| import{_ as e,o as s,c as n,e as i}from"./app-Bx8hKGcu.js";const a={},t=i(`<h1 id="data-matching" tabindex="-1"><a class="header-anchor" href="#data-matching"><span>Data Matching</span></a></h1><h2 id="cov" tabindex="-1"><a class="header-anchor" href="#cov"><span>Cov</span></a></h2><h3 id="usage" tabindex="-1"><a class="header-anchor" href="#usage"><span>Usage</span></a></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"><span>Examples</span></a></h3><p>Input series:</p><div class="language-text line-numbers-mode" data-ext="text" data-title="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" data-title="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" data-title="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"><span>DTW</span></a></h2><h3 id="usage-1" tabindex="-1"><a class="header-anchor" href="#usage-1"><span>Usage</span></a></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"><span>Examples</span></a></h3><p>Input series:</p><div class="language-text line-numbers-mode" data-ext="text" data-title="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" data-title="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" data-title="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"><span>Pearson</span></a></h2><h3 id="usage-2" tabindex="-1"><a class="header-anchor" href="#usage-2"><span>Usage</span></a></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"><span>Examples</span></a></h3><p>Input series:</p><div class="language-text line-numbers-mode" data-ext="text" data-title="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" data-title="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" data-title="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"><span>PtnSym</span></a></h2><h3 id="usage-3" tabindex="-1"><a class="header-anchor" href="#usage-3"><span>Usage</span></a></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's a positive integer and the default value is 10.</li><li><code>threshold</code>: The threshold of the degree of symmetry. It'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"><span>Example</span></a></h3><p>Input series:</p><div class="language-text line-numbers-mode" data-ext="text" data-title="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" data-title="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">'window'</span><span class="token operator">=</span><span class="token string">'5'</span><span class="token punctuation">,</span> <span class="token string">'threshold'</span><span class="token operator">=</span><span class="token string">'0'</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" data-title="text"><pre class="language-text"><code>+-----------------------------+------------------------------------------------------+ |
| | Time|ptnsym(root.test.d1.s4, "window"="5", "threshold"="0")| |
| +-----------------------------+------------------------------------------------------+ |
| |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"><span>XCorr</span></a></h2><h3 id="usage-4" tabindex="-1"><a class="header-anchor" href="#usage-4"><span>Usage</span></a></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<br> $$CR(n) = \\frac{1}{N} \\sum_{m=1}^N S_1[m]S_2[m+n]$$<br> 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 $2N-1$ data points in the series, the center of which represents the cross correlation<br> calculated with pre-aligned series(that is $CR(0)$ 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)<br> $$OS[i] = CR(-N+i) = \\frac{1}{N} \\sum_{m=1}^{i} S_1[m]S_2[N-i+m],\\ if\\ i <= N$$<br> $$OS[i] = CR(i-N) = \\frac{1}{N} \\sum_{m=1}^{2N-i} S_1[i-N+m]S_2[m],\\ if\\ i > N$$</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"><span>Examples</span></a></h3><p>Input series:</p><div class="language-text line-numbers-mode" data-ext="text" data-title="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" data-title="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"><=</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" data-title="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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