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class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Comparison Against SymPy</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Comparison Against SymPy</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/JuliaSymbolics/Symbolics.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/master/docs/src/comparison.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Comparison-of-Julia's-Symbolics.jl-vs-SymPy-for-Symbolic-Computation"><a class="docs-heading-anchor" href="#Comparison-of-Julia's-Symbolics.jl-vs-SymPy-for-Symbolic-Computation">Comparison of Julia's Symbolics.jl vs SymPy for Symbolic Computation</a><a id="Comparison-of-Julia's-Symbolics.jl-vs-SymPy-for-Symbolic-Computation-1"></a><a class="docs-heading-anchor-permalink" href="#Comparison-of-Julia's-Symbolics.jl-vs-SymPy-for-Symbolic-Computation" title="Permalink"></a></h1><p>Symbolics.jl is a symbolic modeling language for Julia, built in Julia. Its goal is very different from Sympy: it was made to support symbolic-numerics, the combination of symbolic computing with numerical methods to allow for extreme performance computing that would not be possible without modifying the model. Because of this, Symbolics.jl excels in many areas due to purposeful design decisions:</p><ul><li>Performance: Symbolics.jl is built in Julia, whereas SymPy was built in Python. Thus, the performance bar for Symbolics.jl is much higher. Symbolics.jl started because SymPy was far too slow and SymEngine was far too inflexible for the projects they were doing. Performance is key to Symbolics.jl. If you find any performance issues, please file an issue.</li><li><code>build_function</code>: <code>lambdify</code> is “fine” for some people, but if you're building a super fast MPI-enabled Julia/C/Fortran simulation code, having a function that hits the Python interpreter is less than optimal. By default, <code>build_function</code> builds fast JIT-compiled functions due to being in Julia. However, it has support for things like static arrays, non-allocating functions via mutation, fast functions on sparse matrices and arrays of arrays, etc.: all core details of doing high performance computing.</li><li>Parallelism: Symbolics.jl has pervasive parallelism. The symbolic simplification via <a href="https://github.com/JuliaSymbolics/SymbolicUtils.jl">SymbolicUtils.jl</a> has built-in parallelism, Symbolics.jl builds functions that parallelize across threads. Symbolics.jl is compatible with GPU libraries like CUDA.jl.</li><li>Extensible: Symbolics.jl and its underlying tools are written in pure Julia. Want to add new or better simplification rules? Add some Julia code! Need to add new derivatives? Add some Julia code! You get the picture. Breaking down these barriers makes it easier for the user to tailor the program to their needs and accelerates the development of the library.</li><li>Deep integration with the Julia ecosystem: Symbolics.jl's integration with neural networks is not the only thing that's deep. Symbolics.jl is built with the same philosophy as other SciML packages, eschewing “monorepos” for a distributed development approach that ties together the work of many developers. The differentiation parts utilize tools from automatic differentiation libraries, all linear algebra functionality comes from tracing Julia Base itself, symbolic rewriting (simplification and substitution) comes from <a href="https://github.com/JuliaSymbolics/SymbolicUtils.jl">SymbolicUtils.jl</a>, parallelism comes from Julia Base libraries, Dagger.jl, etc. SciML Tools like <a href="https://datadriven.sciml.ai/dev/">DataDrivenDiffEq.jl</a> can reconstruct symbolic expressions from neural networks and data, while <a href="https://github.com/SciML/NeuralPDE.jl">NeuralPDE.jl</a> can automatically solve partial differential equations from symbolic descriptions using physics-informed neural networks. The list keeps going. All told, by design Symbolics.jl's development moves fast because it's effectively using the work of hundreds of Julia developers, allowing it to grow fast.</li><li>While Symbolics.jl has many features missing from SymPy, it does not superset SymPy's functionality. For a list of missing features, see <a href="https://github.com/JuliaSymbolics/Symbolics.jl/issues/59">this issue</a>.</li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../manual/faq/">« Frequently Asked Questions</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 12:13">Tuesday 27 February 2024</span>. 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class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Comparison Against SymPy</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Comparison Against SymPy</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/JuliaSymbolics/Symbolics.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/master/docs/src/comparison.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Comparison-of-Julia's-Symbolics.jl-vs-SymPy-for-Symbolic-Computation"><a class="docs-heading-anchor" href="#Comparison-of-Julia's-Symbolics.jl-vs-SymPy-for-Symbolic-Computation">Comparison of Julia's Symbolics.jl vs SymPy for Symbolic Computation</a><a id="Comparison-of-Julia's-Symbolics.jl-vs-SymPy-for-Symbolic-Computation-1"></a><a class="docs-heading-anchor-permalink" href="#Comparison-of-Julia's-Symbolics.jl-vs-SymPy-for-Symbolic-Computation" title="Permalink"></a></h1><p>Symbolics.jl is a symbolic modeling language for Julia, built in Julia. Its goal is very different from Sympy: it was made to support symbolic-numerics, the combination of symbolic computing with numerical methods to allow for extreme performance computing that would not be possible without modifying the model. Because of this, Symbolics.jl excels in many areas due to purposeful design decisions:</p><ul><li>Performance: Symbolics.jl is built in Julia, whereas SymPy was built in Python. Thus, the performance bar for Symbolics.jl is much higher. Symbolics.jl started because SymPy was far too slow and SymEngine was far too inflexible for the projects they were doing. Performance is key to Symbolics.jl. If you find any performance issues, please file an issue.</li><li><code>build_function</code>: <code>lambdify</code> is “fine” for some people, but if you're building a super fast MPI-enabled Julia/C/Fortran simulation code, having a function that hits the Python interpreter is less than optimal. By default, <code>build_function</code> builds fast JIT-compiled functions due to being in Julia. However, it has support for things like static arrays, non-allocating functions via mutation, fast functions on sparse matrices and arrays of arrays, etc.: all core details of doing high performance computing.</li><li>Parallelism: Symbolics.jl has pervasive parallelism. The symbolic simplification via <a href="https://github.com/JuliaSymbolics/SymbolicUtils.jl">SymbolicUtils.jl</a> has built-in parallelism, Symbolics.jl builds functions that parallelize across threads. Symbolics.jl is compatible with GPU libraries like CUDA.jl.</li><li>Extensible: Symbolics.jl and its underlying tools are written in pure Julia. Want to add new or better simplification rules? Add some Julia code! Need to add new derivatives? Add some Julia code! You get the picture. Breaking down these barriers makes it easier for the user to tailor the program to their needs and accelerates the development of the library.</li><li>Deep integration with the Julia ecosystem: Symbolics.jl's integration with neural networks is not the only thing that's deep. Symbolics.jl is built with the same philosophy as other SciML packages, eschewing “monorepos” for a distributed development approach that ties together the work of many developers. The differentiation parts utilize tools from automatic differentiation libraries, all linear algebra functionality comes from tracing Julia Base itself, symbolic rewriting (simplification and substitution) comes from <a href="https://github.com/JuliaSymbolics/SymbolicUtils.jl">SymbolicUtils.jl</a>, parallelism comes from Julia Base libraries, Dagger.jl, etc. SciML Tools like <a href="https://datadriven.sciml.ai/dev/">DataDrivenDiffEq.jl</a> can reconstruct symbolic expressions from neural networks and data, while <a href="https://github.com/SciML/NeuralPDE.jl">NeuralPDE.jl</a> can automatically solve partial differential equations from symbolic descriptions using physics-informed neural networks. The list keeps going. All told, by design Symbolics.jl's development moves fast because it's effectively using the work of hundreds of Julia developers, allowing it to grow fast.</li><li>While Symbolics.jl has many features missing from SymPy, it does not superset SymPy's functionality. For a list of missing features, see <a href="https://github.com/JuliaSymbolics/Symbolics.jl/issues/59">this issue</a>.</li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../manual/faq/">« Frequently Asked Questions</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 13:45">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> diff --git a/previews/PR1079/examples/perturbation/index.html b/previews/PR1079/examples/perturbation/index.html index e0c1f6d4b..8ff7fb7f5 100644 --- a/previews/PR1079/examples/perturbation/index.html +++ b/previews/PR1079/examples/perturbation/index.html @@ -83,4 +83,4 @@ - (𝜀 + 4*𝜀^2 + 10*𝜀^3)*𝑀^3/6 + (𝜀 + 16*𝜀^2 + 91*𝜀^3)*𝑀^5/120</code></pre><p>Comparing the formula to the one for 𝐸 in the <a href="https://en.wikipedia.org/wiki/Kepler%27s_equation">Wikipedia article on the Kepler's equation</a>:</p><p class="math-container">\[ E = \frac{1}{1-\epsilon}M -\frac{\epsilon}{(1-\epsilon)^4} \frac{M^3}{3!} + \frac{(9\epsilon^2 - + \epsilon)}{(1-\epsilon)^7}\frac{M^5}{5!}\cdots\]</p><p>The first deviation is in the coefficient of <span>$\epsilon^3 M^5$</span>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../tutorials/converting_to_C/">« Automatic Conversion of Julia Code to C Functions</a><a class="docs-footer-nextpage" href="../../manual/variables/">Variable and Equation Types »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 12:13">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> + + \epsilon)}{(1-\epsilon)^7}\frac{M^5}{5!}\cdots\]</p><p>The first deviation is in the coefficient of <span>$\epsilon^3 M^5$</span>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../tutorials/converting_to_C/">« Automatic Conversion of Julia Code to C Functions</a><a class="docs-footer-nextpage" href="../../manual/variables/">Variable and Equation Types »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 13:45">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> diff --git a/previews/PR1079/getting_started/index.html b/previews/PR1079/getting_started/index.html index f76aae9d4..bf2857431 100644 --- a/previews/PR1079/getting_started/index.html +++ b/previews/PR1079/getting_started/index.html @@ -220,9 +220,9 @@ out = sparse(rows, cols, zeros(length(cols)), size(sj)...) # pre-allocate, and correct structure myf = eval(last(f_expr)) myf(out, rand(N)) # note that out matches the sparsity structure of sj -out</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">20×10 SparseArrays.SparseMatrixCSC{Float64, Int64} with 18 stored entries: -⎡⠀⠀⠀⠠⢀⎤ -⎢⠀⢐⠀⠠⠂⎥ -⎢⠁⠀⠀⠀⠐⎥ -⎢⠈⠀⠑⠄⠢⎥ -⎣⢀⠠⢀⠀⢀⎦</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../tutorials/auto_parallel/">Automated Sparse Parallelism of Julia Functions via Tracing »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 12:13">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> +out</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">20×10 SparseArrays.SparseMatrixCSC{Float64, Int64} with 25 stored entries: +⎡⠀⠁⠀⠐⠠⎤ +⎢⡂⡀⠨⠐⠠⎥ +⎢⢡⠀⠀⡊⠂⎥ +⎢⠀⠠⠈⠠⠄⎥ +⎣⠀⡈⠁⠀⢀⎦</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../tutorials/auto_parallel/">Automated Sparse Parallelism of Julia Functions via Tracing »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 13:45">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> diff --git a/previews/PR1079/index.html b/previews/PR1079/index.html index 6fb31f937..111d1de52 100644 --- a/previews/PR1079/index.html +++ b/previews/PR1079/index.html @@ -334,4 +334,4 @@ [8e850b90] libblastrampoline_jll v5.8.0+1 [8e850ede] nghttp2_jll v1.52.0+1 [3f19e933] p7zip_jll v17.4.0+2 -Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`</code></pre></details><p>You can also download the <a href="https://github.com/SciML/Symbolics.jl/tree/gh-pages/v5.22.1/assets/Manifest.toml">manifest</a> file and the <a href="https://github.com/SciML/Symbolics.jl/tree/gh-pages/v5.22.1/assets/Project.toml">project</a> file.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="getting_started/">Getting Started with Symbolics.jl »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 12:13">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> +Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`</code></pre></details><p>You can also download the <a href="https://github.com/SciML/Symbolics.jl/tree/gh-pages/v5.22.1/assets/Manifest.toml">manifest</a> file and the <a href="https://github.com/SciML/Symbolics.jl/tree/gh-pages/v5.22.1/assets/Project.toml">project</a> file.