<!doctype html>
<html lang="en-US" data-theme="light">
  <head>
    <meta charset="utf-8" />
    <meta name="viewport" content="width=device-width,initial-scale=1" />
    <meta name="generator" content="VuePress 2.0.0-beta.66" />
    <meta name="theme" content="VuePress Theme Hope" />
    <link rel="alternate" hreflang="zh-cn" href="https://iotdb.apache.org/zh/UserGuide/V1.1.x/Operators-Functions/Data-Matching.html"><meta property="og:url" content="https://iotdb.apache.org/UserGuide/V1.1.x/Operators-Functions/Data-Matching.html"><meta property="og:site_name" content="IoTDB Website"><meta property="og:title" content="Data Matching"><meta property="og:description" content="Cov Usage This function is used to calculate the population covariance. Name: COV Input Series: Only support two input series. The types are both INT32 / INT64 / FLOAT / DOUBLE...."><meta property="og:type" content="article"><meta property="og:locale" content="en-US"><meta property="og:locale:alternate" content="zh-CN"><meta property="og:updated_time" content="2023-07-25T09:36:26.000Z"><meta property="article:modified_time" content="2023-07-25T09:36:26.000Z"><script type="application/ld+json">{"@context":"https://schema.org","@type":"Article","headline":"Data Matching","image":[""],"dateModified":"2023-07-25T09:36:26.000Z","author":[]}</script><link rel="icon" href="/favicon.ico"><meta name="Description" content="Apache IoTDB: Time Series Database for IoT"><meta name="Keywords" content="TSDB, time series, time series database, IoTDB, IoT database, IoT data management,时序数据库, 时间序列管理, IoTDB, 物联网数据库, 实时数据库, 物联网数据管理, 物联网数据"><meta name="baidu-site-verification" content="wfKETzB3OT"><meta name="google-site-verification" content="mZWAoRY0yj_HAr-s47zHCGHzx5Ju-RVm5wDbPnwQYFo"><title>Data Matching | IoTDB Website</title><meta name="description" content="Cov Usage This function is used to calculate the population covariance. Name: COV Input Series: Only support two input series. The types are both INT32 / INT64 / FLOAT / DOUBLE....">
    <style>
      :root {
        --bg-color: #fff;
      }

      html[data-theme="dark"] {
        --bg-color: #1d1e1f;
      }

      html,
      body {
        background: var(--bg-color);
      }
    </style>
    <script>
      const userMode = localStorage.getItem("vuepress-theme-hope-scheme");
      const systemDarkMode =
        window.matchMedia &&
        window.matchMedia("(prefers-color-scheme: dark)").matches;

      if (userMode === "dark" || (userMode !== "light" && systemDarkMode)) {
        document.documentElement.setAttribute("data-theme", "dark");
      }
    </script>
    <link rel="preload" href="/assets/style-35dc1830.css" as="style"><link rel="stylesheet" href="/assets/style-35dc1830.css">
    <link rel="modulepreload" href="/assets/app-d4806199.js"><link rel="modulepreload" href="/assets/Data-Matching.html-906cd3bb.js"><link rel="modulepreload" href="/assets/Data-Matching.html-a2a6a4ee.js">
  </head>
  <body>
    <div id="app"><!--[--><!--[--><!--[--><span tabindex="-1"></span><a href="#main-content" class="vp-skip-link sr-only">Skip to main content</a><!--]--><!--[--><div class="theme-container has-toc"><!--[--><header id="navbar" class="vp-navbar hide-icon"><div class="vp-navbar-start"><button type="button" class="vp-toggle-sidebar-button" title="Toggle Sidebar"><span class="icon"></span></button><!--[--><!----><!--]--><!--[--><a class="vp-link vp-brand" href="/"><img class="vp-nav-logo" src="/logo.png" alt="IoTDB Website"><!----><span class="vp-site-name hide-in-pad">IoTDB Website</span></a><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-center"><!--[--><!----><!--]--><!--[--><!--]--><!--[--><!----><!