Python_Introduction.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Introduction to Python\n",
    "You will need to have a version of Python installed (hopefully a new version like 3.9 and above). You will also need to have some of the standard Python libraries installed, either via 'pip install ...' or via a conda environment. Libraries that you will need for this class include: numpy, scipy, matplotlib. \n",
    "\n",
    "For folks who are used to matlab, note that Python starts with the zero index while Matlab starts with index 1. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n",
      "4\n",
      "1.0\n",
      "-12\n",
      "0\n"
     ]
    }
   ],
   "source": [
    "# Basic Operations \n",
    "# -- similar to many basic programming languages (C, etc.)\n",
    "\n",
    "# use the python function 'print' to print the output\n",
    "print(2 + 2)\n",
    "print(2 * 2)\n",
    "print(2 / 2)\n",
    "print(2 - 2 * 7)  # Order of operations matters\n",
    "print((2 - 2) * 7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Notice a big difference with C or Matlab -- no semicolons needed at the end of statements! However, we will need colon symbols for indicating an indented block (see the loops below)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n"
     ]
    }
   ],
   "source": [
    "# Assign variables using '=' symbol\n",
    "a = 2 + 2\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "45\n"
     ]
    }
   ],
   "source": [
    "# Loops\n",
    "count = 0  # Initialize the variable \"count\"\n",
    "\n",
    "# Add all the numbers 1-10\n",
    "for ii in range(10):  # note that range(10) = [0, 2, ..., 9]\n",
    "    count = ii + count  # indicate a code block to loop over by indenting the code lines\n",
    "    \n",
    "print(count)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n"
     ]
    }
   ],
   "source": [
    "counter = count  # Assign count to counter\n",
    "\n",
    "# Subtract numbers until count is not greater than 10\n",
    "while (counter > 10):\n",
    "    counter = counter - 1\n",
    "print(counter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n",
      "3\n"
     ]
    }
   ],
   "source": [
    "# Create a vector (this is also called an 'array')\n",
    "A_Vector = [1, 2, 3, 4]\n",
    "\n",
    "# Access a particular element of the vector\n",
    "print(A_Vector[2])  # prints 3 because A_vector[0] is the start of the vector!\n",
    "print(A_Vector[-2]) # prints 3 because A_vector[-1] is the end of the vector, i.e. we are counting backwards from the end\n",
    "\n",
    "# best way to work with vectors and multi-dimensional 'arrays'\n",
    "# is to use the NumPy library, which is imported as follows:\n",
    "import numpy as np  # call the numpy library np for shorthand\n",
    "\n",
    "B_Vector = np.ones(4)  # same as B_Vector = [1, 1, 1, 1]\n",
    "A_Vector = np.array([1, 2, 3, 4])\n",
    "\n",
    "# np.zeros(N)  -- make a vector of N elements, all initialized to 0\n",
    "# np.random.randn(N)  -- make a vector of N elements, all randomly initialized between (0, 1)\n",
    "# np.eye(N)  -- make the identity matrix of size N x N\n",
    "\n",
    "# Create a numpy-style Matrix\n",
    "\n",
    "A_Matrix = np.array([[1, 2, 3, 4],\n",
    "                        [5, 6, 7, 8]])\n",
    "\n",
    "# Matrices are like stacks of vectors so [], zeros, ones, eye.. all work to\n",
    "# create matrices as well.\n",
    "\n",
    "# np.zeros((N, N, N)) -- Make a N x N x N tensor with elements all initialized to 0 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[30 70] (2, 4) (4, 2)\n",
      "A =  [[1 2 3 4]\n",
      " [5 6 7 8]]\n",
      "A^2 =  [[ 1  4  9 16]\n",
      " [25 36 49 64]]\n"
     ]
    }
   ],
   "source": [
    "# Operations on Vectors/Matrices\n",
    "\n",
    "# matrices and vectors have to have one matching \n",
    "# dimension to be multiplied together\n",
    "mat_vec_product = A_Matrix @ A_Vector \n",
    "\n",
    "# The dimension of numpy objects can be accessed by .shape and\n",
    "# the .T operator takes the transpose (NxM to MxN)\n",
    "print(mat_vec_product, A_Matrix.shape, A_Matrix.T.shape)\n",
    "\n",
    "# square every element in the matrix A. Note that this is different than doing A @ A\n",
    "elementwise_square = A_Matrix ** 2 \n",
    "\n",
    "# can print multiple things by separating with a comma in the print function\n",
    "print('A = ', A_Matrix)\n",
    "print('A^2 = ', elementwise_square)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a function in Python \n",
