.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "_build/auto_examples/convergence/TangentIntegrationvs_FD.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download__build_auto_examples_convergence_TangentIntegrationvs_FD.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr__build_auto_examples_convergence_TangentIntegrationvs_FD.py:


Valiadation of tangent integration alorithms using Finite Differences
=====================================================================

.. GENERATED FROM PYTHON SOURCE LINES 7-8

Evaluation of relative quadrature error with the following parameters:

.. GENERATED FROM PYTHON SOURCE LINES 8-36

.. code-block:: Python



    ndim = 2

    A = np.random.random((ndim,ndim))

    def fun(t,x):
    
        return np.dot(A,x)

    def gun(t,x):
    
        return np.dot(A,x)*np.dot(x,x)

    def gradfun(t,x,dx):

        return np.dot(A,dx)

    def gradgun(t,x,dx):

        dxr = np.asarray(dx).reshape(-1)
        resr = 2*np.dot(x,dxr)*np.dot(A,x) + np.dot(x,x)*np.dot(A,dxr)
        return resr.reshape(-1,1)



    plt.show()




.. image-sg:: /_build/auto_examples/convergence/images/sphx_glr_TangentIntegrationvs_FD_001.png
   :alt: TangentIntegrationvs FD
   :srcset: /_build/auto_examples/convergence/images/sphx_glr_TangentIntegrationvs_FD_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 120-176

.. code-block:: Python


    plt.close()

    nint = 100

    t_span = (0.,0.01)

    def int_fun(x):
    
        xx = x[:ndim].copy()
        vx = x[ndim:].copy()
    
        resx, resv = choreo.scipy_plus.ODE.ImplicitSymplecticIVP(
            fun         ,
            gun         ,
            t_span      ,
            xx          ,
            vx          ,
            rk          ,
            rk          ,
            nint = nint ,
        )

        return np.ascontiguousarray(np.concatenate((resx,resv)).reshape(-1))

    def int_grad_fun_impl(x,dx):
    
        xx = x[:ndim].copy()
        vx = x[ndim:].copy()
    
        dxx = dx[:ndim].reshape(ndim,-1).copy()
        dxv = dx[ndim:].reshape(ndim,-1).copy()
    
        resx, resv, grad_resx, grad_resv = choreo.scipy_plus.ODE.ImplicitSymplecticIVP(
            fun         ,
            gun         ,
            t_span      ,
            xx          ,
            vx          ,
            rk          ,
            rk          ,
            grad_fun = gradfun  ,
            grad_gun = gradgun  ,
            grad_x0 = dxx       ,
            grad_v0 = dxv       ,
            nint = nint         ,
        )
    
        return np.ascontiguousarray(np.concatenate((grad_resx,grad_resv)).reshape(-1))





    plt.show()




.. image-sg:: /_build/auto_examples/convergence/images/sphx_glr_TangentIntegrationvs_FD_002.png
   :alt: TangentIntegrationvs FD
   :srcset: /_build/auto_examples/convergence/images/sphx_glr_TangentIntegrationvs_FD_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 200-244

.. code-block:: Python


    plt.close()

    def int_grad_fun_expl(x,dx):
    
        xx = x[:ndim].copy()
        vx = x[ndim:].copy()
    
        dxx = dx[:ndim].reshape(ndim,-1).copy()
        dxv = dx[ndim:].reshape(ndim,-1).copy()
    
        resx, resv, grad_resx, grad_resv = choreo.scipy_plus.ODE.ExplicitSymplecticIVP(
            fun         ,
            gun         ,
            t_span      ,
            xx          ,
            vx          ,
            rk_expl          ,
            grad_fun = gradfun  ,
            grad_gun = gradgun  ,
            grad_x0 = dxx       ,
            grad_v0 = dxv       ,
            nint = nint         ,
        )
    
        return np.ascontiguousarray(np.concatenate((grad_resx,grad_resv)).reshape(-1))

    fig, ax = plt.subplots(
        figsize = figsize,
        dpi = dpi   ,
    )

    for i, order in enumerate(orderlist):

        err = choreo.scipy_plus.test.compare_FD_and_exact_grad(int_fun,int_grad_fun_expl,xo,dx=dxo,epslist=epslist,order=order)

        plt.plot(epslist,err)

    ax.set_xscale('log')
    ax.set_yscale('log')

    plt.tight_layout()

    plt.show()



.. image-sg:: /_build/auto_examples/convergence/images/sphx_glr_TangentIntegrationvs_FD_003.png
   :alt: TangentIntegrationvs FD
   :srcset: /_build/auto_examples/convergence/images/sphx_glr_TangentIntegrationvs_FD_003.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 3.115 seconds)


.. _sphx_glr_download__build_auto_examples_convergence_TangentIntegrationvs_FD.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: TangentIntegrationvs_FD.ipynb <TangentIntegrationvs_FD.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: TangentIntegrationvs_FD.py <TangentIntegrationvs_FD.py>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_