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<li><a class="reference internal" href="#">Comparing initial sampling methods</a><ul>
<li><a class="reference internal" href="#random-sampling">Random sampling</a></li>
<li><a class="reference internal" href="#sobol">Sobol’</a></li>
<li><a class="reference internal" href="#classic-latin-hypercube-sampling">Classic Latin hypercube sampling</a></li>
<li><a class="reference internal" href="#centered-latin-hypercube-sampling">Centered Latin hypercube sampling</a></li>
<li><a class="reference internal" href="#maximin-optimized-hypercube-sampling">Maximin optimized hypercube sampling</a></li>
<li><a class="reference internal" href="#correlation-optimized-hypercube-sampling">Correlation optimized hypercube sampling</a></li>
<li><a class="reference internal" href="#ratio-optimized-hypercube-sampling">Ratio optimized hypercube sampling</a></li>
<li><a class="reference internal" href="#halton-sampling">Halton sampling</a></li>
<li><a class="reference internal" href="#hammersly-sampling">Hammersly sampling</a></li>
<li><a class="reference internal" href="#grid-sampling">Grid sampling</a></li>
<li><a class="reference internal" href="#pdist-boxplot-of-all-methods">Pdist boxplot of all methods</a></li>
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<section class="sphx-glr-example-title" id="comparing-initial-sampling-methods">
<span id="sphx-glr-auto-examples-sampler-initial-sampling-method-py"></span><h1>Comparing initial sampling methods<a class="headerlink" href="#comparing-initial-sampling-methods" title="Permalink to this headline">¶</a></h1>
<p>Holger Nahrstaedt 2020 Sigurd Carlsen October 2019</p>
<p>When doing baysian optimization we often want to reserve some of the
early part of the optimization to pure exploration. By default the
optimizer suggests purely random samples for the first n_initial_points
(10 by default). The downside to this is that there is no guarantee that
these samples are spread out evenly across all the dimensions.</p>
<p>Sampling methods as Latin hypercube, Sobol’, Halton and Hammersly
take advantage of the fact that we know beforehand how many random
points we want to sample. Then these points can be “spread out” in
such a way that each dimension is explored.</p>
<p>See also the example on an integer space
<span class="xref std std-ref">sphx_glr_auto_examples_initial_sampling_method_integer.py</span></p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.seed.html#numpy.random.seed" title="numpy.random.seed" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span></a><span class="p">(</span><span class="mi">123</span><span class="p">)</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">skopt.space</span> <span class="kn">import</span> <a href="../../modules/generated/skopt.Space.html#skopt.Space" title="skopt.Space" class="sphx-glr-backref-module-skopt sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Space</span></a>
<span class="kn">from</span> <span class="nn">skopt.sampler</span> <span class="kn">import</span> <a href="../../modules/generated/skopt.sampler.Sobol.html#skopt.sampler.Sobol" title="skopt.sampler.Sobol" class="sphx-glr-backref-module-skopt-sampler sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Sobol</span></a>
<span class="kn">from</span> <span class="nn">skopt.sampler</span> <span class="kn">import</span> <a href="../../modules/generated/skopt.sampler.Lhs.html#skopt.sampler.Lhs" title="skopt.sampler.Lhs" class="sphx-glr-backref-module-skopt-sampler sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Lhs</span></a>
<span class="kn">from</span> <span class="nn">skopt.sampler</span> <span class="kn">import</span> <a href="../../modules/generated/skopt.sampler.Halton.html#skopt.sampler.Halton" title="skopt.sampler.Halton" class="sphx-glr-backref-module-skopt-sampler sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Halton</span></a>
<span class="kn">from</span> <span class="nn">skopt.sampler</span> <span class="kn">import</span> <a href="../../modules/generated/skopt.sampler.Hammersly.html#skopt.sampler.Hammersly" title="skopt.sampler.Hammersly" class="sphx-glr-backref-module-skopt-sampler sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Hammersly</span></a>
<span class="kn">from</span> <span class="nn">skopt.sampler</span> <span class="kn">import</span> <span class="n">Grid</span>
<span class="kn">from</span> <span class="nn">scipy.spatial.distance</span> <span class="kn">import</span> <a href="https://docs.scipy.org/doc/scipy/reference/reference/generated/scipy.spatial.distance.pdist.html#scipy.spatial.distance.pdist" title="scipy.spatial.distance.pdist" class="sphx-glr-backref-module-scipy-spatial-distance sphx-glr-backref-type-py-function"><span class="n">pdist</span></a>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">plot_searchspace</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">title</span><span class="p">):</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">()</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="matplotlib.pyplot.plot" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.array.html#numpy.array" title="numpy.array" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">(</span><span class="n">x</span><span class="p">)[:,</span> <span class="mi">0</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.array.html#numpy.array" title="numpy.array" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">(</span><span