diff --git a/doc/manual/manual/extensions/capd/capd.rst b/doc/manual/manual/extensions/capd/capd.rst index 70db69213..40c23731e 100644 --- a/doc/manual/manual/extensions/capd/capd.rst +++ b/doc/manual/manual/extensions/capd/capd.rst @@ -12,7 +12,6 @@ To use CAPD with Codac, you first need to install the CAPD library. You can find Note that as CAPD is a C++ only library, the content present in this page is **only available in C++**. -.. _subsec-extensions-capd-capd-install: Installing the ``codac-capd`` extension --------------------------------------- @@ -52,6 +51,18 @@ The header of the ``codac-capd`` extension is not included by default. You need #include #include +Furthermore, you need to link the extension to your project, for instance by updating your ``CMakeLists.txt`` with:: + + add_executable(${PROJECT_NAME} main.cpp) + target_compile_options(${PROJECT_NAME} PUBLIC ${CODAC_CXX_FLAGS}) + target_include_directories(${PROJECT_NAME} SYSTEM PUBLIC ${CODAC_INCLUDE_DIRS} ${CODAC_CAPD_INCLUDE_DIR}) + target_link_libraries(${PROJECT_NAME} PRIVATE + ${CODAC_LIBRARIES} + ${CODAC_CAPD_LIBRARY} # linking to the codac-capd extension + capd::capd # linking to CAPD + Ibex::ibex + ) + You can use the functions ``to_capd`` and ``to_codac`` to convert between CAPD and Codac objects as follows: .. tabs:: @@ -200,4 +211,4 @@ The result is the following figure, with in green the initial set (:math:`t=0s`) .. figure:: img/pendulum_result.png :width: 500px - Result of the CAPD integration of the pendulum, enclosed in a Codac tube. + Result of the CAPD integration of the pendulum, enclosed in a Codac tube. \ No newline at end of file diff --git a/doc/manual/manual/extensions/capd/index.rst b/doc/manual/manual/extensions/capd/index.rst index 17ccff750..a40271ca7 100644 --- a/doc/manual/manual/extensions/capd/index.rst +++ b/doc/manual/manual/extensions/capd/index.rst @@ -5,210 +5,7 @@ CAPD (rigorous numerics in dynamical systems) Main author: `Maël Godard `_ -This page describes how to use the CAPD library with Codac. CAPD is a C++ library for rigorous numerics in dynamical systems. +.. toctree:: -To use CAPD with Codac, you first need to install the CAPD library. You can find the installation instructions on the `CAPD website `_. - -Note that as CAPD is a C++ only library, the content present in this page is **only available in C++**. - - -Installing the ``codac-capd`` extension ---------------------------------------- - -To install the ``codac-capd`` extension, you need to install the Codac library from its sources. This can be done :ref:`by using CMake ` with the option ``WITH_CAPD=ON``. For example: - -.. code-block:: bash - - cmake -DCMAKE_INSTALL_PREFIX=$HOME/ibex-lib/build_install -DCMAKE_BUILD_TYPE=Release -DWITH_CAPD=ON .. - -We highly recommend to test the installation of the library with the provided tests. To do so, you can use the following command: - -.. code-block:: bash - - make test - - -Content -------- - -The ``codac-capd`` extension provides functions to convert CAPD objects to Codac objects and vice versa. - -The functions are ``to_capd`` and ``to_codac``. They can be used to convert the following objects: - -- ``capd::Interval`` :math:`\leftrightarrow` ``codac2::Interval`` -- ``capd::IVector`` :math:`\leftrightarrow` ``codac2::IntervalVector`` -- ``capd::IMatrix`` :math:`\leftrightarrow` ``codac2::IntervalMatrix`` -- ``capd::ITimeMap::SolutionCurve`` :math:`\rightarrow` ``codac2::SlicedTube`` - - -How to use ----------- - -The header of the ``codac-capd`` extension is not included by default. You need to include it manually in your code, together with the CAPD library: - -.. code-block:: c++ - - #include - #include - -Furthermore, you need to link the extension to your project, for instance by updating your ``CMakeLists.txt`` with:: - - add_executable(${PROJECT_NAME} main.cpp) - target_compile_options(${PROJECT_NAME} PUBLIC ${CODAC_CXX_FLAGS}) - target_include_directories(${PROJECT_NAME} SYSTEM PUBLIC ${CODAC_INCLUDE_DIRS} ${CODAC_CAPD_INCLUDE_DIR}) - target_link_libraries(${PROJECT_NAME} PRIVATE - ${CODAC_LIBRARIES} - ${CODAC_CAPD_LIBRARY} # linking to the codac-capd extension - capd::capd # linking to CAPD - Ibex::ibex - ) - -You can use the functions ``to_capd`` and ``to_codac`` to convert between CAPD and Codac objects as follows: - -.. tabs:: - - .. code-tab:: c++ - - codac2::Interval codac_interval(0,2); // Codac