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{"documenter":{"julia_version":"1.10.4","generation_timestamp":"2024-06-29T10:10:22","documenter_version":"1.5.0"}}
{"documenter":{"julia_version":"1.10.4","generation_timestamp":"2024-07-01T18:53:39","documenter_version":"1.5.0"}}
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2×3 CxxMatrix:
8.0 0.0 4.0
0.0 48.0 0.0</code></pre><p>For advanced users, there is a <a href="lib/wrapped_fcts/#List-of-wrapped-ADOL-C-drivers">list</a> of all functions, wrapped from ADOL-C.</p><h2 id="API-Reference"><a class="docs-heading-anchor" href="#API-Reference">API Reference</a><a id="API-Reference-1"></a><a class="docs-heading-anchor-permalink" href="#API-Reference" title="Permalink"></a></h2><ul><li><a href="lib/reference/#ADOLC.array_types.CxxMatrix"><code>ADOLC.array_types.CxxMatrix</code></a></li><li><a href="lib/reference/#ADOLC.array_types.CxxTensor"><code>ADOLC.array_types.CxxTensor</code></a></li><li><a href="lib/reference/#ADOLC.array_types.CxxVector"><code>ADOLC.array_types.CxxVector</code></a></li><li><a href="lib/reference/#ADOLC.adolc_format_to_seed_space"><code>ADOLC.adolc_format_to_seed_space</code></a></li><li><a href="lib/reference/#ADOLC.allocator"><code>ADOLC.allocator</code></a></li><li><a href="lib/reference/#ADOLC.array_types.cxx_res_to_jl_res"><code>ADOLC.array_types.cxx_res_to_jl_res</code></a></li><li><a href="lib/reference/#ADOLC.array_types.cxx_res_to_jl_res!"><code>ADOLC.array_types.cxx_res_to_jl_res!</code></a></li><li><a href="lib/reference/#ADOLC.array_types.jl_res_to_cxx_res"><code>ADOLC.array_types.jl_res_to_cxx_res</code></a></li><li><a href="lib/reference/#ADOLC.array_types.jl_res_to_cxx_res!"><code>ADOLC.array_types.jl_res_to_cxx_res!</code></a></li><li><a href="lib/reference/#ADOLC.create_cxx_identity"><code>ADOLC.create_cxx_identity</code></a></li><li><a href="lib/reference/#ADOLC.create_independent"><code>ADOLC.create_independent</code></a></li><li><a href="lib/reference/#ADOLC.create_partial_cxx_identity"><code>ADOLC.create_partial_cxx_identity</code></a></li><li><a href="lib/reference/#ADOLC.derivative"><code>ADOLC.derivative</code></a></li><li><a href="lib/reference/#ADOLC.derivative!"><code>ADOLC.derivative!</code></a></li><li><a href="lib/reference/#ADOLC.jl_allocator"><code>ADOLC.jl_allocator</code></a></li><li><a href="lib/reference/#ADOLC.partial_format_to_seed_space"><code>ADOLC.partial_format_to_seed_space</code></a></li><li><a href="lib/reference/#ADOLC.partial_to_adolc_format"><code>ADOLC.partial_to_adolc_format</code></a></li><li><a href="lib/reference/#ADOLC.partial_to_adolc_format!"><code>ADOLC.partial_to_adolc_format!</code></a></li><li><a href="lib/reference/#ADOLC.seed_idxs_adolc_format"><code>ADOLC.seed_idxs_adolc_format</code></a></li><li><a href="lib/reference/#ADOLC.seed_idxs_partial_format"><code>ADOLC.seed_idxs_partial_format</code></a></li><li><a href="lib/reference/#ADOLC.tensor_address"><code>ADOLC.tensor_address</code></a></li></ul><div class="citation canonical"><dl><dt>[1]</dt><dd><div id="griewank_evaluating_1999">A. Griewank, J. Utke and A. Walther. <em>Evaluating higher derivative tensors by forward propagation of univariate Taylor series</em>. Mathematics of Computation <strong>69</strong> (1999).</div></dd><dt>[2]</dt><dd><div id="Gr13">A. Griewank. <em>On stable piecewise linearization and generalized algorithmic differentiation</em>. Optimization Methods and Software <strong>28</strong> (2013).</div></dd></dl></div></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="lib/guides/">Guides »</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 1.5.0 on <span class="colophon-date" title="Saturday 29 June 2024 10:10">Saturday 29 June 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
