ode_numeric_approx.ipynb

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   "source": [
    "# Comparision of Numerical Methods for solving ODEs"
   ]
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    "## Intro and Motivation\n",
    "\n",
    "> \"It's a mysterious and marvelous fact that our universe obeys the laws of nature that always turn out to be expressible in the language of calculus as sentences called differential equations.\"\n",
    "-Steven Strogatz. Infinite Powers\n",
    "\n",
    "While this may be an admittedly poetic take on the subject, differential equations do have important applications in physics, engineering, and [computer science](https://arxiv.org/abs/1806.07366).\n",
    "\n",
    "So what exaclty is a differential equation? Well, per [wikipedia](https://en.wikipedia.org/wiki/Differential_equation):\n",
    "> \"In mathematics, a differential equation is an equation that relates one or more functions and their derivatives.\"\n",
    "\n",
    "Seems fairly straight forward right? \n",
    "\n",
    "It is desireable to find an explicit *solution* to these differential equations, or rather, a function who is related to its own derivative in the way described by the differential equation. But sometimes (basically almost all the time), they can be incredibly difficult or impossible to solve.\n",
    "\n",
    "Most introductory courses in ordinary differntial equations (Differential equations that don't involve partial derivatives, we refer to them as ODEs) will introduce several specific types of ODEs for which an explicit solution can be found (such as linear ODEs and harmonic oscilators), as well as techniques to solve simpler ones (such as [seperation of variables](https://en.wikipedia.org/wiki/Separation_of_variables) and [integrating factors](https://en.wikipedia.org/wiki/Integrating_factor).\n",
    "\n",
    "For the differential equations that we don't yet have a known method for solving, we turn to numerical approximation algorithms to give us an idea of what the behavior of the solution is like. These numerical methods can be computationally arduous, so it is preferable to write code to compute them for us.\n",
    "\n",
    "In this notebook, I will introduce a three different approximation algorithms written in python. These are ([Euler's Method](https://en.wikipedia.org/wiki/Euler_method), [Heun's Method](https://en.wikipedia.org/wiki/Euler_method), and the [Runge-Kutta Method](https://en.wikipedia.org/wiki/Runge–Kutta_methods)). We will then measure their respective accuracies against a differential equation that we know the solution for.\n",
    "\n",
    "***\n",
    "## Our Differential Equation\n",
    "\n",
    "Our first step is to define our differential equation.\n",
    "\n",
    "\\begin{equation*}\n",
    "\\frac{dy}{dt} = -2ty\n",
    "\\end{equation*}\n",
    "\n",
    "Why this particular equation you might ask? Well, it just so happens that we have a tool in our arsenal to explicitly solve this differential equation. Having a solution will help us measure the accuracy of our approximations. We will use the [seperation of variables](https://en.wikipedia.org/wiki/Separation_of_variables) technique outlined below.\n",
    "\n",
    "\\begin{align}\n",
    "\\frac{dy}{y} & = -2tdt\\\\\n",
    "\\int \\frac{dy}{y} & = \\int -2tdt \\\\\n",
    "ln(y) &= -t^2 + C \\\\\n",
    "y &= e^{-t^2 + C} \\\\\n",
    "\\end{align}\n",
    "\n",
    "Since y is a function of t, we can express our solution as\n",
    "\n",
    "\\begin{align}\n",
    "y(t) &= e^{-t^2 + C} \\\\\n",
    "\\end{align}\n",
    "\n",
    "For our example, we will use the initial conditions\n",
    "\n",
    "\\begin{align}\n",
    "t &= 0 \\\\\n",
    "y(0) &= 1\\\\\n",
    "\\end{align}\n",
    "\n",
    "Plug these into our solution to find C\n",
    "\n",
    "\\begin{align}\n",
    "1 &= e^{-(0)^2 + C} \\\\\n",
    "\\end{align}\n",
    "\n",
    "Thus C = ln(1) = 0. Therefore we can write our solution as\n",
    "\n",
    "\\begin{align}\n",
    "y(t) &= e^{-t^2} \\\\\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "We will be referencing back to these functions throughout this notebook, so I want to make sure that it is very clear what I will be calling them and what they mean:\n",
    "\n",
    "- When we say say *the equation*, or the *differential equation* we are refering to\n",
    "\\begin{equation*}\n",
    "f(t, y) = \\frac{dy}{dt} = -2ty\n",
    "\\end{equation*}\n",
    "and when we evaluate this function at a specific time (t) and solution value (y) we get the rate of change of the solution, or *slope*\n",
