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2 changes: 1 addition & 1 deletion .buildinfo
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# Sphinx build info version 1
# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
config: dd842009ed60594f16eb7ea21fa44100
config: 85f7fe993bfe0527cc14b9eefe836988
tags: 645f666f9bcd5a90fca523b33c5a78b7
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2 changes: 1 addition & 1 deletion _sources/glm_intro.Rmd
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Expand Up @@ -18,7 +18,7 @@ jupyter:

For more detail on the General Linear Model, see [The general linear model and
fMRI: Does love last
forever?](http://matthew.dynevor.org/_downloads/does_glm_love.pdf).
forever?](http://matthew.dynevor.org/research/articles/does_glm_love.pdf).

```{python}
# Import numerical and plotting libraries
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44 changes: 22 additions & 22 deletions arrays_and_images.html
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Expand Up @@ -605,10 +605,10 @@ <h1>Arrays as images, images as arrays<a class="headerlink" href="#arrays-as-ima
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.image.AxesImage at 0x7f3d742153f0&gt;
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.image.AxesImage at 0x7f62cc9a9ae0&gt;
</pre></div>
</div>
<img alt="_images/9f79e956358cc65438d8236f459136be7b06048bb9380b52bc5225b8c3a3051c.png" src="_images/9f79e956358cc65438d8236f459136be7b06048bb9380b52bc5225b8c3a3051c.png" />
<img alt="_images/d3bdaf09ab4de248ada9006c6f3f6aa396b99a66bfa57157f6ea8e325e463d84.png" src="_images/d3bdaf09ab4de248ada9006c6f3f6aa396b99a66bfa57157f6ea8e325e463d84.png" />
</div>
</div>
<p>The image is weirdly colorful. That is because matplotlib is using the default
Expand All @@ -625,10 +625,10 @@ <h1>Arrays as images, images as arrays<a class="headerlink" href="#arrays-as-ima
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.colorbar.Colorbar at 0x7f3d7416fb80&gt;
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.colorbar.Colorbar at 0x7f62cc91c3d0&gt;
</pre></div>
</div>
<img alt="_images/7783e2c46ca78f8508a0fa3df75df3ab5c9620ad093341fdbd01d4b03557f727.png" src="_images/7783e2c46ca78f8508a0fa3df75df3ab5c9620ad093341fdbd01d4b03557f727.png" />
<img alt="_images/7f2041d66705ba898f072957a1e419ad4221effecb638c2f99721a6a701413a8.png" src="_images/7f2041d66705ba898f072957a1e419ad4221effecb638c2f99721a6a701413a8.png" />
</div>
</div>
<p>In our case, our image would make more sense as grayscale, so we use the
Expand All @@ -641,10 +641,10 @@ <h1>Arrays as images, images as arrays<a class="headerlink" href="#arrays-as-ima
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.colorbar.Colorbar at 0x7f3d7404bb50&gt;
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.colorbar.Colorbar at 0x7f62cc7ef9d0&gt;
</pre></div>
</div>
<img alt="_images/49417a5802eedf393d4cc0c350dd08908cdb545eb5b25eb158a7eb6fff411489.png" src="_images/49417a5802eedf393d4cc0c350dd08908cdb545eb5b25eb158a7eb6fff411489.png" />
<img alt="_images/fe16d4e426399645442aeb8f95a9539a2cd871326863a43b068580fae0825035.png" src="_images/fe16d4e426399645442aeb8f95a9539a2cd871326863a43b068580fae0825035.png" />
</div>
</div>
<p>A grayscale image is an array containing numbers giving the pixel intensity
Expand All @@ -668,10 +668,10 @@ <h1>Arrays as images, images as arrays<a class="headerlink" href="#arrays-as-ima
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.colorbar.Colorbar at 0x7f3d740372e0&gt;
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.colorbar.Colorbar at 0x7f62cc6a9fc0&gt;
</pre></div>
</div>
<img alt="_images/49417a5802eedf393d4cc0c350dd08908cdb545eb5b25eb158a7eb6fff411489.png" src="_images/49417a5802eedf393d4cc0c350dd08908cdb545eb5b25eb158a7eb6fff411489.png" />
