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end</code></pre><h2 id="High-Level-API"><a class="docs-heading-anchor" href="#High-Level-API">High Level API</a><a id="High-Level-API-1"></a><a class="docs-heading-anchor-permalink" href="#High-Level-API" title="Permalink"></a></h2><p>We need to perform the following steps to utilize SparseDiffTools:</p><ol><li>Specify a Sparsity Detection Algorithm. There are 3 possible choices currently:<ol><li><code>NoSparsityDetection</code>: This will ignore any AD choice and compute the dense Jacobian</li><li><code>JacPrototypeSparsityDetection</code>: If you already know the sparsity pattern, you can specify it as <code>JacPrototypeSparsityDetection(; jac_prototype=&lt;sparsity pattern&gt;)</code>.</li><li><code>SymbolicsSparsityDetection</code>: This will use <code>Symbolics.jl</code> to automatically detect the sparsity pattern. (Note that <code>Symbolics.jl</code> must be explicitly loaded before using this functionality.)</li></ol></li><li>Now choose an AD backend from <code>ADTypes.jl</code>:<ol><li>If using a Non <code>*Sparse*</code> type, then we will not use sparsity detection.</li><li>All other sparse AD types will internally compute the proper sparsity pattern, and try to exploit that.</li></ol></li><li>Now there are 2 options:<ol><li>Precompute the cache using <code>sparse_jacobian_cache</code> and use the <code>sparse_jacobian</code> or <code>sparse_jacobian!</code> functions to compute the Jacobian. This option is recommended if you are repeatedly computing the Jacobian for the same function.</li><li>Directly use <code>sparse_jacobian</code> or <code>sparse_jacobian!</code> to compute the Jacobian. This option should be used if you are only computing the Jacobian once.</li></ol></li></ol><pre><code class="language-julia hljs">using Symbolics
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sd = SymbolicsSparsityDetection()
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adtype = AutoSparseFiniteDiff()
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adtype = AutoSparse(AutoFiniteDiff())
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x = rand(30)
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y = similar(x)
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autoback_hesvec(f,x,v)</code></pre><h4 id="J*v-and-H*v-Operators"><a class="docs-heading-anchor" href="#J*v-and-H*v-Operators"><code>J*v</code> and <code>H*v</code> Operators</a><a id="J*v-and-H*v-Operators-1"></a><a class="docs-heading-anchor-permalink" href="#J*v-and-H*v-Operators" title="Permalink"></a></h4><p>The following produce matrix-free operators which are used for calculating Jacobian-vector and Hessian-vector products where the differentiation takes place at the vector <code>u</code>:</p><pre><code class="language-julia hljs">JacVec(f,x::AbstractArray;autodiff=true)
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HesVec(f,x::AbstractArray;autodiff=true)
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HesVecGrad(g,x::AbstractArray;autodiff=false)</code></pre><p>These all have the same interface, where <code>J*v</code> utilizes the out-of-place Jacobian-vector or Hessian-vector function, whereas <code>mul!(res,J,v)</code> utilizes the appropriate in-place versions. To update the location of differentiation in the operator, simply mutate the vector <code>u</code>: <code>J.u .= ...</code>.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="sparsedifftools/">API »</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="Friday 19 April 2024 07:47">Friday 19 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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HesVecGrad(g,x::AbstractArray;autodiff=false)</code></pre><p>These all have the same interface, where <code>J*v</code> utilizes the out-of-place Jacobian-vector or Hessian-vector function, whereas <code>mul!(res,J,v)</code> utilizes the appropriate in-place versions. To update the location of differentiation in the operator, simply mutate the vector <code>u</code>: <code>J.u .= ...</code>.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="sparsedifftools/">API »</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="Monday 22 April 2024 13:01">Monday 22 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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