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id="data-matching"><a href="#data-matching" class="header-anchor">#</a> Data Matching</h1> <h2 id="cov"><a href="#cov" class="header-anchor">#</a> Cov</h2> <h3 id="usage"><a href="#usage" class="header-anchor">#</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"><a href="#examples" class="header-anchor">#</a> Examples</h3> <p>Input series:</p> <div class="language- line-numbers-mode"><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-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br><span class="line-number">16</span><br><span class="line-number">17</span><br><span class="line-number">18</span><br><span class="line-number">19</span><br><span class="line-number">20</span><br></div></div><p>SQL for query:</p> <div class="language-sql line-numbers-mode"><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-wrapper"><span class="line-number">1</span><br></div></div><p>Output series:</p> <div class="language- line-numbers-mode"><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-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br></div></div><h2 id="dtw"><a href="#dtw" class="header-anchor">#</a> DTW</h2> <h3 id="usage-2"><a href="#usage-2" class="header-anchor">#</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-2"><a href="#examples-2" class="header-anchor">#</a> Examples</h3> <p>Input series:</p> <div class="language- line-numbers-mode"><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-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br><span class="line-number">16</span><br><span class="line-number">17</span><br><span class="line-number">18</span><br><span class="line-number">19</span><br><span class="line-number">20</span><br><span class="line-number">21</span><br><span class="line-number">22</span><br><span class="line-number">23</span><br><span class="line-number">24</span><br></div></div><p>SQL for query:</p> <div class="language-sql line-numbers-mode"><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-wrapper"><span class="line-number">1</span><br></div></div><p>Output series:</p> <div class="language- line-numbers-mode"><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-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br></div></div><h2 id="pearson"><a href="#pearson" class="header-anchor">#</a> Pearson</h2> <h3 id="usage-3"><a href="#usage-3" class="header-anchor">#</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-3"><a href="#examples-3" class="header-anchor">#</a> Examples</h3> <p>Input series:</p> <div class="language- line-numbers-mode"><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-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br><span class="line-number">16</span><br><span class="line-number">17</span><br><span class="line-number">18</span><br><span class="line-number">19</span><br><span class="line-number">20</span><br></div></div><p>SQL for query:</p> <div class="language-sql line-numbers-mode"><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-wrapper"><span class="line-number">1</span><br></div></div><p>Output series:</p> <div class="language- line-numbers-mode"><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-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br></div></div><h2 id="ptnsym"><a href="#ptnsym" class="header-anchor">#</a> PtnSym</h2> <h3 id="usage-4"><a href="#usage-4" class="header-anchor">#</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. |
| The degree of symmetry is calculated by DTW. |
| 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"><a href="#example" class="header-anchor">#</a> Example</h3> <p>Input series:</p> <div class="language- line-numbers-mode"><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-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br><span class="line-number">14</span><br><span class="line-number">15</span><br><span class="line-number">16</span><br></div></div><p>SQL for query:</p> <div class="language-sql line-numbers-mode"><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-wrapper"><span class="line-number">1</span><br></div></div><p>Output series:</p> <div class="language- line-numbers-mode"><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-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br></div></div><h2 id="xcorr"><a href="#xcorr" class="header-anchor">#</a> XCorr</h2> <h3 id="usage-5"><a href="#usage-5" class="header-anchor">#</a> Usage</h3> <p>This function is used to calculate the cross correlation function of given two time series. |
| For discrete time series, cross correlation is given by |
| $$CR(n) = \frac{1}{N} \sum_{m=1}^N S_1[m]S_2[m+n]$$ |
| 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. |
| There are $2N-1$ data points in the series, the center of which represents the cross correlation |
| calculated with pre-aligned series(that is $CR(0)$ in the formula above), |
| and the previous(or post) values represent those with shifting the latter series forward(or backward otherwise) |
| until the two series are no longer overlapped(not included). |
| In short, the values of output series are given by(index starts from 1) |
| $$OS[i] = CR(-N+i) = \frac{1}{N} \sum_{m=1}^{i} S_1[m]S_2[N-i+m],\ if\ i <= N$$ |
| $$OS[i] = CR(i-N) = \frac{1}{N} \sum_{m=1}^{2N-i} S_1[i-N+m]S_2[m],\ if\ i > N$$</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-4"><a href="#examples-4" class="header-anchor">#</a> Examples</h3> <p>Input series:</p> <div class="language- line-numbers-mode"><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-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br></div></div><p>SQL for query:</p> <div class="language-sql line-numbers-mode"><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-wrapper"><span class="line-number">1</span><br></div></div><p>Output series:</p> <div class="language- line-numbers-mode"><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| |
| +-----------------------------+---------------------------------------+ |
| </code></pre> <div class="line-numbers-wrapper"><span class="line-number">1</span><br><span class="line-number">2</span><br><span class="line-number">3</span><br><span class="line-number">4</span><br><span class="line-number">5</span><br><span class="line-number">6</span><br><span class="line-number">7</span><br><span class="line-number">8</span><br><span class="line-number">9</span><br><span class="line-number">10</span><br><span class="line-number">11</span><br><span class="line-number">12</span><br><span class="line-number">13</span><br></div></div></div> <div class="page-nav"><p class="inner"><span class="prev"> |
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