.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/2d-lsq.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_2d-lsq.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_2d-lsq.py:


===============================
2-Dimensional Least Squares Fit
===============================

.. GENERATED FROM PYTHON SOURCE LINES 6-61



.. image-sg:: /auto_examples/images/sphx_glr_2d-lsq_001.png
   :alt: 2d lsq
   :srcset: /auto_examples/images/sphx_glr_2d-lsq_001.png
   :class: sphx-glr-single-img





.. code-block:: Python
   :lineno-start: 7


    import ndsplines
    import matplotlib.pyplot as plt
    import numpy as np


    NUM_X = 50
    NUM_Y = 50
    x = np.linspace(-3, 3, NUM_X)
    y = np.linspace(-3, 3, NUM_Y)
    meshx, meshy = np.meshgrid(x, y, indexing="ij")
    input_coords = np.stack((meshx, meshy), axis=-1)
    K = np.array(
        [
            [
                1,
                -0.7,
            ],
            [-0.7, 1.5],
        ]
    )
    meshz = np.exp(
        -np.einsum(
            K,
            [
                1,
                2,
            ],
            input_coords,
            [..., 1],
            input_coords,
            [..., 2],
        )
    ) + 0.1 * np.random.randn(NUM_X, NUM_Y)


    xt = [-1, 0, 1]
    yt = [-1, 0, 1]
    k = 3
    xt = np.r_[(x[0],) * (k + 1), xt, (x[-1],) * (k + 1)]
    yt = np.r_[(y[0],) * (k + 1), yt, (y[-1],) * (k + 1)]

    ts = [xt, yt]

    samplex = input_coords.reshape((-1, 2))
    sampley = meshz.reshape((-1))

    spl = ndsplines.make_lsq_spline(samplex, sampley, ts, np.array([3, 3]))

    fig = plt.figure()
    ax = fig.add_subplot(111, projection="3d")

    ax.scatter(meshx, meshy, meshz, alpha=0.25)
    ax.plot_wireframe(meshx, meshy, spl(input_coords), color="C1")
    plt.show()


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

   **Total running time of the script:** (0 minutes 0.118 seconds)


.. _sphx_glr_download_auto_examples_2d-lsq.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: 2d-lsq.ipynb <2d-lsq.ipynb>`

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

      :download:`Download Python source code: 2d-lsq.py <2d-lsq.py>`

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

      :download:`Download zipped: 2d-lsq.zip <2d-lsq.zip>`


.. only:: html

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

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