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dev/examples/Thermal_Generation_Dispatch_Example/index.html

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dev/examples/autotuning-ridge/index.html

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dev/examples/chainrules_unit/index.html

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dev/examples/custom-relu/index.html

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custom_loss(train_X, train_Y) = 1.691865f0
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custom_loss(train_X, train_Y) = 1.610134f0
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custom_loss(train_X, train_Y) = 1.5316879f0
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109.718281 seconds (76.78 M allocations: 4.763 GiB, 1.44% gc time, 0.71% compilation time)</code></pre><p>Although our custom implementation takes time, it is able to reach similar accuracy as the usual ReLU function implementation.</p><h2 id="Accuracy-results"><a class="docs-heading-anchor" href="#Accuracy-results">Accuracy results</a><a id="Accuracy-results-1"></a><a class="docs-heading-anchor-permalink" href="#Accuracy-results" title="Permalink"></a></h2><p>Average of correct guesses</p><pre><code class="language-julia hljs">accuracy(x, y) = Statistics.mean(Flux.onecold(m(x)) .== Flux.onecold(y));</code></pre><p>Training accuracy</p><pre><code class="language-julia hljs">accuracy(train_X, train_Y)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">0.562</code></pre><p>Test accuracy</p><pre><code class="language-julia hljs">accuracy(test_X, test_Y)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">0.478</code></pre><p>Note that the accuracy is low due to simplified training. It is possible to increase the number of samples <code>N</code>, the number of epochs <code>epoch</code> and the connectivity <code>inner</code>.</p><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="../chainrules_unit/">« ChainRules integration demo: Relaxed Unit Commitment</a><a class="docs-footer-nextpage" href="../matrix-inversion-manual/">Differentiating a QP wrt a single variable »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 8 January 2025 17:03">Wednesday 8 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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108.495299 seconds (76.71 M allocations: 4.762 GiB, 1.47% gc time, 0.71% compilation time)</code></pre><p>Although our custom implementation takes time, it is able to reach similar accuracy as the usual ReLU function implementation.</p><h2 id="Accuracy-results"><a class="docs-heading-anchor" href="#Accuracy-results">Accuracy results</a><a id="Accuracy-results-1"></a><a class="docs-heading-anchor-permalink" href="#Accuracy-results" title="Permalink"></a></h2><p>Average of correct guesses</p><pre><code class="language-julia hljs">accuracy(x, y) = Statistics.mean(Flux.onecold(m(x)) .== Flux.onecold(y));</code></pre><p>Training accuracy</p><pre><code class="language-julia hljs">accuracy(train_X, train_Y)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">0.562</code></pre><p>Test accuracy</p><pre><code class="language-julia hljs">accuracy(test_X, test_Y)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">0.478</code></pre><p>Note that the accuracy is low due to simplified training. It is possible to increase the number of samples <code>N</code>, the number of epochs <code>epoch</code> and the connectivity <code>inner</code>.</p><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="../chainrules_unit/">« ChainRules integration demo: Relaxed Unit Commitment</a><a class="docs-footer-nextpage" href="../matrix-inversion-manual/">Differentiating a QP wrt a single variable »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 8 January 2025 22:10">Wednesday 8 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/examples/matrix-inversion-manual/index.html

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0.0 * index(x[1]) - 1.0, # to indicate the direction vector to get directional derivatives
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)</code></pre><p>Note that <code>0.0 * index(x[1])</code> is used to make its type <code>typeof(0.0 * index(x[1]) - 1.0) &lt;: MOI.AbstractScalarFunction</code>. To indicate different direction to get directional derivative, users should replace <code>0.0 * index(x[1]) - 1.0</code> as the form of <code>dG*x - dh</code>, where <code>dG</code> and <code>dh</code> correspond to the elements of direction vectors along <code>G</code> and <code>h</code> axes, respectively.</p><p>Compute derivatives</p><pre><code class="language-julia hljs">DiffOpt.forward_differentiate!(model)</code></pre><p>Query derivative</p><pre><code class="language-julia hljs">dx = MOI.get.(model, DiffOpt.ForwardVariablePrimal(), x)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">2-element Vector{Float64}:
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0.2500000038571342
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0.7500000115714025</code></pre><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="../custom-relu/">« Custom ReLU layer</a><a class="docs-footer-nextpage" href="../nearest_correlation/">Nearest correlation »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 8 January 2025 17:03">Wednesday 8 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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0.7500000115714025</code></pre><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="../custom-relu/">« Custom ReLU layer</a><a class="docs-footer-nextpage" href="../nearest_correlation/">Nearest correlation »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 8 January 2025 22:10">Wednesday 8 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/examples/nearest_correlation/index.html

