..
   Copyright 2021 IRT Saint-Exupéry, https://www.irt-saintexupery.com

   This work is licensed under the Creative Commons Attribution-ShareAlike 4.0
   International License. To view a copy of this license, visit
   http://creativecommons.org/licenses/by-sa/4.0/ or send a letter to Creative
   Commons, PO Box 1866, Mountain View, CA 94042, USA.

.. _gen_ode_algos:

Ordinary differential equations solvers
=======================================

.. warning::
   Some capabilities may require the :ref:`installation <installation>` of |g| with :ref:`all its features <dependencies>`
   and some others may depend on :ref:`plugins <plugins>`.

.. warning::
   All the features of the wrapped libraries may not be exposed through |g|.


.. note::
   The algorithm settings can be passed to a function of the form

   .. code-block:: python

      function(..., settings_model: AlgorithmSettings | None = None, **settings: Any)

   either one by one:

   .. code-block:: python

      function(..., setting_name_1=setting_name_1, setting_name_2=setting_name_2, ...)

   or using the argument name ``"settings_model"`` and the Pydantic model associated with the algorithm:

   .. code-block:: python

      settings_model = AlgorithmSettings(setting_name_1=setting_name_1, setting_name_2=setting_name_2, ...)
      function(..., settings_model=settings_model)








.. _BDF_options:

BDF
---



Module: :class:`gemseo.algos.ode.scipy_ode.scipy_ode`


Implicit multi-step variable-order (1 to 5) method based on a backward differentiation formula for the derivative approximation



.. code-block:: python
   :caption: Pydantic model of the settings for BDF

   from gemseo.settings.ode import BDF_Settings




More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.BDF.html.













































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**atol** : *typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional*

The absolute tolerance.


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**first_step** : *typing.Optional[typing.Annotated[float, Gt(gt=0)]], optional*

The initial step size.

If ``None``, let the algorithm choose.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**jac_sparsity** : *gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[float]] | None, optional*

Sparsity structure of the Jacobian matrix.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**max_step** : *<class 'float'>, optional*

The maximum allowed step size.


By default it is set to inf.


.. raw:: html

    </li>

    <li>

**rtol** : *typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional*

The relative tolerance.


By default it is set to 0.001.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _DOP853_options:

DOP853
------



Module: :class:`gemseo.algos.ode.scipy_ode.scipy_ode`


Explicit Runge-Kutta method of order 8



.. code-block:: python
   :caption: Pydantic model of the settings for DOP853

   from gemseo.settings.ode import DOP853_Settings




More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.DOP853.html.







































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**atol** : *typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional*

The absolute tolerance.


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**first_step** : *typing.Optional[typing.Annotated[float, Gt(gt=0)]], optional*

The initial step size.

If ``None``, let the algorithm choose.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**max_step** : *<class 'float'>, optional*

The maximum allowed step size.


By default it is set to inf.


.. raw:: html

    </li>

    <li>

**rtol** : *typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional*

The relative tolerance.


By default it is set to 0.001.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _LSODA_options:

LSODA
-----



Module: :class:`gemseo.algos.ode.scipy_ode.scipy_ode`


Adams/BDF method with automatic stiffness detection/switching



.. code-block:: python
   :caption: Pydantic model of the settings for LSODA

   from gemseo.settings.ode import LSODA_Settings




More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.LSODA.html.

























































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**atol** : *typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional*

The absolute tolerance.


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**first_step** : *typing.Optional[typing.Annotated[float, Gt(gt=0)]], optional*

The initial step size.

If ``None``, let the algorithm choose.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**lband** : *int | None, optional*

The lower boundary of the bandwidth of the Jacobian.

The SciPy documentation does not mention what happens if ``None``.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**max_step** : *<class 'float'>, optional*

The maximum allowed step size.


By default it is set to inf.


.. raw:: html

    </li>

    <li>

**min_step** : *<class 'int'>, optional*

Minimum allowed step size.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**rtol** : *typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional*

The relative tolerance.


By default it is set to 0.001.


.. raw:: html

    </li>

    <li>

**uband** : *int | None, optional*

The upper boundary of the bandwidth of the Jacobian.

The SciPy documentation does not mention what happens if ``None``.


By default it is set to None.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _PETSC_ODE_ALPHA_options:

PETSC_ODE_ALPHA
---------------


.. note::
    The plugin `gemseo_petsc <https://gitlab.com/gemseo/dev/gemseo-petsc>`_ is required.


Module: :class:`gemseo_petsc.ode.ts_library`






More details about the algorithm and its settings on https://petsc.org/release/manualpages/TS/.



























































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Required settings</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**maximum_steps** : *<class 'int'>*

Total number of time steps to run

.. raw:: html

    </li>

    <li>

**time_step** : *<class 'float'>*

Value of the time step.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**atol** : *<class 'float'>, optional*

The absolute convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**compute_adjoint** : *<class 'bool'>, optional*

Whether to use adjoint to compute the derivatives.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**events_tol** : *<class 'float'>, optional*

Tolerance for event (indicator function) zero crossings.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**events_vtol** : *gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Ge(ge=0)]]] | None, optional*

Array of tolerances, used in preference to  ``events_tol``
           if present. The size of vtol should be equal to the number of events on
           the given process.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to None.


.. raw:: html

    </li>

    <li>

**final_time_behaviour** : *gemseo_petsc.ode.settings.petsc_ts_settings.FinalTimeBehavior | None, optional*

Behaviour to adopt near the final time.
            For more information, see
            https://petsc.org/release/manualpages/TS/TSExactFinalTimeOption/


By default it is set to TS_EXACTFINALTIME_MATCHSTEP.