class="n">x</span><span class="p">)[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="s1">'bo'</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'samples'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="matplotlib.pyplot.plot" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.array.html#numpy.array" title="numpy.array" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">(</span><span class="n">x</span><span class="p">)[:,</span> <span class="mi">0</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.array.html#numpy.array" title="numpy.array" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">(</span><span class="n">x</span><span class="p">)[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="s1">'bo'</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">80</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span>
<span class="c1"># ax.legend(loc="best", numpoints=1)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">"X1"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">([</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">10</span><span class="p">])</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">"X2"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">15</span><span class="p">])</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="n">title</span><span class="p">)</span>
<span class="n">n_samples</span> <span class="o">=</span> <span class="mi">10</span>
<span class="n">space</span> <span class="o">=</span> <a href="../../modules/generated/skopt.Space.html#skopt.Space" title="skopt.Space" class="sphx-glr-backref-module-skopt sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Space</span></a><span class="p">([(</span><span class="o">-</span><span class="mf">5.</span><span class="p">,</span> <span class="mf">10.</span><span class="p">),</span> <span class="p">(</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">15.</span><span class="p">)])</span>
<span class="c1"># space.set_transformer("normalize")</span>
</pre></div>
</div>
<section id="random-sampling">
<h2>Random sampling<a class="headerlink" href="#random-sampling" title="Permalink to this headline">¶</a></h2>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">x</span> <span class="o">=</span> <span class="n">space</span><span class="o">.</span><span class="n">rvs</span><span class="p">(</span><span class="n">n_samples</span><span class="p">)</span>
<span class="n">plot_searchspace</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="s2">"Random samples"</span><span class="p">)</span>
<span class="n">pdist_data</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">x_label</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">pdist_data</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="https://docs.scipy.org/doc/scipy/reference/reference/generated/scipy.spatial.distance.pdist.html#scipy.spatial.distance.pdist" title="scipy.spatial.distance.pdist" class="sphx-glr-backref-module-scipy-spatial-distance sphx-glr-backref-type-py-function"><span class="n">pdist</span></a><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">flatten</span><span class="p">())</span>
<span class="n">x_label</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s2">"random"</span><span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_initial-sampling-method_001.png" srcset="../../_images/sphx_glr_initial-sampling-method_001.png" alt="Random samples" class = "sphx-glr-single-img"/></section>
<section id="sobol">
<h2>Sobol’<a class="headerlink" href="#sobol" title="Permalink to this headline">¶</a></h2>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">sobol</span> <span class="o">=</span> <a href="../../modules/generated/skopt.sampler.Sobol.html#skopt.sampler.Sobol" title="skopt.sampler.Sobol" class="sphx-glr-backref-module-skopt-sampler sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Sobol</span></a><span class="p">()</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">sobol</span><span class="o">.</span><span class="n">generate</span><span class="p">(</span><span class="n">space</span><span class="o">.</span><span class="n">dimensions</span><span class="p">,</span> <span class="n">n_samples</span><span class="p">)</span>
<span class="n">plot_searchspace</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="s2">"Sobol'"</span><span class="p">)</span>
<span class="n">pdist_data</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="https://docs.scipy.org/doc/scipy/reference/reference/generated/scipy.spatial.distance.pdist.html#scipy.spatial.distance.pdist" title="scipy.spatial.distance.pdist" class="sphx-glr-backref-module-scipy-spatial-distance sphx-glr-backref-type-py-function"><span class="n">pdist</span></a><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">flatten</span><span class="p">())</span>
<span class="n">x_label</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s2">"sobol'"</span><span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_initial-sampling-method_002.png" srcset="../../_images/sphx_glr_initial-sampling-method_002.png" alt="Sobol'" class = "sphx-glr-single-img"/><p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>/home/circleci/project/skopt/sampler/sobol.py:246: UserWarning: The balance properties of Sobol' points require n to be a power of 2. 0 points have been previously generated, then: n=0+10=10.
