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Matching</h1><div class="page-info"><!----><!----><span class="page-date-info" aria-label="Writing Date"><svg xmlns="http://www.w3.org/2000/svg" class="icon calendar-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="calendar icon"><path d="M716.4 110.137c0-18.753-14.72-33.473-33.472-33.473-18.753 0-33.473 14.72-33.473 33.473v33.473h66.993v-33.473zm-334.87 0c0-18.753-14.72-33.473-33.473-33.473s-33.52 14.72-33.52 33.473v33.473h66.993v-33.473zm468.81 33.52H716.4v100.465c0 18.753-14.72 33.473-33.472 33.473a33.145 33.145 0 01-33.473-33.473V143.657H381.53v100.465c0 18.753-14.72 33.473-33.473 33.473a33.145 33.145 0 01-33.473-33.473V143.657H180.6A134.314 134.314 0 0046.66 277.595v535.756A134.314 134.314 0 00180.6 947.289h669.74a134.36 134.36 0 00133.94-133.938V277.595a134.314 134.314 0 00-133.94-133.938zm33.473 267.877H147.126a33.145 33.145 0 01-33.473-33.473c0-18.752 14.72-33.473 33.473-33.473h736.687c18.752 0 33.472 14.72 33.472 33.473a33.145 33.145 0 01-33.472 33.473z"></path></svg><span><!----></span><meta property="datePublished" content="2023-08-08T09:39:28.000Z"></span><!----><span class="page-reading-time-info" aria-label="Reading Time"><svg xmlns="http://www.w3.org/2000/svg" class="icon timer-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="timer icon"><path d="M799.387 122.15c4.402-2.978 7.38-7.897 7.38-13.463v-1.165c0-8.933-7.38-16.312-16.312-16.312H256.33c-8.933 0-16.311 7.38-16.311 16.312v1.165c0 5.825 2.977 10.874 7.637 13.592 4.143 194.44 97.22 354.963 220.201 392.763-122.204 37.542-214.893 196.511-220.2 389.397-4.661 5.049-7.638 11.651-7.638 19.03v5.825h566.49v-5.825c0-7.379-2.849-13.981-7.509-18.9-5.049-193.016-97.867-351.985-220.2-389.527 123.24-37.67 216.446-198.453 220.588-392.892zM531.16 450.445v352.632c117.674 1.553 211.787 40.778 211.787 88.676H304.097c0-48.286 95.149-87.382 213.728-88.676V450.445c-93.077-3.107-167.901-81.297-167.901-177.093 0-8.803 6.99-15.793 15.793-15.793 8.803 0 15.794 6.99 15.794 15.793 0 80.261 63.69 145.635 142.01 145.635s142.011-65.374 142.011-145.635c0-8.803 6.99-15.793 15.794-15.793s15.793 6.99 15.793 15.793c0 95.019-73.789 172.82-165.96 177.093z"></path></svg><span>About 5 min</span><meta property="timeRequired" content="PT5M"></span><!----><!----></div><hr></div><div class="toc-place-holder"><aside id="toc"><!--[--><!----><!--]--><div class="toc-header">On This Page<button type="button" class="print-button" title="Print"><svg xmlns="http://www.w3.org/2000/svg" class="icon print-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="print icon"><path d="M819.2 364.8h-44.8V128c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v236.8h-44.8C145.067 364.8 96 413.867 96 473.6v192c0 59.733 49.067 108.8 108.8 108.8h44.8V896c0 17.067 14.933 32 32 32h460.8c17.067 0 32-14.933 32-32V774.4h44.8c59.733 0 108.8-49.067 108.8-108.8v-192c0-59.733-49.067-108.8-108.8-108.8zM313.6 160h396.8v204.8H313.6V160zm396.8 704H313.6V620.8h396.8V864zM864 665.6c0 25.6-19.2 44.8-44.8 44.8h-44.8V588.8c0-17.067-14.933-32-32-32H281.6c-17.067 0-32 14.933-32 32v121.6h-44.8c-25.6 0-44.8-19.2-44.8-44.8v-192c0-25.6 19.2-44.8 44.8-44.8h614.4c25.6 0 44.8 19.2 44.8 44.8v192z"></path></svg></button></div><div class="toc-wrapper"><ul class="toc-list"><!--[--><li class="toc-item"><a class="vp-link toc-link level2" href="/#cov">Cov</a></li><li><ul class="toc-list"><!--[--><li class="toc-item"><a class="vp-link toc-link level3" href="/#usage">Usage</a></li><!----><!--]--><!--[--><li class="toc-item"><a class="vp-link toc-link level3" href="/#examples">Examples</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="toc-item"><a class="vp-link toc-link level2" href="/#dtw">DTW</a></li><li><ul class="toc-list"><!--[--><li class="toc-item"><a class="vp-link toc-link level3" href="/#usage-1">Usage</a></li><!----><!--]--><!--[--><li class="toc-item"><a class="vp-link toc-link level3" href="/#examples-1">Examples</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="toc-item"><a class="vp-link toc-link level2" href="/#pearson">Pearson</a></li><li><ul class="toc-list"><!--[--><li class="toc-item"><a class="vp-link toc-link level3" href="/#usage-2">Usage</a></li><!----><!--]--><!--[--><li class="toc-item"><a class="vp-link toc-link level3" href="/#examples-2">Examples</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="toc-item"><a class="vp-link toc-link level2" href="/#ptnsym">PtnSym</a></li><li><ul class="toc-list"><!