<img alt="_images/fe16d4e426399645442aeb8f95a9539a2cd871326863a43b068580fae0825035.png" src="_images/fe16d4e426399645442aeb8f95a9539a2cd871326863a43b068580fae0825035.png" />
</div>
</div>
<p>Matplotlib does not save this change, so we would have to rerun this command
Expand Down Expand Up @@ -731,10 +731,10 @@ <h1>Arrays as images, images as arrays<a class="headerlink" href="#arrays-as-ima
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[&lt;matplotlib.lines.Line2D at 0x7f3d6cf4fb50&gt;]
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[&lt;matplotlib.lines.Line2D at 0x7f62cc76e890&gt;]
</pre></div>
</div>
<img alt="_images/5d391b53295ca8cc4aeaffea733981bfcdcb621dc7a1f2919ad2f9d1ce4fbda3.png" src="_images/5d391b53295ca8cc4aeaffea733981bfcdcb621dc7a1f2919ad2f9d1ce4fbda3.png" />
<img alt="_images/2b8bb81f4e9577b5fd6a61124fb022b604d30f0a9c02dc7bc38db52b09b63e1d.png" src="_images/2b8bb81f4e9577b5fd6a61124fb022b604d30f0a9c02dc7bc38db52b09b63e1d.png" />
</div>
</div>
<p>The x axis is the column position in the array (0 through 7) and the y axis is
Expand All @@ -748,10 +748,10 @@ <h1>Arrays as images, images as arrays<a class="headerlink" href="#arrays-as-ima
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[&lt;matplotlib.lines.Line2D at 0x7f3d6cdddea0&gt;]
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[&lt;matplotlib.lines.Line2D at 0x7f62cc6041f0&gt;]
</pre></div>
</div>
<img alt="_images/5d391b53295ca8cc4aeaffea733981bfcdcb621dc7a1f2919ad2f9d1ce4fbda3.png" src="_images/5d391b53295ca8cc4aeaffea733981bfcdcb621dc7a1f2919ad2f9d1ce4fbda3.png" />
<img alt="_images/2b8bb81f4e9577b5fd6a61124fb022b604d30f0a9c02dc7bc38db52b09b63e1d.png" src="_images/2b8bb81f4e9577b5fd6a61124fb022b604d30f0a9c02dc7bc38db52b09b63e1d.png" />
</div>
</div>
<p>The plot shows us the 0 values at the edges of the bar of the “i”, and the ramp
Expand Down Expand Up @@ -785,10 +785,10 @@ <h1>Arrays as images, images as arrays<a class="headerlink" href="#arrays-as-ima
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.image.AxesImage at 0x7f3d6cd874c0&gt;
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.image.AxesImage at 0x7f62cc6465c0&gt;
</pre></div>
</div>
<img alt="_images/19fdb351621ad5c5fc9bb595d08d304003cb42172dfd1a4fcf567a8378710a25.png" src="_images/19fdb351621ad5c5fc9bb595d08d304003cb42172dfd1a4fcf567a8378710a25.png" />
<img alt="_images/9bcb92f79177b8fb8f11c684a06580360455b68ab7128fbc898cbd03dae4c906.png" src="_images/9bcb92f79177b8fb8f11c684a06580360455b68ab7128fbc898cbd03dae4c906.png" />
</div>
</div>
<p>We can also reshape the original array to a 1D array, by stacking all the rows
Expand Down Expand Up @@ -888,7 +888,7 @@ <h1>Arrays as images, images as arrays<a class="headerlink" href="#arrays-as-ima
&lt;BarContainer object of 10 artists&gt;)
</pre></div>
</div>
<img alt="_images/1e00d6ed0601e0bf5bb65cf780af9ae2456bacbc075865e874f5d3d03f94edc6.png" src="_images/1e00d6ed0601e0bf5bb65cf780af9ae2456bacbc075865e874f5d3d03f94edc6.png" />
<img alt="_images/f30e659312d04ed688f08c2629bb0df2d0be78f70aedb8d922c1df93a5d8d992.png" src="_images/f30e659312d04ed688f08c2629bb0df2d0be78f70aedb8d922c1df93a5d8d992.png" />
</div>
</div>
<p>By default, the <code class="docutils literal notranslate"><span class="pre">plt.hist</span></code> function uses 50 bins, but you can specify how
Expand Down Expand Up @@ -918,7 +918,7 @@ <h1>Arrays as images, images as arrays<a class="headerlink" href="#arrays-as-ima
&lt;BarContainer object of 75 artists&gt;)
</pre></div>
</div>
<img alt="_images/d176decff4edcba2e1e6e8f2a08cc79acff0a4ba3a40fd37ce053bd6eecd769d.png" src="_images/d176decff4edcba2e1e6e8f2a08cc79acff0a4ba3a40fd37ce053bd6eecd769d.png" />
<img alt="_images/dcf052d895cdf2c87163015893963a108d94e53dd80ccbd837cb194b44f0e834.png" src="_images/dcf052d895cdf2c87163015893963a108d94e53dd80ccbd837cb194b44f0e834.png" />
</div>
</div>
