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<div class="section" id="sve">
<h1>SVE<a class="headerlink" href="#sve" title="Permalink to this headline">¶</a></h1>
<p>SVE is a Python package to perform Quadratic optimization using the simplex vertex-edge (SVE) method. It consists of a Python class and a C shared library extension.</p>
<ul class="simple">
<li><strong>Source:</strong> <a class="reference external" href="https://github.com/yelrew/sve">https://github.com/yelrew/sve</a></li>
<li><strong>Original C sources:</strong> <a class="reference external" href="https://github.com/JorgeStolfi/JSLIBS/tree/main/libminn">https://github.com/JorgeStolfi/JSLIBS/tree/main/libminn</a></li>
<li><strong>Documentation:</strong> <a class="reference external" href="https://yelrew.github.io/s_v_e">https://yelrew.github.io/s_v_e</a></li>
</ul>
<div class="section" id="installation">
<h2>Installation<a class="headerlink" href="#installation" title="Permalink to this headline">¶</a></h2>
<p>SVE can be installed using pip:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">pip</span> <span class="n">install</span> <span class="n">git</span><span class="o">+</span><span class="n">ssh</span><span class="p">:</span><span class="o">//</span><span class="n">git</span><span class="nd">@github</span><span class="o">.</span><span class="n">com</span><span class="o">/</span><span class="n">yelrew</span><span class="o">/</span><span class="n">sve</span><span class="o">.</span><span class="n">git</span>
</pre></div>
</div>
<p>or directly from the sources:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">git</span> <span class="n">clone</span> <span class="n">https</span><span class="p">:</span><span class="o">//</span><span class="n">github</span><span class="o">.</span><span class="n">com</span><span class="o">/</span><span class="n">yelrew</span><span class="o">/</span><span class="n">s_v_e</span><span class="o">.</span><span class="n">git</span> <span class="o">&&</span> <span class="n">cd</span> <span class="n">sve</span> <span class="o">&&</span> <span class="n">pip</span> <span class="n">install</span> <span class="o">-</span><span class="n">e</span> <span class="o">.</span>
</pre></div>
</div>
</div>
<div class="section" id="an-example">
<h2>An example<a class="headerlink" href="#an-example" title="Permalink to this headline">¶</a></h2>
<p>Optimization of the <a class="reference external" href="https://www.sfu.ca/~ssurjano/camel6.html">Six-Hump Camel</a> function</p>
<div class="code python highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sve</span> <span class="k">import</span> <span class="n">Sve</span>
<span class="gp">>>> </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="gp">>>> </span><span class="c1"># Function to be optimized</span>
<span class="gp">>>> </span><span class="k">def</span> <span class="nf">F</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="gp">>>> </span> <span class="n">x1</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="gp">>>> </span> <span class="n">x2</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="gp">>>> </span> <span class="n">f</span> <span class="o">=</span> <span class="p">(</span><span class="mi">4</span> <span class="o">-</span> <span class="mf">2.1</span><span class="o">*</span><span class="n">x1</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="p">(</span><span class="n">x1</span><span class="o">**</span><span class="mi">4</span><span class="p">)</span><span class="o">/</span><span class="mi">3</span><span class="p">)</span><span class="o">*</span><span class="n">x1</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">x1</span><span class="o">*</span><span class="n">x2</span> <span class="o">+</span> <span class="p">(</span><span class="o">-</span><span class="mi">4</span><span class="o">+</span><span class="mi">4</span><span class="o">*</span><span class="n">x2</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">*</span><span class="n">x2</span><span class="o">**</span><span class="mi">2</span>
<span class="gp">>>> </span> <span class="k">return</span> <span class="n">f</span>
<span class="gp">>>> </span><span class="c1"># Simplex parameters</span>
<span class="gp">>>> </span><span class="n">x0</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">]</span> <span class="c1"># initial guess</span>
<span class="gp">>>> </span><span class="n">rMin</span> <span class="o">=</span> <span class="mf">0.0001</span>
<span class="gp">>>> </span><span class="n">rIni</span> <span class="o">=</span> <span class="mf">0.5</span>
<span class="gp">>>> </span><span class="n">rMax</span> <span class="o">=</span> <span class="mf">1.5</span>
<span class="gp">>>> </span><span class="n">stop</span> <span class="o">=</span> <span class="mi">10</span> <span class="o">*</span> <span class="n">rMin</span>
<span class="gp">>>> </span><span class="c1"># Creating the sve object</span>
<span class="gp">>>> </span><span class="n">sve</span> <span class="o">=</span> <span class="n">Sve</span><span class="p">(</span><span class="n">rIni</span><span class="p">,</span> <span class="n">rMin</span><span class="p">,</span> <span class="n">rMax</span><span class="p">,</span> <span class="n">stop</span><span class="p">)</span>
<span class="gp">>>> </span><span class="c1"># Optimizing (the default behavior is to find the minimum of F)</span>
<span class="gp">>>> </span><span class="n">out</span> <span class="o">=</span> <span class="n">sve</span><span class="o">.</span><span class="n">iterate</span><span class="p">(</span><span class="n">x0</span><span class="p">,</span> <span class="n">F</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">X</span><span class="p">,</span> <span class="n">Fx</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">nit</span><span class="p">,</span> <span class="n">nev</span><span class="p">,</span> <span class="n">maxit</span> <span class="o">=</span> <span class="n">out</span><span class="o">.</span><span class="n">values</span><span class="p">()</span>
<span class="gp">>>> </span><span class="c1"># Printing the results</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">set_printoptions</span><span class="p">(</span><span class="n">suppress</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">precision</span><span class="o">=</span><span class="mi">4</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="s1">'</span><span class="se">\n</span><span class="s1">Iterations performed: '</span><span class="p">,</span> <span class="n">nit</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="s1">'Function probes: '</span><span class="p">,</span> <span class="n">nev</span><span class="p">,</span> <span class="s1">'</span><span class="se">\n</span><span class="s1">'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="s1">'Optimal results'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="s1">' x1* :'</span><span class="p">,</span> <span class="n">X</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">])</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="s1">' x2* : '</span><span class="p">,</span> <span class="n">X</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">])</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="s1">' F(x1*,x2*) : '</span><span class="p">,</span> <span class="n">Fx</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="s1">'</span><span class="se">\n</span><span class="s1">Simplex at x*'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
</pre></div>
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