    "# Time, and fuctions of time f(t) are represented by vectors \n",
    "\n",
    "# numpy.linspace(-100, 100, 200) generates a 200-dimensional vector by splitting up the\n",
    "# interval (-100, 100) into a uniform grid. Default is to omit the last point (t=100)\n",
    "the_time = np.linspace(-100, 100, 200) \n",
    "\n",
    "F1 = (the_time ** 2) * np.sin(the_time)  # defining t^2 * sin(t)\n",
    "F2 = (the_time ** 2)  # defining t^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# For plotting, we need to import another standard python library\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(the_time, F1, 'r-', linewidth=2)   # Plots F1(t) in a red solid line\n",
    "plt.plot(the_time, F2, 'k--', linewidth=2)  # Plots F2(t) in a black dashed line\n",
    "plt.xlabel('Time')           # Adds the label \"time\" to the x-axis\n",
    "plt.ylabel('Functions')      # Adds the label \"functions\" to the y-axis\n",
    "plt.legend(['F1','F2'])      # Creates a legend with entries \"F1\", \"F2\"\n",
    "plt.grid(True)               # Turns on the grid lines \n",
    "plt.title('Plots of F1 and F2')  # Gives the plot a title\n",
    "plt.show()  # actually show the plot (more important when not using a Jupyter notebook)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ax - b =  [-1.11022302e-16  1.33226763e-15]\n",
      "sum(AAxx - bb) =  5.917523415721604e-13\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/ky/vcyprjsd5d9f7b_qpyspg2rm0000gn/T/ipykernel_7136/2056396256.py:14: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  x, _, _, _ = np.linalg.lstsq(A, b)\n",
      "/var/folders/ky/vcyprjsd5d9f7b_qpyspg2rm0000gn/T/ipykernel_7136/2056396256.py:22: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  xx, _, _, _ = np.linalg.lstsq(AA, bb)\n"
     ]
    }
   ],
   "source": [
    "# Linear System Solving (2 equations + 2 unknowns) \n",
    "\n",
    "# Imagine we have the following 2 algebraic equations\n",
    "# z  + 2y = 1\n",
    "# 4z + 5y = 1\n",
    "\n",
    "A = np.array([[1, 2], [4, 5]])\n",
    "b = np.array([1, 1])\n",
    "\n",
    "# The following will solve Ax = b in a least-squares sense (if an exact solution doesn't exist)\n",
    "# Note that this is usually what A\\b does in matlab\n",
    "\n",
    "#  if function returns a bunch of stuff, and you don't care about that stuff, use a _\n",
    "x, _, _, _ = np.linalg.lstsq(A, b) \n",
    "print('Ax - b = ', A @ x - b)\n",
    "\n",
    "# Even for very large system\n",
    "\n",
    "AA = np.random.randn(100, 100)\n",
    "bb = np.random.randn(100)\n",
    "\n",
    "xx, _, _, _ = np.linalg.lstsq(AA, bb)  \n",
    "print('sum(AAxx - bb) = ', np.sum(AA @ xx - bb))  # get like 1e-14, pretty close to zero\n",
    "\n",
    "# You might get a FutureWarning here -- this is letting you know something\n",
    "# might be off in the lstsq function -- in this case it is fine"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Ordinary Differential Equations (ODE)\n",
    "from scipy.integrate import solve_ivp  # import the standard ODE solver in Python\n",
    "\n",
    "TSpan = [0, 10]     # Initial Time and Final Time\n",
    "t = np.linspace(0, 10, 1000)\n",
    "X_initial = [1, 0]  # Initial Conditions\n",
    "\n",
    "# solve_ivp wants a true function with arguments -- good time to show how to do that:\n",
    "# define a function that takes t and X0 as arguments, and returns \n",
    "def ode_test(t, X0): \n",
    "    X = np.zeros(2)\n",
    "    lam = 2\n",
    "    zeta = 1\n",
    "    X[0] = X0[1]\n",
    "    X[1] = - lam * X0[0] - zeta * X0[1]\n",
    "    return X\n",
    "\n",
    "# Now that we have defined a function that we want to call, solve the ODE\n",
    "# Calls the function ode_test at each time step and solves for new state\n",
    "# given initial state then repeats at every time step.\n",
    "ode_test_solution = solve_ivp(ode_test, TSpan, X_initial, t_eval=t)\n",
    "T_out = t\n",
    "Y_out = ode_test_solution.y.T  # transpose the solution for indexing later\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(T_out, Y_out)\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Solutions')\n",
    "plt.legend(['Position', 'Velocity'])\n",
    "plt.title('Position and Velocity')\n",
    "plt.grid(True)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(T_out, Y_out[:, 0])  # The \":\" here takes all elements in the rows \n",
    "                              # associated with the first column. This is called\n",
    "                              # index slicing and it is incredibly useful.\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Solutions')\n",
