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<section id="numpy-allclose">
<h1>numpy.allclose<a class="headerlink" href="#numpy-allclose" title="Link to this heading">#</a></h1>
<dl class="py function">
<dt class="sig sig-object py" id="numpy.allclose">
<span class="sig-prename descclassname"><span class="pre">numpy.</span></span><span class="sig-name descname"><span class="pre">allclose</span></span><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">b</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rtol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-05</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">atol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-08</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">equal_nan</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/numpy/numpy/blob/main/numpy/_core/numeric.py#L2243-L2330"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#numpy.allclose" title="Link to this definition">#</a></dt>
<dd><p>Returns True if two arrays are element-wise equal within a tolerance.</p>
<p>The tolerance values are positive, typically very small numbers. The
relative difference (<em class="xref py py-obj">rtol</em> * abs(<em class="xref py py-obj">b</em>)) and the absolute difference
<em class="xref py py-obj">atol</em> are added together to compare against the absolute difference
between <em class="xref py py-obj">a</em> and <em class="xref py py-obj">b</em>.</p>
<div class="admonition warning">
<p class="admonition-title">Warning</p>
<p>The default <em class="xref py py-obj">atol</em> is not appropriate for comparing numbers
with magnitudes much smaller than one (see Notes).</p>
</div>
<p>NaNs are treated as equal if they are in the same place and if
<code class="docutils literal notranslate"><span class="pre">equal_nan=True</span></code>. Infs are treated as equal if they are in the same
place and of the same sign in both arrays.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>a, b</strong><span class="classifier">array_like</span></dt><dd><p>Input arrays to compare.</p>
</dd>
<dt><strong>rtol</strong><span class="classifier">array_like</span></dt><dd><p>The relative tolerance parameter (see Notes).</p>
</dd>
<dt><strong>atol</strong><span class="classifier">array_like</span></dt><dd><p>The absolute tolerance parameter (see Notes).</p>
</dd>
<dt><strong>equal_nan</strong><span class="classifier">bool</span></dt><dd><p>Whether to compare NaN’s as equal. If True, NaN’s in <em class="xref py py-obj">a</em> will be
considered equal to NaN’s in <em class="xref py py-obj">b</em> in the output array.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>allclose</strong><span class="classifier">bool</span></dt><dd><p>Returns True if the two arrays are equal within the given
tolerance; False otherwise.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="numpy.isclose.html#numpy.isclose" title="numpy.isclose"><code class="xref py py-obj docutils literal notranslate"><span class="pre">isclose</span></code></a>, <a class="reference internal" href="numpy.all.html#numpy.all" title="numpy.all"><code class="xref py py-obj docutils literal notranslate"><span class="pre">all</span></code></a>, <a class="reference internal" href="numpy.any.html#numpy.any" title="numpy.any"><code class="xref py py-obj docutils literal notranslate"><span class="pre">any</span></code></a>, <a class="reference internal" href="numpy.equal.html#numpy.equal" title="numpy.equal"><code class="xref py py-obj docutils literal notranslate"><span class="pre">equal</span></code></a></dt><dd></dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p>If the following equation is element-wise True, then allclose returns
True.:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">absolute</span><span class="p">(</span><span class="n">a</span> <span class="o">-</span> <span class="n">b</span><span class="p">)</span> <span class="o"><=</span> <span class="p">(</span><span class="n">atol</span> <span class="o">+</span> <span class="n">rtol</span> <span class="o">*</span> <span class="n">absolute</span><span class="p">(</span><span class="n">b</span><span class="p">))</span>
</pre></div>
</div>
<p>The above equation is not symmetric in <em class="xref py py-obj">a</em> and <em class="xref py py-obj">b</em>, so that
<code class="docutils literal notranslate"><span class="pre">allclose(a,</span> <span class="pre">b)</span></code> might be different from <code class="docutils literal notranslate"><span class="pre">allclose(b,</span> <span class="pre">a)</span></code> in