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="getting_started/">Getting Started with Symbolics.jl »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 13:45">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> diff --git a/previews/PR1079/manual/arrays/index.html b/previews/PR1079/manual/arrays/index.html index e5960ccfd..972cc3e16 100644 --- a/previews/PR1079/manual/arrays/index.html +++ b/previews/PR1079/manual/arrays/index.html @@ -64,4 +64,4 @@ A_{2}ˏ_1 A_{3}ˏ_1 + A_{2}ˏ_2 A_{3}ˏ_2 + A_{2}ˏ_3 A_{3}ˏ_3 \end{equation} \]</p><pre><code class="language-julia hljs">@syms i::Int j::Int -Symbolics.scalarize(AAt[i,j])</code></pre><p>In general, any scalar expression which is derived from array expressions can be scalarized.</p><pre><code class="language-julia hljs">#sum(A[:,1]) + sum(A[2,:])#latexify not working</code></pre><pre><code class="language-julia hljs">Symbolics.scalarize(sum(A[:,1]) + sum(A[2,:]))</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../groebner/">« Groebner bases</a><a class="docs-footer-nextpage" href="../build_function/">Function Building and Compilation (build_function) »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 12:13">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> +Symbolics.scalarize(AAt[i,j])</code></pre><p>In general, any scalar expression which is derived from array expressions can be scalarized.</p><pre><code class="language-julia hljs">#sum(A[:,1]) + sum(A[2,:])#latexify not working</code></pre><pre><code class="language-julia hljs">Symbolics.scalarize(sum(A[:,1]) + sum(A[2,:]))</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../groebner/">« Groebner bases</a><a class="docs-footer-nextpage" href="../build_function/">Function Building and Compilation (build_function) »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 13:45">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> diff --git a/previews/PR1079/manual/build_function/index.html b/previews/PR1079/manual/build_function/index.html index 0a88698ca..e3ea6c9a9 100644 --- a/previews/PR1079/manual/build_function/index.html +++ b/previews/PR1079/manual/build_function/index.html @@ -3,7 +3,7 @@ expression = Val{true}, target = JuliaTarget(), parallel=nothing, - kwargs...)</code></pre><p>Arguments:</p><ul><li><code>ex</code>: The <code>Num</code> to compile</li><li><code>args</code>: The arguments of the function</li><li><code>expression</code>: Whether to generate code or whether to generate the compiled form. By default, <code>expression = Val{true}</code>, which means that the code for the function is returned. If <code>Val{false}</code>, then the returned value is compiled.</li></ul><p>Keyword Arguments:</p><ul><li><code>target</code>: The output target of the compilation process. Possible options are:<ul><li><code>JuliaTarget</code>: Generates a Julia function</li><li><code>CTarget</code>: Generates a C function</li><li><code>StanTarget</code>: Generates a function for compiling with the Stan probabilistic programming language</li><li><code>MATLABTarget</code>: Generates an anonymous function for use in MATLAB and Octave environments</li></ul></li><li><code>parallel</code>: The kind of parallelism to use in the generated function. Defaults to <code>SerialForm()</code>, i.e. no parallelism, if <code>ex</code> is a single expression or an array containing <= 1500 non-zero expressions. If <code>ex</code> is an array of > 1500 non-zero expressions, then <code>ShardedForm(80, 4)</code> is used. See below for more on <code>ShardedForm</code>. Note that the parallel forms are not exported and thus need to be chosen like <code>Symbolics.SerialForm()</code>. The choices are:<ul><li><code>SerialForm()</code>: Serial execution.</li><li><code>ShardedForm(cutoff, ncalls)</code>: splits the output function into sub-functions which contain at most <code>cutoff</code> number of output <code>rhss</code>. These sub-functions are called by the top-level function that <em>build</em>function returns. This helps in reducing the compile time of the generated function.</li><li><code>MultithreadedForm()</code>: Multithreaded execution with a static split, evenly splitting the number of expressions per thread.</li></ul></li><li><code>fname</code>: Used by some targets for the name of the function in the target space.</li></ul><p>Note that not all build targets support the full compilation interface. Check the individual target documentation for details.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/build_function.jl#L36-L85">source</a></section></article><h2 id="Target-Specific-Definitions"><a class="docs-heading-anchor" href="#Target-Specific-Definitions">Target-Specific Definitions</a><a id="Target-Specific-Definitions-1"></a><a class="docs-heading-anchor-permalink" href="#Target-Specific-Definitions" title="Permalink"></a></h2><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="Symbolics._build_function-Tuple{Symbolics.JuliaTarget, AbstractArray, Vararg{Any}}" href="#Symbolics._build_function-Tuple{Symbolics.JuliaTarget, AbstractArray, Vararg{Any}}"><code>Symbolics._build_function</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">_build_function(target::JuliaTarget, rhss::AbstractArray, args...; + kwargs...)</code></pre><p>Arguments:</p><ul><li><code>ex</code>: The <code>Num</code> to compile</li><li><code>args</code>: The arguments of the function</li><li><code>expression</code>: Whether to generate code or whether to generate the compiled form. By default, <code>expression = Val{true}</code>, which means that the code for the function is returned. If <code>Val{false}</code>, then the returned value is compiled.</li></ul><p>Keyword Arguments:</p><ul><li><code>target</code>: The output target of the compilation process. Possible options are:<ul><li><code>JuliaTarget</code>: Generates a Julia function</li><li><code>CTarget</code>: Generates a C function</li><li><code>StanTarget</code>: Generates a function for compiling with the Stan probabilistic programming language</li><li><code>MATLABTarget</code>: Generates an anonymous function for use in MATLAB and Octave environments</li></ul></li><li><code>parallel</code>: The kind of parallelism to use in the generated function. Defaults to <code>SerialForm()</code>, i.e. no parallelism, if <code>ex</code> is a single expression or an array containing <= 1500 non-zero expressions. If <code>ex</code> is an array of > 1500 non-zero expressions, then <code>ShardedForm(80, 4)</code> is used. See below for more on <code>ShardedForm</code>. Note that the parallel forms are not exported and thus need to be chosen like <code>Symbolics.SerialForm()</code>. The choices are:<ul><li><code>SerialForm()</code>: Serial execution.</li><li><code>ShardedForm(cutoff, ncalls)</code>: splits the output function into sub-functions which contain at most <code>cutoff</code> number of output <code>rhss</code>. These sub-functions are called by the top-level function that <em>build</em>function returns. This helps in reducing the compile time of the generated function.</li><li><code>MultithreadedForm()</code>: Multithreaded execution with a static split, evenly splitting the number of expressions per thread.</li></ul></li><li><code>fname</code>: Used by some targets for the name of the function in the target space.</li></ul><p>Note that not all build targets support the full compilation interface. Check the individual target documentation for details.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/build_function.jl#L36-L85">source</a></section></article><h2 id="Target-Specific-Definitions"><a class="docs-heading-anchor" href="#Target-Specific-Definitions">Target-Specific Definitions</a><a id="Target-Specific-Definitions-1"></a><a class="docs-heading-anchor-permalink" href="#Target-Specific-Definitions" title="Permalink"></a></h2><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="Symbolics._build_function-Tuple{Symbolics.JuliaTarget, AbstractArray, Vararg{Any}}" href="#Symbolics._build_function-Tuple{Symbolics.JuliaTarget, AbstractArray, Vararg{Any}}"><code>Symbolics._build_function</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">_build_function(target::JuliaTarget, rhss::AbstractArray, args...; conv=toexpr, expression = Val{true}, expression_module = @__MODULE__(), @@ -26,14 +26,14 @@ convert_oop = true, force_SA = false, skipzeros = outputidxs===nothing, fillzeros = skipzeros && !(typeof(rhss)<:SparseMatrixCSC), - parallel=SerialForm(), kwargs...)</code></pre><p>Generates a Julia function which can then be utilized for further evaluations. If expression=Val{false}, the return is a Julia function which utilizes RuntimeGeneratedFunctions.jl to be free of world-age issues.</p><p>If the <code>rhss</code> is a scalar, the generated function is a function with a scalar output. Otherwise, if it's an <code>AbstractArray</code>, the output is two functions, one for out-of-place AbstractArray output and a second which is a mutating function. The outputted functions match the given argument order, i.e., f(u,p,args...) for the out-of-place and scalar functions and <code>f!(du,u,p,args..)</code> for the in-place version.</p><p>Special Keyword Arguments:</p><ul><li><code>parallel</code>: The kind of parallelism to use in the generated function. Defaults to <code>SerialForm()</code>, i.e. no parallelism. Note that the parallel forms are not exported and thus need to be chosen like <code>Symbolics.SerialForm()</code>. The choices are:<ul><li><code>SerialForm()</code>: Serial execution.</li><li><code>ShardedForm(cutoff, ncalls)</code>: splits the output function into sub-functions which contain at most <code>cutoff</code> number of output <code>rhss</code>. These sub-functions are called by the top-level function that <em>build</em>function returns.</li><li><code>MultithreadedForm()</code>: Multithreaded execution with a static split, evenly splitting the number of expressions per thread.</li></ul></li><li><code>conv</code>: The conversion function of symbolic types to Expr. By default, this uses the <code>toexpr</code> function.</li><li><code>checkbounds</code>: For whether to enable bounds checking inside the generated function. Defaults to false, meaning that <code>@inbounds</code> is applied.</li><li><code>linenumbers</code>: Determines whether the generated function expression retains the line numbers. Defaults to true.</li><li><code>convert_oop</code>: Determines whether the OOP version should try to convert the output to match the type of the first input. This is useful for cases like LabelledArrays or other array types that carry extra information. Defaults to true.</li><li><code>force_SA</code>: Forces the output of the OOP version to be a StaticArray. Defaults to <code>false</code>, and outputs a static array when the first argument is a static array.</li><li><code>skipzeros</code>: Whether to skip filling zeros in the in-place version if the filling function is 0.</li><li><code>fillzeros</code>: Whether to perform <code>fill(out,0)</code> before the calculations to ensure safety with <code>skipzeros</code>.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/build_function.jl#L196-L268">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="Symbolics._build_function-Tuple{Symbolics.CTarget, Array{<:Equation}, Vararg{Any}}" href="#Symbolics._build_function-Tuple{Symbolics.CTarget, Array{<:Equation}, Vararg{Any}}"><code>Symbolics._build_function</code></a> — <span class="docstring-category">Method</span></header><section><div><p>Build function target: <code>CTarget</code></p><pre><code class="language-julia hljs">function _build_function(target::CTarget, eqs::Array{<:Equation}, args...; + parallel=SerialForm(), kwargs...)</code></pre><p>Generates a Julia function which can then be utilized for further evaluations. If expression=Val{false}, the return is a Julia function which utilizes RuntimeGeneratedFunctions.jl to be free of world-age issues.</p><p>If the <code>rhss</code> is a scalar, the generated function is a function with a scalar output. Otherwise, if it's an <code>AbstractArray</code>, the output is two functions, one for out-of-place AbstractArray output and a second which is a mutating function. The outputted functions match the given argument order, i.e., f(u,p,args...) for the out-of-place and scalar functions and <code>f!(du,u,p,args..)</code> for the in-place version.</p><p>Special Keyword Arguments:</p><ul><li><code>parallel</code>: The kind of parallelism to use in the generated function. Defaults to <code>SerialForm()</code>, i.e. no parallelism. Note that the parallel forms are not exported and thus need to be chosen like <code>Symbolics.SerialForm()</code>. The choices are:<ul><li><code>SerialForm()</code>: Serial execution.