{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# B14. Making plots\n",
    "\n",
    "<hr>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "        }\n",
       "    </style>\n",
       "    <div>\n",
       "        <a href=\"https://bokeh.org\" target=\"_blank\" class=\"bk-notebook-logo\"></a>\n",
       "        <span id=\"p1001\">Loading BokehJS ...</span>\n",
       "    </div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function now() {\n",
       "    return new Date();\n",
       "  }\n",
       "\n",
       "  const 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",
       "const JS_MIME_TYPE = 'application/javascript';\n",
       "  const HTML_MIME_TYPE = 'text/html';\n",
       "  const EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
       "  const CLASS_NAME = 'output_bokeh rendered_html';\n",
       "\n",
       "  /**\n",
       "   * Render data to the DOM node\n",
       "   */\n",
       "  function render(props, node) {\n",
       "    const 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",
       "    const cell = handle.cell;\n",
       "\n",
       "    const id = cell.output_area._bokeh_element_id;\n",
       "    const 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",
       "      const cmd_clean = \"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_clean, {\n",
       "        iopub: {\n",
       "          output: function(msg) {\n",
       "            const 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",
       "      const cmd_destroy = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
       "      cell.notebook.kernel.execute(cmd_destroy);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when a new output is added\n",
       "   */\n",
       "  function handleAddOutput(event, handle) {\n",
       "    const output_area = handle.output_area;\n",
       "    const output = handle.output;\n",
       "\n",
       "    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
       "    if ((output.output_type != \"display_data\") || (!Object.prototype.hasOwnProperty.call(output.data, EXEC_MIME_TYPE))) {\n",
       "      return\n",
       "    }\n",
       "\n",
       "    const 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",
       "      const bk_div = document.createElement(\"div\");\n",
       "      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "      const script_attrs = bk_div.children[0].attributes;\n",
       "      for (let 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",
       "      const 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",
       "      const 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",
       "    const events = require('base/js/events');\n",
       "    const 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",
       "  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "    root._bokeh_timeout = Date.now() + 5000;\n",
       "    root._bokeh_failed_load = false;\n",
       "  }\n",
       "\n",
       "  const 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",
       "    const el = document.getElementById(\"p1001\");\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",
       "  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(url) {\n",
       "      console.error(\"failed to load \" + url);\n",
       "    }\n",
       "\n",
       "    for (let i = 0; i < css_urls.length; i++) {\n",
       "      const url = css_urls[i];\n",
       "      const element = document.createElement(\"link\");\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error.bind(null, url);\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",
       "    for (let i = 0; i < js_urls.length; i++) {\n",
       "      const url = js_urls[i];\n",
       "      const element = document.createElement('script');\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error.bind(null, url);\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",
       "  };\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",
       "  const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-3.1.0.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-3.1.0.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-3.1.0.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-3.1.0.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-3.1.0.min.js\"];\n",
       "  const css_urls = [];\n",
       "\n",
       "  const inline_js = [    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "function(Bokeh) {\n",
       "    }\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    if (root.Bokeh !== undefined || force === true) {\n",
       "          for (let 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",
       "      const cell = $(document.getElementById(\"p1001\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\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": "(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  const 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  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  const 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    const el = document.getElementById(\"p1001\");\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  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(url) {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (let i = 0; i < css_urls.length; i++) {\n      const url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error.bind(null, url);\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    for (let i = 0; i < js_urls.length; i++) {\n      const url = js_urls[i];\n      const element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error.bind(null, url);\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  };\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  const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-3.1.0.