    "\n",
    "\n",
    "- When we say *the solution* we are refering to the antiderivative of the differential equation (its solution)\n",
    "\\begin{align}\n",
    "y(t) &= e^{-t^2} \\\\\n",
    "\\end{align}\n",
    "and when we evaluate this function at a given value for t, we get the *value of the solution* at time t.\n",
    "\n",
    "\n",
    "### Translating into Python\n",
    "\n",
    "Our first step is to translate our differential equation into python. Considering differential equation are functions (in our case, of y and t) it is natural to want to create a function in python to evaluate our ODE at different values of y and t. In this case however, I wanted to use the sympy package as it has some powerful features we can exploit. We will create a sympy expression for our ODE that we will then pass into our approximation algorithm functions later on."
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    "# Imports\n",
    "import sympy as sp\n",
    "import numpy as np\n",
    "\n",
    "# Define our ODE\n",
    "y,t = sp.symbols ('y t') #** don't forget to set y and t as symbols so we can evaluate our expressions\n",
    "our_ode = sp.sympify('-2*t*y')\n",
    "our_solution = sp.sympify('E**(-t**2)')"
   ]
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   "source": [
    "To demonstrate how sympy expressions work, we will use the subs method to pass in the value of 0 in for t into our solution."
   ]
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   "cell_type": "code",
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     "data": {
      "text/latex": [
       "$\\displaystyle 1$"
      ],
      "text/plain": [
       "1"
      ]
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     "execution_count": 2,
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   "source": [
    "our_solution.subs([(t,0)])"
   ]
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    "And we get 1 as expected.\n",
    "\n",
    "Next, we have to define the time parameters.\n",
    "\n",
    "These parameters are \n",
    "- the first time point (denoted t_0)\n",
    "- the last time point (denoted t_n)\n",
    "- the step count (n)\n",
    "- the initial value of y (y_0)\n",
    "\n",
    "We will put these into a dictionary called \"our_params\" just for the ease of passing them into our approximation algorithms down the line.\n",
    "\n",
    "We will also define a function that returns a list of timestamps for which we want to approximate values of our solution. We will see how this will come in handy later down the line."
   ]
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    "# time parameters for our approximation\n",
    "# start time, end time, number of steps, initial value\n",
    "our_params = {'t_0': 0., 't_n': 2., 'n': 10, 'y_0': 1.}\n",
    "\n",
    "# function to return list of timestamps\n",
    "def timestamps(param):\n",
    "    # create list of time stamps\n",
    "    t_0 = param['t_0']\n",
    "    t_n = param['t_n']\n",
    "    n = param['n']\n",
    "    t_points = np.arange(t_0, t_n + (t_n-t_0)/n, (t_n-t_0)/n).tolist()\n",
    "    return t_points[:(n+1)]"
   ]
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    "We will come back to revisit these paramaters when we start coding up our algorithms. But first, we must visit the mathematics of the methods.\n",
    "\n",
    "***\n",
    "## (i) Euler's Method\n",
    "\n",
    "The Euler Method is a rather intuitive approximation method. Consider what we are trying to accomplish at the most fundatmental level. We have a differential equation that models the change in a variable with respect to time, and our goal is to explicitly describe the variable as a function of time that is governed by the rate of change described by our differential equation. Recall that this is generally very difficult (if possible) for most differential equations, so we must come up with a reasonable way to estimate the behavior of our variable with respect to time.\n",
    "\n",
    "Given the inital conditions for time and value, Euler's method attempts to model the values of our solution at specific points in time. The method achieves this in a stepwise fashion, where it approximates the value of the solution at points in time seperated by a constant time interval. These intervals are determined by the number of steps in our algorithm. In our case, we are using 10 steps between time 0 and time 2 by approximating the vaue of our solution at the following time points [0.2, 0.4, 0.6, 0.8, 1, 1.2, 1.4, 1.6, 1.8, 2.0].\n",
    "\n",