</li><li><code>ShardedForm(cutoff, ncalls)</code>: splits the output function into sub-functions which contain at most <code>cutoff</code> number of output <code>rhss</code>. These sub-functions are called by the top-level function that <em>build</em>function returns.</li><li><code>MultithreadedForm()</code>: Multithreaded execution with a static split, evenly splitting the number of expressions per thread.</li></ul></li><li><code>conv</code>: The conversion function of symbolic types to Expr. By default, this uses the <code>toexpr</code> function.</li><li><code>checkbounds</code>: For whether to enable bounds checking inside the generated function. Defaults to false, meaning that <code>@inbounds</code> is applied.</li><li><code>linenumbers</code>: Determines whether the generated function expression retains the line numbers. Defaults to true.</li><li><code>convert_oop</code>: Determines whether the OOP version should try to convert the output to match the type of the first input. This is useful for cases like LabelledArrays or other array types that carry extra information. Defaults to true.</li><li><code>force_SA</code>: Forces the output of the OOP version to be a StaticArray. Defaults to <code>false</code>, and outputs a static array when the first argument is a static array.</li><li><code>skipzeros</code>: Whether to skip filling zeros in the in-place version if the filling function is 0.</li><li><code>fillzeros</code>: Whether to perform <code>fill(out,0)</code> before the calculations to ensure safety with <code>skipzeros</code>.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/build_function.jl#L196-L268">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="Symbolics._build_function-Tuple{Symbolics.CTarget, Array{<:Equation}, Vararg{Any}}" href="#Symbolics._build_function-Tuple{Symbolics.CTarget, Array{<:Equation}, Vararg{Any}}"><code>Symbolics._build_function</code></a> — <span class="docstring-category">Method</span></header><section><div><p>Build function target: <code>CTarget</code></p><pre><code class="language-julia hljs">function _build_function(target::CTarget, eqs::Array{<:Equation}, args...; conv = toexpr, expression = Val{true}, fname = :diffeqf, lhsname=:du,rhsnames=[Symbol("RHS$i") for i in 1:length(args)], - libpath=tempname(),compiler=:gcc)</code></pre><p>This builds an in-place C function. Only works on arrays of equations. If <code>expression == Val{false}</code>, then this builds a function in C, compiles it, and returns a lambda to that compiled function. These special keyword arguments control the compilation:</p><ul><li>libpath: the path to store the binary. Defaults to a temporary path.</li><li>compiler: which C compiler to use. Defaults to :gcc, which is currently the only available option.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/build_function.jl#L666-L685">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="Symbolics._build_function-Tuple{Symbolics.StanTarget, Array{<:Equation}, Any, Any, Any}" href="#Symbolics._build_function-Tuple{Symbolics.StanTarget, Array{<:Equation}, Any, Any, Any}"><code>Symbolics._build_function</code></a> — <span class="docstring-category">Method</span></header><section><div><p>Build function target: <code>StanTarget</code></p><pre><code class="language-julia hljs">function _build_function(target::StanTarget, eqs::Array{<:Equation}, vs, ps, iv; + libpath=tempname(),compiler=:gcc)</code></pre><p>This builds an in-place C function. Only works on arrays of equations. If <code>expression == Val{false}</code>, then this builds a function in C, compiles it, and returns a lambda to that compiled function. These special keyword arguments control the compilation:</p><ul><li>libpath: the path to store the binary. Defaults to a temporary path.</li><li>compiler: which C compiler to use. Defaults to :gcc, which is currently the only available option.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/build_function.jl#L666-L685">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="Symbolics._build_function-Tuple{Symbolics.StanTarget, Array{<:Equation}, Any, Any, Any}" href="#Symbolics._build_function-Tuple{Symbolics.StanTarget, Array{<:Equation}, Any, Any, Any}"><code>Symbolics._build_function</code></a> — <span class="docstring-category">Method</span></header><section><div><p>Build function target: <code>StanTarget</code></p><pre><code class="language-julia hljs">function _build_function(target::StanTarget, eqs::Array{<:Equation}, vs, ps, iv; conv = toexpr, expression = Val{true}, fname = :diffeqf, lhsname=:internal_var___du, - rhsnames=[:internal_var___u,:internal_var___p,:internal_var___t])</code></pre><p>This builds an in-place Stan function compatible with the Stan differential equation solvers. Unlike other build targets, this one requires (vs, ps, iv) as the function arguments. Only allowed on arrays of equations.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/build_function.jl#L813-L826">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="Symbolics._build_function-Tuple{Symbolics.MATLABTarget, Array{<:Equation}, Vararg{Any}}" href="#Symbolics._build_function-Tuple{Symbolics.MATLABTarget, Array{<:Equation}, Vararg{Any}}"><code>Symbolics._build_function</code></a> — <span class="docstring-category">Method</span></header><section><div><p>Build function target: <code>MATLABTarget</code></p><pre><code class="language-julia hljs">function _build_function(target::MATLABTarget, eqs::Array{<:Equation}, args...; + rhsnames=[:internal_var___u,:internal_var___p,:internal_var___t])</code></pre><p>This builds an in-place Stan function compatible with the Stan differential equation solvers. Unlike other build targets, this one requires (vs, ps, iv) as the function arguments. Only allowed on arrays of equations.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/build_function.jl#L813-L826">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="Symbolics._build_function-Tuple{Symbolics.MATLABTarget, Array{<:Equation}, Vararg{Any}}" href="#Symbolics._build_function-Tuple{Symbolics.MATLABTarget, Array{<:Equation}, Vararg{Any}}"><code>Symbolics._build_function</code></a> — <span class="docstring-category">Method</span></header><section><div><p>Build function target: <code>MATLABTarget</code></p><pre><code class="language-julia hljs">function _build_function(target::MATLABTarget, eqs::Array{<:Equation}, args...; conv = toexpr, expression = Val{true}, lhsname=:internal_var___du, - rhsnames=[:internal_var___u,:internal_var___p,:internal_var___t])</code></pre><p>This builds an out of place anonymous function @(t,rhsnames[1]) to be used in MATLAB. Compatible with the MATLAB differential equation solvers. Only allowed on expressions, and arrays of expressions.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/build_function.jl#L910-L923">source</a></section></article><h2 id="Limitations"><a class="docs-heading-anchor" href="#Limitations">Limitations</a><a id="Limitations-1"></a><a class="docs-heading-anchor-permalink" href="#Limitations" title="Permalink"></a></h2><p><code>build_function</code> </p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../arrays/">« Symbolic Arrays</a><a class="docs-footer-nextpage" href="../functions/">Function Registration and Tracing »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 12:13">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> + rhsnames=[:internal_var___u,:internal_var___p,:internal_var___t])</code></pre><p>This builds an out of place anonymous function @(t,rhsnames[1]) to be used in MATLAB. Compatible with the MATLAB differential equation solvers. Only allowed on expressions, and arrays of expressions.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/build_function.jl#L910-L923">source</a></section></article><h2 id="Limitations"><a class="docs-heading-anchor" href="#Limitations">Limitations</a><a id="Limitations-1"></a><a class="docs-heading-anchor-permalink" href="#Limitations" title="Permalink"></a></h2><p><code>build_function</code> </p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../arrays/">« Symbolic Arrays</a><a class="docs-footer-nextpage" href="../functions/">Function Registration and Tracing »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 13:45">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> diff --git a/previews/PR1079/manual/derivatives/index.html b/previews/PR1079/manual/derivatives/index.html index d5051be0c..d953f16cf 100644 --- a/previews/PR1079/manual/derivatives/index.html +++ b/previews/PR1079/manual/derivatives/index.html @@ -13,7 +13,7 @@ (D'~x(t)) ∘ (D'~y(t)) julia> D3 = Differential(x)^3 # 3rd order differential operator -(D'~x(t)) ∘ (D'~x(t)) ∘ (D'~x(t))</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/diff.jl#L4">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="Symbolics.expand_derivatives" href="#Symbolics.expand_derivatives"><code>Symbolics.expand_derivatives</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">expand_derivatives(O; ...) +(D'~x(t)) ∘ (D'~x(t)) ∘ (D'~x(t))</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/diff.jl#L4">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="Symbolics.expand_derivatives" href="#Symbolics.expand_derivatives"><code>Symbolics.expand_derivatives</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">expand_derivatives(O; ...) expand_derivatives(O, simplify; occurrences) </code></pre><p>TODO</p><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs"> julia> @variables x y z k; @@ -25,15 +25,15 @@ (::Differential) (generic function with 2 methods) julia> dfx=expand_derivatives(Dx(f)) -(k*((2abs(x - y)) / y - 2z)*IfElse.ifelse(signbit(x - y), -1, 1)) / y</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/diff.jl#L151">source</a></section></article><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>For symbolic differentiation, all registered functions in the symbolic expression need a registered derivative. For more information, see the <a href="../functions/#function_registration">function registration</a> page.</p></div></div><h2 id="High-Level-Differentiation-Functions"><a class="docs-heading-anchor" href="#High-Level-Differentiation-Functions">High-Level Differentiation Functions</a><a id="High-Level-Differentiation-Functions-1"></a><a class="docs-heading-anchor-permalink" href="#High-Level-Differentiation-Functions" title="Permalink"></a></h2><p>The following functions are not exported and thus must be accessed in a namespaced way, i.e. <code>Symbolics.jacobian</code>.</p><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="Symbolics.derivative" href="#Symbolics.derivative"><code>Symbolics.derivative</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">derivative(O, var; simplify) -</code></pre><p>A helper function for computing the derivative of the expression <code>O</code> with respect to <code>var</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/diff.jl#L422">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="Symbolics.jacobian" href="#Symbolics.jacobian"><code>Symbolics.jacobian</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">jacobian(ops, vars; simplify, scalarize) -</code></pre><p>A helper function for computing the Jacobian of an array of expressions with respect to an array of variable expressions.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/diff.jl#L446">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="Symbolics.sparsejacobian" href="#Symbolics.sparsejacobian"><code>Symbolics.sparsejacobian</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">sparsejacobian(ops, vars; simplify) -</code></pre><p>A helper function for computing the sparse Jacobian of an array of expressions with respect to an array of variable expressions.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/diff.jl#L466">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="Symbolics.sparsejacobian_vals" href="#Symbolics.sparsejacobian_vals"><code>Symbolics.sparsejacobian_vals</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">sparsejacobian_vals(ops, vars, I, J; simplify) -</code></pre><p>A helper function for computing the values of the sparse Jacobian of an array of expressions with respect to an array of variable expressions given the sparsity structure.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/diff.jl#L483">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="Symbolics.gradient" href="#Symbolics.gradient"><code>Symbolics.gradient</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">gradient(O, vars; simplify) -</code></pre><p>A helper function for computing the gradient of the expression <code>O</code> with respect to an array of variable expressions.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/diff.jl#L436">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="Symbolics.hessian" href="#Symbolics.hessian"><code>Symbolics.hessian</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">hessian(O, vars; simplify) -</code></pre><p>A helper function for computing the Hessian of the expression <code>O</code> with respect to an array of variable expressions.