--]--></div><div class="vp-navbar-end"><!--[--><!----><!--]--><!--[--><div id="docsearch-container"></div><nav class="vp-nav-links"><div class="nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="Documentation"><span class="title"><!---->Documentation</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a class="vp-link nav-link" href="/UserGuide/V1.1.x/QuickStart/QuickStart.html"><!---->v1.1.x<!----></a></li><li class="dropdown-item"><a class="vp-link nav-link" href="/UserGuide/V1.0.x/QuickStart/QuickStart.html"><!---->v1.0.x<!----></a></li><li class="dropdown-item"><a class="vp-link nav-link" href="/UserGuide/V0.13.x/QuickStart/QuickStart.html"><!---->v0.13.x<!----></a></li></ul></button></div></div><div class="nav-item hide-in-mobile"><a href="https://cwiki.apache.org/confluence/display/IOTDB/System+Design" rel="noopener noreferrer" target="_blank" aria-label="Design" class="nav-link"><!---->Design<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="nav-item hide-in-mobile"><a class="vp-link nav-link" href="/Download/"><!---->Download<!----></a></div><div class="nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="Community"><span class="title"><!---->Community</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a class="vp-link nav-link" href="/Community/About.html"><!---->About<!----></a></li><li class="dropdown-item"><a href="https://cwiki.apache.org/confluence/display/iotdb" rel="noopener noreferrer" target="_blank" aria-label="Wiki" class="nav-link"><!---->Wiki<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a class="vp-link nav-link" href="/Community/Community-Project-Committers.html"><!---->People<!----></a></li><li class="dropdown-item"><a class="vp-link nav-link" href="/Community/Community-Powered-By.html"><!---->Powered  By<!----></a></li><li class="dropdown-item"><a class="vp-link nav-link" href="/Community/Materials.html"><!---->Resources<!----></a></li><li class="dropdown-item"><a class="vp-link nav-link" href="/Community/Feedback.html"><!---->Feedback<!----></a></li></ul></button></div></div><div class="nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="Development"><span class="title"><!---->Development</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a class="vp-link nav-link" href="/Development/VoteRelease.html"><!---->How  to  vote<!----></a></li><li class="dropdown-item"><a class="vp-link nav-link" href="/Development/HowToCommit.html"><!---->How  to  Commit<!----></a></li><li class="dropdown-item"><a class="vp-link nav-link" href="/Development/HowToJoin.html"><!---->Become  a  Contributor<!----></a></li><li class="dropdown-item"><a class="vp-link nav-link" href="/Development/Committer.html"><!---->Become  a  Committer<!----></a></li><li class="dropdown-item"><a class="vp-link nav-link" href="/Development/ContributeGuide.html"><!---->ContributeGuide<!----></a></li><li class="dropdown-item"><a class="vp-link nav-link" href="/Development/HowtoContributeCode.html"><!---->How  to  Contribute  Code<!----></a></li><li class="dropdown-item"><a class="vp-link nav-link" href="/Development/format-changelist.html"><!---->Changelist  of  TsFile<!----></a></li><li class="dropdown-item"><a class="vp-link nav-link" href="/Development/rpc-changelist.html"><!---->Changelist  of  RPC<!----></a></li></ul></button></div></div><div class="nav-item hide-in-mobile"><div class="dropdown-wrapper"><button type="button" class="dropdown-title" aria-label="ASF"><span class="title"><!---->ASF</span><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a href="https://www.apache.org/" rel="noopener noreferrer" target="_blank" aria-label="Foundation" class="nav-link"><!