.ipynb_checkpoints/1DIsing-checkpoint.ipynb

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    "# 1D Ising Model\n",
    "The 1D Ising model using the metropolis-based Monte Carlo method, as described in Fig. 8.8 Schroeder (an undergraduate statistical mechanics/thermodynamics textbook). The magnetization M, the average energy U, the heat capacity C, and the magnetic susceptibility χ are all plotted as functions of temperature."
   ]
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       "    });\n",
       "  }\n",
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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(\"259014\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n\n    function on_error() {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (var i = 0; i < css_urls.length; i++) {\n      var url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.async = false;\n      element.src = url;\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };var element = document.getElementById(\"259014\");\n  if (element == null) {\n    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '259014' but no matching script tag was found. \")\n    return false;\n  }\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.3.1.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.3.1.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.3.1.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.3.1.min.js\"];\n  var css_urls = [];\n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    \n    function(Bokeh) {\n      \n    },\n    function(Bokeh) {} // ensure no trailing comma for IE\n  ];\n\n  function run_inline_js() {\n    \n    if ((root.Bokeh !== undefined) || (force === true)) {\n      for (var i = 0; i < inline_js.length; i++) {\n        inline_js[i].call(root, root.Bokeh);\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(\"259014\")).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 matplotlib.pyplot as plt\n",
    "from bokeh.io import output_notebook, show\n",
    "from bokeh.plotting import figure\n",
    "output_notebook()\n",
    "\n",
    "from numba import jit, njit\n",
    "import numpy as np\n",
    "\n",
    "import random\n",
    "import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Helper functions\n",
    "\n",
    "# Calculate magnetization. \n",
    "# Magnetization is the sum of all spins divided by the total number of spins\n",
    "@njit(fastmath=True)\n",
    "def calcM(s, length):\n",
    "    m = np.abs(s.sum())\n",
    "    return m/length\n",
    "\n",
    "# Calculate interaction energy between spins. Assume periodic boundaries\n",
    "# Interaction energy will be the difference in energy due to flipping spin i,j \n",
    "# (i.e. 2*spin_value*neighboring_spins)\n",
    "@njit(fastmath=True)\n",
    "def deltaU(s, i, length):\n",
    "    alpha = 100\n",
    "    # Nearest neighbors\n",
    "    # left\n",
    "    if i == 0:\n",
    "        l = s[length-1]  # periodic boundary\n",
    "    else:\n",
    "        l = s[i-1]\n",
    "    # right\n",
    "    if i == length-1:\n",
    "        r = s[0]  # periodic boundary\n",
    "    else:\n",
    "        r = s[i+1]\n",
    "        \n",
    "    # Next nearest neighbors\n",
    "    # left left\n",
    "    if i == 1:\n",
    "        ll = s[length-1]  # periodic boundary\n",
    "    elif i == 0:\n",
    "        ll = s[length-2]  # periodic boundary\n",
    "    else:\n",
    "        ll = s[i-2]\n",
    "    # right right\n",
    "    if i == length-1:\n",
    "        rr = s[1]  # periodic boundary\n",
    "    elif i == length-2:\n",
    "        rr = s[0]  # periodic boundary\n",
    "    else:\n",
