CINXE.COM

<!DOCTYPE html><html lang="en"><head> <meta charset="utf-8"/> <meta name="viewport" content="width=device-width, initial-scale=1.0"/> <link rel="icon" href="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/common/resources/images/favicon.20240924193154397.ico" type="image/x-icon"/> <link rel="canonical" href="https://www-dev1.mathworks.com/template-service/help/full-header-footer-offcanvas.html"/> <meta http-equiv="X-UA-Compatible" content="IE=edge"/> <script src="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/components/webvitals.min.20240924193154397.js"></script> <script src="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/components/jquery.min.20240924193154397.js"></script> <script src="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/components/jquery-migrate.min.20240924193154397.js"></script> <link rel="stylesheet" href="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/common/core.min.20240924193154397.css" type="text/css"/> <link rel="stylesheet" href="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/common.min.20240924193154397.css" type="text/css"/> <link rel="stylesheet" href="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/common/footer.min.20240924193154397.css" type="text/css"/> <link rel="stylesheet" href="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/offcanvasv4.min.20240924193154397.css" type="text/css"/> <link rel="stylesheet" href="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/documentation.min.20240924193154397.css" type="text/css"/> <link href="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/common/resources/fonts/roboto/roboto-latin-italic-400.20240924193154397.woff2" rel="preload" as="font" type="font/woff2" crossorigin=""/> <link href="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/common/resources/fonts/roboto/roboto-latin-italic-500.20240924193154397.woff2" rel="preload" as="font" type="font/woff2" crossorigin=""/> <link href="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/common/resources/fonts/roboto/roboto-latin-italic-700.20240924193154397.woff2" rel="preload" as="font" type="font/woff2" crossorigin=""/> <link href="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/common/resources/fonts/roboto/roboto-latin-normal-400.20240924193154397.woff2" rel="preload" as="font" type="font/woff2" crossorigin=""/> <link href="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/common/resources/fonts/roboto/roboto-latin-normal-500.20240924193154397.woff2" rel="preload" as="font" type="font/woff2" crossorigin=""/> <link href="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/common/resources/fonts/roboto/roboto-latin-normal-700.20240924193154397.woff2" rel="preload" as="font" type="font/woff2" crossorigin=""/> <link href="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/common/resources/fonts/mathworks.20240924193154397.woff" rel="preload" as="font" type="font/woff" crossorigin=""/> <script>(function(g,b,d,f){(function(a,c,d){if(a){var e=b.createElement("style");e.id=c;e.innerHTML=d;a.appendChild(e)}})(b.getElementsByTagName("head")[0],"at-body-style",d);setTimeout(function(){var a=b.getElementsByTagName("head")[0];if(a){var c=b.getElementById("at-body-style");c&&a.removeChild(c)}},f)})(window,document,"[class*='personalization-container']:not([id^='web-application']) {opacity: 0 !important}",1E3);</script> <script src="//assets.adobedtm.com/d0cc0600946eb3957f703b9fe43c3590597a8c2c/satelliteLib-e8d23c2e444abadc572df06537e2def59c01db09.js" async=""></script> <title>Computational Biology </title> <meta xmlns="http://www.w3.org/1999/xhtml" http-equiv="Content-Script-Type" content="text/javascript"/> <link xmlns="http://www.w3.org/1999/xhtml" href="/help/releases/R2024b/includes/web/css/doc_center.css" rel="stylesheet" type="text/css"/> <script src="/help/releases/R2024b/includes/shared/equationrenderer/release/MathRenderer.js"></script> <script src="/help/releases/R2024b/includes/shared/scripts/l10n.js"></script> <script src="/help/releases/R2024b/includes/shared/scripts/docscripts.js"></script> <script src="/help/releases/R2024b/includes/shared/scripts/f1help.js"></script> <script src="/help/releases/R2024b/includes/shared/scripts/mw.imageanimation.js"></script> <script src="/help/releases/R2024b/includes/shared/scripts/jquery.highlight.js"></script> <script src="/help/releases/R2024b/includes/product/scripts/underscore-min.js"></script> <script xmlns="http://www.w3.org/1999/xhtml" src="/help/search/R2024b/searchresults.js"></script> <script xmlns="http://www.w3.org/1999/xhtml" src="/help/search/R2024b/tokenize.js"></script> <script xmlns="http://www.w3.org/1999/xhtml" src="/help/search/R2024b/helpcenter_docsearch.js"></script> <script xmlns="http://www.w3.org/1999/xhtml" src="/help/search/R2024b/searchtracking.js"></script> <script xmlns="http://www.w3.org/1999/xhtml" src="/help/releases/R2024b/includes/shared/scripts/localstorage.js"></script> <script src="/help/releases/R2024b/includes/shared/scripts/overload.js"></script> <script src="/help/releases/R2024b/includes/shared/scripts/helpservices.js"></script> <script src="/help/releases/R2024b/includes/product/scripts/productfilter.js"></script> <script src="/help/releases/R2024b/includes/shared/scripts/matlab_dialog_shared.js"></script> <link href="/help/releases/R2024b/includes/shared/highlight/styles/mwdochighlight.min.css" rel="stylesheet" type="text/css"/> <script src="/help/releases/R2024b/includes/shared/highlight/highlight.min.js"></script> <meta name="robots" content="all"/></head> <body id="responsive_offcanvas" class="-is_bootstrap3 no_animate offcanvas_fluid templateservice -has_standardnav"> <a class="skip_link sr-only" href="#skip_link_anchor" tabindex="1">Skip to content</a>  <div class="header visible-xs visible-sm" id="header_mobile"> <nav class="navbar navbar-default" role="navigation" aria-label="Main navigation"> <div class="navbar-header"> <div class="container-fluid"> <div class="row"> <div class="col-xs-3"> <button type="button" class="navbar-toggle topnav_toggle" tabindex="1" data-toggle="collapse" data-target="#topnav_collapse"> <span class="sr-only">Toggle Main Navigation</span> <span class="icon-menu"></span> </button> </div> <div class="col-xs-6"> <div class="text-center"> <a href="/?s_tid=gn_logo" class="svg_link navbar-brand" tabindex="3"> <img src="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/common/resources/images/pic-header-mathworks-logo.20240924193154397.svg" class="mw_logo" alt="MathWorks - Mobile View"/> </a> </div> </div> <div class="col-xs-3"> <div class="matrix_affordance_container_mobile" id="matrix_affordance_container_mobile"> <mw-matrix lang="en" tier="DOTCOM" env="prod" type="mobile" bsversion="bs3" host="https://www.mathworks.com"></mw-matrix> </div> </div> </div> </div> <div class="container-fluid"> <div class="row visible-xs visible-sm"> <div class="col-xs-12"> <div class="navbar-collapse collapse" id="topnav_collapse"> <div class="topNavigation topnavigation containsResourceName resourceClass-topnavigation"> <ul class="nav navbar-nav topnav" id="topnav_mobile"> <li class="headernav_login" style="display: none;"> <a class="mwa-nav_login" tabindex="2" title="Sign In to Your MathWorks Account"><span class="visible-xs visible-sm">Sign In <span class="sr-only visually-hidden">to Your MathWorks Account</span></span></a> </li> <li class="headernav_logout dropdown" style="display: none;"> <a href="#" role="button" title="Access your MathWorks Account" aria-haspopup="menu" aria-controls="mw_nav_mobile" class="dropdown-toggle mwa_image_drop_down" data-toggle="dropdown" tabindex="2"> <span class="visible-xs visible-sm"> <span class="mobile_account_image"></span> <span class="mobile_account_name" aria-hidden="true"></span> <b class="caret"></b> </span> </a> <ul role="menu" class="dropdown-menu" id="mw_nav_mobile"> <li class="mwa-nav_account"><a role="menuitem" class="mwa-account" tabindex="2">My Account</a></li> <li class="mwa-nav_community"><a role="menuitem" class="mwa-community-profile" tabindex="2">My Community Profile</a></li> <li class="mwa-nav_associate"><a role="menuitem" class="mwa-link-license" tabindex="2">Link License</a></li> <li class="mwa-nav_logout"><a role="menuitem" class="mwa-logout" tabindex="2">Sign Out</a> </li> </ul> </li> <li class="topnav_products "> <a href="/products.html" tabindex="2">Products</a> </li> <li class="topnav_solutions "> <a href="/solutions.html?s_tid=nav_solutions" tabindex="2">Solutions</a> </li> <li class="topnav_academia "> <a href="/academia.html?s_tid=gn_acad" tabindex="2">Academia</a> </li> <li class="topnav_support "> <a href="/help/?s_tid=gn_supp" tabindex="2">Support</a> </li> <li class="topnav_community "> <a href="/matlabcentral/?s_tid=gn_mlc" tabindex="2">Community</a> </li> <li class="topnav_events "> <a href="/company/events.html?s_tid=gn_ev" tabindex="2">Events</a> </li> <li class="headernav_store"> <a href="https://login.mathworks.com/embedded-login/landing.html?cid=getmatlab&s_tid=gn_getml" tabindex="2"> <span class="not-logged-in" style="display: none;">Get MATLAB</span> <span class="logged-in" style="display: none;">MATLAB</span> </a> </li> </ul> </div> </div> <div class="navbar-collapse collapse" id="matrix_collapse"> <div class="matrix_menu_container_mobile" id="matrix_menu_container_mobile"></div> </div> </div> </div> </div> </div> </nav> </div>   <div class="header hidden-xs hidden-sm" id="header_desktop"> <nav class="navbar navbar-default" role="navigation" aria-label="Main Navigation"> <div class="container-fluid"> <div class="row"> <div class="col-md-9"> <div class="navbar-header"> <div class="logo_container hidden-xs hidden-sm"> <a href="/?s_tid=gn_logo" class="svg_link pull-left" tabindex="1"> <img src="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/common/resources/images/pic-header-mathworks-logo.20240924193154397.svg" class="mw_logo" alt="MathWorks"/> </a> </div> <div class="navbar-collapse collapse hidden-xs hidden-sm"> <div class="topNavigation topnavigation containsResourceName resourceClass-topnavigation"> <ul id="topnav_desktop" class="nav navbar-nav topnav"> <li class="topnav_products "> <a href="/products.html" tabindex="2">Products</a> </li> <li class="topnav_solutions "> <a href="/solutions.html?s_tid=nav_solutions" tabindex="2">Solutions</a> </li> <li class="topnav_academia "> <a href="/academia.html?s_tid=gn_acad" tabindex="2">Academia</a> </li> <li class="topnav_support "> <a href="/help/?s_tid=gn_supp" tabindex="2">Support</a> </li> <li class="topnav_community "> <a href="/matlabcentral/?s_tid=gn_mlc" tabindex="2">Community</a> </li> <li class="topnav_events "> <a href="/company/events.html?s_tid=gn_ev" tabindex="2">Events</a> </li> </ul> </div> </div> </div> </div> <div class="col-md-3"> <div class="headerNavigation headernavigation containsResourceName resourceClass-headernavigation"> <div class="collapse navbar-collapse" id="headernav_collapse"> <ul class="nav navbar-nav navbar-right" id="headernav"> <li class="headernav_store"> <a href="https://login.mathworks.com/embedded-login/landing.html?cid=getmatlab&s_tid=gn_getml" class="not-logged-in btn btn_color_blue companion_btn btn-xs" tabindex="2" style="display: none;">Get MATLAB</a> <a href="https://login.mathworks.com/embedded-login/landing.html?cid=getmatlab&s_tid=gn_getml" class="logged-in btn btn_color_blue companion_btn btn-xs" tabindex="2" style="display: none;">MATLAB</a> </li> <li class="headernav_login" style="display: none;"> <a class="mwa-nav_login" tabindex="2" title="Sign In to Your MathWorks Account"><span class="visible-xs visible-sm">Sign In <span class="sr-only visually-hidden">to Your MathWorks Account</span></span></a> </li> <li class="headernav_logout dropdown" style="display: none;"> <a href="#" role="button" title="Access your MathWorks Account" aria-haspopup="menu" aria-controls="mw_nav_desktop" class="dropdown-toggle mwa_image_drop_down" data-toggle="dropdown" tabindex="2"> <span class="visible-xs visible-sm"> <span class="mobile_account_image"></span> <span class="mobile_account_name" aria-hidden="true"></span> <b class="caret"></b> </span> </a> <ul role="menu" class="dropdown-menu" id="mw_nav_desktop"> <li class="mwa-nav_account"><a role="menuitem" class="mwa-account" tabindex="2">My Account</a></li> <li class="mwa-nav_community"><a role="menuitem" class="mwa-community-profile" tabindex="2">My Community Profile</a></li> <li class="mwa-nav_associate"><a role="menuitem" class="mwa-link-license" tabindex="2">Link License</a></li> <li class="mwa-nav_logout"><a role="menuitem" class="mwa-logout" tabindex="2">Sign Out</a> </li> </ul> </li> <li id="headernav_matrix" class="headernav_matrix"> <mw-matrix lang="en" tier="DOTCOM" env="prod" host="https://www.mathworks.com"></mw-matrix> </li> </ul> </div></div> </div> </div> </div> </nav> </div>   <div class="section_header level_3"> <div class="container-fluid"> <div class="row" id="mobile_search_row"> <div class="col-sm-6 col-md-7" id="section_header_title"> <div><div class="sectionHead sectionhead containsResourceName resourceClass-sectionhead"> <div class="section_header_content"> <div class="section_header_title"> <p class="h1"> <a href="/help" class="add_cursor_pointer">Help Center</a> </p> </div> </div> </div> </div> </div> <div class="col-xs-12 col-sm-6 col-md-5" id="mobile_search"> <div><div class="sectionHeadSearchBox sectionheadsearchbox containsResourceName resourceClass-sectionheadsearchbox"> <script src="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/components/sectionheadsearchbox.min.20240924193154397.js"></script> <div class="search_nested_content_container"> <div id="search_scope_doc" class="collapse in"><form name="docsearch_form" id="docsearch_form" data-release="R2024b" data-language="en" action="/support/search.html" method="get"> <div class="input-group tokenized_search_field"> <label class="sr-only">Search MATLAB Documentation</label> <input type="search" class="form-control conjoined_search" autocomplete="off" name="q" placeholder="Search Help Center" id="docsearch"/> <input type="hidden" name="selectedsource" value="mw" id="selected_source"/> <div class="input-group-btn"> <button type="submit" name="submitsearch" id="submitsearch" class="btn icon-search btn_search_adjacent btn_search