    "***The end goal of the approximation algorithm is to get as close as possible to the real value of the solution to our differential equation at time 2 (given the initial conditions).***\n",
    "\n",
    "For our case, the inital time value is 0 and the intial value of y is 1. We can use our differntial equation to get the value of the slope of our solution at these initial conditions. \n",
    "\n",
    "\\begin{equation*}\n",
    "f(t = 0, y = 1) = -2*(0)*(1) = 0\n",
    "\\end{equation*}\n",
    "\n",
    "We find that the slope of our solution at the point t = 0 (with initial condition y = 1 at t = 0) is 0. Euler's method uses this slope value to approximate the value of our solution at the next time point, t = 0.2, using the formula for our differential equation and the length of our time step, 0.2, which we denote using *dt*:\n",
    "\n",
    "\\begin{align}\n",
    "y_{t+1} &= y_t + m_t*dt \\\\\n",
    "y_{0.2} &= y_{0} + m_{0}*dt \\\\\n",
    "y_{0.2} &= 1 + 0*(0.2) \\\\\n",
    "y_{0.2} &= 1 \\\\\n",
    "\\end{align}\n",
    "\n",
    "We now have a value of our solution with which we can approximate a slope at time t = 0.2\n",
    "\n",
    "\\begin{equation*}\n",
    "f(t = 0.2, y = 1) = -2*(0.2)*(1) = -0.4 \\\\\n",
    "\\end{equation*}\n",
    "\n",
    "and can continue the process of approximating subsequent values using the slopes at the previous time points.\n",
    "\n",
    "\\begin{align}\n",
    "y_{0.4} &= y_{0.2} + m_{0.2}*dt \\\\\n",
    "y_{0.4} &= 1 + (-0.4)*(0.2) \\\\\n",
    "y_{0.4} &= 0.92\n",
    "\\end{align}\n",
    "\n",
    "From this point forward, we simply rinse, wash, and repeat to obtain the approximate values of our solution at each remaining time point.\n",
    "\n",
    "### Euler's Method Function\n",
    "\n",
    "For our Euler's Method approximation algorithm, we will define a function that takes in our differential equation as well as the time paramater dictionary we created above as arguments. The function will determine the size of the time step, (*dt* in our explanation above), and will use an approximation function that calculates the predicted value of our solution given the current value, its slope, and our time step. The last part of our function is a simple loop that iterates over our time points and calculates the approximated value of our solution at each point."
   ]
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    "def euler(de, param):\n",
    "    \n",
    "    # size of each time step\n",
    "    dt = (param['t_n']-param['t_0'])/param['n']\n",
    "    \n",
    "    # initilize list\n",
    "    y_hat = [param['y_0']]\n",
    "    for k in range(0, param['n']):\n",
    "        t_k = param['t_0'] + k * dt\n",
    "        y_k = y_hat[len(y_hat)-1]\n",
    "        \n",
    "        # calculated estimated value\n",
    "        y_k_hat = y_k + de.subs([(y,y_k), (t,t_k)]) * dt\n",
    "        \n",
    "        # append estimated value\n",
    "        y_hat.append(y_k_hat)\n",
    "        \n",
    "    return np.array(y_hat).tolist()\n",
    "\n",
    "our_euler_approx = euler(our_ode, our_params)"
   ]
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   "cell_type": "markdown",
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   "source": [
    "### Analyzing the Performance of Euler's Method\n",
    "\n",
    "The accuracy of numerical approximation algorithm is generally measured by the difference between the predicted value of the solution at the final time point. In our case, we want to see the difference between our approximate value at time 2 and the real value at time 2. We will report the error as the absolute value of the difference to avoid reporting negative values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0127890466726292\n"
     ]
    }
   ],
   "source": [
    "# value of euler's method approximation at the last time_step\n",
    "euler_at_n = our_euler_approx[-1] \n",
    "# value of the solution at the last time step\n",
    "solution_at_n = our_solution.subs([(t,our_params['t_n'])]).evalf()\n",
    "\n",
    "# error\n",
    "euler_error = abs(euler_at_n - solution_at_n)\n",
    "print(euler_error)"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "We see that the absolute error for our Euler's Method approximation is 0.0128. This is a pretty good result, and we will compare this result with the error from other algorithms down the track.\n",
    "\n",
    "### Plotting Euler's Method Solution\n",
    "\n",