.. raw:: html

    </li>

    <li>

**max_disk_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on the disk.
            When zero, no maximum is set.
            For more information on checkpoints, see:
            [https://petsc4py.readthedocs.io/en/stable/manual/sensitivity_analysis/#checkpointing]
            Maps the PETSC.TS ts_trajectory_max_cps_disk option.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**max_memory_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on in memory.
            When zero, no maximum is set.
            Maps the PETSC.TS ts_trajectory_max_cps_ram option.
            When both max_memory_checkpoints and max_disk_checkpoints are set,
            an automatic mix checkpointing (disk and RAM) scheme is setup.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**ode_solver_type** : *gemseo_petsc.ode.settings.petsc_ts_settings.ODESolverType | None, optional*

The type of ODE solver.


By default it is set to PETSC_ODE_RK.


.. raw:: html

    </li>

    <li>

**rtol** : *<class 'float'>, optional*

The relative convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**use_jacobian** : *<class 'bool'>, optional*

Whether to use the jacobian of the RHS.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**use_memory_checkpoints** : *<class 'bool'>, optional*

Whether to store checkpoints in the RAM.
            By default the checkpoints are stored on the disk as binary files.
            Maps the PETSC.TS ts_trajectory_type memory option.


By default it is set to False.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _PETSC_ODE_BASICSYMPLECTIC_options:

PETSC_ODE_BASICSYMPLECTIC
-------------------------


.. note::
    The plugin `gemseo_petsc <https://gitlab.com/gemseo/dev/gemseo-petsc>`_ is required.


Module: :class:`gemseo_petsc.ode.ts_library`






More details about the algorithm and its settings on https://petsc.org/release/manualpages/TS/.



























































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Required settings</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**maximum_steps** : *<class 'int'>*

Total number of time steps to run

.. raw:: html

    </li>

    <li>

**time_step** : *<class 'float'>*

Value of the time step.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**atol** : *<class 'float'>, optional*

The absolute convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**compute_adjoint** : *<class 'bool'>, optional*

Whether to use adjoint to compute the derivatives.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**events_tol** : *<class 'float'>, optional*

Tolerance for event (indicator function) zero crossings.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**events_vtol** : *gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Ge(ge=0)]]] | None, optional*

Array of tolerances, used in preference to  ``events_tol``
           if present. The size of vtol should be equal to the number of events on
           the given process.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to None.


.. raw:: html

    </li>

    <li>

**final_time_behaviour** : *gemseo_petsc.ode.settings.petsc_ts_settings.FinalTimeBehavior | None, optional*

Behaviour to adopt near the final time.
            For more information, see
            https://petsc.org/release/manualpages/TS/TSExactFinalTimeOption/


By default it is set to TS_EXACTFINALTIME_MATCHSTEP.


.. raw:: html

    </li>

    <li>

**max_disk_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on the disk.
            When zero, no maximum is set.
            For more information on checkpoints, see:
            [https://petsc4py.readthedocs.io/en/stable/manual/sensitivity_analysis/#checkpointing]
            Maps the PETSC.TS ts_trajectory_max_cps_disk option.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**max_memory_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on in memory.
            When zero, no maximum is set.
            Maps the PETSC.TS ts_trajectory_max_cps_ram option.
            When both max_memory_checkpoints and max_disk_checkpoints are set,
            an automatic mix checkpointing (disk and RAM) scheme is setup.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**ode_solver_type** : *gemseo_petsc.ode.settings.petsc_ts_settings.ODESolverType | None, optional*

The type of ODE solver.


By default it is set to PETSC_ODE_RK.


.. raw:: html

    </li>

    <li>

**rtol** : *<class 'float'>, optional*

The relative convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**use_jacobian** : *<class 'bool'>, optional*

Whether to use the jacobian of the RHS.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**use_memory_checkpoints** : *<class 'bool'>, optional*

Whether to store checkpoints in the RAM.
            By default the checkpoints are stored on the disk as binary files.
            Maps the PETSC.TS ts_trajectory_type memory option.


By default it is set to False.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _PETSC_ODE_BEULER_options:

PETSC_ODE_BEULER
----------------


.. note::
    The plugin `gemseo_petsc <https://gitlab.com/gemseo/dev/gemseo-petsc>`_ is required.


Module: :class:`gemseo_petsc.ode.ts_library`






More details about the algorithm and its settings on https://petsc.org/release/manualpages/TS/.



























































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Required settings</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**maximum_steps** : *<class 'int'>*

Total number of time steps to run

.. raw:: html

    </li>

    <li>

**time_step** : *<class 'float'>*

Value of the time step.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**atol** : *<class 'float'>, optional*

The absolute convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**compute_adjoint** : *<class 'bool'>, optional*

Whether to use adjoint to compute the derivatives.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**events_tol** : *<class 'float'>, optional*

Tolerance for event (indicator function) zero crossings.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**events_vtol** : *gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Ge(ge=0)]]] | None, optional*

Array of tolerances, used in preference to  ``events_tol``
           if present. The size of vtol should be equal to the number of events on
           the given process.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to None.


.. raw:: html

    </li>

    <li>

**final_time_behaviour** : *gemseo_petsc.ode.settings.petsc_ts_settings.FinalTimeBehavior | None, optional*

Behaviour to adopt near the final time.
            For more information, see
            https://petsc.org/release/manualpages/TS/TSExactFinalTimeOption/


By default it is set to TS_EXACTFINALTIME_MATCHSTEP.


.. raw:: html

    </li>

    <li>

**max_disk_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on the disk.
            When zero, no maximum is set.
            For more information on checkpoints, see:
            [https://petsc4py.readthedocs.io/en/stable/manual/sensitivity_analysis/#checkpointing]
            Maps the PETSC.TS ts_trajectory_max_cps_disk option.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**max_memory_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on in memory.
            When zero, no maximum is set.
            Maps the PETSC.TS ts_trajectory_max_cps_ram option.
            When both max_memory_checkpoints and max_disk_checkpoints are set,
            an automatic mix checkpointing (disk and RAM) scheme is setup.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**ode_solver_type** : *gemseo_petsc.ode.settings.petsc_ts_settings.ODESolverType | None, optional*

The type of ODE solver.


By default it is set to PETSC_ODE_RK.


