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

.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_example_plot_energy_example.py>`
        to download the full example code

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

.. _sphx_glr_auto_example_plot_energy_example.py:


Energy computation example
==========================

This page provides an example of energy 
computation for a given sample.

.. GENERATED FROM PYTHON SOURCE LINES 8-14

.. code-block:: default

    import numpy as np
    import openturns as ot
    import otkerneldesign as otkd
    import matplotlib.pyplot as plt
    from matplotlib import cm








.. GENERATED FROM PYTHON SOURCE LINES 15-16

Bivariate uniform distribution

.. GENERATED FROM PYTHON SOURCE LINES 16-21

.. code-block:: default


    unifrom = ot.Uniform(0., 1.)
    dimension = 5
    distribution = ot.ComposedDistribution([unifrom] * dimension)








.. GENERATED FROM PYTHON SOURCE LINES 22-24

Standard and tensorized kernel herding 
--------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 24-45

.. code-block:: default


    size = 300
    # Kernel definition
    theta = 0.3
    ker_list = [ot.MaternModel([theta], [1.0], 2.5)] * dimension
    kernel = ot.ProductCovarianceModel(ker_list)
    # Kernel herding design
    kh = otkd.KernelHerding(
        kernel=kernel,
        candidate_set_size=2 ** 14,
        distribution=distribution
    )
    kh_design = kh.select_design(size)
    # Tensorized kernel herding design
    kht = otkd.KernelHerdingTensorized(
        kernel=kernel,
        candidate_set_size=2 ** 14,
        distribution=distribution
    )
    kht_design = kht.select_design(size)








.. GENERATED FROM PYTHON SOURCE LINES 46-55

Energy convergence
------------------
The main difference between the two classes is 
the way to compute the target potential function. 
With independent inputs and a covariance kernel
built as the product of one-dimensional kernels,
the TensorizedKernelHerding 
allows to write the multivariate potential as a product 
of univariate potentials, easing its computation in high dimension.

.. GENERATED FROM PYTHON SOURCE LINES 55-64

.. code-block:: default


    kh_target_energy = kh._target_energy
    kht_target_energy = kht._target_energy

    target_energy_aerror = np.abs(kh_target_energy - kht_target_energy)
    target_energy_rerror = np.abs(kh_target_energy - kht_target_energy) / kh_target_energy
    print("Target energy absolute error: {:.4}".format(target_energy_aerror))
    print("Target energy relative error: {:.3%}".format(target_energy_rerror))





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

 .. code-block:: none

    Target energy absolute error: 7.503e-05
    Target energy relative error: 0.169%




.. GENERATED FROM PYTHON SOURCE LINES 65-67

Draw the energy convergence of KernelHerding and TensorizedKernelHerding designs.
 Notice how they both converge towards their respective target energies.

.. GENERATED FROM PYTHON SOURCE LINES 67-83

.. code-block:: default


    fig1, plot_data1 = kh.draw_energy_convergence(kh.get_indices(kh_design))
    fig2, plot_data2 = kht.draw_energy_convergence(kht.get_indices(kht_design))

    fig3, ax3 = plt.subplots(1, sharey=True, sharex=True)
    # Plot data from fig1 and fig2
    ax3.plot(plot_data1.get_data()[0], np.log(plot_data1.get_data()[1]), label=kh._method_label + 'standard')
    ax3.plot(plot_data2.get_data()[0], np.log(plot_data2.get_data()[1]), label=kht._method_label)
    ax3.axhline(np.log(kh_target_energy), color='C0', linestyle='dashed', label='target energy standard')
    ax3.axhline(np.log(kht_target_energy), color='C1', linestyle='dashed', label='target energy tensorized')
    ax3.set_title('Energy convergence')
    ax3.set_xlabel('design size ($n$)')
    ax3.set_ylabel('Energy (log-scale)')
    ax3.legend(loc='best')
    plt.show()




.. image-sg:: /auto_example/images/sphx_glr_plot_energy_example_001.png
   :alt: Energy convergence
   :srcset: /auto_example/images/sphx_glr_plot_energy_example_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    /usr/share/miniconda3/envs/test/lib/python3.10/site-packages/otkerneldesign-0.1.4-py3.10.egg/otkerneldesign/KernelHerding.py:312: RuntimeWarning: Mean of empty slice.
    /usr/share/miniconda3/envs/test/lib/python3.10/site-packages/numpy/core/_methods.py:190: RuntimeWarning: invalid value encountered in double_scalars
      ret = ret.dtype.type(ret / rcount)





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

   **Total running time of the script:** ( 0 minutes  35.473 seconds)


.. _sphx_glr_download_auto_example_plot_energy_example.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_energy_example.py <plot_energy_example.py>`

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

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