<p>As you can imagine, it’s not hard to go back to the 2D shape, by splitting the
Expand All @@ -932,10 +932,10 @@ <h1>Arrays as images, images as arrays<a class="headerlink" href="#arrays-as-ima
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.image.AxesImage at 0x7f3d6cbefa60&gt;
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.image.AxesImage at 0x7f62cc554c10&gt;
</pre></div>
</div>
<img alt="_images/2c07d917b9a5ffe6d1e8c1fed4ec2cfeccfd3249ad511d943c4773cf2ae78138.png" src="_images/2c07d917b9a5ffe6d1e8c1fed4ec2cfeccfd3249ad511d943c4773cf2ae78138.png" />
<img alt="_images/18c626fa333ccff444a9c11a6cc744f5e6d415ebd17dcb03858b11315228feb1.png" src="_images/18c626fa333ccff444a9c11a6cc744f5e6d415ebd17dcb03858b11315228feb1.png" />
</div>
</div>
<p>In numpy, basic operations like multiplication, addition, comparison, are
Expand Down Expand Up @@ -1003,10 +1003,10 @@ <h1>Arrays as images, images as arrays<a class="headerlink" href="#arrays-as-ima
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.image.AxesImage at 0x7f3d6cac49d0&gt;
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.image.AxesImage at 0x7f62cc2e4100&gt;
</pre></div>
</div>
<img alt="_images/421ceda8a2a1e048176c37e168600e004211abe25bf2dfe9168ca0dad41571dc.png" src="_images/421ceda8a2a1e048176c37e168600e004211abe25bf2dfe9168ca0dad41571dc.png" />
<img alt="_images/61f258561c288035a850ceefdaec326ed1f81c4ed252d89a938ef76cdfb3161d.png" src="_images/61f258561c288035a850ceefdaec326ed1f81c4ed252d89a938ef76cdfb3161d.png" />
</div>
</div>
<p>We can slice arrays as we slice strings or lists. The difference for arrays is
Expand All @@ -1021,10 +1021,10 @@ <h1>Arrays as images, images as arrays<a class="headerlink" href="#arrays-as-ima
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.image.AxesImage at 0x7f3d6cb31d50&gt;
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.image.AxesImage at 0x7f62cc34d510&gt;
</pre></div>
</div>
<img alt="_images/030e9c517b3935b445e0233f49b9473fabc462863164694346cdacdbaa57fc48.png" src="_images/030e9c517b3935b445e0233f49b9473fabc462863164694346cdacdbaa57fc48.png" />
<img alt="_images/18ccb330c61b39ab784fa743c5ee5421b6ac6715a76520699ab647c2394864e6.png" src="_images/18ccb330c61b39ab784fa743c5ee5421b6ac6715a76520699ab647c2394864e6.png" />
</div>
</div>
</section>
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16 changes: 8 additions & 8 deletions convolution_background.html
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Expand Up @@ -644,10 +644,10 @@ <h2>Using scipy<a class="headerlink" href="#using-scipy" title="Permalink to thi
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.legend.Legend at 0x7fc5bf38a8c0&gt;
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.legend.Legend at 0x7f30b06d7070&gt;
</pre></div>
</div>
<img alt="_images/d4359026746993760efb628e90d457b041a59c11f0a5362121de9081845e3eff.png" src="_images/d4359026746993760efb628e90d457b041a59c11f0a5362121de9081845e3eff.png" />
<img alt="_images/0170cc68185e9ab7419932303ccc53ec987d9657652ed654d94c7c59fdedf026.png" src="_images/0170cc68185e9ab7419932303ccc53ec987d9657652ed654d94c7c59fdedf026.png" />
</div>
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</section>
Expand Down Expand Up @@ -692,7 +692,7 @@ <h2>Constructing a hemodynamic response function<a class="headerlink" href="#con
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Text(0, 0.5, &#39;HRF model of signal&#39;)
</pre></div>
</div>
<img alt="_images/57d2afac80e9c61436654358257796810716be6826a62225ae907de528647142.png" src="_images/57d2afac80e9c61436654358257796810716be6826a62225ae907de528647142.png" />
<img alt="_images/c053c3d9550d63f9f64421bc68ff89629f9e9c3174dc204238f6a8e303795800.png" src="_images/c053c3d9550d63f9f64421bc68ff89629f9e9c3174dc204238f6a8e303795800.png" />
</div>
</div>
<p>We can sample from the function, to get the estimates at the times of our TRs.
