{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## hvPlot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* 以 Bokeh 為基礎的高階 Library\n",
    "* 轉成 PDF 會顯示不出來，但因為能互動，適合作研究用\n",
    "    * [這裡](https://github.com/holoviz/holoviews/issues/1057)說加下面這個就會好，但實測失敗\n",
    "* [把動畫放上 RTD 的例子](https://scikit-fdiff.readthedocs.io/en/latest/introduction.html#quickstart)，不過 code 在 GitLab 上\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import holoviews as hv\n",
    "hv.notebook_extension(display_formats=['html','png'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bokeh\n",
    "\n",
    "This does not render in RTD. Possible solutions are [here](https://stackoverflow.com/questions/37096106/how-to-load-external-javascript-in-sphinx-doc) which [this issue](https://github.com/spatialaudio/nbsphinx/issues/61) mentioned."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <div class=\"bk-root\">\n",
       "        <a href=\"https://bokeh.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
       "        <span id=\"1001\">Loading BokehJS ...</span>\n",
       "    </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "(function(root) {\n",
       "  function now() {\n",
       "    return new Date();\n",
       "  }\n",
       "\n",
       "  var force = true;\n",
       "\n",
       "  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n",
       "    root._bokeh_onload_callbacks = [];\n",
       "    root._bokeh_is_loading = undefined;\n",
       "  }\n",
       "\n",
       "  var JS_MIME_TYPE = 'application/javascript';\n",
       "  var HTML_MIME_TYPE = 'text/html';\n",
       "  var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
       "  var CLASS_NAME = 'output_bokeh rendered_html';\n",
       "\n",
       "  /**\n",
       "   * Render data to the DOM node\n",
       "   */\n",
       "  function render(props, node) {\n",
       "    var script = document.createElement(\"script\");\n",
       "    node.appendChild(script);\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when an output is cleared or removed\n",
       "   */\n",
       "  function handleClearOutput(event, handle) {\n",
       "    var cell = handle.cell;\n",
       "\n",
       "    var id = cell.output_area._bokeh_element_id;\n",
       "    var server_id = cell.output_area._bokeh_server_id;\n",
       "    // Clean up Bokeh references\n",
       "    if (id != null && id in Bokeh.index) {\n",
       "      Bokeh.index[id].model.document.clear();\n",
       "      delete Bokeh.index[id];\n",
       "    }\n",
       "\n",
       "    if (server_id !== undefined) {\n",
       "      // Clean up Bokeh references\n",
       "      var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
       "      cell.notebook.kernel.execute(cmd, {\n",
       "        iopub: {\n",
       "          output: function(msg) {\n",
       "            var id = msg.content.text.trim();\n",
       "            if (id in Bokeh.index) {\n",
       "              Bokeh.index[id].model.document.clear();\n",
       "              delete Bokeh.index[id];\n",
       "            }\n",
       "          }\n",
       "        }\n",
       "      });\n",
       "      // Destroy server and session\n",
       "      var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
       "      cell.notebook.kernel.execute(cmd);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when a new output is added\n",
       "   */\n",
       "  function handleAddOutput(event, handle) {\n",
       "    var output_area = handle.output_area;\n",
       "    var output = handle.output;\n",
       "\n",
       "    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
       "    if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n",
       "      return\n",
       "    }\n",
       "\n",
       "    var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
       "\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
       "      toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
       "      // store reference to embed id on output_area\n",
