コード例 #1
0
def test_torque_driven(with_contact, with_external_force, cx):
    # Prepare the program
    nlp = NonLinearProgram()
    nlp.model = biorbd.Model(
        TestUtils.bioptim_folder() + "/examples/getting_started/models/2segments_4dof_2contacts.bioMod"
    )
    nlp.ns = 5
    nlp.cx = cx

    nlp.x_bounds = np.zeros((nlp.model.nbQ() * 3, 1))
    nlp.u_bounds = np.zeros((nlp.model.nbQ(), 1))
    ocp = OptimalControlProgram(nlp)
    nlp.control_type = ControlType.CONSTANT
    NonLinearProgram.add(ocp, "dynamics_type", Dynamics(DynamicsFcn.TORQUE_DRIVEN, with_contact=with_contact), False)

    np.random.seed(42)
    if with_external_force:
        external_forces = [np.random.rand(6, nlp.model.nbSegment(), nlp.ns)]
        nlp.external_forces = BiorbdInterface.convert_array_to_external_forces(external_forces)[0]

    # Prepare the dynamics
    ConfigureProblem.initialize(ocp, nlp)

    # Test the results
    states = np.random.rand(nlp.states.shape, nlp.ns)
    controls = np.random.rand(nlp.controls.shape, nlp.ns)
    params = np.random.rand(nlp.parameters.shape, nlp.ns)
    x_out = np.array(nlp.dynamics_func(states, controls, params))

    if with_contact:
        contact_out = np.array(nlp.contact_forces_func(states, controls, params))
        if with_external_force:
            np.testing.assert_almost_equal(
                x_out[:, 0],
                [0.8631034, 0.3251833, 0.1195942, 0.4937956, -7.7700092, -7.5782306, 21.7073786, -16.3059315],
            )
            np.testing.assert_almost_equal(contact_out[:, 0], [-47.8131136, 111.1726516, -24.4449121])
        else:
            np.testing.assert_almost_equal(
                x_out[:, 0], [0.6118529, 0.785176, 0.6075449, 0.8083973, -0.3214905, -0.1912131, 0.6507164, -0.2359716]
            )
            np.testing.assert_almost_equal(contact_out[:, 0], [-2.444071, 128.8816865, 2.7245124])

    else:
        if with_external_force:
            np.testing.assert_almost_equal(
                x_out[:, 0],
                [0.86310343, 0.32518332, 0.11959425, 0.4937956, 0.30731739, -9.97912778, 1.15263778, 36.02430956],
            )
        else:
            np.testing.assert_almost_equal(
                x_out[:, 0],
                [0.61185289, 0.78517596, 0.60754485, 0.80839735, -0.30241366, -10.38503791, 1.60445173, 35.80238642],
            )
コード例 #2
0
ファイル: test_dynamics.py プロジェクト: pyomeca/bioptim
def test_muscle_driven(with_excitations, with_contact, with_torque,
                       with_external_force, implicit, cx):
    # Prepare the program
    nlp = NonLinearProgram()
    nlp.model = biorbd.Model(
        TestUtils.bioptim_folder() +
        "/examples/muscle_driven_ocp/models/arm26_with_contact.bioMod")
    nlp.ns = 5
    nlp.cx = cx

    nlp.x_bounds = np.zeros((nlp.model.nbQ() * 2 + nlp.model.nbMuscles(), 1))
    nlp.u_bounds = np.zeros((nlp.model.nbMuscles(), 1))
    nlp.phase_idx = 0

    ocp = OptimalControlProgram(nlp)
    nlp.control_type = ControlType.CONSTANT
    NonLinearProgram.add(
        ocp,
        "dynamics_type",
        Dynamics(
            DynamicsFcn.MUSCLE_DRIVEN,
            with_torque=with_torque,
            with_excitations=with_excitations,
            with_contact=with_contact,
            implicit_dynamics=implicit,
        ),
        False,
    )

    np.random.seed(42)
    if with_external_force:
        external_forces = [np.random.rand(6, nlp.model.nbSegment(), nlp.ns)]
        nlp.external_forces = BiorbdInterface.convert_array_to_external_forces(
            external_forces)[0]