.. raw:: html

    </li>

    <li>

**rtol** : *<class 'float'>, optional*

The relative convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**use_jacobian** : *<class 'bool'>, optional*

Whether to use the jacobian of the RHS.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**use_memory_checkpoints** : *<class 'bool'>, optional*

Whether to store checkpoints in the RAM.
            By default the checkpoints are stored on the disk as binary files.
            Maps the PETSC.TS ts_trajectory_type memory option.


By default it is set to False.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _PETSC_ODE_CN_options:

PETSC_ODE_CN
------------


.. note::
    The plugin `gemseo_petsc <https://gitlab.com/gemseo/dev/gemseo-petsc>`_ is required.


Module: :class:`gemseo_petsc.ode.ts_library`






More details about the algorithm and its settings on https://petsc.org/release/manualpages/TS/.



























































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Required settings</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**maximum_steps** : *<class 'int'>*

Total number of time steps to run

.. raw:: html

    </li>

    <li>

**time_step** : *<class 'float'>*

Value of the time step.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**atol** : *<class 'float'>, optional*

The absolute convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**compute_adjoint** : *<class 'bool'>, optional*

Whether to use adjoint to compute the derivatives.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**events_tol** : *<class 'float'>, optional*

Tolerance for event (indicator function) zero crossings.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**events_vtol** : *gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Ge(ge=0)]]] | None, optional*

Array of tolerances, used in preference to  ``events_tol``
           if present. The size of vtol should be equal to the number of events on
           the given process.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to None.


.. raw:: html

    </li>

    <li>

**final_time_behaviour** : *gemseo_petsc.ode.settings.petsc_ts_settings.FinalTimeBehavior | None, optional*

Behaviour to adopt near the final time.
            For more information, see
            https://petsc.org/release/manualpages/TS/TSExactFinalTimeOption/


By default it is set to TS_EXACTFINALTIME_MATCHSTEP.


.. raw:: html

    </li>

    <li>

**max_disk_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on the disk.
            When zero, no maximum is set.
            For more information on checkpoints, see:
            [https://petsc4py.readthedocs.io/en/stable/manual/sensitivity_analysis/#checkpointing]
            Maps the PETSC.TS ts_trajectory_max_cps_disk option.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**max_memory_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on in memory.
            When zero, no maximum is set.
            Maps the PETSC.TS ts_trajectory_max_cps_ram option.
            When both max_memory_checkpoints and max_disk_checkpoints are set,
            an automatic mix checkpointing (disk and RAM) scheme is setup.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**ode_solver_type** : *gemseo_petsc.ode.settings.petsc_ts_settings.ODESolverType | None, optional*

The type of ODE solver.


By default it is set to PETSC_ODE_RK.


.. raw:: html

    </li>

    <li>

**rtol** : *<class 'float'>, optional*

The relative convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**use_jacobian** : *<class 'bool'>, optional*

Whether to use the jacobian of the RHS.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**use_memory_checkpoints** : *<class 'bool'>, optional*

Whether to store checkpoints in the RAM.
            By default the checkpoints are stored on the disk as binary files.
            Maps the PETSC.TS ts_trajectory_type memory option.


By default it is set to False.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _PETSC_ODE_EIMEX_options:

PETSC_ODE_EIMEX
---------------


.. note::
    The plugin `gemseo_petsc <https://gitlab.com/gemseo/dev/gemseo-petsc>`_ is required.


Module: :class:`gemseo_petsc.ode.ts_library`






More details about the algorithm and its settings on https://petsc.org/release/manualpages/TS/.



























































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Required settings</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**maximum_steps** : *<class 'int'>*

Total number of time steps to run

.. raw:: html

    </li>

    <li>

**time_step** : *<class 'float'>*

Value of the time step.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**atol** : *<class 'float'>, optional*

The absolute convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**compute_adjoint** : *<class 'bool'>, optional*

Whether to use adjoint to compute the derivatives.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**events_tol** : *<class 'float'>, optional*

Tolerance for event (indicator function) zero crossings.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**events_vtol** : *gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Ge(ge=0)]]] | None, optional*

Array of tolerances, used in preference to  ``events_tol``
           if present. The size of vtol should be equal to the number of events on
           the given process.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to None.


.. raw:: html

    </li>

    <li>

**final_time_behaviour** : *gemseo_petsc.ode.settings.petsc_ts_settings.FinalTimeBehavior | None, optional*

Behaviour to adopt near the final time.
            For more information, see
            https://petsc.org/release/manualpages/TS/TSExactFinalTimeOption/


By default it is set to TS_EXACTFINALTIME_MATCHSTEP.


.. raw:: html

    </li>

    <li>

**max_disk_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on the disk.
            When zero, no maximum is set.
            For more information on checkpoints, see:
            [https://petsc4py.readthedocs.io/en/stable/manual/sensitivity_analysis/#checkpointing]
            Maps the PETSC.TS ts_trajectory_max_cps_disk option.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**max_memory_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on in memory.
            When zero, no maximum is set.
            Maps the PETSC.TS ts_trajectory_max_cps_ram option.
            When both max_memory_checkpoints and max_disk_checkpoints are set,
            an automatic mix checkpointing (disk and RAM) scheme is setup.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**ode_solver_type** : *gemseo_petsc.ode.settings.petsc_ts_settings.ODESolverType | None, optional*

The type of ODE solver.


By default it is set to PETSC_ODE_RK.


.. raw:: html

    </li>

    <li>

**rtol** : *<class 'float'>, optional*

The relative convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**use_jacobian** : *<class 'bool'>, optional*

Whether to use the jacobian of the RHS.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**use_memory_checkpoints** : *<class 'bool'>, optional*

Whether to store checkpoints in the RAM.
            By default the checkpoints are stored on the disk as binary files.
            Maps the PETSC.TS ts_trajectory_type memory option.


