{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": "(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n  var py_version = '3.2.2'.replace('rc', '-rc.').replace('.dev', '-dev.');\n  var is_dev = py_version.indexOf(\"+\") !== -1 || py_version.indexOf(\"-\") !== -1;\n  var reloading = false;\n  var Bokeh = root.Bokeh;\n  var bokeh_loaded = Bokeh != null && (Bokeh.version === py_version || (Bokeh.versions !== undefined && Bokeh.versions.has(py_version)));\n\n  if (typeof (root._bokeh_timeout) === \"undefined\" || force) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks;\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, js_modules, js_exports, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n    if (js_modules == null) js_modules = [];\n    if (js_exports == null) js_exports = {};\n\n    root._bokeh_onload_callbacks.push(callback);\n\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls.length === 0 && js_modules.length === 0 && Object.keys(js_exports).length === 0) {\n      run_callbacks();\n      return null;\n    }\n    if (!reloading) {\n      console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    }\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n    window._bokeh_on_load = on_load\n\n    function on_error() {\n      console.error(\"failed to load \" + url);\n    }\n\n    var skip = [];\n    if (window.requirejs) {\n      window.requirejs.config({'packages': {}, 'paths': {'xtermjs': 'https://cdn.jsdelivr.net/npm/xterm@4.14.1/lib/xterm', 'xtermjsweblinks': 'https://cdn.jsdelivr.net/npm/xterm-addon-web-links@0.4.0/lib/xterm-addon-web-links', 'tabulator': 'https://cdn.jsdelivr.net/npm/tabulator-tables@5.5.0/dist/js/tabulator', 'moment': 'https://cdn.jsdelivr.net/npm/luxon/build/global/luxon.min', 'plotly': 'https://cdn.plot.ly/plotly-2.18.0.min', 'mathjax': '//cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-AMS_HTML', 'ace': '//cdnjs.cloudflare.com/ajax/libs/ace/1.4.7', 'jspanel': 'https://cdn.jsdelivr.net/npm/jspanel4@4.12.0/dist/jspanel', 'jspanel-modal': 'https://cdn.jsdelivr.net/npm/jspanel4@4.12.0/dist/extensions/modal/jspanel.modal', 'jspanel-tooltip': 'https://cdn.jsdelivr.net/npm/jspanel4@4.12.0/dist/extensions/tooltip/jspanel.tooltip', 'jspanel-hint': 'https://cdn.jsdelivr.net/npm/jspanel4@4.12.0/dist/extensions/hint/jspanel.hint', 'jspanel-layout': 'https://cdn.jsdelivr.net/npm/jspanel4@4.12.0/dist/extensions/layout/jspanel.layout', 'jspanel-contextmenu': 'https://cdn.jsdelivr.net/npm/jspanel4@4.12.0/dist/extensions/contextmenu/jspanel.contextmenu', 'jspanel-dock': 'https://cdn.jsdelivr.net/npm/jspanel4@4.12.0/dist/extensions/dock/jspanel.dock', 'gridstack': 'https://cdn.jsdelivr.net/npm/gridstack@7.2.3/dist/gridstack-all', 'notyf': 'https://cdn.jsdelivr.net/npm/notyf@3/notyf.min'}, 'shim': {'xtermjsweblinks': {'exports': 'WebLinksAddon', 'deps': ['xtermjs']}, 'mathjax': {'exports': 'MathJax'}, 'ace/ext-language_tools': {'deps': ['ace/ace']}, 'ace/ext-modelist': {'deps': ['ace/ace']}, 'jspanel': {'exports': 'jsPanel'}, 'gridstack': {'exports': 'GridStack'}}});\n      require([\"xtermjs\"], function(xtermjs) {\n\twindow.xtermjs = xtermjs\n\ton_load()\n      })\n      require([\"xtermjsweblinks\"], function(WebLinksAddon) {\n\twindow.WebLinksAddon = WebLinksAddon\n\ton_load()\n      })\n      require([\"tabulator\"], function(Tabulator) {\n\twindow.Tabulator = Tabulator\n\ton_load()\n      })\n      require([\"moment\"], function(moment) {\n\twindow.moment = moment\n\ton_load()\n      })\n      require([\"plotly\"], function(Plotly) {\n\twindow.Plotly = Plotly\n\ton_load()\n      })\n      require([\"mathjax\"], function() {\n\ton_load()\n      })\n      require([\"ace/ace\"], function(ace) {\n\twindow.ace = ace\n\ton_load()\n      })\n      require([\"ace/ext-language_tools\"], function() {\n\ton_load()\n      })\n      