Simulate.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "bbe206c9-7380-4a7e-921c-2b16f1171f79",
   "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",
       "  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",
       "\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(\"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",
       "    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",
       "  \n",
       "  const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.1.min.js\"];\n",
       "  const css_urls = [];\n",
       "  \n",
       "\n",
       "  const 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 (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(\"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  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\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(\"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    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  \n  const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.1.min.js\"];\n  const css_urls = [];\n  \n\n  const 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 (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(\"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": [
    "from simulator import *\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set_context('talk')\n",
    "output_notebook()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8210b98d-8912-4139-966f-ae050521f366",
   "metadata": {},
   "source": [
    "# Full GUI"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7a02f475-601d-427c-9106-3ce8cb4cfd84",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.bokehjs_exec.v0+json": "",
      "text/html": [
       "\n",
       "<script id=\"1003\">\n",
       "  (function() {\n",
       "    const xhr = new XMLHttpRequest()\n",
       "    xhr.responseType = 'blob';\n",
       "    xhr.open('GET', \"http://localhost:38219/autoload.js?bokeh-autoload-element=1003&bokeh-absolute-url=http://localhost:38219&resources=none\", true);\n",
       "    \n",
       "    xhr.onload = function (event) {\n",
       "      const script = document.createElement('script');\n",
       "      const src = URL.createObjectURL(event.target.response);\n",
       "      script.src = src;\n",
       "      document.body.appendChild(script);\n",
       "    };\n",
       "    xhr.send();\n",
       "  })();\n",
       "</script>"
      ]
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "server_id": "7e999e616cff43429343721675b32a5c"
      }
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:bokeh.core.validation.check:W-1000 (MISSING_RENDERERS): Plot has no renderers: Figure(id='1035', ...)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Run clicked, simulating...\n",
      "Eqn_params: [0.01, 1.0, 0.0, 0.0, 'POWER']\n",
      "Simulating... t = 1.0/1.0\n",
      "Simulation Completed\n"
     ]
    }
   ],
   "source": [
    "show(start_jupyter)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3183480-2716-409a-9fa7-0ffb4bdf99f8",
   "metadata": {},
   "source": [
    "# Manually Simulating"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2f54b101-198c-4f59-8b16-a8fe6694d336",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulating... t = 1.0/1"
     ]
    }
   ],
   "source": [
    "N,L,dt,x_axis,R_mass,M,rho_1,rho_0,rho_J,phi_0_array,dot_0_array,y0 = initialize()\n",
    "phi1,dot1,t1 = simulate(C0=1e-2,c_th=1,D0=0,d_th=0,\n",
    "                        ti=0,tf=1,dt=dt,\n",
    "                        save_interval=0.01,\n",
    "                        method='RK4',model='POWER')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "9b344cac-321f-46c4-89ba-2e9c6d7aa3bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7efe200ce820>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax,_ = plot(x_axis,phi1,t1,20,yscale='linear',return_axes=True)\n",
    "ax.plot(x_axis,rho_J/np.max(rho_J)*np.max(phi1[-1]),lw=4,linestyle='--',c='orange',zorder=5,label='Relative Density')\n",
    "ax.legend(frameon=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c9fbb2dd-bd22-4c2a-b618-88ae7b227e02",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python3 (base3)",
   "language": "python",
   "name": "base3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}