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

.. only:: html

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

        Click :ref:`here <sphx_glr_download_dynamics_floquet_tutorial.py>`
        to download the full example code

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

.. _sphx_glr_dynamics_floquet_tutorial.py:


Floquet Tutorial
==================

.. GENERATED FROM PYTHON SOURCE LINES 6-11

.. code-block:: default

    import torch, pypose as pp
    import math, matplotlib.pyplot as plt

    device = torch.device("cuda" if torch.cuda.is_available() else "cpu")








.. GENERATED FROM PYTHON SOURCE LINES 12-16

Preparation
-------------
We consider a Floquet system, which is periodic and an example of time-varying systems


.. GENERATED FROM PYTHON SOURCE LINES 16-46

.. code-block:: default



    class Floquet(pp.module.NLS):
        '''
        Floquet system is periodic and time-varying.
        '''
        def __init__(self):
            super().__init__()

        def state_transition(self, state, input, t):
            cc = (2 * math.pi * t / 100).cos()
            ss = (2 * math.pi * t / 100).sin()
            A = torch.tensor([[   1.,  cc/10],
                              [cc/10,     1.]], device=t.device)
            B = torch.tensor([[ss],
                              [1.]], device=t.device)

            return A @ state + B @ input

        def observation(self, state, input, t):
            return state + t


    def subPlot(ax, x, y, xlabel=None, ylabel=None):
        x = x.detach().cpu().numpy()
        y = y.detach().cpu().numpy()
        ax.plot(x, y)
        ax.set_xlabel(xlabel)
        ax.set_ylabel(ylabel)








.. GENERATED FROM PYTHON SOURCE LINES 47-49

Number of time steps
---------------------

.. GENERATED FROM PYTHON SOURCE LINES 49-53

.. code-block:: default


    N = 100    









.. GENERATED FROM PYTHON SOURCE LINES 54-55

Time, Input, Initial state

.. GENERATED FROM PYTHON SOURCE LINES 55-63

.. code-block:: default


    time  = torch.arange(0, N, device=device)
    input = (2 * math.pi * time / 50).sin()

    state = torch.zeros(N, 2, device=device)
    state[0] = torch.tensor([1., 1.], device=device)
    obser = torch.zeros(N, 2, device=device)








.. GENERATED FROM PYTHON SOURCE LINES 64-65

Create dynamics solver object

.. GENERATED FROM PYTHON SOURCE LINES 65-67

.. code-block:: default

    model = Floquet().to(device)








.. GENERATED FROM PYTHON SOURCE LINES 68-70

Calculate trajectory


.. GENERATED FROM PYTHON SOURCE LINES 70-74

.. code-block:: default


    for i in range(N - 1):
        state[i + 1], obser[i] = model(state[i], input[i])








.. GENERATED FROM PYTHON SOURCE LINES 75-76

Jacobian computation - Find jacobians at the last step

.. GENERATED FROM PYTHON SOURCE LINES 76-81

.. code-block:: default

    vars = ['A', 'B', 'C', 'D', 'c1', 'c2']
    model.set_refpoint()
    [print(v, getattr(model, v)) for v in vars]






.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    A tensor([[1.0000, 0.0998],
            [0.0998, 1.0000]], device='cuda:0')
    B tensor([[-0.0628],
            [ 1.0000]], device='cuda:0')
    C tensor([[1., 0.],
            [0., 1.]], device='cuda:0')
    D tensor([[0.],
            [0.]], device='cuda:0')
    c1 tensor([ 2.9802e-08, -1.4901e-08], device='cuda:0')
    c2 tensor([99., 99.], device='cuda:0')

    [None, None, None, None, None, None]



.. GENERATED FROM PYTHON SOURCE LINES 82-83

Jacobian computation - Find jacobians at the 5th step

.. GENERATED FROM PYTHON SOURCE LINES 83-87

.. code-block:: default

    idx = 5
    model.set_refpoint(state=state[idx], input=input[idx], t=time[idx])
    [print(v, getattr(model, v)) for v in vars]





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    A tensor([[1.0000, 0.0951],
            [0.0951, 1.0000]], device='cuda:0')
    B tensor([[0.3090],
            [1.0000]], device='cuda:0')
    C tensor([[1., 0.],
            [0., 1.]], device='cuda:0')
    D tensor([[0.],
            [0.]], device='cuda:0')
    c1 tensor([-1.4901e-08,  0.0000e+00], device='cuda:0')
    c2 tensor([5., 5.], device='cuda:0')

    [None, None, None, None, None, None]



.. GENERATED FROM PYTHON SOURCE LINES 88-89

Create time plots to show dynamics

.. GENERATED FROM PYTHON SOURCE LINES 89-95

.. code-block:: default


    f, ax = plt.subplots(nrows=4, sharex=True)
    subPlot(ax[0], time, state[:, 0], ylabel='State[0]')
    subPlot(ax[1], time, state[:, 1], ylabel='State[1]')
    subPlot(ax[2], time[:-1], obser[:-1, 0], ylabel='Observe[0]')
    subPlot(ax[3], time[:-1], obser[:-1, 1], ylabel='Observe[1]', xlabel='Time')
    plt.show()


.. image-sg:: /dynamics/images/sphx_glr_floquet_tutorial_001.png
   :alt: floquet tutorial
   :srcset: /dynamics/images/sphx_glr_floquet_tutorial_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.101 seconds)


.. _sphx_glr_download_dynamics_floquet_tutorial.py:

.. only:: html

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


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

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

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

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


.. only:: html

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

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