require([\"ace/ext-modelist\"], function() {\n\ton_load()\n      })\n      require([\"jspanel\"], function(jsPanel) {\n\twindow.jsPanel = jsPanel\n\ton_load()\n      })\n      require([\"jspanel-modal\"], function() {\n\ton_load()\n      })\n      require([\"jspanel-tooltip\"], function() {\n\ton_load()\n      })\n      require([\"jspanel-hint\"], function() {\n\ton_load()\n      })\n      require([\"jspanel-layout\"], function() {\n\ton_load()\n      })\n      require([\"jspanel-contextmenu\"], function() {\n\ton_load()\n      })\n      require([\"jspanel-dock\"], function() {\n\ton_load()\n      })\n      require([\"gridstack\"], function(GridStack) {\n\twindow.GridStack = GridStack\n\ton_load()\n      })\n      require([\"notyf\"], function() {\n\ton_load()\n      })\n      root._bokeh_is_loading = css_urls.length + 18;\n    } else {\n      root._bokeh_is_loading = css_urls.length + js_urls.length + js_modules.length + Object.keys(js_exports).length;\n    }\n\n    var existing_stylesheets = []\n    var links = document.getElementsByTagName('link')\n    for (var i = 0; i < links.length; i++) {\n      var link = links[i]\n      if (link.href != null) {\n\texisting_stylesheets.push(link.href)\n      }\n    }\n    for (var i = 0; i < css_urls.length; i++) {\n      var url = css_urls[i];\n      if (existing_stylesheets.indexOf(url) !== -1) {\n\ton_load()\n\tcontinue;\n      }\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }    if (((window['xtermjs'] !== undefined) && (!(window['xtermjs'] instanceof HTMLElement))) || window.requirejs) {\n      var urls = ['https://cdn.holoviz.org/panel/1.2.3/dist/bundled/terminal/xterm@4.14.1/lib/xterm.js', 'https://cdn.holoviz.org/panel/1.2.3/dist/bundled/terminal/xterm-addon-web-links@0.4.0/lib/xterm-addon-web-links.js'];\n      for (var i = 0; i < urls.length; i++) {\n        skip.push(urls[i])\n      }\n    }    if (((window['Tabulator'] !== undefined) && (!(window['Tabulator'] instanceof HTMLElement))) || window.requirejs) {\n      var urls = ['https://cdn.holoviz.org/panel/1.2.3/dist/bundled/datatabulator/tabulator-tables@5.5.0/dist/js/tabulator.js'];\n      for (var i = 0; i < urls.length; i++) {\n        skip.push(urls[i])\n      }\n    }    if (((window['moment'] !== undefined) && (!(window['moment'] instanceof HTMLElement))) || window.requirejs) {\n      var urls = ['https://cdn.holoviz.org/panel/1.2.3/dist/bundled/datatabulator/luxon/build/global/luxon.min.js'];\n      for (var i = 0; i < urls.length; i++) {\n        skip.push(urls[i])\n      }\n    }    if (((window['Plotly'] !== undefined) && (!(window['Plotly'] instanceof HTMLElement))) || window.requirejs) {\n      var urls = ['https://cdn.holoviz.org/panel/1.2.3/dist/bundled/plotlyplot/plotly-2.18.0.min.js'];\n      for (var i = 0; i < urls.length; i++) {\n        skip.push(urls[i])\n      }\n    }    if (((window['MathJax'] !== undefined) && (!(window['MathJax'] instanceof HTMLElement))) || window.requirejs) {\n      var urls = ['https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-MML-AM_CHTML'];\n      for (var i = 0; i < urls.length; i++) {\n        skip.push(urls[i])\n      }\n    }    if (((window['ace'] !== undefined) && (!(window['ace'] instanceof HTMLElement))) || window.requirejs) {\n      var urls = ['https://cdnjs.cloudflare.com/ajax/libs/ace/1.4.11/ace.js', 'https://cdnjs.cloudflare.com/ajax/libs/ace/1.4.11/ext-language_tools.js', 'https://cdnjs.cloudflare.com/ajax/libs/ace/1.4.11/ext-modelist.js'];\n      for (var i = 0; i < urls.length; i++) {\n        skip.push(urls[i])\n      }\n    }    if (((window['jsPanel'] !== undefined) && (!