       "      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
       "    }\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
       "      var bk_div = document.createElement(\"div\");\n",
       "      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "      var script_attrs = bk_div.children[0].attributes;\n",
       "      for (var i = 0; i < script_attrs.length; i++) {\n",
       "        toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
       "        toinsert[toinsert.length - 1].firstChild.textContent = bk_div.children[0].textContent\n",
       "      }\n",
       "      // store reference to server id on output_area\n",
       "      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
       "    }\n",
       "  }\n",
       "\n",
       "  function register_renderer(events, OutputArea) {\n",
       "\n",
       "    function append_mime(data, metadata, element) {\n",
       "      // create a DOM node to render to\n",
       "      var toinsert = this.create_output_subarea(\n",
       "        metadata,\n",
       "        CLASS_NAME,\n",
       "        EXEC_MIME_TYPE\n",
       "      );\n",
       "      this.keyboard_manager.register_events(toinsert);\n",
       "      // Render to node\n",
       "      var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
       "      render(props, toinsert[toinsert.length - 1]);\n",
       "      element.append(toinsert);\n",
       "      return toinsert\n",
       "    }\n",
       "\n",
       "    /* Handle when an output is cleared or removed */\n",
       "    events.on('clear_output.CodeCell', handleClearOutput);\n",
       "    events.on('delete.Cell', handleClearOutput);\n",
       "\n",
       "    /* Handle when a new output is added */\n",
       "    events.on('output_added.OutputArea', handleAddOutput);\n",
       "\n",
       "    /**\n",
       "     * Register the mime type and append_mime function with output_area\n",
       "     */\n",
       "    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
       "      /* Is output safe? */\n",
       "      safe: true,\n",
       "      /* Index of renderer in `output_area.display_order` */\n",
       "      index: 0\n",
       "    });\n",
       "  }\n",
       "\n",
       "  // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
       "  if (root.Jupyter !== undefined) {\n",
       "    var events = require('base/js/events');\n",
       "    var OutputArea = require('notebook/js/outputarea').OutputArea;\n",
       "\n",
       "    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
       "      register_renderer(events, OutputArea);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  \n",
       "  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "    root._bokeh_timeout = Date.now() + 5000;\n",
       "    root._bokeh_failed_load = false;\n",
       "  }\n",
       "\n",
       "  var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
       "\n",
       "  function display_loaded() {\n",
       "    var el = document.getElementById(\"1001\");\n",
       "    if (el != null) {\n",
       "      el.textContent = \"BokehJS is loading...\";\n",
       "    }\n",
       "    if (root.Bokeh !== undefined) {\n",
       "      if (el != null) {\n",
       "        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
       "      }\n",
       "    } else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(display_loaded, 100)\n",
       "    }\n",
       "  }\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, callback) {\n",
       "    if (css_urls == null) css_urls = [];\n",
       "    if (js_urls == null) js_urls = [];\n",
       "\n",
       "    root._bokeh_onload_callbacks.push(callback);\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 == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = css_urls.length + js_urls.length;\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",
       "\n",
       "    function on_error() {\n",