0.0 48.0 0.0</code></pre><p>For advanced users, there is a <a href="lib/wrapped_fcts/#List-of-wrapped-ADOL-C-drivers">list</a> of all functions, wrapped from ADOL-C.</p><h2 id="API-Reference"><a class="docs-heading-anchor" href="#API-Reference">API Reference</a><a id="API-Reference-1"></a><a class="docs-heading-anchor-permalink" href="#API-Reference" title="Permalink"></a></h2><ul><li><a href="lib/reference/#ADOLC.array_types.CxxMatrix"><code>ADOLC.array_types.CxxMatrix</code></a></li><li><a href="lib/reference/#ADOLC.array_types.CxxTensor"><code>ADOLC.array_types.CxxTensor</code></a></li><li><a href="lib/reference/#ADOLC.array_types.CxxVector"><code>ADOLC.array_types.CxxVector</code></a></li><li><a href="lib/reference/#ADOLC.adolc_format_to_seed_space"><code>ADOLC.adolc_format_to_seed_space</code></a></li><li><a href="lib/reference/#ADOLC.allocator"><code>ADOLC.allocator</code></a></li><li><a href="lib/reference/#ADOLC.array_types.cxx_res_to_jl_res"><code>ADOLC.array_types.cxx_res_to_jl_res</code></a></li><li><a href="lib/reference/#ADOLC.array_types.cxx_res_to_jl_res!"><code>ADOLC.array_types.cxx_res_to_jl_res!</code></a></li><li><a href="lib/reference/#ADOLC.array_types.jl_res_to_cxx_res"><code>ADOLC.array_types.jl_res_to_cxx_res</code></a></li><li><a href="lib/reference/#ADOLC.array_types.jl_res_to_cxx_res!"><code>ADOLC.array_types.jl_res_to_cxx_res!</code></a></li><li><a href="lib/reference/#ADOLC.create_cxx_identity"><code>ADOLC.create_cxx_identity</code></a></li><li><a href="lib/reference/#ADOLC.create_independent"><code>ADOLC.create_independent</code></a></li><li><a href="lib/reference/#ADOLC.create_partial_cxx_identity"><code>ADOLC.create_partial_cxx_identity</code></a></li><li><a href="lib/reference/#ADOLC.derivative"><code>ADOLC.derivative</code></a></li><li><a href="lib/reference/#ADOLC.derivative!"><code>ADOLC.derivative!</code></a></li><li><a href="lib/reference/#ADOLC.jl_allocator"><code>ADOLC.jl_allocator</code></a></li><li><a href="lib/reference/#ADOLC.partial_format_to_seed_space"><code>ADOLC.partial_format_to_seed_space</code></a></li><li><a href="lib/reference/#ADOLC.partial_to_adolc_format"><code>ADOLC.partial_to_adolc_format</code></a></li><li><a href="lib/reference/#ADOLC.partial_to_adolc_format!"><code>ADOLC.partial_to_adolc_format!</code></a></li><li><a href="lib/reference/#ADOLC.seed_idxs_adolc_format"><code>ADOLC.seed_idxs_adolc_format</code></a></li><li><a href="lib/reference/#ADOLC.seed_idxs_partial_format"><code>ADOLC.seed_idxs_partial_format</code></a></li><li><a href="lib/reference/#ADOLC.tensor_address"><code>ADOLC.tensor_address</code></a></li></ul><div class="citation canonical"><dl><dt>[1]</dt><dd><div id="griewank_evaluating_1999">A. Griewank, J. Utke and A. Walther. <em>Evaluating higher derivative tensors by forward propagation of univariate Taylor series</em>. Mathematics of Computation <strong>69</strong> (1999).</div></dd><dt>[2]</dt><dd><div id="Gr13">A. Griewank. <em>On stable piecewise linearization and generalized algorithmic differentiation</em>. Optimization Methods and Software <strong>28</strong> (2013).</div></dd></dl></div></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="lib/guides/">Guides »</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 1.5.0 on <span class="colophon-date" title="Monday 1 July 2024 18:53">Monday 1 July 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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[2, 3, 0, 0],
[0, 0, 4, 0],
[2, 0, 0, 0]