--[--><li class="toc-item"><a class="vp-link toc-link level3" href="/#usage-3">Usage</a></li><!----><!--]--><!--[--><li class="toc-item"><a class="vp-link toc-link level3" href="/#example">Example</a></li><!----><!--]--></ul></li><!--]--><!--[--><li class="toc-item"><a class="vp-link toc-link level2" href="/#xcorr">XCorr</a></li><li><ul class="toc-list"><!--[--><li class="toc-item"><a class="vp-link toc-link level3" href="/#usage-4">Usage</a></li><!----><!--]--><!--[--><li class="toc-item"><a class="vp-link toc-link level3" href="/#examples-3">Examples</a></li><!----><!--]--></ul></li><!--]--></ul><div class="toc-marker" style="top:-1.7rem;"></div></div><!--[--><!----><!--]--></aside></div><!----><div class="theme-hope-content"><!--

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--><h1 id="data-matching" tabindex="-1"><a class="header-anchor" href="#data-matching" aria-hidden="true">#</a> Data Matching</h1><h2 id="cov" tabindex="-1"><a class="header-anchor" href="#cov" aria-hidden="true">#</a> Cov</h2><h3 id="usage" tabindex="-1"><a class="header-anchor" href="#usage" aria-hidden="true">#</a> Usage</h3><p>This function is used to calculate the population covariance.</p><p><strong>Name:</strong> COV</p><p><strong>Input Series:</strong> Only support two input series. The types are both INT32 / INT64 / FLOAT / DOUBLE.</p><p><strong>Output Series:</strong> Output a single series. The type is DOUBLE. There is only one data point in the series, whose timestamp is 0 and value is the population covariance.</p><p><strong>Note:</strong></p><ul><li>If a row contains missing points, null points or <code>NaN</code>, it will be ignored;</li><li>If all rows are ignored, <code>NaN</code> will be output.</li></ul><h3 id="examples" tabindex="-1"><a class="header-anchor" href="#examples" aria-hidden="true">#</a> Examples</h3><p>Input series:</p><div class="language-text line-numbers-mode" data-ext="text"><pre class="language-text"><code>+-----------------------------+---------------+---------------+
|                         Time|root.test.d2.s1|root.test.d2.s2|
+-----------------------------+---------------+---------------+
|2020-01-01T00:00:02.000+08:00|          100.0|          101.0|
|2020-01-01T00:00:03.000+08:00|          101.0|           null|
|2020-01-01T00:00:04.000+08:00|          102.0|          101.0|
|2020-01-01T00:00:06.000+08:00|          104.0|          102.0|
|2020-01-01T00:00:08.000+08:00|          126.0|          102.0|
|2020-01-01T00:00:10.000+08:00|          108.0|          103.0|
|2020-01-01T00:00:12.000+08:00|           null|          103.0|
|2020-01-01T00:00:14.000+08:00|          112.0|          104.0|
|2020-01-01T00:00:15.000+08:00|          113.0|           null|
|2020-01-01T00:00:16.000+08:00|          114.0|          104.0|
|2020-01-01T00:00:18.000+08:00|          116.0|          105.0|
|2020-01-01T00:00:20.000+08:00|          118.0|          105.0|
|2020-01-01T00:00:22.000+08:00|          100.0|          106.0|
|2020-01-01T00:00:26.000+08:00|          124.0|          108.0|
|2020-01-01T00:00:28.000+08:00|          126.0|          108.0|
|2020-01-01T00:00:30.000+08:00|            NaN|          108.0|
+-----------------------------+---------------+---------------+
</code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><p>SQL for query:</p><div class="language-sql line-numbers-mode" data-ext="sql"><pre class="language-sql"><code><span class="token keyword">select</span> cov<span class="token punctuation">(</span>s1<span class="token punctuation">,</span>s2<span class="token punctuation">)</span> <span class="token keyword">from</span> root<span class="token punctuation">.</span>test<span class="token punctuation">.</span>d2
</code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div></div></div><p>Output series:</p><div class="language-text line-numbers-mode" data-ext="text"><pre class="language-text"><code>+-----------------------------+-------------------------------------+
|                         Time|cov(root.test.d2.s1, root.test.d2.s2)|
+-----------------------------+-------------------------------------+
|1970-01-01T08:00:00.000+08:00|                   12.291666666666666|
+-----------------------------+-------------------------------------+