       "      console.error(\"failed to load \" + url);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < css_urls.length; i++) {\n",
       "      var url = css_urls[i];\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",
       "    }\n",
       "\n",
       "    const hashes = {\"https://cdn.bokeh.org/bokeh/release/bokeh-2.2.3.min.js\": \"T2yuo9Oe71Cz/I4X9Ac5+gpEa5a8PpJCDlqKYO0CfAuEszu1JrXLl8YugMqYe3sM\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.2.3.min.js\": \"98GDGJ0kOMCUMUePhksaQ/GYgB3+NH9h996V88sh3aOiUNX3N+fLXAtry6xctSZ6\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.2.3.min.js\": \"89bArO+nlbP3sgakeHjCo1JYxYR5wufVgA3IbUvDY+K7w4zyxJqssu7wVnfeKCq8\"};\n",
       "\n",
       "    for (var i = 0; i < js_urls.length; i++) {\n",
       "      var url = js_urls[i];\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",
       "      if (url in hashes) {\n",
       "        element.crossOrigin = \"anonymous\";\n",
       "        element.integrity = \"sha384-\" + hashes[url];\n",
       "      }\n",
       "      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.head.appendChild(element);\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",
       "  \n",
       "  var js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.2.3.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.2.3.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.2.3.min.js\"];\n",
       "  var css_urls = [];\n",
       "  \n",
       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    function(Bokeh) {\n",
       "    \n",
       "    \n",
       "    }\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if (root.Bokeh !== undefined || force === true) {\n",
       "      \n",
       "    for (var i = 0; i < inline_js.length; i++) {\n",
       "      inline_js[i].call(root, root.Bokeh);\n",
       "    }\n",
       "    if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      var cell = $(document.getElementById(\"1001\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(css_urls, js_urls, function() {\n",
       "      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"1001\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\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, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\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 == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\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\n    function on_error() {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (var i = 0; i < css_urls.length; i++) {\n      var url = css_urls[i];\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    }\n\n    const hashes = {\"https://cdn.bokeh.org/bokeh/release/bokeh-2.2.3.min.js\": \"T2yuo9Oe71Cz/I4X9Ac5+gpEa5a8PpJCDlqKYO0CfAuEszu1JrXLl8YugMqYe3sM\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.2.3.min.js\": \"98GDGJ0kOMCUMUePhksaQ/GYgB3+NH9h996V88sh3aOiUNX3N+fLXAtry6xctSZ6\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.2.3.min.js\": \"89bArO+nlbP3sgakeHjCo1JYxYR5wufVgA3IbUvDY+K7w4zyxJqssu7wVnfeKCq8\"};\n\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\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      if (url in hashes) {\n        element.crossOrigin = \"anonymous\";\n        element.integrity = \"sha384-\" + hashes[url];\n      }\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\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  \n  var js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.2.3.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.2.3.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.2.3.min.js\"];\n  var css_urls = [];\n  \n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    function(Bokeh) {\n    \n    \n    }\n  ];\n\n  function run_inline_js() {\n    \n    if (root.Bokeh !== undefined || force === true) {\n      \n    for (var i = 0; i < inline_js.length; i++) {\n      inline_js[i].call(root, root.Bokeh);\n    }\n    if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"1001\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"3b127335-cc6c-481f-b7e4-f3121eb8ebf1\" data-root-id=\"1092\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