---->Foundation<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://www.apache.org/licenses/" rel="noopener noreferrer" target="_blank" aria-label="License" class="nav-link"><!---->License<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://www.apache.org/security/" rel="noopener noreferrer" target="_blank" aria-label="Security" class="nav-link"><!---->Security<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://www.apache.org/foundation/sponsorship.html" rel="noopener noreferrer" target="_blank" aria-label="Sponsorship" class="nav-link"><!---->Sponsorship<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://www.apache.org/foundation/thanks.html" rel="noopener noreferrer" target="_blank" aria-label="Thanks" class="nav-link"><!---->Thanks<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li><li class="dropdown-item"><a href="https://www.apache.org/events/current-event" rel="noopener noreferrer" target="_blank" aria-label="Current  Events" class="nav-link"><!---->Current  Events<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></li></ul></button></div></div></nav><div class="nav-item"><div class="dropdown-wrapper i18n-dropdown"><button type="button" class="dropdown-title" aria-label="Select language"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon i18n-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="i18n icon" style="width:1rem;height:1rem;vertical-align:middle;"><path d="M379.392 460.8 494.08 575.488l-42.496 102.4L307.2 532.48 138.24 701.44l-71.68-72.704L234.496 460.8l-45.056-45.056c-27.136-27.136-51.2-66.56-66.56-108.544h112.64c7.68 14.336 16.896 27.136 26.112 35.84l45.568 46.08 45.056-45.056C382.976 312.32 409.6 247.808 409.6 204.8H0V102.4h256V0h102.4v102.4h256v102.4H512c0 70.144-37.888 161.28-87.04 210.944L378.88 460.8zM576 870.4 512 1024H409.6l256-614.4H768l256 614.4H921.6l-64-153.6H576zM618.496 768h196.608L716.8 532.48 618.496 768z"></path></svg><!--]--><span class="arrow"></span><ul class="nav-dropdown"><li class="dropdown-item"><a class="vp-link nav-link active" href="/UserGuide/V1.1.x/Operators-Functions/Data-Matching.html"><!---->English<!----></a></li><li class="dropdown-item"><a class="vp-link nav-link" href="/zh/UserGuide/V1.1.x/Operators-Functions/Data-Matching.html"><!---->简体中文<!----></a></li></ul></button></div></div><div class="nav-item hide-in-mobile"><button type="button" id="appearance-switch"><svg xmlns="http://www.w3.org/2000/svg" class="icon auto-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="auto icon" style="display:block;"><path d="M512 992C246.92 992 32 777.08 32 512S246.92 32 512 32s480 214.92 480 480-214.92 480-480 480zm0-840c-198.78 0-360 161.22-360 360 0 198.84 161.22 360 360 360s360-161.16 360-360c0-198.78-161.22-360-360-360zm0 660V212c165.72 0 300 134.34 300 300 0 165.72-134.28 300-300 300z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon dark-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="dark icon" style="display:none;"><path d="M524.8 938.667h-4.267a439.893 439.893 0 0 1-313.173-134.4 446.293 446.293 0 0 1-11.093-597.334A432.213 432.213 0 0 1 366.933 90.027a42.667 42.667 0 0 1 45.227 9.386 42.667 42.667 0 0 1 10.24 42.667 358.4 358.4 0 0 0 82.773 375.893 361.387 361.387 0 0 0 376.747 82.774 42.667 42.667 0 0 1 54.187 55.04 433.493 433.493 0 0 1-99.84 154.88 438.613 438.613 0 0 1-311.467 128z"></path></svg><svg xmlns="http://www.w3.org/2000/svg" class="icon light-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="light icon" style="display:none;"><path d="M952 552h-80a40 40 0 0 1 0-80h80a40 40 0 0 1 0 80zM801.88 280.08a41 41 0 0 1-57.96-57.96l57.96-58a41.04 41.04 0 0 1 58 58l-58 57.96zM512 752a240 240 0 1 1 0-480 240 240 0 0 1 0 480zm0-560a40 40 0 0 1-40-40V72a40 40 0 0 1 80 0v80a40 40 0 