        points = kornia.geometry.conversions.convert_points_from_homogeneous(points_h)
        assert points.shape == points.shape[:-1] + (2,)

    def test_points(self, device, dtype):
        # generate input data
        points_h = torch.tensor(
            [[1.0, 2.0, 1.0], [0.0, 1.0, 2.0], [2.0, 1.0, 0.0], [-1.0, -2.0, -1.0], [0.0, 1.0, -2.0]],
            device=device,
            dtype=dtype,
        )

        expected = torch.tensor(
            [[1.0, 2.0], [0.0, 0.5], [2.0, 1.0], [1.0, 2.0], [0.0, -0.5]], device=device, dtype=dtype
        )

        # to euclidean
        points = kornia.geometry.conversions.convert_points_from_homogeneous(points_h)
        self.assert_close(points, expected, atol=1e-4, rtol=1e-4)

    def test_points_batch(self, device, dtype):
        # generate input data
        points_h = torch.tensor([[[2.0, 1.0, 0.0]], [[0.0, 1.0, 2.0]], [[0.0, 1.0, -2.0]]], device=device, dtype=dtype)

        expected = torch.tensor([[[2.0, 1.0]], [[0.0, 0.5]], [[0.0, -0.5]]], device=device, dtype=dtype)

        # to euclidean
        points = kornia.geometry.conversions.convert_points_from_homogeneous(points_h)
        self.assert_close(points, expected, atol=1e-4, rtol=1e-4)

    def test_gradcheck(self, device):
        points_h = torch.ones(1, 10, 3, device=device, dtype=torch.float64)

        # evaluate function gradient
        self.gradcheck(kornia.geometry.conversions.convert_points_from_homogeneous, (points_h,))

    def test_gradcheck_zvec_zeros(self, device):
        # generate input data
        points_h = torch.tensor([[1.0, 2.0, 0.0], [0.0, 1.0, 0.1], [2.0, 1.0, 0.1]], device=device, dtype=torch.float64)

        # evaluate function gradient
        self.gradcheck(kornia.geometry.conversions.convert_points_from_homogeneous, (points_h,), eps=1e-8)

    def test_dynamo(self, device, dtype, torch_optimizer):
        points_h = torch.zeros(1, 2, 3, device=device, dtype=dtype)

        op = kornia.geometry.conversions.convert_points_from_homogeneous
        op_optimized = torch_optimizer(op)

        actual = op_optimized(points_h)
        expected = op(points_h)

        self.assert_close(actual, expected)


class TestNormalizePixelCoordinates(BaseTester):
    def test_tensor_bhw2(self, device, dtype, atol, rtol):
        eps = torch.finfo(dtype).eps
        height, width = 3, 4
        grid = kornia.geometry.create_meshgrid(height, width, normalized_coordinates=False, device=device).to(
            dtype=dtype
        )

        expected = kornia.geometry.create_meshgrid(height, width, normalized_coordinates=True, device=device).to(
            dtype=dtype
        )

        grid_norm = kornia.geometry.conversions.normalize_pixel_coordinates(grid, height, width, eps=eps)

        self.assert_close(grid_norm, expected, atol=atol, rtol=rtol)

    def test_list(self, device, dtype, atol, rtol):
        eps = torch.finfo(dtype).eps
        height, width = 3, 4
        grid = kornia.geometry.create_meshgrid(height, width, normalized_coordinates=False, device=device).to(
            dtype=dtype
        )
        grid = grid.contiguous().view(-1, 2)

        expected = kornia.geometry.create_meshgrid(height, width, normalized_coordinates=True, device=device).to(
            dtype=dtype
        )
        expected = expected.contiguous().view(-1, 2)

        grid_norm = kornia.geometry.conversions.normalize_pixel_coordinates(grid, height, width, eps=eps)

        self.assert_close(grid_norm, expected, atol=atol, rtol=rtol)

    def test_dynamo(self, device, dtype, torch_optimizer):
        if device == torch.device("cpu"):
            pytest.skip("NormalizePixelCoordinates not working on CPU with dynamo!")