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:{\"src_out\":{\"id\":\"1003\"}},\"code\":\"\\n    var data = src_out.data\\n    var n_outliers = cb_obj.value\\n    var pt_alpha = data['pt_alpha']\\n    var em_alpha = data['em_alpha']\\n    var mcd_alpha = data['mcd_alpha']\\n    \\n    for (var i = 0; i < pt_alpha.length; i++) {\\n        em_alpha[i] = 0\\n        mcd_alpha[i] = 0\\n        if (i < n_outliers)\\n            pt_alpha[i] = 1\\n        else\\n            pt_alpha[i] = 0\\n    }\\n    em_alpha[n_outliers] = 1\\n    mcd_alpha[n_outliers] = 1\\n    \\n    src_out.change.emit()\\n\"},\"id\":\"1090\",\"type\":\"CustomJS\"},{\"attributes\":{\"source\":{\"id\":\"1049\"}},\"id\":\"1053\",\"type\":\"CDSView\"},{\"attributes\":{\"source\":{\"id\":\"1002\"}},\"id\":\"1033\",\"type\":\"CDSView\"},{\"attributes\":{\"fill_alpha\":{\"field\":\"pt_alpha\"},\"fill_color\":{\"value\":\"red\"},\"line_color\":{\"value\":null},\"size\":{\"units\":\"screen\",\"value\":6},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1035\",\"type\":\"Circle\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"orange\",\"line_width\":2.5,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1051\",\"type\":\"Line\"},{\"attributes\":{\"line_color\":\"orange\",\"line_width\":2.5,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1050\",\"type\":\"Line\"},{\"attributes\":{\"angle\":{\"field\":\"mcd_th\",\"units\":\"rad\"},\"fill_alpha\":{\"value\":0},\"fill_color\":{\"value\":\"#1f77b4\"},\"height\":{\"field\":\"mcd_h\",\"units\":\"data\"},\"line_alpha\":{\"field\":\"mcd_alpha\"},\"line_color\":{\"value\":\"orange\"},\"line_width\":{\"value\":2.5},\"width\":{\"field\":\"mcd_w\",\"units\":\"data\"},\"x\":{\"value\":0},\"y\":{\"value\":0}},\"id\":\"1040\",\"type\":\"Ellipse\"},{\"attributes\":{\"end\":19,\"format\":\"0[.]00\",\"js_property_callbacks\":{\"change:value\":[{\"id\":\"1090\"}]},\"start\":0,\"title\":\"n_outliers\",\"value\":0},\"id\":\"1091\",\"type\":\"Slider\"},{\"attributes\":{\"overlay\":{\"id\":\"1024\"}},\"id\":\"1021\",\"type\":\"BoxZoomTool\"},{\"attributes\":{\"data_source\":{\"id\":\"1003\"},\"glyph\":{\"id\":\"1040\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"1041\"},\"selection_glyph\":null,\"view\":{\"id\":\"1043\"}},\"id\":\"1042\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"1056\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"1061\",\"type\":\"Selection\"},{\"attributes\":{\"below\":[{\"id\":\"1013\"}],\"center\":[{\"id\":\"1016\"},{\"id\":\"1020\"},{\"id\":\"1067\"}],\"left\":[{\"id\":\"1017\"}],\"plot_height\":400,\"plot_width\":400,\"renderers\":[{\"id\":\"1032\"},{\"id\":\"1037\"},{\"id\":\"1042\"},{\"id\":\"1047\"},{\"id\":\"1052\"},{\"id\":\"1072\"}],\"title\":{\"id\":\"1054\"},\"toolbar\":{\"id\":\"1025\"},\"x_range\":{\"id\":\"1005\"},\"x_scale\":{\"id\":\"1009\"},\"y_range\":{\"id\":\"1007\"},\"y_scale\":{\"id\":\"1011\"}},\"id\":\"1004\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{\"data_source\":{\"id\":\"1049\"},\"glyph\":{\"id\":\"1050\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"1051\"},\"selection_glyph\":null,\"view\":{\"id\":\"1053\"}},\"id\":\"1052\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"fill_color\":{\"value\":\"black\"},\"line_color\":{\"value\":null},\"size\":{\"units\":\"screen\",\"value\":6},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1030\",\"type\":\"Circle\"},{\"attributes\":{\"source\":{\"id\":\"1003\"}},\"id\":\"1043\",\"type\":\"CDSView\"},{\"attributes\":{\"axis\":{\"id\":\"1017\"},\"dimension\":1,\"ticker\":null},\"id\":\"1020\",\"type\":\"Grid\"},{\"attributes\":{\"angle\":{\"field\":\"em_th\",\"units\":\"rad\"},\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"#1f77b4\"},\"height\":{\"field\":\"em_h\",\"units\":\"data\"},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"green\"},\"line_width\":{\"value\":2.5},\"width\":{\"field\":\"em_w\",\"units\":\"data\"},\"x\":{\"value\":0},\"y\":{\"value\":0}},\"id\":\"1046\",\"type\":\"Ellipse\"},{\"attributes\":{\"data_source\":{\"id\":\"1003\"},\"glyph\":{\"id\":\"1035\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"1036\"},\"selection_glyph\":null,\"view\":{\"id\":\"1038\"}},\"id\":\"1037\",\"type\":\"GlyphRenderer\"}],\"root_ids\":[\"1092\"]},\"title\":\"Bokeh Application\",\"version\":\"2.2.3\"}};\n",