(window['jsPanel'] instanceof HTMLElement))) || window.requirejs) {\n      var urls = ['https://cdn.holoviz.org/panel/1.2.3/dist/bundled/floatpanel/jspanel4@4.12.0/dist/jspanel.js', 'https://cdn.holoviz.org/panel/1.2.3/dist/bundled/floatpanel/jspanel4@4.12.0/dist/extensions/modal/jspanel.modal.js', 'https://cdn.holoviz.org/panel/1.2.3/dist/bundled/floatpanel/jspanel4@4.12.0/dist/extensions/tooltip/jspanel.tooltip.js', 'https://cdn.holoviz.org/panel/1.2.3/dist/bundled/floatpanel/jspanel4@4.12.0/dist/extensions/hint/jspanel.hint.js', 'https://cdn.holoviz.org/panel/1.2.3/dist/bundled/floatpanel/jspanel4@4.12.0/dist/extensions/layout/jspanel.layout.js', 'https://cdn.holoviz.org/panel/1.2.3/dist/bundled/floatpanel/jspanel4@4.12.0/dist/extensions/contextmenu/jspanel.contextmenu.js', 'https://cdn.holoviz.org/panel/1.2.3/dist/bundled/floatpanel/jspanel4@4.12.0/dist/extensions/dock/jspanel.dock.js'];\n      for (var i = 0; i < urls.length; i++) {\n        skip.push(urls[i])\n      }\n    }    if (((window['GridStack'] !== undefined) && (!(window['GridStack'] instanceof HTMLElement))) || window.requirejs) {\n      var urls = ['https://cdn.holoviz.org/panel/1.2.3/dist/bundled/gridstack/gridstack@7.2.3/dist/gridstack-all.js'];\n      for (var i = 0; i < urls.length; i++) {\n        skip.push(urls[i])\n      }\n    }    if (((window['Notyf'] !== undefined) && (!(window['Notyf'] instanceof HTMLElement))) || window.requirejs) {\n      var urls = ['https://cdn.holoviz.org/panel/1.2.3/dist/bundled/notificationarea/notyf@3/notyf.min.js'];\n      for (var i = 0; i < urls.length; i++) {\n        skip.push(urls[i])\n      }\n    }    var existing_scripts = []\n    var scripts = document.getElementsByTagName('script')\n    for (var i = 0; i < scripts.length; i++) {\n      var script = scripts[i]\n      if (script.src != null) {\n\texisting_scripts.push(script.src)\n      }\n    }\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      if (skip.indexOf(url) !== -1 || existing_scripts.indexOf(url) !== -1) {\n\tif (!window.requirejs) {\n\t  on_load();\n\t}\n\tcontinue;\n      }\n      var element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.async = false;\n      element.src = url;\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n    for (var i = 0; i < js_modules.length; i++) {\n      var url = js_modules[i];\n      if (skip.indexOf(url) !== -1 || existing_scripts.indexOf(url) !== -1) {\n\tif (!window.requirejs) {\n\t  on_load();\n\t}\n\tcontinue;\n      }\n      var element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.async = false;\n      element.src = url;\n      element.type = \"module\";\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n    for (const name in js_exports) {\n      var url = js_exports[name];\n      if (skip.indexOf(url) >= 0 || root[name] != null) {\n\tif (!window.requirejs) {\n\t  on_load();\n\t}\n\tcontinue;\n      }\n      var element = document.createElement('script');\n      element.onerror = on_error;\n      element.async = false;\n      element.type = \"module\";\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      element.textContent = `\n      import ${name} from \"${url}\"\n      window.${name} = ${name}\n      window._bokeh_on_load()\n      `\n      document.head.appendChild(element);\n    }\n    if (!js_urls.length && !js_modules.length) {\n      on_load()\n    }\n  };\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  var js_urls = [\"https://cdnjs.cloudflare.com/ajax/libs/ace/1.4.11/ace.js\", \"https://cdnjs.cloudflare.com/ajax/libs/ace/1.4.11/ext-language_tools.js\", \"https://cdnjs.cloudflare.com/ajax/libs/ace/1.4.11/ext-modelist.js\", \"https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-MML-AM_CHTML\", \"https://cdn.holoviz.org/panel/1.2.3/dist/bundled/jquery/jquery.slim.min.js\", \"https://cdn.holoviz.org/panel/1.2.3/dist/bundled/plotlyplot/plotly-2.18.0.min.js\", \"https://cdn.holoviz.org/panel/1.2.3/dist/bundled/datatabulator/tabulator-tables@5.5.0/dist/js/tabulator.js\", \"https://cdn.holoviz.org/panel/1.2.3/dist/bundled/datatabulator/luxon/build/global/luxon.min.js\", \"https://cdn.holoviz.org/panel/1.2.3/dist/bundled/terminal/xterm@4.14.1/lib/xterm.js\", \"https://cdn.holoviz.org/panel/1.2.3/dist/bundled/terminal/xterm-addon-web-links@0.4.0/lib/xterm-addon-web-links.