        op = kornia.geometry.conversions.normalize_pixel_coordinates
        op_optimized = torch_optimizer(op)

        height, width = 3, 4
        grid = kornia.geometry.create_meshgrid(height, width, normalized_coordinates=True, device=device).to(
            dtype=dtype
        )

        actual = op_optimized(grid, height, width)
        expected = op(grid, height, width)

        self.assert_close(actual, expected)


class TestDenormalizePixelCoordinates(BaseTester):
    def test_tensor_bhw2(self, device, dtype):
        height, width = 3, 4
        grid = kornia.geometry.create_meshgrid(height, width, normalized_coordinates=True, device=device).to(
            dtype=dtype
        )

        expected = kornia.geometry.create_meshgrid(height, width, normalized_coordinates=False, device=device).to(
            dtype=dtype
        )

        grid_norm = kornia.geometry.conversions.denormalize_pixel_coordinates(grid, height, width)

        self.assert_close(grid_norm, expected, atol=1e-4, rtol=1e-4)

    def test_list(self, device, dtype):
        height, width = 3, 4
        grid = kornia.geometry.create_meshgrid(height, width, normalized_coordinates=True, device=device).to(
            dtype=dtype
        )
        grid = grid.contiguous().view(-1, 2)

        expected = kornia.geometry.create_meshgrid(height, width, normalized_coordinates=False, device=device).to(
            dtype=dtype
        )
        expected = expected.contiguous().view(-1, 2)

        grid_norm = kornia.geometry.conversions.denormalize_pixel_coordinates(grid, height, width)

        self.assert_close(grid_norm, expected, atol=1e-4, rtol=1e-4)

    def test_dynamo(self, device, dtype, torch_optimizer):
        if device == torch.device("cpu"):
            pytest.xfail("DenormalizePixelCoordinates not working on CPU with dynamo!")

        op = kornia.geometry.conversions.denormalize_pixel_coordinates
        op_optimized = torch_optimizer(op)

        height, width = 3, 4
        grid = kornia.geometry.create_meshgrid(height, width, normalized_coordinates=True, device=device).to(
            dtype=dtype
        )

        actual = op_optimized(grid, height, width)
        expected = op(grid, height, width)

        self.assert_close(actual, expected)


class TestProjectPoints(BaseTester):
    def test_smoke(self, device, dtype):
        point_3d = torch.zeros(1, 3, device=device, dtype=dtype)
        camera_matrix = torch.eye(3, device=device, dtype=dtype).expand(1, -1, -1)
        point_2d = kornia.geometry.camera.project_points(point_3d, camera_matrix)
        assert point_2d.shape == (1, 2)

    def test_smoke_batch(self, device, dtype):
        point_3d = torch.zeros(2, 3, device=device, dtype=dtype)
        camera_matrix = torch.eye(3, device=device, dtype=dtype).expand(2, -1, -1)
        point_2d = kornia.geometry.camera.project_points(point_3d, camera_matrix)
        assert point_2d.shape == (2, 2)

    def test_smoke_batch_multi(self, device, dtype):
        point_3d = torch.zeros(2, 4, 3, device=device, dtype=dtype)
        camera_matrix = torch.eye(3, device=device, dtype=dtype).expand(2, 4, -1, -1)
        point_2d = kornia.geometry.camera.project_points(point_3d, camera_matrix)
        assert point_2d.shape == (2, 4, 2)

    def test_project_and_unproject(self, device, dtype):
        point_3d = torch.tensor([[10.0, 2.0, 30.0]], device=device, dtype=dtype)
        depth = point_3d[..., -1:]
        camera_matrix = torch.tensor(
            [[[2746.0, 0.0, 991.0], [0.0, 2748.0, 619.0], [0.0, 0.0, 1.0]]], device=device, dtype=dtype
        )
        point_2d = kornia.geometry.camera.project_points(point_3d, camera_matrix)
        point_3d_hat = kornia.geometry.camera.unproject_points(point_2d, depth, camera_matrix)
        self.assert_close(point_3d, point_3d_hat, atol=1e-4, rtol=1e-4)

    def test_gradcheck(self, device):
        # TODO: point [0, 0, 0] crashes
        points_3d = torch.ones(1, 3, device=device, dtype=torch.float64)
        camera_matrix = torch.eye(3, device=device, dtype=torch.float64).expand(1, -1, -1)

