build based on 75269d7

dev/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.10.4","generation_timestamp":"2024-08-23T09:35:01","documenter_version":"1.6.0"}}
+{"documenter":{"julia_version":"1.10.4","generation_timestamp":"2024-08-23T09:35:44","documenter_version":"1.6.0"}}

dev/generated/examples/compressed_sensing/index.html

@@ -5,25 +5,25 @@
 size(image)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(256, 256)</code></pre><p>This produces a 256x256 image of a Shepp-Logan phantom.</p><p>In this example, we consider a problem in which we randomly sample a third of the pixels in the image. Such a problem and the corresponding measurement can be constructed with the packages LinearOperatorCollection and Random:</p><p>We first randomly shuffle the indices of the image and then select the first third of the indices to sample.</p><pre><code class="language-julia hljs">using Random, LinearOperatorCollection
 randomIndices = shuffle(eachindex(image))
 sampledIndices = sort(randomIndices[1:div(end, 3)])</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">21845-element Vector{Int64}:
+     1
      3
      4
      5
      7
-     9
-    10
-    17
-    19
-    21
-    29
+    12
+    13
+    14
+    20
+    26
      ⋮
- 65516
- 65517
  65519
- 65520
+ 65521
  65522
- 65526
- 65527
- 65531
+ 65524
+ 65528
+ 65529
+ 65532
+ 65535
  65536</code></pre><p>Afterwards we build a sampling operator which samples the image at the selected indices.</p><pre><code class="language-julia hljs">A = SamplingOp(eltype(image), pattern = sampledIndices , shape = size(image));</code></pre><p>Then we apply the sampling operator to the vectorized image to obtain the sampled measurement vector</p><pre><code class="language-julia hljs">b = A*vec(image);</code></pre><p>To visualize our image we can use CairoMakie:</p><pre><code class="language-julia hljs">using CairoMakie
 function plot_image(figPos, img; title = &quot;&quot;, width = 150, height = 150)
   ax = CairoMakie.Axis(figPos; yreversed=true, title, width, height)
@@ -36,30 +36,30 @@
 samplingMask[sampledIndices] .= true
 plot_image(fig[1,2], image .* samplingMask, title = &quot;Sampled Image&quot;)
 resize_to_layout!(fig)
-fig</code></pre><img src="0e280db2.png" alt="Example block output"/><p>As we can see in the right image, only a third of the pixels are sampled. The goal of the inverse problem is to recover the original image from this measurement vector.</p><h2 id="Solving-the-Inverse-Problem"><a class="docs-heading-anchor" href="#Solving-the-Inverse-Problem">Solving the Inverse Problem</a><a id="Solving-the-Inverse-Problem-1"></a><a class="docs-heading-anchor-permalink" href="#Solving-the-Inverse-Problem" title="Permalink"></a></h2><p>To recover the image from the measurement vector, we solve the TV-regularized least squares problem:</p><p class="math-container">\[\begin{equation}
+fig</code></pre><img src="a03acae3.png" alt="Example block output"/><p>As we can see in the right image, only a third of the pixels are sampled. The goal of the inverse problem is to recover the original image from this measurement vector.</p><h2 id="Solving-the-Inverse-Problem"><a class="docs-heading-anchor" href="#Solving-the-Inverse-Problem">Solving the Inverse Problem</a><a id="Solving-the-Inverse-Problem-1"></a><a class="docs-heading-anchor-permalink" href="#Solving-the-Inverse-Problem" title="Permalink"></a></h2><p>To recover the image from the measurement vector, we solve the TV-regularized least squares problem:</p><p class="math-container">\[\begin{equation}
   \underset{\mathbf{x}}{argmin} \frac{1}{2}\vert\vert \mathbf{A}\mathbf{x}-\mathbf{b} \vert\vert_2^2 + \lambda\vert\vert\mathbf{x}\vert\vert_{\text{TV}} .
 \end{equation}\]</p><p>For this purpose we build a TV regularizer with regularization parameter <span>$λ=0.01$</span></p><pre><code class="language-julia hljs">using RegularizedLeastSquares
 reg = TVRegularization(0.01; shape=size(image));</code></pre><p>We will use the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) to solve our inverse problem. Thus, we build the corresponding solver</p><pre><code class="language-julia hljs">solver = createLinearSolver(FISTA, A; reg=reg, iterations=20);</code></pre><p>and apply it to our measurement vector</p><pre><code class="language-julia hljs">img_approx = solve!(solver,b)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">65536-element Vector{Float32}:
- 8.0653537f-19
- 1.4146734f-18
- 3.1340643f-18
- 7.135224f-18
- 1.5831074f-17
- 3.5051153f-17
- 7.9196204f-17
- 1.7715744f-16
- 3.7596116f-16
- 7.5909044f-16
+ 5.479949f-19
+ 1.0197881f-18
+ 2.3187864f-18
+ 5.21343f-18
+ 1.11894665f-17
+ 2.3435446f-17
+ 4.9866213f-17
+ 1.07909926f-16
+ 2.3241126f-16
+ 5.017118f-16
  ⋮
- 5.1193374f-16
- 2.3678025f-16
- 1.04729774f-16
- 4.8417316f-17
- 2.390231f-17
- 1.1638979f-17
- 5.3584624f-18
- 2.4544577f-18
- 1.3536931f-18</code></pre><p>To visualize the reconstructed image, we need to reshape the result vector to the correct shape. Afterwards we can use CairoMakie again:</p><pre><code class="language-julia hljs">img_approx = reshape(img_approx,size(image));
+ 4.608231f-16
+ 2.1284327f-16
+ 9.824584f-17
+ 4.5602487f-17
+ 2.132212f-17
+ 1.01756814f-17
+ 4.889565f-18
+ 2.3502145f-18
+ 1.3239986f-18</code></pre><p>To visualize the reconstructed image, we need to reshape the result vector to the correct shape. Afterwards we can use CairoMakie again:</p><pre><code class="language-julia hljs">img_approx = reshape(img_approx,size(image));
 plot_image(fig[1,3], img_approx, title = &quot;Reconstructed Image&quot;)
 resize_to_layout!(fig)
-fig</code></pre><img src="14aca95e.png" alt="Example block output"/><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../getting_started/">« Getting Started</a><a class="docs-footer-nextpage" href="../computed_tomography/">Computed Tomography »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.6.0 on <span class="colophon-date" title="Friday 23 August 2024 09:35">Friday 23 August 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+fig</code></pre><img src="3073c051.png" alt="Example block output"/><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../getting_started/">« Getting Started</a><a class="docs-footer-nextpage" href="../computed_tomography/">Computed Tomography »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.6.0 on <span class="colophon-date" title="Friday 23 August 2024 09:35">Friday 23 August 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/generated/howto/callbacks/index.html