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-3.1.0.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-3.1.0.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-3.1.0.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-3.1.0.min.js\"];\n  const css_urls = [];\n\n  const inline_js = [    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\nfunction(Bokeh) {\n    }\n  ];\n\n  function run_inline_js() {\n    if (root.Bokeh !== undefined || force === true) {\n          for (let i = 0; i < inline_js.length; i++) {\n      inline_js[i].call(root, root.Bokeh);\n    }\nif (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      const cell = $(document.getElementById(\"p1001\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\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"
    }
   ],
   "source": [
    "# Colab setup ------------------\n",
    "import os, sys\n",
    "if \"google.colab\" in sys.modules:\n",
    "    data_path = \"https://biocircuits.github.io/chapters/data/\"\n",
    "else:\n",
    "    data_path = \"data/\"\n",
    "# ------------------------------\n",
    "\n",
    "import numpy as np\n",
    "import scipy.special\n",
    "import pandas as pd\n",
    "\n",
    "import colorcet\n",
    "\n",
    "# Our main plotting package (must have explicit import of submodules)\n",
    "import bokeh.io\n",
    "import bokeh.models\n",
    "import bokeh.plotting\n",
    "\n",
    "# Enable viewing Bokeh plots in the notebook\n",
    "bokeh.io.output_notebook()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "\n",
    "We have seen that Pandas is a power tool for loading and organizing data sets, as well as computing summary statistics from them. In nearly all applications with data, and indeed with theoretical models, we want to be able to _plot_ them. In this section, we will learn about how to make plots with [Bokeh](https://bokeh.org).\n",
    "\n",
    "Importantly, note that Bokeh's submodules often have to be explicitly imported, as we did in the code cell at the top of this notebook. Note also that if you want your plots to be viewable (and interactive) in the notebook, you need to execute\n",
    "\n",
    "```python\n",
    "bokeh.io.output_notebook()\n",
    "```\n",
    "\n",
    "at the top of the notebook (as we have done). Finally, note that we also have to have installed the Bokeh JupyterLab extension, which we did in [Chapter 0](../chapters/00_setting_up_python_computing_environment.ipynb)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bokeh's grammar and our first plot with Bokeh\n",
    "\n",
    "Constructing a plot with Bokeh consists of four main steps.\n",
    "\n",
    "1. Creating a figure on which to populate **glyphs** (symbols that represent data, e.g., dots for a scatter plot). Think of this figure as a \"canvas\" which sets the space on which you will \"paint\" your glyphs.\n",
    "2. Defining a data source that is the reference used to place the glyphs.\n",
    "3. Choose the kind of glyph you would like.\n",
    "4. Annotate the columns of data source to determine how they are used to place (and possibly color, scale, etc.) the glyph.\n",
    "\n",
    "After completing these steps, you need to render the graphic.\n",
    "\n",
    "Let's go through these steps in generating a scatter plot of the data set  So you have the concrete example in mind, the final graphic will look like this:\n",
    "\n",
    "<div style=\"margin: auto; width: 400px;\">\n",
    "    \n",
    "![first_bokeh_plot](first_bokeh_plot.png)\n",
    "\n",
    "</div>\n",
    "\n",
    "Before plotting, we of course to load in the data set and compute the normalized intensity for each strain as we did in the [previous section](b13_split_apply_combine.ipynb)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(os.path.join(data_path, \"elowitz_et_al_2002_fig_3a.csv\"))\n",
    "\n",
    "df[[\"norm CFP\", \"norm YFP\"]] = df.groupby(\"strain\", group_keys=False)[\n",
    "    [\"CFP\", \"YFP\"]\n",
    "].apply(lambda x: x / x.mean())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the data set ready, we can proceed to plotting.\n",
    "\n",
    "1. Our first step is creating a figure, our \"canvas.\" In creating the figure, we are implicitly thinking about what kind of representation for our data we want. That is, we have to specify axes and their labels. We might also want to specify the title of the figure, whether or not to have grid lines, and all sorts of other customizations. Naturally, we also want to specify the shape of the figure.\n",
    "\n",
    "(Almost) all of this is accomplished in Bokeh by making a call to `bokeh.plotting.figure()` with the appropriate keyword arguments. Note that we set the `x_range` and `y_range` keyword arguments such that the x- and y-axes have the same scale."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create the figure, stored in variable `p`\n",
    "p = bokeh.plotting.figure(\n",
    "    frame_width=300,\n",
    "    frame_height=300,\n",
    "    x_axis_label='norm. CFP intensity',\n",
    "    y_axis_label='norm. YFP intensity',\n",
    "    x_range=[0.65, 1.45],\n",
    "    y_range=[0.65, 1.45],\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are many more keyword attributes you can assign, including [all of those listed in the Bokeh Plot class](https://bokeh.pydata.org/en/latest/docs/reference/models/plots.html#bokeh.models.plots.Plot) and [the additional ones listed in the Bokeh Figure class](https://bokeh.pydata.org/en/latest/docs/reference/plotting.html#bokeh.plotting.figure.Figure).\n",