        # evaluate function gradient
        self.gradcheck(kornia.geometry.camera.project_points, (points_3d, camera_matrix))

    def test_dynamo(self, device, dtype, torch_optimizer):
        points_3d = torch.zeros(1, 3, device=device, dtype=dtype)
        camera_matrix = torch.eye(3, device=device, dtype=dtype).expand(1, -1, -1)
        op = kornia.geometry.camera.project_points
        op_optimized = torch_optimizer(op)

        actual = op_optimized(points_3d, camera_matrix)
        expected = op(points_3d, camera_matrix)

        self.assert_close(actual, expected)


class TestDenormalizePointsWithIntrinsics(BaseTester):
    def test_smoke(self, device, dtype):
        points_2d = torch.zeros(1, 2, device=device, dtype=dtype)
        camera_matrix = torch.eye(3, device=device, dtype=dtype).expand(1, -1, -1)
        points_norm = kornia.geometry.conversions.denormalize_points_with_intrinsics(points_2d, camera_matrix)
        assert points_norm.shape == (1, 2)

    def test_smoke_batch(self, device, dtype):
        points_2d = torch.zeros(2, 2, device=device, dtype=dtype)
        camera_matrix = torch.eye(3, device=device, dtype=dtype).expand(2, -1, -1)
        points_norm = kornia.geometry.conversions.denormalize_points_with_intrinsics(points_2d, camera_matrix)
        assert points_norm.shape == (2, 2)

    def test_smoke_batch_n(self, device, dtype):
        points_2d = torch.zeros(2, 9, 2, device=device, dtype=dtype)
        camera_matrix = torch.eye(3, device=device, dtype=dtype).expand(2, -1, -1)
        points_norm = kornia.geometry.conversions.denormalize_points_with_intrinsics(points_2d, camera_matrix)
        assert points_norm.shape == (2, 9, 2)

    def test_toy(self, device, dtype):
        point_2d = torch.tensor([[1.0, 1.0]], device=device, dtype=dtype)
        camera_matrix = torch.tensor(
            [[64.0, 0.0, 128.0], [0.0, 64.0, 128.0], [0.0, 0.0, 1.0]], device=device, dtype=dtype
        )
        op = kornia.geometry.conversions.denormalize_points_with_intrinsics
        expected = torch.tensor([[192.0, 192.0]], device=device, dtype=dtype)
        self.assert_close(op(point_2d, camera_matrix), expected, atol=1e-4, rtol=1e-4)

    def test_gradcheck(self, device):
        points_2d = torch.zeros(1, 2, device=device, dtype=torch.float64)
        camera_matrix = torch.eye(3, device=device, dtype=torch.float64).expand(1, -1, -1)

        # evaluate function gradient
        self.gradcheck(kornia.geometry.conversions.denormalize_points_with_intrinsics, (points_2d, camera_matrix))

    def test_dynamo(self, device, dtype, torch_optimizer):
        points_2d = torch.zeros(1, 2, device=device, dtype=dtype)
        camera_matrix = torch.eye(3, device=device, dtype=dtype).expand(1, -1, -1)
        op = kornia.geometry.conversions.denormalize_points_with_intrinsics
        op_optimized = torch_optimizer(op)

        actual = op_optimized(points_2d, camera_matrix)
        expected = op(points_2d, camera_matrix)

        self.assert_close(actual, expected)


class TestNormalizePointsWithIntrinsics(BaseTester):
    def test_smoke(self, device, dtype):
        points_2d = torch.zeros(1, 2, device=device, dtype=dtype)
        camera_matrix = torch.eye(3, device=device, dtype=dtype).expand(1, -1, -1)
        points_norm = kornia.geometry.conversions.normalize_points_with_intrinsics(points_2d, camera_matrix)
        assert points_norm.shape == (1, 2)

