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

.. only:: html

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

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

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

.. _sphx_glr_generated_examples_whittaker_plot_lam_effects.py:


`lam` effects
-------------

This example shows the influence of the `lam` parameter that is used when
fitting any algorithm that is based on Whittaker-smoothing. Note that the
exact `lam` values used in this example are unimportant, just the changes
in their scale.

For this example, the :meth:`~.Baseline.arpls` algorithm will be used, which performs
well in the presence of noise.

.. GENERATED FROM PYTHON SOURCE LINES 15-39

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from pybaselines import Baseline
    from pybaselines.utils import gaussian


    x = np.linspace(0, 1000, 1000)
    signal = (
        gaussian(x, 9, 100, 12)
        + gaussian(x, 6, 180, 5)
        + gaussian(x, 8, 350, 11)
        + gaussian(x, 15, 400, 18)
        + gaussian(x, 6, 550, 6)
        + gaussian(x, 13, 700, 8)
        + gaussian(x, 9, 800, 9)
        + gaussian(x, 9, 880, 7)
    )
    baseline = 5 + 10 * np.exp(-x / 800)
    noise = np.random.default_rng(0).normal(0, 0.2, len(x))
    y = signal + baseline + noise

    baseline_fitter = Baseline(x_data=x)







.. GENERATED FROM PYTHON SOURCE LINES 41-44

For extremely small `lam` values, the algorithm's output is more comparable
with smoothing than baseline correction (which would be the desired result if
using pure Whittaker smoothing).

.. GENERATED FROM PYTHON SOURCE LINES 44-49

.. code-block:: Python

    plt.plot(y, label='data')
    lam = 1
    plt.plot(baseline_fitter.arpls(y, lam=lam)[0], label=f'lam=10$^{np.log10(lam):.0f}$')
    plt.legend()




.. image-sg:: /generated/examples/whittaker/images/sphx_glr_plot_lam_effects_001.png
   :alt: plot lam effects
   :srcset: /generated/examples/whittaker/images/sphx_glr_plot_lam_effects_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 50-52

Increasing the `lam` value produces results that more resemble the baseline. However,
the baseline is still too flexible and cuts into the larger peaks.

.. GENERATED FROM PYTHON SOURCE LINES 52-59

.. code-block:: Python

    plt.figure()
    plt.plot(y, label='data')
    lam = 1e3
    plt.plot(baseline_fitter.arpls(y, lam=lam)[0], label=f'lam=10$^{np.log10(lam):.0f}$')
    plt.legend()





.. image-sg:: /generated/examples/whittaker/images/sphx_glr_plot_lam_effects_002.png
   :alt: plot lam effects
   :srcset: /generated/examples/whittaker/images/sphx_glr_plot_lam_effects_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 60-62

Increasing the `lam` value further produces the desired result and follows the
expected baseline without reducing the peak area.

.. GENERATED FROM PYTHON SOURCE LINES 62-69

.. code-block:: Python

    plt.figure()
    plt.plot(y, label='data')
    lam = 1e6
    plt.plot(baseline_fitter.arpls(y, lam=lam)[0], label=f'lam=10$^{np.log10(lam):.0f}$')
    plt.legend()





.. image-sg:: /generated/examples/whittaker/images/sphx_glr_plot_lam_effects_003.png
   :alt: plot lam effects
   :srcset: /generated/examples/whittaker/images/sphx_glr_plot_lam_effects_003.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 70-72

Further increasing the `lam` value then makes the baseline too stiff and unable
to follow the curve of the data.

.. GENERATED FROM PYTHON SOURCE LINES 72-78

.. code-block:: Python

    plt.figure()
    plt.plot(y, label='data')
    lam = 1e10
    plt.plot(baseline_fitter.arpls(y, lam=lam)[0], label=f'lam=10$^{{{np.log10(lam):.0f}}}$')
    plt.legend()




.. image-sg:: /generated/examples/whittaker/images/sphx_glr_plot_lam_effects_004.png
   :alt: plot lam effects
   :srcset: /generated/examples/whittaker/images/sphx_glr_plot_lam_effects_004.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 79-81

Finally, put together all the results to show the change in the baseline
as `lam` increases.

.. GENERATED FROM PYTHON SOURCE LINES 81-88

.. code-block:: Python

    plt.figure()
    plt.plot(y, label='data')
    for lam in (1, 1e3, 1e6, 1e10):
        plt.plot(baseline_fitter.arpls(y, lam=lam)[0], label=f'lam=10$^{{{np.log10(lam):.0f}}}$')
    plt.legend()

    plt.show()



.. image-sg:: /generated/examples/whittaker/images/sphx_glr_plot_lam_effects_005.png
   :alt: plot lam effects
   :srcset: /generated/examples/whittaker/images/sphx_glr_plot_lam_effects_005.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.352 seconds)


.. _sphx_glr_download_generated_examples_whittaker_plot_lam_effects.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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