.. note::
    :class: sphx-glr-download-link-note

    Click :ref:`here <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
===============================



.. image:: /auto_examples/images/sphx_glr_2d-lsq_001.png
    :class: sphx-glr-single-img





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


    import ndsplines 
    from scipy import interpolate
    import matplotlib.pyplot as plt
    import numpy as np

    from mpl_toolkits.mplot3d import Axes3D


    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  0.287 seconds)


.. _sphx_glr_download_auto_examples_2d-lsq.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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