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<div class="section" id="torch-linalg-tensorinv">
<h1>torch.linalg.tensorinv<a class="headerlink" href="#torch-linalg-tensorinv" title="Permalink to this headline">¶</a></h1>
<dl class="py function">
<dt id="torch.linalg.tensorinv">
<code class="sig-prename descclassname"><span class="pre">torch.linalg.</span></code><code class="sig-name descname"><span class="pre">tensorinv</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">A</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ind</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">out</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span> → <span class="pre">Tensor</span><a class="headerlink" href="#torch.linalg.tensorinv" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the multiplicative inverse of <a class="reference internal" href="torch.tensordot.html#torch.tensordot" title="torch.tensordot"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.tensordot()</span></code></a>.</p>
<p>If <cite>m</cite> is the product of the first <code class="xref py py-attr docutils literal notranslate"><span class="pre">ind</span></code> dimensions of <code class="xref py py-attr docutils literal notranslate"><span class="pre">A</span></code> and <cite>n</cite> is the product of
the rest of the dimensions, this function expects <cite>m</cite> and <cite>n</cite> to be equal.
If this is the case, it computes a tensor <cite>X</cite> such that
<cite>tensordot(</cite><code class="xref py py-attr docutils literal notranslate"><span class="pre">A</span></code><cite>, X, </cite><code class="xref py py-attr docutils literal notranslate"><span class="pre">ind</span></code><cite>)</cite> is the identity matrix in dimension <cite>m</cite>.
<cite>X</cite> will have the shape of <code class="xref py py-attr docutils literal notranslate"><span class="pre">A</span></code> but with the first <code class="xref py py-attr docutils literal notranslate"><span class="pre">ind</span></code> dimensions pushed back to the end</p>
<div class="highlight-text notranslate"><div class="highlight"><pre><span></span>X.shape == A.shape[ind:] + A.shape[:ind]
</pre></div>
</div>
<p>Supports input of float, double, cfloat and cdouble dtypes.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>When <code class="xref py py-attr docutils literal notranslate"><span class="pre">A</span></code> is a <cite>2</cite>-dimensional tensor and <code class="xref py py-attr docutils literal notranslate"><span class="pre">ind</span></code><cite>= 1</cite>,
this function computes the (multiplicative) inverse of <code class="xref py py-attr docutils literal notranslate"><span class="pre">A</span></code>
(see <a class="reference internal" href="torch.linalg.inv.html#torch.linalg.inv" title="torch.linalg.inv"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.linalg.inv()</span></code></a>).</p>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Consider using <a class="reference internal" href="torch.linalg.tensorsolve.html#torch.linalg.tensorsolve" title="torch.linalg.tensorsolve"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.linalg.tensorsolve()</span></code></a> if possible for multiplying a tensor on the left
by the tensor inverse, as:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">tensorsolve</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">)</span> <span class="o">==</span> <span class="n">torch</span><span class="o">.</span><span class="n">tensordot</span><span class="p">(</span><span class="n">tensorinv</span><span class="p">(</span><span class="n">A</span><span class="p">),</span> <span class="n">B</span><span class="p">)</span>
</pre></div>
</div>
<p>It is always prefered to use <a class="reference internal" href="torch.linalg.tensorsolve.html#torch.linalg.tensorsolve" title="torch.linalg.tensorsolve"><code class="xref py py-func docutils literal notranslate"><span class="pre">tensorsolve()</span></code></a> when possible, as it is faster and more
numerically stable than computing the pseudoinverse explicitly.</p>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="torch.linalg.tensorsolve.html#torch.linalg.tensorsolve" title="torch.linalg.tensorsolve"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.linalg.tensorsolve()</span></code></a> computes
<cite>torch.tensordot(tensorinv(</cite><code class="xref py py-attr docutils literal notranslate"><span class="pre">A</span></code><cite>), </cite><code class="xref py py-attr docutils literal notranslate"><span class="pre">B</span></code><cite>)</cite>.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>A</strong> (<a class="reference internal" href="../tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – tensor to invert. Its shape must satisfy
<cite>prod(</cite><code class="xref py py-attr docutils literal notranslate"><span class="pre">A</span></code><cite>.shape[:</cite><code class="xref py py-attr docutils literal notranslate"><span class="pre">ind</span></code><cite>]) ==
prod(</cite><code class="xref py py-attr docutils literal notranslate"><span class="pre">A</span></code><cite>.shape[</cite><code class="xref py py-attr docutils literal notranslate"><span class="pre">ind</span></code><cite>:])</cite>.</p></li>
<li><p><strong>ind</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.10)"><em>int</em></a>) – index at which to compute the inverse of <a class="reference internal" href="torch.tensordot.html#torch.tensordot" title="torch.tensordot"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.tensordot()</span></code></a>. Default: <cite>2</cite>.</p></li>
</ul>
</dd>
<dt class="field-even">Keyword Arguments</dt>
<dd class="field-even"><p><strong>out</strong> (<a class="reference internal" href="../tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a><em>, </em><em>optional</em>) – output tensor. Ignored if <cite>None</cite>. Default: <cite>None</cite>.</p>
</dd>
<dt class="field-odd">Raises</dt>
<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/exceptions.html#RuntimeError" title="(in Python v3.10)"><strong>RuntimeError</strong></a> – if the reshaped <code class="xref py py-attr docutils literal notranslate"><span class="pre">A</span></code> is not invertible or the product of the first
<code class="xref py py-attr docutils literal notranslate"><span class="pre">ind</span></code> dimensions is not equal to the product of the rest.</p>
</dd>
</dl>
<p>Examples:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></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">eye</span><span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="mi">6</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="mi">4</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
<span class="gp">>>> </span><span class="n">Ainv</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">tensorinv</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">ind</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">Ainv</span><span class="o">.</span><span class="n">shape</span>
<span class="go">torch.Size([8, 3, 4, 6])</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">randn</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">6</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">tensordot</span><span class="p">(</span><span class="n">Ainv</span><span class="p">,</span> <span class="n">B</span><span class="p">),</span> <span class="n">torch</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">tensorsolve</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">))</span>
<span class="go">True</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">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">Atensorinv</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">tensorinv</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">ind</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">Ainv</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inverse</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">allclose</span><span class="p">(</span><span class="n">Atensorinv</span><span class="p">,</span> <span class="n">Ainv</span><span class="p">)</span>
<span class="go">True</span>
</pre></div>
</div>
</dd></dl>
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