    "\n",
    "2. Now that we have set up our canvas, we can decide on the data source. It is convenient to create a **ColumnDataSource**, a special Bokeh object that holds data to be displayed in a plot. (We will later see that we can change the data in a ColumnDataSource and the plot will automatically update!) Conveniently, we can instantiate a ColumnDataSource directly from a Pandas data frame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "source = bokeh.models.ColumnDataSource(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could also instantiate a data source using a dictionary of arrays, like\n",
    "\n",
    "    source = bokeh.models.ColumnDataSource(dict(x=[1, 2, 3, 4], y=[1, 4, 9, 16]))\n",
    "\n",
    "3. We will choose dots (or circles) as our glyph. This kind of glyph requires that we specify  which column of the data source will serve to place the glyphs along the $x$-axis and which will serve to place the glyphs along the $y$-axis.\n",
    "\n",
    "4. We choose the `'norm CFP'` column to specify the $x$-coordinate of the glyph and the `'norm YFP'` column to specify the $y$-coordinate. We already made this decision when we set up our axis labels, but we did not necessarily have to make that decision at that point.\n",
    "\n",
    "Steps 3 and 4 are accomplished by calling one of the **glyph methods** of the Bokeh `Figure` instance, `p`. Since we are choosing dots, the appropriate method is `p.circle()`, and we use the `source`, `x`, and `y` kwargs to specify the positions of the glyphs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "p.circle(\n",
    "    source=source,\n",
    "    x='norm CFP',\n",
    "    y='norm YFP'\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have built the plot, we can render it in the notebook using `bokeh.io.show()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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       "  const render_items = [{\"docid\":\"9339a04a-ab64-47b7-889f-79681417742f\",\"roots\":{\"p1002\":\"5698a9f7-0baf-4606-ac81-722a81d3289f\"},\"root_ids\":[\"p1002\"]}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    let attempts = 0;\n",
       "    const 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": "p1002"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bokeh.io.show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In looking at the plot, notice a toolbar to right of the plot that enables you to zoom and pan within the plot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The importance of tidy data frames\n",
    "\n",
    "It might be clear for you now that building a plot in this way requires that the data frame you use be [tidy](b13_split_apply_combine.ipynb). The organization of tidy data is really what enables this and high level plotting functionality. There is a well-specified organization of the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Coloring with other dimensions\n",
    "\n",
    "In the above plot, we did not distinguish the two strains. We really want m22 in one color and d22 in another. To do this, we take advantage of two features of Bokeh.\n",
    "\n",
    "1. We can make multiple calls to `p.circle()` to populate more and more glyphs.\n",
    "2. `p.circle()`, like all of the glyph methods, has many keyword arguments, including `color` and `legend_label`, which will enable us to color the glyphs and include a legend.\n",
    "\n",
    "We can loop through the data frame grouped by `'strain'` and populate the glyphs as we go along. We will want different colors for the glyphs, depending on which strain they correspond to. The [colorcet package](https://colorcet.holoviz.org/) conveniently provides nice color palettes for plots, and we will use the colors in its Category10 palette, since we are coloring according to strain, which is a categorical variable (as opposed to a quantitative variable)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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YFP\",{\"type\":\"ndarray\",\"array\":{\"type\":\"bytes\",\"data\":\"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\"},\"shape\":[250],\"dtype\":\"float64\",\"order\":\"little\"}]]}}},\"view\":{\"type\":\"object\",\"name\":\"CDSView\",\"id\":\"p1219\",\"attributes\":{\"filter\":{\"type\":\"object\",\"name\":\"AllIndices\",\"id\":\"p1220\"}}},\"glyph\":{\"type\":\"object\",\"name\":\"Circle\",\"id\":\"p1215\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"norm CFP\"},\"y\":{\"type\":\"field\",\"field\":\"norm YFP\"},\"line_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"},\"fill_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"},\"hatch_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"}}},\"nonselection_glyph\":{\"type\":\"object\",\"name\":\"Circle\",\"id\":\"p1216\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"norm CFP\"},\"y\":{\"type\":\"field\",\"field\":\"norm YFP\"},\"line_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"},\"line_alpha\":{\"type\":\"value\",\"value\":0.1},\"fill_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"},\"fill_alpha\":{\"type\":\"value\",\"value\":0.1},\"hatch_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"},\"hatch_alpha\":{\"type\":\"value\",\"value\":0.1}}},\"muted_glyph\":{\"type\":\"object\",\"name\":\"Circle\",\"id\":\"p1217\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"norm CFP\"},\"y\":{\"type\":\"field\",\"field\":\"norm