    "        rr = s[i+2]\n",
    "    return 2*s[i]*(r+l) + 2*s[i]*(rr+ll)/(2**alpha)  # difference in energy if i,j is flipped\n",
    "\n",
    "# Monte carlo cycle\n",
    "@njit(fastmath=True)\n",
    "def montecc(s, T, cycles, length):\n",
    "    for m in range(cycles):\n",
    "        i = random.randrange(length)  # choose random site\n",
    "        ediff = deltaU(s, i, length)\n",
    "        if ediff <= 0:\n",
    "            s[i] = -s[i]  # flip spin\n",
    "        elif random.random() < np.exp(-ediff/T):\n",
    "            s[i] = -s[i]\n",
    "    return s\n",
    "\n",
    "# Compute physical quantities\n",
    "@njit(fastmath=True)\n",
    "def computePQ(s, T, cycles, length):\n",
    "    Mg = 0\n",
    "    Mg_sq = 0\n",
    "    for p in range(cycles):\n",
    "        s = montecc(s, T, 1, length)\n",
    "        M = calcM(s, length)\n",
    "        Mg += M\n",
    "        Mg_sq += M*M\n",
    "    sus = (Mg_sq/cycles-(Mg/cycles)**2)/T\n",
    "    return sus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "ename": "ZeroDivisionError",
     "evalue": "division by zero",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mZeroDivisionError\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-254-b95114a37ab5>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     14\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mind\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mT\u001b[0m \u001b[0;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtemps\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     15\u001b[0m     \u001b[0;31m# Cycle spins\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 16\u001b[0;31m     \u001b[0ms\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmontecc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mT\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcycles\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlength\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     17\u001b[0m     \u001b[0msus_16\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mind\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcomputePQ\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mT\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcycles\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlength\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     18\u001b[0m \u001b[0mend\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtime\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mZeroDivisionError\u001b[0m: division by zero"
     ]
    }
   ],
   "source": [
    "# Initial parameters\n",
    "length = 16  # length of spin chain\n",
    "s = np.random.choice([1,-1], size=(length))  # initial spin sites randomly (+1 or -1)\n",
    "cycles = 300000\n",
    "\n",
    "# Initlaize temperature range (crosses critical temperature)\n",
    "temps = np.arange(0.02, 3.2, 0.08)\n",
    "\n",
    "# Inititalize magnetization, average energy, heat capacity, and susceptibility\n",
    "sus_16 = np.zeros(len(temps))\n",
    "\n",
    "start = time.time()\n",
    "# Compute physical quanities (magnetization, etc.)\n",
    "for ind, T in enumerate(temps):\n",
    "    # Cycle spins\n",
    "    s = montecc(s, T, cycles, length)\n",
    "    sus_16[ind] = computePQ(s, T, cycles, length)\n",
    "end = time.time()\n",
    "print(\"Elapsed = %s\" % (end - start))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed = 21.994175910949707\n"
     ]
    }
   ],
   "source": [
    "# Initial parameters\n",
    "\n",
    "length = 32  # length of spin chain\n",
    "s = np.random.choice([1,-1], size=(length))  # initial spin sites randomly (+1 or -1)\n",
    "\n",
