.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/distributions/multivariate/plot_multivariate_copulas.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_distributions_multivariate_plot_multivariate_copulas.py>`
        to download the full example code or to run this example in your browser via Binder

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_distributions_multivariate_plot_multivariate_copulas.py:


Multivariate from independent marginals and copula
==================================================

.. GENERATED FROM PYTHON SOURCE LINES 9-12

- How to define α bivariate distribution from independent marginals and change its structure based on a copula supported by UQpy
- How to plot the pdf of the distribution
- How to modify the parameters of the distribution

.. GENERATED FROM PYTHON SOURCE LINES 17-18

Import the necessary modules.

.. GENERATED FROM PYTHON SOURCE LINES 21-25

.. code-block:: default


    import numpy as np
    import matplotlib.pyplot as plt








.. GENERATED FROM PYTHON SOURCE LINES 26-28

Example of a multivariate distribution from joint independent marginals
------------------------------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 32-35

.. code-block:: default

    from UQpy.distributions import Normal, JointIndependent
    from UQpy.distributions import Gumbel, JointCopula








.. GENERATED FROM PYTHON SOURCE LINES 36-40

Define a Copula
---------------
The definition of bivariate distribution with a copula, is similar to defining a multivariate distribution from
independent marginals. In both cases a list of marginals needs to be defined. In case of 

.. GENERATED FROM PYTHON SOURCE LINES 43-56

.. code-block:: default

    marginals = [Normal(loc=0., scale=1), Normal(loc=0., scale=1)]
    copula = Gumbel(theta=3.)

    # dist_1 is a multivariate normal with independent marginals
    dist_1 = JointIndependent(marginals)
    print('Does the distribution with independent marginals have an rvs method?')
    print(hasattr(dist_1, 'rvs'))

    # dist_2 exhibits dependence between the two dimensions, defined using a gumbel copula
    dist_2 = JointCopula(marginals=marginals, copula=copula)
    print('Does the distribution with copula have an rvs method?')
    print(hasattr(dist_2, 'rvs'))





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Does the distribution with independent marginals have an rvs method?
    True
    Does the distribution with copula have an rvs method?
    False




.. GENERATED FROM PYTHON SOURCE LINES 57-60

Plot the pdf of the distribution before and after the copula
-------------------------------------------------------------


.. GENERATED FROM PYTHON SOURCE LINES 63-85

.. code-block:: default


    fig, ax = plt.subplots(ncols=2, figsize=(10, 4))

    x = np.arange(-3, 3, 0.1)
    y = np.arange(-3, 3, 0.1)
    X, Y = np.meshgrid(x, y)
    Z = dist_1.pdf(x=np.concatenate([X.reshape((-1, 1)), Y.reshape((-1, 1))], axis=1))
    CS = ax[0].contour(X, Y, Z.reshape(X.shape))
    ax[0].clabel(CS, inline=1, fontsize=10)
    ax[0].set_title('Contour plot of pdf - independent normals')

    x = np.arange(-3, 3, 0.1)
    y = np.arange(-3, 3, 0.1)
    X, Y = np.meshgrid(x, y)
    Z = dist_2.pdf(x=np.concatenate([X.reshape((-1, 1)), Y.reshape((-1, 1))], axis=1))
    CS = ax[1].contour(X, Y, Z.reshape(X.shape))
    ax[1].clabel(CS, inline=1, fontsize=10)
    ax[1].set_title('Contour plot of pdf - normals with Gumbel copula')
    plt.show()






.. image-sg:: /auto_examples/distributions/multivariate/images/sphx_glr_plot_multivariate_copulas_001.png
   :alt: Contour plot of pdf - independent normals, Contour plot of pdf - normals with Gumbel copula
   :srcset: /auto_examples/distributions/multivariate/images/sphx_glr_plot_multivariate_copulas_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 86-90

Modify the parameters of the multivariate copula.
-------------------------------------------------

Use the update_parameters method.

.. GENERATED FROM PYTHON SOURCE LINES 93-95

.. code-block:: default

    print(dist_2.copula.parameters)
    dist_2.update_parameters(theta_c=2.)
    print(dist_2.copula.parameters)



.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    {'theta': 3.0}
    {'theta': 2.0}





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  0.105 seconds)


.. _sphx_glr_download_auto_examples_distributions_multivariate_plot_multivariate_copulas.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example


    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/SURGroup/UQpy/master?urlpath=lab/tree/notebooks/auto_examples/distributions/multivariate/plot_multivariate_copulas.ipynb
        :alt: Launch binder
        :width: 150 px



    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_multivariate_copulas.py <plot_multivariate_copulas.py>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_multivariate_copulas.ipynb <plot_multivariate_copulas.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_