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/diff.jl#L606">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="Symbolics.sparsehessian" href="#Symbolics.sparsehessian"><code>Symbolics.sparsehessian</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">sparsehessian(op, vars; simplify, full) -</code></pre><p>A helper function for computing the sparse Hessian of an expression with respect to an array of variable expressions.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/diff.jl#L743">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="Symbolics.sparsehessian_vals" href="#Symbolics.sparsehessian_vals"><code>Symbolics.sparsehessian_vals</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">sparsehessian_vals(op, vars, I, J; simplify) -</code></pre><p>A helper function for computing the values of the sparse Hessian of an expression with respect to an array of variable expressions given the sparsity structure.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/diff.jl#L767">source</a></section></article><h2 id="Adding-Analytical-Derivatives"><a class="docs-heading-anchor" href="#Adding-Analytical-Derivatives">Adding Analytical Derivatives</a><a id="Adding-Analytical-Derivatives-1"></a><a class="docs-heading-anchor-permalink" href="#Adding-Analytical-Derivatives" title="Permalink"></a></h2><p>There are many derivatives pre-defined by <a href="https://github.com/JuliaDiff/DiffRules.jl">DiffRules.jl</a>. For example,</p><pre><code class="language-julia hljs">using Symbolics +(k*((2abs(x - y)) / y - 2z)*IfElse.ifelse(signbit(x - y), -1, 1)) / y</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/diff.jl#L151">source</a></section></article><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>For symbolic differentiation, all registered functions in the symbolic expression need a registered derivative. For more information, see the <a href="../functions/#function_registration">function registration</a> page.</p></div></div><h2 id="High-Level-Differentiation-Functions"><a class="docs-heading-anchor" href="#High-Level-Differentiation-Functions">High-Level Differentiation Functions</a><a id="High-Level-Differentiation-Functions-1"></a><a class="docs-heading-anchor-permalink" href="#High-Level-Differentiation-Functions" title="Permalink"></a></h2><p>The following functions are not exported and thus must be accessed in a namespaced way, i.e. <code>Symbolics.jacobian</code>.</p><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="Symbolics.derivative" href="#Symbolics.derivative"><code>Symbolics.derivative</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">derivative(O, var; simplify) +</code></pre><p>A helper function for computing the derivative of the expression <code>O</code> with respect to <code>var</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/diff.jl#L422">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="Symbolics.jacobian" href="#Symbolics.jacobian"><code>Symbolics.jacobian</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">jacobian(ops, vars; simplify, scalarize) +</code></pre><p>A helper function for computing the Jacobian of an array of expressions with respect to an array of variable expressions.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/diff.jl#L446">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="Symbolics.sparsejacobian" href="#Symbolics.sparsejacobian"><code>Symbolics.sparsejacobian</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">sparsejacobian(ops, vars; simplify) +</code></pre><p>A helper function for computing the sparse Jacobian of an array of expressions with respect to an array of variable expressions.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/diff.jl#L466">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="Symbolics.sparsejacobian_vals" href="#Symbolics.sparsejacobian_vals"><code>Symbolics.sparsejacobian_vals</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">sparsejacobian_vals(ops, vars, I, J; simplify) +</code></pre><p>A helper function for computing the values of the sparse Jacobian of an array of expressions with respect to an array of variable expressions given the sparsity structure.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/diff.jl#L483">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="Symbolics.gradient" href="#Symbolics.gradient"><code>Symbolics.gradient</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">gradient(O, vars; simplify) +</code></pre><p>A helper function for computing the gradient of the expression <code>O</code> with respect to an array of variable expressions.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/diff.jl#L436">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="Symbolics.hessian" href="#Symbolics.hessian"><code>Symbolics.hessian</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">hessian(O, vars; simplify) +</code></pre><p>A helper function for computing the Hessian of the expression <code>O</code> with respect to an array of variable expressions.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/diff.jl#L606">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="Symbolics.sparsehessian" href="#Symbolics.sparsehessian"><code>Symbolics.sparsehessian</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">sparsehessian(op, vars; simplify, full) +</code></pre><p>A helper function for computing the sparse Hessian of an expression with respect to an array of variable expressions.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/diff.jl#L743">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="Symbolics.sparsehessian_vals" href="#Symbolics.sparsehessian_vals"><code>Symbolics.sparsehessian_vals</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">sparsehessian_vals(op, vars, I, J; simplify) +</code></pre><p>A helper function for computing the values of the sparse Hessian of an expression with respect to an array of variable expressions given the sparsity structure.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/diff.jl#L767">source</a></section></article><h2 id="Adding-Analytical-Derivatives"><a class="docs-heading-anchor" href="#Adding-Analytical-Derivatives">Adding Analytical Derivatives</a><a id="Adding-Analytical-Derivatives-1"></a><a class="docs-heading-anchor-permalink" href="#Adding-Analytical-Derivatives" title="Permalink"></a></h2><p>There are many derivatives pre-defined by <a href="https://github.com/JuliaDiff/DiffRules.jl">DiffRules.jl</a>. For example,</p><pre><code class="language-julia hljs">using Symbolics @variables x y z f(x,y,z) = x^2 + sin(x+y) - z</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">f (generic function with 1 method)</code></pre><p><code>f</code> automatically has the derivatives defined via the tracing mechanism. It will do this by directly building the internals of your function and differentiating that.</p><p>However, often you may want to define your own derivatives so that way automatic Jacobian etc. calculations can utilize this information. This can allow for more succinct versions of the derivatives to be calculated to scale to larger systems. You can define derivatives for your function via the dispatch:</p><pre><code class="language-julia hljs"># `N` arguments are accepted by the relevant method of `my_function` -Symbolics.derivative(::typeof(my_function), args::NTuple{N,Any}, ::Val{i})</code></pre><p>where <code>i</code> means that it's the derivative with respect to the <code>i</code>th argument. <code>args</code> is the array of arguments, so, for example, if your function is <code>f(x,t)</code>, then <code>args = [x,t]</code>. You should return an <code>Term</code> for the derivative of your function.</p><p>For example, <code>sin(t)</code>'s derivative (by <code>t</code>) is given by the following:</p><pre><code class="language-julia hljs">Symbolics.derivative(::typeof(sin), args::NTuple{1,Any}, ::Val{1}) = cos(args[1])</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../expression_manipulation/">« Expression Manipulation</a><a class="docs-footer-nextpage" href="../groebner/">Groebner bases »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 12:13">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> +Symbolics.derivative(::typeof(my_function), args::NTuple{N,Any}, ::Val{i})</code></pre><p>where <code>i</code> means that it's the derivative with respect to the <code>i</code>th argument. <code>args</code> is the array of arguments, so, for example, if your function is <code>f(x,t)</code>, then <code>args = [x,t]</code>. You should return an <code>Term</code> for the derivative of your function.</p><p>For example, <code>sin(t)</code>'s derivative (by <code>t</code>) is given by the following:</p><pre><code class="language-julia hljs">Symbolics.derivative(::typeof(sin), args::NTuple{1,Any}, ::Val{1}) = cos(args[1])</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../expression_manipulation/">« Expression Manipulation</a><a class="docs-footer-nextpage" href="../groebner/">Groebner bases »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 13:45">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> diff --git a/previews/PR1079/manual/expression_manipulation/index.html b/previews/PR1079/manual/expression_manipulation/index.html index cfa8ac801..b4b201c66 100644 --- a/previews/PR1079/manual/expression_manipulation/index.html +++ b/previews/PR1079/manual/expression_manipulation/index.html @@ -8,7 +8,7 @@ julia> ex = x + y + sin(z) (x + y) + sin(z(t)) julia> substitute(ex, Dict([x => z, sin(z) => z^2])) -(z(t) + y) + (z(t) ^ 2)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/Symbolics.jl#L55-L72">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="SymbolicUtils.simplify" href="#SymbolicUtils.simplify"><code>SymbolicUtils.simplify</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">simplify(x; expand=false, +(z(t) + y) + (z(t) ^ 2)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/Symbolics.jl#L55-L72">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="SymbolicUtils.simplify" href="#SymbolicUtils.simplify"><code>SymbolicUtils.simplify</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">simplify(x; expand=false, threaded=false, thread_subtree_cutoff=100, rewriter=nothing)</code></pre><p>Simplify an expression (<code>x</code>) by applying <code>rewriter</code> until there are no changes. <code>expand=true</code> applies <a href="/api/#expand"><code>expand</code></a> in the beginning of each fixpoint iteration.</p><p>By default, simplify will assume denominators are not zero and allow cancellation in fractions. Pass <code>simplify_fractions=false</code> to prevent this.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/SymbolicUtils.jl/blob/v1.5.0/src/simplify.jl#L2-L15">source</a></section></article><p>Documentation for <code>rewriter</code> can be found <a href="https://symbolicutils.juliasymbolics.org/rewrite/">here</a>, using the <code>@rule</code> macro or the <code>@acrule</code> macro from SymbolicUtils.jl.</p><h2 id="Additional-Manipulation-Functions"><a class="docs-heading-anchor" href="#Additional-Manipulation-Functions">Additional Manipulation Functions</a><a id="Additional-Manipulation-Functions-1"></a><a class="docs-heading-anchor-permalink" href="#Additional-Manipulation-Functions" title="Permalink"></a></h2><p>Other additional manipulation functions are given below.</p><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="Symbolics.get_variables" href="#Symbolics.get_variables"><code>Symbolics.get_variables</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">get_variables(O) -> Vector{BasicSymbolic}</code></pre><p>Returns the variables in the expression. Note that the returned variables are not wrapped in the <code>Num</code> type.</p><p><strong>Examples</strong></p><pre><code class="language-julia hljs">julia> @variables t x y z(t) @@ -25,7 +25,7 @@ 3-element Vector{Any}: x y - z(t)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/utils.jl#L22-L46">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="Symbolics.tosymbol" href="#Symbolics.tosymbol"><code>Symbolics.tosymbol</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">tosymbol(x::Union{Num,Symbolic}; states=nothing, escape=true) -> Symbol</code></pre><p>Convert <code>x</code> to a symbol. <code>states</code> are the states of a system, and <code>escape</code> means if the target has escapes like <code>val"y(t)"</code>. If <code>escape</code> is false, then it will only output <code>y</code> instead of <code>y(t)</code>.