icon_16" tabindex="-1"></button> </div> </div> </form> </div> <script> $(".search_scope_trigger").on('click', function handlerSearch(event) { var target1 = event.target.parentNode.attributes.getNamedItem("data-groupid").nodeValue; $('#' + target1).removeClass("in"); }); </script> </div> <button class="btn icon-remove btn_search pull-right icon_32 visible-xs" data-toggle="collapse" data-target="#mobile_search" aria-expanded="false" aria-controls="mobile_search"><span class="sr-only">Close Mobile Search</span> </button> </div> </div> </div> <div class="visible-xs" id="search_actuator"> <button class="btn icon-search btn_search pull-right icon_16 containsResourceName resourceClass-button" data-toggle="collapse" data-target="#mobile_search" aria-expanded="false" aria-controls="mobile_search"><span class="sr-only">Close Mobile Search</span></button> </div> </div>   </div> </div> <div class="row-offcanvas row-offcanvas-left" id="row-offcanvas"> <div id="sidebar_offcanvas_mobile_pointer"> <div class="sidebar-offcanvas" id="sidebar"> <nav class="offcanvas_nav" aria-label="Filter Navigation"> <div class="offcanvas_actuator" data-toggle="offcanvas" data-target="#sidebar" id="nav_toggle"> <button type="button" class="btn"> <span class="sr-only">Toggle navigation</span> <span class="icon-menu"></span> </button> <span class="offcanvas_actuator_label" id="translation_icon-menu" tabindex="-1" aria-hidden="true"> Contents </span> </div> <div class="nav_list_wrapper" id="nav_list_wrapper"><nav class="offcanvas_nav" role="navigation"> <div class="personalization-container" id="web-application-offcanvas-container"> <ul xmlns="http://www.w3.org/1999/xhtml" class="nav_breadcrumb" id="ul_left_nav_ancestors"> <li itemscope="" itemtype="http://www.data-vocabulary.org/Breadcrumb" itemprop="breadcrumb"> <a href="/help/index.html?s_tid=CRUX_lftnav" itemprop="url"><span itemprop="title">Documentation Home</span> </a> </li> </ul> <div xmlns="http://www.w3.org/1999/xhtml" id="left_nav_categories"> <div class="search_refine" style="margin-bottom:2px;"> <h3 class="add_clear_both">Category</h3> </div> <div class="search_refine" id="productgroup_grouping"><h3>Using MATLAB</h3><ul class="nav_toc"><li><a href="/help/matlab/index.html?s_tid=CRUX_lftnav">MATLAB</a></li></ul></div> <div class="search_refine" id="productgroup_grouping"><h3>Using Simulink</h3><ul class="nav_toc"><li><a href="/help/simulink/index.html?s_tid=CRUX_lftnav">Simulink</a></li><li><a href="/help/overview/physical-modeling.html?s_tid=CRUX_lftnav">Physical Modeling</a></li><li><a href="/help/overview/event-based-modeling.html?s_tid=CRUX_lftnav">Event-Based Modeling</a></li><li><a href="/help/overview/real-time-simulation-and-testing.html?s_tid=CRUX_lftnav">Real-Time Simulation and Testing</a></li></ul></div> <div class="search_refine" id="productgroup_grouping"><h3>Workflows</h3><ul class="nav_toc"><li><a href="/help/overview/parallel-computing.html?s_tid=CRUX_lftnav">Parallel Computing</a></li><li><a href="/help/overview/reporting-and-database-access.html?s_tid=CRUX_lftnav">Reporting and Database Access</a></li><li><a href="/help/overview/systems-engineering.html?s_tid=CRUX_lftnav">Systems Engineering</a></li><li><a href="/help/overview/code-generation.html?s_tid=CRUX_lftnav">Code Generation</a></li><li><a href="/help/overview/application-deployment.html?s_tid=CRUX_lftnav">Application Deployment</a></li><li><a href="/help/overview/verification-validation-and-test.html?s_tid=CRUX_lftnav">Verification, Validation, and Test</a></li><li><a href="/help/overview/cloud-capabilities.html?s_tid=CRUX_lftnav">Cloud Capabilities</a></li><li><a href="/help/overview/teaching-and-learning.html?s_tid=CRUX_lftnav">Teaching and Learning</a></li></ul></div> <div class="search_refine" id="productgroup_grouping"><h3>Applications</h3><ul class="nav_toc"><li><a href="/help/overview/ai-and-statistics.html?s_tid=CRUX_lftnav">AI and Statistics</a></li><li><a href="/help/overview/mathematics-and-optimization.html?s_tid=CRUX_lftnav">Mathematics and Optimization</a></li><li><a href="/help/overview/signal-processing.html?s_tid=CRUX_lftnav">Signal Processing</a></li><li><a href="/help/overview/image-processing-and-computer-vision.html?s_tid=CRUX_lftnav">Image Processing and Computer Vision</a></li><li><a href="/help/overview/control-systems.html?s_tid=CRUX_lftnav">Control Systems</a></li><li><a href="/help/overview/test-and-measurement.html?s_tid=CRUX_lftnav">Test and Measurement</a></li><li><a href="/help/overview/rf-and-mixed-signal.html?s_tid=CRUX_lftnav">RF and Mixed Signal</a></li><li><a href="/help/overview/wireless-communications.html?s_tid=CRUX_lftnav">Wireless Communications</a></li><li><a href="/help/overview/radar.html?s_tid=CRUX_lftnav">Radar</a></li><li><a href="/help/overview/robotics-and-autonomous-systems.html?s_tid=CRUX_lftnav">Robotics and Autonomous Systems</a></li><li><a href="/help/overview/fpga-asic-and-soc-development.html?s_tid=CRUX_lftnav">FPGA, ASIC, and SoC Development</a></li><li><a href="/help/overview/computational-finance.html?s_tid=CRUX_lftnav">Computational Finance</a></li><li class="active"><a href="/help/overview/computational-biology.html?s_tid=CRUX_lftnav">Computational Biology</a><ul class="nav_toc"><li><a href="/help/bioinfo/index.html?s_tid=CRUX_lftnav">Bioinformatics Toolbox</a></li><li><a href="/help/simbio/index.html?s_tid=CRUX_lftnav">SimBiology</a></li></ul></li><li><a href="/help/overview/code-verification.html?s_tid=CRUX_lftnav">Code Verification</a></li><li><a href="/help/overview/aerospace-and-defense.html?s_tid=CRUX_lftnav">Aerospace and Defense</a></li><li><a href="/help/overview/automotive.html?s_tid=CRUX_lftnav">Automotive</a></li></ul></div> </div></div> </nav> <div class="sidebar parsys containsResourceName resourceClass-parsys"><div class="targetcontainer containsResourceName resourceClass-targetcontainer section"> </div> </div> </div> </nav> </div> </div> <div class="offcanvas_content_container"> <div class="sticky_header_container"> <div class="horizontal_nav"> <div class="horizontal_nav_container"> <div class="offcanvas_horizontal_nav"> <div class="container-fluid"> <div class="row"> <div class="col-md-7 col-lg-8 hidden-xs"> <nav class="navbar navbar-default" role="navigation" id="subnav" aria-label="Sub navigation"><div> <ul class="crux_resource_list_default nav navbar-nav list-unstyled add_margin_0" style="display:none;"> <li class="crux_resource"><a href="/help/overview/computational-biology.html?s_tid=CRUX_topnav">Documentation</a></li> <li class="crux_resource"><a href="/help/overview/examples.html?category=computational-biology&s_tid=CRUX_topnav">Examples</a></li> <li class="crux_resource"><a href="/help/overview/referencelist.html?category=computational-biology&s_tid=CRUX_topnav&type=function">Functions</a></li> <li class="crux_resource"><a href="/help/overview/referencelist.html?category=computational-biology&s_tid=CRUX_topnav&type=app">Apps</a></li> <li class="crux_resource"><a href="/support/search.html?fq%5B%5D=asset_type_name:video&fq%5B%5D=category:overview/computational-biology&page=1&s_tid=CRUX_topnav">Videos</a></li> <li class="crux_resource"><a