].\]</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>Internally, there is, at some point, a conversion from <a href="#Partial-Format">Partial-Format</a> to <a href="#ADOLC-Format">ADOLC-Format</a> since the access to the higher-order tensor computed with ADOL-C is based on the <a href="#ADOLC-Format">ADOLC-Format</a>. However, only one entry is converted at a time, meaning that the benefits of both modes, as explained below, are still valid.</p></div></div><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>Both formats have their benefits. The <a href="#ADOLC-Format">ADOLC-Format</a> should be used if the total derivative degree is small compared to the number of independents <span>$n$</span>. Otherwise, <a href="#Partial-Format">Partial-Format</a> should be used.</p></div></div><p>There are utilities to convert between the formats: <a href="../reference/#ADOLC.partial_to_adolc_format"><code>partial_to_adolc_format</code></a></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../guides/">« Guides</a><a class="docs-footer-nextpage" href="../reference/">Reference »</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 1.5.0 on <span class="colophon-date" title="Saturday 29 June 2024 10:10">Saturday 29 June 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
].\]</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>Internally, there is, at some point, a conversion from <a href="#Partial-Format">Partial-Format</a> to <a href="#ADOLC-Format">ADOLC-Format</a> since the access to the higher-order tensor computed with ADOL-C is based on the <a href="#ADOLC-Format">ADOLC-Format</a>. However, only one entry is converted at a time, meaning that the benefits of both modes, as explained below, are still valid.</p></div></div><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>Both formats have their benefits. The <a href="#ADOLC-Format">ADOLC-Format</a> should be used if the total derivative degree is small compared to the number of independents <span>$n$</span>. Otherwise, <a href="#Partial-Format">Partial-Format</a> should be used.</p></div></div><p>There are utilities to convert between the formats: <a href="../reference/#ADOLC.partial_to_adolc_format"><code>partial_to_adolc_format</code></a></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../guides/">« Guides</a><a class="docs-footer-nextpage" href="../reference/">Reference »</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 1.5.0 on <span class="colophon-date" title="Monday 1 July 2024 18:53">Monday 1 July 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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# update x ...
derivative!(cxx_res, f, m, n, x, mode, dir=dir, tape_id=tape_id, reuse_tape=true)
# do computations ...
end</code></pre><p>Moreover, for <a href="../derivative_modes/#Higher-Order">higher-order</a> derivatives you might consider the generation of a <code>seed</code>. However, if you do not pass a <code>seed</code> to the <a href="../reference/#ADOLC.derivative!"><code>derivative!</code></a> (<a href="../reference/#ADOLC.derivative"><code>derivative</code></a>) driver, the partial identity is created as the <code>seed</code> automatically (see <a href="#Seed-Matrix">here</a>). </p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../">« Home</a><a class="docs-footer-nextpage" href="../derivative_modes/">Derivative Modes »</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 1.5.0 on <span class="colophon-date" title="Saturday 29 June 2024 10:10">Saturday 29 June 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
end</code></pre><p>Moreover, for <a href="../derivative_modes/#Higher-Order">higher-order</a> derivatives you might consider the generation of a <code>seed</code>. However, if you do not pass a <code>seed</code> to the <a href="../reference/#ADOLC.derivative!"><code>derivative!</code></a> (<a href="../reference/#ADOLC.derivative"><code>derivative</code></a>) driver, the partial identity is created as the <code>seed</code> automatically (see <a href="#Seed-Matrix">here</a>). </p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../">« Home</a><a class="docs-footer-nextpage" href="../derivative_modes/">Derivative Modes »</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 1.5.0 on <span class="colophon-date" title="Monday 1 July 2024 18:53">Monday 1 July 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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