    def test_smoke_batch(self, device, dtype):
        points_2d = torch.zeros(2, 2, device=device, dtype=dtype)
        camera_matrix = torch.eye(3, device=device, dtype=dtype).expand(2, -1, -1)
        points_norm = kornia.geometry.conversions.normalize_points_with_intrinsics(points_2d, camera_matrix)
        assert points_norm.shape == (2, 2)

    def test_smoke_batch_n(self, device, dtype):
        points_2d = torch.zeros(2, 10, 2, device=device, dtype=dtype)
        camera_matrix = torch.eye(3, device=device, dtype=dtype).expand(2, -1, -1)
        points_norm = kornia.geometry.conversions.normalize_points_with_intrinsics(points_2d, camera_matrix)
        assert points_norm.shape == (2, 10, 2)

    def test_norm_unnorm(self, device, dtype):
        point_2d = torch.tensor([[128.0, 128.0]], device=device, dtype=dtype)
        camera_matrix = torch.tensor(
            [[64.0, 0.0, 128.0], [0.0, 64.0, 128.0], [0.0, 0.0, 1.0]], device=device, dtype=dtype
        )
        op = kornia.geometry.conversions.normalize_points_with_intrinsics
        back = kornia.geometry.conversions.denormalize_points_with_intrinsics
        point_2d_norm = op(point_2d, camera_matrix)
        point_2d_hat = back(point_2d_norm, camera_matrix)
        self.assert_close(point_2d, point_2d_hat, atol=1e-4, rtol=1e-4)

    def test_toy(self, device, dtype):
        point_2d = torch.tensor([[192.0, 192.0]], device=device, dtype=dtype)
        camera_matrix = torch.tensor(
            [[64.0, 0.0, 128.0], [0.0, 64.0, 128.0], [0.0, 0.0, 1.0]], device=device, dtype=dtype
        )
        op = kornia.geometry.conversions.normalize_points_with_intrinsics
        out = op(point_2d, camera_matrix)
        expected = torch.tensor([[1.0, 1.0]], device=device, dtype=dtype)
        self.assert_close(out, expected, atol=1e-4, rtol=1e-4)

    def test_gradcheck(self, device):
        points_2d = torch.zeros(1, 2, device=device, dtype=torch.float64)
        camera_matrix = torch.eye(3, device=device, dtype=torch.float64).expand(1, -1, -1)

        # evaluate function gradient
        self.gradcheck(kornia.geometry.conversions.normalize_points_with_intrinsics, (points_2d, camera_matrix))

    def test_dynamo(self, device, dtype, torch_optimizer):
        points_2d = torch.zeros(1, 2, device=device, dtype=dtype)
        camera_matrix = torch.eye(3, device=device, dtype=dtype).expand(1, -1, -1)
        op = kornia.geometry.conversions.normalize_points_with_intrinsics
        op_optimized = torch_optimizer(op)

        actual = op_optimized(points_2d, camera_matrix)
        expected = op(points_2d, camera_matrix)

        self.assert_close(actual, expected)


class TestRt2Extrinsics(BaseTester):
    @pytest.mark.parametrize("batch_size", [1, 2, 3])
    def test_everything(self, batch_size, device, dtype):
        # generate input data
        R = torch.rand(batch_size, 3, 3, dtype=dtype, device=device)
        t = torch.rand(batch_size, 3, 1, dtype=dtype, device=device)

        Rt = Rt_to_matrix4x4(R, t)
        assert Rt.shape == (batch_size, 4, 4)

        R2, t2 = matrix4x4_to_Rt(Rt)
        assert R2.shape == (batch_size, 3, 3)
        assert t2.shape == (batch_size, 3, 1)

        self.assert_close(R, R2, rtol=1e-4, atol=1e-5)
        self.assert_close(t, t2, rtol=1e-4, atol=1e-5)

