.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_04_radioactive_decay.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_04_radioactive_decay.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_plot_04_radioactive_decay.py:


Radioactive decay with background
=================================

Counts from a short-lived isotope are recorded in 10-s intervals. The counts follow Poisson
statistics, so the uncertainty of each value is √N. A constant background from the
environment adds to the decay.

.. GENERATED FROM PYTHON SOURCE LINES 11-23

.. code-block:: Python

    import numpy as np

    import fitwise as fw

    rng = np.random.default_rng(5)
    t = np.arange(0, 600, 10.0)  # s
    expected = 850 * np.exp(-t / 140) + 25
    counts = rng.poisson(expected).astype(float)

    result = fw.fit(fw.models.exponential + fw.models.constant, t, counts, yerr=np.sqrt(counts))
    print(result)





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

 .. code-block:: none

    Model:      exponential(x; amp, tau) + constant(x; c)
    Method:     Trust Region Reflective (scipy least_squares) (auto: nonlinear)
    Converged:  yes (11 evals)
    Data:       60 points, yerr given (absolute)
    Start:      amp, tau: log-linear fit · c: edge baseline

    Parameter   Value   ± Std.Err     Rel.   Bounds
    amp           851          12    1.4 %   –
    tau         141.1         3.0    2.1 %   –
    c            23.4         2.6   11.3 %   –

    χ²/ndf = 0.972 (57 dof, p = 0.54)    R² = 0.9930    AIC = 1.2
    Correlations > 0.5:  tau–c (-0.82), amp–tau (-0.61)
    Warnings:   none




.. GENERATED FROM PYTHON SOURCE LINES 24-25

The half-life follows from the decay time: T½ = τ · ln 2.

.. GENERATED FROM PYTHON SOURCE LINES 25-28

.. code-block:: Python

    tau = result.params["tau"]
    print(f"T½ = {tau.value * np.log(2):.1f} ± {tau.stderr * np.log(2):.1f} s")





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

 .. code-block:: none

    T½ = 97.8 ± 2.1 s




.. GENERATED FROM PYTHON SOURCE LINES 29-33

.. code-block:: Python

    fig, axes = result.plot()
    axes[0].set_yscale("log")
    axes[0].set_ylabel("counts per 10 s")
    axes[1].set_xlabel("t (s)")



.. image-sg:: /auto_examples/images/sphx_glr_plot_04_radioactive_decay_001.png
   :alt: plot 04 radioactive decay
   :srcset: /auto_examples/images/sphx_glr_plot_04_radioactive_decay_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    Text(0.5, 18.503588541666666, 't (s)')




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

   **Total running time of the script:** (0 minutes 0.184 seconds)


.. _sphx_glr_download_auto_examples_plot_04_radioactive_decay.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_04_radioactive_decay.ipynb <plot_04_radioactive_decay.ipynb>`

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

      :download:`Download Python source code: plot_04_radioactive_decay.py <plot_04_radioactive_decay.py>`

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

      :download:`Download zipped: plot_04_radioactive_decay.zip <plot_04_radioactive_decay.zip>`


.. only:: html

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

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