    # Prepare the dynamics
    if implicit:
        pass
    ConfigureProblem.initialize(ocp, nlp)

    # Test the results
    states = np.random.rand(nlp.states.shape, nlp.ns)
    controls = np.random.rand(nlp.controls.shape, nlp.ns)
    params = np.random.rand(nlp.parameters.shape, nlp.ns)
    x_out = np.array(nlp.dynamics_func(states, controls, params))

    if with_contact:  # Warning this test is a bit bogus, there since the model does not have contacts
        if implicit:
            if with_torque:
                if with_excitations:
                    if with_external_force:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                0.6158501,
                                0.5031363,
                                0.6424193,
                                0.7009691,
                                0.0848377,
                                0.9472486,
                                46.8792802,
                                -1.8018903,
                                53.3914525,
                                48.3005692,
                                63.6937337,
                                -28.1570099,
                            ],
                        )
                    else:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                0.183405,
                                0.611853,
                                0.785176,
                                0.249292,
                                0.289751,
                                0.871461,
                                8.606308,
                                3.194336,
                                29.740561,
                                -20.275423,
                                -23.246778,
                                -41.913501,
                            ],
                            decimal=6,
                        )
                else:
                    if with_external_force:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                0.61585, 0.503136, 0.642419, 0.895523,
                                0.319314, 0.448446
                            ],
                            decimal=6,
                        )
                    else:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                0.183405, 0.611853, 0.785176, 0.729007,
                                0.863103, 0.325183
                            ],
                            decimal=6,
                        )

            else:
                if with_excitations:
                    if with_external_force:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                0.6158501,
                                0.5031363,
                                0.6424193,
                                0.791579,
                                0.5495289,
                                0.1429917,
                                55.6555782,
                                50.4705269,
                                0.3602559,
                                58.9237749,
                                29.7009419,
                                -15.1353494,
                            ],
                        )
                    else:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                1.83404510e-01,
                                6.11852895e-01,
                                7.85175961e-01,
                                1.19594246e-01,
                                4.93795596e-01,
                                3.14291857e-02,
                                -7.72228930e00,
                                -1.13759732e01,
                                9.51906209e01,
                                4.45077128e00,
                                -5.20261014e00,
                                -2.80864106e01,
                            ],
                            decimal=6,
                        )
                else:
                    if with_external_force:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                0.6158501, 0.5031363, 0.6424193, 0.9905051,
                                0.9307573, 0.1031239
                            ],
                        )
                    else:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                0.183405, 0.611853, 0.785176, 0.388677,
                                0.542696, 0.772245
                            ],
                            decimal=6,
                        )
        else:
            if with_torque:
                if with_excitations:
                    if with_external_force:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                0.6158501,
                                0.50313626,
                                0.64241928,
                                1.46421499,
                                -45.27535002,
                                73.61890834,
                                46.87928022,
                                -1.80189035,
                                53.3914525,
                                48.30056919,
                                63.69373374,
                                -28.15700995,
                            ],
                        )
                    else:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                1.83404510e-01,
                                6.11852895e-01,
                                7.85175961e-01,
                                -9.06144782e00,
                                2.93915658e02,
                                -9.24229516e02,
                                8.60630831e00,
                                3.19433638e00,
                                2.97405608e01,
                                -2.02754226e01,
                                -2.32467778e01,
                                -4.19135012e01,
                            ],
                            decimal=6,
                        )
                else:
                    if with_external_force:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                6.15850098e-01,
                                5.03136259e-01,
                                6.42419278e-01,
                                -7.67236491e00,
                                2.30765930e02,
                                -7.34713354e02,
                            ],
                            decimal=6,
                        )
                    else:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                1.83404510e-01,
                                6.11852895e-01,
                                7.85175961e-01,
                                -3.57374110e00,
                                1.13519647e02,
                                -4.07165959e02,
                            ],
                            decimal=6,
                        )