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-3.2.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-3.2.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-3.2.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-3.2.2.min.js\", \"https://cdn.holoviz.org/panel/1.2.3/dist/bundled/gridstack/gridstack@7.2.3/dist/gridstack-all.js\", \"https://cdn.holoviz.org/panel/1.2.3/dist/bundled/notificationarea/notyf@3/notyf.min.js\", \"https://cdn.holoviz.org/panel/1.2.3/dist/bundled/material-components-web@7.0.0/dist/material-components-web.min.js\", \"https://cdn.holoviz.org/panel/1.2.3/dist/panel.min.js\"];\n  var js_modules = [];\n  var js_exports = {};\n  var css_urls = [\"https://cdn.holoviz.org/panel/1.2.3/dist/bundled/datatabulator/tabulator-tables@5.5.0/dist/css/tabulator_simple.min.css\", \"https://cdn.holoviz.org/panel/1.2.3/dist/bundled/terminal/xterm@4.11.0/css/xterm.css\", \"https://cdn.holoviz.org/panel/1.2.3/dist/bundled/gridstack/gridstack@7.2.3/dist/gridstack.min.css\", \"https://cdn.holoviz.org/panel/1.2.3/dist/bundled/gridstack/gridstack@7.2.3/dist/gridstack-extra.min.css\", \"https://cdn.holoviz.org/panel/1.2.3/dist/bundled/notificationarea/notyf@3/notyf.min.css\", \"https://cdn.holoviz.org/panel/1.2.3/dist/bundled/font-awesome/css/all.min.css\", \"https://fonts.googleapis.com/css?family=Roboto:300,400,500\", \"https://fonts.googleapis.com/css?family=Material+Icons&display=block\"];\n  var inline_js = [    function(Bokeh) {\n      inject_raw_css(\".tabulator{position:relative;border:1px solid #999;font-size:14px;text-align:left;overflow:hidden;-webkit-transform:translateZ(0);-moz-transform:translateZ(0);-ms-transform:translateZ(0);-o-transform:translateZ(0);transform:translateZ(0)}.tabulator[tabulator-layout=fitDataFill] .tabulator-tableholder .tabulator-table{min-width:100%}.tabulator[tabulator-layout=fitDataTable]{display:inline-block}.tabulator.tabulator-block-select{user-select:none}.tabulator .tabulator-header{position:relative;box-sizing:border-box;width:100%;border-bottom:1px solid #999;background-color:#fff;color:#555;font-weight:700;white-space:nowrap;overflow:hidden;-moz-user-select:none;-khtml-user-select:none;-webkit-user-select:none;-o-user-select:none}.tabulator .tabulator-header.tabulator-header-hidden{display:none}.tabulator .tabulator-header .tabulator-header-contents{position:relative;overflow:hidden}.tabulator .tabulator-header .tabulator-header-contents .tabulator-headers{display:inline-block}.tabulator .tabulator-header .tabulator-col{display:inline-flex;position:relative;box-sizing:border-box;flex-direction:column;justify-content:flex-start;border-right:1px solid #ddd;background:#fff;text-align:left;vertical-align:bottom;overflow:hidden}.tabulator .tabulator-header .tabulator-col.tabulator-moving{position:absolute;border:1px solid #999;background:#e6e6e6;pointer-events:none}.tabulator .tabulator-header .tabulator-col .tabulator-col-content{box-sizing:border-box;position:relative;padding:4px}.tabulator .tabulator-header .tabulator-col .tabulator-col-content .tabulator-header-popup-button{padding:0 8px}.tabulator .tabulator-header .tabulator-col .tabulator-col-content .tabulator-header-popup-button:hover{cursor:pointer;opacity:.6}.tabulator .tabulator-header .tabulator-col .tabulator-col-content .tabulator-col-title-holder{position:relative}.tabulator .tabulator-header .tabulator-col .tabulator-col-content .tabulator-col-title{box-sizing:border-box;width:100%;white-space:nowrap;overflow:hidden;text-overflow:ellipsis;vertical-align:bottom}.tabulator .tabulator-header .tabulator-col .tabulator-col-content .tabulator-col-title.tabulator-col-title-wrap{white-space:normal;text-overflow:clip}.tabulator .tabulator-header .tabulator-col .tabulator-col-content .tabulator-col-title .tabulator-title-editor{box-sizing:border-box;width:100%;border:1px solid #999;padding:1px;background:#fff}.tabulator .tabulator-header .tabulator-col .tabulator-col-content .tabulator-col-title .tabulator-header-popup-button+.tabulator-title-editor{width:calc(100% - 22px)}.tabulator .tabulator-header .tabulator-col .tabulator-col-content .tabulator-col-sorter{display:flex;align-items:center;position:absolute;top:0;bottom:0;right:4px}.tabulator .tabulator-header .tabulator-col .tabulator-col-content .tabulator-col-sorter .tabulator-arrow{width:0;height:0;border-left:6px solid transparent;border-right:6px solid transparent;border-bottom:6px solid #bbb}.tabulator .tabulator-header .tabulator-col.tabulator-col-group .tabulator-col-group-cols{position:relative;display:flex;border-top:1px solid #ddd;overflow:hidden;margin-right:-1px}.tabulator .tabulator-header .tabulator-col .tabulator-header-filter{position:relative;box-sizing:border-box;margin-top:2px;width:100%;text-align:center}.tabulator .tabulator-header .tabulator-col .tabulator-header-filter textarea{height:auto!important}.tabulator .tabulator-header .tabulator-col .tabulator-header-filter svg{margin-top:3px}.tabulator .tabulator-header .tabulator-col .tabulator-header-filter input::-ms-clear{width:0;height:0}.tabulator .tabulator-header .tabulator-col.tabulator-sortable .tabulator-col-title{padding-right:25px}@media (hover:hover) and (pointer:fine){.tabulator .tabulator-header .tabulator-col.tabulator-sortable.tabulator-col-sorter-element:hover{cursor:pointer;background-color:#e6e6e6}}.tabulator .tabulator-header .tabulator-col.tabulator-sortable[aria-sort=none] .tabulator-col-content .tabulator-col-sorter{color:#bbb}@media (hover:hover) and (pointer:fine){.tabulator .tabulator-header .tabulator-col.tabulator-sortable[aria-sort=none] .tabulator-col-content .tabulator-col-sorter.tabulator-col-sorter-element .tabulator-arrow:hover{cursor:pointer;border-bottom:6px solid #555}}.tabulator .tabulator-header .tabulator-col.tabulator-sortable[aria-sort=none] .tabulator-col-content .tabulator-col-sorter .tabulator-arrow{border-top:none;border-bottom:6px solid #bbb}.tabulator .tabulator-header .tabulator-col.tabulator-sortable[aria-sort=ascending] .tabulator-col-content .tabulator-col-sorter{color:#666}@media (hover:hover) and (pointer:fine){.tabulator .tabulator-header .tabulator-col.tabulator-sortable[aria-sort=ascending] .tabulator-col-content .tabulator-col-sorter.tabulator-col-sorter-element .tabulator-arrow:hover{cursor:pointer;border-bottom:6px solid #555}}.tabulator .tabulator-header .tabulator-col.tabulator-sortable[aria-sort=ascending] .tabulator-col-content .tabulator-col-sorter .tabulator-arrow{border-top:none;border-bottom:6px solid #666}.tabulator .tabulator-header .tabulator-col.tabulator-sortable[aria-sort=descending] .tabulator-col-content .tabulator-col-sorter{color:#666}@media (hover:hover) and (pointer:fine){.tabulator .tabulator-header .tabulator-col.tabulator-sortable[aria-sort=descending] .tabulator-col-content .tabulator-col-sorter.tabulator-col-sorter-element .tabulator-arrow:hover{cursor:pointer;border-top:6px solid #555}}.tabulator .tabulator-header .tabulator-col.tabulator-sortable[aria-sort=descending] .tabulator-col-content .tabulator-col-sorter 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All rights reserved.\\n * Copyright (c) 2012-2013, Christopher Jeffrey (MIT License)\\n * https://github.com/chjj/term.js\\n * @license MIT\\n *\\n * Permission is hereby granted, free of charge, to any person obtaining a copy\\n * of this software and associated documentation files (the \\\"Software\\\"), to deal\\n * in the Software without restriction, including without limitation the rights\\n * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell\\n * copies of the Software, and to permit persons to whom the Software is\\n * furnished to do so, subject to the following conditions:\\n *\\n * The above copyright notice and this permission notice shall be included in\\n * all copies or substantial portions of the Software.