</code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="dtw" tabindex="-1"><a class="header-anchor" href="#dtw" aria-hidden="true">#</a> DTW</h2><h3 id="usage-1" tabindex="-1"><a class="header-anchor" href="#usage-1" aria-hidden="true">#</a> Usage</h3><p>This function is used to calculate the DTW distance between two input series.</p><p><strong>Name:</strong> DTW</p><p><strong>Input Series:</strong> Only support two input series. The types are both INT32 / INT64 / FLOAT / DOUBLE.</p><p><strong>Output Series:</strong> Output a single series. The type is DOUBLE. There is only one data point in the series, whose timestamp is 0 and value is the DTW distance.</p><p><strong>Note:</strong></p><ul><li>If a row contains missing points, null points or <code>NaN</code>, it will be ignored;</li><li>If all rows are ignored, <code>0</code> will be output.</li></ul><h3 id="examples-1" tabindex="-1"><a class="header-anchor" href="#examples-1" aria-hidden="true">#</a> Examples</h3><p>Input series:</p><div class="language-text line-numbers-mode" data-ext="text"><pre class="language-text"><code>+-----------------------------+---------------+---------------+
|                         Time|root.test.d2.s1|root.test.d2.s2|
+-----------------------------+---------------+---------------+
|1970-01-01T08:00:00.001+08:00|            1.0|            2.0|
|1970-01-01T08:00:00.002+08:00|            1.0|            2.0|
|1970-01-01T08:00:00.003+08:00|            1.0|            2.0|
|1970-01-01T08:00:00.004+08:00|            1.0|            2.0|
|1970-01-01T08:00:00.005+08:00|            1.0|            2.0|
|1970-01-01T08:00:00.006+08:00|            1.0|            2.0|
|1970-01-01T08:00:00.007+08:00|            1.0|            2.0|
|1970-01-01T08:00:00.008+08:00|            1.0|            2.0|
|1970-01-01T08:00:00.009+08:00|            1.0|            2.0|
|1970-01-01T08:00:00.010+08:00|            1.0|            2.0|
|1970-01-01T08:00:00.011+08:00|            1.0|            2.0|
|1970-01-01T08:00:00.012+08:00|            1.0|            2.0|
|1970-01-01T08:00:00.013+08:00|            1.0|            2.0|
|1970-01-01T08:00:00.014+08:00|            1.0|            2.0|
|1970-01-01T08:00:00.015+08:00|            1.0|            2.0|
|1970-01-01T08:00:00.016+08:00|            1.0|            2.0|
|1970-01-01T08:00:00.017+08:00|            1.0|            2.0|
|1970-01-01T08:00:00.018+08:00|            1.0|            2.0|
|1970-01-01T08:00:00.019+08:00|            1.0|            2.0|
|1970-01-01T08:00:00.020+08:00|            1.0|            2.0|
+-----------------------------+---------------+---------------+
</code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><p>SQL for query:</p><div class="language-sql line-numbers-mode" data-ext="sql"><pre class="language-sql"><code><span class="token keyword">select</span> dtw<span class="token punctuation">(</span>s1<span class="token punctuation">,</span>s2<span class="token punctuation">)</span> <span class="token keyword">from</span> root<span class="token punctuation">.</span>test<span class="token punctuation">.</span>d2
</code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div></div></div><p>Output series:</p><div class="language-text line-numbers-mode" data-ext="text"><pre class="language-text"><code>+-----------------------------+-------------------------------------+
|                         Time|dtw(root.test.d2.s1, root.test.d2.s2)|
+-----------------------------+-------------------------------------+
|1970-01-01T08:00:00.000+08:00|                                 20.0|
+-----------------------------+-------------------------------------+
</code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="pearson" tabindex="-1"><a class="header-anchor" href="#pearson" aria-hidden="true">#</a> Pearson</h2><h3 id="usage-2" tabindex="-1"><a class="header-anchor" href="#usage-2" aria-hidden="true">#</a> Usage</h3><p>This function is used to calculate the Pearson Correlation Coefficient.</p><p><strong>Name:</strong> PEARSON</p><p><strong>Input Series:</strong> Only support two input series. The types are both INT32 / INT64 / FLOAT / DOUBLE.</p><p><strong>Output Series:</strong> Output a single series. The type is DOUBLE. There is only one data point in the series, whose timestamp is 0 and value is the Pearson Correlation Coefficient.</p><p><strong>Note:</strong></p><ul><li>If a row contains missing points, null points or <code>NaN</code>, it will be ignored;</li><li>If all rows are ignored, <code>NaN</code> will be output.</li></ul><h3 id="examples-2" tabindex="-1"><a class="header-anchor" href="#examples-2" aria-hidden="true">#</a> Examples</h3><p>Input series:</p><div class="language-text line-numbers-mode" data-ext="text"><pre class="language-text"><code>+-----------------------------+---------------+---------------+