            else:
                if with_excitations:
                    if with_external_force:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                0.6158501,
                                0.50313626,
                                0.64241928,
                                1.31194581,
                                -50.56193318,
                                82.71912199,
                                55.65557816,
                                50.47052688,
                                0.36025589,
                                58.92377491,
                                29.70094194,
                                -15.13534937,
                            ],
                        )
                    else:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                1.83404510e-01,
                                6.11852895e-01,
                                7.85175961e-01,
                                -9.49194254e00,
                                3.03909766e02,
                                -9.56600268e02,
                                -7.72228930e00,
                                -1.13759732e01,
                                9.51906209e01,
                                4.45077128e00,
                                -5.20261014e00,
                                -2.80864106e01,
                            ],
                            decimal=6,
                        )
                else:
                    if with_external_force:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                0.6158501, 0.50313626, 0.64241928, 1.31194581,
                                -50.56193318, 82.71912199
                            ],
                        )
                    else:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                1.83404510e-01,
                                6.11852895e-01,
                                7.85175961e-01,
                                -9.49194254e00,
                                3.03909766e02,
                                -9.56600268e02,
                            ],
                            decimal=6,
                        )
    else:
        if implicit:
            if with_torque:
                if with_excitations:
                    if with_external_force:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                0.6158501,
                                0.5031363,
                                0.6424193,
                                0.7009691,
                                0.0848377,
                                0.9472486,
                                46.8792802,
                                -1.8018903,
                                53.3914525,
                                48.3005692,
                                63.6937337,
                                -28.1570099,
                            ],
                        )
                    else:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                0.183405,
                                0.611853,
                                0.785176,
                                0.249292,
                                0.289751,
                                0.871461,
                                8.606308,
                                3.194336,
                                29.740561,
                                -20.275423,
                                -23.246778,
                                -41.913501,
                            ],
                            decimal=6,
                        )
                else:
                    if with_external_force:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                0.61585, 0.503136, 0.642419, 0.895523,
                                0.319314, 0.448446
                            ],
                            decimal=6,
                        )
                    else:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                0.183405, 0.611853, 0.785176, 0.729007,
                                0.863103, 0.325183
                            ],
                            decimal=6,
                        )

            else:
                if with_excitations:
                    if with_external_force:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                0.6158501,
                                0.50313626,
                                0.64241928,
                                0.79157904,
                                0.54952888,
                                0.14299168,
                                55.65557816,
                                50.47052688,
                                0.36025589,
                                58.92377491,
                                29.70094194,
                                -15.13534937,
                            ],
                        )
                    else:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                1.83404510e-01,
                                6.11852895e-01,
                                7.85175961e-01,
                                1.19594246e-01,
                                4.93795596e-01,
                                3.14291857e-02,
                                -7.72228930e00,
                                -1.13759732e01,
                                9.51906209e01,
                                4.45077128e00,
                                -5.20261014e00,
                                -2.80864106e01,
                            ],
                            decimal=6,
                        )
                else:
                    if with_external_force:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                0.6158501, 0.5031363, 0.6424193, 0.9905051,
                                0.9307573, 0.1031239
                            ],
                        )
                    else:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                0.183405, 0.611853, 0.785176, 0.388677,
                                0.542696, 0.772245
                            ],
                            decimal=6,
                        )
        else:
            if with_torque:
                if with_excitations:
                    if with_external_force:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                0.6158501,
                                0.50313626,
                                0.64241928,
                                1.46421499,
                                -45.27535002,
                                73.61890834,
                                46.87928022,
                                -1.80189035,
                                53.3914525,
                                48.30056919,
                                63.69373374,
                                -28.15700995,
                            ],
                        )
                    else:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                1.83404510e-01,
                                6.11852895e-01,
                                7.85175961e-01,
                                -9.06144782e00,
                                2.93915658e02,
                                -9.24229516e02,
                                8.60630831e00,
                                3.19433638e00,
                                2.97405608e01,
                                -2.02754226e01,
                                -2.32467778e01,
                                -4.19135012e01,
                            ],
                            decimal=6,
                        )
                else:
                    if with_external_force:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                6.15850098e-01,
                                5.03136259e-01,
                                6.42419278e-01,
                                -7.67236491e00,
                                2.30765930e02,
                                -7.34713354e02,
                            ],
                            decimal=6,
                        )
                    else:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                1.83404510e-01,
                                6.11852895e-01,
                                7.85175961e-01,
                                -3.57374110e00,
                                1.13519647e02,
                                -4.07165959e02,
                            ],
                            decimal=6,
                        )

