.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "tutorials/scaling_problem.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

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

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

.. _sphx_glr_tutorials_scaling_problem.py:


08. Scaling Dependent Stepsize Problem
======================================
In earlier tests it was noticed that the size of the weighting parameters
has an effect on the solution while keeping the ratio constant.
Meanwhile the problem has been identified as a too small number of iterations.
Overall, the default parameters have been adjusted, but in this example,
we will briefly show what the effect looks like.

.. GENERATED FROM PYTHON SOURCE LINES 12-15

A grey image is created and viewed in an area [0, 1].
The relation of the weighting between dataterm and regularization
remains the same, but is adjusted in its absolute value too.

.. GENERATED FROM PYTHON SOURCE LINES 15-62

.. code-block:: default

    import numpy as np
    import matplotlib.pyplot as plt

    from recon.interfaces import Smoothing
    from recon.utils.images import two_smooth_squares

    scaled_image = two_smooth_squares(256, 200)

    sigma = 0.3  # the percentage portion standard deviation for normal (Gaussian) distribution.

    noise_image = scaled_image + np.random.normal(0, sigma*np.max(scaled_image), size=scaled_image.shape)

    weights = [(0.2, 0.2), (1, 1), (2, 2)]

    rows = ['{}'.format(row) for row in weights]

    f = plt.figure(figsize=(6, 3*len(weights)))

    for i, weight in enumerate(weights):
        tv_scaled_obj = Smoothing(domain_shape=scaled_image.shape,
                                  reg_mode='tv',
                                  lam=weight[0],
                                  alpha=weight[1],
                                  tau="calc")
        scaled_tv_solution = tv_scaled_obj.solve(noise_image, max_iter=5550, tol=1e-4)

        tv_unscaled_obj = Smoothing(domain_shape=scaled_image.shape,
                                    reg_mode='tv',
                                    lam=weight[0],
                                    alpha=weight[1],
                                    tau="calc")
        unscaled_tv_solution = tv_unscaled_obj.solve(noise_image, max_iter=550, tol=1e-4)

        f.add_subplot(3, 2, i*2+1)
        plt.gray()
        plt.axis('off')
        plt.imshow(scaled_tv_solution)
        plt.title("Long-Run: weight " + str(weight))
        f.add_subplot(3, 2, (i+1)*2)

        plt.gray()
        plt.imshow(unscaled_tv_solution)
        plt.title("Short-Run: weight " + str(weight))
        plt.axis('off')
    plt.tight_layout()
    plt.show()




.. image:: /tutorials/images/sphx_glr_scaling_problem_001.png
    :alt: Long-Run: weight (0.2, 0.2), Short-Run: weight (0.2, 0.2), Long-Run: weight (1, 1), Short-Run: weight (1, 1), Long-Run: weight (2, 2), Short-Run: weight (2, 2)
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none

     Early stopping.
     Early stopping.
     Early stopping.
     Early stopping.
     Early stopping.
     Early stopping.




.. GENERATED FROM PYTHON SOURCE LINES 63-66

Conclusion
Be careful with max_iter and tol parameter
or with the interpretation of result if the number of iteration is too small.


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

   **Total running time of the script:** ( 0 minutes  42.344 seconds)


.. _sphx_glr_download_tutorials_scaling_problem.py:


.. only :: html

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



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

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



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

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


.. only:: html

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

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