YFP\"},\"line_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"},\"line_alpha\":{\"type\":\"value\",\"value\":0.2},\"fill_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"},\"fill_alpha\":{\"type\":\"value\",\"value\":0.2},\"hatch_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"},\"hatch_alpha\":{\"type\":\"value\",\"value\":0.2}}}}}],\"toolbar\":{\"type\":\"object\",\"name\":\"Toolbar\",\"id\":\"p1155\",\"attributes\":{\"tools\":[{\"type\":\"object\",\"name\":\"PanTool\",\"id\":\"p1180\"},{\"type\":\"object\",\"name\":\"WheelZoomTool\",\"id\":\"p1181\"},{\"type\":\"object\",\"name\":\"BoxZoomTool\",\"id\":\"p1182\",\"attributes\":{\"overlay\":{\"type\":\"object\",\"name\":\"BoxAnnotation\",\"id\":\"p1183\",\"attributes\":{\"syncable\":false,\"level\":\"overlay\",\"visible\":false,\"left_units\":\"canvas\",\"right_units\":\"canvas\",\"bottom_units\":\"canvas\",\"top_units\":\"canvas\",\"line_color\":\"black\",\"line_alpha\":1.0,\"line_width\":2,\"line_dash\":[4,4],\"fill_color\":\"lightgrey\",\"fill_alpha\":0.5}}}},{\"type\":\"object\",\"name\":\"SaveTool\",\"id\":\"p1184\"},{\"type\":\"object\",\"name\":\"ResetTool\",\"id\":\"p1185\"},{\"type\":\"object\",\"name\":\"HelpTool\",\"id\":\"p1186\"}]}},\"left\":[{\"type\":\"object\",\"name\":\"LinearAxis\",\"id\":\"p1173\",\"attributes\":{\"ticker\":{\"type\":\"object\",\"name\":\"BasicTicker\",\"id\":\"p1174\",\"attributes\":{\"mantissas\":[1,2,5]}},\"formatter\":{\"type\":\"object\",\"name\":\"BasicTickFormatter\",\"id\":\"p1176\"},\"axis_label\":\"norm. YFP intensity\",\"major_label_policy\":{\"type\":\"object\",\"name\":\"AllLabels\",\"id\":\"p1175\"}}}],\"below\":[{\"type\":\"object\",\"name\":\"LinearAxis\",\"id\":\"p1166\",\"attributes\":{\"ticker\":{\"type\":\"object\",\"name\":\"BasicTicker\",\"id\":\"p1167\",\"attributes\":{\"mantissas\":[1,2,5]}},\"formatter\":{\"type\":\"object\",\"name\":\"BasicTickFormatter\",\"id\":\"p1169\"},\"axis_label\":\"norm. CFP intensity\",\"major_label_policy\":{\"type\":\"object\",\"name\":\"AllLabels\",\"id\":\"p1168\"}}}],\"center\":[{\"type\":\"object\",\"name\":\"Grid\",\"id\":\"p1172\",\"attributes\":{\"axis\":{\"id\":\"p1166\"}}},{\"type\":\"object\",\"name\":\"Grid\",\"id\":\"p1179\",\"attributes\":{\"dimension\":1,\"axis\":{\"id\":\"p1173\"}}},{\"type\":\"object\",\"name\":\"Legend\",\"id\":\"p1207\",\"attributes\":{\"items\":[{\"type\":\"object\",\"name\":\"LegendItem\",\"id\":\"p1208\",\"attributes\":{\"label\":{\"type\":\"value\",\"value\":\"d22\"},\"renderers\":[{\"id\":\"p1204\"}]}},{\"type\":\"object\",\"name\":\"LegendItem\",\"id\":\"p1221\",\"attributes\":{\"label\":{\"type\":\"value\",\"value\":\"m22\"},\"renderers\":[{\"id\":\"p1218\"}]}}]}}],\"frame_width\":300,\"frame_height\":300}}],\"callbacks\":{\"type\":\"map\"}}};\n",
       "  const render_items = [{\"docid\":\"cd1df815-74db-4b31-9cf4-fa6dd2c8cbf0\",\"roots\":{\"p1149\":\"a9497672-5952-4d98-8a11-8d61b8f669b8\"},\"root_ids\":[\"p1149\"]}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    let attempts = 0;\n",
       "    const 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": "p1149"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Color palette we will use, from colorcet\n",
    "colors = colorcet.b_glasbey_category10\n",
    "\n",
    "# Create the figure, stored in variable `p`\n",
    "p = bokeh.plotting.figure(\n",
    "    frame_width=300,\n",
    "    frame_height=300,\n",
    "    x_axis_label='norm. CFP intensity',\n",
    "    y_axis_label='norm. YFP intensity',\n",
    "    x_range=[0.65, 1.45],\n",
    "    y_range=[0.65, 1.45],\n",
    ")\n",
    "\n",
    "# Add glyphs\n",
    "for color, (strain, g) in zip(colors, df.groupby('strain')):\n",
    "    p.circle(source=g, x='norm CFP', y='norm YFP', color=color, legend_label=strain)\n",
    "\n",
    "bokeh.io.show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We got the plot we wanted, but we may want to move the legend. Fortunately, Bokeh allows us to set attributes of the figure whenever we like. (We will further discuss styling Bokeh plots in a future lesson.) We can therefore set the legend position to be in the upper left corner. We will also set the `click_policy` for the legend to be `'hide'`, which will hide glyphs if you click the legend, which can be convenient for viewing cluttered plots (though this one is not cluttered, really)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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CFP\"},\"y\":{\"type\":\"field\",\"field\":\"norm YFP\"},\"line_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"},\"fill_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"},\"hatch_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"}}},\"nonselection_glyph\":{\"type\":\"object\",\"name\":\"Circle\",\"id\":\"p1216\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"norm CFP\"},\"y\":{\"type\":\"field\",\"field\":\"norm YFP\"},\"line_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"},\"line_alpha\":{\"type\":\"value\",\"value\":0.1},\"fill_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"},\"fill_alpha\":{\"type\":\"value\",\"value\":0.1},\"hatch_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"},\"hatch_alpha\":{\"type\":\"value\",\"value\":0.1}}},\"muted_glyph\":{\"type\":\"object\",\"name\":\"Circle\",\"id\":\"p1217\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"norm CFP\"},\"y\":{\"type\":\"field\",\"field\":\"norm