By default it is set to False.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _PETSC_ODE_ERKIMEX_options:

PETSC_ODE_ERKIMEX
-----------------


.. note::
    The plugin `gemseo_petsc <https://gitlab.com/gemseo/dev/gemseo-petsc>`_ is required.


Module: :class:`gemseo_petsc.ode.ts_library`






More details about the algorithm and its settings on https://petsc.org/release/manualpages/TS/.



























































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Required settings</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**maximum_steps** : *<class 'int'>*

Total number of time steps to run

.. raw:: html

    </li>

    <li>

**time_step** : *<class 'float'>*

Value of the time step.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**atol** : *<class 'float'>, optional*

The absolute convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**compute_adjoint** : *<class 'bool'>, optional*

Whether to use adjoint to compute the derivatives.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**events_tol** : *<class 'float'>, optional*

Tolerance for event (indicator function) zero crossings.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**events_vtol** : *gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Ge(ge=0)]]] | None, optional*

Array of tolerances, used in preference to  ``events_tol``
           if present. The size of vtol should be equal to the number of events on
           the given process.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to None.


.. raw:: html

    </li>

    <li>

**final_time_behaviour** : *gemseo_petsc.ode.settings.petsc_ts_settings.FinalTimeBehavior | None, optional*

Behaviour to adopt near the final time.
            For more information, see
            https://petsc.org/release/manualpages/TS/TSExactFinalTimeOption/


By default it is set to TS_EXACTFINALTIME_MATCHSTEP.


.. raw:: html

    </li>

    <li>

**max_disk_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on the disk.
            When zero, no maximum is set.
            For more information on checkpoints, see:
            [https://petsc4py.readthedocs.io/en/stable/manual/sensitivity_analysis/#checkpointing]
            Maps the PETSC.TS ts_trajectory_max_cps_disk option.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**max_memory_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on in memory.
            When zero, no maximum is set.
            Maps the PETSC.TS ts_trajectory_max_cps_ram option.
            When both max_memory_checkpoints and max_disk_checkpoints are set,
            an automatic mix checkpointing (disk and RAM) scheme is setup.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**ode_solver_type** : *gemseo_petsc.ode.settings.petsc_ts_settings.ODESolverType | None, optional*

The type of ODE solver.


By default it is set to PETSC_ODE_RK.


.. raw:: html

    </li>

    <li>

**rtol** : *<class 'float'>, optional*

The relative convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**use_jacobian** : *<class 'bool'>, optional*

Whether to use the jacobian of the RHS.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**use_memory_checkpoints** : *<class 'bool'>, optional*

Whether to store checkpoints in the RAM.
            By default the checkpoints are stored on the disk as binary files.
            Maps the PETSC.TS ts_trajectory_type memory option.


By default it is set to False.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _PETSC_ODE_EULER_options:

PETSC_ODE_EULER
---------------


.. note::
    The plugin `gemseo_petsc <https://gitlab.com/gemseo/dev/gemseo-petsc>`_ is required.


Module: :class:`gemseo_petsc.ode.ts_library`






More details about the algorithm and its settings on https://petsc.org/release/manualpages/TS/.



























































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Required settings</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**maximum_steps** : *<class 'int'>*

Total number of time steps to run

.. raw:: html

    </li>

    <li>

**time_step** : *<class 'float'>*

Value of the time step.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**atol** : *<class 'float'>, optional*

The absolute convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**compute_adjoint** : *<class 'bool'>, optional*

Whether to use adjoint to compute the derivatives.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**events_tol** : *<class 'float'>, optional*

Tolerance for event (indicator function) zero crossings.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**events_vtol** : *gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Ge(ge=0)]]] | None, optional*

Array of tolerances, used in preference to  ``events_tol``
           if present. The size of vtol should be equal to the number of events on
           the given process.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to None.


.. raw:: html

    </li>

    <li>

**final_time_behaviour** : *gemseo_petsc.ode.settings.petsc_ts_settings.FinalTimeBehavior | None, optional*

Behaviour to adopt near the final time.
            For more information, see
            https://petsc.org/release/manualpages/TS/TSExactFinalTimeOption/


By default it is set to TS_EXACTFINALTIME_MATCHSTEP.


.. raw:: html

    </li>

    <li>

**max_disk_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on the disk.
            When zero, no maximum is set.
            For more information on checkpoints, see:
            [https://petsc4py.readthedocs.io/en/stable/manual/sensitivity_analysis/#checkpointing]
            Maps the PETSC.TS ts_trajectory_max_cps_disk option.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**max_memory_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on in memory.
            When zero, no maximum is set.
            Maps the PETSC.TS ts_trajectory_max_cps_ram option.
            When both max_memory_checkpoints and max_disk_checkpoints are set,
            an automatic mix checkpointing (disk and RAM) scheme is setup.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**ode_solver_type** : *gemseo_petsc.ode.settings.petsc_ts_settings.ODESolverType | None, optional*

The type of ODE solver.


By default it is set to PETSC_ODE_RK.


.. raw:: html

    </li>

    <li>

**rtol** : *<class 'float'>, optional*

The relative convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**use_jacobian** : *<class 'bool'>, optional*

Whether to use the jacobian of the RHS.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**use_memory_checkpoints** : *<class 'bool'>, optional*

Whether to store checkpoints in the RAM.
            By default the checkpoints are stored on the disk as binary files.
            Maps the PETSC.TS ts_trajectory_type memory option.


By default it is set to False.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _PETSC_ODE_GL_options:

PETSC_ODE_GL
------------


.. note::
    The plugin `gemseo_petsc <https://gitlab.com/gemseo/dev/gemseo-petsc>`_ is required.


Module: :class:`gemseo_petsc.ode.ts_library`






More details about the algorithm and its settings on https://petsc.org/release/manualpages/TS/.



























































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Required settings</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**maximum_steps** : *<class 'int'>*

Total number of time steps to run

.. raw:: html

    </li>

    <li>

**time_step** : *<class 'float'>*

Value of the time step.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**atol** : *<class 'float'>, optional*

The absolute convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**compute_adjoint** : *<class 'bool'>, optional*

Whether to use adjoint to compute the derivatives.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**events_tol** : *<class 'float'>, optional*

Tolerance for event (indicator function) zero crossings.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**events_vtol** : *gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Ge(ge=0)]]] | None, optional*

Array of tolerances, used in preference to  ``events_tol``
           if present. The size of vtol should be equal to the number of events on
           the given process.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to None.