href="/support/search.html?fq%5B%5D=asset_type_name:answer&fq%5B%5D=category:overview/computational-biology&page=1&s_tid=CRUX_topnav">Answers</a></li> </ul> <ul class="crux_resource_list crux_browse nav navbar-nav" id="crux_browse"> <li class="crux_resource active " data-nav-id="crux_nav_documentation"> <a href="/help/overview/computational-biology.html?s_tid=CRUX_topnav" data-id=""> Documentation </a></li> <li class="crux_resource " data-nav-id="crux_nav_examples"> <a href="/help/overview/examples.html?category=computational-biology&s_tid=CRUX_topnav" data-id=""> Examples </a></li> <li class="crux_resource " data-nav-id="crux_nav_functions"> <a href="/help/overview/referencelist.html?category=computational-biology&s_tid=CRUX_topnav&type=function" data-id=""> Functions </a></li> <li class="crux_resource " data-nav-id="crux_nav_apps"> <a href="/help/overview/referencelist.html?category=computational-biology&s_tid=CRUX_topnav&type=app" data-id=""> Apps </a></li> <li class="crux_resource " data-nav-id="crux_nav_video"> <a href="/support/search.html?fq%5B%5D=asset_type_name:video&fq%5B%5D=category:overview/computational-biology&page=1&s_tid=CRUX_topnav" data-id=""> Videos </a></li> <li class="crux_resource " data-nav-id="crux_nav_answers"> <a href="/support/search.html?fq%5B%5D=asset_type_name:answer&fq%5B%5D=category:overview/computational-biology&page=1&s_tid=CRUX_topnav" data-id=""> Answers </a></li> </ul> </div></nav> </div> <div class="visible-xs"> <div class="container-fluid"> <div class="row"> <div class="col-xs-9"> <div class="mobile_crux_nav_trigger crux_nav">  <div class="btn-group"> <button type="button" class="btn btn-default dropdown-toggle" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false"> Resources <span class="icon-arrow-down icon_16"></span> </button> <div class="dropdown-menu" role="navigation" aria-label="Resource filter navigation"> <ul class="crux_resource_list_default nav list-unstyled add_margin_0" style="display:none;"> <li class="crux_resource"><a href="/help/overview/computational-biology.html?s_tid=CRUX_topnav">Documentation</a></li> <li class="crux_resource"><a href="/help/overview/examples.html?category=computational-biology&s_tid=CRUX_topnav">Examples</a></li> <li class="crux_resource"><a href="/help/overview/referencelist.html?category=computational-biology&s_tid=CRUX_topnav&type=function">Functions</a></li> <li class="crux_resource"><a href="/help/overview/referencelist.html?category=computational-biology&s_tid=CRUX_topnav&type=app">Apps</a></li> <li class="crux_resource"><a href="/support/search.html?fq%5B%5D=asset_type_name:video&fq%5B%5D=category:overview/computational-biology&page=1&s_tid=CRUX_topnav">Videos</a></li> <li class="crux_resource"><a href="/support/search.html?fq%5B%5D=asset_type_name:answer&fq%5B%5D=category:overview/computational-biology&page=1&s_tid=CRUX_topnav">Answers</a></li> </ul> <ul class="crux_resource_list list-unstyled add_margin_0"> <li class=" " data-nav-id="crux_nav_documentation"> <a href="/help/overview/computational-biology.html?s_tid=CRUX_topnav" data-id=""> Documentation</a> </li> <li class=" " data-nav-id="crux_nav_examples"> <a href="/help/overview/examples.html?category=computational-biology&s_tid=CRUX_topnav" data-id=""> Examples</a> </li> <li class=" " data-nav-id="crux_nav_functions"> <a href="/help/overview/referencelist.html?category=computational-biology&s_tid=CRUX_topnav&type=function" data-id=""> Functions</a> </li> <li class=" " data-nav-id="crux_nav_apps"> <a href="/help/overview/referencelist.html?category=computational-biology&s_tid=CRUX_topnav&type=app" data-id=""> Apps</a> </li> <li class=" " data-nav-id="crux_nav_video"> <a href="/support/search.html?fq%5B%5D=asset_type_name:video&fq%5B%5D=category:overview/computational-biology&page=1&s_tid=CRUX_topnav" data-id=""> Videos</a> </li> <li class=" " data-nav-id="crux_nav_answers"> <a href="/support/search.html?fq%5B%5D=asset_type_name:answer&fq%5B%5D=category:overview/computational-biology&page=1&s_tid=CRUX_topnav" data-id=""> Answers</a> </li> </ul> </div> </div> </div> </div> <div class="col-xs-3"> <div class="translate_placeholder"></div> </div> </div> </div> </div> <div class="col-md-5 col-lg-4 hidden-xs hidden-sm"> <div><div class="callToAction calltoactionheader containsResourceName resourceClass-calltoactionheader"> <div class="cta_box"> <ul class="list-inline"> <li class="cta_item cta_item_general"> <a href="/campaigns/products/trials.html?s_tid=doc_trial_gate_tb" class="icon-download " data-link="lead" data-offertype="trial"> Trial software</a> </li> <li class="cta_item cta_item_general"> <a href="/downloads/web_downloads/?s_tid=doc_downloads" class="icon-download "> Product updates</a> </li> </ul> </div> </div> </div> </div> </div> </div> </div> </div> </div> </div> <div class="introParsys parsys containsResourceName resourceClass-parsys"><div class="cssjs containsResourceName section resourceClass-cssjs"> <div class="search_crux" data-label-more-dropdown="More"></div> </div> </div> <div class="content_container" id="content_container"> <div id="sidebar_offcanvas_desktop_pointer"></div> <main id="skip_link_anchor" tabindex="-1"> <div class="container-fluid"> <div id="offcanvas_focus_actuator" tabindex="0" class="visible-xs"><span class="sr-only">Main Content</span></div> <section><div class="mainParsys parsys containsResourceName resourceClass-parsys"><div class="targetcontainer containsResourceName resourceClass-targetcontainer section"> <div class="personalization-container " id="web-application-body-container"> <section xmlns="http://www.w3.org/1999/xhtml" id="doc_center_content" itemprop="content" lang="en" data-language="en"><div id="pgtype-category"> <h1 class="r2024b" itemprop="content title">Computational Biology</h1><div class="doc_topic_desc" itemprop="content purpose">Analyze, visualize, and model biological data and systems</div> <div class="start_here_container" id="starthere"> <div id="start_here_content"><div itemprop="content"> <p>MathWorks<sup>®</sup> computational biology products provide tools to perform various analysis workflows for bioinformatics and systems pharmacology applications.</p> <p>Build end-to-end bioinformatics pipelines using an app or at the command line and run these analysis workflows locally or in cluster environments. You can view and explore integrated next generation sequencing (NGS) data using an app, identify differentially expressed genes or features, and discover copy number variants from NGS data.</p> <p>Using integrated apps or at the command line, create and analyze dynamic models for quantitative systems pharmacology (QSP), physiologically based pharmacokinetic (PBPK), and pharmacokinetic/pharmacodynamic (PK/PD) applications. For instance, you can run parallel simulations and parameter scans to assess target feasibility and characterize biological variability. You can also use local and global sensitivity analyses to identify key parameters and estimate model parameters with nonlinear regression and mixed-effects techniques. Then, share your work and models using autogenerated reports and deployed applications.