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-{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-09-28T10:08:08","documenter_version":"1.1.0"}}
+{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-09-28T10:11:04","documenter_version":"1.1.0"}}

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@@ -4,28 +4,28 @@
 julia> A_inv = cholinv(A);
 
 julia> A_inv ≈ inv(A)
-true</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/biaslab/FastCholesky.jl/blob/0f6f2a886a48e9438bdf0a6a4c587e1125344874/src/FastCholesky.jl#L97-L110">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastCholesky.cholinv_logdet-Tuple{Any}" href="#FastCholesky.cholinv_logdet-Tuple{Any}"><code>FastCholesky.cholinv_logdet</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">cholinv_logdet(input)</code></pre><p>Calculate the inverse and the natural logarithm of the determinant of the input matrix <code>input</code> simultaneously using Cholesky factorization.</p><pre><code class="language-julia hljs">julia&gt; A = [4.0 2.0; 2.0 5.0];
+true</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/biaslab/FastCholesky.jl/blob/c4a49f96e7156e46f0630c2b0fd01b639ab019d4/src/FastCholesky.jl#L97-L110">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastCholesky.cholinv_logdet-Tuple{Any}" href="#FastCholesky.cholinv_logdet-Tuple{Any}"><code>FastCholesky.cholinv_logdet</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">cholinv_logdet(input)</code></pre><p>Calculate the inverse and the natural logarithm of the determinant of the input matrix <code>input</code> simultaneously using Cholesky factorization.</p><pre><code class="language-julia hljs">julia&gt; A = [4.0 2.0; 2.0 5.0];
 
 julia&gt; A_inv, logdet_A = cholinv_logdet(A);
 
 julia&gt; isapprox(A_inv * A, I)
 true
 
 julia&gt; isapprox(logdet_A, log(det(A)))
-true</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/biaslab/FastCholesky.jl/blob/0f6f2a886a48e9438bdf0a6a4c587e1125344874/src/FastCholesky.jl#L163-L179">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastCholesky.chollogdet-Tuple{Any}" href="#FastCholesky.chollogdet-Tuple{Any}"><code>FastCholesky.chollogdet</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">chollogdet(input)</code></pre><p>Calculate the log-determinant of the input matrix <code>input</code> using Cholesky factorization. This function is an alias for <code>logdet(fastcholesky(input))</code>.</p><pre><code class="language-julia-repl hljs">julia&gt; A = [4.0 2.0; 2.0 5.0];
+true</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/biaslab/FastCholesky.jl/blob/c4a49f96e7156e46f0630c2b0fd01b639ab019d4/src/FastCholesky.jl#L163-L179">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastCholesky.chollogdet-Tuple{Any}" href="#FastCholesky.chollogdet-Tuple{Any}"><code>FastCholesky.chollogdet</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">chollogdet(input)</code></pre><p>Calculate the log-determinant of the input matrix <code>input</code> using Cholesky factorization. This function is an alias for <code>logdet(fastcholesky(input))</code>.</p><pre><code class="language-julia-repl hljs">julia&gt; A = [4.0 2.0; 2.0 5.0];
 
 julia&gt; logdet_A = chollogdet(A);
 
 julia&gt; isapprox(logdet_A, log(det(A)))
-true</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/biaslab/FastCholesky.jl/blob/0f6f2a886a48e9438bdf0a6a4c587e1125344874/src/FastCholesky.jl#L143-L156">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastCholesky.cholsqrt-Tuple{Any}" href="#FastCholesky.cholsqrt-Tuple{Any}"><code>FastCholesky.cholsqrt</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">cholsqrt(input)</code></pre><p>Calculate the square root of the input matrix <code>input</code> using Cholesky factorization. This function is an alias for <code>fastcholesky(input).L</code>.</p><pre><code class="language-julia-repl hljs">julia&gt; A = [4.0 2.0; 2.0 5.0];
+true</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/biaslab/FastCholesky.jl/blob/c4a49f96e7156e46f0630c2b0fd01b639ab019d4/src/FastCholesky.jl#L143-L156">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastCholesky.cholsqrt-Tuple{Any}" href="#FastCholesky.cholsqrt-Tuple{Any}"><code>FastCholesky.cholsqrt</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">cholsqrt(input)</code></pre><p>Calculate the square root of the input matrix <code>input</code> using Cholesky factorization. This function is an alias for <code>fastcholesky(input).L</code>.</p><pre><code class="language-julia-repl hljs">julia&gt; A = [4.0 2.0; 2.0 5.0];
 
 julia&gt; A_sqrt = cholsqrt(A);
 