            else:
                if with_excitations:
                    if with_external_force:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                0.6158501,
                                0.50313626,
                                0.64241928,
                                1.31194581,
                                -50.56193318,
                                82.71912199,
                                55.65557816,
                                50.47052688,
                                0.36025589,
                                58.92377491,
                                29.70094194,
                                -15.13534937,
                            ],
                        )
                    else:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                1.83404510e-01,
                                6.11852895e-01,
                                7.85175961e-01,
                                -9.49194254e00,
                                3.03909766e02,
                                -9.56600268e02,
                                -7.72228930e00,
                                -1.13759732e01,
                                9.51906209e01,
                                4.45077128e00,
                                -5.20261014e00,
                                -2.80864106e01,
                            ],
                            decimal=6,
                        )
                else:
                    if with_external_force:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                0.6158501, 0.50313626, 0.64241928, 1.31194581,
                                -50.56193318, 82.71912199
                            ],
                        )
                    else:
                        np.testing.assert_almost_equal(
                            x_out[:, 0],
                            [
                                1.83404510e-01,
                                6.11852895e-01,
                                7.85175961e-01,
                                -9.49194254e00,
                                3.03909766e02,
                                -9.56600268e02,
                            ],
                            decimal=6,
                        )
コード例 #3
0
ファイル: test_dynamics.py プロジェクト: pyomeca/bioptim
def test_torque_activation_driven(with_contact, with_external_force, cx):
    # Prepare the program
    nlp = NonLinearProgram()
    nlp.model = biorbd.Model(
        TestUtils.bioptim_folder() +
        "/examples/getting_started/models/2segments_4dof_2contacts.bioMod")
    nlp.ns = 5
    nlp.cx = cx
    nlp.x_bounds = np.zeros((nlp.model.nbQ() * 2, 1))
    nlp.u_bounds = np.zeros((nlp.model.nbQ(), 1))
    ocp = OptimalControlProgram(nlp)
    nlp.control_type = ControlType.CONSTANT
    NonLinearProgram.add(
        ocp, "dynamics_type",
        Dynamics(DynamicsFcn.TORQUE_ACTIVATIONS_DRIVEN,
                 with_contact=with_contact), False)

    np.random.seed(42)
    if with_external_force:
        external_forces = [np.random.rand(6, nlp.model.nbSegment(), nlp.ns)]
        nlp.external_forces = BiorbdInterface.convert_array_to_external_forces(
            external_forces)[0]

    # Prepare the dynamics
    ConfigureProblem.initialize(ocp, nlp)

    # Test the results
    states = np.random.rand(nlp.states.shape, nlp.ns)
    controls = np.random.rand(nlp.controls.shape, nlp.ns)
    params = np.random.rand(nlp.parameters.shape, nlp.ns)
    x_out = np.array(nlp.dynamics_func(states, controls, params))

    if with_contact:
        contact_out = np.array(
            nlp.contact_forces_func(states, controls, params))
        if with_external_force:
            np.testing.assert_almost_equal(
                x_out[:, 0],
                [
                    0.8631, 0.32518, 0.11959, 0.4938, 19.01887, 18.51503,
                    -53.08574, 58.48719
                ],
                decimal=5,
            )
            np.testing.assert_almost_equal(
                contact_out[:, 0], [109.8086936, 3790.3932439, -3571.7858574])
        else:
            np.testing.assert_almost_equal(
                x_out[:, 0],
                [
                    0.61185289, 0.78517596, 0.60754485, 0.80839735, 0.78455384,
                    -0.16844256, -1.56184114, 1.97658587
                ],
                decimal=5,
            )
            np.testing.assert_almost_equal(
                contact_out[:, 0], [-7.88958997, 329.70828173, -263.55516549])