warnings.warn("The balance properties of Sobol' points require "
</pre></div>
</div>
</section>
<section id="classic-latin-hypercube-sampling">
<h2>Classic Latin hypercube sampling<a class="headerlink" href="#classic-latin-hypercube-sampling" title="Permalink to this headline">¶</a></h2>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">lhs</span> <span class="o">=</span> <a href="../../modules/generated/skopt.sampler.Lhs.html#skopt.sampler.Lhs" title="skopt.sampler.Lhs" class="sphx-glr-backref-module-skopt-sampler sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Lhs</span></a><span class="p">(</span><span class="n">lhs_type</span><span class="o">=</span><span class="s2">"classic"</span><span class="p">,</span> <span class="n">criterion</span><span class="o">=</span><span class="kc">None</span><span class="p">)</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">lhs</span><span class="o">.</span><span class="n">generate</span><span class="p">(</span><span class="n">space</span><span class="o">.</span><span class="n">dimensions</span><span class="p">,</span> <span class="n">n_samples</span><span class="p">)</span>
<span class="n">plot_searchspace</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="s1">'classic LHS'</span><span class="p">)</span>
<span class="n">pdist_data</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="https://docs.scipy.org/doc/scipy/reference/reference/generated/scipy.spatial.distance.pdist.html#scipy.spatial.distance.pdist" title="scipy.spatial.distance.pdist" class="sphx-glr-backref-module-scipy-spatial-distance sphx-glr-backref-type-py-function"><span class="n">pdist</span></a><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">flatten</span><span class="p">())</span>
<span class="n">x_label</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s2">"lhs"</span><span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_initial-sampling-method_003.png" srcset="../../_images/sphx_glr_initial-sampling-method_003.png" alt="classic LHS" class = "sphx-glr-single-img"/></section>
<section id="centered-latin-hypercube-sampling">
<h2>Centered Latin hypercube sampling<a class="headerlink" href="#centered-latin-hypercube-sampling" title="Permalink to this headline">¶</a></h2>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">lhs</span> <span class="o">=</span> <a href="../../modules/generated/skopt.sampler.Lhs.html#skopt.sampler.Lhs" title="skopt.sampler.Lhs" class="sphx-glr-backref-module-skopt-sampler sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Lhs</span></a><span class="p">(</span><span class="n">lhs_type</span><span class="o">=</span><span class="s2">"centered"</span><span class="p">,</span> <span class="n">criterion</span><span class="o">=</span><span class="kc">None</span><span class="p">)</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">lhs</span><span class="o">.</span><span class="n">generate</span><span class="p">(</span><span class="n">space</span><span class="o">.</span><span class="n">dimensions</span><span class="p">,</span> <span class="n">n_samples</span><span class="p">)</span>
<span class="n">plot_searchspace</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="s1">'centered LHS'</span><span class="p">)</span>
<span class="n">pdist_data</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="https://docs.scipy.org/doc/scipy/reference/reference/generated/scipy.spatial.distance.pdist.html#scipy.spatial.distance.pdist" title="scipy.spatial.distance.pdist" class="sphx-glr-backref-module-scipy-spatial-distance sphx-glr-backref-type-py-function"><span class="n">pdist</span></a><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">flatten</span><span class="p">())</span>
<span class="n">x_label</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s2">"center"</span><span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_initial-sampling-method_004.png" srcset="../../_images/sphx_glr_initial-sampling-method_004.png" alt="centered LHS" class = "sphx-glr-single-img"/></section>
<section id="maximin-optimized-hypercube-sampling">
<h2>Maximin optimized hypercube sampling<a class="headerlink" href="#maximin-optimized-hypercube-sampling" title="Permalink to this headline">¶</a></h2>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">lhs</span> <span class="o">=</span> <a href="../../modules/generated/skopt.sampler.Lhs.html#skopt.sampler.Lhs" title="skopt.sampler.Lhs" class="sphx-glr-backref-module-skopt-sampler sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Lhs</span></a><span class="p">(</span><span class="n">criterion</span><span class="o">=</span><span class="s2">"maximin"</span><span class="p">,</span> <span class="n">iterations</span><span class="o">=</span><span class="mi">10000</span><span class="p">)</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">lhs</span><span class="o">.</span><span class="n">generate</span><span class="p">(</span><span class="n">space</span><span class="o">.</span><span class="n">dimensions</span><span class="p">,</span> <span class="n">n_samples</span><span class="p">)</span>
<span class="n">plot_searchspace</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="s1">'maximin LHS'</span><span class="p">)</span>
<span class="n">pdist_data</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="https://docs.scipy.org/doc/scipy/reference/reference/generated/scipy.spatial.distance.pdist.html#scipy.spatial.distance.pdist" title="scipy.spatial.distance.pdist" class="sphx-glr-backref-module-scipy-spatial-distance sphx-glr-backref-type-py-function"><span class="n">pdist</span></a><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">flatten</span><span class="p">())</span>