Expand All @@ -717,7 +717,7 @@ <h2>Constructing a hemodynamic response function<a class="headerlink" href="#con
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Text(0, 0.5, &#39;HRF sampled every 2.5 seconds&#39;)
</pre></div>
</div>
<img alt="_images/2d2cdc21dd593071ad3d9c894572e81cc5b8492143db1106c8287cf7ba12c92d.png" src="_images/2d2cdc21dd593071ad3d9c894572e81cc5b8492143db1106c8287cf7ba12c92d.png" />
<img alt="_images/f491550b9a441ad52de6ae2a6a2a073efcb74f6ba35f0346f8bcd81d014fabc7.png" src="_images/f491550b9a441ad52de6ae2a6a2a073efcb74f6ba35f0346f8bcd81d014fabc7.png" />
</div>
</div>
<p>We can use this to convolve our neural (on-off) prediction. This will give us
Expand Down Expand Up @@ -757,10 +757,10 @@ <h2>Constructing a hemodynamic response function<a class="headerlink" href="#con
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[&lt;matplotlib.lines.Line2D at 0x7fc5bce4bc10&gt;]
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[&lt;matplotlib.lines.Line2D at 0x7f30add30100&gt;]
</pre></div>
</div>
<img alt="_images/8642318e381446f275829c852a311ab47cd26203ab0c39617e4ef624c2649e87.png" src="_images/8642318e381446f275829c852a311ab47cd26203ab0c39617e4ef624c2649e87.png" />
<img alt="_images/0f940e22064def4586fdfd195e230b51e64ed860ca059c7d39444abad42eb14c.png" src="_images/0f940e22064def4586fdfd195e230b51e64ed860ca059c7d39444abad42eb14c.png" />
</div>
</div>
<p>When we convolve, the output is length N + M-1, where N is the number of values
Expand Down Expand Up @@ -804,10 +804,10 @@ <h2>Constructing a hemodynamic response function<a class="headerlink" href="#con
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[&lt;matplotlib.lines.Line2D at 0x7fc5bccf0430&gt;]
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[&lt;matplotlib.lines.Line2D at 0x7f30adda0f70&gt;]
</pre></div>
</div>
<img alt="_images/2b50effc423b013561ddfc1d3a871350193da761ed7ef17ba0449c349232ac59.png" src="_images/2b50effc423b013561ddfc1d3a871350193da761ed7ef17ba0449c349232ac59.png" />
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<p>For our future use, might want to save our convolved time course to a numpy
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Expand Up @@ -628,7 +628,7 @@ <h2>Neural and hemodynamic prediction<a class="headerlink" href="#neural-and-hem
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Text(0.5, 1.0, &#39;Predicted BOLD signal from convolution, 1 second resolution&#39;)
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<p>Our algorithm, which turned out to give convolution, had us add a shifted,
Expand Down Expand Up @@ -693,7 +693,7 @@ <h2>Neural and hemodynamic prediction<a class="headerlink" href="#neural-and-hem
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Text(0.5, 1.0, &#39;Predicted BOLD signal from convolution, 1 second resolution&#39;)
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<p>We can also do exactly the same operation by first making an array with the
Expand Down Expand Up @@ -730,10 +730,10 @@ <h2>Neural and hemodynamic prediction<a class="headerlink" href="#neural-and-hem
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<p>Each new row of <code class="docutils literal notranslate"><span class="pre">shifted_hrfs</span></code> corresponds to the HRF, shifted by one more
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<p>Now remember how matrix multiplication works:</p>
Expand Down Expand Up @@ -824,10 +824,10 @@ <h2>Convolution is like cross-correlation with the reversed HRF<a class="headerl
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<p>The column contains a <em>reversed</em> copy of the HRF signal, where the first value
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