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<div class="section" id="torch-pinverse">
<h1>torch.pinverse<a class="headerlink" href="#torch-pinverse" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="torch.pinverse">
<code class="sig-prename descclassname">torch.</code><code class="sig-name descname">pinverse</code><span class="sig-paren">(</span><em class="sig-param">input</em>, <em class="sig-param">rcond=1e-15</em><span class="sig-paren">)</span> → Tensor<a class="headerlink" href="#torch.pinverse" title="Permalink to this definition">¶</a></dt>
<dd><p>Calculates the pseudo-inverse (also known as the Moore-Penrose inverse) of a 2D tensor.
Please look at <a class="reference external" href="https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_inverse">Moore-Penrose inverse</a> for more details</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>This method is implemented using the Singular Value Decomposition.</p>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>The pseudo-inverse is not necessarily a continuous function in the elements of the matrix <a class="reference external" href="https://epubs.siam.org/doi/10.1137/0117004">[1]</a>.
Therefore, derivatives are not always existent, and exist for a constant rank only <a class="reference external" href="https://www.jstor.org/stable/2156365">[2]</a>.
However, this method is backprop-able due to the implementation by using SVD results, and
could be unstable. Double-backward will also be unstable due to the usage of SVD internally.
See <a class="reference internal" href="torch.svd.html#torch.svd" title="torch.svd"><code class="xref py py-meth docutils literal notranslate"><span class="pre">svd()</span></code></a> for more details.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>input</strong> (<a class="reference internal" href="../tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – The input tensor of size <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mo>∗</mo><mo separator="true">,</mo><mi>m</mi><mo separator="true">,</mo><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(*, m, n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">∗</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">m</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">n</span><span class="mclose">)</span></span></span></span>
</span> where <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∗</mo></mrow><annotation encoding="application/x-tex">*</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.46528em;vertical-align:0em;"></span><span class="mord">∗</span></span></span></span>
</span> is zero or more batch dimensions</p></li>
<li><p><strong>rcond</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a>) – A floating point value to determine the cutoff for small singular values.
Default: 1e-15</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>The pseudo-inverse of <code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code> of dimensions <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mo>∗</mo><mo separator="true">,</mo><mi>n</mi><mo separator="true">,</mo><mi>m</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(*, n, m)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">∗</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">n</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">m</span><span class="mclose">)</span></span></span></span>
</span></p>
</dd>
</dl>
<p>Example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="nb">input</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">input</span>
<span class="go">tensor([[ 0.5495, 0.0979, -1.4092, -0.1128, 0.4132],</span>
<span class="go"> [-1.1143, -0.3662, 0.3042, 1.6374, -0.9294],</span>
<span class="go"> [-0.3269, -0.5745, -0.0382, -0.5922, -0.6759]])</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">pinverse</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
<span class="go">tensor([[ 0.0600, -0.1933, -0.2090],</span>
<span class="go"> [-0.0903, -0.0817, -0.4752],</span>
<span class="go"> [-0.7124, -0.1631, -0.2272],</span>
<span class="go"> [ 0.1356, 0.3933, -0.5023],</span>
<span class="go"> [-0.0308, -0.1725, -0.5216]])</span>
<span class="gp">>>> </span><span class="c1"># Batched pinverse example</span>
<span class="gp">>>> </span><span class="n">a</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">6</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">b</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">pinverse</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span>
<span class="go">tensor([[[ 1.0000e+00, 1.6391e-07, -1.1548e-07],</span>
<span class="go"> [ 8.3121e-08, 1.0000e+00, -2.7567e-07],</span>
<span class="go"> [ 3.5390e-08, 1.4901e-08, 1.0000e+00]],</span>
<span class="go"> [[ 1.0000e+00, -8.9407e-08, 2.9802e-08],</span>
<span class="go"> [-2.2352e-07, 1.0000e+00, 1.1921e-07],</span>
<span class="go"> [ 0.0000e+00, 8.9407e-08, 1.0000e+00]]])</span>
</pre></div>
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