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+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Usage from Python · RationalFunctionApproximation.jl</title><meta name="title" content="Usage from Python · RationalFunctionApproximation.jl"/><meta property="og:title" content="Usage from Python · RationalFunctionApproximation.jl"/><meta property="twitter:title" content="Usage from Python · RationalFunctionApproximation.jl"/><meta name="description" content="Documentation for RationalFunctionApproximation.jl."/><meta property="og:description" content="Documentation for RationalFunctionApproximation.jl."/><meta property="twitter:description" content="Documentation for RationalFunctionApproximation.jl."/><meta property="og:url" content="https://complexvariables.github.io/RationalFunctionApproximation.jl/python/"/><meta property="twitter:url" content="https://complexvariables.github.io/RationalFunctionApproximation.jl/python/"/><link rel="canonical" 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class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">RationalFunctionApproximation.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../">Walkthrough</a></li><li><a class="tocitem" href="../convergence/">Convergence</a></li><li><a class="tocitem" href="../minimax/">Minimax</a></li><li><a class="tocitem" href="../domains/">Domains</a></li><li><a class="tocitem" href="../mode/">Discrete vs. continuous</a></li><li class="is-active"><a class="tocitem" href>Usage from Python</a><ul class="internal"><li><a class="tocitem" href="#Installation"><span>Installation</span></a></li><li><a class="tocitem" href="#Usage"><span>Usage</span></a></li><li><a class="tocitem" href="#Passing-Python-functions"><span>Passing Python functions</span></a></li></ul></li><li><a class="tocitem" href="../functions/">Function API</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 class="is-active"><a href>Usage from Python</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Usage from Python</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/complexvariables/RationalFunctionApproximation.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/complexvariables/RationalFunctionApproximation.jl/blob/main/docs/src/python.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="Calling-from-Python"><a class="docs-heading-anchor" href="#Calling-from-Python">Calling from Python</a><a id="Calling-from-Python-1"></a><a class="docs-heading-anchor-permalink" href="#Calling-from-Python" title="Permalink"></a></h1><p>You can call the functions in this package from Python using the <a href="https://juliapy.github.io/PythonCall.jl/stable/"><code>PythonCall</code>/<code>JuliaCall</code></a> package. </p><h2 id="Installation"><a class="docs-heading-anchor" href="#Installation">Installation</a><a id="Installation-1"></a><a class="docs-heading-anchor-permalink" href="#Installation" title="Permalink"></a></h2><p>It&#39;s recommended to create a new virtual environment to try this out. In Python, you need to install <code>juliacall</code> via</p><pre><code class="language-bash hljs">pip install juliacall</code></pre><p>Then you start Python and run:</p><pre><code class="language-python hljs">from juliacall import Main as jl</code></pre><p>This will download and initialize a copy of Julia. Finally, you need to install this package in that Julia environment:</p><pre><code class="language-python hljs">jl.seval(&#39;using Pkg; Pkg.add(&quot;RationalFunctionApproximation&quot;)&#39;)</code></pre><p>That should be all you need in the Python environment.</p><h2 id="Usage"><a class="docs-heading-anchor" href="#Usage">Usage</a><a id="Usage-1"></a><a class="docs-heading-anchor-permalink" href="#Usage" title="Permalink"></a></h2><p>In each new Python session, you need to load the packages:</p><pre><code class="language-python hljs">from juliacall import Main as jl
+jl.seval(&#39;using RationalFunctionApproximation, PythonCall&#39;)</code></pre><p>All the functions and constants exposed to Julia by this package are available using the <code>jl</code> object. For example, to use the discrete AAA algorithm:</p><pre><code class="language-python hljs">import numpy as np    # if installed in Python
+x = np.linspace(-1, 1, 1000)
+y = np.tanh(5 * (x - 0.2))
+r = jl.aaa(x, y)
+print(r)</code></pre><pre><code class="nohighlight hljs">Barycentric rational function of type (11,11)</code></pre><p>This will return a wrapped Julia object that you can use in Python as if it were a Python object. For example, you can evaluate the approximation at a point:</p><pre><code class="language-python hljs">r(0.5)</code></pre><pre><code class="nohighlight hljs">0.9051482536448658</code></pre><p>If you want to apply the function at multiple points, you can use comprehensions or vectorize it in numpy:</p><pre><code class="language-python hljs">rv = np.vectorize(r)
+rv(np.array([0.5, 0.6, 0.7]))</code></pre><pre><code class="nohighlight hljs">array([0.90514825, 0.96402758, 0.9866143 ])</code></pre><p>You can get information about the approximation using any documented function in the package, e.g.:</p><pre><code class="language-python hljs">print(jl.poles(r))    # returns wrapped Julia type</code></pre><pre><code class="nohighlight hljs">ComplexF64[0.20000000000544785 - 0.31415926535542893im, 0.20000000000544788 + 0.31415926535542893im, 0.20000207991810143 - 0.942477292594254im, 0.20000207991810143 + 0.9424772925942541im, 0.20308324780986833 - 1.5724812056318853im, 0.20308324780986833 + 1.5724812056318853im, 0.29268586746842673 - 2.3408220889660796im, 0.29268586746842673 + 2.34082208896608im, 0.9695028397625358 + 4.390786420000105im, 0.969502839762536 - 4.390786420000105im, 21.59156666159181 + 0.0im]</code></pre><pre><code class="language-python hljs">print(np.array(jl.residues(r)))    # converts to numpy array</code></pre><pre><code class="nohighlight hljs">[  0.2       +2.72029915e-11j   0.2       -2.72031942e-11j
+   0.19999893+6.55140711e-06j   0.19999893-6.55140637e-06j
+   0.20352821+4.86975387e-03j   0.20352821-4.86975387e-03j
+   0.33454619+6.91112099e-02j   0.33454619-6.91112099e-02j
+   1.25164001-5.59634589e-01j   1.25164001+5.59634589e-01j
+ -32.51419889+0.00000000e+00j]</code></pre><h2 id="Passing-Python-functions"><a class="docs-heading-anchor" href="#Passing-Python-functions">Passing Python functions</a><a id="Passing-Python-functions-1"></a><a class="docs-heading-anchor-permalink" href="#Passing-Python-functions" title="Permalink"></a></h2><p>To use continuous approximation, you can pass a Python function to the <code>approximate</code> function.</p><pre><code class="language-python hljs">def f(x):
+    return np.tanh(5 * (x - 0.2))
+
+r = jl.approximate(f, jl.unit_interval)
+r(.5)</code></pre><pre><code class="nohighlight hljs">0.9051482536448647</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../mode/">« Discrete vs. continuous</a><a class="docs-footer-nextpage" href="../functions/">Function API »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.5.0 on <span class="colophon-date" title="Tuesday 2 July 2024 14:44">Tuesday 2 July 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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