YFP\"},\"line_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"},\"line_alpha\":{\"type\":\"value\",\"value\":0.2},\"fill_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"},\"fill_alpha\":{\"type\":\"value\",\"value\":0.2},\"hatch_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"},\"hatch_alpha\":{\"type\":\"value\",\"value\":0.2}}}}}],\"toolbar\":{\"type\":\"object\",\"name\":\"Toolbar\",\"id\":\"p1155\",\"attributes\":{\"tools\":[{\"type\":\"object\",\"name\":\"PanTool\",\"id\":\"p1180\"},{\"type\":\"object\",\"name\":\"WheelZoomTool\",\"id\":\"p1181\"},{\"type\":\"object\",\"name\":\"BoxZoomTool\",\"id\":\"p1182\",\"attributes\":{\"overlay\":{\"type\":\"object\",\"name\":\"BoxAnnotation\",\"id\":\"p1183\",\"attributes\":{\"syncable\":false,\"level\":\"overlay\",\"visible\":false,\"left_units\":\"canvas\",\"right_units\":\"canvas\",\"bottom_units\":\"canvas\",\"top_units\":\"canvas\",\"line_color\":\"black\",\"line_alpha\":1.0,\"line_width\":2,\"line_dash\":[4,4],\"fill_color\":\"lightgrey\",\"fill_alpha\":0.5}}}},{\"type\":\"object\",\"name\":\"SaveTool\",\"id\":\"p1184\"},{\"type\":\"object\",\"name\":\"ResetTool\",\"id\":\"p1185\"},{\"type\":\"object\",\"name\":\"HelpTool\",\"id\":\"p1186\"}]}},\"left\":[{\"type\":\"object\",\"name\":\"LinearAxis\",\"id\":\"p1173\",\"attributes\":{\"ticker\":{\"type\":\"object\",\"name\":\"BasicTicker\",\"id\":\"p1174\",\"attributes\":{\"mantissas\":[1,2,5]}},\"formatter\":{\"type\":\"object\",\"name\":\"BasicTickFormatter\",\"id\":\"p1176\"},\"axis_label\":\"norm. YFP intensity\",\"major_label_policy\":{\"type\":\"object\",\"name\":\"AllLabels\",\"id\":\"p1175\"}}}],\"below\":[{\"type\":\"object\",\"name\":\"LinearAxis\",\"id\":\"p1166\",\"attributes\":{\"ticker\":{\"type\":\"object\",\"name\":\"BasicTicker\",\"id\":\"p1167\",\"attributes\":{\"mantissas\":[1,2,5]}},\"formatter\":{\"type\":\"object\",\"name\":\"BasicTickFormatter\",\"id\":\"p1169\"},\"axis_label\":\"norm. CFP intensity\",\"major_label_policy\":{\"type\":\"object\",\"name\":\"AllLabels\",\"id\":\"p1168\"}}}],\"center\":[{\"type\":\"object\",\"name\":\"Grid\",\"id\":\"p1172\",\"attributes\":{\"axis\":{\"id\":\"p1166\"}}},{\"type\":\"object\",\"name\":\"Grid\",\"id\":\"p1179\",\"attributes\":{\"dimension\":1,\"axis\":{\"id\":\"p1173\"}}},{\"type\":\"object\",\"name\":\"Legend\",\"id\":\"p1207\",\"attributes\":{\"location\":\"bottom_right\",\"click_policy\":\"hide\",\"items\":[{\"type\":\"object\",\"name\":\"LegendItem\",\"id\":\"p1208\",\"attributes\":{\"label\":{\"type\":\"value\",\"value\":\"d22\"},\"renderers\":[{\"id\":\"p1204\"}]}},{\"type\":\"object\",\"name\":\"LegendItem\",\"id\":\"p1221\",\"attributes\":{\"label\":{\"type\":\"value\",\"value\":\"m22\"},\"renderers\":[{\"id\":\"p1218\"}]}}]}}],\"frame_width\":300,\"frame_height\":300}}],\"callbacks\":{\"type\":\"map\"}}};\n",
       "  const render_items = [{\"docid\":\"7e35ebf2-c553-48aa-b54b-9d868635be4a\",\"roots\":{\"p1149\":\"8fda1c95-ab51-4bfb-95aa-54ae35b81260\"},\"root_ids\":[\"p1149\"]}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    let attempts = 0;\n",
       "    const 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": "p1149"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p.legend.location = 'bottom_right'\n",
    "p.legend.click_policy = 'hide'\n",
    "\n",
    "bokeh.io.show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Saving Bokeh plots\n",
    "\n",
    "After you create your plot, you can save it to a variety of formats. Most commonly you would save them as PNG (for presentations), SVG (for publications in the paper of the past), and HTML (for interactivity or sharing with colleagues). \n",
    "\n",
    "To save as a PNG for quick use, you can click the download icon in the tool bar. \n",
    "\n",
    "To save to SVG, you first change the output backend to `'svg'` and then you can click the download icon again, and you will get an SVG rendering of the plot. After saving the SVG, you should change the output backend back to `'canvas'` because it has much better in-browser performance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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YFP\",{\"type\":\"ndarray\",\"array\":{\"type\":\"bytes\",\"data\":\"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\"},\"shape\":[250],\"dtype\":\"float64\",\"order\":\"little\"}]]}}},\"view\":{\"type\":\"object\",\"name\":\"CDSView\",\"id\":\"p1219\",\"attributes\":{\"filter\":{\"type\":\"object\",\"name\":\"AllIndices\",\"id\":\"p1220\"}}},\"glyph\":{\"type\":\"object\",\"name\":\"Circle\",\"id\":\"p1215\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"norm CFP\"},\"y\":{\"type\":\"field\",\"field\":\"norm YFP\"},\"line_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"},\"fill_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"},\"hatch_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"}}},\"nonselection_glyph\":{\"type\":\"object\",\"name\":\"Circle\",\"id\":\"p1216\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"norm CFP\"},\"y\":{\"type\":\"field\",\"field\":\"norm YFP\"},\"line_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"},\"line_alpha\":{\"type\":\"value\",\"value\":0.1},\"fill_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"},\"fill_alpha\":{\"type\":\"value\",\"value\":0.1},\"hatch_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"},\"hatch_alpha\":{\"type\":\"value\",\"value\":0.1}}},\"muted_glyph\":{\"type\":\"object\",\"name\":\"Circle\",\"id\":\"p1217\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"norm CFP\"},\"y\":{\"type\":\"field\",\"field\":\"norm