.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_01_gaussian_peak.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_plot_01_gaussian_peak.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_plot_01_gaussian_peak.py:


Gaussian peak in three lines
============================

The shortest possible fit: a built-in model, data with uncertainties, a report and a plot.
No starting values are needed; fitwise estimates them from the data.

.. GENERATED FROM PYTHON SOURCE LINES 10-11

Simulated measurement: a Gaussian peak with known noise of 0.05.

.. GENERATED FROM PYTHON SOURCE LINES 11-18

.. code-block:: Python

    import numpy as np

    rng = np.random.default_rng(1)
    x = np.linspace(-4, 6, 80)
    y = 3.2 * np.exp(-((x - 1.1) ** 2) / (2 * 0.8**2)) + rng.normal(0, 0.05, x.size)
    dy = np.full_like(x, 0.05)








.. GENERATED FROM PYTHON SOURCE LINES 19-20

The fit itself:

.. GENERATED FROM PYTHON SOURCE LINES 20-25

.. code-block:: Python

    import fitwise as fw

    result = fw.fit(fw.models.gaussian, x, y, yerr=dy)
    print(result)





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

 .. code-block:: none

    Model:      gaussian(x; amp, cen, sigma)
    Method:     Trust Region Reflective (scipy least_squares) (auto: nonlinear)
    Converged:  yes (13 evals)
    Data:       80 points, yerr given (absolute)
    Start:      amp, cen, sigma: peak heuristic

    Parameter    Value   ± Std.Err    Rel.   Bounds
    amp          3.179       0.018   0.6 %   –
    cen         1.0984      0.0053   0.5 %   –
    sigma       0.8057      0.0053   0.7 %   –

    χ²/ndf = 0.718 (77 dof, p = 0.97)    R² = 0.9983    AIC = -23.6
    Correlations > 0.5:  amp–sigma (-0.58)
    Warnings:   none




.. GENERATED FROM PYTHON SOURCE LINES 26-27

``plot()`` shows the data, the fit and the residuals in units of ``yerr``.

.. GENERATED FROM PYTHON SOURCE LINES 27-29

.. code-block:: Python

    fig, axes = result.plot()




.. image-sg:: /auto_examples/images/sphx_glr_plot_01_gaussian_peak_001.png
   :alt: plot 01 gaussian peak
   :srcset: /auto_examples/images/sphx_glr_plot_01_gaussian_peak_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 30-31

Individual parameters are available by name, with value and standard error:

.. GENERATED FROM PYTHON SOURCE LINES 31-33

.. code-block:: Python

    sigma = result.params["sigma"]
    print(f"FWHM = {2.3548 * sigma.value:.3f} ± {2.3548 * sigma.stderr:.3f}")




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

 .. code-block:: none

    FWHM = 1.897 ± 0.013





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

   **Total running time of the script:** (0 minutes 0.160 seconds)


.. _sphx_glr_download_auto_examples_plot_01_gaussian_peak.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_01_gaussian_peak.ipynb <plot_01_gaussian_peak.ipynb>`

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

      :download:`Download Python source code: plot_01_gaussian_peak.py <plot_01_gaussian_peak.py>`

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

      :download:`Download zipped: plot_01_gaussian_peak.zip <plot_01_gaussian_peak.zip>`


.. only:: html

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

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