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<div class="section" id="torch-linalg-cond">
<h1>torch.linalg.cond<a class="headerlink" href="#torch-linalg-cond" title="Permalink to this headline">¶</a></h1>
<dl class="py function">
<dt id="torch.linalg.cond">
<code class="sig-prename descclassname"><span class="pre">torch.linalg.</span></code><code class="sig-name descname"><span class="pre">cond</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">p</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</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.cond" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the condition number of a matrix with respect to a matrix norm.</p>
<p>Letting <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="double-struck">K</mi></mrow><annotation encoding="application/x-tex">\mathbb{K}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6889em;"></span><span class="mord mathbb">K</span></span></span></span></span> be <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow><annotation encoding="application/x-tex">\mathbb{R}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6889em;"></span><span class="mord mathbb">R</span></span></span></span></span> or <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="double-struck">C</mi></mrow><annotation encoding="application/x-tex">\mathbb{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6889em;"></span><span class="mord mathbb">C</span></span></span></span></span>,
the <strong>condition number</strong> <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>κ</mi></mrow><annotation encoding="application/x-tex">\kappa</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">κ</span></span></span></span></span> of a matrix
<span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>∈</mo><msup><mi mathvariant="double-struck">K</mi><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow></msup></mrow><annotation encoding="application/x-tex">A \in \mathbb{K}^{n \times n}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7224em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7713em;"></span><span class="mord"><span class="mord mathbb">K</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7713em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">×</span><span class="mord mathnormal mtight">n</span></span></span></span></span></span></span></span></span></span></span></span></span> is defined as</p>
<div class="math">
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>κ</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo><mo>=</mo><mi mathvariant="normal">∥</mi><mi>A</mi><msub><mi mathvariant="normal">∥</mi><mi>p</mi></msub><mi mathvariant="normal">∥</mi><msup><mi>A</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><msub><mi mathvariant="normal">∥</mi><mi>p</mi></msub></mrow><annotation encoding="application/x-tex">\kappa(A) = \|A\|_p\|A^{-1}\|_p</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="mord mathnormal">κ</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1502em;vertical-align:-0.2861em;"></span><span class="mord">∥</span><span class="mord mathnormal">A</span><span class="mord"><span class="mord">∥</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">p</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mord">∥</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span><span class="mord"><span class="mord">∥</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">p</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></span></span></div><p>The condition number of <code class="xref py py-attr docutils literal notranslate"><span class="pre">A</span></code> measures the numerical stability of the linear system <cite>AX = B</cite>
with respect to a matrix norm.</p>
<p>Supports input of float, double, cfloat and cdouble dtypes.
Also supports batches of matrices, and if <code class="xref py py-attr docutils literal notranslate"><span class="pre">A</span></code> is a batch of matrices then
the output has the same batch dimensions.</p>
<p><code class="xref py py-attr docutils literal notranslate"><span class="pre">p</span></code> defines the matrix norm that is computed. The following norms are supported:</p>
<table class="docutils colwidths-auto align-default">
<thead>
<tr class="row-odd"><th class="head"><p><code class="xref py py-attr docutils literal notranslate"><span class="pre">p</span></code></p></th>
<th class="head"><p>matrix norm</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p><cite>None</cite></p></td>
<td><p><cite>2</cite>-norm (largest singular value)</p></td>
</tr>
<tr class="row-odd"><td><p><cite>‘fro’</cite></p></td>
<td><p>Frobenius norm</p></td>
</tr>
<tr class="row-even"><td><p><cite>‘nuc’</cite></p></td>
<td><p>nuclear norm</p></td>
</tr>
<tr class="row-odd"><td><p><cite>inf</cite></p></td>
<td><p><cite>max(sum(abs(x), dim=1))</cite></p></td>
</tr>
<tr class="row-even"><td><p><cite>-inf</cite></p></td>
<td><p><cite>min(sum(abs(x), dim=1))</cite></p></td>
</tr>
<tr class="row-odd"><td><p><cite>1</cite></p></td>
<td><p><cite>max(sum(abs(x), dim=0))</cite></p></td>
</tr>
<tr class="row-even"><td><p><cite>-1</cite></p></td>
<td><p><cite>min(sum(abs(x), dim=0))</cite></p></td>
</tr>
<tr class="row-odd"><td><p><cite>2</cite></p></td>
<td><p>largest singular value</p></td>
</tr>
<tr class="row-even"><td><p><cite>-2</cite></p></td>
<td><p>smallest singular value</p></td>
</tr>
</tbody>
</table>
<p>where <cite>inf</cite> refers to <cite>float(‘inf’)</cite>, NumPy’s <cite>inf</cite> object, or any equivalent object.</p>
<p>For <code class="xref py py-attr docutils literal notranslate"><span class="pre">p</span></code> is one of <cite>(‘fro’, ‘nuc’, inf, -inf, 1, -1)</cite>, this function uses
<a class="reference internal" href="torch.linalg.norm.html#torch.linalg.norm" title="torch.linalg.norm"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.linalg.norm()</span></code></a> and <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>.
