.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/general_examples/plot_03_empr_hdmr_2d.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_general_examples_plot_03_empr_hdmr_2d.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_general_examples_plot_03_empr_hdmr_2d.py:


EMPR vs HDMR on a 2D Tensor
===========================

Run EMPR and HDMR on the same 2D tensor, compare the reconstructions,
and visualize the remaining approximation errors.

.. GENERATED FROM PYTHON SOURCE LINES 8-81



.. image-sg:: /auto_examples/general_examples/images/sphx_glr_plot_03_empr_hdmr_2d_001.png
   :alt: Original tensor, EMPR reconstruction, HDMR reconstruction, EMPR absolute error, HDMR absolute error, Absolute difference
   :srcset: /auto_examples/general_examples/images/sphx_glr_plot_03_empr_hdmr_2d_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    Input shape: (32, 32)
    EMPR mean absolute error: 4.1843427594362437e-19
    HDMR mean absolute error: 2.879912020664621e-20
    Mean absolute difference between reconstructions: 4.0657581468206416e-19






|

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from hdmrlib import EMPR, HDMR


    x = np.linspace(0.0, 1.0, 32)
    y = np.linspace(0.0, 1.0, 32)

    X = (
        0.5
        + np.sin(np.pi * x)[:, None]
        + 0.8 * np.cos(np.pi * y)[None, :]
        + 0.5 * np.outer(x, y)
        + 0.3 * np.exp(-40.0 * ((x[:, None] - 0.7) ** 2 + (y[None, :] - 0.3) ** 2))
    )

    empr = EMPR(X, order=2)
    X_empr = np.asarray(empr.reconstruct(), dtype=np.float64)

    hdmr = HDMR(X, order=2)
    X_hdmr = np.asarray(hdmr.reconstruct(), dtype=np.float64)

    empr_abs_err = np.abs(X - X_empr)
    hdmr_abs_err = np.abs(X - X_hdmr)
    recon_diff = np.abs(X_empr - X_hdmr)

    print("Input shape:", X.shape)
    print("EMPR mean absolute error:", float(np.mean(empr_abs_err)))
    print("HDMR mean absolute error:", float(np.mean(hdmr_abs_err)))
    print("Mean absolute difference between reconstructions:", float(np.mean(recon_diff)))

    vmin = min(X.min(), X_empr.min(), X_hdmr.min())
    vmax = max(X.max(), X_empr.max(), X_hdmr.max())

    err_vmax = max(empr_abs_err.max(), hdmr_abs_err.max(), recon_diff.max())

    fig = plt.figure(figsize=(12, 7), constrained_layout=True)
    gs = fig.add_gridspec(2, 4, width_ratios=[1, 1, 1, 0.05])

    ax00 = fig.add_subplot(gs[0, 0])
    ax01 = fig.add_subplot(gs[0, 1])
    ax02 = fig.add_subplot(gs[0, 2])
    cax0 = fig.add_subplot(gs[0, 3])

    ax10 = fig.add_subplot(gs[1, 0])
    ax11 = fig.add_subplot(gs[1, 1])
    ax12 = fig.add_subplot(gs[1, 2])
    cax1 = fig.add_subplot(gs[1, 3])

    im0 = ax00.imshow(X, aspect="auto", vmin=vmin, vmax=vmax, interpolation="nearest")
    ax00.set_title("Original tensor")

    ax01.imshow(X_empr, aspect="auto", vmin=vmin, vmax=vmax, interpolation="nearest")
    ax01.set_title("EMPR reconstruction")

    ax02.imshow(X_hdmr, aspect="auto", vmin=vmin, vmax=vmax, interpolation="nearest")
    ax02.set_title("HDMR reconstruction")

    fig.colorbar(im0, cax=cax0)

    im1 = ax10.imshow(empr_abs_err, aspect="auto", vmin=0.0, vmax=err_vmax, interpolation="nearest")
    ax10.set_title("EMPR absolute error")

    ax11.imshow(hdmr_abs_err, aspect="auto", vmin=0.0, vmax=err_vmax, interpolation="nearest")
    ax11.set_title("HDMR absolute error")

    ax12.imshow(recon_diff, aspect="auto", vmin=0.0, vmax=err_vmax, interpolation="nearest")
    ax12.set_title("Absolute difference")

    fig.colorbar(im1, cax=cax1)

    plt.show()

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

   **Total running time of the script:** (0 minutes 0.618 seconds)


.. _sphx_glr_download_auto_examples_general_examples_plot_03_empr_hdmr_2d.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_03_empr_hdmr_2d.ipynb <plot_03_empr_hdmr_2d.ipynb>`

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

      :download:`Download Python source code: plot_03_empr_hdmr_2d.py <plot_03_empr_hdmr_2d.py>`

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

      :download:`Download zipped: plot_03_empr_hdmr_2d.zip <plot_03_empr_hdmr_2d.zip>`


.. only:: html

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

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