.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_examples_04_glm_first_level_plot_design_matrix.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_design_matrix.py:


Examples of design matrices
===========================

Three examples of design matrices specification and computation for first-level
fMRI data analysis (event-related design, block design, FIR design).

This examples requires matplotlib.


.. code-block:: default


    try:
        import matplotlib.pyplot as plt
    except ImportError:
        raise RuntimeError("This script needs the matplotlib library")








Define parameters
----------------------------------
At first, we define parameters related to the images acquisition.


.. code-block:: default

    import numpy as np
    tr = 1.0  # repetition time is 1 second
    n_scans = 128  # the acquisition comprises 128 scans
    frame_times = np.arange(n_scans) * tr  # here are the corresponding frame times








Then we define parameters related to the experimental design.


.. code-block:: default


    # these are the types of the different trials
    conditions = ['c0', 'c0', 'c0', 'c1', 'c1', 'c1', 'c3', 'c3', 'c3']
    duration = [1., 1., 1., 1., 1., 1., 1., 1., 1.]
    # these are the corresponding onset times
    onsets = [30., 70., 100., 10., 30., 90., 30., 40., 60.]
    # Next, we simulate 6 motion parameters jointly observed with fMRI acquisitions
    motion = np.cumsum(np.random.randn(n_scans, 6), 0)
    # The 6 parameters correspond to three translations and three
    # rotations describing rigid body motion
    add_reg_names = ['tx', 'ty', 'tz', 'rx', 'ry', 'rz']








Create design matrices
-------------------------------------
The same parameters allow us to obtain a variety of design matrices.
We first create an events object.


.. code-block:: default

    import pandas as pd
    events = pd.DataFrame({'trial_type': conditions, 'onset': onsets,
                           'duration': duration})








We sample the events into a design matrix, also including additional
regressors.


.. code-block:: default

    hrf_model = 'glover'
    from nilearn.glm.first_level import make_first_level_design_matrix
    X1 = make_first_level_design_matrix(
        frame_times, events, drift_model='polynomial', drift_order=3,
        add_regs=motion, add_reg_names=add_reg_names, hrf_model=hrf_model)








Now we compute a block design matrix. We add duration to create the blocks.
For this we first define an event structure that includes the duration
parameter.


.. code-block:: default

    duration = 7. * np.ones(len(conditions))
    events = pd.DataFrame({'trial_type': conditions, 'onset': onsets,
                           'duration': duration})








Then we sample the design matrix.


.. code-block:: default

    X2 = make_first_level_design_matrix(frame_times, events,
                                        drift_model='polynomial', drift_order=3,
                                        hrf_model=hrf_model)








Finally we compute a FIR model


.. code-block:: default

    events = pd.DataFrame({'trial_type': conditions, 'onset': onsets,
                           'duration': duration})
    hrf_model = 'FIR'
    X3 = make_first_level_design_matrix(frame_times, events, hrf_model='fir',
                                        drift_model='polynomial', drift_order=3,
                                        fir_delays=np.arange(1, 6))








Here are the three designs side by side.


.. code-block:: default

    from nilearn.plotting import plot_design_matrix
    fig, (ax1, ax2, ax3) = plt.subplots(figsize=(10, 6), nrows=1, ncols=3)
    plot_design_matrix(X1, ax=ax1)
    ax1.set_title('Event-related design matrix', fontsize=12)
    plot_design_matrix(X2, ax=ax2)
    ax2.set_title('Block design matrix', fontsize=12)
    plot_design_matrix(X3, ax=ax3)
    ax3.set_title('FIR design matrix', fontsize=12)




.. image:: /auto_examples/04_glm_first_level/images/sphx_glr_plot_design_matrix_001.png
    :alt: Event-related design matrix, Block design matrix, FIR design matrix
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none


    Text(0.5, 1.1753015208063937, 'FIR design matrix')



Let's improve the layout and show the result.


.. code-block:: default

    plt.subplots_adjust(left=0.08, top=0.9, bottom=0.21, right=0.96, wspace=0.3)
    plt.show()



.. image:: /auto_examples/04_glm_first_level/images/sphx_glr_plot_design_matrix_002.png
    :alt: plot design matrix
    :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.372 seconds)


.. _sphx_glr_download_auto_examples_04_glm_first_level_plot_design_matrix.py:


.. only :: html

 .. container:: sphx-glr-footer
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