.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_10_two_peaks_background.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_10_two_peaks_background.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_plot_10_two_peaks_background.py:


Two peaks on a sloped background
================================

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 :meth:`~fitwise.Model.with_prefix`.

The wavelength is measured relative to the center of the spectrum (655 nm). The intercept of
the background is then the background *in* the spectrum. With absolute wavelengths it would be
the background at 0 nm, an extrapolation over 650 nm, and slope and intercept would be almost
fully correlated; fitwise would warn about that.

.. GENERATED FROM PYTHON SOURCE LINES 16-35

.. code-block:: Python

    import numpy as np

    import fitwise as fw
    from fitwise.models import gaussian, linear

    rng = np.random.default_rng(10)
    wavelength = np.linspace(640, 670, 300)  # nm
    intensity = (
        gaussian(wavelength, 820, 651.2, 1.1)
        + gaussian(wavelength, 310, 655.0, 1.4)
        + 2.5 * (wavelength - 640)
        + 40
    )
    intensity = rng.poisson(intensity).astype(float)
    shift = wavelength - 655.0  # nm relative to the center

    model = gaussian.with_prefix("a_") + gaussian.with_prefix("b_") + linear
    print(model.param_names)





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

 .. code-block:: none

    ('a_amp', 'a_cen', 'a_sigma', 'b_amp', 'b_cen', 'b_sigma', 'slope', 'intercept')




.. GENERATED FROM PYTHON SOURCE LINES 36-38

The starting values come from a sequential estimate: background from the edges, then the
strongest peak, then the second peak on what remains.

.. GENERATED FROM PYTHON SOURCE LINES 38-41

.. code-block:: Python

    result = fw.fit(model, shift, intensity, yerr=np.sqrt(intensity))
    print(result)





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

 .. code-block:: none

    Model:      gaussian(x; a_amp, a_cen, a_sigma) + gaussian(x; b_amp, b_cen, b_sigma) + linear(x; slope, intercept)
    Method:     Trust Region Reflective (scipy least_squares) (auto: nonlinear)
    Converged:  yes (31 evals)
    Data:       300 points, yerr given (absolute)
    Start:      a_amp, a_cen, a_sigma, b_amp, b_cen, b_sigma: peak heuristic · slope, intercept: edge baseline

    Parameter    Value   ± Std.Err     Rel.   Bounds
    a_amp        821.0         7.8    0.9 %   –
    a_cen       -3.805       0.015    0.4 %   –
    a_sigma      1.081       0.011    1.0 %   –
    b_amp        310.4         4.6    1.5 %   –
    b_cen       -0.057       0.039   67.4 %   –
    b_sigma      1.441       0.033    2.3 %   –
    slope        2.513       0.058    2.3 %   –
    intercept    76.50        0.62    0.8 %   –

    χ²/ndf = 0.916 (292 dof, p = 0.85)    R² = 0.9907    AIC = -18.4
    Correlations > 0.5:  a_cen–b_cen (+0.71), b_cen–b_sigma (-0.70), a_cen–b_sigma (-0.66), a_sigma–b_cen (+0.64), a_cen–a_sigma (+0.60), a_sigma–b_sigma (-0.53)
    Warnings:   none




.. GENERATED FROM PYTHON SOURCE LINES 42-52

.. code-block:: Python

    fig, axes = result.plot()
    x = np.linspace(-15, 15, 600)
    p = result.params.values_dict()
    background = linear.eval(x, p)
    for prefix, color in [("a_", "C2"), ("b_", "C3")]:
        peak = gaussian.with_prefix(prefix).eval(x, p)
        axes[0].fill_between(x, background, background + peak, color=color, alpha=0.3, lw=0)
    axes[0].set_ylabel("counts")
    axes[1].set_xlabel("wavelength − 655 nm")




.. image-sg:: /auto_examples/images/sphx_glr_plot_10_two_peaks_background_001.png
   :alt: plot 10 two peaks background
   :srcset: /auto_examples/images/sphx_glr_plot_10_two_peaks_background_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    Text(0.5, 18.503588541666666, 'wavelength − 655 nm')



.. GENERATED FROM PYTHON SOURCE LINES 53-54

Line positions in absolute wavelength:

.. GENERATED FROM PYTHON SOURCE LINES 54-58

.. code-block:: Python

    for prefix in ("a_", "b_"):
        cen = result.params[prefix + "cen"]
        print(f"line {prefix[0]}: {655 + cen.value:.3f} ± {cen.stderr:.3f} nm")





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

 .. code-block:: none

    line a: 651.195 ± 0.015 nm
    line b: 654.943 ± 0.039 nm




.. GENERATED FROM PYTHON SOURCE LINES 59-61

The line ratio with its uncertainty. ``as_ufloat()`` takes the correlation of the two
amplitudes into account automatically:

.. GENERATED FROM PYTHON SOURCE LINES 61-64

.. code-block:: Python

    u = result.params.as_ufloat()
    ratio = u["b_amp"] / u["a_amp"]
    print(f"I_b / I_a = {ratio:.2uS}")




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

 .. code-block:: none

    I_b / I_a = 0.3781(62)





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

   **Total running time of the script:** (0 minutes 0.141 seconds)


.. _sphx_glr_download_auto_examples_plot_10_two_peaks_background.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_10_two_peaks_background.ipynb <plot_10_two_peaks_background.ipynb>`

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

      :download:`Download Python source code: plot_10_two_peaks_background.py <plot_10_two_peaks_background.py>`

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

      :download:`Download zipped: plot_10_two_peaks_background.zip <plot_10_two_peaks_background.zip>`


.. only:: html

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

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