interval [0, 2] - capd::Interval capd_interval = to_capd(codac_interval); // convert to CAPD interval - codac2::Interval codac_interval2 = to_codac(capd_interval); // convert back to Codac interval - - -Example -------- - -.. image:: img/pendulum.png - :alt: State variables of the pendulum - :align: right - :width: 130px - -For this example we will consider the pendulum with friction. - -The state variables of the pendulum are its angle :math:`\theta` and its angular velocity :math:`\omega`. The pendulum follows the following dynamic: - -.. math:: - - \left(\begin{array}{c} - \dot{\theta}\\ - \dot{\omega} - \end{array}\right)=\left(\begin{array}{c} - \omega\\ - -\sin(\theta)\cdot\frac{g}{l}-0.5\omega - \end{array}\right), - - -where :math:`g` is the gravity constant and :math:`l` is the length of the pendulum. - -This equation can be passed to the CAPD library as follows: - -.. tabs:: - - .. group-tab:: C++ - - .. literalinclude:: src.cpp - :language: c++ - :start-after: [codac-capd-2-beg] - :end-before: [codac-capd-2-end] - :dedent: 2 - -To solve this ODE, an ``IOdeSolver`` object is necessary. - -.. tabs:: - - .. group-tab:: C++ - - .. literalinclude:: src.cpp - :language: c++ - :start-after: [codac-capd-3-beg] - :end-before: [codac-capd-3-end] - :dedent: 2 - -CAPD then uses an ``ITimeMap`` to make the link between a time step and the solution of the ODE at this time. The ``I`` here stands for ``Interval`` as the solution is an interval guaranteed to enclose the solution. Here we will integrate the ODE between :math:`t_0=0s` and :math:`t_f=20s`. - -.. tabs:: - - .. group-tab:: C++ - - .. literalinclude:: src.cpp - :language: c++ - :start-after: [codac-capd-4-beg] - :end-before: [codac-capd-4-end] - :dedent: 2 - -To completly define the ODE, we need to define the initial conditions. Here we will set the initial angle to :math:`\theta_0=-\frac{\pi}{2}` and the -initial angular velocity to :math:`\omega_0=0`. For the purpose of this example, we will add a small uncertainty to the initial conditions. The initial conditions are then defined as follows: - -.. tabs:: - - .. group-tab:: C++ - - .. literalinclude:: src.cpp - :language: c++ - :start-after: [codac-capd-5-beg] - :end-before: [codac-capd-5-end] - :dedent: 2 - -There are then two ways to get the result of the integration depending on the use case. - -If the desired result is the solution of the ODE at a given time (here say :math:`T=1s`), we can do as follows: - -.. tabs:: - - .. group-tab:: C++ - - .. literalinclude:: src.cpp - :language: c++ - :start-after: [codac-capd-6-beg] - :end-before: [codac-capd-6-end] - :dedent: 2 - -**Be careful, this method modifies the initial set** ``s`` **in place**. - -If the desired result is the solution curve (or tube) of the ODE on the time domain :math:`[t_0,t_f]`, we can do as follows: - -.. tabs:: - - .. group-tab:: C++ - - .. literalinclude:: src.cpp - :language: c++ - :start-after: [codac-capd-7-beg] - :end-before: [codac-capd-7-end] - :dedent: 2 - -The variable ``solution`` is the desired solution curve (or tube). The operator ``solution(t)`` gives the solution at time :math:`t`. -It can be converted into a Codac ``SlicedTube`` with the function ``to_codac``. This functions takes two arguments: - -- the ``capd::ITimeMap::SolutionCurve`` to convert. -- a ``codac2::TDomain`` object defining the temporal domain of the tube. - -The resulting ``SlicedTube`` will have the same time domain as the one given in argument, completed with the CAPD gates. An example of conversion is : - -.. tabs:: - - .. group-tab:: C++ - - .. literalinclude:: src.cpp - :language: c++ - :start-after: [codac-capd-8-beg] - :end-before: [codac-capd-8-end] - :dedent: 2 - -A full display can be done with the following code: - -.. tabs:: - - .. group-tab:: C++ - - .. literalinclude:: src.cpp - :language: c++ - :start-after: [codac-capd-9-beg] - :end-before: [codac-capd-9-end] - :dedent: 4 - -The result is the following figure, with in green the initial set (:math:`t=0s`) and in red the final set (:math:`t=20s`). The ``SlicedTube`` is displayed in blue with a black edge for better visibility. The orange rectangles correspond to the gates (degenerate slices). - -.. figure:: img/pendulum_result.png - :width: 500px - - Result of the CAPD integration of the pendulum, enclosed in a Codac tube. \ No newline at end of file + capd.rst + peibos_capd.rst \ No newline at end of file