\\n *\\n * THE SOFTWARE IS PROVIDED \\\"AS IS\\\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\\n * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN\\n * THE SOFTWARE.\\n *\\n * Originally forked from (with the author's permission):\\n *   Fabrice Bellard's javascript vt100 for jslinux:\\n *   http://bellard.org/jslinux/\\n *   Copyright (c) 2011 Fabrice Bellard\\n *   The original design remains. 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   "source": [
    "import manganite\n",
    "%load_ext manganite"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Traveling Salesman Problem\n",
    "The Traveling Salesman Problem (TSP) is one of the most famous combinatorial optimization problems. \n",
    "The TSP goal is to find the shortest possible route that visits each city once and returns to the original city.\n",
    "It is classified as an NP-hard problem in the field of combinatorial optimization."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem Description\n",
    "The TSP can be defined as follows: for a given list of cities and the distances between each pair of them, we want to find the shortest possible route that goes to each city once and returns to the origin city.\n",
    "\n",
    "There is a class of Traveling Salesman Problems that assumes that the distance of going from city $$i$$ to city $j$  is the same as going form city $j$ to city $i$, this type of Traveling Salesman Problem  is also known as the symmetric Traveling Salesman Problem. In this example, we use Euclidean distances, but the TSP model formulation is valid independent of the way in which the individual distances are determined.\n",
    "\n",
    "\n",
    "## Solution Approach\n",
    "\n",
    "Mathematical programming is a declarative approach where the modeler formulates a mathematical optimization model that captures the key aspects of a complex decision problem. The Gurobi Optimizer solves such models using state-of-the-art mathematics and computer science.\n",
    "\n",
    "A mathematical optimization model has five components, namely:\n",
    "\n",
    "* Sets and indices.\n",
    "* Parameters.\n",
    "* Decision variables.\n",
    "* Objective function(s).\n",
    "* Constraints.\n",
    "\n",
    "We now present a MIP formulation of the TSP that identifies the shortest route that goes to all the cities once and returns to the origin city.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Python Implementation\n",
    "\n",
    "Consider a salesperson that needs to visit customers at each state capital of the continental US. The salesperson wants to identify the shortest route that goes to all the state capitals.\n",
    "\n",
    "This modeling example requires the following libraries that are not part of the standard Python distribution:\n",
    "* **manganite**: to create the dashboard\n",
    "* **folium**: to create maps.\n",
    "* **gurobipy**: provides Gurobi algorithms to solve MIP models.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import json\n",
    "import math\n",
    "from itertools import combinations\n",
    "import gurobipy as gp\n",
    "from gurobipy import GRB\n",
    "import pandas as pd\n",
    "import plotly.express as px"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "capitals_json = json.load(open('capitals.json'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "region_list = [ 'All', 'West', 'Pacific']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%mnn widget --type radio region_list --tab \"Capitals\" --header \"Region\" --var r --position 0 0 1\n",