0 1-40 40zm-289.88 88.08-58-57.96a41.04 41.04 0 0 1 58-58l57.96 58a41 41 0 0 1-57.96 57.96zM192 512a40 40 0 0 1-40 40H72a40 40 0 0 1 0-80h80a40 40 0 0 1 40 40zm30.12 231.92a41 41 0 0 1 57.96 57.96l-57.96 58a41.04 41.04 0 0 1-58-58l58-57.96zM512 832a40 40 0 0 1 40 40v80a40 40 0 0 1-80 0v-80a40 40 0 0 1 40-40zm289.88-88.08 58 57.96a41.04 41.04 0 0 1-58 58l-57.96-58a41 41 0 0 1 57.96-57.96z"></path></svg></button></div><div class="nav-item vp-repo"><a class="vp-repo-link" href="https://github.com/apache/iotdb" target="_blank" rel="noopener noreferrer" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="icon github-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="github icon" style="width:1.25rem;height:1.25rem;vertical-align:middle;"><path d="M511.957 21.333C241.024 21.333 21.333 240.981 21.333 512c0 216.832 140.544 400.725 335.574 465.664 24.49 4.395 32.256-10.07 32.256-23.083 0-11.69.256-44.245 0-85.205-136.448 29.61-164.736-64.64-164.736-64.64-22.315-56.704-54.4-71.765-54.4-71.765-44.587-30.464 3.285-29.824 3.285-29.824 49.195 3.413 75.179 50.517 75.179 50.517 43.776 75.008 114.816 53.333 142.762 40.79 4.523-31.66 17.152-53.377 31.19-65.537-108.971-12.458-223.488-54.485-223.488-242.602 0-53.547 19.114-97.323 50.517-131.67-5.035-12.33-21.93-62.293 4.779-129.834 0 0 41.258-13.184 134.912 50.346a469.803 469.803 0 0 1 122.88-16.554c41.642.213 83.626 5.632 122.88 16.554 93.653-63.488 134.784-50.346 134.784-50.346 26.752 67.541 9.898 117.504 4.864 129.834 31.402 34.347 50.474 78.123 50.474 131.67 0 188.586-114.73 230.016-224.042 242.09 17.578 15.232 33.578 44.672 33.578 90.454v135.85c0 13.142 7.936 27.606 32.854 22.87C862.25 912.597 1002.667 728.747 1002.667 512c0-271.019-219.648-490.667-490.71-490.667z"></path></svg></a></div><!--]--><!--[--><!----><!--]--><button type="button" class="vp-toggle-navbar-button" aria-label="Toggle Navbar" aria-expanded="false" aria-controls="nav-screen"><span><span class="vp-top"></span><span class="vp-middle"></span><span class="vp-bottom"></span></span></button></div></header><!----><!--]--><!----><div class="toggle-sidebar-wrapper"><span class="arrow start"></span></div><aside id="sidebar" class="vp-sidebar"><!--[--><!----><!--]--><ul class="vp-sidebar-links"><li><section class="vp-sidebar-group"><p class="vp-sidebar-heading"><!----><span class="vp-sidebar-title">IoTDB User Guide (V1.1.x)</span><!----></p><ul class="vp-sidebar-links"></ul></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-heading clickable" type="button"><!----><span class="vp-sidebar-title">About IoTDB</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-heading clickable" type="button"><!----><span class="vp-sidebar-title">Quick Start</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-heading clickable" type="button"><!----><span class="vp-sidebar-title">Data Concept</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-heading clickable" type="button"><!----><span class="vp-sidebar-title">Syntax Conventions</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-heading clickable" type="button"><!----><span class="vp-sidebar-title">API</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-heading clickable" type="button"><!----><span class="vp-sidebar-title">Operate Metadata</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-heading clickable" type="button"><!----><span class="vp-sidebar-title">Write Data (Update Data)</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-heading clickable" type="button"><!----><span class="vp-sidebar-title">Delete Data</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-heading clickable" type="button"><!