|                         Time|root.test.d2.s1|root.test.d2.s2|
+-----------------------------+---------------+---------------+
|2020-01-01T00:00:02.000+08:00|          100.0|          101.0|
|2020-01-01T00:00:03.000+08:00|          101.0|           null|
|2020-01-01T00:00:04.000+08:00|          102.0|          101.0|
|2020-01-01T00:00:06.000+08:00|          104.0|          102.0|
|2020-01-01T00:00:08.000+08:00|          126.0|          102.0|
|2020-01-01T00:00:10.000+08:00|          108.0|          103.0|
|2020-01-01T00:00:12.000+08:00|           null|          103.0|
|2020-01-01T00:00:14.000+08:00|          112.0|          104.0|
|2020-01-01T00:00:15.000+08:00|          113.0|           null|
|2020-01-01T00:00:16.000+08:00|          114.0|          104.0|
|2020-01-01T00:00:18.000+08:00|          116.0|          105.0|
|2020-01-01T00:00:20.000+08:00|          118.0|          105.0|
|2020-01-01T00:00:22.000+08:00|          100.0|          106.0|
|2020-01-01T00:00:26.000+08:00|          124.0|          108.0|
|2020-01-01T00:00:28.000+08:00|          126.0|          108.0|
|2020-01-01T00:00:30.000+08:00|            NaN|          108.0|
+-----------------------------+---------------+---------------+
</code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><p>SQL for query:</p><div class="language-sql line-numbers-mode" data-ext="sql"><pre class="language-sql"><code><span class="token keyword">select</span> pearson<span class="token punctuation">(</span>s1<span class="token punctuation">,</span>s2<span class="token punctuation">)</span> <span class="token keyword">from</span> root<span class="token punctuation">.</span>test<span class="token punctuation">.</span>d2
</code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div></div></div><p>Output series:</p><div class="language-text line-numbers-mode" data-ext="text"><pre class="language-text"><code>+-----------------------------+-----------------------------------------+
|                         Time|pearson(root.test.d2.s1, root.test.d2.s2)|
+-----------------------------+-----------------------------------------+
|1970-01-01T08:00:00.000+08:00|                       0.5630881927754872|
+-----------------------------+-----------------------------------------+
</code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="ptnsym" tabindex="-1"><a class="header-anchor" href="#ptnsym" aria-hidden="true">#</a> PtnSym</h2><h3 id="usage-3" tabindex="-1"><a class="header-anchor" href="#usage-3" aria-hidden="true">#</a> Usage</h3><p>This function is used to find all symmetric subseries in the input whose degree of symmetry is less than the threshold.<br> The degree of symmetry is calculated by DTW.<br> The smaller the degree, the more symmetrical the series is.</p><p><strong>Name:</strong> PATTERNSYMMETRIC</p><p><strong>Input Series:</strong> Only support a single input series. The type is INT32 / INT64 / FLOAT / DOUBLE</p><p><strong>Parameter:</strong></p><ul><li><code>window</code>: The length of the symmetric subseries. It&#39;s a positive integer and the default value is 10.</li><li><code>threshold</code>: The threshold of the degree of symmetry. It&#39;s non-negative. Only the subseries whose degree of symmetry is below it will be output. By default, all subseries will be output.</li></ul><p><strong>Output Series:</strong> Output a single series. The type is DOUBLE. Each data point in the output series corresponds to a symmetric subseries. The output timestamp is the starting timestamp of the subseries and the output value is the degree of symmetry.</p><h3 id="example" tabindex="-1"><a class="header-anchor" href="#example" aria-hidden="true">#</a> Example</h3><p>Input series:</p><div class="language-text line-numbers-mode" data-ext="text"><pre class="language-text"><code>+-----------------------------+---------------+
|                         Time|root.test.d1.s4|
+-----------------------------+---------------+
|2021-01-01T12:00:00.000+08:00|            1.0|
|2021-01-01T12:00:01.000+08:00|            2.0|
|2021-01-01T12:00:02.000+08:00|            3.0|
|2021-01-01T12:00:03.000+08:00|            2.0|
|2021-01-01T12:00:04.000+08:00|            1.0|
|2021-01-01T12:00:05.000+08:00|            1.0|
|2021-01-01T12:00:06.000+08:00|            1.0|
|2021-01-01T12:00:07.000+08:00|            1.0|
|2021-01-01T12:00:08.000+08:00|            2.0|
|2021-01-01T12:00:09.000+08:00|            3.0|