<span class="n">x_label</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s2">"maximin"</span><span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_initial-sampling-method_005.png" srcset="../../_images/sphx_glr_initial-sampling-method_005.png" alt="maximin LHS" class = "sphx-glr-single-img"/></section>
<section id="correlation-optimized-hypercube-sampling">
<h2>Correlation optimized hypercube sampling<a class="headerlink" href="#correlation-optimized-hypercube-sampling" title="Permalink to this headline">¶</a></h2>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">lhs</span> <span class="o">=</span> <a href="../../modules/generated/skopt.sampler.Lhs.html#skopt.sampler.Lhs" title="skopt.sampler.Lhs" class="sphx-glr-backref-module-skopt-sampler sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Lhs</span></a><span class="p">(</span><span class="n">criterion</span><span class="o">=</span><span class="s2">"correlation"</span><span class="p">,</span> <span class="n">iterations</span><span class="o">=</span><span class="mi">10000</span><span class="p">)</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">lhs</span><span class="o">.</span><span class="n">generate</span><span class="p">(</span><span class="n">space</span><span class="o">.</span><span class="n">dimensions</span><span class="p">,</span> <span class="n">n_samples</span><span class="p">)</span>
<span class="n">plot_searchspace</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="s1">'correlation LHS'</span><span class="p">)</span>
<span class="n">pdist_data</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="https://docs.scipy.org/doc/scipy/reference/reference/generated/scipy.spatial.distance.pdist.html#scipy.spatial.distance.pdist" title="scipy.spatial.distance.pdist" class="sphx-glr-backref-module-scipy-spatial-distance sphx-glr-backref-type-py-function"><span class="n">pdist</span></a><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">flatten</span><span class="p">())</span>
<span class="n">x_label</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s2">"corr"</span><span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_initial-sampling-method_006.png" srcset="../../_images/sphx_glr_initial-sampling-method_006.png" alt="correlation LHS" class = "sphx-glr-single-img"/></section>
<section id="ratio-optimized-hypercube-sampling">
<h2>Ratio optimized hypercube sampling<a class="headerlink" href="#ratio-optimized-hypercube-sampling" title="Permalink to this headline">¶</a></h2>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">lhs</span> <span class="o">=</span> <a href="../../modules/generated/skopt.sampler.Lhs.html#skopt.sampler.Lhs" title="skopt.sampler.Lhs" class="sphx-glr-backref-module-skopt-sampler sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Lhs</span></a><span class="p">(</span><span class="n">criterion</span><span class="o">=</span><span class="s2">"ratio"</span><span class="p">,</span> <span class="n">iterations</span><span class="o">=</span><span class="mi">10000</span><span class="p">)</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">lhs</span><span class="o">.</span><span class="n">generate</span><span class="p">(</span><span class="n">space</span><span class="o">.</span><span class="n">dimensions</span><span class="p">,</span> <span class="n">n_samples</span><span class="p">)</span>
<span class="n">plot_searchspace</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="s1">'ratio LHS'</span><span class="p">)</span>
<span class="n">pdist_data</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="https://docs.scipy.org/doc/scipy/reference/reference/generated/scipy.spatial.distance.pdist.html#scipy.spatial.distance.pdist" title="scipy.spatial.distance.pdist" class="sphx-glr-backref-module-scipy-spatial-distance sphx-glr-backref-type-py-function"><span class="n">pdist</span></a><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">flatten</span><span class="p">())</span>
<span class="n">x_label</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s2">"ratio"</span><span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_initial-sampling-method_007.png" srcset="../../_images/sphx_glr_initial-sampling-method_007.png" alt="ratio LHS" class = "sphx-glr-single-img"/></section>
<section id="halton-sampling">
<h2>Halton sampling<a class="headerlink" href="#halton-sampling" title="Permalink to this headline">¶</a></h2>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">halton</span> <span class="o">=</span> <a href="../../modules/generated/skopt.sampler.Halton.html#skopt.sampler.Halton" title="skopt.sampler.Halton" class="sphx-glr-backref-module-skopt-sampler sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Halton</span></a><span class="p">()</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">halton</span><span class="o">.</span><span class="n">generate</span><span class="p">(</span><span class="n">space</span><span class="o">.</span><span class="n">dimensions</span><span class="p">,</span> <span class="n">n_samples</span><span class="p">)</span>
<span class="n">plot_searchspace</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="s1">'Halton'</span><span class="p">)</span>