    else:
        if with_external_force:
            np.testing.assert_almost_equal(
                x_out[:, 0],
                [
                    8.63103426e-01,
                    3.25183322e-01,
                    1.19594246e-01,
                    4.93795596e-01,
                    1.73558072e01,
                    -4.69891264e01,
                    1.81396922e02,
                    3.61170139e03,
                ],
                decimal=5,
            )
        else:
            np.testing.assert_almost_equal(
                x_out[:, 0],
                [
                    6.11852895e-01,
                    7.85175961e-01,
                    6.07544852e-01,
                    8.08397348e-01,
                    -2.38262975e01,
                    -5.82033454e01,
                    1.27439020e02,
                    3.66531163e03,
                ],
                decimal=5,
            )
コード例 #4
0
ファイル: test_dynamics.py プロジェクト: Naassila/bioptim
def test_muscle_driven(with_excitations, with_contact, with_residual_torque, with_external_force, cx):
    # Prepare the program
    nlp = NonLinearProgram()
    nlp.model = biorbd.Model(TestUtils.bioptim_folder() + "/examples/muscle_driven_ocp/arm26_with_contact.bioMod")
    nlp.ns = 5
    nlp.cx = cx

    nlp.x_bounds = np.zeros((nlp.model.nbQ() * 2 + nlp.model.nbMuscles(), 1))
    nlp.u_bounds = np.zeros((nlp.model.nbMuscles(), 1))
    ocp = OptimalControlProgram(nlp)
    nlp.control_type = ControlType.CONSTANT
    NonLinearProgram.add(
        ocp,
        "dynamics_type",
        Dynamics(
            DynamicsFcn.MUSCLE_DRIVEN,
            with_residual_torque=with_residual_torque,
            with_excitations=with_excitations,
            with_contact=with_contact,
        ),
        False,
    )

    np.random.seed(42)
    if with_external_force:
        external_forces = [np.random.rand(6, nlp.model.nbSegment(), nlp.ns)]
        nlp.external_forces = BiorbdInterface.convert_array_to_external_forces(external_forces)[0]

    # Prepare the dynamics
    ConfigureProblem.initialize(ocp, nlp)

    # Test the results
    states = np.random.rand(nlp.states.shape, nlp.ns)
    controls = np.random.rand(nlp.controls.shape, nlp.ns)
    params = np.random.rand(nlp.parameters.shape, nlp.ns)
    x_out = np.array(nlp.dynamics_func(states, controls, params))

    if with_contact:  # Warning this test is a bit bogus, there since the model does not have contacts
        if with_residual_torque:
            if with_excitations:
                if with_external_force:
                    np.testing.assert_almost_equal(
                        x_out[:, 0],
                        [
                            0.6158501,
                            0.50313626,
                            0.64241928,
                            1.07179591,
                            -33.76216759,
                            36.218136,
                            46.87928022,
                            -1.80189035,
                            53.3914525,
                            48.30056919,
                            63.69373374,
                            -28.15700995,
                        ],
                    )
                else:
                    np.testing.assert_almost_equal(
                        x_out[:, 0],
                        [
                            1.83404510e-01,
                            6.11852895e-01,
                            7.85175961e-01,
                            -9.29661929e00,
                            3.00871754e02,
                            -9.50353966e02,
                            8.60630831e00,
                            3.19433638e00,
                            2.97405608e01,
                            -2.02754226e01,
                            -2.32467778e01,
                            -4.19135012e01,
                        ],
                        decimal=6,
                    )
            else:
                if with_external_force:
                    np.testing.assert_almost_equal(
                        x_out[:, 0],
                        [6.15850098e-01, 5.03136259e-01, 6.42419278e-01, -8.06477702e00, 2.42278904e02, -7.72113478e02],
                        decimal=6,
                    )
                else:
                    np.testing.assert_almost_equal(
                        x_out[:, 0],
                        [1.83404510e-01, 6.11852895e-01, 7.85175961e-01, -3.80891773e00, 1.20475911e02, -4.33290914e02],
                        decimal=6,
                    )