----><span class="vp-sidebar-title">Query Data</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-heading clickable active" type="button"><!----><span class="vp-sidebar-title">Operators and Functions</span><span class="vp-arrow down"></span></button><ul class="vp-sidebar-links"><li><!--[--><a class="vp-link nav-link vp-sidebar-link vp-sidebar-page" href="/UserGuide/V1.1.x/Operators-Functions/Overview.html"><!---->Overview<!----></a><ul class="vp-sidebar-sub-headers"></ul><!--]--></li><li><!--[--><a class="vp-link nav-link vp-sidebar-link vp-sidebar-page" href="/UserGuide/V1.1.x/Operators-Functions/User-Defined-Function.html"><!---->UDF (User Defined Function)<!----></a><ul class="vp-sidebar-sub-headers"></ul><!--]--></li><li><!--[--><a class="vp-link nav-link vp-sidebar-link vp-sidebar-page" href="/UserGuide/V1.1.x/Operators-Functions/Aggregation.html"><!---->Aggregation<!----></a><ul class="vp-sidebar-sub-headers"></ul><!--]--></li><li><!--[--><a class="vp-link nav-link vp-sidebar-link vp-sidebar-page" href="/UserGuide/V1.1.x/Operators-Functions/Mathematical.html"><!---->Mathematical<!----></a><ul class="vp-sidebar-sub-headers"></ul><!--]--></li><li><!--[--><a class="vp-link nav-link vp-sidebar-link vp-sidebar-page" href="/UserGuide/V1.1.x/Operators-Functions/Comparison.html"><!---->Comparison<!----></a><ul class="vp-sidebar-sub-headers"></ul><!--]--></li><li><!--[--><a class="vp-link nav-link vp-sidebar-link vp-sidebar-page" href="/UserGuide/V1.1.x/Operators-Functions/Logical.html"><!---->Logical<!----></a><ul class="vp-sidebar-sub-headers"></ul><!--]--></li><li><!--[--><a class="vp-link nav-link vp-sidebar-link vp-sidebar-page" href="/UserGuide/V1.1.x/Operators-Functions/Conversion.html"><!---->Conversion<!----></a><ul class="vp-sidebar-sub-headers"></ul><!--]--></li><li><!--[--><a class="vp-link nav-link vp-sidebar-link vp-sidebar-page" href="/UserGuide/V1.1.x/Operators-Functions/Constant.html"><!---->Constant<!----></a><ul class="vp-sidebar-sub-headers"></ul><!--]--></li><li><!--[--><a class="vp-link nav-link vp-sidebar-link vp-sidebar-page" href="/UserGuide/V1.1.x/Operators-Functions/Selection.html"><!---->Selection<!----></a><ul class="vp-sidebar-sub-headers"></ul><!--]--></li><li><!--[--><a class="vp-link nav-link vp-sidebar-link vp-sidebar-page" href="/UserGuide/V1.1.x/Operators-Functions/Continuous-Interval.html"><!---->Continuous Interval<!----></a><ul class="vp-sidebar-sub-headers"></ul><!--]--></li><li><!--[--><a class="vp-link nav-link vp-sidebar-link vp-sidebar-page" href="/UserGuide/V1.1.x/Operators-Functions/Variation-Trend.html"><!---->Variation Trend<!----></a><ul class="vp-sidebar-sub-headers"></ul><!--]--></li><li><!--[--><a class="vp-link nav-link vp-sidebar-link vp-sidebar-page" href="/UserGuide/V1.1.x/Operators-Functions/Sample.html"><!---->Sample<!----></a><ul class="vp-sidebar-sub-headers"></ul><!--]--></li><li><!--[--><a class="vp-link nav-link vp-sidebar-link vp-sidebar-page" href="/UserGuide/V1.1.x/Operators-Functions/Time-Series.html"><!---->Time-Series<!----></a><ul class="vp-sidebar-sub-headers"></ul><!--]--></li><li><!--[--><a class="vp-link nav-link vp-sidebar-link vp-sidebar-page" href="/UserGuide/V1.1.x/Operators-Functions/Lambda.html"><!---->Lambda<!----></a><ul class="vp-sidebar-sub-headers"></ul><!--]--></li><li><!--[--><a class="vp-link nav-link vp-sidebar-link vp-sidebar-page" href="/UserGuide/V1.1.x/Operators-Functions/Data-Profiling.html"><!---->Data Profiling<!----></a><ul class="vp-sidebar-sub-headers"></ul><!--]--></li><li><!--[--><a class="vp-link nav-link vp-sidebar-link vp-sidebar-page" href="/UserGuide/V1.1.x/Operators-Functions/Anomaly-Detection.html"><!---->Anomaly Detection<!----></a><ul class="vp-sidebar-sub-headers"></ul><!--]--></li><li><!