YFP\"},\"line_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"},\"line_alpha\":{\"type\":\"value\",\"value\":0.2},\"fill_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"},\"fill_alpha\":{\"type\":\"value\",\"value\":0.2},\"hatch_color\":{\"type\":\"value\",\"value\":\"#ff7e0e\"},\"hatch_alpha\":{\"type\":\"value\",\"value\":0.2}}}}}],\"toolbar\":{\"type\":\"object\",\"name\":\"Toolbar\",\"id\":\"p1155\",\"attributes\":{\"tools\":[{\"type\":\"object\",\"name\":\"PanTool\",\"id\":\"p1180\"},{\"type\":\"object\",\"name\":\"WheelZoomTool\",\"id\":\"p1181\"},{\"type\":\"object\",\"name\":\"BoxZoomTool\",\"id\":\"p1182\",\"attributes\":{\"overlay\":{\"type\":\"object\",\"name\":\"BoxAnnotation\",\"id\":\"p1183\",\"attributes\":{\"syncable\":false,\"level\":\"overlay\",\"visible\":false,\"left_units\":\"canvas\",\"right_units\":\"canvas\",\"bottom_units\":\"canvas\",\"top_units\":\"canvas\",\"line_color\":\"black\",\"line_alpha\":1.0,\"line_width\":2,\"line_dash\":[4,4],\"fill_color\":\"lightgrey\",\"fill_alpha\":0.5}}}},{\"type\":\"object\",\"name\":\"SaveTool\",\"id\":\"p1184\"},{\"type\":\"object\",\"name\":\"ResetTool\",\"id\":\"p1185\"},{\"type\":\"object\",\"name\":\"HelpTool\",\"id\":\"p1186\"}]}},\"left\":[{\"type\":\"object\",\"name\":\"LinearAxis\",\"id\":\"p1173\",\"attributes\":{\"ticker\":{\"type\":\"object\",\"name\":\"BasicTicker\",\"id\":\"p1174\",\"attributes\":{\"mantissas\":[1,2,5]}},\"formatter\":{\"type\":\"object\",\"name\":\"BasicTickFormatter\",\"id\":\"p1176\"},\"axis_label\":\"norm. YFP intensity\",\"major_label_policy\":{\"type\":\"object\",\"name\":\"AllLabels\",\"id\":\"p1175\"}}}],\"below\":[{\"type\":\"object\",\"name\":\"LinearAxis\",\"id\":\"p1166\",\"attributes\":{\"ticker\":{\"type\":\"object\",\"name\":\"BasicTicker\",\"id\":\"p1167\",\"attributes\":{\"mantissas\":[1,2,5]}},\"formatter\":{\"type\":\"object\",\"name\":\"BasicTickFormatter\",\"id\":\"p1169\"},\"axis_label\":\"norm. CFP intensity\",\"major_label_policy\":{\"type\":\"object\",\"name\":\"AllLabels\",\"id\":\"p1168\"}}}],\"center\":[{\"type\":\"object\",\"name\":\"Grid\",\"id\":\"p1172\",\"attributes\":{\"axis\":{\"id\":\"p1166\"}}},{\"type\":\"object\",\"name\":\"Grid\",\"id\":\"p1179\",\"attributes\":{\"dimension\":1,\"axis\":{\"id\":\"p1173\"}}},{\"type\":\"object\",\"name\":\"Legend\",\"id\":\"p1207\",\"attributes\":{\"location\":\"bottom_right\",\"click_policy\":\"hide\",\"items\":[{\"type\":\"object\",\"name\":\"LegendItem\",\"id\":\"p1208\",\"attributes\":{\"label\":{\"type\":\"value\",\"value\":\"d22\"},\"renderers\":[{\"id\":\"p1204\"}]}},{\"type\":\"object\",\"name\":\"LegendItem\",\"id\":\"p1221\",\"attributes\":{\"label\":{\"type\":\"value\",\"value\":\"m22\"},\"renderers\":[{\"id\":\"p1218\"}]}}]}}],\"frame_width\":300,\"frame_height\":300,\"output_backend\":\"svg\"}}],\"callbacks\":{\"type\":\"map\"}}};\n",
       "  const render_items = [{\"docid\":\"3c9ddf30-18e5-4873-b993-6243f0280e7a\",\"roots\":{\"p1149\":\"855ae550-f9ee-48b8-a781-e29c829bde8c\"},\"root_ids\":[\"p1149\"]}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    let attempts = 0;\n",
       "    const 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": "p1149"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p.output_backend = 'svg'\n",
    "\n",
    "bokeh.io.show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, click the disk icon in the plot above to save it.\n",
    "\n",
    "After saving, we should switch back to canvas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "p.output_backend = 'canvas'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also save the figure programmatically using the `bokeh.io.export_svgs()` function. This requires additional installations, so we will not do it here, but show the code to do it. Again, this will only work if the output backed is `'svg'`.\n",
    "\n",
    "```python\n",
    "p.output_backend = 'svg'\n",
    "bokeh.io.export_svgs(p, filename='insomniac_confidence_correct.svg')\n",
    "p.output_backend = 'canvas'\n",
    "```\n",
    "\n",
    "Finally, to save as HTML, you can use the `bokeh.io.save()` function. This saves your plot as a standalone HTML page. Note that the `title` kwarg is not the title of the plot, but the title of the web page that will appear on your Browser tab."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "bokeh.io.save(\n",
    "    p, \n",
    "    filename='our_first_bokeh_plot.html', \n",
    "    title='Bokeh plot',\n",
    "    resources=bokeh.resources.CDN,\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The resulting HTML page has all of the interactivity of the plot and you can, for example, email it to your collaborators for them to explore."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting generated data\n",
    "\n",
    "You're now a pro at plotting measured data. But sometimes, you want to plot smooth functions. To do this, you can use Numpy and/or Scipy to generate arrays of values of smooth functions.\n",
    "\n",
    "We will plot the [Airy disk](https://en.wikipedia.org/wiki/Airy_disk), which we encounter in biology when doing microscopy as the diffraction pattern of light passing through a pinhole. Here is a picture of the diffraction pattern from a laser (with the main peak overexposed).\n",
    "\n",
    "<div style=\"margin: auto; width: 300px;\">\n",
    "    \n",
    "![Airy disk](airy_disk.png)\n",
    "\n",
    "</div>\n",
    "    \n",
    "The equation for the radial light intensity of an Airy disk is\n",
    "\n",
    "\\begin{align}\n",
    "\\frac{I(x)}{I_0} = 4 \\left(\\frac{J_1(x)}{x}\\right)^2,\n",
    "\\end{align}\n",
    "\n",
    "where $I_0$ is the maximum intensity (the intensity at the center of the image) and $x$ is the radial distance from the center. Here, $J_1(x)$ is the first order Bessel function of the first kind. Yeesh. How do we plot *that*?\n",