.. raw:: html

    </li>

    <li>

**final_time_behaviour** : *gemseo_petsc.ode.settings.petsc_ts_settings.FinalTimeBehavior | None, optional*

Behaviour to adopt near the final time.
            For more information, see
            https://petsc.org/release/manualpages/TS/TSExactFinalTimeOption/


By default it is set to TS_EXACTFINALTIME_MATCHSTEP.


.. raw:: html

    </li>

    <li>

**max_disk_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on the disk.
            When zero, no maximum is set.
            For more information on checkpoints, see:
            [https://petsc4py.readthedocs.io/en/stable/manual/sensitivity_analysis/#checkpointing]
            Maps the PETSC.TS ts_trajectory_max_cps_disk option.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**max_memory_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on in memory.
            When zero, no maximum is set.
            Maps the PETSC.TS ts_trajectory_max_cps_ram option.
            When both max_memory_checkpoints and max_disk_checkpoints are set,
            an automatic mix checkpointing (disk and RAM) scheme is setup.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**ode_solver_type** : *gemseo_petsc.ode.settings.petsc_ts_settings.ODESolverType | None, optional*

The type of ODE solver.


By default it is set to PETSC_ODE_RK.


.. raw:: html

    </li>

    <li>

**rtol** : *<class 'float'>, optional*

The relative convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**use_jacobian** : *<class 'bool'>, optional*

Whether to use the jacobian of the RHS.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**use_memory_checkpoints** : *<class 'bool'>, optional*

Whether to store checkpoints in the RAM.
            By default the checkpoints are stored on the disk as binary files.
            Maps the PETSC.TS ts_trajectory_type memory option.


By default it is set to False.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _PETSC_ODE_GLEE_options:

PETSC_ODE_GLEE
--------------


.. note::
    The plugin `gemseo_petsc <https://gitlab.com/gemseo/dev/gemseo-petsc>`_ is required.


Module: :class:`gemseo_petsc.ode.ts_library`






More details about the algorithm and its settings on https://petsc.org/release/manualpages/TS/.



























































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Required settings</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**maximum_steps** : *<class 'int'>*

Total number of time steps to run

.. raw:: html

    </li>

    <li>

**time_step** : *<class 'float'>*

Value of the time step.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**atol** : *<class 'float'>, optional*

The absolute convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**compute_adjoint** : *<class 'bool'>, optional*

Whether to use adjoint to compute the derivatives.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**events_tol** : *<class 'float'>, optional*

Tolerance for event (indicator function) zero crossings.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**events_vtol** : *gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Ge(ge=0)]]] | None, optional*

Array of tolerances, used in preference to  ``events_tol``
           if present. The size of vtol should be equal to the number of events on
           the given process.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to None.


.. raw:: html

    </li>

    <li>

**final_time_behaviour** : *gemseo_petsc.ode.settings.petsc_ts_settings.FinalTimeBehavior | None, optional*

Behaviour to adopt near the final time.
            For more information, see
            https://petsc.org/release/manualpages/TS/TSExactFinalTimeOption/


By default it is set to TS_EXACTFINALTIME_MATCHSTEP.


.. raw:: html

    </li>

    <li>

**max_disk_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on the disk.
            When zero, no maximum is set.
            For more information on checkpoints, see:
            [https://petsc4py.readthedocs.io/en/stable/manual/sensitivity_analysis/#checkpointing]
            Maps the PETSC.TS ts_trajectory_max_cps_disk option.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**max_memory_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on in memory.
            When zero, no maximum is set.
            Maps the PETSC.TS ts_trajectory_max_cps_ram option.
            When both max_memory_checkpoints and max_disk_checkpoints are set,
            an automatic mix checkpointing (disk and RAM) scheme is setup.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**ode_solver_type** : *gemseo_petsc.ode.settings.petsc_ts_settings.ODESolverType | None, optional*

The type of ODE solver.


By default it is set to PETSC_ODE_RK.


.. raw:: html

    </li>

    <li>

**rtol** : *<class 'float'>, optional*

The relative convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**use_jacobian** : *<class 'bool'>, optional*

Whether to use the jacobian of the RHS.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**use_memory_checkpoints** : *<class 'bool'>, optional*

Whether to store checkpoints in the RAM.
            By default the checkpoints are stored on the disk as binary files.
            Maps the PETSC.TS ts_trajectory_type memory option.


By default it is set to False.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _PETSC_ODE_IRK_options:

PETSC_ODE_IRK
-------------


.. note::
    The plugin `gemseo_petsc <https://gitlab.com/gemseo/dev/gemseo-petsc>`_ is required.


Module: :class:`gemseo_petsc.ode.ts_library`






More details about the algorithm and its settings on https://petsc.org/release/manualpages/TS/.



























































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Required settings</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**maximum_steps** : *<class 'int'>*

Total number of time steps to run

.. raw:: html

    </li>

    <li>

**time_step** : *<class 'float'>*

Value of the time step.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**atol** : *<class 'float'>, optional*

The absolute convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**compute_adjoint** : *<class 'bool'>, optional*

Whether to use adjoint to compute the derivatives.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**events_tol** : *<class 'float'>, optional*

Tolerance for event (indicator function) zero crossings.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**events_vtol** : *gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Ge(ge=0)]]] | None, optional*

Array of tolerances, used in preference to  ``events_tol``
           if present. The size of vtol should be equal to the number of events on
           the given process.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to None.


