.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_examples_04_glm_first_level_plot_hrf.py>`     to download the full example code or to run this example in your browser via Binder
    .. rst-class:: sphx-glr-example-title

    .. _sphx_glr_auto_examples_04_glm_first_level_plot_hrf.py:

Example of hemodynamic reponse functions.
=========================================

Within this example we are going to plot the hemodynamic reponse function (hrf)
model in SPM together with the hrf shape proposed by G.Glover, as well as their
time and dispersion derivatives.

This example requires matplotlib.

The hrf is the filter that couples neural responses to the metabolic-related
changes in the MRI signal.  hrf models are simply phenomenological.

In current analysis frameworks, the choice of hrf model is essentially left to
the user. Fortunately, using the spm or Glover model does not make a huge
difference.  Adding derivatives should be considered whenever timing
information has some degree of uncertainty. It is actually useful to detect
timing issues.

Set up some parameters for model display
----------------------------------------

To get an impulse reponse, we simulate a single event occurring at time t=0,
with duration 1s.


.. code-block:: default


    import numpy as np
    frame_times = np.linspace(0, 30, 61)
    onset, amplitude, duration = 0., 1., 1.
    exp_condition = np.array((onset, duration, amplitude)).reshape(3, 1)








We sample this on a fris for display


.. code-block:: default

    stim = np.zeros_like(frame_times)
    stim[(frame_times > onset) * (frame_times <= onset + duration)] = amplitude








Now we have to define the candidate hrf models.


.. code-block:: default

    hrf_models = [None, 'glover + derivative', 'glover + derivative + dispersion']








Sample the hrf
--------------


.. code-block:: default

    from nilearn.glm.first_level import compute_regressor
    import matplotlib.pyplot as plt

    fig = plt.figure(figsize=(9, 4))
    for i, hrf_model in enumerate(hrf_models):
        # obtain the signal of interest by convolution
        signal, name = compute_regressor(
            exp_condition, hrf_model, frame_times, con_id='main',
            oversampling=16)

        # plot this
        plt.subplot(1, 3, i + 1)
        plt.fill(frame_times, stim, 'k', alpha=.5, label='stimulus')
        for j in range(signal.shape[1]):
            plt.plot(frame_times, signal.T[j], label=name[j])
        plt.xlabel('time (s)')
        plt.legend(loc=1)
        plt.title(hrf_model)

    # adjust the plot
    plt.subplots_adjust(bottom=.12)
    plt.show()



.. image:: /auto_examples/04_glm_first_level/images/sphx_glr_plot_hrf_001.png
    :alt: glover + derivative, glover + derivative + dispersion
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none

    /home/varoquau/dev/nilearn/examples/04_glm_first_level/plot_hrf.py:65: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
      plt.show()





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

   **Total running time of the script:** ( 0 minutes  0.359 seconds)


.. _sphx_glr_download_auto_examples_04_glm_first_level_plot_hrf.py:


.. only :: html

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


  .. container:: binder-badge

    .. image:: https://mybinder.org/badge_logo.svg
      :target: https://mybinder.org/v2/gh/nilearn/nilearn.github.io/master?filepath=examples/auto_examples/04_glm_first_level/plot_hrf.ipynb
      :width: 150 px


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

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



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

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


.. only:: html

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

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