.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/fluorescence_decay/plot_fit23_usage_2.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_fluorescence_decay_plot_fit23_usage_2.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_fluorescence_decay_plot_fit23_usage_2.py:


===============================
MLE fit23: Usage example 2
===============================

1) Compute model function
2) Simulate data for computed model function
3) Fit simulated data with model function

.. GENERATED FROM PYTHON SOURCE LINES 11-84



.. image-sg:: /auto_examples/fluorescence_decay/images/sphx_glr_plot_fit23_usage_2_001.png
   :alt: plot fit23 usage 2
   :srcset: /auto_examples/fluorescence_decay/images/sphx_glr_plot_fit23_usage_2_001.png
   :class: sphx-glr-single-img





.. code-block:: Python

    import tttrlib
    import numpy as np
    import scipy.stats
    import pylab as p


    def model_irf(
            n_channels: int = 256,
            period: float = 32,
            irf_position_p: float = 2.0,
            irf_position_s: float = 18.0,
            irf_width: float = 0.25
    ):
        time_axis = np.linspace(0, period, n_channels * 2)
        irf_np = scipy.stats.norm.pdf(time_axis, loc=irf_position_p, scale=irf_width) + \
                 scipy.stats.norm.pdf(time_axis, loc=irf_position_s, scale=irf_width)
        return irf_np, time_axis


    # setup some parameters
    n_channels = 128
    n_corrections = 5
    n_photons = 120
    irf_position_p = 2.0
    irf_position_s = 18.0
    irf_width = 0.25
    period, g, l1, l2, conv_stop = 32, 1.0, 0.1, 0.1, n_channels // 2 - 1
    tau, gamma, r0, rho = 2.0, 0.01, 0.38, 1.2
    np.random.seed(0)

    irf_np, time_axis = model_irf(
        n_channels=n_channels,
        period=period,
        irf_position_p=irf_position_p,
        irf_position_s=irf_position_s,
        irf_width=irf_width
    )
    dt = time_axis[1] - time_axis[0]
    conv_stop = min(len(time_axis), conv_stop)
    param = np.array([tau, gamma, r0, rho])
    corrections = np.array([period, g, l1, l2, conv_stop])

    # compute a model function that is later used as "data"
    model = np.zeros_like(time_axis)
    bg = np.zeros_like(time_axis)
    tttrlib.DecayFit23.modelf(param, irf_np, bg, dt, corrections, model)
    # add poisson noise to model and use as data
    data = np.random.poisson(model * n_photons)

    # create MParam structure that contains all parameters for fitting
    m_param = tttrlib.CreateMParam(
        irf=irf_np,
        background=bg,
        data=data.astype(np.int32),
        corrections=corrections,
        dt=dt
    )

    tau, gamma, r0, rho = 4., 0.01, 0.38, 1.5
    bifl_scatter = -1
    p_2s = 0
    x = np.zeros(8, dtype=np.float64)
    x[:6] = [tau, gamma, r0, rho, bifl_scatter, p_2s]

    # test fitting
    fixed = np.array([0, 1, 1, 1], dtype=np.int16)
    chi2 = tttrlib.DecayFit23.fit(x, fixed, m_param)

    m = np.array([m for m in m_param.get_model()])
    p.plot(m)
    p.plot(data)
    p.plot(irf_np / max(irf_np) * max(data))
    p.show()


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

   **Total running time of the script:** (0 minutes 0.103 seconds)


.. _sphx_glr_download_auto_examples_fluorescence_decay_plot_fit23_usage_2.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_fit23_usage_2.ipynb <plot_fit23_usage_2.ipynb>`

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

      :download:`Download Python source code: plot_fit23_usage_2.py <plot_fit23_usage_2.py>`


.. only:: html

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

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