.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "11_demos\itom\dataProcessing\demo_FitData.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        Click :ref:`here <sphx_glr_download_11_demos_itom_dataProcessing_demo_FitData.py>`
        to download the full example code

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

.. _sphx_glr_11_demos_itom_dataProcessing_demo_FitData.py:

Fit data
===========

This demo shows how data fitting can be performed using the ``itom.dataObject`` and ``itom.algorithms``.

.. GENERATED FROM PYTHON SOURCE LINES 5-11

.. code-block:: default



    import numpy as np
    from itom import dataObject
    from itom import algorithms








.. GENERATED FROM PYTHON SOURCE LINES 13-14

Polynomial of order 2 in x- and y-direction

.. GENERATED FROM PYTHON SOURCE LINES 14-18

.. code-block:: default

    def polyFuncOrder2x2(x: float, y:float) -> float:
        return 2.5 * x ** 2 + -1.7 * y ** 2 + 1.3 * x * y + 0.7 * x - 0.3 * y + 3.2









.. GENERATED FROM PYTHON SOURCE LINES 19-20

Vectorize this function to be evaluated over an array of x and y-coordinates

.. GENERATED FROM PYTHON SOURCE LINES 20-26

.. code-block:: default

    f = np.vectorize(polyFuncOrder2x2)

    [X, Y] = np.meshgrid(np.arange(-10, 10.5, 0.5), np.arange(-10, 10.5, 0.5))
    Z = f(X, Y)
    total = np.prod(Z.shape)








.. GENERATED FROM PYTHON SOURCE LINES 27-30

First create a 2d polynomial fit with order x = 2 and order y = 2.
Z_ must be a regular grid where the x- and y- values are
defined by its axisScales and axisOffsets attributes. 

.. GENERATED FROM PYTHON SOURCE LINES 30-45

.. code-block:: default

    Z_ = dataObject(Z)
    Z_.axisScales = (0.5, 0.5)
    Z_.axisOffsets = (20, 20)

    coeffs = algorithms.polyfitWeighted2D(Z_, 2, 2)
    print("coefficients: ", coeffs)

    # Reconstruct the fitted sphere using the determined coefficients.
    # First, create a ``dataObject`` with the desired size, scaling and offset for the
    # the grid of x- and y- values. The z-values are then calculated.
    Z_reconstruction = Z_.copy()
    Z_reconstruction[:, :] = float("nan")

    algorithms.polyval2D(Z_reconstruction, coeffs, 2, 2)





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

 .. code-block:: none

    coefficients:  (3.1999999999995303, -0.2999999999999668, -1.6999999999999904, 0.6999999999999899, 1.3000000000000003, 2.499999999999999)




.. GENERATED FROM PYTHON SOURCE LINES 46-47

Randomly select a number of samples unique values in the range ``[0,total)``.

.. GENERATED FROM PYTHON SOURCE LINES 47-60

.. code-block:: default

    samples = 100
    randomUniqueValues = np.random.choice(total, samples)
    X2 = dataObject([1, samples], "float64")
    Y2 = dataObject([1, samples], "float64")
    Z2 = dataObject([1, samples], "float64")
    c = Z.shape[1]

    for i in range(samples):
        idx = randomUniqueValues[i]
        X2[0, i] = X[int(idx / c), idx % c]
        Y2[0, i] = Y[int(idx / c), idx % c]
        Z2[0, i] = Z[int(idx / c), idx % c]








.. GENERATED FROM PYTHON SOURCE LINES 61-62

Determine the polyonimal coefficients only using the random samples.

.. GENERATED FROM PYTHON SOURCE LINES 62-66

.. code-block:: default

    coeffs2 = algorithms.polyfitWeighted2DSinglePoints( X2, Y2, Z2, 2, 2)
    # coeffs and coeffs2 must be the same!
    print("fitted coefficient: ", coeffs2)





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

 .. code-block:: none

    fitted coefficient:  (3.2000000000001094, -0.3000000000000037, -1.6999999999999997, 0.7000000000000003, 1.300000000000001, 2.499999999999998)




.. GENERATED FROM PYTHON SOURCE LINES 67-68

And reconstruct the entire surface for X and Y values.

.. GENERATED FROM PYTHON SOURCE LINES 68-79

.. code-block:: default

    Z2_reconstruction = dataObject()
    algorithms.polyval2DSinglePoints(
        dataObject(X),
        dataObject(Y),
        Z2_reconstruction,
        coeffs2,
        2,
        2,
    )

    sample_reconstruction = dataObject()
    algorithms.polyval2DSinglePoints(X2, Y2, sample_reconstruction, coeffs2, 2, 2)







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

   **Total running time of the script:** ( 0 minutes  0.013 seconds)


.. _sphx_glr_download_11_demos_itom_dataProcessing_demo_FitData.py:

.. only:: html

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


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

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

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

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