    @pytest.mark.parametrize("batch_size", [5])
    def test_gradcheck(self, batch_size, device):
        R = torch.rand(batch_size, 3, 3, dtype=torch.float64, device=device)
        t = torch.rand(batch_size, 3, 1, dtype=torch.float64, device=device)
        self.gradcheck(kornia.geometry.conversions.Rt_to_matrix4x4, (R, t))


class TestCamtoworldGraphicsToVision(BaseTester):
    @pytest.mark.parametrize("batch_size", [1, 2, 3])
    def test_everything(self, batch_size, device, dtype):
        # generate input data
        t_vis = torch.tensor([2, 3, 4], device=device, dtype=dtype).view(1, 3, 1).repeat(batch_size, 1, 1)
        angles = torch.tensor([0, kornia.pi / 2.0, 0.0], device=device, dtype=dtype)[None]
        R_vis = kornia.geometry.axis_angle_to_rotation_matrix(angles).repeat(batch_size, 1, 1)
        K_vis = Rt_to_matrix4x4(R_vis, t_vis)
        K_graf = camtoworld_vision_to_graphics_4x4(K_vis)

        expected = torch.tensor(
            [[0, 0, -1, 2], [0, -1, 0, 3], [-1, 0, 0, 4], [0, 0, 0, 1]], device=device, dtype=dtype
        )[None].repeat(batch_size, 1, 1)

        self.assert_close(K_graf, expected, rtol=1e-4, atol=1e-5)
        R_graf, t_graf = camtoworld_vision_to_graphics_Rt(R_vis, t_vis)
        expected_R = torch.tensor([[0, 0, -1], [0, -1, 0], [-1, 0, 0]], device=device, dtype=dtype)[None].repeat(
            batch_size, 1, 1
        )
        expected_t = torch.tensor([2, 3, 4], device=device, dtype=dtype).reshape(1, 3, 1).repeat(batch_size, 1, 1)

        self.assert_close(t_graf, expected_t, rtol=1e-4, atol=1e-5)
        self.assert_close(R_graf, expected_R, rtol=1e-4, atol=1e-5)

        Kvis_back = camtoworld_graphics_to_vision_4x4(K_graf)
        self.assert_close(Kvis_back, K_vis, rtol=1e-4, atol=1e-5)

        R_vis_back, t_vis_back = camtoworld_graphics_to_vision_Rt(R_graf, t_graf)
        self.assert_close(R_vis_back, R_vis, rtol=1e-4, atol=1e-5)
        self.assert_close(t_vis_back, t_vis, rtol=1e-4, atol=1e-5)

    @pytest.mark.parametrize("batch_size", [4])
    def test_gradcheck(self, batch_size, device):
        t_vis = torch.tensor([2, 3, 4], device=device, dtype=torch.float64).view(1, 3, 1).repeat(batch_size, 1, 1)
        angles = torch.tensor([0, kornia.pi / 2.0, 0.0], device=device, dtype=torch.float64)[None]
        R_vis = kornia.geometry.axis_angle_to_rotation_matrix(angles).repeat(batch_size, 1, 1)
        K_vis = Rt_to_matrix4x4(R_vis, t_vis)
        self.gradcheck(camtoworld_graphics_to_vision_4x4, (K_vis,))
        self.gradcheck(camtoworld_vision_to_graphics_4x4, (K_vis,))


class TestCamtoworldRtToPoseRt(BaseTester):
    @pytest.mark.parametrize("batch_size", [1, 2, 3])
    def test_everything(self, batch_size, device, dtype):
        # generate input data
        t = torch.tensor([2, 3, 4], device=device, dtype=dtype).view(1, 3, 1).repeat(batch_size, 1, 1)
        angles = torch.tensor([0, kornia.pi / 2.0, 0.0], device=device, dtype=dtype)[None]
        R = kornia.geometry.axis_angle_to_rotation_matrix(angles).repeat(batch_size, 1, 1)

        Rp, tp = camtoworld_to_worldtocam_Rt(R, t)

        expected_Rp = torch.tensor([[0, 0, -1], [0, 1, 0], [1, 0, 0]], device=device, dtype=dtype)[None].repeat(
            batch_size, 1, 1
        )
        expected_tp = torch.tensor([4, -3, -2], device=device, dtype=dtype).view(1, 3, 1).repeat(batch_size, 1, 1)
        self.assert_close(Rp, expected_Rp, rtol=1e-4, atol=1e-5)
        self.assert_close(tp, expected_tp, rtol=1e-4, atol=1e-5)