|2021-01-01T12:00:10.000+08:00|            2.0|
|2021-01-01T12:00:11.000+08:00|            1.0|
+-----------------------------+---------------+
</code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><p>SQL for query:</p><div class="language-sql line-numbers-mode" data-ext="sql"><pre class="language-sql"><code><span class="token keyword">select</span> ptnsym<span class="token punctuation">(</span>s4<span class="token punctuation">,</span> <span class="token string">&#39;window&#39;</span><span class="token operator">=</span><span class="token string">&#39;5&#39;</span><span class="token punctuation">,</span> <span class="token string">&#39;threshold&#39;</span><span class="token operator">=</span><span class="token string">&#39;0&#39;</span><span class="token punctuation">)</span> <span class="token keyword">from</span> root<span class="token punctuation">.</span>test<span class="token punctuation">.</span>d1
</code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div></div></div><p>Output series:</p><div class="language-text line-numbers-mode" data-ext="text"><pre class="language-text"><code>+-----------------------------+------------------------------------------------------+
|                         Time|ptnsym(root.test.d1.s4, &quot;window&quot;=&quot;5&quot;, &quot;threshold&quot;=&quot;0&quot;)|
+-----------------------------+------------------------------------------------------+
|2021-01-01T12:00:00.000+08:00|                                                   0.0|
|2021-01-01T12:00:07.000+08:00|                                                   0.0|
+-----------------------------+------------------------------------------------------+
</code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="xcorr" tabindex="-1"><a class="header-anchor" href="#xcorr" aria-hidden="true">#</a> XCorr</h2><h3 id="usage-4" tabindex="-1"><a class="header-anchor" href="#usage-4" aria-hidden="true">#</a> Usage</h3><p>This function is used to calculate the cross correlation function of given two time series.<br> For discrete time series, cross correlation is given by</p><p class="katex-block"><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>C</mi><mi>R</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mn>1</mn><mi>N</mi></mfrac><munderover><mo>∑</mo><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><msub><mi>S</mi><mn>1</mn></msub><mo stretchy="false">[</mo><mi>m</mi><mo stretchy="false">]</mo><msub><mi>S</mi><mn>2</mn></msub><mo stretchy="false">[</mo><mi>m</mi><mo>+</mo><mi>n</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex"> CR(n) = \frac{1}{N} \sum_{m=1}^N S_1[m]S_2[m+n] </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" style="margin-right:0.00773em;">CR</span><span class="mopen">(</span><span class="mord mathnormal">n</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:3.0954em;vertical-align:-1.2671em;"></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:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">N</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">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8283em;"><span style="top:-1.8829em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">m</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.05em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2671em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">S</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:-0.0576em;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="mopen">[</span><span class="mord mathnormal">m</span><span class="mclose">]</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">S</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:-0.0576em;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">m</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">n</span><span class="mclose">]</span></span></span></span></span></p><p>which represent the similarities between two series with different index shifts.</p><p><strong>Name:</strong> XCORR</p><p><strong>Input Series:</strong> Only support two input numeric series. The type is INT32 / INT64 / FLOAT / DOUBLE.</p><p><strong>Output Series:</strong> Output a single series with DOUBLE as datatype.