some rare cases.</p>
<p>The default value of <em class="xref py py-obj">atol</em> is not appropriate when the reference value
<em class="xref py py-obj">b</em> has magnitude smaller than one. For example, it is unlikely that
<code class="docutils literal notranslate"><span class="pre">a</span> <span class="pre">=</span> <span class="pre">1e-9</span></code> and <code class="docutils literal notranslate"><span class="pre">b</span> <span class="pre">=</span> <span class="pre">2e-9</span></code> should be considered “close”, yet
<code class="docutils literal notranslate"><span class="pre">allclose(1e-9,</span> <span class="pre">2e-9)</span></code> is <code class="docutils literal notranslate"><span class="pre">True</span></code> with default settings. Be sure
to select <em class="xref py py-obj">atol</em> for the use case at hand, especially for defining the
threshold below which a non-zero value in <em class="xref py py-obj">a</em> will be considered “close”
to a very small or zero value in <em class="xref py py-obj">b</em>.</p>
<p>The comparison of <em class="xref py py-obj">a</em> and <em class="xref py py-obj">b</em> uses standard broadcasting, which
means that <em class="xref py py-obj">a</em> and <em class="xref py py-obj">b</em> need not have the same shape in order for
<code class="docutils literal notranslate"><span class="pre">allclose(a,</span> <span class="pre">b)</span></code> to evaluate to True. The same is true for
<a class="reference internal" href="numpy.equal.html#numpy.equal" title="numpy.equal"><code class="xref py py-obj docutils literal notranslate"><span class="pre">equal</span></code></a> but not <a class="reference internal" href="numpy.array_equal.html#numpy.array_equal" title="numpy.array_equal"><code class="xref py py-obj docutils literal notranslate"><span class="pre">array_equal</span></code></a>.</p>
<p><a class="reference internal" href="#numpy.allclose" title="numpy.allclose"><code class="xref py py-obj docutils literal notranslate"><span class="pre">allclose</span></code></a> is not defined for non-numeric data types.
<a class="reference internal" href="../arrays.scalars.html#numpy.bool" title="numpy.bool"><code class="xref py py-obj docutils literal notranslate"><span class="pre">bool</span></code></a> is considered a numeric data-type for this purpose.</p>
<p class="rubric">Examples</p>
<div class="try_examples_outer_container docutils container" id="63467bbc-a8a9-4da1-90dc-f45b97793ec2">
<div class="try_examples_button_container"><button class="try_examples_button" onclick="window.tryExamplesShowIframe('63467bbc-a8a9-4da1-90dc-f45b97793ec2','3ea7cd15-f6ff-4ac7-bb51-3bbc0358f0d0','1e9711a0-8f44-4815-8d25-fb1e8fa4af98','../../lite/tree/../notebooks/index.html?path=ca147171_ab77_4f89_9cf2_37325159dec8.ipynb','None')">Try it in your browser!</button></div><div class="try_examples_content docutils container">
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">allclose</span><span class="p">([</span><span class="mf">1e10</span><span class="p">,</span><span class="mf">1e-7</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.00001e10</span><span class="p">,</span><span class="mf">1e-8</span><span class="p">])</span>
<span class="go">False</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">allclose</span><span class="p">([</span><span class="mf">1e10</span><span class="p">,</span><span class="mf">1e-8</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.00001e10</span><span class="p">,</span><span class="mf">1e-9</span><span class="p">])</span>
<span class="go">True</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">allclose</span><span class="p">([</span><span class="mf">1e10</span><span class="p">,</span><span class="mf">1e-8</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0001e10</span><span class="p">,</span><span class="mf">1e-9</span><span class="p">])</span>
<span class="go">False</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">allclose</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">])</span>
<span class="go">False</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">allclose</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">],</span> <span class="n">equal_nan</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="go">True</span>
</pre></div>
</div>
</div>
</div>
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