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------------------------------------------------------------------
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iter | pri res | dua res | gap | obj | scale | time (s)
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timings: total: 3.79e-04s = setup: 4.94e-05s + solve: 3.30e-04s
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timings: total: 3.69e-04s = setup: 4.65e-05s + solve: 3.22e-04s
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lin-sys: 2.29e-05s, cones: 2.04e-04s, accel: 3.92e-06s
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------------------------------------------------------------------
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------------------------------------------------------------------</code></pre><p>The projection of <code>A</code> is:</p><pre><code class="language-julia hljs">X</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">3×3 Matrix{Float64}:
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-0.0490976 -0.0880952 0.228658 0.101794</code></pre><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="../matrix-inversion-manual/">« Differentiating a QP wrt a single variable</a><a class="docs-footer-nextpage" href="../polyhedral_project/">Polyhedral QP layer »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 8 January 2025 17:03">Wednesday 8 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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-0.0490976 -0.0880952 0.228658 0.101794</code></pre><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="../matrix-inversion-manual/">« Differentiating a QP wrt a single variable</a><a class="docs-footer-nextpage" href="../polyhedral_project/">Polyhedral QP layer »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 8 January 2025 22:10">Wednesday 8 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/examples/polyhedral_project/index.html

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64.838840 seconds (35.89 M allocations: 4.149 GiB, 2.35% gc time, 1.40% compilation time)</code></pre><p>Although our custom implementation takes time, it is able to reach similar accuracy as the usual ReLU function implementation.</p><h2 id="Accuracy-results"><a class="docs-heading-anchor" href="#Accuracy-results">Accuracy results</a><a id="Accuracy-results-1"></a><a class="docs-heading-anchor-permalink" href="#Accuracy-results" title="Permalink"></a></h2><p>Average of correct guesses</p><pre><code class="language-julia hljs">accuracy(x, y) = Statistics.mean(Flux.onecold(m(x)) .== Flux.onecold(y));</code></pre><p>Training accuracy</p><pre><code class="language-julia hljs">accuracy(train_X, train_Y)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">0.9</code></pre><p>Test accuracy</p><pre><code class="language-julia hljs">accuracy(test_X, test_Y)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">0.744</code></pre><p>Note that the accuracy is low due to simplified training. It is possible to increase the number of samples <code>N</code>, the number of epochs <code>epoch</code> and the connectivity <code>inner</code>.</p><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="../nearest_correlation/">« Nearest correlation</a><a class="docs-footer-nextpage" href="../sensitivity-analysis-ridge/">Sensitivity Analysis of Ridge Regression »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 8 January 2025 17:03">Wednesday 8 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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64.343004 seconds (35.89 M allocations: 4.149 GiB, 2.37% gc time, 1.43% compilation time)</code></pre><p>Although our custom implementation takes time, it is able to reach similar accuracy as the usual ReLU function implementation.</p><h2 id="Accuracy-results"><a class="docs-heading-anchor" href="#Accuracy-results">Accuracy results</a><a id="Accuracy-results-1"></a><a class="docs-heading-anchor-permalink" href="#Accuracy-results" title="Permalink"></a></h2><p>Average of correct guesses</p><pre><code class="language-julia hljs">accuracy(x, y) = Statistics.mean(Flux.onecold(m(x)) .== Flux.onecold(y));</code></pre><p>Training accuracy</p><pre><code class="language-julia hljs">accuracy(train_X, train_Y)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">0.9</code></pre><p>Test accuracy</p><pre><code class="language-julia hljs">accuracy(test_X, test_Y)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">0.744</code></pre><p>Note that the accuracy is low due to simplified training. It is possible to increase the number of samples <code>N</code>, the number of epochs <code>epoch</code> and the connectivity <code>inner</code>.</p><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="../nearest_correlation/">« Nearest correlation</a><a class="docs-footer-nextpage" href="../sensitivity-analysis-ridge/">Sensitivity Analysis of Ridge Regression »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 8 January 2025 22:10">Wednesday 8 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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