<br> There are <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mi>N</mi><mo>−</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">2N-1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7667em;vertical-align:-0.0833em;"></span><span class="mord">2</span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span> data points in the series, the center of which represents the cross correlation<br> calculated with pre-aligned series(that is <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>R</mi><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">CR(0)</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" style="margin-right:0.00773em;">CR</span><span class="mopen">(</span><span class="mord">0</span><span class="mclose">)</span></span></span></span> in the formula above),<br> and the previous(or post) values represent those with shifting the latter series forward(or backward otherwise)<br> until the two series are no longer overlapped(not included).<br> In short, the values of output series are given by(index starts from 1)</p><p class="katex-block"><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>O</mi><mi>S</mi><mo stretchy="false">[</mo><mi>i</mi><mo stretchy="false">]</mo><mo>=</mo><mi>C</mi><mi>R</mi><mo stretchy="false">(</mo><mo>−</mo><mi>N</mi><mo>+</mo><mi>i</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mn>1</mn><mi>N</mi></mfrac><munderover><mo>∑</mo><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mi>i</mi></munderover><msub><mi>S</mi><mn>1</mn></msub><mo stretchy="false">[</mo><mi>m</mi><mo stretchy="false">]</mo><msub><mi>S</mi><mn>2</mn></msub><mo stretchy="false">[</mo><mi>N</mi><mo>−</mo><mi>i</mi><mo>+</mo><mi>m</mi><mo stretchy="false">]</mo><mo separator="true">,</mo><mtext> </mtext><mi>i</mi><mi>f</mi><mtext> </mtext><mi>i</mi><mo>&lt;</mo><mo>=</mo><mi>N</mi></mrow><annotation encoding="application/x-tex"> OS[i] = CR(-N+i) = \frac{1}{N} \sum_{m=1}^{i} S_1[m]S_2[N-i+m],\ if\ i &lt;= N </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" style="margin-right:0.05764em;">OS</span><span class="mopen">[</span><span class="mord mathnormal">i</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:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">CR</span><span class="mopen">(</span><span class="mord">−</span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">i</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:3.0788em;vertical-align:-1.2671em;"></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:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">N</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">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8117em;"><span style="top:-1.8829em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">m</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.05em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2671em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">S</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:-0.0576em;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="mopen">[</span><span class="mord mathnormal">m</span><span class="mclose">]</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">S</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:-0.0576em;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" style="margin-right:0.10903em;">N</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7429em;vertical-align:-0.0833em;"></span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">m</span><span class="mclose">]</span><span class="mpunct">,</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace"> </span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span></span></span></span></span></p><p class="katex-block"><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>O</mi><mi>S</mi><mo stretchy="false">[</mo><mi>i</mi><mo stretchy="false">]</mo><mo>=</mo><mi>C</mi><mi>R</mi><mo stretchy="false">(</mo><mi>i</mi><mo>−</mo><mi>N</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mn>1</mn><mi>N</mi></mfrac><munderover><mo>∑</mo><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mrow><mn>2</mn><mi>N</mi><mo>−</mo><mi>i</mi></mrow></munderover><msub><mi>S</mi><mn>1</mn></msub><mo stretchy="false">[</mo><mi>i</mi><mo>−</mo><mi>N</mi><mo>+</mo><mi>m</mi><mo stretchy="false">]</mo><msub><mi>S</mi><mn>2</mn></msub><mo stretchy="false">[</mo><mi>m</mi><mo stretchy="false">]</mo><mo separator="true">,</mo><mtext> </mtext><mi>i</mi><mi>f</mi><mtext> </mtext><mi>i</mi><mo>&gt;</mo><mi>N</mi></mrow><annotation encoding="application/x-tex"> OS[i] = CR(i-N) = \frac{1}{N} \sum_{m=1}^{2N-i} S_1[i-N+m]S_2[m],\ if\ i &gt; N </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" style="margin-right:0.05764em;">OS</span><span