.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/uncertainty/distributions/plot_ot_distribution.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_examples_uncertainty_distributions_plot_ot_distribution.py: Probability distributions based on OpenTURNS ============================================ In this example, we seek to create a probability distribution based on the OpenTURNS library. .. GENERATED FROM PYTHON SOURCE LINES 28-37 .. code-block:: default from __future__ import annotations from gemseo.api import configure_logger from gemseo.uncertainty.api import create_distribution from gemseo.uncertainty.api import get_available_distributions from matplotlib import pyplot as plt configure_logger() .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 38-40 First of all, we can access the names of the available probability distributions from the API: .. GENERATED FROM PYTHON SOURCE LINES 40-43 .. code-block:: default all_distributions = get_available_distributions() print(all_distributions) .. rst-class:: sphx-glr-script-out .. code-block:: none ['ComposedDistribution', 'OTComposedDistribution', 'OTDiracDistribution', 'OTDistribution', 'OTExponentialDistribution', 'OTNormalDistribution', 'OTTriangularDistribution', 'OTUniformDistribution', 'SPComposedDistribution', 'SPDistribution', 'SPExponentialDistribution', 'SPNormalDistribution', 'SPTriangularDistribution', 'SPUniformDistribution'] .. GENERATED FROM PYTHON SOURCE LINES 44-46 and filter the ones based on the OpenTURNS library (their names start with the acronym 'OT'): .. GENERATED FROM PYTHON SOURCE LINES 46-49 .. code-block:: default ot_distributions = [dist for dist in all_distributions if dist.startswith("OT")] print(ot_distributions) .. rst-class:: sphx-glr-script-out .. code-block:: none ['OTComposedDistribution', 'OTDiracDistribution', 'OTDistribution', 'OTExponentialDistribution', 'OTNormalDistribution', 'OTTriangularDistribution', 'OTUniformDistribution'] .. GENERATED FROM PYTHON SOURCE LINES 50-56 Create a distribution --------------------- Then, we can create a probability distribution for a two-dimensional random variable whose components are independent and distributed as the standard normal distribution (mean = 0 and standard deviation = 1): .. GENERATED FROM PYTHON SOURCE LINES 56-59 .. code-block:: default distribution_0_1 = create_distribution("x", "OTNormalDistribution", 2) print(distribution_0_1) .. rst-class:: sphx-glr-script-out .. code-block:: none Normal(mu=0.0, sigma=1.0) .. GENERATED FROM PYTHON SOURCE LINES 60-62 or create another distribution with mean = 1 and standard deviation = 2 for the marginal distributions: .. GENERATED FROM PYTHON SOURCE LINES 62-67 .. code-block:: default distribution_1_2 = create_distribution( "x", "OTNormalDistribution", 2, mu=1.0, sigma=2.0 ) print(distribution_1_2) .. rst-class:: sphx-glr-script-out .. code-block:: none Normal(mu=1.0, sigma=2.0) .. GENERATED FROM PYTHON SOURCE LINES 68-71 We could also use the generic :class:`.OTDistribution` which allows access to all the OpenTURNS distributions but this requires to know the signature of the methods of this library: .. GENERATED FROM PYTHON SOURCE LINES 71-76 .. code-block:: default distribution_1_2 = create_distribution( "x", "OTDistribution", 2, interfaced_distribution="Normal", parameters=(1.0, 2.0) ) print(distribution_1_2) .. rst-class:: sphx-glr-script-out .. code-block:: none Normal(1.0, 2.0) .. GENERATED FROM PYTHON SOURCE LINES 77-81 Plot the distribution --------------------- We can plot both cumulative and probability density functions for the first marginal: .. GENERATED FROM PYTHON SOURCE LINES 81-85 .. code-block:: default distribution_0_1.plot(show=False) # Workaround for HTML rendering, instead of ``show=True`` plt.show() .. image-sg:: /examples/uncertainty/distributions/images/sphx_glr_plot_ot_distribution_001.png :alt: Probability distribution of x(0), PDF, Cumulative density function :srcset: /examples/uncertainty/distributions/images/sphx_glr_plot_ot_distribution_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 86-92 .. note:: We can provide a marginal index as first argument of the :meth:`.Distribution.plot` method but in the current version of |g|, all components have the same distributions and so the plot will be the same. .. GENERATED FROM PYTHON SOURCE LINES 94-97 Get mean -------- We can access the mean of the distribution: .. GENERATED FROM PYTHON SOURCE LINES 97-99 .. code-block:: default print(distribution_0_1.mean) .. rst-class:: sphx-glr-script-out .. code-block:: none [0. 0.] .. GENERATED FROM PYTHON SOURCE LINES 100-103 Get standard deviation ---------------------- We can access the standard deviation of the distribution: .. GENERATED FROM PYTHON SOURCE LINES 103-105 .. code-block:: default print(distribution_0_1.standard_deviation) .. rst-class:: sphx-glr-script-out .. code-block:: none [1. 1.] .. GENERATED FROM PYTHON SOURCE LINES 106-110 Get numerical range ------------------- We can access the range, ie. the difference between the numerical minimum and maximum, of the distribution: .. GENERATED FROM PYTHON SOURCE LINES 110-112 .. code-block:: default print(distribution_0_1.range) .. rst-class:: sphx-glr-script-out .. code-block:: none [array([-7.65062809, 7.65062809]), array([-7.65062809, 7.65062809])] .. GENERATED FROM PYTHON SOURCE LINES 113-117 Get mathematical support ------------------------ We can access the range, ie. the difference between the minimum and maximum, of the distribution: .. GENERATED FROM PYTHON SOURCE LINES 117-119 .. code-block:: default print(distribution_0_1.support) .. rst-class:: sphx-glr-script-out .. code-block:: none [array([-inf, inf]), array([-inf, inf])] .. GENERATED FROM PYTHON SOURCE LINES 120-123 Generate samples ---------------- We can generate 10 samples of the distribution: .. GENERATED FROM PYTHON SOURCE LINES 123-125 .. code-block:: default print(distribution_0_1.compute_samples(10)) .. rst-class:: sphx-glr-script-out .. code-block:: none [[ 1.43360432 -0.21131498] [-0.22736098 0.71315714] [-0.38085859 1.09602106] [ 0.79766649 -0.20274454] [-1.36069266 -0.73384049] [-0.9452202 -1.50261139] [ 0.86127906 1.07794488] [-0.49622029 1.60805988] [ 2.10526732 0.25936155] [-0.72830578 1.67838523]] .. GENERATED FROM PYTHON SOURCE LINES 126-131 Compute CDF ----------- We can compute the cumulative density function component per component (here the probability that the first component is lower than 0. and that the second one is lower than 1.):: .. GENERATED FROM PYTHON SOURCE LINES 131-133 .. code-block:: default print(distribution_0_1.compute_cdf([0.0, 1.0])) .. rst-class:: sphx-glr-script-out .. code-block:: none [0.5 0.84134475] .. GENERATED FROM PYTHON SOURCE LINES 134-140 Compute inverse CDF ------------------- We can compute the inverse cumulative density function component per component (here the quantile at 50% for the first component and the quantile at 97.5% for the second one): .. GENERATED FROM PYTHON SOURCE LINES 140-141 .. code-block:: default print(distribution_0_1.compute_inverse_cdf([0.5, 0.975])) .. rst-class:: sphx-glr-script-out .. code-block:: none [0. 1.95996398] .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 0.192 seconds) .. _sphx_glr_download_examples_uncertainty_distributions_plot_ot_distribution.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_ot_distribution.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_ot_distribution.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_