    "\n",
    "Fortunately, SciPy has lots of special functions available. Specifically, `scipy.special.j1()` computes exactly what we are after! We pass in a NumPy array that has the values of $x$ we want to plot and then compute the $y$-values using the expression for the normalized intensity.\n",
    "\n",
    "To plot a smooth curve, we use the `np.linspace()` function with lots of points. We then connect the points with straight lines, which to the eye look like a smooth curve. Let's try it. We'll use 400 points, which I find is a good rule of thumb for not-too-oscillating functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The x-values we want\n",
    "x = np.linspace(-15, 15, 400)\n",
    "\n",
    "# The normalized intensity\n",
    "norm_I = 4 * (scipy.special.j1(x) / x)**2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have the values we want to plot, we could construct a Pandas `DataFrame` to pass in as the `source` to `p.line()`. We do not need to take this extra step, though. If we instead leave `source` unspecified, and pass in NumPy arrays for `x` and `y`, Bokeh will directly use those in constructing the plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
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p1744\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"x\"},\"y\":{\"type\":\"field\",\"field\":\"y\"},\"line_color\":\"#1f77b4\",\"line_width\":2}},\"nonselection_glyph\":{\"type\":\"object\",\"name\":\"Line\",\"id\":\"p1745\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"x\"},\"y\":{\"type\":\"field\",\"field\":\"y\"},\"line_color\":\"#1f77b4\",\"line_alpha\":0.1,\"line_width\":2}},\"muted_glyph\":{\"type\":\"object\",\"name\":\"Line\",\"id\":\"p1746\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"x\"},\"y\":{\"type\":\"field\",\"field\":\"y\"},\"line_color\":\"#1f77b4\",\"line_alpha\":0.2,\"line_width\":2}}}}],\"toolbar\":{\"type\":\"object\",\"name\":\"Toolbar\",\"id\":\"p1701\",\"attributes\":{\"tools\":[{\"type\":\"object\",\"name\":\"PanTool\",\"id\":\"p1726\"},{\"type\":\"object\",\"name\":\"WheelZoomTool\",\"id\":\"p1727\"},{\"type\":\"object\",\"name\":\"BoxZoomTool\",\"id\":\"p1728\",\"attributes\":{\"overlay\":{\"type\":\"object\",\"name\":\"BoxAnnotation\",\"id\":\"p1729\",\"attributes\":{\"syncable\":false,\"level\":\"overlay\",\"visible\":false,\"left_units\":\"canvas\",\"right_units\":\"canvas\",\"bottom_units\":\"canvas\",\"top_units\":\"canvas\",\"line_color\":\"black\",\"line_alpha\":1.0,\"line_width\":2,\"line_dash\":[4,4],\"fill_color\":\"lightgrey\",\"fill_alpha\":0.5}}}},{\"type\":\"object\",\"name\":\"SaveTool\",\"id\":\"p1730\"},{\"type\":\"object\",\"name\":\"ResetTool\",\"id\":\"p1731\"},{\"type\":\"object\",\"name\":\"HelpTool\",\"id\":\"p1732\"}]}},\"left\":[{\"type\":\"object\",\"name\":\"LinearAxis\",\"id\":\"p1719\",\"attributes\":{\"ticker\":{\"type\":\"object\",\"name\":\"BasicTicker\",\"id\":\"p1720\",\"attributes\":{\"mantissas\":[1,2,5]}},\"formatter\":{\"type\":\"object\",\"name\":\"BasicTickFormatter\",\"id\":\"p1722\"},\"axis_label\":\"I(x)/I\\u2080\",\"major_label_policy\":{\"type\":\"object\",\"name\":\"AllLabels\",\"id\":\"p1721\"}}}],\"below\":[{\"type\":\"object\",\"name\":\"LinearAxis\",\"id\":\"p1712\",\"attributes\":{\"ticker\":{\"type\":\"object\",\"name\":\"BasicTicker\",\"id\":\"p1713\",\"attributes\":{\"mantissas\":[1,2,5]}},\"formatter\":{\"type\":\"object\",\"name\":\"BasicTickFormatter\",\"id\":\"p1715\"},\"axis_label\":\"x\",\"major_label_policy\":{\"type\":\"object\",\"name\":\"AllLabels\",\"id\":\"p1714\"}}}],\"center\":[{\"type\":\"object\",\"name\":\"Grid\",\"id\":\"p1718\",\"attributes\":{\"axis\":{\"id\":\"p1712\"}}},{\"type\":\"object\",\"name\":\"Grid\",\"id\":\"p1725\",\"attributes\":{\"dimension\":1,\"axis\":{\"id\":\"p1719\"}}}],\"frame_width\":550,\"frame_height\":250}}],\"callbacks\":{\"type\":\"map\"}}};\n",
       "  const render_items = [{\"docid\":\"f24c2ed5-ddee-4cf7-966e-a4d5a014f1ae\",\"roots\":{\"p1695\":\"665674a3-a844-4b8f-a4fc-b142cda8126d\"},\"root_ids\":[\"p1695\"]}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    let attempts = 0;\n",
       "    const 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": "p1695"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = bokeh.plotting.figure(\n",
    "    frame_height=250,\n",
    "    frame_width=550,\n",
    "    x_axis_label=\"x\",\n",
    "    y_axis_label=\"I(x)/I₀\",\n",
    "    x_range=[-15, 15],\n",
    ")\n",
    "\n",
    "p.line(\n",
    "    x=x,\n",
    "    y=norm_I,\n",
    "    line_width=2,\n",
    ")\n",
    "\n",
    "bokeh.io.show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could also plot dots (which doesn't make sense here, but we'll show it just to see how the line joining works to make a plot of a smooth function)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "  <div id=\"16ab32e0-7224-481c-a1ef-9760e85fc85b\" data-root-id=\"p1695\" style=\"display: contents;\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "  const docs_json = {\"eff1a2a0-9433-4df4-8b42-5ef566be93c3\":{\"version\":\"3.1.0\",\"title\":\"Bokeh 