</p><p><strong>Examples</strong></p><pre><code class="language-julia hljs">julia> @variables t z(t) + z(t)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/utils.jl#L22-L46">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="Symbolics.tosymbol" href="#Symbolics.tosymbol"><code>Symbolics.tosymbol</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">tosymbol(x::Union{Num,Symbolic}; states=nothing, escape=true) -> Symbol</code></pre><p>Convert <code>x</code> to a symbol. <code>states</code> are the states of a system, and <code>escape</code> means if the target has escapes like <code>val"y(t)"</code>. If <code>escape</code> is false, then it will only output <code>y</code> instead of <code>y(t)</code>.</p><p><strong>Examples</strong></p><pre><code class="language-julia hljs">julia> @variables t z(t) 2-element Vector{Num}: t z(t) @@ -34,13 +34,13 @@ Symbol("z(t)") julia> Symbolics.tosymbol(z; escape=false) -:z</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/utils.jl#L135-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="Symbolics.diff2term" href="#Symbolics.diff2term"><code>Symbolics.diff2term</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">diff2term(x) -> Symbolic</code></pre><p>Convert a differential variable to a <code>Term</code>. Note that it only takes a <code>Term</code> not a <code>Num</code>.</p><pre><code class="language-julia hljs">julia> @variables x t u(x, t) z(t)[1:2]; Dt = Differential(t); Dx = Differential(x); +:z</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/utils.jl#L135-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="Symbolics.diff2term" href="#Symbolics.diff2term"><code>Symbolics.diff2term</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">diff2term(x) -> Symbolic</code></pre><p>Convert a differential variable to a <code>Term</code>. Note that it only takes a <code>Term</code> not a <code>Num</code>.</p><pre><code class="language-julia hljs">julia> @variables x t u(x, t) z(t)[1:2]; Dt = Differential(t); Dx = Differential(x); julia> Symbolics.diff2term(Symbolics.value(Dx(Dt(u)))) uˍtx(x, t) julia> Symbolics.diff2term(Symbolics.value(Dt(z[1]))) -var"z(t)[1]ˍt"</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/utils.jl#L85-L100">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="Symbolics.solve_for" href="#Symbolics.solve_for"><code>Symbolics.solve_for</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">solve_for(eq, var; simplify, check) -> Any +var"z(t)[1]ˍt"</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/utils.jl#L85-L100">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="Symbolics.solve_for" href="#Symbolics.solve_for"><code>Symbolics.solve_for</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">solve_for(eq, var; simplify, check) -> Any </code></pre><p>Solve equation(s) <code>eqs</code> for a set of variables <code>vars</code>.</p><p>Assumes <code>length(eqs) == length(vars)</code></p><p>Currently only works if all equations are linear. <code>check</code> if the expr is linear w.r.t <code>vars</code>.</p><p><strong>Examples</strong></p><pre><code class="language-julia hljs">julia> @variables x y 2-element Vector{Num}: x @@ -52,7 +52,7 @@ julia> Symbolics.solve_for([x + y ~ 0, x - y ~ 2], [x, y]) 2-element Vector{Float64}: 1.0 - -1.0</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/linear_algebra.jl#L70">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="Symbolics.degree" href="#Symbolics.degree"><code>Symbolics.degree</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">degree(p, sym=nothing)</code></pre><p>Extract the degree of <code>p</code> with respect to <code>sym</code>.</p><p><strong>Examples</strong></p><pre><code class="language-julia hljs">julia> @variables x; + -1.0</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/linear_algebra.jl#L70">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="Symbolics.degree" href="#Symbolics.degree"><code>Symbolics.degree</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">degree(p, sym=nothing)</code></pre><p>Extract the degree of <code>p</code> with respect to <code>sym</code>.</p><p><strong>Examples</strong></p><pre><code class="language-julia hljs">julia> @variables x; julia> Symbolics.degree(x^0) 0 @@ -61,7 +61,7 @@ 1 julia> Symbolics.degree(x^2) -2</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/utils.jl#L232-L251">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="Symbolics.coeff" href="#Symbolics.coeff"><code>Symbolics.coeff</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">coeff(p, sym=nothing)</code></pre><p>Extract the coefficient of <code>p</code> with respect to <code>sym</code>. Note that <code>p</code> might need to be expanded and/or simplified with <code>expand</code> and/or <code>simplify</code>.</p><p><strong>Examples</strong></p><pre><code class="language-julia hljs">julia> @variables a x y; +2</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/utils.jl#L232-L251">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="Symbolics.coeff" href="#Symbolics.coeff"><code>Symbolics.coeff</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">coeff(p, sym=nothing)</code></pre><p>Extract the coefficient of <code>p</code> with respect to <code>sym</code>. Note that <code>p</code> might need to be expanded and/or simplified with <code>expand</code> and/or <code>simplify</code>.</p><p><strong>Examples</strong></p><pre><code class="language-julia hljs">julia> @variables a x y; julia> Symbolics.coeff(2a, x) 0 @@ -70,4 +70,4 @@ 2 julia> Symbolics.coeff(x^2 + y, x^2) -1</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/utils.jl#L285-L305">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../variables/">« Variable and Equation Types</a><a class="docs-footer-nextpage" href="../derivatives/">Derivatives and Differentials »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 12:13">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> +1</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/utils.jl#L285-L305">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../variables/">« Variable and Equation Types</a><a class="docs-footer-nextpage" href="../derivatives/">Derivatives and Differentials »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 13:45">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> diff --git a/previews/PR1079/manual/faq/index.html b/previews/PR1079/manual/faq/index.html index 6a7c26a91..f91d8ea05 100644 --- a/previews/PR1079/manual/faq/index.html +++ b/previews/PR1079/manual/faq/index.html @@ -16,4 +16,4 @@ x in [x] catch e e -end</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">TypeError(:if, "", Bool, x == x)</code></pre><pre><code class="language-julia hljs">x in Set([x])</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">true</code></pre><pre><code class="language-julia hljs">any(isequal(x), [x])</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">true</code></pre><p>If <code>==</code> is used instead, you will receive <code>TypeError: non-boolean (Num) used in boolean context</code>. What this error is telling you is that the symbolic <code>x == y</code> expression is being used where a <code>Bool</code> is required, such as <code>if x == y</code>, and since the symbolic expression is held lazily this will error because the appropriate branch cannot be selected (since <code>x == y</code> is unknown for arbitrary symbolic values!). This is why the check <code>isequal(x,y)</code> is required, since this is a non-lazy check of whether the symbol <code>x</code> is always equal to the symbol <code>y</code>, rather than an expression of whether <code>x</code> and <code>y</code> currently have the same value.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../types/">« Supported types and dispatch in Symbolics</a><a class="docs-footer-nextpage" href="../../comparison/">Comparison Against SymPy »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 12:13">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> +end</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">TypeError(:if, "", Bool, x == x)</code></pre><pre><code class="language-julia hljs">x in Set([x])</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">true</code></pre><pre><code class="language-julia hljs">any(isequal(x), [x])</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">true</code></pre><p>If <code>==</code> is used instead, you will receive <code>TypeError: non-boolean (Num) used in boolean context</code>. What this error is telling you is that the symbolic <code>x == y</code> expression is being used where a <code>Bool</code> is required, such as <code>if x == y</code>, and since the symbolic expression is held lazily this will error because the appropriate branch cannot be selected (since <code>x == y</code> is unknown for arbitrary symbolic values!). This is why the check <code>isequal(x,y)</code> is required, since this is a non-lazy check of whether the symbol <code>x</code> is always equal to the symbol <code>y</code>, rather than an expression of whether <code>x</code> and <code>y</code> currently have the same value.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../types/">« Supported types and dispatch in Symbolics</a><a class="docs-footer-nextpage" href="../../comparison/">Comparison Against SymPy »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 13:45">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> diff --git a/previews/PR1079/manual/functions/index.html b/previews/PR1079/manual/functions/index.html index 9c66f6855..2ed8256c2 100644 --- a/previews/PR1079/manual/functions/index.html +++ b/previews/PR1079/manual/functions/index.html @@ -31,11 +31,11 @@ end</code></pre><p>is the partial derivative of the Julia <code>min(x,y)</code> function with respect to <code>x</code>.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>Downstream symbolic derivative functionality only work if every partial derivative that is required in the derivative expression is defined. Note that you only need to define the partial derivatives which are actually computed.</p></div></div><h2 id="Registration-API"><a class="docs-heading-anchor" href="#Registration-API">Registration API</a><a id="Registration-API-1"></a><a class="docs-heading-anchor-permalink" href="#Registration-API" title="Permalink"></a></h2><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="Symbolics.@register_symbolic" href="#Symbolics.@register_symbolic"><code>Symbolics.@register_symbolic</code></a> — <span class="docstring-category">Macro</span></header><section><div><pre><code class="language-julia hljs">@register_symbolic(expr, define_promotion = true, Ts = [Real])</code></pre><p>Overload appropriate methods so that Symbolics can stop tracing into the registered function. If <code>define_promotion</code> is true, then a promotion method in the form of</p><pre><code class="language-julia hljs">SymbolicUtils.promote_symtype(::typeof(f_registered), args...) = Real # or the annotated return type</code></pre><p>is defined for the register function. Note that when defining multiple register overloads for one function, all the rest of the registers must set <code>define_promotion</code> to <code>false</code> except for the first one, to avoid method overwriting.</p><p><strong>Examples</strong></p><pre><code class="language-julia hljs">@register_symbolic foo(x, y) @register_symbolic foo(x, y::Bool) false # do not overload a duplicate promotion rule @register_symbolic goo(x, y::Int) # `y` is not overloaded to take symbolic objects -@register_symbolic hoo(x, y)::Int # `hoo` returns `Int`</code></pre><p>See <code>@register_array_symbolic</code> to register functions which return arrays.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/register.jl#L3-L25">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="Symbolics.@register_array_symbolic" href="#Symbolics.@register_array_symbolic"><code>Symbolics.@register_array_symbolic</code></a> — <span class="docstring-category">Macro</span></header><section><div><pre><code class="language-julia hljs">@register_array_symbolic(expr)</code></pre><p>Example:</p><pre><code class="language-julia hljs"># Let's say vandermonde takes an n-vector and returns an n x n matrix +@register_symbolic hoo(x, y)::Int # `hoo` returns `Int`</code></pre><p>See <code>@register_array_symbolic</code> to register functions which return arrays.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/register.jl#L3-L25">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="Symbolics.@register_array_symbolic" href="#Symbolics.@register_array_symbolic"><code>Symbolics.@register_array_symbolic</code></a> — <span class="docstring-category">Macro</span></header><section><div><pre><code class="language-julia hljs">@register_array_symbolic(expr)</code></pre><p>Example:</p><pre><code class="language-julia hljs"># Let's say vandermonde takes an n-vector and returns an n x n matrix @register_array_symbolic vandermonde(x::AbstractVector) begin size=(length(x), length(x)) eltype=eltype(x) # optional, will default to the promoted eltypes of x end</code></pre><p>You can also register calls on callable structs:</p><pre><code class="language-julia hljs">@register_array_symbolic (c::Conv)(x::AbstractMatrix) begin size=size(x) .- size(c.kernel) .