.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_probabilistic_modeling/stochastic_processes/plot_field_manipulation.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_field_manipulation.py: Draw a field ============ .. GENERATED FROM PYTHON SOURCE LINES 6-12 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. .. GENERATED FROM PYTHON SOURCE LINES 14-20 .. code-block:: default 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) .. GENERATED FROM PYTHON SOURCE LINES 21-22 First, define a regular 2-d mesh .. GENERATED FROM PYTHON SOURCE LINES 22-32 .. 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-sg:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_field_manipulation_001.png :alt: Regular 2-d mesh :srcset: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_field_manipulation_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 33-34 Create a field as a realization of a process .. GENERATED FROM PYTHON SOURCE LINES 34-40 .. code-block:: default amplitude = [1.0] scale = [0.2]*2 myCovModel = ot.ExponentialModel(scale, amplitude) myProcess = ot.GaussianProcess(myCovModel, mesh) field = myProcess.getRealization() .. GENERATED FROM PYTHON SOURCE LINES 41-42 Create a field from a mesh and some values .. GENERATED FROM PYTHON SOURCE LINES 42-52 .. 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-sg:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_field_manipulation_002.png :alt: Field on 2-d mesh and 2-d values :srcset: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_field_manipulation_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 53-54 Compute the input mean of the field .. GENERATED FROM PYTHON SOURCE LINES 54-56 .. code-block:: default field.getInputMean() .. raw:: html

[0.0226606,-0.00545012]



.. GENERATED FROM PYTHON SOURCE LINES 57-58 Draw the field without interpolation .. GENERATED FROM PYTHON SOURCE LINES 58-62 .. code-block:: default graph = field.drawMarginal(0, False) graph.setTitle('Marginal field (no interpolation)') view = viewer.View(graph) .. image-sg:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_field_manipulation_003.png :alt: Marginal field (no interpolation) :srcset: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_field_manipulation_003.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 63-64 Draw the field with interpolation .. GENERATED FROM PYTHON SOURCE LINES 64-68 .. code-block:: default graph = field.drawMarginal(0) graph.setTitle('Marginal field (with interpolation)') view = viewer.View(graph) .. image-sg:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_field_manipulation_004.png :alt: Marginal field (with interpolation) :srcset: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_field_manipulation_004.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 69-71 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) .. GENERATED FROM PYTHON SOURCE LINES 71-75 .. code-block:: default graph = field.asDeformedMesh().draw() graph.setTitle('Deformed 2-d mesh') view = viewer.View(graph) .. image-sg:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_field_manipulation_005.png :alt: Deformed 2-d mesh :srcset: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_field_manipulation_005.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 76-77 Export to the VTK format .. GENERATED FROM PYTHON SOURCE LINES 77-82 .. 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 1.687 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 ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_field_manipulation.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_