class="mopen">[</span><span class="mord mathnormal">i</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:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">CR</span><span class="mopen">(</span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">N</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:3.0954em;vertical-align:-1.2671em;"></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:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">N</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">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8283em;"><span style="top:-1.8829em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">m</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.05em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2671em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">S</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:-0.0576em;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="mopen">[</span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">m</span><span class="mclose">]</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">S</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:-0.0576em;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">m</span><span class="mclose">]</span><span class="mpunct">,</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace"> </span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span></span></span></span></span></p><p><strong>Note:</strong></p><ul><li><code>null</code> and <code>NaN</code> values in the input series will be ignored and treated as 0.</li></ul><h3 id="examples-3" tabindex="-1"><a class="header-anchor" href="#examples-3" aria-hidden="true">#</a> Examples</h3><p>Input series:</p><div class="language-text line-numbers-mode" data-ext="text"><pre class="language-text"><code>+-----------------------------+---------------+---------------+
|                         Time|root.test.d1.s1|root.test.d1.s2|
+-----------------------------+---------------+---------------+
|2020-01-01T00:00:01.000+08:00|           null|              6|
|2020-01-01T00:00:02.000+08:00|              2|              7|
|2020-01-01T00:00:03.000+08:00|              3|            NaN|
|2020-01-01T00:00:04.000+08:00|              4|              9|
|2020-01-01T00:00:05.000+08:00|              5|             10|
+-----------------------------+---------------+---------------+
</code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><p>SQL for query:</p><div class="language-sql line-numbers-mode" data-ext="sql"><pre class="language-sql"><code><span class="token keyword">select</span> xcorr<span class="token punctuation">(</span>s1<span class="token punctuation">,</span> s2<span class="token punctuation">)</span> <span class="token keyword">from</span> root<span class="token punctuation">.</span>test<span class="token punctuation">.</span>d1 <span class="token keyword">where</span> <span class="token keyword">time</span> <span class="token operator">&lt;=</span> <span class="token number">2020</span><span class="token operator">-</span><span class="token number">01</span><span class="token operator">-</span><span class="token number">01</span> <span class="token number">00</span>:<span class="token number">00</span>:<span class="token number">05</span>
</code></pre><div class="line-numbers" aria-hidden="true"><div class="line-number"></div></div></div><p>Output series:</p><div class="language-text line-numbers-mode" data-ext="text"><pre class="language-text"><code>+-----------------------------+---------------------------------------+
|                         Time|xcorr(root.test.d1.s1, root.test.d1.s2)|
+-----------------------------+---------------------------------------+
|1970-01-01T08:00:00.001+08:00|                                    0.0|
|1970-01-01T08:00:00.002+08:00|                                    4.0|
|1970-01-01T08:00:00.003+08:00|                                    9.6|
|1970-01-01T08:00:00.004+08:00|                                   13.4|
|1970-01-01T08:00:00.005+08:00|                                   20.0|
|1970-01-01T08:00:00.006+08:00|                                   15.6|
|1970-01-01T08:00:00.007+08:00|                                    9.2|
|1970-01-01T08:00:00.008+08:00|                                   11.8|
|1970-01-01T08:00:00.009+08:00|                                    6.0|
+-----------------------------+---------------------------------------+
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