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<div class="section" id="torch-trapz">
<h1>torch.trapz<a class="headerlink" href="#torch-trapz" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="torch.trapz">
<code class="sig-prename descclassname">torch.</code><code class="sig-name descname">trapz</code><span class="sig-paren">(</span><em class="sig-param">y</em>, <em class="sig-param">x</em>, <em class="sig-param">*</em>, <em class="sig-param">dim=-1</em><span class="sig-paren">)</span> → Tensor<a class="headerlink" href="#torch.trapz" title="Permalink to this definition">¶</a></dt>
<dd><p>Estimate <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∫</mo><mi>y</mi><mtext> </mtext><mi>d</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">\int y\,dx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.11112em;vertical-align:-0.30612em;"></span><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0005599999999999772em;">∫</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">d</span><span class="mord mathnormal">x</span></span></span></span>
</span> along <cite>dim</cite>, using the trapezoid rule.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>y</strong> (<a class="reference internal" href="../tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – The values of the function to integrate</p></li>
<li><p><strong>x</strong> (<a class="reference internal" href="../tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – The points at which the function <cite>y</cite> is sampled.
If <cite>x</cite> is not in ascending order, intervals on which it is decreasing
contribute negatively to the estimated integral (i.e., the convention
<span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mo>∫</mo><mi>a</mi><mi>b</mi></msubsup><mi>f</mi><mo>=</mo><mo>−</mo><msubsup><mo>∫</mo><mi>b</mi><mi>a</mi></msubsup><mi>f</mi></mrow><annotation encoding="application/x-tex">\int_a^b f = -\int_b^a f</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.399828em;vertical-align:-0.35582em;"></span><span class="mop"><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0005599999999999772em;">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.044008em;"><span style="top:-2.34418em;margin-left:-0.19445em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">a</span></span></span><span style="top:-3.2579000000000002em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">b</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.35582em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</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:1.215112em;vertical-align:-0.35582em;"></span><span class="mord">−</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop"><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0005599999999999772em;">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8592920000000001em;"><span style="top:-2.34418em;margin-left:-0.19445em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">b</span></span></span><span style="top:-3.2579000000000002em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">a</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.35582em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span></span></span></span>
</span> is followed).</p></li>
<li><p><strong>dim</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a>) – The dimension along which to integrate.
By default, use the last dimension.</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>A Tensor with the same shape as the input, except with <cite>dim</cite> removed.
Each element of the returned tensor represents the estimated integral
<span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∫</mo><mi>y</mi><mtext> </mtext><mi>d</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">\int y\,dx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.11112em;vertical-align:-0.30612em;"></span><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0005599999999999772em;">∫</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">d</span><span class="mord mathnormal">x</span></span></span></span>
</span> along <cite>dim</cite>.</p>
</dd>
</dl>
<p>Example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">y</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="gp">>>> </span><span class="n">y</span>
<span class="go">tensor([[-2.1156, 0.6857, -0.2700],</span>
<span class="go"> [-1.2145, 0.5540, 2.0431]])</span>
<span class="gp">>>> </span><span class="n">x</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="mi">1</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="p">[</span><span class="mi">1</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="gp">>>> </span><span class="n">torch</span><span class="o">.</span><span class="n">trapz</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
<span class="go">tensor([-1.2220, 0.9683])</span>
</pre></div>
</div>
<dl class="function">
<dt>
<code class="sig-prename descclassname">torch.</code><code class="sig-name descname">trapz</code><span class="sig-paren">(</span><em class="sig-param">y</em>, <em class="sig-param">*</em>, <em class="sig-param">dx=1</em>, <em class="sig-param">dim=-1</em><span class="sig-paren">)</span> → Tensor</dt>
<dd></dd></dl>
<p>As above, but the sample points are spaced uniformly at a distance of <cite>dx</cite>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>y</strong> (<a class="reference internal" href="../tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – The values of the function to integrate</p></li>
<li><p><strong>dx</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.9)"><em>float</em></a>) – The distance between points at which <cite>y</cite> is sampled.</p></li>
<li><p><strong>dim</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.9)"><em>int</em></a>) – The dimension along which to integrate.
By default, use the last dimension.</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>A Tensor with the same shape as the input, except with <cite>dim</cite> removed.
Each element of the returned tensor represents the estimated integral
<span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∫</mo><mi>y</mi><mtext> </mtext><mi>d</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">\int y\,dx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.11112em;vertical-align:-0.30612em;"></span><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0005599999999999772em;">∫</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">d</span><span class="mord mathnormal">x</span></span></span></span>
</span> along <cite>dim</cite>.</p>
</dd>
</dl>
</dd></dl>
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