{"cells": [{"cell_type": "markdown", "metadata": {}, "source": ["# Exercise 7.3: Understanding and building ECDFs\n", "\n", "<hr>"]}, {"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=\"1002\">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\") || (!Object.prototype.hasOwnProperty.call(output.data, 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(\"1002\");\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(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", "    const hashes = {\"https://cdn.bokeh.org/bokeh/release/bokeh-2.3.2.min.js\": \"XypntL49z55iwGVUW4qsEu83zKL3XEcz0MjuGOQ9SlaaQ68X/g+k1FcioZi7oQAc\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.3.2.min.js\": \"bEsM86IHGDTLCS0Zod8a8WM6Y4+lafAL/eSiyQcuPzinmWNgNO2/olUF0Z2Dkn5i\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.3.2.min.js\": \"TX0gSQTdXTTeScqxj6PVQxTiRW8DOoGVwinyi1D3kxv7wuxQ02XkOxv0xwiypcAH\"};\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", "      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-2.3.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.3.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.3.2.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(\"1002\")).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(\"1002\");\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(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    const hashes = {\"https://cdn.bokeh.org/bokeh/release/bokeh-2.3.2.min.js\": \"XypntL49z55iwGVUW4qsEu83zKL3XEcz0MjuGOQ9SlaaQ68X/g+k1FcioZi7oQAc\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.3.2.min.js\": \"bEsM86IHGDTLCS0Zod8a8WM6Y4+lafAL/eSiyQcuPzinmWNgNO2/olUF0Z2Dkn5i\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.3.2.min.js\": \"TX0gSQTdXTTeScqxj6PVQxTiRW8DOoGVwinyi1D3kxv7wuxQ02XkOxv0xwiypcAH\"};\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      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-2.3.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.3.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.3.2.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(\"1002\")).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"}], "source": ["import numpy as np\n", "import pandas as pd\n", "\n", "import bokeh.io\n", "import bokeh.plotting\n", "\n", "bokeh.io.output_notebook()"]}, {"cell_type": "markdown", "metadata": {}, "source": ["<hr>\n", "\n", "As a reminder, the empirical cumulative distribution function for a set of data point evaluated at x is \n", "\n", ">ECDF(x) = fraction of data points \u2264 x.\n", "\n", "In a previous lesson, we saw that if we have a Pandas `Series` stored in a variable named `data`, we can compute the values for the ECDF as `data.rank(method='first') / len(data)`. If we had our data as a Pandas `Series`, we could use this method to make an ECDF plot as follows (which is more or less what is happening under the hood in `bokeh_catplot.ecdf()`."]}, {"cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [{"data": {"text/html": ["\n", "\n", "\n", "\n", "\n", "\n", "  <div class=\"bk-root\" id=\"394de8be-08fe-4613-93a0-3d4c90755404\" data-root-id=\"1003\"></div>\n"]}, "metadata": {}, "output_type": "display_data"}, {"data": {"application/javascript": ["(function(root) {\n", "  function embed_document(root) {\n", "    \n", "  var docs_json = 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"output_type": "display_data"}], "source": ["# Dummy data set as a Pandas Series\n", "rg = np.random.default_rng()\n", "data = pd.Series(rg.normal(0, 1, size=100))\n", "\n", "# Compute y-values for ECDF\n", "ecdf_y = data.rank(method='first') / len(data)\n", "\n", "# Make the plot\n", "p = bokeh.plotting.figure(\n", "    frame_height=200,\n", "    frame_width=300,\n", "    x_axis_label='x',\n", "    y_axis_label='ECDF',\n", ")\n", "\n", "p.circle(data, ecdf_y)\n", "\n", "bokeh.io.show(p)"]}, {"cell_type": "markdown", "metadata": {}, "source": ["The `rank()` method is not available for Numpy arrays. What we would like is a function we could call with a Numpy array as input that returns the x and y values for plotting. We do not want to have to convert the array to a Pandas `Series` first. Plus, doing this exercise helps you understand what an ECDF is, and therefore will help you interpret it.\n", "\n", "Write a function with call signature\n", "\n", "```python\n", "ecdf_vals(data)\n", "```\n", "\n", "which takes a one-dimensional NumPy array of data and returns the `x` and `y` values for plotting a \"dot-style\" ECDF. That is, each dot has a `y` value given by the ECDF evaluated at `x`.\n", "\n", "When writing a function, you should have detailed doc strings and checking of input. However, here the focus is on your understanding of ECDFs and developing skills with NumPy, so you do not need to have a very descriptive doc string nor lots of input checking.\n", "\n", "*Hint*: The functions `np.sort()` and `np.arange()` may be useful."]}, {"cell_type": "markdown", "metadata": {}, "source": ["<br />"]}], "metadata": {"anaconda-cloud": {}, "kernelspec": {"display_name": "Python 3", "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": "3.8.10"}}, "nbformat": 4, "nbformat_minor": 4}