.. raw:: html

    </li>

    <li>

**final_time_behaviour** : *gemseo_petsc.ode.settings.petsc_ts_settings.FinalTimeBehavior | None, optional*

Behaviour to adopt near the final time.
            For more information, see
            https://petsc.org/release/manualpages/TS/TSExactFinalTimeOption/


By default it is set to TS_EXACTFINALTIME_MATCHSTEP.


.. raw:: html

    </li>

    <li>

**max_disk_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on the disk.
            When zero, no maximum is set.
            For more information on checkpoints, see:
            [https://petsc4py.readthedocs.io/en/stable/manual/sensitivity_analysis/#checkpointing]
            Maps the PETSC.TS ts_trajectory_max_cps_disk option.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**max_memory_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on in memory.
            When zero, no maximum is set.
            Maps the PETSC.TS ts_trajectory_max_cps_ram option.
            When both max_memory_checkpoints and max_disk_checkpoints are set,
            an automatic mix checkpointing (disk and RAM) scheme is setup.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**ode_solver_type** : *gemseo_petsc.ode.settings.petsc_ts_settings.ODESolverType | None, optional*

The type of ODE solver.


By default it is set to PETSC_ODE_RK.


.. raw:: html

    </li>

    <li>

**rtol** : *<class 'float'>, optional*

The relative convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**use_jacobian** : *<class 'bool'>, optional*

Whether to use the jacobian of the RHS.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**use_memory_checkpoints** : *<class 'bool'>, optional*

Whether to store checkpoints in the RAM.
            By default the checkpoints are stored on the disk as binary files.
            Maps the PETSC.TS ts_trajectory_type memory option.


By default it is set to False.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _PETSC_ODE_MPRK_options:

PETSC_ODE_MPRK
--------------


.. note::
    The plugin `gemseo_petsc <https://gitlab.com/gemseo/dev/gemseo-petsc>`_ is required.


Module: :class:`gemseo_petsc.ode.ts_library`






More details about the algorithm and its settings on https://petsc.org/release/manualpages/TS/.



























































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Required settings</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**maximum_steps** : *<class 'int'>*

Total number of time steps to run

.. raw:: html

    </li>

    <li>

**time_step** : *<class 'float'>*

Value of the time step.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**atol** : *<class 'float'>, optional*

The absolute convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**compute_adjoint** : *<class 'bool'>, optional*

Whether to use adjoint to compute the derivatives.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**events_tol** : *<class 'float'>, optional*

Tolerance for event (indicator function) zero crossings.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**events_vtol** : *gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Ge(ge=0)]]] | None, optional*

Array of tolerances, used in preference to  ``events_tol``
           if present. The size of vtol should be equal to the number of events on
           the given process.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to None.


.. raw:: html

    </li>

    <li>

**final_time_behaviour** : *gemseo_petsc.ode.settings.petsc_ts_settings.FinalTimeBehavior | None, optional*

Behaviour to adopt near the final time.
            For more information, see
            https://petsc.org/release/manualpages/TS/TSExactFinalTimeOption/


By default it is set to TS_EXACTFINALTIME_MATCHSTEP.


.. raw:: html

    </li>

    <li>

**max_disk_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on the disk.
            When zero, no maximum is set.
            For more information on checkpoints, see:
            [https://petsc4py.readthedocs.io/en/stable/manual/sensitivity_analysis/#checkpointing]
            Maps the PETSC.TS ts_trajectory_max_cps_disk option.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**max_memory_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on in memory.
            When zero, no maximum is set.
            Maps the PETSC.TS ts_trajectory_max_cps_ram option.
            When both max_memory_checkpoints and max_disk_checkpoints are set,
            an automatic mix checkpointing (disk and RAM) scheme is setup.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**ode_solver_type** : *gemseo_petsc.ode.settings.petsc_ts_settings.ODESolverType | None, optional*

The type of ODE solver.


By default it is set to PETSC_ODE_RK.


.. raw:: html

    </li>

    <li>

**rtol** : *<class 'float'>, optional*

The relative convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**use_jacobian** : *<class 'bool'>, optional*

Whether to use the jacobian of the RHS.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**use_memory_checkpoints** : *<class 'bool'>, optional*

Whether to store checkpoints in the RAM.
            By default the checkpoints are stored on the disk as binary files.
            Maps the PETSC.TS ts_trajectory_type memory option.


By default it is set to False.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _PETSC_ODE_RK_options:

PETSC_ODE_RK
------------


.. note::
    The plugin `gemseo_petsc <https://gitlab.com/gemseo/dev/gemseo-petsc>`_ is required.


Module: :class:`gemseo_petsc.ode.ts_library`






More details about the algorithm and its settings on https://petsc.org/release/manualpages/TS/.



























































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Required settings</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**maximum_steps** : *<class 'int'>*

Total number of time steps to run

.. raw:: html

    </li>

    <li>

**time_step** : *<class 'float'>*

Value of the time step.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**atol** : *<class 'float'>, optional*

The absolute convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**compute_adjoint** : *<class 'bool'>, optional*

Whether to use adjoint to compute the derivatives.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**events_tol** : *<class 'float'>, optional*

Tolerance for event (indicator function) zero crossings.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**events_vtol** : *gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Ge(ge=0)]]] | None, optional*

Array of tolerances, used in preference to  ``events_tol``
           if present. The size of vtol should be equal to the number of events on
           the given process.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to None.


.. raw:: html

    </li>

    <li>

**final_time_behaviour** : *gemseo_petsc.ode.settings.petsc_ts_settings.FinalTimeBehavior | None, optional*

Behaviour to adopt near the final time.
            For more information, see
            https://petsc.org/release/manualpages/TS/TSExactFinalTimeOption/


By default it is set to TS_EXACTFINALTIME_MATCHSTEP.