    "plt.legend('Position')\n",
    "plt.title('Just Position')\n",
    "plt.grid(True)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Animate your plots (if time)\n",
    "import matplotlib.animation as animation  # import the standard animation library\n",
    "\n",
    "# Enable an interactive plot in a Jupyter notebook\n",
    "%matplotlib notebook\n",
    "\n",
    "# Define a function to update your animation\n",
    "def update_line(num, t, data, line):\n",
    "    line.set_data(t[:num], data[:num])\n",
    "    return line,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "/* global mpl */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function () {\n",
       "    if (typeof WebSocket !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof MozWebSocket !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert(\n",
       "            'Your browser does not have WebSocket support. ' +\n",
       "                'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "                'Firefox 4 and 5 are also supported but you ' +\n",
       "                'have to enable WebSockets in about:config.'\n",
       "        );\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = this.ws.binaryType !== undefined;\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById('mpl-warnings');\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent =\n",
       "                'This browser does not support binary websocket messages. ' +\n",
       "                'Performance may be slow.';\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
       "    this._root_extra_style(this.root);\n",
       "\n",
       "    parent_element.appendChild(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen = function () {\n",
       "        fig.send_message('supports_binary', { value: fig.supports_binary });\n",
       "        fig.send_message('send_image_mode', {});\n",
       "        if (fig.ratio !== 1) {\n",
       "            fig.send_message('set_device_pixel_ratio', {\n",
       "                device_pixel_ratio: fig.ratio,\n",
       "            });\n",
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       "\n",
       "    this.imageObj.onload = function () {\n",
       "        if (fig.image_mode === 'full') {\n",
       "            // Full images could contain transparency (where diff images\n",
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       "            // there is no ghosting.\n",
       "            fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "        }\n",
       "        fig.context.drawImage(fig.imageObj, 0, 0);\n",
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       "\n",
       "    this.imageObj.onunload = function () {\n",
       "        fig.ws.close();\n",
       "    };\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_header = function () {\n",
       "    var titlebar = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    // Apply a ponyfill if ResizeObserver is not implemented by browser.\n",
       "    if (this.ResizeObserver === undefined) {\n",
       "        if (window.ResizeObserver !== undefined) {\n",
       "            this.ResizeObserver = window.ResizeObserver;\n",
       "        } else {\n",
       "            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n",
       "            this.ResizeObserver = obs.ResizeObserver;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    this.resizeObserverInstance.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'dblclick',\n",
       "        on_mouse_event_closure('dblclick')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus() {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    fig.rubberband_canvas.style.cursor = msg['cursor'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from https://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * https://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"639.9999861283738\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function () {\n",
       "    if (typeof WebSocket !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof MozWebSocket !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert(\n",
       "            'Your browser does not have WebSocket support. ' +\n",
       "                'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "                'Firefox 4 and 5 are also supported but you ' +\n",
       "                'have to enable WebSockets in about:config.'\n",