</p> </div></div> </div> <div id="productgroup"><h2>Products for Computational Biology</h2><div class="doc_panel_container"><div class="panel panel-default doc_panel doc_product_panel" id="bioinfo"><a href="../bioinfo/index.html?s_tid=hc_product_card"><div class="panel-body"><h3>Bioinformatics Toolbox</h3><p>Read, analyze, and visualize genomic and proteomic data</p></div></a></div><div class="panel panel-default doc_panel doc_product_panel" id="simbio"><a href="../simbio/index.html?s_tid=hc_product_card"><div class="panel-body"><h3>SimBiology</h3><p>Model, simulate, and analyze biological systems</p></div></a></div></div></div><div class="moreabout_container"><h2>Topics</h2> <div itemprop="content"> <div class="doc_subgroup_container" itemprop="content"> <h3>Next Generation Sequencing</h3> <ul class="list-unstyled"><li><strong><a href="../bioinfo/ug/count-rna-seq-reads-biopipeline-designer.html" class="a">Count RNA-Seq Reads Using Biopipeline Designer</a><span role="cross_prod"> (Bioinformatics Toolbox)</span></strong><br/> Create a bioinformatics pipeline to count RNA-Seq reads that are mapped to genomic features. </li><li><strong><a href="../bioinfo/ug/visualize-NGS-data-using-genomics-viewer.html" class="a">Visualize NGS Data Using Genomics Viewer App</a><span role="cross_prod"> (Bioinformatics Toolbox)</span></strong><br/> View NGS alignment data for single nucleotide variation in cytochrome p450 gene. </li><li><strong><a href="../bioinfo/ug/identifying-differentially-expressed-genes-from-rna-seq-data.html" class="a">Identifying Differentially Expressed Genes from RNA-Seq Data</a><span role="cross_prod"> (Bioinformatics Toolbox)</span></strong><br/> Use a negative binomial model to test RNA-Seq data for differentially expressed genes. </li></ul></div> <div class="doc_subgroup_container" itemprop="content"> <h3>Quantitative Systems Pharmacology</h3> <ul class="list-unstyled"><li><strong><a href="../simbio/ug/build-sglt2-glucose-insulin-model.html" class="a">Incorporate SGLT2 Inhibition into Physiologically Based Glucose-Insulin Model Using SimBiology Model Builder</a><span role="cross_prod"> (SimBiology)</span></strong><br/> Update a glucose-insulin model to integrate sodium-glucose co-transporter 2 (SGLT2) receptor inhibition by a hypothetical compound. </li><li><strong><a href="../simbio/ug/perform-GSA-global-sensitivity-analysis-simbiology-model-analyzer.html" class="a">Find Important Parameters for Receptor Occupancy with Global Sensitivity Analysis Using SimBiology Model Analyzer</a><span role="cross_prod"> (SimBiology)</span></strong><br/> Perform GSA analyses, such as Sobol indices, elementary effects, and multiparametric GSA, to find important model parameters in a target-mediated drug disposition model. </li><li><strong><a href="../simbio/ug/generate-virtual-population.html" class="a">Explore Biological Variability with Virtual Patients Using SimBiology Model Analyzer</a><span role="cross_prod"> (SimBiology)</span></strong><br/> Generate sample values for model parameters to represent virtual patients, simulate to explore tumor growth variability, and investigate the effects of dosing regimens on tumor size. </li></ul></div> <div class="doc_subgroup_container" itemprop="content"> <h3>PBPK and PK/PD Modeling</h3> <ul class="list-unstyled"><li><strong><a href="../simbio/ug/create-and-simulate-a-simple-model.html" class="a">Create Model of Receptor-Ligand Kinetics</a><span role="cross_prod"> (SimBiology)</span></strong><br/> Create and simulate a simple receptor-ligand kinetics model using SimBiology apps. </li><li><strong><a href="../simbio/ug/calculate-NCA-and-estimate-PKPD-parameters.html" class="a">Calculate NCA Parameters and Fit Model to PK/PD Data Using SimBiology Model Analyzer</a><span role="cross_prod"> (SimBiology)</span></strong><br/> Calibrate model parameters by performing noncompartmental analysis and fitting to experimental PKPD data using nonlinear regression. </li><li><strong><a href="../simbio/ug/modeling-the-population-pharmacokinetics-of-phenobarbital-in-neonates.html" class="a">Model the Population Pharmacokinetics of Phenobarbital in Neonates</a><span role="cross_prod"> (SimBiology)</span></strong><br/> Perform nonlinear mixed-effects modeling using clinical pharmacokinetic data. </li><li><strong><a href="../simbio/ug/estimating-the-bioavailability-of-a-drug.html" class="a">Estimate the Bioavailability of a Drug</a><span role="cross_prod"> (SimBiology)</span></strong><br/> Fit a model of absorption and excretion of the drug ondansetron to estimate its bioavailability. </li></ul></div> </div> </div> <div class="moreabout_container"><h2>Related Information</h2> <div itemprop="content"> <ul class="list-unstyled"><li><strong><a href="https://www.mathworks.com/support/search.html/videos/what-is-simbiology-1605793306685.html?fq[]=asset_type_name:video&fq[]=category:simbio/index&page=1" class="video">What Is SimBiology?</a></strong><br/></li> <li><strong><a href="https://www.mathworks.com/support/search.html/videos/simulating-a-model-in-simbiology-117245.html?fq%5B%5D=asset_type_name:video&fq%5B%5D=category:matlab/ordinary-differential-equations&page=1" class="video">Simulating a Model in SimBiology</a></strong><br/></li> <li><strong><a href="https://www.mathworks.com/support/search.html/videos/simbiology-tutorials-for-qsp-pbpk-and-pk-pd-modeling-and-analysis-stratifying-data-for-visualization-in-simbiology-1576844776342.html?fq%5B%5D=asset_type_name:video&fq%5B%5D=category:simbio/index&page=1" class="video">Stratifying Data for Visualization in SimBiology</a></strong><br/></li> </ul></div> </div> <h2>Featured Examples</h2><section class="mw_cards_container" id="featured_examples_container"><div class="mw_card -has_metadata"><div class="mw_card_header"><div class="mw_card_image" style="background-image:url(../examples/simbio/win64/antibioticdemo_02.png);"><a tabindex="-1" href="../simbio/ug/pk-pd-modeling-and-simulation-to-guide-dosing-strategy-for-antibiotics.html"><img alt="Perform PK/PD Modeling and Simulation to Guide Dosing Strategy for Antibiotics" src="../examples/simbio/win64/antibioticdemo_02.png"/></a></div></div><div class="mw_card_body"><h3 class="mw_card_title"><a href="../simbio/ug/pk-pd-modeling-and-simulation-to-guide-dosing-strategy-for-antibiotics.html">Perform PK/PD Modeling and Simulation to Guide Dosing Strategy for Antibiotics</a></h3><p class="mw_card_description">Perform a Monte Carlo simulation of a pharmacokinetic/pharmacodynamic (PK/PD) model for an antibacterial agent. This example is adapted from Katsube et al. [1] This example also shows how to use the SimBiology® <code class="literal">SimFunction</code> object to perform parameter scans in parallel.</p><p class="mw_card_meta_product">(SimBiology)</p></div><div class="mw_card_footer"><ul class="list-unstyled"><li class="coming_from_product"></li></ul></div></div><div class="mw_card -has_metadata"><div class="mw_card_header"><div class="mw_card_image" style="background-image:url(../examples/simbio/win64/insulindemo_09.png);"><a tabindex="-1" href="../simbio/ug/simulating-the-glucose-insulin-response.html"><img alt="Simulate the Glucose-Insulin Response" src="../examples/simbio/win64/insulindemo_09.png"/></a></div></div><div class="mw_card_body"><h3 class="mw_card_title"><a href="../simbio/ug/simulating-the-glucose-insulin-response.html">Simulate the Glucose-Insulin Response</a></h3><p class="mw_card_description">Simulate and analyze a physiologically based glucose-insulin model for normal and diabetic patients.