        else:
            if with_excitations:
                if with_external_force:
                    np.testing.assert_almost_equal(
                        x_out[:, 0],
                        [
                            0.6158501,
                            0.50313626,
                            0.64241928,
                            0.91952666,
                            -39.04874824,
                            45.31834295,
                            55.65557816,
                            50.47052688,
                            0.36025589,
                            58.92377491,
                            29.70094194,
                            -15.13534937,
                        ],
                    )
                else:
                    np.testing.assert_almost_equal(
                        x_out[:, 0],
                        [
                            1.83404510e-01,
                            6.11852895e-01,
                            7.85175961e-01,
                            -9.72711369e00,
                            3.10865851e02,
                            -9.82724687e02,
                            -7.72228930e00,
                            -1.13759732e01,
                            9.51906209e01,
                            4.45077128e00,
                            -5.20261014e00,
                            -2.80864106e01,
                        ],
                        decimal=6,
                    )
            else:
                if with_external_force:
                    np.testing.assert_almost_equal(
                        x_out[:, 0],
                        [0.6158501, 0.50313626, 0.64241928, 0.91952666, -39.04874824, 45.31834295],
                    )
                else:
                    np.testing.assert_almost_equal(
                        x_out[:, 0],
                        [1.83404510e-01, 6.11852895e-01, 7.85175961e-01, -9.72711369e00, 3.10865851e02, -9.82724687e02],
                        decimal=6,
                    )

    else:
        if with_residual_torque:
            if with_excitations:
                if with_external_force:
                    np.testing.assert_almost_equal(
                        x_out[:, 0],
                        [
                            0.6158501,
                            0.50313626,
                            0.64241928,
                            1.07179591,
                            -33.76216759,
                            36.218136,
                            46.87928022,
                            -1.80189035,
                            53.3914525,
                            48.30056919,
                            63.69373374,
                            -28.15700995,
                        ],
                    )
                else:
                    np.testing.assert_almost_equal(
                        x_out[:, 0],
                        [
                            1.83404510e-01,
                            6.11852895e-01,
                            7.85175961e-01,
                            -9.29661929e00,
                            3.00871754e02,
                            -9.50353966e02,
                            8.60630831e00,
                            3.19433638e00,
                            2.97405608e01,
                            -2.02754226e01,
                            -2.32467778e01,
                            -4.19135012e01,
                        ],
                        decimal=6,
                    )
            else:
                if with_external_force:
                    np.testing.assert_almost_equal(
                        x_out[:, 0],
                        [6.15850098e-01, 5.03136259e-01, 6.42419278e-01, -8.06477702e00, 2.42278904e02, -7.72113478e02],
                        decimal=6,
                    )
                else:
                    np.testing.assert_almost_equal(
                        x_out[:, 0],
                        [1.83404510e-01, 6.11852895e-01, 7.85175961e-01, -3.80891773e00, 1.20475911e02, -4.33290914e02],
                        decimal=6,
                    )

        else:
            if with_excitations:
                if with_external_force:
                    np.testing.assert_almost_equal(
                        x_out[:, 0],
                        [
                            0.6158501,
                            0.5031363,
                            0.6424193,
                            0.9195267,
                            -39.0487482,
                            45.3183429,
                            55.6555782,
                            50.4705269,
                            0.3602559,
                            58.9237749,
                            29.7009419,
                            -15.1353494,
                        ],
                    )
                else:
                    np.testing.assert_almost_equal(
                        x_out[:, 0],
                        [
                            1.83404510e-01,
                            6.11852895e-01,
                            7.85175961e-01,
                            -9.72711369e00,
                            3.10865851e02,
                            -9.82724687e02,
                            -7.72228930e00,
                            -1.13759732e01,
                            9.51906209e01,
                            4.45077128e00,
                            -5.20261014e00,
                            -2.80864106e01,
                        ],
                        decimal=6,
                    )
            else:
                if with_external_force:
                    np.testing.assert_almost_equal(
                        x_out[:, 0],
                        [0.6158501, 0.50313626, 0.64241928, 0.91952666, -39.04874824, 45.31834295],
                    )
                else:
                    np.testing.assert_almost_equal(
                        x_out[:, 0],
                        [1.83404510e-01, 6.11852895e-01, 7.85175961e-01, -9.72711369e00, 3.10865851e02, -9.82724687e02],
                        decimal=6,
                    )