As such, in this case, the matrix (or every matrix in the batch) <code class="xref py py-attr docutils literal notranslate"><span class="pre">A</span></code> has to be square
and invertible.</p>
<p>For <code class="xref py py-attr docutils literal notranslate"><span class="pre">p</span></code> in <cite>(2, -2)</cite>, this function can be computed in terms of the singular values
<span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>σ</mi><mn>1</mn></msub><mo>≥</mo><mo>…</mo><mo>≥</mo><msub><mi>σ</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">\sigma_1 \geq \ldots \geq \sigma_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.786em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></p>
<div class="math">
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>κ</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><msub><mi>σ</mi><mn>1</mn></msub><msub><mi>σ</mi><mi>n</mi></msub></mfrac><mspace width="2em"/><msub><mi>κ</mi><mrow><mo>−</mo><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><msub><mi>σ</mi><mi>n</mi></msub><msub><mi>σ</mi><mn>1</mn></msub></mfrac></mrow><annotation encoding="application/x-tex">\kappa_2(A) = \frac{\sigma_1}{\sigma_n}\qquad \kappa_{-2}(A) = \frac{\sigma_n}{\sigma_1}</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="mord"><span class="mord mathnormal">κ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.9436em;vertical-align:-0.836em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1076em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.836em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:2em;"></span><span class="mord"><span class="mord mathnormal">κ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2083em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.9436em;vertical-align:-0.836em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1076em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.836em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>In these cases, it is computed using <a class="reference internal" href="torch.linalg.svdvals.html#torch.linalg.svdvals" title="torch.linalg.svdvals"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.linalg.svdvals()</span></code></a>. For these norms, the matrix
(or every matrix in the batch) <code class="xref py py-attr docutils literal notranslate"><span class="pre">A</span></code> may have any shape.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>When inputs are on a CUDA device, this function synchronizes that device with the CPU
if <code class="xref py py-attr docutils literal notranslate"><span class="pre">p</span></code> is one of <cite>(‘fro’, ‘nuc’, inf, -inf, 1, -1)</cite>.</p>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="torch.linalg.solve.html#torch.linalg.solve" title="torch.linalg.solve"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.linalg.solve()</span></code></a> for a function that solves linear systems of square matrices.</p>
<p><a class="reference internal" href="torch.linalg.lstsq.html#torch.linalg.lstsq" title="torch.linalg.lstsq"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.linalg.lstsq()</span></code></a> for a function that solves linear systems of general matrices.</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 of shape <cite>(*, m, n)</cite> where <cite>*</cite> is zero or more batch dimensions
for <code class="xref py py-attr docutils literal notranslate"><span class="pre">p</span></code> in <cite>(2, -2)</cite>, and of shape <cite>(*, n, n)</cite> where every matrix
is invertible for <code class="xref py py-attr docutils literal notranslate"><span class="pre">p</span></code> in <cite>(‘fro’, ‘nuc’, inf, -inf, 1, -1)</cite>.</p></li>
<li><p><strong>p</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.10)"><em>int</em></a><em>, </em><em>inf</em><em>, </em><em>-inf</em><em>, </em><em>'fro'</em><em>, </em><em>'nuc'</em><em>, </em><em>optional</em>) – the type of the matrix norm to use in the computations (see above). Default: <cite>None</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">Returns</dt>
<dd class="field-odd"><p>A real-valued tensor, even when <code class="xref py py-attr docutils literal notranslate"><span class="pre">A</span></code> is complex.</p>
</dd>
<dt class="field-even">Raises</dt>
<dd class="field-even"><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 <code class="xref py py-attr docutils literal notranslate"><span class="pre">p</span></code> is one of <cite>(‘fro’, ‘nuc’, inf, -inf, 1, -1)</cite>
and the <code class="xref py py-attr docutils literal notranslate"><span class="pre">A</span></code> matrix or any matrix in the batch <code class="xref py py-attr docutils literal notranslate"><span class="pre">A</span></code> is not square
or invertible.</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">randn</span><span class="p">(</span><span class="mi">3</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="n">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">complex64</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">cond</span><span class="p">(</span><span class="n">A</span><span class="p">)</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">tensor</span><span class="p">([[</span><span class="mf">1.</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">cond</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
<span class="go">tensor([1.4142])</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">cond</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="s1">'fro'</span><span class="p">)</span>
<span class="go">tensor(3.1623)</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">cond</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="s1">'nuc'</span><span class="p">)</span>
<span class="go">tensor(9.2426)</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">cond</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="nb">float</span><span class="p">(</span><span class="s1">'inf'</span><span class="p">))</span>
<span class="go">tensor(2.)</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">cond</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="nb">float</span><span class="p">(</span><span class="s1">'-inf'</span><span class="p">))</span>
<span class="go">tensor(1.)</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">cond</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="go">tensor(2.)</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">cond</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="go">tensor(1.)</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">cond</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="go">tensor([1.4142])</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">cond</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">)</span>
<span class="go">tensor([0.7071])</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">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">cond</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
<span class="go">tensor([[9.5917],</span>
<span class="go"> [3.2538]])</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">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">complex64</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">cond</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
<span class="go">tensor([[4.6245],</span>
<span class="go"> [4.5671]])</span>
</pre></div>
</div>
</dd></dl>
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