       "  var render_items = [{\"docid\":\"a566191f-8b3f-4fca-84df-a1317e302e0d\",\"root_ids\":[\"1092\"],\"roots\":{\"1092\":\"3b127335-cc6c-481f-b7e4-f3121eb8ebf1\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "1092"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from bokeh.layouts import column\n",
    "# from ipywidgets import interact\n",
    "from bokeh.io import push_notebook, output_notebook, output_file, show\n",
    "from bokeh.plotting import figure\n",
    "from math import pi\n",
    "from bokeh.models import CustomJS, ColumnDataSource, Slider\n",
    "from sklearn.covariance import EmpiricalCovariance, MinCovDet\n",
    "from pandas import DataFrame\n",
    "import numpy as np\n",
    "\n",
    "# output_file('mcd.html')\n",
    "# output_notebook(hide_banner=True)\n",
    "output_notebook()\n",
    "\n",
    "n_inliers = 250\n",
    "n_all_outliers = 20\n",
    "\n",
    "np.random.seed(20)\n",
    "\n",
    "# generate data with 20 outliers\n",
    "inliers_cov = [[2, 0], [0, 1]]\n",
    "outliers_cov = [[1, 4], [4, 1]]\n",
    "inliers = np.dot(np.random.randn(n_inliers, 2), inliers_cov)\n",
    "outliers = np.dot(np.random.randn(n_all_outliers, 2), outliers_cov)\n",
    "\n",
    "df_in = DataFrame(inliers, columns=['x', 'y'])\n",
    "df_out = DataFrame(outliers, columns=['x', 'y'])\n",
    "df_out['pt_alpha'] = 0\n",
    "df_out['em_alpha'] = 0\n",
    "df_out['mcd_alpha'] = 0\n",
    "df_out.loc[0, 'em_alpha'] = 1\n",
    "df_out.loc[0, 'mcd_alpha'] = 1\n",
    "\n",
    "em_ellipse_param = []\n",
    "mcd_ellipse_param = []\n",
    "for n_outliers in range(n_all_outliers):\n",
    "    cov = EmpiricalCovariance(assume_centered=True).fit(np.append(inliers, outliers[:n_outliers, :], axis=0)).covariance_\n",
    "    cov_inv = np.linalg.inv(cov)\n",
    "    z11, z22, z12 = cov_inv[0, 0], cov_inv[1, 1], cov_inv[0, 1]\n",
    "    theta = np.arctan(2*z12/(z11-z22))/2\n",
    "    rot = np.array([[np.cos(theta), -np.sin(theta)], [np.sin(theta), np.cos(theta)]])\n",
    "    wh = rot.transpose() @ cov_inv @ rot\n",
    "    width, height = 6/np.sqrt([wh[0, 0], wh[1, 1]])\n",
    "    em_ellipse_param.append((height, width, theta))\n",
    "\n",
    "    cov = MinCovDet(assume_centered=True).fit(np.append(inliers, outliers[:n_outliers, :], axis=0)).covariance_\n",
    "    cov_inv = np.linalg.inv(cov)\n",
    "    z11, z22, z12 = cov_inv[0, 0], cov_inv[1, 1], cov_inv[0, 1]\n",
    "    theta = np.arctan(2*z12/(z11-z22))/2\n",
    "    rot = np.array([[np.cos(theta), -np.sin(theta)], [np.sin(theta), np.cos(theta)]])\n",
    "    wh = rot.transpose() @ cov_inv @ rot\n",
    "    width, height = 6/np.sqrt([wh[0, 0], wh[1, 1]])\n",
    "    mcd_ellipse_param.append((height, width, theta))\n",
    "\n",
    "df_out['em_h'], df_out['em_w'], df_out['em_th'] = np.array(em_ellipse_param).T\n",
    "df_out['mcd_h'], df_out['mcd_w'], df_out['mcd_th'] = np.array(mcd_ellipse_param).T\n",
    "\n",
    "src_in = ColumnDataSource(df_in)\n",
    "src_out = ColumnDataSource(df_out)\n",
    "\n",
    "TOOLTIPS = [(\"(x, y)\", \"(@x, @y)\")]\n",
    "p = figure(tools='box_zoom,reset,save', \n",
    "#            tooltips=TOOLTIPS, \n",
    "           plot_height=400, \n",
    "           plot_width=400, \n",
    "           x_range=(-10, 10), y_range=(-10, 10)\n",
    "          )\n",
    "p.circle(x='x', y='y', fill_color='black', line_color=None, size=6, source=src_in)\n",
    "p.circle(x='x', y='y', fill_color='red', line_color=None, size=6, source=src_out, fill_alpha='pt_alpha')\n",
