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

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_gallery_inverse_fit_linear_scale.py>`
        to download the full example code.

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

.. _sphx_glr_gallery_inverse_fit_linear_scale.py:


Fit a scalar scale factor
=========================

Fit one bounded parameter to a small analytic forward model. This is the
smallest complete inverse-problem setup: a callable, an observation, and one
or more ``FitParameter`` objects.

The fitted ``scale`` is approximately 2.0 (dimensionless). Predictions and
residuals have shape ``(3,)``. With these exact synthetic observations, the
residuals approach zero.

.. GENERATED FROM PYTHON SOURCE LINES 13-33




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

 .. code-block:: none

    converged (42 model evaluations)
    objective = 0.000000
    {'scale': 2.0}






|

.. code-block:: Python

    import numpy as np

    from PyMieSim import FitParameter, MeasuredData, fit_parameters

    x = np.array([1.0, 2.0, 3.0])
    observation = MeasuredData(values=np.array([2.0, 4.0, 6.0]))


    def model(parameters):
        return parameters["scale"] * x


    result = fit_parameters(
        model=model,
        observation=observation,
        parameters=[FitParameter(name="scale", initial=0.8, bounds=(0.0, 4.0))],
    )

    print(result.summary())
    print(result.parameters)


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

   **Total running time of the script:** (0 minutes 0.002 seconds)


.. _sphx_glr_download_gallery_inverse_fit_linear_scale.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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