</p><p class="mw_card_meta_product">(SimBiology)</p></div><div class="mw_card_footer"><ul class="list-unstyled"><li class="coming_from_product"></li></ul></div></div><div class="mw_card -has_metadata"><div class="mw_card_header"><div class="mw_card_image" style="background-image:url(../examples/bioinfo/win64/chipseqpedemo_11.png);"><a tabindex="-1" href="../bioinfo/ug/exploring-protein-dna-binding-sites-from-paired-end-chip-seq-data.html"><img alt="Exploring Protein-DNA Binding Sites from Paired-End ChIP-Seq Data" src="../examples/bioinfo/win64/chipseqpedemo_11.png"/></a></div></div><div class="mw_card_body"><h3 class="mw_card_title"><a href="../bioinfo/ug/exploring-protein-dna-binding-sites-from-paired-end-chip-seq-data.html">Exploring Protein-DNA Binding Sites from Paired-End ChIP-Seq Data</a></h3><p class="mw_card_description">Perform a genome-wide analysis of a transcription factor in the <span class="emphasis"><em>Arabidopsis Thaliana</em></span> (Thale Cress) model organism.</p><p class="mw_card_meta_product">(Bioinformatics Toolbox)</p></div><div class="mw_card_footer"><ul class="list-unstyled"><li class="coming_from_product"></li></ul></div></div></section></div></section><div class="clearfix"></div> <div align="center" class="feedbackblock" id="mw_docsurvey"><script src="/help/includes/shared/docsurvey/docfeedback.js"></script> <script>loadSurveyHidden();</script> <link rel="stylesheet" href="/help/includes/shared/docsurvey/release/index-css.css" type="text/css"/> <script src="/help/includes/shared/docsurvey/release/bundle.index.js"></script> <script>initDocSurvey();</script></div> <div class="modal fade" id="matlab-command-dialog" tabindex="-1" role="dialog" aria-labelledby="matlabCommandDialogLabel" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h2 class="modal-title">MATLAB Command</h2> </div> <div class="modal-body" id="dialog-body"> <p>You clicked a link that corresponds to this MATLAB command: </p> <pre id="dialog-matlab-command"></pre> <p>Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.</p> </div> <div class="modal-footer"> <button type="button" class="btn btn_secondary" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div><div class="targetContent parsys containsResourceName resourceClass-parsys"><div class="cqColumns containsResourceName section resourceClass-columns"><div class="row "> <div class=" col-xs-12 "><div class="2420e633-83fe-4c2d-9b62-4248985f27d2 parsys containsResourceName resourceClass-parsys"> </div> </div> </div> </div> </div> </div> </div></div> </div> </section> <div><div class="modalParsys parsys containsResourceName resourceClass-parsys"> </div> </div> <div id="location_content" style="display:none;"></div> <div class="modal fade" id="country-unselected" tabindex="-1" role="dialog" aria-labelledby="country-unselected-title" translate="no"> <div class="modal-dialog modal-lg"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <img src="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/common/resources/images/pic-header-mathworks-logo.20240924193154397.svg" style="width:167px; height:auto;" class="mw_logo" alt="MathWorks - Domain Selector"/> </div> <div class="modal-body"> <div class="row add_margin_40"> <div class="col-xs-12"> <p class="h1 icon-globe add_icon_color_darkblue" id="country-unselected-title">Select a Web Site</p> <p>Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: <strong class="recommended-country"></strong>. </p> <div class="default-recommendation"> <a href="#" id="recommended_domain_button" class="btn btn_color_blue containsResourceName resourceClass-button"><span class="recommended-country"></span></a> </div> <div class="ch-recommendation" style="display:none;"> <ul class="list-inline"> <li class="add_display_block_xs add_margin_10_xs"><a href="//ch.mathworks.com" class="recommendation-button btn companion_btn btn-md add_display_block_xs" data-subdomain="ch" data-lang="en" data-recommended-text="Switzerland" data-default-lang="true" data-do-not-rewrite="true"><strong class="recommended-country"></strong> (English)</a></li> <li class="add_display_block_xs add_margin_10_xs"><a href="//ch.mathworks.com" class="recommendation-button btn companion_btn btn-md add_display_block_xs" data-subdomain="ch" data-lang="de" data-recommended-text="Schweiz" data-do-not-rewrite="true"><strong class="recommended-country"></strong> (Deutsch)</a></li> <li class="add_display_block_xs"><a href="//ch.mathworks.com" class="recommendation-button btn companion_btn btn-md add_display_block_xs" data-subdomain="ch" data-lang="fr" data-recommended-text="Suisse" data-do-not-rewrite="true"><strong class="recommended-country"></strong> (Français)</a></li> </ul> </div> <div class="zh-recommendation" style="display:none;"> <ul class="list-inline"> <li class="add_display_block_xs add_margin_10_xs"><a href="//ww2.mathworks.cn" class="recommendation-button btn companion_btn btn-md add_display_block_xs" data-subdomain="ww2" data-lang="zh" data-recommended-text="中国" data-default-lang="true" data-do-not-rewrite="true"><strong class="recommended-country"></strong>（简体中文）</a></li> <li class="add_display_block_xs"><a href="//ww2.mathworks.cn" class="recommendation-button btn companion_btn btn-md add_display_block_xs" data-subdomain="ww2" data-lang="en" data-recommended-text="China" data-do-not-rewrite="true"><strong class="recommended-country"></strong> (English)</a></li> </ul> </div> </div> </div> <p>You can also select a web site from the following list</p> <div class="alert alert-warning" role="alert" id="china_performance_alert" style="display:none;"><span class="alert_icon icon-alert-warning"></span> <p class="h2">How to Get Best Site Performance</p> <p>Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.