.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_hv_approx.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_plot_hv_approx.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_plot_hv_approx.py:

Comparing methods for approximating the hypervolume
===================================================

This example shows how to approximate the hypervolume metric of the ``CPFs.txt`` dataset using both HypE, :func:`moocore.whv_hype()`, and DZ2019, :func:`moocore.hv_approx()` for several
values of the number of samples between :math:`10^1` and :math:`10^5`. We repeat each
calculation 10 times to account for stochasticity.

.. GENERATED FROM PYTHON SOURCE LINES 8-38

.. code-block:: Python


    import numpy as np
    import moocore

    ref = 2.1
    x = moocore.get_dataset("CPFs.txt")[:, :-1]
    x = moocore.filter_dominated(x)
    x = moocore.normalise(x, to_range=[1, 2])
    true_hv = moocore.hypervolume(x, ref=ref)
    rng1 = np.random.default_rng(42)
    rng2 = np.random.default_rng(42)

    hype = {}
    dz = {}
    for i in range(1, 6):
        hype[i] = []
        dz[i] = []
        for r in range(15):
            res = moocore.whv_hype(x, ref=ref, ideal=0, nsamples=10**i, seed=rng1)
            hype[i].append(res)
            res = moocore.hv_approx(x, ref=ref, nsamples=10**i, seed=rng2)
            dz[i].append(res)
    print(
        f"True HV    : {true_hv:.5f}",
        f"Mean HYPE  : {np.mean(hype[5]):.5f} [{np.min(hype[5]):.5f}, {np.max(hype[5]):.5f}]",
        f"Mean DZ2019: {np.mean(dz[5]):.5f} [{np.min(dz[5]):.5f}, {np.max(dz[5]):.5f}]",
        sep="\n",
    )






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

 .. code-block:: none

    True HV    : 1.05704
    Mean HYPE  : 1.05601 [1.04504, 1.06391]
    Mean DZ2019: 1.05698 [1.05652, 1.05776]




.. GENERATED FROM PYTHON SOURCE LINES 39-40

Next, we plot the results.

.. GENERATED FROM PYTHON SOURCE LINES 40-61

.. code-block:: Python


    import pandas as pd

    hype = pd.DataFrame(hype)
    dz = pd.DataFrame(dz)
    hype["Method"] = "HypE"
    dz["Method"] = "DZ2019"
    df = (
        pd.concat([hype, dz])
        .reset_index(names="rep")
        .melt(id_vars=["rep", "Method"], var_name="samples")
    )
    df["samples"] = 10 ** df["samples"]
    df["value"] = np.abs(df["value"] - true_hv) / true_hv

    import matplotlib.pyplot as plt
    import seaborn as sns

    ax = sns.lineplot(x="samples", y="value", hue="Method", data=df, marker="o")
    ax.set(xscale="log", yscale="log", ylabel="Relative error")
    plt.show()



.. image-sg:: /auto_examples/images/sphx_glr_plot_hv_approx_001.png
   :alt: plot hv approx
   :srcset: /auto_examples/images/sphx_glr_plot_hv_approx_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 18.867 seconds)


.. _sphx_glr_download_auto_examples_plot_hv_approx.py:

.. only:: html

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

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

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

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_hv_approx.zip <plot_hv_approx.zip>`


.. only:: html

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

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