--[--><a class="vp-link nav-link active vp-sidebar-link vp-sidebar-page active" href="/UserGuide/V1.1.x/Operators-Functions/Data-Matching.html"><!---->Data Matching<!----></a><ul class="vp-sidebar-sub-headers"><li class="vp-sidebar-sub-header"><a class="vp-link nav-link vp-sidebar-link vp-heading" href="/UserGuide/V1.1.x/Operators-Functions/Data-Matching.html#cov"><!---->Cov<!----></a><ul class="vp-sidebar-sub-headers"><li class="vp-sidebar-sub-header"><a class="vp-link nav-link vp-sidebar-link vp-heading" href="/UserGuide/V1.1.x/Operators-Functions/Data-Matching.html#usage"><!---->Usage<!----></a><ul class="vp-sidebar-sub-headers"></ul></li><li class="vp-sidebar-sub-header"><a class="vp-link nav-link vp-sidebar-link vp-heading" href="/UserGuide/V1.1.x/Operators-Functions/Data-Matching.html#examples"><!---->Examples<!----></a><ul class="vp-sidebar-sub-headers"></ul></li></ul></li><li class="vp-sidebar-sub-header"><a class="vp-link nav-link vp-sidebar-link vp-heading" href="/UserGuide/V1.1.x/Operators-Functions/Data-Matching.html#dtw"><!---->DTW<!----></a><ul class="vp-sidebar-sub-headers"><li class="vp-sidebar-sub-header"><a class="vp-link nav-link vp-sidebar-link vp-heading" href="/UserGuide/V1.1.x/Operators-Functions/Data-Matching.html#usage-1"><!---->Usage<!----></a><ul class="vp-sidebar-sub-headers"></ul></li><li class="vp-sidebar-sub-header"><a class="vp-link nav-link vp-sidebar-link vp-heading" href="/UserGuide/V1.1.x/Operators-Functions/Data-Matching.html#examples-1"><!---->Examples<!----></a><ul class="vp-sidebar-sub-headers"></ul></li></ul></li><li class="vp-sidebar-sub-header"><a class="vp-link nav-link vp-sidebar-link vp-heading" href="/UserGuide/V1.1.x/Operators-Functions/Data-Matching.html#pearson"><!---->Pearson<!----></a><ul class="vp-sidebar-sub-headers"><li class="vp-sidebar-sub-header"><a class="vp-link nav-link vp-sidebar-link vp-heading" href="/UserGuide/V1.1.x/Operators-Functions/Data-Matching.html#usage-2"><!---->Usage<!----></a><ul class="vp-sidebar-sub-headers"></ul></li><li class="vp-sidebar-sub-header"><a class="vp-link nav-link vp-sidebar-link vp-heading" href="/UserGuide/V1.1.x/Operators-Functions/Data-Matching.html#examples-2"><!---->Examples<!----></a><ul class="vp-sidebar-sub-headers"></ul></li></ul></li><li class="vp-sidebar-sub-header"><a class="vp-link nav-link vp-sidebar-link vp-heading" href="/UserGuide/V1.1.x/Operators-Functions/Data-Matching.html#ptnsym"><!---->PtnSym<!----></a><ul class="vp-sidebar-sub-headers"><li class="vp-sidebar-sub-header"><a class="vp-link nav-link vp-sidebar-link vp-heading" href="/UserGuide/V1.1.x/Operators-Functions/Data-Matching.html#usage-3"><!---->Usage<!----></a><ul class="vp-sidebar-sub-headers"></ul></li><li class="vp-sidebar-sub-header"><a class="vp-link nav-link vp-sidebar-link vp-heading" href="/UserGuide/V1.1.x/Operators-Functions/Data-Matching.html#example"><!---->Example<!----></a><ul class="vp-sidebar-sub-headers"></ul></li></ul></li><li class="vp-sidebar-sub-header"><a class="vp-link nav-link vp-sidebar-link vp-heading" href="/UserGuide/V1.1.x/Operators-Functions/Data-Matching.html#xcorr"><!---->XCorr<!----></a><ul class="vp-sidebar-sub-headers"><li class="vp-sidebar-sub-header"><a class="vp-link nav-link vp-sidebar-link vp-heading" href="/UserGuide/V1.1.x/Operators-Functions/Data-Matching.html#usage-4"><!---->Usage<!----></a><ul class="vp-sidebar-sub-headers"></ul></li><li class="vp-sidebar-sub-header"><a class="vp-link nav-link vp-sidebar-link vp-heading" href="/UserGuide/V1.1.x/Operators-Functions/Data-Matching.html#examples-3"><!---->Examples<!----></a><ul class="vp-sidebar-sub-headers"></ul></li></ul></li></ul><!--]--></li><li><!