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skbio.stats.composition.multi\_replace
======================================

.. currentmodule:: skbio.stats.composition

.. autofunction:: multi_replace
24 changes: 12 additions & 12 deletions docs/dev/generated/skbio.stats.composition.alr.html
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<li class="toctree-l1"><a class="reference internal" href="skbio.stats.power.html">Empirical Power Estimation (<code class="xref py py-mod docutils literal notranslate"><span class="pre">skbio.stats.power</span></code>)</a></li>
<li class="toctree-l1 current active has-children"><a class="reference internal" href="skbio.stats.composition.html">Composition Statistics (<code class="xref py py-mod docutils literal notranslate"><span class="pre">skbio.stats.composition</span></code>)</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
<li class="toctree-l2"><a class="reference internal" href="skbio.stats.composition.closure.html">skbio.stats.composition.closure</a></li>
<li class="toctree-l2"><a class="reference internal" href="skbio.stats.composition.multi_replace.html">skbio.stats.composition.multi_replace</a></li>
<li class="toctree-l2"><a class="reference internal" href="skbio.stats.composition.multiplicative_replacement.html">skbio.stats.composition.multiplicative_replacement</a></li>
<li class="toctree-l2"><a class="reference internal" href="skbio.stats.composition.perturb.html">skbio.stats.composition.perturb</a></li>
<li class="toctree-l2"><a class="reference internal" href="skbio.stats.composition.perturb_inv.html">skbio.stats.composition.perturb_inv</a></li>
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<h1>skbio.stats.composition.alr<a class="headerlink" href="#skbio-stats-composition-alr" title="Link to this heading">#</a></h1>
<dl class="py function">
<dt class="sig sig-object py" id="skbio.stats.composition.alr">
<span class="sig-prename descclassname"><span class="pre">skbio.stats.composition.</span></span><span class="sig-name descname"><span class="pre">alr</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mat</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">denominator_idx</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-bio/scikit-bio/blob/main/skbio/stats/composition.py#L649"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#skbio.stats.composition.alr" title="Link to this definition">#</a></dt>
<span class="sig-prename descclassname"><span class="pre">skbio.stats.composition.</span></span><span class="sig-name descname"><span class="pre">alr</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mat</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">denominator_idx</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-bio/scikit-bio/blob/main/skbio/stats/composition.py#L655"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#skbio.stats.composition.alr" title="Link to this definition">#</a></dt>
<dd><p>Perform additive log ratio transformation.</p>
<p>This function transforms compositions from a D-part Aitchison simplex to
a non-isometric real space of D-1 dimensions. The argument
<cite>denominator_col</cite> defines the index of the column used as the common
denominator. The :math: <cite>alr</cite> transformed data are amenable to multivariate
<code class="docutils literal notranslate"><span class="pre">denominator_col</span></code> defines the index of the column used as the common
denominator. The <span class="math notranslate nohighlight">\(alr\)</span> transformed data are amenable to multivariate
analysis as long as statistics don’t involve distances.</p>
<p><span class="math notranslate nohighlight">\(alr: S^D \rightarrow \mathbb{R}^{D-1}\)</span></p>
<div class="math notranslate nohighlight">
\[alr: S^D \rightarrow \mathbb{R}^{D-1}\]</div>
<p>The alr transformation is defined as follows</p>
<div class="math notranslate nohighlight">
\[alr(x) = \left[ \ln \frac{x_1}{x_D}, \ldots,
Expand All @@ -712,20 +714,18 @@ <h1>skbio.stats.composition.alr<a class="headerlink" href="#skbio-stats-composit
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>mat: numpy.ndarray</strong></dt><dd><p>a matrix of proportions where
rows = compositions and
columns = components</p>
<dt><strong>mat</strong><span class="classifier">array_like of shape (n_compositions, n_components)</span></dt><dd><p>A matrix of proportions.</p>
</dd>
<dt><strong>denominator_idx: int</strong></dt><dd><p>the index of the column (2D-matrix) or position (vector) of
<cite>mat</cite> which should be used as the reference composition. By default
<cite>denominator_idx=0</cite> to specify the first column or position.</p>
<dt><strong>denominator_idx</strong><span class="classifier">int</span></dt><dd><p>The index of the column (2-D matrix) or position (vector) of <code class="docutils literal notranslate"><span class="pre">mat</span></code>
which should be used as the reference composition. Default is 0 which
specifies the first column or position.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt>numpy.ndarray</dt><dd><p>alr-transformed data projected in a non-isometric real space
of D-1 dimensions for a D-parts composition</p>
