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

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

.. _sphx_glr_auto_examples_temporal-response-functions_trf_intro.py:


.. _exa-trf_intro:
.. currentmodule:: eelbrain

Introduction to Temporal Response Functions (TRFs)
==================================================

A Temporal Response Function (TRF) is a linear stimulus-response model.
The predicted response is a linear convolution of the stimulus with the TRF.
A simple illustration of this is that
every impulse in the stimulus is associated with a corresponding response,
shaped like the TRF:

.. GENERATED FROM PYTHON SOURCE LINES 15-36

.. code-block:: Python

    from eelbrain import *
    import numpy as np

    # Construct a 10 s long stimulus
    time = UTS(0, 0.01, 1000)
    x = NDVar(np.zeros(len(time)), time)
    # add a few impulses
    x[1] = 1
    x[3] = 1
    x[5] = 1

    # Construct a TRF of length 500 ms
    trf_time = UTS(0, 0.01, 50)
    trf = gaussian(0.200, 0.050, trf_time) - gaussian(0.300, 0.050, trf_time)

    # The response is the convolution of the stimulus with the TRF
    y = convolve(trf, x)

    plot_args = dict(columns=1, axh=2, w=10, frame='t', legend=False, colors='r')
    p = plot.UTS([x, trf, y], ylabel=['Stimulus (x)', 'TRF', 'Response (y)'], **plot_args)




.. image-sg:: /auto_examples/temporal-response-functions/images/sphx_glr_trf_intro_001.png
   :alt: trf intro
   :srcset: /auto_examples/temporal-response-functions/images/sphx_glr_trf_intro_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 37-41

Because the convolution is linear:

 - Scaled stimuli cause scaled responses
 - Overlapping responses add up

.. GENERATED FROM PYTHON SOURCE LINES 41-53

.. code-block:: Python


    x[2] = 0.66
    x[5.2] = 1
    x[7] = 0.8
    x[7.2] = 0.3
    x[8.8] = 0.2
    x[9] = 0.5
    x[9.2] = 0.7

    y = convolve(trf, x)
    p = plot.UTS([x, trf, y], ylabel=['Stimulus (x)', 'TRF', 'Response (y)'], **plot_args)




.. image-sg:: /auto_examples/temporal-response-functions/images/sphx_glr_trf_intro_002.png
   :alt: trf intro
   :srcset: /auto_examples/temporal-response-functions/images/sphx_glr_trf_intro_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 54-56

When the stimulus contains only non-zero elements this works just the same,
but the TRF shape may not be apparent in the response anymore:

.. GENERATED FROM PYTHON SOURCE LINES 56-62

.. code-block:: Python


    x += np.random.normal(0, 0.1, x.shape)
    filter_data(x, 1, 40)
    y = convolve(trf, x)
    p = plot.UTS([x, trf, y], ylabel=['Stimulus (x)', 'TRF', 'Response (y)'], **plot_args)




.. image-sg:: /auto_examples/temporal-response-functions/images/sphx_glr_trf_intro_003.png
   :alt: trf intro
   :srcset: /auto_examples/temporal-response-functions/images/sphx_glr_trf_intro_003.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 63-66

Given a stimulus and a response, there are different methods to reconstruct
the TRF. Eelbrain comes with an implementation of :func:`boosting`, a
coordinate descent algorithm with early stopping based on cross-validation:

.. GENERATED FROM PYTHON SOURCE LINES 66-70

.. code-block:: Python


    fit = boosting(y, x, 0.000, 0.500, basis=0.050, partitions=2)
    plot_args = {**plot_args, 'columns': 3}
    p = plot.UTS([trf, fit.h, None], axtitle=["Model TRF", "Reconstructed TRF"], **plot_args)



.. image-sg:: /auto_examples/temporal-response-functions/images/sphx_glr_trf_intro_004.png
   :alt: Model TRF, Reconstructed TRF
   :srcset: /auto_examples/temporal-response-functions/images/sphx_glr_trf_intro_004.png
   :class: sphx-glr-single-img






.. _sphx_glr_download_auto_examples_temporal-response-functions_trf_intro.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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