<span class="n">pdist_data</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="https://docs.scipy.org/doc/scipy/reference/reference/generated/scipy.spatial.distance.pdist.html#scipy.spatial.distance.pdist" title="scipy.spatial.distance.pdist" class="sphx-glr-backref-module-scipy-spatial-distance sphx-glr-backref-type-py-function"><span class="n">pdist</span></a><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">flatten</span><span class="p">())</span>
<span class="n">x_label</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s2">"halton"</span><span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_initial-sampling-method_008.png" srcset="../../_images/sphx_glr_initial-sampling-method_008.png" alt="Halton" class = "sphx-glr-single-img"/></section>
<section id="hammersly-sampling">
<h2>Hammersly sampling<a class="headerlink" href="#hammersly-sampling" title="Permalink to this headline">¶</a></h2>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">hammersly</span> <span class="o">=</span> <a href="../../modules/generated/skopt.sampler.Hammersly.html#skopt.sampler.Hammersly" title="skopt.sampler.Hammersly" class="sphx-glr-backref-module-skopt-sampler sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Hammersly</span></a><span class="p">()</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">hammersly</span><span class="o">.</span><span class="n">generate</span><span class="p">(</span><span class="n">space</span><span class="o">.</span><span class="n">dimensions</span><span class="p">,</span> <span class="n">n_samples</span><span class="p">)</span>
<span class="n">plot_searchspace</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="s1">'Hammersly'</span><span class="p">)</span>
<span class="n">pdist_data</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="https://docs.scipy.org/doc/scipy/reference/reference/generated/scipy.spatial.distance.pdist.html#scipy.spatial.distance.pdist" title="scipy.spatial.distance.pdist" class="sphx-glr-backref-module-scipy-spatial-distance sphx-glr-backref-type-py-function"><span class="n">pdist</span></a><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">flatten</span><span class="p">())</span>
<span class="n">x_label</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s2">"hammersly"</span><span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_initial-sampling-method_009.png" srcset="../../_images/sphx_glr_initial-sampling-method_009.png" alt="Hammersly" class = "sphx-glr-single-img"/></section>
<section id="grid-sampling">
<h2>Grid sampling<a class="headerlink" href="#grid-sampling" title="Permalink to this headline">¶</a></h2>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">grid</span> <span class="o">=</span> <span class="n">Grid</span><span class="p">(</span><span class="n">border</span><span class="o">=</span><span class="s2">"include"</span><span class="p">,</span> <span class="n">use_full_layout</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">grid</span><span class="o">.</span><span class="n">generate</span><span class="p">(</span><span class="n">space</span><span class="o">.</span><span class="n">dimensions</span><span class="p">,</span> <span class="n">n_samples</span><span class="p">)</span>
<span class="n">plot_searchspace</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="s1">'Grid'</span><span class="p">)</span>
<span class="n">pdist_data</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="https://docs.scipy.org/doc/scipy/reference/reference/generated/scipy.spatial.distance.pdist.html#scipy.spatial.distance.pdist" title="scipy.spatial.distance.pdist" class="sphx-glr-backref-module-scipy-spatial-distance sphx-glr-backref-type-py-function"><span class="n">pdist</span></a><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">flatten</span><span class="p">())</span>
<span class="n">x_label</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s2">"grid"</span><span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_initial-sampling-method_010.png" srcset="../../_images/sphx_glr_initial-sampling-method_010.png" alt="Grid" class = "sphx-glr-single-img"/></section>
<section id="pdist-boxplot-of-all-methods">
<h2>Pdist boxplot of all methods<a class="headerlink" href="#pdist-boxplot-of-all-methods" title="Permalink to this headline">¶</a></h2>
<p>This boxplot shows the distance between all generated points using
Euclidian distance. The higher the value, the better the sampling method.
It can be seen that random has the worst performance</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">()</span>
<span class="n">ax</span><span class="o">.</span><span class="n">boxplot</span><span class="p">(</span><span class="n">pdist_data</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.grid.html#matplotlib.pyplot.grid" title="matplotlib.pyplot.grid" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">grid</span></a><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.ylabel.html#matplotlib.pyplot.ylabel" title="matplotlib.pyplot.ylabel" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span></a><span class="p">(</span><span class="s2">"pdist"</span><span class="p">)</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">12</span><span class="p">)</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">set_xticklabels</span><span class="p">(</span><span class="n">x_label</span><span class="p">,</span> <span class="n">rotation</span><span class="o">=</span><span class="mi">45</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">8</span><span class="p">)</span>
</pre></div>
</div>
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