--[--><a class="vp-link nav-link vp-sidebar-link vp-sidebar-page" href="/UserGuide/V1.1.x/Operators-Functions/Frequency-Domain.html"><!---->Frequency Domain<!----></a><ul class="vp-sidebar-sub-headers"></ul><!--]--></li><li><!--[--><a class="vp-link nav-link vp-sidebar-link vp-sidebar-page" href="/UserGuide/V1.1.x/Operators-Functions/Data-Quality.html"><!---->Data Quality<!----></a><ul class="vp-sidebar-sub-headers"></ul><!--]--></li><li><!--[--><a class="vp-link nav-link vp-sidebar-link vp-sidebar-page" href="/UserGuide/V1.1.x/Operators-Functions/Data-Repairing.html"><!---->Data Repairing<!----></a><ul class="vp-sidebar-sub-headers"></ul><!--]--></li><li><!--[--><a class="vp-link nav-link vp-sidebar-link vp-sidebar-page" href="/UserGuide/V1.1.x/Operators-Functions/Series-Discovery.html"><!---->Series Discovery<!----></a><ul class="vp-sidebar-sub-headers"></ul><!--]--></li><li><!--[--><a class="vp-link nav-link vp-sidebar-link vp-sidebar-page" href="/UserGuide/V1.1.x/Operators-Functions/Machine-Learning.html"><!---->Machine Learning<!----></a><ul class="vp-sidebar-sub-headers"></ul><!--]--></li></ul></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-heading clickable" type="button"><!----><span class="vp-sidebar-title">Trigger</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-heading clickable" type="button"><!----><span class="vp-sidebar-title">Monitor and Alert</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-heading clickable" type="button"><!----><span class="vp-sidebar-title">Administration Management</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-heading clickable" type="button"><!----><span class="vp-sidebar-title">Maintenance Tools</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-heading clickable" type="button"><!----><span class="vp-sidebar-title">Collaboration of Edge and Cloud</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-heading clickable" type="button"><!----><span class="vp-sidebar-title">Ecosystem Integration</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-heading clickable" type="button"><!----><span class="vp-sidebar-title">Cluster</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-heading clickable" type="button"><!----><span class="vp-sidebar-title">FAQ</span><span class="vp-arrow end"></span></button><!----></section></li><li><section class="vp-sidebar-group"><button class="vp-sidebar-heading clickable" type="button"><!----><span class="vp-sidebar-title">Reference</span><span class="vp-arrow end"></span></button><!----></section></li></ul><!--[--><!----><!--]--></aside><!--[--><main id="main-content" class="vp-page"><!--[--><!----><!----><nav class="vp-breadcrumb disable"></nav><div class="vp-page-title"><h1><!---->Data 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="2023-07-25T09:36:26.000Z"></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"><!--

​    Licensed to the Apache Software Foundation (ASF) under one
​    or more contributor license agreements.  See the NOTICE file
​    distributed with this work for additional information
​    regarding copyright ownership.  The ASF licenses this file
​    to you under the Apache License, Version 2.0 (the
​    "License"); you may not use this file except in compliance
​    with the License.  You may obtain a copy of the License at
​
​        http://www.apache.org/licenses/LICENSE-2.0
​
​    Unless required by applicable law or agreed to in writing,
​    software distributed under the License is distributed on an
​    "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
​    KIND, either express or implied.  See the License for the
​    specific language governing permissions and limitations
​    under the License.

