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

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

.. _sphx_glr_auto_examples_decomposition_workflows_plot_lower_order_reconstruction.py:


Lower-Order Reconstruction
==========================

Compare full and lower-order reconstructions and relate the approximation
quality to the retained component terms.

.. GENERATED FROM PYTHON SOURCE LINES 8-78



.. image-sg:: /auto_examples/decomposition_workflows/images/sphx_glr_plot_lower_order_reconstruction_001.png
   :alt: Reconstruction error, Component magnitudes, Order-1 absolute error
   :srcset: /auto_examples/decomposition_workflows/images/sphx_glr_plot_lower_order_reconstruction_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    Available component keys: ['g_0', 'g_1', 'g_2', 'g_1,2']
    Full reconstruction MAE: 8.250100906256885e-19
    Order-1 reconstruction MAE: 0.6063038502324416






|

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from hdmrlib import EMPR


    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]
        + np.cos(np.pi * y)[None, :]
        + 0.35 * np.outer(x, y)
    )

    empr = EMPR(X, order=2)
    components = empr.components()

    X_full = np.asarray(empr.reconstruct(order=2), dtype=np.float64)
    X_order1 = np.asarray(empr.reconstruct(order=1), dtype=np.float64)

    full_mae = float(np.mean(np.abs(X - X_full)))
    order1_mae = float(np.mean(np.abs(X - X_order1)))

    keys = list(components.keys())
    norms = [float(np.linalg.norm(np.asarray(components[key]))) for key in keys]

    pairs = sorted(zip(keys, norms), key=lambda t: t[1], reverse=True)
    sorted_keys = [str(k) for k, _ in pairs]
    sorted_norms = [v for _, v in pairs]

    print("Available component keys:", keys)
    print("Full reconstruction MAE:", full_mae)
    print("Order-1 reconstruction MAE:", order1_mae)

    fig, axes = plt.subplots(1, 3, figsize=(12, 4), constrained_layout=True)

    # Panel 1: reconstruction error comparison
    axes[0].bar(
        ["Order 2", "Order 1"],
        [full_mae, order1_mae],
    )
    axes[0].set_title("Reconstruction error")
    axes[0].set_ylabel("Mean absolute error")

    # Panel 2: retained component magnitudes
    bars = axes[1].bar(sorted_keys, sorted_norms)
    axes[1].set_title("Component magnitudes")
    axes[1].set_xlabel("Component key")
    axes[1].set_ylabel("Frobenius norm")
    axes[1].tick_params(axis="x", rotation=30)

    for bar, value in zip(bars, sorted_norms):
        axes[1].text(
            bar.get_x() + bar.get_width() / 2,
            bar.get_height(),
            f"{value:.2f}",
            ha="center",
            va="bottom",
            fontsize=9,
        )

    # Panel 3: spatial error for lower-order reconstruction
    order1_error = np.abs(X - X_order1)
    im = axes[2].imshow(order1_error, aspect="auto", interpolation="nearest")
    axes[2].set_title("Order-1 absolute error")
    fig.colorbar(im, ax=axes[2], fraction=0.046, pad=0.04)

    plt.show()

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

   **Total running time of the script:** (0 minutes 0.292 seconds)


.. _sphx_glr_download_auto_examples_decomposition_workflows_plot_lower_order_reconstruction.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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