    "r = region_list[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%mnn widget --type plot --tab \"Capitals\" --header \"Map\" --var fig_select --position 0 1 4\n",
    "\n",
    "capitals = []\n",
    "coordinates_lat = []\n",
    "coordinates_long = []\n",
    "if r == 'All':\n",
    "    for state in capitals_json:\n",
    "        if state not in ['AK', 'HI']:\n",
    "            capital = capitals_json[state]['capital']\n",
    "            capitals.append(capital)\n",
    "            coordinates_lat.append(float(capitals_json[state]['lat']))\n",
    "            coordinates_long.append(float(capitals_json[state]['long']))\n",
    "    marker_color = 'blue'\n",
    "elif r == 'West':\n",
    "    west_states = ['AZ','CA','CO','ID' , 'MT', 'NV', 'NM', 'OR', 'UT', 'WA', 'WY']\n",
    "    for state in capitals_json:\n",
    "        if state in west_states:\n",
    "            capital = capitals_json[state]['capital']\n",
    "            capitals.append(capital)\n",
    "            coordinates_lat.append(float(capitals_json[state]['lat']))\n",
    "            coordinates_long.append(float(capitals_json[state]['long']))\n",
    "    marker_color = 'green'\n",
    "elif r == 'Pacific':\n",
    "    west_states = ['AZ','CA','CO','ID' , 'MT', 'NV', 'NM', 'OR', 'UT', 'WA', 'WY']\n",
    "    for state in capitals_json:\n",
    "        if state not in (west_states +  ['AK', 'HI']):\n",
    "            capital = capitals_json[state]['capital']\n",
    "            capitals.append(capital)\n",
    "            coordinates_lat.append(float(capitals_json[state]['lat']))\n",
    "            coordinates_long.append(float(capitals_json[state]['long']))\n",
    "    marker_color = 'red'\n",
    "\n",
    "\n",
    "\n",
    "df_cap = pd.DataFrame({'Capital' : capitals, 'coordinates_lat' : coordinates_lat, 'coordinates_long': coordinates_long})\n",
    "\n",
    "capitals = df_cap['Capital'].values.tolist()\n",
    "coordinates = {}\n",
    "\n",
    "for index, row in df_cap.iterrows():\n",
    "    coordinates[row['Capital']] = (row['coordinates_lat'], row['coordinates_long'])\n",
    "\n",
    "fig_select = px.scatter_mapbox(df_cap, lat=\"coordinates_lat\", lon=\"coordinates_long\", zoom=3,  hover_name = 'Capital')\n",
    "\n",
    "fig_select.update_layout(mapbox_style=\"open-street-map\", mapbox_zoom=3, mapbox_center_lat = 41,\n",
    "                      margin={\"r\":0,\"t\":0,\"l\":0,\"b\":0},\n",
    "                      )\n",
    "\n",
    "fig_select.update_traces(\n",
    "    marker = {'color': marker_color, 'size': 10},\n",
    ")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "# Compute pairwise distance matrix\n",
    "\n",
    "def distance(city1, city2):\n",
    "    c1 = coordinates[city1]\n",
    "    c2 = coordinates[city2]\n",
    "    diff = (c1[0]-c2[0], c1[1]-c2[1])\n",
    "    return math.sqrt(diff[0]*diff[0]+diff[1]*diff[1])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Callback - use lazy constraints to eliminate sub-tours\n",
    "\n",
    "def subtourelim(model, where):\n",
    "    if where == GRB.Callback.MIPSOL:\n",
    "        # make a list of edges selected in the solution\n",
    "        vals = model.cbGetSolution(model._vars)\n",
    "        selected = gp.tuplelist((i, j) for i, j in model._vars.keys()\n",
    "                             if vals[i, j] > 0.5)\n",
    "        # find the shortest cycle in the selected edge list\n",
    "        tour = subtour(selected)\n",
    "        if len(tour) < len(capitals):\n",
    "            # add subtour elimination constr. for every pair of cities in subtour\n",
    "            model.cbLazy(gp.quicksum(model._vars[i, j] for i, j in combinations(tour, 2))\n",
    "                         <= len(tour)-1)\n",
    "\n",