       "        );\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = this.ws.binaryType !== undefined;\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById('mpl-warnings');\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent =\n",
       "                'This browser does not support binary websocket messages. ' +\n",
       "                'Performance may be slow.';\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
       "    this._root_extra_style(this.root);\n",
       "\n",
       "    parent_element.appendChild(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen = function () {\n",
       "        fig.send_message('supports_binary', { value: fig.supports_binary });\n",
       "        fig.send_message('send_image_mode', {});\n",
       "        if (fig.ratio !== 1) {\n",
       "            fig.send_message('set_device_pixel_ratio', {\n",
       "                device_pixel_ratio: fig.ratio,\n",
       "            });\n",
       "        }\n",
       "        fig.send_message('refresh', {});\n",
       "    };\n",
       "\n",
       "    this.imageObj.onload = function () {\n",
       "        if (fig.image_mode === 'full') {\n",
       "            // Full images could contain transparency (where diff images\n",
       "            // almost always do), so we need to clear the canvas so that\n",
       "            // there is no ghosting.\n",
       "            fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "        }\n",
       "        fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "    };\n",
       "\n",
       "    this.imageObj.onunload = function () {\n",
       "        fig.ws.close();\n",
       "    };\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_header = function () {\n",
       "    var titlebar = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    // Apply a ponyfill if ResizeObserver is not implemented by browser.\n",
       "    if (this.ResizeObserver === undefined) {\n",
       "        if (window.ResizeObserver !== undefined) {\n",
       "            this.ResizeObserver = window.ResizeObserver;\n",
       "        } else {\n",
       "            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n",
       "            this.ResizeObserver = obs.ResizeObserver;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    this.resizeObserverInstance.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'dblclick',\n",
       "        on_mouse_event_closure('dblclick')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus() {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    fig.rubberband_canvas.style.cursor = msg['cursor'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from https://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * https://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"639.9999861283738\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "l, = plt.plot([], [], 'b')  # this code looks like nonsense but stick with it\n",
    "plt.xlim(0, 10)\n",
    "plt.ylim(-1, 1)\n",
    "plt.grid(True)\n",
    "easy_anim = animation.FuncAnimation(fig, update_line, range(0, 1000, 50), fargs=(T_out, Y_out[:, 0], l))\n",
    "\n",
    "# repeat for v\n",
    "fig = plt.figure()\n",
    "l, = plt.plot([], [], 'r')  # this code looks like nonsense but stick with it\n",
    "plt.xlim(0, 10)\n",
    "plt.ylim(-1, 1)\n",
    "plt.grid(True)\n",
    "easy_anim = animation.FuncAnimation(fig, update_line, range(0, 1000, 50), fargs=(T_out, Y_out[:, 1], l))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9 yo\n",
      "8 yo\n",
      "7 yo\n",
      "ya\n",
      "ya\n",
      "4 yo\n",
      "3 yo\n",
      "2 yo\n",
      "1 yo\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "k = 10\n",
    "for i in range(9, 0, -1): \n",
    "    if i == 5 or i == 6:\n",
    "        print('ya')\n",
    "        continue\n",
    "    print(i,'yo')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-4 -3 -2]\n",
      "0.5\n"
     ]
    }
   ],
   "source": [
    "a = np.array([1, 2, 3.5])\n",
    "b = np.array([1, 2, 3])\n",
    "c = 5\n",
    "print(b-c)\n",
    "print(np.max(a-b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10   9\n"
     ]
    }
   ],
   "source": [
    "a=0\n",
    "b=0\n",
    "for i in range(10):\n",
    "\n",
    "    a+=1\n",
    "    if i==9:\n",
    "        break\n",
    "    b=a\n",
    "print(a, ' ', b)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10.]   [10.]\n"
     ]
    }
   ],
   "source": [
    "a=np.zeros(1)\n",
    "b=np.zeros(1)\n",
    "for i in range(10):\n",
    "\n",
    "    a+=1\n",