+ 1 eltype=promote_type(eltype(x), eltype(c)) -end</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/register.jl#L114-L135">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../build_function/">« Function Building and Compilation (build_function)</a><a class="docs-footer-nextpage" href="../parsing/">Parsing Julia Expressions to Symbolic Expressions »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 12:13">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> +end</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/register.jl#L114-L135">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../build_function/">« Function Building and Compilation (build_function)</a><a class="docs-footer-nextpage" href="../parsing/">Parsing Julia Expressions to Symbolic Expressions »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 13:45">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> diff --git a/previews/PR1079/manual/groebner/index.html b/previews/PR1079/manual/groebner/index.html index e4705a387..86a190e70 100644 --- a/previews/PR1079/manual/groebner/index.html +++ b/previews/PR1079/manual/groebner/index.html @@ -1,2 +1,2 @@ <!DOCTYPE html> -<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Groebner bases · Symbolics.jl</title><meta name="title" content="Groebner bases · Symbolics.jl"/><meta property="og:title" content="Groebner bases · Symbolics.jl"/><meta property="twitter:title" content="Groebner bases · Symbolics.jl"/><meta name="description" content="Documentation for Symbolics.jl."/><meta property="og:description" content="Documentation for Symbolics.jl."/><meta property="twitter:description" content="Documentation for Symbolics.jl."/><meta property="og:url" 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and dispatch in Symbolics</a></li><li><a class="tocitem" href="../faq/">Frequently Asked Questions</a></li></ul></li><li><a class="tocitem" href="../../comparison/">Comparison Against SymPy</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Manual</a></li><li class="is-active"><a href>Groebner bases</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Groebner bases</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/JuliaSymbolics/Symbolics.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/master/docs/src/manual/groebner.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Groebner-bases"><a class="docs-heading-anchor" href="#Groebner-bases">Groebner bases</a><a id="Groebner-bases-1"></a><a class="docs-heading-anchor-permalink" href="#Groebner-bases" title="Permalink"></a></h1><p>Groebner bases use the implementation of the F4 algorithm from Groebner.jl package as its backend. We refer to the <a href="https://sumiya11.github.io/Groebner.jl/">documentation of Groebner.jl</a>, which lists some implementations details and possible use-cases of Groebner bases.</p><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="Symbolics.groebner_basis" href="#Symbolics.groebner_basis"><code>Symbolics.groebner_basis</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">groebner_basis(polynomials)</code></pre><p>Computes a Groebner basis of the ideal generated by the given <code>polynomials</code>.</p><p>This function requires a Groebner bases backend (such as Groebner.jl) to be loaded.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/groebner_basis.jl#L5-L11">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../derivatives/">« Derivatives and Differentials</a><a class="docs-footer-nextpage" href="../arrays/">Symbolic Arrays »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 12:13">Tuesday 27 February 2024</span>. 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class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Manual</a></li><li class="is-active"><a href>Groebner bases</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Groebner bases</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/JuliaSymbolics/Symbolics.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/master/docs/src/manual/groebner.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Groebner-bases"><a class="docs-heading-anchor" href="#Groebner-bases">Groebner bases</a><a id="Groebner-bases-1"></a><a class="docs-heading-anchor-permalink" href="#Groebner-bases" title="Permalink"></a></h1><p>Groebner bases use the implementation of the F4 algorithm from Groebner.jl package as its backend. We refer to the <a href="https://sumiya11.github.io/Groebner.jl/">documentation of Groebner.jl</a>, which lists some implementations details and possible use-cases of Groebner bases.</p><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="Symbolics.groebner_basis" href="#Symbolics.groebner_basis"><code>Symbolics.groebner_basis</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">groebner_basis(polynomials)</code></pre><p>Computes a Groebner basis of the ideal generated by the given <code>polynomials</code>.</p><p>This function requires a Groebner bases backend (such as Groebner.jl) to be loaded.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/groebner_basis.jl#L5-L11">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../derivatives/">« Derivatives and Differentials</a><a class="docs-footer-nextpage" href="../arrays/">Symbolic Arrays »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 13:45">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> diff --git a/previews/PR1079/manual/io/index.html b/previews/PR1079/manual/io/index.html index ae8d44b68..4c482de93 100644 --- a/previews/PR1079/manual/io/index.html +++ b/previews/PR1079/manual/io/index.html @@ -6,4 +6,4 @@ end ex1, ex2 = build_function(f(u),u) write("function.jl", string(ex2))</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">898</code></pre><p>Now we can do something like:</p><pre><code class="language-julia hljs">g = include("function.jl")</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">#1 (generic function with 1 method)</code></pre><p>and that will load the function back in. Note that this can be done to save the transformation results of Symbolics.jl so that they can be stored and used in a precompiled Julia package.</p><h2 id="Latexification"><a class="docs-heading-anchor" href="#Latexification">Latexification</a><a id="Latexification-1"></a><a class="docs-heading-anchor-permalink" href="#Latexification" title="Permalink"></a></h2><p>Symbolics.jl's expressions support Latexify.jl, and thus</p><pre><code class="language-julia hljs">using Latexify -latexify(ex)</code></pre><p>will produce LaTeX output from Symbolics models and expressions. This works on basics like <code>Term</code> all the way to higher primitives like <code>ODESystem</code> and <code>ReactionSystem</code>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../parsing/">« Parsing Julia Expressions to Symbolic Expressions</a><a class="docs-footer-nextpage" href="../sparsity_detection/">Structure and Sparsity Detection »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 12:13">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> +latexify(ex)</code></pre><p>will produce LaTeX output from Symbolics models and expressions. This works on basics like <code>Term</code> all the way to higher primitives like <code>ODESystem</code> and <code>ReactionSystem</code>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../parsing/">« Parsing Julia Expressions to Symbolic Expressions</a><a class="docs-footer-nextpage" href="../sparsity_detection/">Structure and Sparsity Detection »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 13:45">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> diff --git a/previews/PR1079/manual/parsing/index.html b/previews/PR1079/manual/parsing/index.html index 6a7460e2c..96e4637e2 100644 --- a/previews/PR1079/manual/parsing/index.html +++ b/previews/PR1079/manual/parsing/index.html @@ -15,4 +15,4 @@ z ~ 2] all(isequal.(eqs,ex)) # true</code></pre><p><strong>Limitations</strong></p><p><strong>Symbolic-ness Tied to Environment Definitions</strong></p><p>The parsing to a symbolic expression has to be able to recognize the difference between functions, numbers, and globals defined within one's Julia environment and those that are to be made symbolic. The way this functionality handles this problem is that it does not define anything as symbolic that is already defined in the chosen <code>mod</code> module. For example, <code>f(x,y)</code> will have <code>f</code> as non-symbolic if the function <code>f</code> (named <code>f</code>) is defined in <code>mod</code>, i.e. if <code>isdefined(mod,:f)</code> is true. When the symbol is defined, it will be replaced by its value. Notably, this means that the parsing behavior changes depending on the environment that it is applied.</p><p>For example:</p><pre><code class="language-julia hljs">parse_expr_to_symbolic(:(x - y),@__MODULE__) # x - y x = 2.0 -parse_expr_to_symbolic(:(x - y),@__MODULE__) # 2.0 - y</code></pre><p>This is required to detect that standard functions like <code>-</code> are functions instead of symbolic symbols. For safety, one should create anonymous modules or other sub-environments to ensure no stray variables are defined.</p><p><strong>Metadata is Blank</strong></p><p>Because all the variables defined by the expressions are not defined with the standard <code>@variables</code>, there is no metadata that is or can be associated with any of the generated variables. Instead, they all have blank metadata, but are defined in the <code>Real</code> domain. Thus, the variables which come out of this parsing may not evaluate as equal to a symbolic variable defined elsewhere.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/parsing.jl#L1-L66">source</a></section></article><div class="admonition is-warning"><header class="admonition-header">Missing docstring.</header><div class="admonition-body"><p>Missing docstring for <code>@parse_expr_to_symbolic</code>. Check Documenter's build log for details.</p></div></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../functions/">« Function Registration and Tracing</a><a class="docs-footer-nextpage" href="../io/">I/O, Saving, and Latex »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 12:13">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> +parse_expr_to_symbolic(:(x - y),@__MODULE__) # 2.0 - y</code></pre><p>This is required to detect that standard functions like <code>-</code> are functions instead of symbolic symbols. For safety, one should create anonymous modules or other sub-environments to ensure no stray variables are defined.</p><p><strong>Metadata is Blank</strong></p><p>Because all the variables defined by the expressions are not defined with the standard <code>@variables</code>, there is no metadata that is or can be associated with any of the generated variables. Instead, they all have blank metadata, but are defined in the <code>Real</code> domain. Thus, the variables which come out of this parsing may not evaluate as equal to a symbolic variable defined elsewhere.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/parsing.jl#L1-L66">source</a></section></article><div class="admonition is-warning"><header class="admonition-header">Missing docstring.</header><div class="admonition-body"><p>Missing docstring for <code>@parse_expr_to_symbolic</code>. Check Documenter's build log for details.</p></div></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../functions/">« Function Registration and Tracing</a><a class="docs-footer-nextpage" href="../io/">I/O, Saving, and Latex »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 13:45">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> diff --git a/previews/PR1079/manual/sparsity_detection/index.html b/previews/PR1079/manual/sparsity_detection/index.html index af5ee5e29..ff2c139f9 100644 --- a/previews/PR1079/manual/sparsity_detection/index.html +++ b/previews/PR1079/manual/sparsity_detection/index.html @@ -17,7 +17,7 @@ 3×2 SparseArrays.SparseMatrixCSC{Bool, Int64} with 4 stored entries: 1 ⋅ ⋅ 1 - 1 1</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/diff.jl#L501">source</a></section><section><div><pre><code class="language-julia hljs">jacobian_sparsity( + 1 1</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/diff.jl#L501">source</a></section><section><div><pre><code class="language-julia hljs">jacobian_sparsity( f!::Function, output::AbstractArray, input::AbstractArray, @@ -36,7 +36,7 @@ 3×2 SparseArrays.SparseMatrixCSC{Bool, Int64} with 4 stored entries: ⋅ 1 1 ⋅ - 1 1</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/diff.jl#L556">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="Symbolics.hessian_sparsity" href="#Symbolics.hessian_sparsity"><code>Symbolics.hessian_sparsity</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">hessian_sparsity( + 1 1</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/diff.jl#L556">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="Symbolics.hessian_sparsity" href="#Symbolics.hessian_sparsity"><code>Symbolics.hessian_sparsity</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">hessian_sparsity( expr, vars::AbstractVector; full @@ -50,7 +50,7 @@ julia> Symbolics.hessian_sparsity(expr, vars) 2×2 SparseArrays.SparseMatrixCSC{Bool, Int64} with 3 stored entries: 1 1 - 1 ⋅</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/diff.jl#L660">source</a></section><section><div><pre><code class="language-julia hljs">hessian_sparsity( + 1 ⋅</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/diff.jl#L660">source</a></section><section><div><pre><code class="language-julia hljs">hessian_sparsity( f::Function, input::AbstractVector, args...; @@ -66,6 +66,6 @@ julia> Symbolics.hessian_sparsity(f, input) 2×2 SparseArrays.SparseMatrixCSC{Bool, Int64} with 3 stored entries: ⋅ 1 - 1 1</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/diff.jl#L696">source</a></section></article><h2 id="Structure-Detection"><a class="docs-heading-anchor" href="#Structure-Detection">Structure Detection</a><a id="Structure-Detection-1"></a><a class="docs-heading-anchor-permalink" href="#Structure-Detection" title="Permalink"></a></h2><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="Symbolics.islinear" href="#Symbolics.islinear"><code>Symbolics.islinear</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">islinear(ex, u) -</code></pre><p>Check if an expression is linear with respect to a list of variable expressions.