</p> </div> <div class="row add_margin_20"> <div class="col-sm-4 col-md-3"> <p class="h3 add_bottom_rule">Americas</p> <ul class="list-unstyled"> <li><a href="//la.mathworks.com" class="domain_selector_link" data-country-code="LA" data-subdomain="la" data-lang="es" data-default-lang="true" data-selected-text="América Latina" data-recommended-text="América Latina" data-do-not-rewrite="true">América Latina</a> (Español) </li> <li><a href="//www.mathworks.com" class="domain_selector_link" data-country-code="CA" data-subdomain="www" data-lang="en" data-do-not-rewrite="true">Canada</a> (English) </li> <li><a href="//www.mathworks.com" class="domain_selector_link" data-country-code="US" data-subdomain="www" data-lang="en" data-default-lang="true" data-selected-text="United States" data-recommended-text="United States" data-do-not-rewrite="true">United States</a> (English) </li> </ul> </div> <div class="col-sm-4 col-md-6"> <p class="h3 add_bottom_rule">Europe</p> <div class="row"> <div class="col-xs-6 col-sm-12 col-md-6"> <ul class="list-unstyled add_margin_0_sm"> <li><a href="//nl.mathworks.com" class="domain_selector_link" data-country-code="BE" data-subdomain="nl" data-lang="en" data-do-not-rewrite="true">Belgium</a> (English) </li> <li><a href="//se.mathworks.com" class="domain_selector_link" data-country-code="DK" data-subdomain="se" data-lang="en" data-do-not-rewrite="true">Denmark</a> (English) </li> <li><a href="//de.mathworks.com" class="domain_selector_link" data-country-code="DE" data-subdomain="de" data-lang="de" data-default-lang="true" data-selected-text="Deutschland" data-recommended-text="Deutschland" data-do-not-rewrite="true">Deutschland</a> (Deutsch) </li> <li><a href="//es.mathworks.com" class="domain_selector_link" data-country-code="ES" data-subdomain="es" data-lang="es" data-default-lang="true" data-selected-text="España" data-recommended-text="España" data-do-not-rewrite="true">España</a> (Español) </li> <li><a href="//se.mathworks.com" class="domain_selector_link" data-country-code="FI" data-subdomain="se" data-lang="en" data-do-not-rewrite="true">Finland</a> (English) </li> <li><a href="//fr.mathworks.com" class="domain_selector_link" data-country-code="FR" data-subdomain="fr" data-lang="fr" data-default-lang="true" data-selected-text="France" data-recommended-text="France" data-do-not-rewrite="true">France</a> (Français) </li> <li><a href="//uk.mathworks.com" class="domain_selector_link" data-country-code="IE" data-subdomain="uk" data-lang="en" data-do-not-rewrite="true">Ireland</a> (English) </li> <li><a href="//it.mathworks.com" class="domain_selector_link" data-country-code="IT" data-subdomain="it" data-lang="it" data-default-lang="true" data-selected-text="Italia" data-recommended-text="Italia" data-do-not-rewrite="true">Italia</a> (Italiano) </li> <li><a href="//nl.mathworks.com" class="domain_selector_link" data-country-code="LU" data-subdomain="nl" data-lang="en" data-do-not-rewrite="true">Luxembourg</a> (English) </li> </ul> </div> <div class="col-xs-6 col-sm-12 col-md-6"> <ul class="list-unstyled"> <li><a href="//nl.mathworks.com" class="domain_selector_link" data-country-code="NL" data-subdomain="nl" data-lang="en" data-default-lang="true" data-selected-text="Benelux" data-recommended-text="Netherlands" data-do-not-rewrite="true">Netherlands</a> (English) </li> <li><a href="//se.mathworks.com" class="domain_selector_link" data-country-code="NO" data-subdomain="se" data-lang="en" data-do-not-rewrite="true">Norway</a> (English) </li> <li><a href="//de.mathworks.com" class="domain_selector_link" data-country-code="AT" data-subdomain="de" data-lang="de" data-do-not-rewrite="true">Österreich</a> (Deutsch) </li> <li><a href="//www.mathworks.com" class="domain_selector_link" data-country-code="PT" data-subdomain="www" data-lang="en" data-do-not-rewrite="true">Portugal</a> (English) </li> <li><a href="//se.mathworks.com" class="domain_selector_link" data-country-code="SE" data-subdomain="se" data-lang="en" data-default-lang="true" data-selected-text="Nordic" data-recommended-text="Sweden" data-do-not-rewrite="true">Sweden</a> (English) </li> <li>Switzerland <ul class="list-unstyled add_indent_20"> <li><a href="//ch.mathworks.com" class="domain_selector_link" data-country-code="CH" data-subdomain="ch" data-lang="de" data-selected-text="Schweiz" data-recommended-text="Schweiz" data-do-not-rewrite="true">Deutsch</a> </li> <li><a href="//ch.mathworks.com" class="domain_selector_link" data-country-code="CH" data-subdomain="ch" data-lang="en" data-default-lang="true" data-selected-text="Switzerland" data-recommended-text="Switzerland" data-do-not-rewrite="true">English</a> </li> <li><a href="//ch.mathworks.com" class="domain_selector_link" data-country-code="CH" data-subdomain="ch" data-lang="fr" data-selected-text="Suisse" data-recommended-text="Suisse" data-do-not-rewrite="true">Français</a> </li> </ul> </li> <li><a href="//uk.mathworks.com" class="domain_selector_link" data-country-code="GB" data-subdomain="uk" data-lang="en" data-default-lang="true" data-selected-text="United Kingdom" data-recommended-text="United Kingdom" data-do-not-rewrite="true">United Kingdom</a> (English) </li> </ul> </div> </div> </div> <div class="col-sm-4 col-md-3"> <p class="h3 add_bottom_rule">Asia Pacific</p> <ul class="list-unstyled"> <li><a href="//au.mathworks.com" class="domain_selector_link" data-country-code="AU" data-subdomain="au" data-lang="en" data-default-lang="true" data-selected-text="Australia" data-recommended-text="Australia" data-do-not-rewrite="true">Australia</a> (English) </li> <li><a href="//in.mathworks.com" class="domain_selector_link" data-country-code="IN" data-subdomain="in" data-lang="en" data-default-lang="true" data-selected-text="India" data-recommended-text="India" data-do-not-rewrite="true">India</a> (English) </li> <li><a href="//au.mathworks.com" class="domain_selector_link" data-country-code="NZ" data-subdomain="au" data-lang="en" data-do-not-rewrite="true">New Zealand</a> (English) </li> <li>中国 <ul class="list-unstyled add_indent_20"> <li><a href="//ww2.mathworks.cn" class="domain_selector_link" data-country-code="CN" data-subdomain="ww2" data-lang="zh" data-default-lang="true" data-selected-text="中国" data-recommended-text="中国" data-do-not-rewrite="true">简体中文<span class="sr-only">Chinese</span> </a> </li> <li><a href="//ww2.mathworks.cn" class="domain_selector_link" data-country-code="CN" data-subdomain="ww2" data-lang="en" data-default-lang="true" data-selected-text="China" data-recommended-text="China" data-do-not-rewrite="true">English</a> </li> </ul> </li> <li><a href="//jp.mathworks.com" class="domain_selector_link" data-country-code="JP" data-subdomain="jp" data-lang="ja" data-default-lang="true" data-selected-text="日本" data-recommended-text="日本" data-do-not-rewrite="true">日本<span class="sr-only">Japanese</span></a> (日本語) </li> <li><a href="//kr.mathworks.com" class="domain_selector_link" data-country-code="KR" data-subdomain="kr" data-lang="ko" data-default-lang="true" data-selected-text="한국" data-recommended-text="한국" data-do-not-rewrite="true">한국<span class="sr-only">Korean</span></a> (한국어) </li> </ul> </div> </div> <p class="text-center"><a href="#" class="worldwide_link" data-do-not-rewrite="true">Contact your local office</a></p> </div> </div> </div> </div> <script src="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/components/domainselector.min.20240924193154397.js"></script> </div> </main> </div> <div class="cta_container_mobile visible-sm visible-xs"> <div class="container-fluid"> <div class="row"> <div class="col-xs-12"> <div><div class="callToAction calltoactionheader containsResourceName resourceClass-calltoactionheader"> <div class="cta_box"> <ul class="list-inline"> <li class="cta_item cta_item_general"> <a href="/campaigns/products/trials.html?s_tid=doc_trial_gate_tb" class="icon-download " data-link="lead" data-offertype="trial"> Trial software</a> </li> <li class="cta_item cta_item_general"> <a href="/downloads/web_downloads/?s_tid=doc_downloads" class="icon-download "> Product updates</a> </li> </ul> </div> </div> </div> </div> </div> </div> </div> <footer id="footer" class="bs-footer">  <div class="container-fluid"> <div class="footer"> <div class="row"> <div class="col-xs-12 col-md-9" role="navigation" aria-label="Footer navigation"> <ul class="countrynav">  <li class="footernav_country"> <a href="#" data-toggle="modal" id="domainButton" data-target="#country-unselected"> <span class="sr-only">Select a Web Site</span> <span class="icon-globe icon_color_quinary icon_16"></span><span id="countrySelectorButtonText">United States</span> </a> </li> </ul> <div class="clearfix"></div> <div><div class="footerNavigation footernavigation containsResourceName resourceClass-footernavigation"> <ul class="footernav " id="footernav" data-privacy="Your Privacy Choices"> <li class="footernav_footernav_patents"> <a href="/company/aboutus/policies_statements/trust-center.html?s_tid=gf_tc"> Trust Center</a> </li> <li class="footernav_footernav_trademarks"> <a href="/company/aboutus/policies_statements/trademarks.html?s_tid=gf_trd"> Trademarks</a> </li> <li class="footernav_footernav_privacy"> <a href="/company/aboutus/policies_statements.html?s_tid=gf_priv"> Privacy Policy</a> </li> <li class="footernav_footernav_piracy"> <a href="/company/aboutus/policies_statements/piracy.html?s_tid=gf_pir"> Preventing Piracy</a> </li> <li class="footernav_footernav_status"> <a href="https://status.mathworks.com/?s_tid=gf_application"> Application Status</a> </li> </ul> <script src="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/components/footernavigation.min.20240924193154397.js"></script> </div> </div> <div><div class="footerCompanyAddress footercompanyaddress containsResourceName resourceClass-footercompanyaddress"> <div class="cq-placeholder" data-emptytext="Footer Company Address"></div> </div> </div> <div><div class="footerParsys iparsys parsys resourceClass-iparsys containsResourceName"><div class="section"><div class="new containsResourceName resourceClass-new"></div> </div><div class="iparys_inherited"><div class="footerParsys iparsys parsys containsResourceName resourceClass-par"></div> </div> </div> </div> <div class="clearfix"></div> <p class="copyright">© 1994-2024 The MathWorks, Inc.</p> </div> <div class="clearfix visible-sm add_margin_10"></div> <div class="col-xs-12 col-md-3"> <div><div class="socialMediaIconParsys iparsys parsys resourceClass-iparsys containsResourceName"><div class="section"><div class="new containsResourceName resourceClass-new"></div> </div><div class="iparys_inherited"><div class="socialMediaIconParsys iparsys parsys containsResourceName resourceClass-par"><div class="socialmediaicon containsResourceName resourceClass-socialmediaicon section"> <div class="social_media "> <ul class="social_media_icons list-unstyled "> <li> <a href="https://www.facebook.com/MATLAB" class="svg_link" rel="noreferrer" target="_blank"> <img class="ico_facebook" alt="Facebook" src="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/common/resources/images/ico-facebook.20240924193154397.svg"/> </a> </li> <li> <a href="https://x.com/MATLAB" class="svg_link" rel="noreferrer" target="_blank"> <img class="ico_twitter" alt="Twitter" src="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/common/resources/images/ico-twitter.20240924193154397.svg"/> </a> </li> <li> <a href="https://www.instagram.com/matlab/" class="svg_link" rel="noreferrer" target="_blank"> <img class="ico_instagram" alt="Instagram" src="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/common/resources/images/ico-instagram.20240924193154397.svg"/> </a> </li> <li> <a href="https://www.youtube.com/user/MATLAB" class="svg_link" rel="noreferrer" target="_blank"> <img class="ico_youtube" alt="YouTube" src="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/common/resources/images/ico-youtube.20240924193154397.svg"/> </a> </li> <li> <a href="https://www.linkedin.com/company/the-mathworks_2" class="svg_link" rel="noreferrer" target="_blank"> <img class="ico_linkedin" alt="LinkedIn" src="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/common/resources/images/ico-linkedin.20240924193154397.svg"/> </a> </li> <li> <a href="/company/rss.html" class="svg_link" rel="noreferrer"> <img class="ico_rss" alt="RSS" src="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/common/resources/images/ico-rss.20240924193154397.svg"/> </a> </li> </ul> <div class="clearfix"></div> </div> </div> </div> </div> </div> </div> <div class="clearfix"></div> <p class="pull_right_sm pull_right_md pull_right_lg"><small class="percent_90"><em>Join the conversation</em></small></p> </div> </div> </div> </div>  </footer> </div> </div> <script src="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/components/domainredirect.min.20240924193154397.js"></script> <script src="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/akamai.min.20240924193154397.js"></script> <script src="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/components/lodash.min.20240924193154397.js"></script> <script src="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/common/core.min.20240924193154397.js"></script> <script src="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/common.min.20240924193154397.js"></script> <script src="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/templates/offcanvasv4.min.20240924193154397.js"></script> <script src="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/components/truncatenav.min.20240924193154397.js"></script> <div id="web-application-footer-assets"></div> <link rel="stylesheet" href="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/components/matrixmenu.min.20240924193154397.css" type="text/css"/> <script src="https://www.mathworks.com/etc.clientlibs/mathworks/clientlibs/customer-ui/components/matrixmenu.min.20240924193154397.js"></script> <script> $('.matrix_affordance_container_mobile button').on('click', function() { $('#matrix_collapse').collapse('toggle') }) </script> <script src="/help/releases/R2024b/includes/shared/scripts/localstorage.js"></script> <script src="/help/releases/R2024b/includes/shared/scripts/saxonjs/SaxonJS2.rt.js"></script> <script src="/help/releases/R2024b/includes/shared/scripts/above_product_landing.js"></script> <script xmlns="http://www.w3.org/1999/xhtml"> window.history.replaceState(window.location.href, null, ""); // Initialize document.addEventListener('DOMContentLoaded', function() { mystylesheetLocation = "/help/releases/R2024b/includes/shared/scripts/product_group-sef.json"; mysourceLocation = "/help/releases/R2024b/docset.xml"; doccentertype = "web"; langcode = ""; getProductFilteredList(mystylesheetLocation, mysourceLocation, doccentertype, langcode); }); </script><script src="/help/includes/web/scripts/livecontrolpopoverhandler.js?202409"></script><script src="/help/includes/web/scripts/livetaskpopoverhandler.js?202409"></script><script src="https://matlab.mathworks.com/open/openwith.js?202403"></script><style>.examples_short_list a.btn {display: none;}</style><script src="/help/includes/web/scripts/openInBrowser.js"></script> <script type="text/javascript" nonce="09e2087baff839c5019cafed3fcc03b2" src="/G-KjqKJMr3SMrocH3w/Ou9VbtXDJDLmY7/M3MLaQE/DVtLD/S45CT8"></script></body></html>