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ct\",\"name\":\"AllIndices\",\"id\":\"p1880\"}}},\"glyph\":{\"type\":\"object\",\"name\":\"Circle\",\"id\":\"p1875\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"x\"},\"y\":{\"type\":\"field\",\"field\":\"y\"},\"size\":{\"type\":\"value\",\"value\":2},\"line_color\":{\"type\":\"value\",\"value\":\"orange\"},\"fill_color\":{\"type\":\"value\",\"value\":\"orange\"},\"hatch_color\":{\"type\":\"value\",\"value\":\"orange\"}}},\"nonselection_glyph\":{\"type\":\"object\",\"name\":\"Circle\",\"id\":\"p1876\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"x\"},\"y\":{\"type\":\"field\",\"field\":\"y\"},\"size\":{\"type\":\"value\",\"value\":2},\"line_color\":{\"type\":\"value\",\"value\":\"orange\"},\"line_alpha\":{\"type\":\"value\",\"value\":0.1},\"fill_color\":{\"type\":\"value\",\"value\":\"orange\"},\"fill_alpha\":{\"type\":\"value\",\"value\":0.1},\"hatch_color\":{\"type\":\"value\",\"value\":\"orange\"},\"hatch_alpha\":{\"type\":\"value\",\"value\":0.1}}},\"muted_glyph\":{\"type\":\"object\",\"name\":\"Circle\",\"id\":\"p1877\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"x\"},\"y\":{\"type\":\"field\",\"field\":\"y\"},\"size\":{\"type\":\"value\",\"value\":2},\"line_color\":{\"type\":\"value\",\"value\":\"orange\"},\"line_alpha\":{\"type\":\"value\",\"value\":0.2},\"fill_color\":{\"type\":\"value\",\"value\":\"orange\"},\"fill_alpha\":{\"type\":\"value\",\"value\":0.2},\"hatch_color\":{\"type\":\"value\",\"value\":\"orange\"},\"hatch_alpha\":{\"type\":\"value\",\"value\":0.2}}}}}],\"toolbar\":{\"type\":\"object\",\"name\":\"Toolbar\",\"id\":\"p1701\",\"attributes\":{\"tools\":[{\"type\":\"object\",\"name\":\"PanTool\",\"id\":\"p1726\"},{\"type\":\"object\",\"name\":\"WheelZoomTool\",\"id\":\"p1727\"},{\"type\":\"object\",\"name\":\"BoxZoomTool\",\"id\":\"p1728\",\"attributes\":{\"overlay\":{\"type\":\"object\",\"name\":\"BoxAnnotation\",\"id\":\"p1729\",\"attributes\":{\"syncable\":false,\"level\":\"overlay\",\"visible\":false,\"left_units\":\"canvas\",\"right_units\":\"canvas\",\"bottom_units\":\"canvas\",\"top_units\":\"canvas\",\"line_color\":\"black\",\"line_alpha\":1.0,\"line_width\":2,\"line_dash\":[4,4],\"fill_color\":\"lightgrey\",\"fill_alpha\":0.5}}}},{\"type\":\"object\",\"name\":\"SaveTool\",\"id\":\"p1730\"},{\"type\":\"object\",\"name\":\"ResetTool\",\"id\":\"p1731\"},{\"type\":\"object\",\"name\":\"HelpTool\",\"id\":\"p1732\"}]}},\"left\":[{\"type\":\"object\",\"name\":\"LinearAxis\",\"id\":\"p1719\",\"attributes\":{\"ticker\":{\"type\":\"object\",\"name\":\"BasicTicker\",\"id\":\"p1720\",\"attributes\":{\"mantissas\":[1,2,5]}},\"formatter\":{\"type\":\"object\",\"name\":\"BasicTickFormatter\",\"id\":\"p1722\"},\"axis_label\":\"I(x)/I\\u2080\",\"major_label_policy\":{\"type\":\"object\",\"name\":\"AllLabels\",\"id\":\"p1721\"}}}],\"below\":[{\"type\":\"object\",\"name\":\"LinearAxis\",\"id\":\"p1712\",\"attributes\":{\"ticker\":{\"type\":\"object\",\"name\":\"BasicTicker\",\"id\":\"p1713\",\"attributes\":{\"mantissas\":[1,2,5]}},\"formatter\":{\"type\":\"object\",\"name\":\"BasicTickFormatter\",\"id\":\"p1715\"},\"axis_label\":\"x\",\"major_label_policy\":{\"type\":\"object\",\"name\":\"AllLabels\",\"id\":\"p1714\"}}}],\"center\":[{\"type\":\"object\",\"name\":\"Grid\",\"id\":\"p1718\",\"attributes\":{\"axis\":{\"id\":\"p1712\"}}},{\"type\":\"object\",\"name\":\"Grid\",\"id\":\"p1725\",\"attributes\":{\"dimension\":1,\"axis\":{\"id\":\"p1719\"}}}],\"frame_width\":550,\"frame_height\":250}}],\"callbacks\":{\"type\":\"map\"}}};\n",
       "  const render_items = [{\"docid\":\"eff1a2a0-9433-4df4-8b42-5ef566be93c3\",\"roots\":{\"p1695\":\"16ab32e0-7224-481c-a1ef-9760e85fc85b\"},\"root_ids\":[\"p1695\"]}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    let attempts = 0;\n",
       "    const 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": "p1695"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p.circle(\n",
    "    x=x,\n",
    "    y=norm_I,\n",
    "    size=2,\n",
    "    color=\"orange\"\n",
    ")\n",
    "\n",
    "bokeh.io.show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is one detail I swept under the rug here. What happens if we compute the function for $x = 0$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/j_/c5r9ch0913v3h1w4bdwzm0lh0000gn/T/ipykernel_46931/1311113470.py:1: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  4 * (scipy.special.j1(0) / 0)**2\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "nan"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "4 * (scipy.special.j1(0) / 0)**2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We get a `RuntimeWarning` because we divided by zero. We know that\n",
    "\n",
    "\\begin{align}\n",
    "\\lim_{x\\to 0} \\frac{J_1(x)}{x} = \\frac{1}{2},\n",
    "\\end{align}\n",
    "\n",
    "so we could write a new function that checks if $x = 0$ and returns the appropriate limit for $x = 0$. In the `x` array I constructed for the plot, we hopped over zero, so it was never evaluated. If we were being careful, we could write our own Airy function that deals with this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def airy_disk(x):\n",
    "    \"\"\"Compute the Airy disk.\"\"\"\n",
    "    # Set up output array\n",
    "    res = np.empty_like(x)\n",
    "   \n",
    "    # Where x is very close to zero (use np.isclose)\n",
    "    near_zero = np.isclose(x, 0)\n",
    "    \n",
    "    # Compute values where x is close to zero\n",
    "    res[near_zero] = 1.0\n",
    "\n",
    "    # Everywhere else\n",
    "    x_vals = x[~near_zero]\n",
    "    res[~near_zero] = 4 * (scipy.special.j1(x_vals) / x_vals)**2\n",
    "    \n",
    "    return res"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python implementation: CPython\n",
      "Python version       : 3.10.10\n",
      "IPython version      : 8.10.0\n",
      "\n",
      "pandas    : 1.5.3\n",
      "bokeh     : 3.1.0\n",
      "jupyterlab: 3.5.3\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -v -p pandas,bokeh,jupyterlab"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}