.. 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_functional_basis_process.py: Create a functional basis process ================================= The objective of this example is to define :math:X: \Omega \times \mathcal{D} \rightarrow \mathbb{R}^d a multivariate stochastic process of dimension :math:d where :math:\mathcal{D} \in \mathbb{R}^n, as a linear combination of :math:K deterministic functions :math:(\phi_i)_{i=1,\dots,K}: \mathbb{R}^n \rightarrow \mathbb{R}^d: .. math:: \begin{aligned} X(\omega,\underline{t})=\sum_{i=1}^KA_i(\omega)\phi_i(\underline{t}) \end{aligned} where :math:\underline{A}=(A_1,\dots, A_K) is a random vector of dimension :math:K. We suppose that :math:\mathcal{M} is discretized on the mesh :math:\mathcal{M} which has :math:N vertices. A realization of :math:X on :math:\mathcal{M} consists in generating a realization :math:\underline{\alpha} of the random vector :math:\underline{A} and in evaluating the functions :math:(\phi_i)_{i=1,\dots,K} on the mesh :math:\mathcal{M}. If we note :math:(\underline{x}_0, \dots, \underline{x}_{N-1}) the realization of :math:X, where :math:X(\omega, \underline{t}_k) = \underline{x}_k, we have: .. math:: \begin{aligned} \forall k \in [0, N-1], \quad \underline{x}_k = \sum_{i=1}^K\alpha_i\phi_i(\underline{t}_k) \end{aligned} .. 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) Define the coefficients distribution .. code-block:: default mu = [2.0]*2 sigma = [5.0]*2 R = ot.CorrelationMatrix(2) coefDist = ot.Normal(mu, sigma, R) Create a basis of functions .. code-block:: default phi_1 = ot.SymbolicFunction(['t'], ['sin(t)']) phi_2 = ot.SymbolicFunction(['t'], ['cos(t)^2']) myBasis = ot.Basis([phi_1, phi_2]) Create the mesh .. code-block:: default myMesh = ot.RegularGrid(0.0, 0.1, 100) Create the process .. code-block:: default process = ot.FunctionalBasisProcess(coefDist, myBasis, myMesh) Draw a sample .. code-block:: default N = 6 sample = process.getSample(N) graph = sample.drawMarginal(0) graph.setTitle(str(N)+' realizations of functional basis process') view = viewer.View(graph) .. image:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_functional_basis_process_001.png :alt: 6 realizations of functional basis process :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 0.075 seconds) .. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_functional_basis_process.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_functional_basis_process.py  .. container:: sphx-glr-download sphx-glr-download-jupyter :download:Download Jupyter notebook: plot_functional_basis_process.ipynb  .. only:: html .. rst-class:: sphx-glr-signature Gallery generated by Sphinx-Gallery _