    "# Inititalize magnetization, average energy, heat capacity, and susceptibility\n",
    "sus_32 = np.zeros(len(temps))\n",
    "\n",
    "start = time.time()\n",
    "# Compute physical quanities (magnetization, etc.)\n",
    "for ind, T in enumerate(temps):\n",
    "    # Cycle spins\n",
    "    s = montecc(s, T, cycles, length)\n",
    "    sus_32[ind] = computePQ(s, T, cycles, length)\n",
    "end = time.time()\n",
    "print(\"Elapsed = %s\" % (end - start))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed = 44.98649287223816\n"
     ]
    }
   ],
   "source": [
    "# Initial parameters\n",
    "\n",
    "length = 64  # length of spin chain\n",
    "s = np.random.choice([1,-1], size=(length))  # initial spin sites randomly (+1 or -1)\n",
    "\n",
    "# Inititalize magnetization, average energy, heat capacity, and susceptibility\n",
    "sus_64 = np.zeros(len(temps))\n",
    "\n",
    "start = time.time()\n",
    "# Compute physical quanities (magnetization, etc.)\n",
    "for ind, T in enumerate(temps):\n",
    "    # Cycle spins\n",
    "    s = montecc(s, T, cycles, length)\n",
    "    sus_64[ind] = computePQ(s, T, cycles, length)\n",
    "end = time.time()\n",
    "print(\"Elapsed = %s\" % (end - start))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Collapse to Compute Critical Exponents"
   ]
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  {
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   "source": [
    "nu = 2\n",
    "eta = 3.5\n",
    "tc = 2.34\n",
    "t = (temps-tc)/tc\n",
    "x16 = t * (16)**(1/nu)\n",
    "y16 = sus_16 * (16)**(eta - 2)\n",
    "x32 = t * (32)**(1/nu)\n",
    "y32 = sus_32 * (32)**(eta - 2)\n",
    "x64 = t * (64)**(1/nu)\n",
    "y64 = sus_64 * (64)**(eta - 2)\n",
    "\n",
    "#Interactive plot\n",
    "p = figure(plot_width=700, plot_height=350)\n",
    "p.line(x16, y16, color='red')\n",
    "p.line(x32, y32, color='blue')\n",
    "p.line(x64, y64, color='brown')\n",
    "show(p)"
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:{\"callback\":null},\"id\":\"261624\",\"type\":\"DataRange1d\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"#1f77b4\"},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"#1f77b4\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"261665\",\"type\":\"Scatter\"},{\"attributes\":{\"callback\":null},\"id\":\"261622\",\"type\":\"DataRange1d\"},{\"attributes\":{\"data_source\":{\"id\":\"261663\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"261664\",\"type\":\"Scatter\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"261665\",\"type\":\"Scatter\"},\"selection_glyph\":null,\"view\":{\"id\":\"261667\",\"type\":\"CDSView\"}},\"id\":\"261666\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"261643\",\"type\":\"SaveTool\"},{\"attributes\":{\"text\":\"\"},\"id\":\"264149\",\"type\":\"Title\"},{\"attributes\":{\"fill_color\":{\"value\":\"red\"},\"line_color\":{\"value\":\"red\"},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"261654\",\"type\":\"Scatter\"},{\"attributes\":{\"active_drag\":\"auto\",\"active_inspect\":\"auto\",\"active_multi\":null,\"active_scroll\":\"auto\",\"active_tap\":\"auto\",\"tools\":[{\"id\":\"261640\",\"type\":\"PanTool\"},{\"id\":\"261641\",\"type\":\"WheelZoomTool\"},{\"id\":\"261642\",\"type\":\"BoxZoomTool\"},{\"id\":\"261643\",\"type\":\"SaveTool\"},{\"id\":\"261644\",\"type\":\"ResetTool\"},{\"id\":\"261645\",\"type\":\"HelpTool\"}]},\"id\":\"261646\",\"type\":\"Toolbar\"},{\"attributes\":{\"callback\":null,\"data\":{\"x\":{\"__ndarray__\":\"ZmZmZmZm/j8K16NwPQr/P65H4XoUrv8/KVyPwvUoAEB7FK5H4XoAQM3MzMzMzABAH4XrUbgeAUBxPQrXo3ABQMP1KFyPwgFAFa5H4XoUAkBnZmZmZmYCQLkehetRuAJAC9ejcD0KA0Bdj8L1KFwDQK9H4XoUrgNAAQAAAAAABEBTuB6F61EEQKVwPQrXowRA9yhcj8L1BEBJ4XoUrkcFQJuZmZmZmQVA7VG4HoXrBUA/CtejcD0GQJHC9ShcjwZA43oUrkfhBkA1MzMzMzMHQIfrUbgehQdA2aNwPQrXB0ArXI/C9SgIQH0UrkfheghAz8zMzMzMCEAhhetRuB4JQHM9CtejcAlA\",\"dtype\":\"float64\",\"shape\":[33]},\"y\":{\"__ndarray__\":\"u1EVrzuISj9gqHIJ5ZdUP4teDJYKZ1E/bkh5R7z8Uz9egAwK47VhPysJEPzP+2g/VoavKXd6bz9NEDVHkVx+P+l5QlUiBoU/F83rm2zJiD8SbR6iNuyRP/NzsZHmfZI/PivcsUHXlD9UWzJB7viYP93fY8zPEJY/U1rnGVpQkz93GdD2MEqSP+xA9lgSdJE/GZGk1PYCiz9voGHFZ8GIP+Phyj+wpIY/vM8NmSsThD/fO++Ix3SCP6naBeTKY38/FSz7RO5ufD+7UKtZ+Fl6P8m4/pQsznY/IIayGn24dz9Jwk9lQhp0P/ycJAbdOnI/Fxqg5WBFcT+lYpG9d/hwP1FPHZKxJ28/\",\"dtype\":\"float64\",\"shape\":[33]}},\"selected\":{\"id\":\"264155\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"264156\",\"type\":\"UnionRenderers\"}},\"id\":\"261653\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"source\":{\"id\":\"261663\",\"type\":\"ColumnDataSource\"}},\"id\":\"261667\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"264154\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"261640\",\"type\":\"PanTool\"},{\"attributes\":{},\"id\":\"264152\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"264155\",\"type\":\"Selection\"},{\"attributes\":{\"callback\":null,\"data\":{\"x\":{\"__ndarray__\":\"ZmZmZmZm/j8K16NwPQr/P65H4XoUrv8/KVyPwvUoAEB7FK5H4XoAQM3MzMzMzABAH4XrUbgeAUBxPQrXo3ABQMP1KFyPwgFAFa5H4XoUAkBnZmZmZmYCQLkehetRuAJAC9ejcD0KA0Bdj8L1KFwDQK9H4XoUrgNAAQAAAAAABEBTuB6F61EEQKVwPQrXowRA9yhcj8L1BEBJ4XoUrkcFQJuZmZmZmQVA7VG4HoXrBUA/CtejcD0GQJHC9ShcjwZA43oUrkfhBkA1MzMzMzMHQIfrUbgehQdA2aNwPQrXB0ArXI/C9SgIQH0UrkfheghAz8zMzMzMCEAhhetRuB4JQHM9CtejcAlA\",\"dtype\":\"float64\",\"shape\":[33]},\"y\":{\"__ndarray__\":\"3ZujMi9FKj93d6dnUrwsP/aW/Yv5oTQ/K54ipakyOj8IS9oStG5APwZIfAQBTFI/ZmBM0FKTaD8bLZABR4lZP8ADE5kHRnI/zCq4nd03gD+e18LGIHCSP6o1f/59qpE/BgpAB0CrkD8rhDBcvbiGP30sJQM0S4c/wb4BToimdD9SGCB92ah3PxnZYosd5HM/T7zyXDFScT8VDW+Ex0xtP+9cUMfwzWk/HkCAKjCuaD8KBBtPN4FfPzWG6uadzGA/QpSStaxPYD8KPgAOpfpdP/C1qwmjm1k/3GIsb6GeVT9oBBMcsqNVP/ERQKoYCVE/Umpz6XdCVD9fAFLyTDxNP6IL1Wn/OFA/\",\"dtype\":\"float64\",\"shape\":[33]}},\"selected\":{\"id\":\"264157\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"264158\",\"type\":\"UnionRenderers\"}},\"id\":\"261658\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"264156\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"dimension\":1,\"ticker\":{\"id\":\"261636\",\"type\":\"BasicTicker\"}},\"id\":\"261639\",\"type\":\"Grid\"},{\"attributes\":{\"overlay\":{\"id\":\"264161\",\"type\":\"BoxAnnotation\"}},\"id\":\"261642\",\"type\":\"BoxZoomTool\"},{\"attributes\":{},\"id\":\"261645\",\"type\":\"HelpTool\"},{\"attributes\":{},\"id\":\"264157\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"261641\",\"type\":\"WheelZoomTool\"},{\"attributes\":{},\"id\":\"264158\",\"type\":\"UnionRenderers\"},{\"attributes\":{},\"id\":\"261644\",\"type\":\"ResetTool\"}],\"root_ids\":[\"261621\"]},\"title\":\"Bokeh Application\",\"version\":\"1.3.1\"}};\n",
       "  var render_items = [{\"docid\":\"740a0420-1738-4c77-ae9b-2c842cd30e67\",\"roots\":{\"261621\":\"fd7a15a4-b459-4d50-b806-5c9a24979b2f\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "261621"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot calculated stuff\n",
    "\n",
    "p = figure(plot_width=600, plot_height=400)\n",
    "p.scatter(temps, sus_16, color='red')\n",
    "p.scatter(temps, sus_32, color='blue')\n",
    "p.scatter(temps, sus_64, color='brown')\n",
    "\n",
    "show(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
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   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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