    "    if i==9:\n",
    "        break\n",
    "    b=a\n",
    "print(a, ' ', b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/henrychang/opt/anaconda3/lib/python3.9/site-packages/matplotlib/animation.py:889: UserWarning: Animation was deleted without rendering anything. This is most likely not intended. To prevent deletion, assign the Animation to a variable, e.g. `anim`, that exists until you have outputted the Animation using `plt.show()` or `anim.save()`.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "ename": "TypeError",
     "evalue": "'tuple' object does not support item assignment",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Input \u001b[0;32mIn [18]\u001b[0m, in \u001b[0;36m<cell line: 3>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      2\u001b[0m b\u001b[38;5;241m=\u001b[39m(\u001b[38;5;241m1\u001b[39m,)\n\u001b[1;32m      3\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(\u001b[38;5;241m10\u001b[39m):\n\u001b[0;32m----> 5\u001b[0m     a[\u001b[38;5;241m0\u001b[39m]\u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m1\u001b[39m\n\u001b[1;32m      6\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m i\u001b[38;5;241m==\u001b[39m\u001b[38;5;241m9\u001b[39m:\n\u001b[1;32m      7\u001b[0m         \u001b[38;5;28;01mbreak\u001b[39;00m\n",
      "\u001b[0;31mTypeError\u001b[0m: 'tuple' object does not support item assignment"
     ]
    }
   ],
   "source": [
    "a=(1,)\n",
    "b=(1,)\n",
    "for i in range(10):\n",
    "\n",
    "    a[0]+=1\n",
    "    if i==9:\n",
    "        break\n",
    "    b=a\n",
    "print(a, ' ', b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The index of disney+ is: 2\n"
     ]
    }
   ],
   "source": [
    "streaming = ['netflix', 'hulu', 'disney+', 'appletv+']\n",
    "\n",
    "index = streaming.index('disney+')\n",
    "print('The index of disney+ is:', index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The index of 15 is: 1\n"
     ]
    }
   ],
   "source": [
    "streaming = ['14', '15', '24', '25']\n",
    "\n",
    "index = streaming.index('15')\n",
    "print('The index of 15 is:', index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "max number is:  25\n",
      "The index of max number is: 3\n"
     ]
    }
   ],
   "source": [
    "streaming = [14, 15, 24, 25]\n",
    "\n",
    "index = streaming.index(np.max(streaming))\n",
    "print('max number is: ', np.max(streaming))\n",
    "print('The index of max number is:', index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 0. 0. 0.]\n",
      " [0. 1. 0. 0.]\n",
      " [0. 0. 1. 0.]\n",
      " [0. 0. 0. 1.]]\n",
      "[[2. 0. 0. 0.]\n",
      " [0. 2. 7. 0.]\n",
      " [0. 0. 2. 0.]\n",
      " [0. 0. 0. 2.]]\n"
     ]
    }
   ],
   "source": [
    "a = np.eye(4)\n",
    "print(a)\n",
    "a[1][2] = 3.5\n",
    "print(2*a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n",
      "5\n"
     ]
    }
   ],
   "source": [
    "a = np.zeros((4,5))\n",
    "b = np.zeros((5,4))\n",
    "print(len(a))\n",
    "print(len(b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-135.0\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "print(np.arctan2(-1,-1)/np.pi*180)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "3.0002710819244385\n"
     ]
    }
   ],
   "source": [
    "# import the builtin time module\n",
    "import time\n",
    "\n",
    "# Grab Currrent Time Before Running the Code\n",
    "start = time.time()\n",
    "\n",
    "time.sleep(3)\n",
    "\n",
    "# Grab Currrent Time After Running the Code\n",
    "end = time.time()\n",
    "\n",
    "#Subtract Start Time from The End Time\n",
    "total_time = end - start\n",
    "print(\"\\n\"+ str(total_time))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 18.33333333   9.33333333]\n",
      " [-23.33333333 -11.33333333]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from numpy.linalg import inv\n",
    "T = np.array([[1., 1.], [-5., -2.]])\n",
    "A = np.array([[0, 1],[-10, 7]])\n",
    "Tinv = inv(T)\n",
    "print(Tinv@A@T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.413410905215903"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-np.sin(2)*np.cos(1)*np.sin(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2946625130576682"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-np.cos(2)*np.sin(1)*np.sin(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.1214843234894742"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.cos(2)*np.cos(1)*np.cos(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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