.. only:: html

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

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

    .. _sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_field_manipulation.py:


Field manipulation
==================

The objective here is to create and manipulate a field. A field is the agregation of a mesh :math:`\mathcal{M}` of a domain :math:`\mathcal{D} \in \mathbb{R}^n` and a sample of values in :math:`\mathbb{R}^d` associated to each vertex of the mesh.

We note :math:`(\underline{t}_0, \dots, \underline{t}_{N-1})` the vertices of :math:`\mathcal{M}` and :math:`(\underline{x}_0, \dots, \underline{x}_{N-1})` the associated values in :math:`\mathbb{R}^d`.

A field is stored in the *Field* object that stores the mesh and the values at each vertex of the mesh.
It can be built from a mesh and values or as a realization of a stochastic process.


.. 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)








First, define a regular 2-d mesh


.. code-block:: default

    discretization = [10, 5]
    mesher = ot.IntervalMesher(discretization)
    lowerBound = [0.0, 0.0]
    upperBound = [2.0, 1.0]
    interval = ot.Interval(lowerBound, upperBound)
    mesh = mesher.build(interval)
    graph = mesh.draw()
    graph.setTitle('Regular 2-d mesh')
    view = viewer.View(graph)




.. image:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_field_manipulation_001.png
    :alt: Regular 2-d mesh
    :class: sphx-glr-single-img





Create a field as a realization of a process


.. code-block:: default

    amplitude = [1.0]
    scale = [0.2]*2
    myCovModel = ot.ExponentialModel(scale, amplitude)
    myProcess = ot.GaussianProcess(myCovModel, mesh)
    field = myProcess.getRealization()








Create a field from a mesh and some values


.. code-block:: default

    values = ot.Normal([0.0]*2, [1.0]*2, ot.CorrelationMatrix(2)).getSample(len(mesh.getVertices()))
    for i in range(len(values)):
        x = values[i]
        values[i] = 0.05 * x / x.norm()
    field = ot.Field(mesh, values)
    graph = field.draw()
    graph.setTitle('Field on 2-d mesh and 2-d values')
    view = viewer.View(graph)




.. image:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_field_manipulation_002.png
    :alt: Field on 2-d mesh and 2-d values
    :class: sphx-glr-single-img





Compute the input mean of the field


.. code-block:: default

    field.getInputMean()






.. raw:: html

    <p>[-0.00840808,0.00576205]</p>
    <br />
    <br />

Draw the field without interpolation


.. code-block:: default

    graph = field.drawMarginal(0, False)
    graph.setTitle('Marginal field (no interpolation)')
    view = viewer.View(graph)




.. image:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_field_manipulation_003.png
    :alt: Marginal field (no interpolation)
    :class: sphx-glr-single-img





Draw the field with interpolation


.. code-block:: default

    graph = field.drawMarginal(0)
    graph.setTitle('Marginal field (with interpolation)')
    view = viewer.View(graph)




.. image:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_field_manipulation_004.png
    :alt: Marginal field (with interpolation)
    :class: sphx-glr-single-img





Deform the mesh from the field according to the values of the field
The dimension of the mesh (ie of its vertices) must be the same as the dimension of the field (ie its values)


.. code-block:: default

    graph = field.asDeformedMesh().draw()
    graph.setTitle('Deformed 2-d mesh')
    view = viewer.View(graph)




.. image:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_field_manipulation_005.png
    :alt: Deformed 2-d mesh
    :class: sphx-glr-single-img





Export to the VTK format


.. code-block:: default

    field.exportToVTKFile('field.vtk')
    with open('field.vtk') as f:
        print(f.read()[:100])

    plt.show()




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

 Out:

 .. code-block:: none

    # vtk DataFile Version 3.0
    Unnamed
    ASCII

    DATASET UNSTRUCTURED_GRID
    POINTS 66 float
    0 0 0.0
    0.2 0 0.





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

   **Total running time of the script:** ( 0 minutes  1.774 seconds)


.. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_field_manipulation.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_field_manipulation.py <plot_field_manipulation.py>`



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

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


.. only:: html

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

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