    "p.ellipse(x=0, y=0, width='mcd_w', height='mcd_h', angle='mcd_th', line_alpha='mcd_alpha', line_color='orange', fill_alpha=0, line_width=2.5, source=src_out)\n",
    "p.ellipse(x=0, y=0, width='em_w', height='em_h', angle='em_th', line_alpha='em_alpha', line_color='green', fill_alpha=0, line_width=2.5, source=src_out)\n",
    "p.line(x=[-20], y=[0], line_width=2.5, color='orange', legend_label='MCD')\n",
    "p.line(x=[-20], y=[0], line_width=2.5, color='green', legend_label='MLE')\n",
    "p.legend.location = \"top_right\"\n",
    "\n",
    "callback_code = \"\"\"\n",
    "    var data = src_out.data\n",
    "    var n_outliers = cb_obj.value\n",
    "    var pt_alpha = data['pt_alpha']\n",
    "    var em_alpha = data['em_alpha']\n",
    "    var mcd_alpha = data['mcd_alpha']\n",
    "    \n",
    "    for (var i = 0; i < pt_alpha.length; i++) {\n",
    "        em_alpha[i] = 0\n",
    "        mcd_alpha[i] = 0\n",
    "        if (i < n_outliers)\n",
    "            pt_alpha[i] = 1\n",
    "        else\n",
    "            pt_alpha[i] = 0\n",
    "    }\n",
    "    em_alpha[n_outliers] = 1\n",
    "    mcd_alpha[n_outliers] = 1\n",
    "    \n",
    "    src_out.change.emit()\n",
    "\"\"\"\n",
    "callback = CustomJS(args=dict(src_out=src_out), code=callback_code)\n",
    "slider = Slider(start=0, end=n_outliers, value=0, step=1, title='n_outliers')\n",
    "slider.js_on_change('value', callback)\n",
    "\n",
    "layout = column(slider, p)\n",
    "\n",
    "show(layout)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ipywidgets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0ad87d069f0140e29d44f5a04d773f9c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, description='m', max=2.0, min=-2.0), FloatSlider(value=0.0, descr…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from ipywidgets import interactive\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "def f(m, b):\n",
    "    plt.figure(2)\n",
    "    x = np.linspace(-10, 10, num=1000)\n",
    "    plt.plot(x, m * x + b)\n",
    "    plt.ylim(-5, 5)\n",
    "    plt.show()\n",
    "\n",
    "interactive_plot = interactive(f, m=(-2.0, 2.0), b=(-3, 3, 0.5))\n",
    "output = interactive_plot.children[-1]\n",
    "output.layout.height = '350px'\n",
    "interactive_plot\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [SGT](https://en.wikipedia.org/wiki/Skewed_generalized_t_distribution)\n",
    "\n",
    "Theodossiou's Skewed Generalized $t$ Distribution. See [this notebook](https://github.com/beginnerSC/mscf/blob/master/FDS%20II/Homeworks/2/chunyuac_HW2.ipynb) for cdf, ppf and more."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9b302abf1fb64018b5e1c5ef1a3c9780",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, description='mu', max=3.0, min=-3.0), FloatSlider(value=0.5, desc…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "from pandas import DataFrame\n",
    "from scipy.special import beta\n",
    "from ipywidgets import interact\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "def pdf(x, mu, k, n, lam, sigma2):\n",
    "    '''\n",
    "    k > 0, n > 2, sigma2 > 0, -1 < lam < 1\n",
    "    '''\n",
    "    sigma = np.sqrt(sigma2)\n",
    "    S = np.sqrt(1 + 3*(lam**2) - 4*(lam**2)*((beta(2/k, (n-1)/k)**2)/(beta(1/k, n/k)*beta(3/k, (n-2)/k))))\n",
    "    c = 0.5*k*np.sqrt((beta(1/k, n/k)**(-3))*beta(3/k, (n-2)/k))*S/sigma\n",
    "    theta = ((k/(n-2))**(1/k))*np.sqrt(beta(1/k, n/k)/beta(3/k, (n-2)/k))/S\n",
    "    return c*(1+(k/(n-2))*(np.abs(x-mu)/(sigma*theta*(1 + np.sign(x-mu)*lam)))**k)**(-(n+1)/k)\n",
    "\n",
    "@interact(mu=(-3, 3, 0.1), k=(0.1, 5, 0.1), n=(2.1, 10, 0.1), sigma2=(0.1, 3, 0.1), lam=(-0.9, 0.9, 0.1))\n",
    "def f(mu=0, k=0.5, n=2.5, sigma2=0.1, lam=0):\n",
    "    fig, ax = plt.subplots()\n",
    "    DataFrame([(x, pdf(x, mu, k, n, lam, sigma2)) for x in np.linspace(-2, 2, 500)], columns=['x', 'pdf']).set_index('x').plot(ax=ax)\n",
    "    ax.set(xlim=(-2, 2), ylim=(0, 20))\n",
    "    plt.show()"
   ]
  }
 ],
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