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<div class="section" id="torch-tril">
<h1>torch.tril<a class="headerlink" href="#torch-tril" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="torch.tril">
<code class="sig-prename descclassname">torch.</code><code class="sig-name descname">tril</code><span class="sig-paren">(</span><em class="sig-param">input</em>, <em class="sig-param">diagonal=0</em>, <em class="sig-param">*</em>, <em class="sig-param">out=None</em><span class="sig-paren">)</span> → Tensor<a class="headerlink" href="#torch.tril" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the lower triangular part of the matrix (2-D tensor) or batch of matrices
<code class="xref py py-attr docutils literal notranslate"><span class="pre">input</span></code>, the other elements of the result tensor <code class="xref py py-attr docutils literal notranslate"><span class="pre">out</span></code> are set to 0.</p>
<p>The lower triangular part of the matrix is defined as the elements on and
below the diagonal.</p>
<p>The argument <a class="reference internal" href="torch.diagonal.html#torch.diagonal" title="torch.diagonal"><code class="xref py py-attr docutils literal notranslate"><span class="pre">diagonal</span></code></a> controls which diagonal to consider. If
<a class="reference internal" href="torch.diagonal.html#torch.diagonal" title="torch.diagonal"><code class="xref py py-attr docutils literal notranslate"><span class="pre">diagonal</span></code></a> = 0, all elements on and below the main diagonal are
retained. A positive value includes just as many diagonals above the main
diagonal, and similarly a negative value excludes just as many diagonals below
the main diagonal. The main diagonal are the set of indices
<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 stretchy="false">(</mo><mi>i</mi><mo separator="true">,</mo><mi>i</mi><mo stretchy="false">)</mo><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">\lbrace (i, i) \rbrace</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="mopen">(</span><span class="mord mathnormal">i</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">i</span><span class="mclose">)</span><span class="mclose">}</span></span></span></span>
</span> for <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi><mo>∈</mo><mo stretchy="false">[</mo><mn>0</mn><mo separator="true">,</mo><mi>min</mi><mo></mo><mo stretchy="false">{</mo><msub><mi>d</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>d</mi><mn>2</mn></msub><mo stretchy="false">}</mo><mo>−</mo><mn>1</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">i \in [0, \min\{d_{1}, d_{2}\} - 1]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69862em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">[</span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop">min</span><span class="mopen">{</span><span class="mord"><span class="mord mathnormal">d</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;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">1</span></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="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal">d</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;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">2</span></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="mclose">}</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</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><msub><mi>d</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>d</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">d_{1}, d_{2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">d</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;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">1</span></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="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal">d</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;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">2</span></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> are the dimensions of the matrix.</p>
<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.</p></li>
<li><p><strong>diagonal</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a><em>, </em><em>optional</em>) – the diagonal to consider</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>) – the output tensor.</p>
</dd>
</dl>
<p>Example:</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">3</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">a</span>
<span class="go">tensor([[-1.0813, -0.8619, 0.7105],</span>
<span class="go"> [ 0.0935, 0.1380, 2.2112],</span>
<span class="go"> [-0.3409, -0.9828, 0.0289]])</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">tril</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="go">tensor([[-1.0813, 0.0000, 0.0000],</span>
<span class="go"> [ 0.0935, 0.1380, 0.0000],</span>
<span class="go"> [-0.3409, -0.9828, 0.0289]])</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">b</span>
<span class="go">tensor([[ 1.2219, 0.5653, -0.2521, -0.2345, 1.2544, 0.3461],</span>
<span class="go"> [ 0.4785, -0.4477, 0.6049, 0.6368, 0.8775, 0.7145],</span>
<span class="go"> [ 1.1502, 3.2716, -1.1243, -0.5413, 0.3615, 0.6864],</span>
<span class="go"> [-0.0614, -0.7344, -1.3164, -0.7648, -1.4024, 0.0978]])</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">tril</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">diagonal</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="go">tensor([[ 1.2219, 0.5653, 0.0000, 0.0000, 0.0000, 0.0000],</span>
<span class="go"> [ 0.4785, -0.4477, 0.6049, 0.0000, 0.0000, 0.0000],</span>
<span class="go"> [ 1.1502, 3.2716, -1.1243, -0.5413, 0.0000, 0.0000],</span>
<span class="go"> [-0.0614, -0.7344, -1.3164, -0.7648, -1.4024, 0.0000]])</span>
<span class="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">tril</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">diagonal</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
<span class="go">tensor([[ 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000],</span>
<span class="go"> [ 0.4785, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000],</span>
<span class="go"> [ 1.1502, 3.2716, 0.0000, 0.0000, 0.0000, 0.0000],</span>
<span class="go"> [-0.0614, -0.7344, -1.3164, 0.0000, 0.0000, 0.0000]])</span>
</pre></div>
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