:orphan:

Examples
========

Worked examples from typical lab courses and measurement tasks. Each one shows a complete
fit with report and plot.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="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.">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_01_gaussian_peak_thumb.png
    :alt:

  :doc:`/auto_examples/plot_01_gaussian_peak`

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      <div class="sphx-glr-thumbnail-title">Gaussian peak in three lines</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="The pH during the titration of a weak acid with sodium hydroxide rises in a step around the equivalence point. A logistic step on top of a constant describes the curve well enough to locate the equivalence point precisely.">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_06_titration_thumb.png
    :alt:

  :doc:`/auto_examples/plot_06_titration`

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      <div class="sphx-glr-thumbnail-title">Titration curve</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="A capacitor discharges through a known resistor. The voltage decays exponentially towards a small offset of the measuring device. From the time constant τ = RC we obtain the capacitance.">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_03_rc_discharge_thumb.png
    :alt:

  :doc:`/auto_examples/plot_03_rc_discharge`

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      <div class="sphx-glr-thumbnail-title">RC discharge</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="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.">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_04_radioactive_decay_thumb.png
    :alt:

  :doc:`/auto_examples/plot_04_radioactive_decay`

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      <div class="sphx-glr-thumbnail-title">Radioactive decay with background</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="A thermocouple voltage is calibrated against reference temperatures. The model is a straight line; each voltage reading has its own uncertainty.">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_02_calibration_line_thumb.png
    :alt:

  :doc:`/auto_examples/plot_02_calibration_line`

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      <div class="sphx-glr-thumbnail-title">Calibration line</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="The amplitude of a driven oscillator near resonance is approximately Lorentzian. The quality factor follows from the resonance frequency and the width: Q = f₀ / (2γ), where γ is the half width at half maximum. The detector has a small constant offset.">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_09_resonance_thumb.png
    :alt:

  :doc:`/auto_examples/plot_09_resonance`

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      <div class="sphx-glr-thumbnail-title">Resonance curve</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="The angle of a pendulum is recorded with a rotary encoder. The oscillation decays exponentially; the encoder has a small zero offset. Frequency, phase and decay time are estimated automatically from a periodogram.">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_05_damped_pendulum_thumb.png
    :alt:

  :doc:`/auto_examples/plot_05_damped_pendulum`

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      <div class="sphx-glr-thumbnail-title">Damped pendulum</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="In a vacuum diode, the space-charge limited anode current follows the Child–Langmuir law I = k · U^(3/2). Fitting a general power law tests whether the exponent really is 3/2.">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_08_child_langmuir_thumb.png
    :alt:

  :doc:`/auto_examples/plot_08_child_langmuir`

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      <div class="sphx-glr-thumbnail-title">Power law: vacuum diode</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="A temperature sensor cools down in air, and the logger records a few corrupted readings. An ordinary least-squares fit is pulled towards them; loss=&quot;huber&quot; downweights them. The model is written as text.">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_11_outliers_thumb.png
    :alt:

  :doc:`/auto_examples/plot_11_outliers`

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      <div class="sphx-glr-thumbnail-title">Outliers: a robust fit</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="A resistor is characterized with a voltmeter and an ammeter. Both readings have uncertainties, the current even more than the voltage. An ordinary fit treats x as exact and underestimates the uncertainty of the resistance. With xerr, fitwise uses orthogonal distance regression, which accounts for the errors in both variables.">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_12_errors_in_x_and_y_thumb.png
    :alt:

  :doc:`/auto_examples/plot_12_errors_in_x_and_y`

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      <div class="sphx-glr-thumbnail-title">Errors in x and y: Ohm's law</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Any Python function can be a model. Here the rate constant of a reaction is measured at several temperatures and described by the Arrhenius law k = A · exp(−Eₐ / RT).">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_07_arrhenius_thumb.png
    :alt:

  :doc:`/auto_examples/plot_07_arrhenius`

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      <div class="sphx-glr-thumbnail-title">Arrhenius law with your own function</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="A spectrum with two overlapping emission lines on a linear background. Models are combined with +. Parameter names that occur twice get automatic prefixes; to choose your own names, use with_prefix.">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_10_two_peaks_background_thumb.png
    :alt:

  :doc:`/auto_examples/plot_10_two_peaks_background`

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      <div class="sphx-glr-thumbnail-title">Two peaks on a sloped background</div>
    </div>


.. thumbnail-parent-div-close

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    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_01_gaussian_peak
   /auto_examples/plot_06_titration
   /auto_examples/plot_03_rc_discharge
   /auto_examples/plot_04_radioactive_decay
   /auto_examples/plot_02_calibration_line
   /auto_examples/plot_09_resonance
   /auto_examples/plot_05_damped_pendulum
   /auto_examples/plot_08_child_langmuir
   /auto_examples/plot_11_outliers
   /auto_examples/plot_12_errors_in_x_and_y
   /auto_examples/plot_07_arrhenius
   /auto_examples/plot_10_two_peaks_background



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

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