.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/general_examples/plot_02_hdmr_2d_distinct_comp.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_02_hdmr_2d_distinct_comp.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_general_examples_plot_02_hdmr_2d_distinct_comp.py:


HDMR on a 2D Tensor with Interaction Terms
===================

Run HDMR on a structured 2D tensor and inspect the resulting additive and
interaction terms.

.. GENERATED FROM PYTHON SOURCE LINES 8-110



.. image-sg:: /auto_examples/general_examples/images/sphx_glr_plot_02_hdmr_2d_distinct_comp_001.png
   :alt: Original tensor, Additive part: g_0 + g_1 + g_2, Interaction term: g_1,2, First-order term g_1, First-order term g_2, Residual after additive part
   :srcset: /auto_examples/general_examples/images/sphx_glr_plot_02_hdmr_2d_distinct_comp_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    Input shape: (64, 64)
    Available component keys: ['g_0', 'g_1', 'g_2', 'g_1,2']






|

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from hdmrlib import HDMR


    def to_scalar(component):
        arr = np.asarray(component)
        return float(np.squeeze(arr))


    def to_vector(component):
        arr = np.asarray(component)
        arr = np.squeeze(arr)

        if arr.ndim != 1:
            raise ValueError(f"Expected a 1D component, got shape {arr.shape!r}")

        return arr


    def to_matrix(component):
        arr = np.asarray(component)
        arr = np.squeeze(arr)

        if arr.ndim != 2:
            raise ValueError(f"Expected a 2D component, got shape {arr.shape!r}")

        return arr


    # Build a tensor with clearly visible first-order and interaction structure.
    x = np.linspace(-1.0, 1.0, 64)
    y = np.linspace(-1.0, 1.0, 64)

    X = (
        0.2
        + 0.9 * np.sin(np.pi * x)[:, None]
        + 0.7 * np.cos(np.pi * y)[None, :]
        + 1.2 * np.outer(x, y)
    )

    hdmr = HDMR(X, order=2)
    components = hdmr.components()

    print("Input shape:", X.shape)
    print("Available component keys:", list(components.keys()))

    g0 = to_scalar(components["g_0"])
    g1 = to_vector(components["g_1"])
    g2 = to_vector(components["g_2"])
    g12 = to_matrix(components["g_1,2"])

    additive = g0 + g1[:, None] + g2[None, :]

    interaction_max = np.max(np.abs(g12))

    fig = plt.figure(figsize=(12, 8))

    ax1 = plt.subplot(2, 3, 1)
    im1 = ax1.imshow(X, aspect="auto", cmap="viridis")
    ax1.set_title("Original tensor")
    plt.colorbar(im1, ax=ax1, fraction=0.046, pad=0.04)

    ax2 = plt.subplot(2, 3, 2)
    im2 = ax2.imshow(additive, aspect="auto", cmap="viridis")
    ax2.set_title("Additive part: g_0 + g_1 + g_2")
    plt.colorbar(im2, ax=ax2, fraction=0.046, pad=0.04)

    ax3 = plt.subplot(2, 3, 3)
    im3 = ax3.imshow(
        g12,
        aspect="auto",
        cmap="coolwarm",
        vmin=-interaction_max,
        vmax=interaction_max,
    )
    ax3.set_title("Interaction term: g_1,2")
    plt.colorbar(im3, ax=ax3, fraction=0.046, pad=0.04)

    ax4 = plt.subplot(2, 3, 4)
    ax4.plot(x, g1)
    ax4.set_title("First-order term g_1")
    ax4.set_xlabel("x")
    ax4.set_ylabel("Contribution")
    ax4.grid(True, alpha=0.3)

    ax5 = plt.subplot(2, 3, 5)
    ax5.plot(y, g2)
    ax5.set_title("First-order term g_2")
    ax5.set_xlabel("y")
    ax5.set_ylabel("Contribution")
    ax5.grid(True, alpha=0.3)

    ax6 = plt.subplot(2, 3, 6)
    residual = X - additive
    im6 = ax6.imshow(residual, aspect="auto", cmap="coolwarm")
    ax6.set_title("Residual after additive part")
    plt.colorbar(im6, ax=ax6, fraction=0.046, pad=0.04)

    plt.tight_layout()
    plt.show()

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

   **Total running time of the script:** (0 minutes 0.568 seconds)


.. _sphx_glr_download_auto_examples_general_examples_plot_02_hdmr_2d_distinct_comp.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_02_hdmr_2d_distinct_comp.ipynb <plot_02_hdmr_2d_distinct_comp.ipynb>`

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

      :download:`Download Python source code: plot_02_hdmr_2d_distinct_comp.py <plot_02_hdmr_2d_distinct_comp.py>`

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

      :download:`Download zipped: plot_02_hdmr_2d_distinct_comp.zip <plot_02_hdmr_2d_distinct_comp.zip>`


.. only:: html

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

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