@@ -24,24 +24,24 @@
     global idx += 1
   end
 end</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">65536-element Vector{Float32}:
- 1.7135411f-18
- 2.7601063f-18
- 5.4401928f-18
- 1.15541895f-17
- 2.591213f-17
- 5.997569f-17
- 1.3439096f-16
- 2.8001165f-16
- 5.522529f-16
- 1.0699407f-15
+ 1.3395445f-18
+ 2.2707473f-18
+ 4.587327f-18
+ 9.4164355f-18
+ 1.8923826f-17
+ 3.7065722f-17
+ 6.92436f-17
+ 1.2172425f-16
+ 2.1890205f-16
+ 4.555531f-16
  ⋮
- 1.6165244f-16
- 7.236208f-17
- 3.3924986f-17
- 1.6492023f-17
- 7.8633195f-18
- 3.500851f-18
- 1.454752f-18
- 6.157437f-19
- 3.3014668f-19</code></pre><p>In the callback we have to copy the solution, as the solver will update it in place. As is explained in the solver section, each features fields that are intended to be immutable during a <code>solve!</code> call and a state that is modified in each iteration. Depending on the solvers parameters and the measurement input, the state can differ in its fields and their type. Ideally, one tries to avoid accessing the state directly and uses the provided functions to access the state.</p><p>The resulting figure shows the reconstructed image after 0, 4, 8, 12, 16 and 20 iterations:</p><pre><code class="language-julia hljs">resize_to_layout!(fig)
-fig</code></pre><img src="00c5faaa.png" alt="Example block output"/><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../efficient_kaczmarz/">« Efficient Kaczmarz</a><a class="docs-footer-nextpage" href="../plug-and-play/">Plug-and-Play Regularization »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.6.0 on <span class="colophon-date" title="Friday 23 August 2024 09:35">Friday 23 August 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+ 5.26216f-16
+ 2.5074618f-16
+ 1.1923106f-16
+ 5.605712f-17
+ 2.562969f-17
+ 1.1559917f-17
+ 5.309755f-18
+ 2.5478933f-18
+ 1.452134f-18</code></pre><p>In the callback we have to copy the solution, as the solver will update it in place. As is explained in the solver section, each features fields that are intended to be immutable during a <code>solve!</code> call and a state that is modified in each iteration. Depending on the solvers parameters and the measurement input, the state can differ in its fields and their type. Ideally, one tries to avoid accessing the state directly and uses the provided functions to access the state.</p><p>The resulting figure shows the reconstructed image after 0, 4, 8, 12, 16 and 20 iterations:</p><pre><code class="language-julia hljs">resize_to_layout!(fig)
+fig</code></pre><img src="1dcf3132.png" alt="Example block output"/><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../efficient_kaczmarz/">« Efficient Kaczmarz</a><a class="docs-footer-nextpage" href="../plug-and-play/">Plug-and-Play Regularization »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.6.0 on <span class="colophon-date" title="Friday 23 August 2024 09:35">Friday 23 August 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>