.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/uncertainty/distributions/plot_sp_distribution.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_examples_uncertainty_distributions_plot_sp_distribution.py: Probability distributions based on SciPy ======================================== In this example, we seek to create a probability distribution based on the SciPy library. .. GENERATED FROM PYTHON SOURCE LINES 28-36 .. code-block:: default from __future__ import annotations from gemseo import configure_logger from gemseo.uncertainty import create_distribution from gemseo.uncertainty import get_available_distributions configure_logger() .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 37-39 First of all, we can access the names of the available probability distributions from the API: .. GENERATED FROM PYTHON SOURCE LINES 39-42 .. code-block:: default all_distributions = get_available_distributions() all_distributions .. rst-class:: sphx-glr-script-out .. code-block:: none ['OTComposedDistribution', 'OTDiracDistribution', 'OTDistribution', 'OTExponentialDistribution', 'OTNormalDistribution', 'OTTriangularDistribution', 'OTUniformDistribution', 'SPComposedDistribution', 'SPDistribution', 'SPExponentialDistribution', 'SPNormalDistribution', 'SPTriangularDistribution', 'SPUniformDistribution'] .. GENERATED FROM PYTHON SOURCE LINES 43-45 and filter the ones based on the SciPy library (their names start with the acronym 'SP'): .. GENERATED FROM PYTHON SOURCE LINES 45-48 .. code-block:: default sp_distributions = [dist for dist in all_distributions if dist.startswith("SP")] sp_distributions .. rst-class:: sphx-glr-script-out .. code-block:: none ['SPComposedDistribution', 'SPDistribution', 'SPExponentialDistribution', 'SPNormalDistribution', 'SPTriangularDistribution', 'SPUniformDistribution'] .. GENERATED FROM PYTHON SOURCE LINES 49-55 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 55-58 .. code-block:: default distribution_0_1 = create_distribution("x", "SPNormalDistribution", 2) distribution_0_1 .. rst-class:: sphx-glr-script-out .. code-block:: none norm[2](mu=0.0, sigma=1.0) .. GENERATED FROM PYTHON SOURCE LINES 59-61 or create another distribution with mean = 1 and standard deviation = 2 for the marginal distributions: .. GENERATED FROM PYTHON SOURCE LINES 61-66 .. code-block:: default distribution_1_2 = create_distribution( "x", "SPNormalDistribution", 2, mu=1.0, sigma=2.0 ) distribution_1_2 .. rst-class:: sphx-glr-script-out .. code-block:: none norm[2](mu=1.0, sigma=2.0) .. GENERATED FROM PYTHON SOURCE LINES 67-70 We could also use the generic :class:`.SPDistribution` which allows access to all the SciPy distributions but this requires to know the signature of the methods of this library: .. GENERATED FROM PYTHON SOURCE LINES 70-79 .. code-block:: default distribution_1_2 = create_distribution( "x", "SPDistribution", 2, interfaced_distribution="norm", parameters={"loc": 1.0, "scale": 2.0}, ) distribution_1_2 .. rst-class:: sphx-glr-script-out .. code-block:: none norm[2](loc=1.0, scale=2.0) .. GENERATED FROM PYTHON SOURCE LINES 80-84 Plot the distribution --------------------- We can plot both cumulative and probability density functions for the first marginal: .. GENERATED FROM PYTHON SOURCE LINES 84-86 .. code-block:: default distribution_0_1.plot() .. image-sg:: /examples/uncertainty/distributions/images/sphx_glr_plot_sp_distribution_001.png :alt: Probability distribution of x[0] :srcset: /examples/uncertainty/distributions/images/sphx_glr_plot_sp_distribution_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none
.. GENERATED FROM PYTHON SOURCE LINES 87-93 .. 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 95-98 Get mean -------- We can access the mean of the distribution: .. GENERATED FROM PYTHON SOURCE LINES 98-100 .. code-block:: default distribution_0_1.mean .. rst-class:: sphx-glr-script-out .. code-block:: none array([0., 0.]) .. GENERATED FROM PYTHON SOURCE LINES 101-104 Get standard deviation ---------------------- We can access the standard deviation of the distribution: .. GENERATED FROM PYTHON SOURCE LINES 104-106 .. code-block:: default distribution_0_1.standard_deviation .. rst-class:: sphx-glr-script-out .. code-block:: none array([1., 1.]) .. GENERATED FROM PYTHON SOURCE LINES 107-112 Get numerical range ------------------- We can access the range, i.e. the difference between the numerical minimum and maximum, of the distribution: .. GENERATED FROM PYTHON SOURCE LINES 112-114 .. code-block:: default distribution_0_1.range .. rst-class:: sphx-glr-script-out .. code-block:: none [array([-7.03448383, 7.03448691]), array([-7.03448383, 7.03448691])] .. GENERATED FROM PYTHON SOURCE LINES 115-120 Get mathematical support ------------------------ We can access the range, i.e. the difference between the minimum and maximum, of the distribution: .. GENERATED FROM PYTHON SOURCE LINES 120-122 .. code-block:: default distribution_0_1.support .. rst-class:: sphx-glr-script-out .. code-block:: none [array([-inf, inf]), array([-inf, inf])] .. GENERATED FROM PYTHON SOURCE LINES 123-126 Generate samples ---------------- We can generate 10 samples of the distribution: .. GENERATED FROM PYTHON SOURCE LINES 126-128 .. code-block:: default distribution_0_1.compute_samples(10) .. rst-class:: sphx-glr-script-out .. code-block:: none array([[-0.44712856, -1.37311732], [ 1.2245077 , 0.31515939], [ 0.40349164, 0.84616065], [ 0.59357852, -0.85951594], [-1.09491185, 0.35054598], [ 0.16938243, -1.31228341], [ 0.74055645, -0.03869551], [-0.9537006 , -1.61577235], [-0.26621851, 1.12141771], [ 0.03261455, 0.40890054]]) .. GENERATED FROM PYTHON SOURCE LINES 129-134 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 134-136 .. code-block:: default distribution_0_1.compute_cdf([0.0, 1.0]) .. rst-class:: sphx-glr-script-out .. code-block:: none array([0.5 , 0.84134475]) .. GENERATED FROM PYTHON SOURCE LINES 137-143 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 143-144 .. code-block:: default distribution_0_1.compute_inverse_cdf([0.5, 0.975]) .. rst-class:: sphx-glr-script-out .. code-block:: none array([0. , 1.95996398]) .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.197 seconds) .. _sphx_glr_download_examples_uncertainty_distributions_plot_sp_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_sp_distribution.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_sp_distribution.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_