 julia&gt; isapprox(A_sqrt * A_sqrt&#39;, A)
-true</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/biaslab/FastCholesky.jl/blob/0f6f2a886a48e9438bdf0a6a4c587e1125344874/src/FastCholesky.jl#L123-L136">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastCholesky.fastcholesky!" href="#FastCholesky.fastcholesky!"><code>FastCholesky.fastcholesky!</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">fastcholesky!(input)</code></pre><p>Calculate the Cholesky factorization of the input matrix <code>input</code> in-place. This function is an in-place version of <code>fastcholesky</code>,  and it does not check the positive-definiteness of the input matrix or throw errors. You can use <code>LinearAlgebra.issuccess</code> to check if the result is a proper Cholesky factorization.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>This function does not verify the positive-definiteness of the input matrix and does not throw errors. Ensure that the input matrix is appropriate for Cholesky factorization before using this function.</p></div></div><pre><code class="language-julia-repl hljs">julia&gt; C = fastcholesky!([ 1.0 0.5; 0.5 1.0 ]);
+true</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/biaslab/FastCholesky.jl/blob/c4a49f96e7156e46f0630c2b0fd01b639ab019d4/src/FastCholesky.jl#L123-L136">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastCholesky.fastcholesky!" href="#FastCholesky.fastcholesky!"><code>FastCholesky.fastcholesky!</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">fastcholesky!(input)</code></pre><p>Calculate the Cholesky factorization of the input matrix <code>input</code> in-place. This function is an in-place version of <code>fastcholesky</code>,  and it does not check the positive-definiteness of the input matrix or throw errors. You can use <code>LinearAlgebra.issuccess</code> to check if the result is a proper Cholesky factorization.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>This function does not verify the positive-definiteness of the input matrix and does not throw errors. Ensure that the input matrix is appropriate for Cholesky factorization before using this function.</p></div></div><pre><code class="language-julia-repl hljs">julia&gt; C = fastcholesky!([ 1.0 0.5; 0.5 1.0 ]);
 
 julia&gt; C.L * C.L&#39; ≈ [ 1.0 0.5; 0.5 1.0 ]
-true</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/biaslab/FastCholesky.jl/blob/0f6f2a886a48e9438bdf0a6a4c587e1125344874/src/FastCholesky.jl#L52-L67">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastCholesky.fastcholesky-Tuple{AbstractMatrix}" href="#FastCholesky.fastcholesky-Tuple{AbstractMatrix}"><code>FastCholesky.fastcholesky</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">fastcholesky(input)</code></pre><p>Calculate the Cholesky factorization of the input matrix <code>input</code>.  This function provides a more efficient implementation for certain input matrices compared to the standard <code>LinearAlgebra.cholesky</code> function.  By default, it falls back to using <code>LinearAlgebra.cholesky(PositiveFactorizations.Positive, input)</code>, which means it does not require the input matrix to be perfectly symmetric.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>This function assumes that the input matrix is nearly positive definite, and it will attempt to make the smallest possible adjustments  to the matrix to ensure it becomes positive definite. Note that the magnitude of these adjustments may not necessarily be small, so it&#39;s important to use  this function only when you expect the input matrix to be nearly positive definite.</p></div></div><pre><code class="language-julia-repl hljs">julia&gt; C = fastcholesky([ 1.0 0.5; 0.5 1.0 ]);
+true</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/biaslab/FastCholesky.jl/blob/c4a49f96e7156e46f0630c2b0fd01b639ab019d4/src/FastCholesky.jl#L52-L67">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastCholesky.fastcholesky-Tuple{AbstractMatrix}" href="#FastCholesky.fastcholesky-Tuple{AbstractMatrix}"><code>FastCholesky.fastcholesky</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">fastcholesky(input)</code></pre><p>Calculate the Cholesky factorization of the input matrix <code>input</code>.  This function provides a more efficient implementation for certain input matrices compared to the standard <code>LinearAlgebra.cholesky</code> function.  By default, it falls back to using <code>LinearAlgebra.cholesky(PositiveFactorizations.Positive, input)</code>, which means it does not require the input matrix to be perfectly symmetric.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>This function assumes that the input matrix is nearly positive definite, and it will attempt to make the smallest possible adjustments  to the matrix to ensure it becomes positive definite. Note that the magnitude of these adjustments may not necessarily be small, so it&#39;s important to use  this function only when you expect the input matrix to be nearly positive definite.</p></div></div><pre><code class="language-julia-repl hljs">julia&gt; C = fastcholesky([ 1.0 0.5; 0.5 1.0 ]);
 
 julia&gt; C.L * C.L&#39; ≈ [ 1.0 0.5; 0.5 1.0 ]
-true</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/biaslab/FastCholesky.jl/blob/0f6f2a886a48e9438bdf0a6a4c587e1125344874/src/FastCholesky.jl#L10-L28">source</a></section></article></article><nav class="docs-footer"><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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.0 on <span class="colophon-date" title="Thursday 28 September 2023 10:08">Thursday 28 September 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+true</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/biaslab/FastCholesky.jl/blob/c4a49f96e7156e46f0630c2b0fd01b639ab019d4/src/FastCholesky.jl#L10-L28">source</a></section></article></article><nav class="docs-footer"><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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.0 on <span class="colophon-date" title="Thursday 28 September 2023 10:11">Thursday 28 September 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>