.. 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_userdefined_covariance_model.py: Create a custom covariance model ================================ This example illustrates how the user can define his own covariance model. .. 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) Create the time grid .. code-block:: default N = 32 a = 4.0 mesh = ot.IntervalMesher([N]).build(ot.Interval(-a, a)) Create the covariance function at (s,t) .. code-block:: default def C(s, t): return m.exp( -4.0 * abs(s - t) / (1 + (s * s + t * t))) Create the large covariance matrix .. code-block:: default covariance = ot.CovarianceMatrix(mesh.getVerticesNumber()) for k in range(mesh.getVerticesNumber()): t = mesh.getVertices()[k] for l in range(k + 1): s = mesh.getVertices()[l] covariance[k, l] = C(s[0], t[0]) Create the covariance model .. code-block:: default covmodel = ot.UserDefinedCovarianceModel(mesh, covariance) Draw the covariance model .. code-block:: default def f(x): return [covmodel([x[0]], [x[1]])[0, 0]] func = ot.PythonFunction(2, 1, f) func.setDescription(['$s$', '$t$', '$cov$']) cov_graph = func.draw([-a] * 2, [a] * 2, [512] * 2) cov_graph.setLegendPosition('') view = viewer.View(cov_graph) plt.show() .. image:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_userdefined_covariance_model_001.png :alt: $cov$ as a function of ($s$,$t$) :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 1.617 seconds) .. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_userdefined_covariance_model.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_userdefined_covariance_model.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_userdefined_covariance_model.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_