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/diff.jl#L734">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="Symbolics.isaffine" href="#Symbolics.isaffine"><code>Symbolics.isaffine</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">isaffine(ex, u) -</code></pre><p>Check if an expression is affine with respect to a list of variable expressions.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/diff.jl#L725">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../io/">« I/O, Saving, and Latex</a><a class="docs-footer-nextpage" href="../types/">Supported types and dispatch in Symbolics »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 12:13">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> + 1 1</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/diff.jl#L696">source</a></section></article><h2 id="Structure-Detection"><a class="docs-heading-anchor" href="#Structure-Detection">Structure Detection</a><a id="Structure-Detection-1"></a><a class="docs-heading-anchor-permalink" href="#Structure-Detection" title="Permalink"></a></h2><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="Symbolics.islinear" href="#Symbolics.islinear"><code>Symbolics.islinear</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">islinear(ex, u) +</code></pre><p>Check if an expression is linear with respect to a list of variable expressions.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/diff.jl#L734">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="Symbolics.isaffine" href="#Symbolics.isaffine"><code>Symbolics.isaffine</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">isaffine(ex, u) +</code></pre><p>Check if an expression is affine with respect to a list of variable expressions.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/diff.jl#L725">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../io/">« I/O, Saving, and Latex</a><a class="docs-footer-nextpage" href="../types/">Supported types and dispatch in Symbolics »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 13:45">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> diff --git a/previews/PR1079/manual/types/index.html b/previews/PR1079/manual/types/index.html index 7afbdb032..5627dc2ba 100644 --- a/previews/PR1079/manual/types/index.html +++ b/previews/PR1079/manual/types/index.html @@ -5,4 +5,4 @@ z X[1:10,1:10] Z[1:10] - s</code></pre><pre><code class="language-julia hljs">typeof(x)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Num</code></pre><pre><code class="language-julia hljs">typeof(z)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Complex{Num}</code></pre><pre><code class="language-julia hljs">typeof(X)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Symbolics.Arr{Num, 2}</code></pre><pre><code class="language-julia hljs">typeof(Z)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Symbolics.Arr{Complex{Num}, 1}</code></pre><pre><code class="language-julia hljs">typeof(s)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">SymbolicUtils.BasicSymbolic{String}</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../sparsity_detection/">« Structure and Sparsity Detection</a><a class="docs-footer-nextpage" href="../faq/">Frequently Asked Questions »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 12:13">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> + s</code></pre><pre><code class="language-julia hljs">typeof(x)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Num</code></pre><pre><code class="language-julia hljs">typeof(z)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Complex{Num}</code></pre><pre><code class="language-julia hljs">typeof(X)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Symbolics.Arr{Num, 2}</code></pre><pre><code class="language-julia hljs">typeof(Z)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Symbolics.Arr{Complex{Num}, 1}</code></pre><pre><code class="language-julia hljs">typeof(s)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">SymbolicUtils.BasicSymbolic{String}</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../sparsity_detection/">« Structure and Sparsity Detection</a><a class="docs-footer-nextpage" href="../faq/">Frequently Asked Questions »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 13:45">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> diff --git a/previews/PR1079/manual/variables/index.html b/previews/PR1079/manual/variables/index.html index 8b5f49503..ed695e28a 100644 --- a/previews/PR1079/manual/variables/index.html +++ b/previews/PR1079/manual/variables/index.html @@ -28,15 +28,15 @@ (value_c(t))[1:3] julia> (t, a, b, c) -(t, :runtime_symbol_value, :value_b, :value_c)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/variable.jl#L313-L375">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="Symbolics.variable" href="#Symbolics.variable"><code>Symbolics.variable</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">variable(name::Symbol, idx::Integer...; T=Real)</code></pre><p>Create a variable with the given name along with subscripted indices with the <code>symtype=T</code>. When <code>T=FnType</code>, it creates a symbolic function.</p><pre><code class="language-julia-repl hljs">julia> Symbolics.variable(:x, 4, 2, 0) +(t, :runtime_symbol_value, :value_b, :value_c)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/variable.jl#L313-L375">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="Symbolics.variable" href="#Symbolics.variable"><code>Symbolics.variable</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">variable(name::Symbol, idx::Integer...; T=Real)</code></pre><p>Create a variable with the given name along with subscripted indices with the <code>symtype=T</code>. When <code>T=FnType</code>, it creates a symbolic function.</p><pre><code class="language-julia-repl hljs">julia> Symbolics.variable(:x, 4, 2, 0) x₄ˏ₂ˏ₀ julia> Symbolics.variable(:x, 4, 2, 0, T=Symbolics.FnType) -x₄ˏ₂ˏ₀⋆</code></pre><p>Also see <code>variables</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/variable.jl#L456-L471">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="Symbolics.variables" href="#Symbolics.variables"><code>Symbolics.variables</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">variables(name::Symbol, indices...)</code></pre><p>Create a multi-dimensional array of individual variables named with subscript notation. Use <code>@variables</code> instead to create symbolic array variables (as opposed to array of variables). See <code>variable</code> to create one variable with subscripts.</p><pre><code class="language-julia-repl hljs">julia> Symbolics.variables(:x, 1:3, 3:6) +x₄ˏ₂ˏ₀⋆</code></pre><p>Also see <code>variables</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/variable.jl#L456-L471">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="Symbolics.variables" href="#Symbolics.variables"><code>Symbolics.variables</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">variables(name::Symbol, indices...)</code></pre><p>Create a multi-dimensional array of individual variables named with subscript notation. Use <code>@variables</code> instead to create symbolic array variables (as opposed to array of variables). See <code>variable</code> to create one variable with subscripts.</p><pre><code class="language-julia-repl hljs">julia> Symbolics.variables(:x, 1:3, 3:6) 3×4 Matrix{Num}: x₁ˏ₃ x₁ˏ₄ x₁ˏ₅ x₁ˏ₆ x₂ˏ₃ x₂ˏ₄ x₂ˏ₅ x₂ˏ₆ - x₃ˏ₃ x₃ˏ₄ x₃ˏ₅ x₃ˏ₆</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/variable.jl#L436-L451">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="Symbolics.Equation" href="#Symbolics.Equation"><code>Symbolics.Equation</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">struct Equation</code></pre><p>An equality relationship between two expressions.</p><p><strong>Fields</strong></p><ul><li><p><code>lhs</code>: The expression on the left-hand side of the equation.</p></li><li><p><code>rhs</code>: The expression on the right-hand side of the equation.</p></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/equations.jl#L102">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="Base.:~-Tuple{Num, Num}" href="#Base.:~-Tuple{Num, Num}"><code>Base.:~</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">~(lhs, rhs) -> Any + x₃ˏ₃ x₃ˏ₄ x₃ˏ₅ x₃ˏ₆</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/variable.jl#L436-L451">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="Symbolics.Equation" href="#Symbolics.Equation"><code>Symbolics.Equation</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">struct Equation</code></pre><p>An equality relationship between two expressions.</p><p><strong>Fields</strong></p><ul><li><p><code>lhs</code>: The expression on the left-hand side of the equation.</p></li><li><p><code>rhs</code>: The expression on the right-hand side of the equation.</p></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/equations.jl#L102">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="Base.:~-Tuple{Num, Num}" href="#Base.:~-Tuple{Num, Num}"><code>Base.:~</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">~(lhs, rhs) -> Any </code></pre><p>Create an <a href="#Symbolics.Equation"><code>Equation</code></a> out of two <a href="@ref"><code>Num</code></a> instances, or an <code>Num</code> and a <code>Number</code>.</p><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia> using Symbolics julia> @variables x y; @@ -53,7 +53,7 @@ (broadcast(~, A, B))[1:3,1:3] julia> A .~ 3x -(broadcast(~, A, 3x))[1:3,1:3]</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/1acbc9b82d3221d63fc6bf4f3fec85be5d5b783c/src/equations.jl#L150">source</a></section></article><h2 id="A-note-about-functions-restricted-to-Numbers"><a class="docs-heading-anchor" href="#A-note-about-functions-restricted-to-Numbers">A note about functions restricted to <code>Number</code>s</a><a id="A-note-about-functions-restricted-to-Numbers-1"></a><a class="docs-heading-anchor-permalink" href="#A-note-about-functions-restricted-to-Numbers" title="Permalink"></a></h2><p><code>Sym</code> and <code>Term</code> objects are NOT subtypes of <code>Number</code>. Symbolics provides a simple wrapper type called <code>Num</code> which is a subtype of <code>Real</code>. <code>Num</code> wraps either a Sym or a Term or any other object, defines the same set of operations as symbolic expressions and forwards those to the values it wraps. You can use <code>Symbolics.value</code> function to unwrap a <code>Num</code>.</p><p>By default, the <code>@variables</code> macros return Num-wrapped objects to allow calling functions which are restricted to <code>Number</code> or <code>Real</code>.</p><pre><code class="language-julia hljs">using Symbolics +(broadcast(~, A, 3x))[1:3,1:3]</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/Symbolics.jl/blob/58faaee6f88bd0d96cc10f0b46788e59ebdee4e8/src/equations.jl#L150">source</a></section></article><h2 id="A-note-about-functions-restricted-to-Numbers"><a class="docs-heading-anchor" href="#A-note-about-functions-restricted-to-Numbers">A note about functions restricted to <code>Number</code>s</a><a id="A-note-about-functions-restricted-to-Numbers-1"></a><a class="docs-heading-anchor-permalink" href="#A-note-about-functions-restricted-to-Numbers" title="Permalink"></a></h2><p><code>Sym</code> and <code>Term</code> objects are NOT subtypes of <code>Number</code>. Symbolics provides a simple wrapper type called <code>Num</code> which is a subtype of <code>Real</code>. <code>Num</code> wraps either a Sym or a Term or any other object, defines the same set of operations as symbolic expressions and forwards those to the values it wraps. You can use <code>Symbolics.value</code> function to unwrap a <code>Num</code>.