.. raw:: html

    </li>

    <li>

**max_disk_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on the disk.
            When zero, no maximum is set.
            For more information on checkpoints, see:
            [https://petsc4py.readthedocs.io/en/stable/manual/sensitivity_analysis/#checkpointing]
            Maps the PETSC.TS ts_trajectory_max_cps_disk option.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**max_memory_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on in memory.
            When zero, no maximum is set.
            Maps the PETSC.TS ts_trajectory_max_cps_ram option.
            When both max_memory_checkpoints and max_disk_checkpoints are set,
            an automatic mix checkpointing (disk and RAM) scheme is setup.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**ode_solver_type** : *gemseo_petsc.ode.settings.petsc_ts_settings.ODESolverType | None, optional*

The type of ODE solver.


By default it is set to PETSC_ODE_RK.


.. raw:: html

    </li>

    <li>

**rtol** : *<class 'float'>, optional*

The relative convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**use_jacobian** : *<class 'bool'>, optional*

Whether to use the jacobian of the RHS.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**use_memory_checkpoints** : *<class 'bool'>, optional*

Whether to store checkpoints in the RAM.
            By default the checkpoints are stored on the disk as binary files.
            Maps the PETSC.TS ts_trajectory_type memory option.


By default it is set to False.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _PETSC_ODE_ROSW_options:

PETSC_ODE_ROSW
--------------


.. note::
    The plugin `gemseo_petsc <https://gitlab.com/gemseo/dev/gemseo-petsc>`_ is required.


Module: :class:`gemseo_petsc.ode.ts_library`






More details about the algorithm and its settings on https://petsc.org/release/manualpages/TS/.



























































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Required settings</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**maximum_steps** : *<class 'int'>*

Total number of time steps to run

.. raw:: html

    </li>

    <li>

**time_step** : *<class 'float'>*

Value of the time step.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**atol** : *<class 'float'>, optional*

The absolute convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**compute_adjoint** : *<class 'bool'>, optional*

Whether to use adjoint to compute the derivatives.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**events_tol** : *<class 'float'>, optional*

Tolerance for event (indicator function) zero crossings.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**events_vtol** : *gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Ge(ge=0)]]] | None, optional*

Array of tolerances, used in preference to  ``events_tol``
           if present. The size of vtol should be equal to the number of events on
           the given process.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to None.


.. raw:: html

    </li>

    <li>

**final_time_behaviour** : *gemseo_petsc.ode.settings.petsc_ts_settings.FinalTimeBehavior | None, optional*

Behaviour to adopt near the final time.
            For more information, see
            https://petsc.org/release/manualpages/TS/TSExactFinalTimeOption/


By default it is set to TS_EXACTFINALTIME_MATCHSTEP.


.. raw:: html

    </li>

    <li>

**max_disk_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on the disk.
            When zero, no maximum is set.
            For more information on checkpoints, see:
            [https://petsc4py.readthedocs.io/en/stable/manual/sensitivity_analysis/#checkpointing]
            Maps the PETSC.TS ts_trajectory_max_cps_disk option.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**max_memory_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on in memory.
            When zero, no maximum is set.
            Maps the PETSC.TS ts_trajectory_max_cps_ram option.
            When both max_memory_checkpoints and max_disk_checkpoints are set,
            an automatic mix checkpointing (disk and RAM) scheme is setup.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**ode_solver_type** : *gemseo_petsc.ode.settings.petsc_ts_settings.ODESolverType | None, optional*

The type of ODE solver.


By default it is set to PETSC_ODE_RK.


.. raw:: html

    </li>

    <li>

**rtol** : *<class 'float'>, optional*

The relative convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**use_jacobian** : *<class 'bool'>, optional*

Whether to use the jacobian of the RHS.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**use_memory_checkpoints** : *<class 'bool'>, optional*

Whether to store checkpoints in the RAM.
            By default the checkpoints are stored on the disk as binary files.
            Maps the PETSC.TS ts_trajectory_type memory option.


By default it is set to False.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _PETSC_ODE_SSP_options:

PETSC_ODE_SSP
-------------


.. note::
    The plugin `gemseo_petsc <https://gitlab.com/gemseo/dev/gemseo-petsc>`_ is required.


Module: :class:`gemseo_petsc.ode.ts_library`






More details about the algorithm and its settings on https://petsc.org/release/manualpages/TS/.



























































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Required settings</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**maximum_steps** : *<class 'int'>*

Total number of time steps to run

.. raw:: html

    </li>

    <li>

**time_step** : *<class 'float'>*

Value of the time step.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**atol** : *<class 'float'>, optional*

The absolute convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**compute_adjoint** : *<class 'bool'>, optional*

Whether to use adjoint to compute the derivatives.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**events_tol** : *<class 'float'>, optional*

Tolerance for event (indicator function) zero crossings.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**events_vtol** : *gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Ge(ge=0)]]] | None, optional*

Array of tolerances, used in preference to  ``events_tol``
           if present. The size of vtol should be equal to the number of events on
           the given process.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to None.


.. raw:: html

    </li>

    <li>

**final_time_behaviour** : *gemseo_petsc.ode.settings.petsc_ts_settings.FinalTimeBehavior | None, optional*

Behaviour to adopt near the final time.
            For more information, see
            https://petsc.org/release/manualpages/TS/TSExactFinalTimeOption/


By default it is set to TS_EXACTFINALTIME_MATCHSTEP.


.. raw:: html

    </li>

    <li>

**max_disk_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on the disk.
            When zero, no maximum is set.
            For more information on checkpoints, see:
            [https://petsc4py.readthedocs.io/en/stable/manual/sensitivity_analysis/#checkpointing]
            Maps the PETSC.TS ts_trajectory_max_cps_disk option.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**max_memory_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on in memory.
            When zero, no maximum is set.
            Maps the PETSC.TS ts_trajectory_max_cps_ram option.
            When both max_memory_checkpoints and max_disk_checkpoints are set,
            an automatic mix checkpointing (disk and RAM) scheme is setup.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**ode_solver_type** : *gemseo_petsc.ode.settings.petsc_ts_settings.ODESolverType | None, optional*

The type of ODE solver.


By default it is set to PETSC_ODE_RK.