--><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|
+-----------------------------+---------------------------------------+
</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></div></div><!----><footer class="page-meta"><div class="meta-item edit-link"><a href="https://github.com/apache/iotdb-docs/edit/main/src/UserGuide/V1.1.x/Operators-Functions/Data-Matching.md" rel="noopener noreferrer" target="_blank" aria-label="Found Error? Edit this page on GitHub" class="nav-link label"><!--[--><svg xmlns="http://www.w3.org/2000/svg" class="icon edit-icon" viewBox="0 0 1024 1024" fill="currentColor" aria-label="edit icon"><path d="M430.818 653.65a60.46 60.46 0 0 1-50.96-93.281l71.69-114.012 7.773-10.365L816.038 80.138A60.46 60.46 0 0 1 859.225 62a60.46 60.46 0 0 1 43.186 18.138l43.186 43.186a60.46 60.46 0 0 1 0 86.373L588.879 565.55l-8.637 8.637-117.466 68.234a60.46 60.46 0 0 1-31.958 11.229z"></path><path d="M728.802 962H252.891A190.883 190.883 0 0 1 62.008 771.98V296.934a190.883 190.883 0 0 1 190.883-192.61h267.754a60.46 60.46 0 0 1 0 120.92H252.891a69.962 69.962 0 0 0-69.098 69.099V771.98a69.962 69.962 0 0 0 69.098 69.098h475.911A69.962 69.962 0 0 0 797.9 771.98V503.363a60.46 60.46 0 1 1 120.922 0V771.98A190.883 190.883 0 0 1 728.802 962z"></path></svg><!--]-->Found Error? Edit this page on GitHub<span><svg class="external-link-icon" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path><polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg><span class="external-link-icon-sr-only">open in new window</span></span><!----></a></div><div class="meta-item git-info"><div class="update-time"><span class="label">Last update: </span><!----></div><div class="contributors"><span class="label">Contributors: </span><!--[--><!--[--><span class="contributor" title="email: 105700158+wanghui42@users.noreply.github.com">wanghui42</span><!--]--><!--]--></div></div></footer><nav class="vp-page-nav"><a class="vp-link nav-link prev" href="/UserGuide/V1.1.x/Operators-Functions/Anomaly-Detection.html"><div class="hint"><span class="arrow start"></span>Prev</div><div class="link"><!---->Anomaly Detection</div></a><a class="vp-link nav-link next" href="/UserGuide/V1.1.x/Operators-Functions/Frequency-Domain.html"><div class="hint">Next<span class="arrow end"></span></div><div class="link">Frequency Domain<!----></div></a></nav><!----><!----><!--]--></main><!--]--><footer style="padding-bottom:2rem;"><span id="doc-version" style="display:none;">rel/1.1</span><p style="text-align:center;color:#909399;font-size:12px;margin:0 30px;">Copyright © 2023 The Apache Software Foundation.<br> Apache and the Apache feather logo are trademarks of The Apache Software Foundation</p><p style="text-align:center;margin-top:10px;color:#909399;font-size:12px;margin:0 30px;"><strong>Have a question?</strong> Connect with us on QQ, WeChat, or Slack. <a href="https://github.com/apache/iotdb/issues/1995">Join the community</a> now.</p><p style="text-align:center;margin-top:10px;color:#909399;font-size:12px;margin:0 30px;"> We use <a href="https://analytics.google.com">Google Analytics</a> to collect anonymous, aggregated usage information. </p></footer></div><!--]--><!--]--><!----><!--]--></div>
    <script type="module" src="/assets/app-d4806199.js" defer></script>
  </body>
</html>