        Rback, tback = worldtocam_to_camtoworld_Rt(Rp, tp)
        self.assert_close(Rback, R, rtol=1e-4, atol=1e-5)
        self.assert_close(tback, t, rtol=1e-4, atol=1e-5)

    @pytest.mark.parametrize("batch_size", [4])
    def test_gradcheck(self, batch_size, device):
        t = torch.tensor([2, 3, 4], device=device, dtype=torch.float64).view(1, 3, 1).repeat(batch_size, 1, 1)
        angles = torch.tensor([0, kornia.pi / 2.0, 0.0], device=device, dtype=torch.float64)[None]
        R = kornia.geometry.axis_angle_to_rotation_matrix(angles).repeat(batch_size, 1, 1)
        self.gradcheck(camtoworld_to_worldtocam_Rt, (R, t))
        self.gradcheck(worldtocam_to_camtoworld_Rt, (R, t))


class TestCARKitToColmap(BaseTester):
    def test_everything(self, device, dtype):
        # generate input data
        t = torch.tensor([1, 0, 0], device=device, dtype=dtype).view(1, 3, 1)
        ang_deg = torch.tensor([45, 60.0, 0.0], device=device, dtype=dtype)[None]
        ang_rad = kornia.geometry.conversions.deg2rad(ang_deg)
        qvec = kornia.geometry.axis_angle_to_quaternion(ang_rad)

        q_colmap, t_colmap = ARKitQTVecs_to_ColmapQTVecs(qvec, t)

        angles_colmap = kornia.geometry.conversions.quaternion_to_axis_angle(q_colmap)
        angles_colmap = kornia.geometry.conversions.rad2deg(angles_colmap)
        expected_angles = torch.tensor([[116.8870620728, 0.0, -71.7524719238]], device=device, dtype=dtype)
        expected_t = torch.tensor([[[-0.5256], [0.3558], [0.7727]]], device=device, dtype=dtype)

        self.assert_close(angles_colmap, expected_angles, rtol=1e-4, atol=1e-5)
        self.assert_close(t_colmap, expected_t, rtol=1e-4, atol=1e-5)


class TestEulerFromQuaternion(BaseTester):
    def test_smoke(self, device, dtype):
        q = Quaternion.random(batch_size=1)
        q = q.to(device, dtype)
        roll, pitch, yaw = euler_from_quaternion(q.w, q.x, q.y, q.z)
        assert roll.shape == pitch.shape
        assert pitch.shape == yaw.shape

    @pytest.mark.parametrize("batch_size", ((1, 3, 4)))
    def test_cardinality(self, device, dtype, batch_size):
        q = Quaternion.random(batch_size=batch_size)
        q = q.to(device, dtype)
        roll, pitch, yaw = euler_from_quaternion(q.w, q.x, q.y, q.z)
        assert roll.shape[0] == batch_size
        assert pitch.shape[0] == batch_size
        assert yaw.shape[0] == batch_size

    def test_exception(self, device, dtype):
        q = Quaternion.random(batch_size=2)
        q = q.to(device, dtype)
        with pytest.raises(Exception):
            euler_from_quaternion(q.w, torch.rand(1), q.y, q.z)

    def test_gradcheck(self, device):
        q = Quaternion.random(batch_size=1).to(device, torch.float64)
        self.gradcheck(euler_from_quaternion, (q.w, q.x, q.y, q.z))

