.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_regular_grid_creation.py>`     to download the full example code
    .. rst-class:: sphx-glr-example-title

    .. _sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_regular_grid_creation.py:


Creation of a regular grid
==========================

In this example we will demonstrate how to create a regular grid. Note that a regular grid is a particular mesh of :math:`\mathcal{D}=[0,T] \in \mathbb{R}`.

Here we will assume it represents the time :math:`t` as it is often the case, but it can represent any physical quantity.

A regular time grid is a regular discretization of the interval :math:`[0, T] \in \mathbb{R}` into :math:`N` points, noted :math:`(t_0, \dots, t_{N-1})`.

The time grid can be defined using :math:`(t_{Min}, \Delta t, N)` where :math:`N` is the number of points in the time grid. :math:`\Delta t` the time step between two consecutive instants and :math:`t_0 = t_{Min}`. Then,  :math:`t_k = t_{Min} + k \Delta t` and :math:`t_{Max} = t_{Min} +  (N-1) \Delta t`.


Consider :math:`X: \Omega \times \mathcal{D} \rightarrow \mathbb{R}^d` a multivariate stochastic process of dimension :math:`d`,  where :math:`n=1`, :math:`\mathcal{D}=[0,T]` and :math:`t\in \mathcal{D}` is interpreted as a time stamp. Then the mesh associated to the process :math:`X` is a (regular) time grid.


.. code-block:: default

    from __future__ import print_function
    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pylab as plt
    import math as m
    ot.Log.Show(ot.Log.NONE)









.. code-block:: default

    tMin = 0.
    tStep = 0.1
    n = 10

    # Create the grid
    time_grid = ot.RegularGrid(tMin, tStep, n)








Get the first and the last instants,
the step and the number of points


.. code-block:: default

    start = time_grid.getStart()
    step = time_grid.getStep()
    grid_size = time_grid.getN()
    end = time_grid.getEnd()
    print('start=', start, 'step=', step, 'grid_size=', grid_size, 'end=', end)





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

 Out:

 .. code-block:: none

    start= 0.0 step= 0.1 grid_size= 10 end= 1.0




draw the grid


.. code-block:: default

    time_grid.setName('time')
    graph = time_grid.draw()
    view = viewer.View(graph)
    plt.show()



.. image:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_regular_grid_creation_001.png
    :alt: Mesh time
    :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.069 seconds)


.. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_regular_grid_creation.py:


.. only :: html

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



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

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



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

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


.. only:: html

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

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