</p><p>By default, the <code>@variables</code> macros return Num-wrapped objects to allow calling functions which are restricted to <code>Number</code> or <code>Real</code>.</p><pre><code class="language-julia hljs">using Symbolics @variables t x y z(t); Symbolics.operation(Symbolics.value(x + y))</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">+ (generic function with 482 methods)</code></pre><pre><code class="language-julia hljs">Symbolics.operation(Symbolics.value(z))</code></pre><p class="math-container">\[ \begin{equation} z @@ -68,4 +68,4 @@ f(t)</code></pre><p class="math-container">\[ \begin{equation} 1 + t \left( \frac{2}{3} + \frac{4}{5} \mathrm{identity}\left( \pi \right) \right) \end{equation} - \]</p><p>This will work for any floating-point input, as well as symbolic input.</p><h2 id="Symbolic-Control-Flow"><a class="docs-heading-anchor" href="#Symbolic-Control-Flow">Symbolic Control Flow</a><a id="Symbolic-Control-Flow-1"></a><a class="docs-heading-anchor-permalink" href="#Symbolic-Control-Flow" title="Permalink"></a></h2><p>Control flow can be expressed in Symbolics.jl in the following ways:</p><ul><li><code>IfElse.ifelse(cond,x,y)</code>: this is a dispatch-able version of the <code>ifelse</code> function provided by <code>IfElse.jl</code> which allows for encoding conditionals in the symbolic branches.</li></ul><h2 id="Inspection-Functions"><a class="docs-heading-anchor" href="#Inspection-Functions">Inspection Functions</a><a id="Inspection-Functions-1"></a><a class="docs-heading-anchor-permalink" href="#Inspection-Functions" title="Permalink"></a></h2><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="SymbolicUtils.istree" href="#SymbolicUtils.istree"><code>SymbolicUtils.istree</code></a> — <span class="docstring-category">Function</span></header><section><div><p>istree(x)</p><p>Returns <code>true</code> if <code>x</code> is a term. If true, <code>operation</code>, <code>arguments</code> must also be defined for <code>x</code> appropriately.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/SymbolicUtils.jl/blob/v1.5.0/src/interface.jl#L1-L6">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="SymbolicUtils.operation" href="#SymbolicUtils.operation"><code>SymbolicUtils.operation</code></a> — <span class="docstring-category">Function</span></header><section><div><p>operation(x)</p><p>If <code>x</code> is a term as defined by <code>istree(x)</code>, <code>operation(x)</code> returns the head of the term if <code>x</code> represents a function call, for example, the head is the function being called.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/SymbolicUtils.jl/blob/v1.5.0/src/interface.jl#L29-L35">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="SymbolicUtils.arguments" href="#SymbolicUtils.arguments"><code>SymbolicUtils.arguments</code></a> — <span class="docstring-category">Function</span></header><section><div><p>arguments(x)</p><p>Get the arguments of <code>x</code>, must be defined if <code>istree(x)</code> is <code>true</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/SymbolicUtils.jl/blob/v1.5.0/src/interface.jl#L38-L42">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../examples/perturbation/">« Mixed Symbolic-Numeric Perturbation Theory</a><a class="docs-footer-nextpage" href="../expression_manipulation/">Expression Manipulation »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 12:13">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> + \]</p><p>This will work for any floating-point input, as well as symbolic input.</p><h2 id="Symbolic-Control-Flow"><a class="docs-heading-anchor" href="#Symbolic-Control-Flow">Symbolic Control Flow</a><a id="Symbolic-Control-Flow-1"></a><a class="docs-heading-anchor-permalink" href="#Symbolic-Control-Flow" title="Permalink"></a></h2><p>Control flow can be expressed in Symbolics.jl in the following ways:</p><ul><li><code>IfElse.ifelse(cond,x,y)</code>: this is a dispatch-able version of the <code>ifelse</code> function provided by <code>IfElse.jl</code> which allows for encoding conditionals in the symbolic branches.</li></ul><h2 id="Inspection-Functions"><a class="docs-heading-anchor" href="#Inspection-Functions">Inspection Functions</a><a id="Inspection-Functions-1"></a><a class="docs-heading-anchor-permalink" href="#Inspection-Functions" title="Permalink"></a></h2><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="SymbolicUtils.istree" href="#SymbolicUtils.istree"><code>SymbolicUtils.istree</code></a> — <span class="docstring-category">Function</span></header><section><div><p>istree(x)</p><p>Returns <code>true</code> if <code>x</code> is a term. If true, <code>operation</code>, <code>arguments</code> must also be defined for <code>x</code> appropriately.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/SymbolicUtils.jl/blob/v1.5.0/src/interface.jl#L1-L6">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="SymbolicUtils.operation" href="#SymbolicUtils.operation"><code>SymbolicUtils.operation</code></a> — <span class="docstring-category">Function</span></header><section><div><p>operation(x)</p><p>If <code>x</code> is a term as defined by <code>istree(x)</code>, <code>operation(x)</code> returns the head of the term if <code>x</code> represents a function call, for example, the head is the function being called.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/SymbolicUtils.jl/blob/v1.5.0/src/interface.jl#L29-L35">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="SymbolicUtils.arguments" href="#SymbolicUtils.arguments"><code>SymbolicUtils.arguments</code></a> — <span class="docstring-category">Function</span></header><section><div><p>arguments(x)</p><p>Get the arguments of <code>x</code>, must be defined if <code>istree(x)</code> is <code>true</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaSymbolics/SymbolicUtils.jl/blob/v1.5.0/src/interface.jl#L38-L42">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../examples/perturbation/">« Mixed Symbolic-Numeric Perturbation Theory</a><a class="docs-footer-nextpage" href="../expression_manipulation/">Expression Manipulation »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 13:45">Tuesday 27 February 2024</span>. 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cy="88.4184" r="3.6" fill="#000000" fill-rule="evenodd" fill-opacity="1" stroke="none"/> +<circle clip-path="url(#clip992)" cx="2291.2" cy="88.4184" r="3.6" fill="#000000" fill-rule="evenodd" fill-opacity="1" stroke="none"/> +<circle clip-path="url(#clip992)" cx="938.124" cy="87.9763" r="3.6" fill="#000000" fill-rule="evenodd" fill-opacity="1" stroke="none"/> +<circle clip-path="url(#clip992)" cx="1614.99" cy="87.9763" r="3.6" fill="#000000" fill-rule="evenodd" fill-opacity="1" stroke="none"/> +<circle clip-path="url(#clip992)" cx="2291.86" cy="87.9763" r="3.6" fill="#000000" fill-rule="evenodd" fill-opacity="1" stroke="none"/> </svg> diff --git a/previews/PR1079/tutorials/auto_parallel/index.html b/previews/PR1079/tutorials/auto_parallel/index.html index 62af95c14..a92260525 100644 --- a/previews/PR1079/tutorials/auto_parallel/index.html +++ b/previews/PR1079/tutorials/auto_parallel/index.html @@ -59,7 +59,7 @@ \]</p><p>The output, here the in-place modified <code>du</code>, is a symbolic representation of each output of the function. We can then utilize this in the Symbolics functionality. For example, let's build a parallel version of <code>f</code> first:</p><pre><code class="language-julia hljs">fastf = eval(Symbolics.build_function(du,u, parallel=Symbolics.MultithreadedForm())[2])</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">#13 (generic function with 1 method)</code></pre><p>Now let's compute the sparse Jacobian function and compile a fast multithreaded version:</p><pre><code class="language-julia hljs">jac = Symbolics.sparsejacobian(vec(du), vec(u)) row,col,val = findnz(jac) -scatter(row,col,legend=false,ms=1,c=:black)</code></pre><img src="6bf53748.svg" alt="Example block output"/><pre><code class="language-julia hljs">fjac = eval(Symbolics.build_function(jac,u, +scatter(row,col,legend=false,ms=1,c=:black)</code></pre><img src="c2c29a29.svg" alt="Example block output"/><pre><code class="language-julia hljs">fjac = eval(Symbolics.build_function(jac,u, parallel=Symbolics.MultithreadedForm())[2])</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">#15 (generic function with 1 method)</code></pre><p>It takes awhile for this to generate, but the results will be worth it! Now let's set up the parabolic PDE to be solved by DifferentialEquations.jl. We will set up the vanilla version and the sparse multithreaded version:</p><pre><code class="language-julia hljs">using OrdinaryDiffEq u0 = zeros(N, N, 3) MyA = zeros(N, N); @@ -139,4 +139,4 @@ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0</code></pre><p>Let's see the timing difference:</p><pre><code class="language-julia hljs">using BenchmarkTools #@btime solve(prob, TRBDF2()); # 33.073 s (895404 allocations: 23.87 GiB) #warning the following solve takes a long time to compile, but afterwards is very fast. -#@btime solve(fastprob, TRBDF2()); # 209.670 ms (8208 allocations: 109.25 MiB)</code></pre><p>Boom, an automatic 157x acceleration that grows as the size of the problem increases!</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../getting_started/">« Getting Started with Symbolics.jl</a><a class="docs-footer-nextpage" href="../converting_to_C/">Automatic Conversion of Julia Code to C Functions »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 12:13">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> +#@btime solve(fastprob, TRBDF2()); # 209.670 ms (8208 allocations: 109.25 MiB)</code></pre><p>Boom, an automatic 157x acceleration that grows as the size of the problem increases!</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../getting_started/">« Getting Started with Symbolics.jl</a><a class="docs-footer-nextpage" href="../converting_to_C/">Automatic Conversion of Julia Code to C Functions »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 13:45">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> diff --git a/previews/PR1079/tutorials/converting_to_C/index.html b/previews/PR1079/tutorials/converting_to_C/index.html index bda9b8e45..12cbb8ad3 100644 --- a/previews/PR1079/tutorials/converting_to_C/index.html +++ b/previews/PR1079/tutorials/converting_to_C/index.html @@ -18,11 +18,11 @@ \end{equation} \]</p><p>and then we build the function:</p><pre><code class="language-julia hljs">build_function(du, u, p, t, target=Symbolics.CTarget())</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">"#include <math.h>\nvoid diffeqf(double* du, const double* RHS1, const double* RHS2, const double RHS3) {\n du[0] = RHS2[0] * RHS1[0] + -1 * RHS2[1] * RHS1[0] * RHS1[1];\n du[1] = -1 * RHS2[2] * RHS1[1] + RHS2[3] * RHS1[0] * RHS1[1];\n}\n"</code></pre><p>If we want to compile this, we do <code>expression=Val{false}</code>:</p><pre><code class="language-julia hljs">f = build_function(du, u, p, t, target=Symbolics.CTarget(), expression=Val{false})</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">RuntimeGeneratedFunction(#=in Symbolics=#, #=using Symbolics=#, :((du, u, p, t)->begin #= /home/runner/work/Symbolics.jl/Symbolics.jl/src/build_function.jl:800 =# - ccall(("diffeqf", "/tmp/jl_wz6J2VGtCp"), Cvoid, (Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Float64), du, u, p, t) + ccall(("diffeqf", "/tmp/jl_cTqL8fu7aP"), Cvoid, (Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Float64), du, u, p, t) end))</code></pre><p>now we check it computes the same thing:</p><pre><code class="language-julia hljs">du = rand(2); du2 = rand(2) u = rand(2) p = rand(4) t = rand() f(du, u, p, t) lotka_volterra!(du2, u, p, t) -du == du2 # true!</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">true</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../auto_parallel/">« Automated Sparse Parallelism of Julia Functions via Tracing</a><a class="docs-footer-nextpage" href="../../examples/perturbation/">Mixed Symbolic-Numeric Perturbation Theory »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 12:13">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> +du == du2 # true!</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">true</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../auto_parallel/">« Automated Sparse Parallelism of Julia Functions via Tracing</a><a class="docs-footer-nextpage" href="../../examples/perturbation/">Mixed Symbolic-Numeric Perturbation Theory »</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><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 1.2.1 on <span class="colophon-date" title="Tuesday 27 February 2024 13:45">Tuesday 27 February 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>