    @pytest.mark.skipif(
        torch_version() in {"2.0.1", "2.1.2", "2.2.2", "2.3.1"} and sys.version_info.minor == 8,
        reason="Not working on 2.0",
    )
    def test_dynamo(self, device, dtype, torch_optimizer):
        q = Quaternion.random(batch_size=1)
        q = q.to(device, dtype)
        op = euler_from_quaternion
        op_optimized = torch_optimizer(op)
        self.assert_close(op(q.w, q.x, q.y, q.z), op_optimized(q.w, q.x, q.y, q.z))

    def test_forth_and_back(self, device, dtype):
        q = Quaternion.random(batch_size=2)
        q = q.to(device, dtype)
        roll, pitch, yaw = euler_from_quaternion(q.w, q.x, q.y, q.z)
        qw, qx, qy, qz = quaternion_from_euler(roll, pitch, yaw)
        # TODO: check hwo to prevent getting inverted angles sometimes
        self.assert_close(q.w.abs(), qw.abs())
        self.assert_close(q.x.abs(), qx.abs())
        self.assert_close(q.y.abs(), qy.abs())
        self.assert_close(q.z.abs(), qz.abs())


class TestQuaternionFromEuler(BaseTester):
    def test_smoke(self, device, dtype):
        roll, pitch, yaw = torch.rand(3, device=device, dtype=dtype)
        qw, qx, qy, qz = quaternion_from_euler(roll, pitch, yaw)
        assert qw.shape == qx.shape
        assert qx.shape == qy.shape
        assert qy.shape == qz.shape

    @pytest.mark.parametrize("batch_size", ((1, 3, 4)))
    def test_cardinality(self, device, dtype, batch_size):
        roll, pitch, yaw = torch.rand(3, batch_size, device=device, dtype=dtype)
        qw, qx, qy, qz = quaternion_from_euler(roll, pitch, yaw)
        assert qw.shape[0] == batch_size
        assert qx.shape[0] == batch_size
        assert qy.shape[0] == batch_size
        assert qz.shape[0] == batch_size

    def test_exception(self, device, dtype):
        _, pitch, yaw = torch.rand(3, 2, device=device, dtype=dtype)
        with pytest.raises(Exception):
            quaternion_from_euler(torch.rand(1), pitch, yaw)

    def test_gradcheck(self, device):
        roll, pitch, yaw = torch.rand(3, 2, device=device, dtype=torch.float64, requires_grad=True)
        self.gradcheck(quaternion_from_euler, (roll, pitch, yaw))

    def test_dynamo(self, device, dtype, torch_optimizer):
        roll, pitch, yaw = torch.rand(3, 2, device=device, dtype=dtype)

        op = quaternion_from_euler
        op_optimized = torch_optimizer(op)

        actual = op_optimized(roll, pitch, yaw)
        expected = op(roll, pitch, yaw)

        self.assert_close(actual[0], expected[0])
        self.assert_close(actual[1], expected[1])
        self.assert_close(actual[2], expected[2])

    def test_forth_and_back(self, device, dtype):
        roll, pitch, yaw = torch.rand(3, 2, device=device, dtype=dtype)
        qw, qx, qy, qz = quaternion_from_euler(roll, pitch, yaw)
        roll_new, pitch_new, yaw_new = euler_from_quaternion(qw, qx, qy, qz)
        self.assert_close(roll, roll_new)
        self.assert_close(pitch, pitch_new)
        self.assert_close(yaw, yaw_new)

    def test_values(self, device, dtype):
        # num_samples = 5
        # data = 2 * torch.rand(3, num_samples, device=device, dtype=dtype) - 1
        # roll, pitch, yaw = torch.pi * data
        roll = torch.tensor(
            [2.6518599987, 0.0612506270, 1.2417907715, 2.8829660416, -1.9961174726], device=device, dtype=dtype
        )

        pitch = torch.tensor(
            [2.3267219067, -2.7309591770, -1.4011553526, -2.1962766647, 2.1454355717], device=device, dtype=dtype
        )

        yaw = torch.tensor(
            [-0.8856627345, 0.2605336905, 0.4579202533, -1.3095731735, 0.6096843481], device=device, dtype=dtype
        )

        euler_expected = torch.tensor(
            [
                [-0.4897327125, 0.8148705959, 2.2559301853],
                [-3.0803420544, -0.4106334746, -2.8810589314],
                [1.2417914867, -1.4011553526, 0.4579201937],
                [-0.2586266696, -0.9453159571, 1.8320195675],
                [1.1454752684, 0.9961569905, -2.5319085121],
            ],
            device=device,
            dtype=dtype,
        )

        qw, qx, qy, qz = quaternion_from_euler(roll, pitch, yaw)
        euler = euler_from_quaternion(qw, qx, qy, qz)
        euler = torch.stack(euler, -1)

        self.assert_close(euler, euler_expected, 1e-4, 1e-4)