<dt>ndarray of shape (n_compositions, n_components - 1)</dt><dd><p>Alr-transformed data projected in a non-isometric real space of
<span class="math notranslate nohighlight">\(D - 1\)</span> dimensions for a <em>D</em>-parts composition.</p>
</dd>
</dl>
</dd>
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18 changes: 10 additions & 8 deletions docs/dev/generated/skbio.stats.composition.alr_inv.html
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<li class="toctree-l1"><a class="reference internal" href="skbio.stats.power.html">Empirical Power Estimation (<code class="xref py py-mod docutils literal notranslate"><span class="pre">skbio.stats.power</span></code>)</a></li>
<li class="toctree-l1 current active has-children"><a class="reference internal" href="skbio.stats.composition.html">Composition Statistics (<code class="xref py py-mod docutils literal notranslate"><span class="pre">skbio.stats.composition</span></code>)</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
<li class="toctree-l2"><a class="reference internal" href="skbio.stats.composition.closure.html">skbio.stats.composition.closure</a></li>
<li class="toctree-l2"><a class="reference internal" href="skbio.stats.composition.multi_replace.html">skbio.stats.composition.multi_replace</a></li>
<li class="toctree-l2"><a class="reference internal" href="skbio.stats.composition.multiplicative_replacement.html">skbio.stats.composition.multiplicative_replacement</a></li>
<li class="toctree-l2"><a class="reference internal" href="skbio.stats.composition.perturb.html">skbio.stats.composition.perturb</a></li>
<li class="toctree-l2"><a class="reference internal" href="skbio.stats.composition.perturb_inv.html">skbio.stats.composition.perturb_inv</a></li>
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<h1>skbio.stats.composition.alr_inv<a class="headerlink" href="#skbio-stats-composition-alr-inv" title="Link to this heading">#</a></h1>
<dl class="py function">
<dt class="sig sig-object py" id="skbio.stats.composition.alr_inv">
<span class="sig-prename descclassname"><span class="pre">skbio.stats.composition.</span></span><span class="sig-name descname"><span class="pre">alr_inv</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mat</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">denominator_idx</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-bio/scikit-bio/blob/main/skbio/stats/composition.py#L710"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#skbio.stats.composition.alr_inv" title="Link to this definition">#</a></dt>
<span class="sig-prename descclassname"><span class="pre">skbio.stats.composition.</span></span><span class="sig-name descname"><span class="pre">alr_inv</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mat</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">denominator_idx</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-bio/scikit-bio/blob/main/skbio/stats/composition.py#L714"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#skbio.stats.composition.alr_inv" title="Link to this definition">#</a></dt>
<dd><p>Perform inverse additive log ratio transform.</p>
<p>This function transforms compositions from the non-isometric real space of
alrs to Aitchison geometry.</p>
<p><span class="math notranslate nohighlight">\(alr^{-1}: \mathbb{R}^{D-1} \rightarrow S^D\)</span></p>
<p>The inverse alr transformation is defined as follows</p>
<div class="math notranslate nohighlight">
\[alr^{-1}: \mathbb{R}^{D-1} \rightarrow S^D\]</div>
<p>The inverse alr transformation is defined as follows:</p>
<div class="math notranslate nohighlight">
\[alr^{-1}(x) = C[exp([y_1, y_2, ..., y_{D-1}, 0])]\]</div>
<p>where <span class="math notranslate nohighlight">\(C[x]\)</span> is the closure operation defined as</p>
Expand All @@ -713,17 +715,17 @@ <h1>skbio.stats.composition.alr_inv<a class="headerlink" href="#skbio-stats-comp
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>mat: numpy.ndarray</strong></dt><dd><p>a matrix of alr-transformed data</p>
<dt><strong>mat</strong><span class="classifier">array_like of shape (n_compositions, n_components - 1)</span></dt><dd><p>A matrix of alr-transformed data.</p>
</dd>
<dt><strong>denominator_idx: int</strong></dt><dd><p>the index of the column (2D-composition) or position (1D-composition) of
the output where the common denominator should be placed. By default
<cite>denominator_idx=0</cite> to specify the first column or position.</p>
<dt><strong>denominator_idx</strong><span class="classifier">int</span></dt><dd><p>The index of the column (2-D matrix) or position (vector) of <code class="docutils literal notranslate"><span class="pre">mat</span></code>
which should be used as the reference composition. Default is 0 which
specifies the first column or position.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt>numpy.ndarray</dt><dd><p>Inverse alr transformed matrix or vector where rows sum to 1.</p>
<dt>ndarray of shape (n_compositions, n_components)</dt><dd><p>Inverse alr-transformed matrix or vector where rows sum to 1.</p>
</dd>
</dl>
</dd>
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