.. raw:: html

    </li>

    <li>

**rtol** : *<class 'float'>, optional*

The relative convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**use_jacobian** : *<class 'bool'>, optional*

Whether to use the jacobian of the RHS.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**use_memory_checkpoints** : *<class 'bool'>, optional*

Whether to store checkpoints in the RAM.
            By default the checkpoints are stored on the disk as binary files.
            Maps the PETSC.TS ts_trajectory_type memory option.


By default it is set to False.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _PETSC_ODE_THETA*_options:

PETSC_ODE_THETA*
----------------


.. note::
    The plugin `gemseo_petsc <https://gitlab.com/gemseo/dev/gemseo-petsc>`_ is required.


Module: :class:`gemseo_petsc.ode.ts_library`






More details about the algorithm and its settings on https://petsc.org/release/manualpages/TS/.



























































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Required settings</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**maximum_steps** : *<class 'int'>*

Total number of time steps to run

.. raw:: html

    </li>

    <li>

**time_step** : *<class 'float'>*

Value of the time step.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**atol** : *<class 'float'>, optional*

The absolute convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**compute_adjoint** : *<class 'bool'>, optional*

Whether to use adjoint to compute the derivatives.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**events_tol** : *<class 'float'>, optional*

Tolerance for event (indicator function) zero crossings.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**events_vtol** : *gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Ge(ge=0)]]] | None, optional*

Array of tolerances, used in preference to  ``events_tol``
           if present. The size of vtol should be equal to the number of events on
           the given process.
           For more information, see
           https://petsc.org/release/manualpages/TS/TSSetEventTolerances/


By default it is set to None.


.. raw:: html

    </li>

    <li>

**final_time_behaviour** : *gemseo_petsc.ode.settings.petsc_ts_settings.FinalTimeBehavior | None, optional*

Behaviour to adopt near the final time.
            For more information, see
            https://petsc.org/release/manualpages/TS/TSExactFinalTimeOption/


By default it is set to TS_EXACTFINALTIME_MATCHSTEP.


.. raw:: html

    </li>

    <li>

**max_disk_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on the disk.
            When zero, no maximum is set.
            For more information on checkpoints, see:
            [https://petsc4py.readthedocs.io/en/stable/manual/sensitivity_analysis/#checkpointing]
            Maps the PETSC.TS ts_trajectory_max_cps_disk option.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**max_memory_checkpoints** : *<class 'int'>, optional*

Maximum number of checkpoints stored on in memory.
            When zero, no maximum is set.
            Maps the PETSC.TS ts_trajectory_max_cps_ram option.
            When both max_memory_checkpoints and max_disk_checkpoints are set,
            an automatic mix checkpointing (disk and RAM) scheme is setup.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**ode_solver_type** : *gemseo_petsc.ode.settings.petsc_ts_settings.ODESolverType | None, optional*

The type of ODE solver.


By default it is set to PETSC_ODE_RK.


.. raw:: html

    </li>

    <li>

**rtol** : *<class 'float'>, optional*

The relative convergence tolerance.

Set tolerance for local truncation error when using an adaptive controller. See:
[https://petsc.org/main/manualpages/TS/TSSetTolerances/]


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**use_jacobian** : *<class 'bool'>, optional*

Whether to use the jacobian of the RHS.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**use_memory_checkpoints** : *<class 'bool'>, optional*

Whether to store checkpoints in the RAM.
            By default the checkpoints are stored on the disk as binary files.
            Maps the PETSC.TS ts_trajectory_type memory option.


By default it is set to False.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _RK23_options:

RK23
----



Module: :class:`gemseo.algos.ode.scipy_ode.scipy_ode`


Explicit Runge-Kutta method of order 3(2)



.. code-block:: python
   :caption: Pydantic model of the settings for RK23

   from gemseo.settings.ode import RK23_Settings




More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.RK23.html.







































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**atol** : *typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional*

The absolute tolerance.


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**first_step** : *typing.Optional[typing.Annotated[float, Gt(gt=0)]], optional*

The initial step size.

If ``None``, let the algorithm choose.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**max_step** : *<class 'float'>, optional*

The maximum allowed step size.


By default it is set to inf.


.. raw:: html

    </li>

    <li>

**rtol** : *typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional*

The relative tolerance.


By default it is set to 0.001.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _RK45_options:

RK45
----



Module: :class:`gemseo.algos.ode.scipy_ode.scipy_ode`


Explicit Runge-Kutta method of order 5(4)



.. code-block:: python
   :caption: Pydantic model of the settings for RK45

   from gemseo.settings.ode import RK45_Settings




More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.RK45.html.







































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**atol** : *typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional*

The absolute tolerance.


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**first_step** : *typing.Optional[typing.Annotated[float, Gt(gt=0)]], optional*

The initial step size.

If ``None``, let the algorithm choose.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**max_step** : *<class 'float'>, optional*

The maximum allowed step size.


By default it is set to inf.


.. raw:: html

    </li>

    <li>

**rtol** : *typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional*

The relative tolerance.


By default it is set to 0.001.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _Radau_options:

Radau
-----



Module: :class:`gemseo.algos.ode.scipy_ode.scipy_ode`


Implicit Runge-Kutta method of the Radau IIA type of order 5



.. code-block:: python
   :caption: Pydantic model of the settings for Radau

   from gemseo.settings.ode import Radau_Settings




More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.Radau.html.













































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**atol** : *typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional*

The absolute tolerance.


By default it is set to 1e-06.


.. raw:: html

    </li>

    <li>

**first_step** : *typing.Optional[typing.Annotated[float, Gt(gt=0)]], optional*

The initial step size.

If ``None``, let the algorithm choose.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**jac_sparsity** : *gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[float]] | None, optional*

Sparsity structure of the Jacobian matrix.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**max_step** : *<class 'float'>, optional*

The maximum allowed step size.


By default it is set to inf.


.. raw:: html

    </li>

    <li>

**rtol** : *typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional*

The relative tolerance.


By default it is set to 0.001.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>