    "# Given a tuplelist of edges, find the shortest subtour\n",
    "\n",
    "def subtour(edges):\n",
    "    unvisited = capitals[:]\n",
    "    cycle = capitals[:] # Dummy - guaranteed to be replaced\n",
    "    while unvisited:  # true if list is non-empty\n",
    "        thiscycle = []\n",
    "        neighbors = unvisited\n",
    "        while neighbors:\n",
    "            current = neighbors[0]\n",
    "            thiscycle.append(current)\n",
    "            unvisited.remove(current)\n",
    "            neighbors = [j for i, j in edges.select(current, '*')\n",
    "                         if j in unvisited]\n",
    "        if len(thiscycle) <= len(cycle):\n",
    "            cycle = thiscycle # New shortest subtour\n",
    "    return cycle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%mnn execute --on button \"Optimize routes\" --returns tour_df\n",
    "\n",
    "dist = {(c1, c2): distance(c1, c2) for c1, c2 in combinations(capitals, 2)}\n",
    "\n",
    "# tested with Python 3.7 & Gurobi 9.0.0\n",
    "\n",
    "m = gp.Model()\n",
    "\n",
    "# Variables: is city 'i' adjacent to city 'j' on the tour?\n",
    "vars = m.addVars(dist.keys(), obj=dist, vtype=GRB.BINARY, name='x')\n",
    "\n",
    "# Symmetric direction: Copy the object\n",
    "for i, j in vars.keys():\n",
    "    vars[j, i] = vars[i, j]  # edge in opposite direction\n",
    "\n",
    "# Constraints: two edges incident to each city\n",
    "cons = m.addConstrs(vars.sum(c, '*') == 2 for c in capitals)\n",
    "\n",
    "m._vars = vars\n",
    "m.Params.lazyConstraints = 1\n",
    "m.optimize(subtourelim)\n",
    "\n",
    "# Retrieve solution\n",
    "\n",
    "vals = m.getAttr('x', vars)\n",
    "selected = gp.tuplelist((i, j) for i, j in vals.keys() if vals[i, j] > 0.5)\n",
    "\n",
    "tour = subtour(selected)\n",
    "assert len(tour) == len(capitals)\n",
    "\n",
    "tour_lat = []\n",
    "tour_lon = []\n",
    "for city in tour:\n",
    "    tour_lat.append(coordinates[city][0])\n",
    "    tour_lon.append(coordinates[city][1])\n",
    "\n",
    "tour_df = pd.DataFrame({'Capital': tour, 'lat': tour_lat, 'lon':tour_lon})  \n",
    "\n",
    "print('Optimal solution found')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%mnn widget --type plot --var fig_map --tab \"Optimal Route\"  --header \"Solution Map\" --position 0 0 6\n",
    "\n",
    "fig_map = px.line_mapbox(tour_df, lat=\"lat\", lon=\"lon\", zoom=3,  hover_name = 'Capital')\n",
    "\n",
    "fig_map.update_layout(mapbox_style=\"open-street-map\", mapbox_zoom=3, mapbox_center_lat = 41,\n",
    "    margin={\"r\":0,\"t\":0,\"l\":0,\"b\":0})\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusions\n",
    "\n",
    "The Traveling Salesman Problem (TSP) is the most popular combinatorial optimization problem. This problem is very easy to explain, although it is very complicated to solve. The largest TSP problem solved has 85,900 cities. The TSP is a source of discovery for new approaches to solve complex combinatorial optimization problems and has led to many applications.\n",
    "\n",
    "In this modeling example, we have shown how to formulate the symmetric Traveling Salesman Problem as a MIP problem. We also showed how to dynamically eliminate subtours by using lazy constraints. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "[1] D. L. Applegate, R. E. Bixby, V. Chvatal and W. J. Cook , The Traveling Salesman Problem: A Computational Study, Princeton University Press, Princeton, 2006.\n",
    "\n",
    "[2] http://www.math.uwaterloo.ca/tsp/index.html\n",
    "\n",
    "[3] https://www.youtube.com/watch?v=q8nQTNvCrjE&t=35s\n",
    "\n",
    "[4] http://www.math.uwaterloo.ca/tsp/concorde.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Copyright © 2020 Gurobi Optimization, LLC"
   ]
  }
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