        # this test is passing: pip install transforms3d
        # import transforms3d as tf3
        # out = [tf3.euler.euler2quat(roll[i], pitch[i], yaw[i]) for i in range(num_samples)]
        # out = torch.tensor(out, device=device, dtype=dtype)
        # self.assert_close(torch.stack((qw, qx, qy, qz), -1), out)

        # out = [tf3.euler.quat2euler((qw[i], qx[i], qy[i], qz[i])) for i in range(num_samples)]
        # out = torch.tensor(out, device=device, dtype=dtype)


@pytest.mark.parametrize("batch_size", (None, 1, 2, 5))
def test_vector_to_skew_symmetric_matrix(batch_size, device, dtype):
    if batch_size is None:
        vector = torch.rand(3, device=device, dtype=dtype)
    else:
        vector = torch.rand((batch_size, 3), device=device, dtype=dtype)
    skew_symmetric_matrix = kornia.geometry.conversions.vector_to_skew_symmetric_matrix(vector)
    assert skew_symmetric_matrix.shape[-1] == 3
    assert skew_symmetric_matrix.shape[-2] == 3
    z = torch.zeros_like(vector[..., 0])
    assert_close(skew_symmetric_matrix[..., 0, 0], z)
    assert_close(skew_symmetric_matrix[..., 1, 1], z)
    assert_close(skew_symmetric_matrix[..., 2, 2], z)
    assert_close(skew_symmetric_matrix[..., 0, 1], -vector[..., 2])
    assert_close(skew_symmetric_matrix[..., 1, 0], vector[..., 2])
    assert_close(skew_symmetric_matrix[..., 0, 2], vector[..., 1])
    assert_close(skew_symmetric_matrix[..., 2, 0], -vector[..., 1])
    assert_close(skew_symmetric_matrix[..., 1, 2], -vector[..., 0])
    assert_close(skew_symmetric_matrix[..., 2, 1], vector[..., 0])


class TestAxisAngleToRotationMatrix:
    def test_identity_rotation(self):
        aa = torch.zeros(1, 3, dtype=torch.float64, requires_grad=True)
        R = axis_angle_to_rotation_matrix(aa)
        Id = torch.eye(3, dtype=torch.float64).unsqueeze(0)
        assert torch.allclose(R, Id, atol=1e-6)

    def test_90deg_x_axis(self):
        aa = torch.tensor([[torch.pi / 2, 0.0, 0.0]], dtype=torch.float64)
        R = axis_angle_to_rotation_matrix(aa).squeeze(0)
        expected = torch.tensor(
            [
                [1.0, 0.0, 0.0],
                [0.0, 0.0, -1.0],
                [0.0, 1.0, 0.0],
            ],
            dtype=torch.float64,
        )
        assert torch.allclose(R, expected, atol=1e-6)

    def test_180deg_y_axis(self):
        aa = torch.tensor([[0.0, torch.pi, 0.0]], dtype=torch.float64)
        R = axis_angle_to_rotation_matrix(aa).squeeze(0)
        expected = torch.tensor(
            [
                [-1.0, 0.0, 0.0],
                [0.0, 1.0, 0.0],
                [0.0, 0.0, -1.0],
            ],
            dtype=torch.float64,
        )
        assert torch.allclose(R, expected, atol=1e-6)

    def test_batched_input(self):
        aa = torch.tensor(
            [
                [0.0, 0.0, 0.0],
                [torch.pi / 2, 0.0, 0.0],
                [0.0, torch.pi, 0.0],
            ],
            dtype=torch.float64,
        )
        R = axis_angle_to_rotation_matrix(aa)
        assert R.shape == (3, 3, 3)