    "Above we determined the error of our Euler's Method approximation algorithm. While knowing how close we ended up getting is very important, I personally believe it is worth while looking at how we got there. In order to achieve this, let's create a function that will plot our approximation against the actual solution values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot Function\n",
    "%matplotlib notebook\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('ggplot')\n",
    "\n",
    "def plot_approx(approx, param, approx_lab, color):\n",
    "    # time stamp\n",
    "    time_stamp = timestamps(param)\n",
    "\n",
    "    # solution (more granular than our time step for plotting purposes)\n",
    "    solution_time_stamp = np.arange(0,2,0.01)\n",
    "    solution_array = [our_solution.subs(t,x) for x in solution_time_stamp]\n",
    "\n",
    "    # Plot\n",
    "    fig=plt.figure()\n",
    "    ax=fig.add_subplot(111)\n",
    "\n",
    "    ax.plot(solution_time_stamp, solution_array, c='k', label=\"Solution\",fillstyle='none')\n",
    "    ax.plot(time_stamp, approx, c=color, label=approx_lab,fillstyle='none')\n",
    "    ax.set_title(label = 'Numerical Approx via '+approx_lab)\n",
    "    ax.set_xlabel(xlabel = 't')\n",
    "    ax.set_ylabel(ylabel = 'y(t)')\n",
    "\n",
    "    plt.legend(loc=3)\n",
    "    plt.show()"
   ]
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       "                    '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 (width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    resizeObserver.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",
       "    // 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",
       "    var cursor = msg['cursor'];\n",
       "    switch (cursor) {\n",
       "        case 0:\n",
       "            cursor = 'pointer';\n",
       "            break;\n",
       "        case 1:\n",
       "            cursor = 'default';\n",
       "            break;\n",
       "        case 2:\n",
       "            cursor = 'crosshair';\n",
       "            break;\n",
       "        case 3:\n",
       "            cursor = 'move';\n",
       "            break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = 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",
       "            /* 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",
       "            evt.data.type = 'image/png';\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",
       "                evt.data\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 http://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",
       " * http://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.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\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",
       "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, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"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.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",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['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.one(\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",
       "\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",
       "    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",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager) {\n",
       "        manager = IPython.keyboard_manager;\n",
       "    }\n",
       "\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"
    },
    {
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\" width=\"639.999990463257\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_approx(our_euler_approx, our_params, \"Euler's Method\", 'r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is interesting to observe how close the approximations were at each time step. As we move forward, we will be able to compare more sophisticated algorithms to Euler's Method and see how the accuracy improves.\n",
    "\n",
    "***\n",
    "\n",
    "## (ii) Heun's Method\n",
    "\n",
    "Heun's Method is very similar to Euler's Method in the sense that it is using the slopes from our differential equation at specific time points to approximate the values of the solution, but there is one key difference.\n",
    "Recall in Euler's Method how we used the following equation to approximate the value of the solution at an aribtrary time point: \n",
    "\n",
    "\\begin{equation*}\n",
    "y_{t+1} = y_t + m_t*dt \\\\\n",
    "\\end{equation*}\n",
    "\n",
    "Where dt is the change in time, and m_t is the value of the differential equation at the given time and value:\n",
    "\n",
    "\\begin{equation*}\n",
    "m_t = f(t, y_t) = -2*t*y\n",
    "\\end{equation*}\n",
    "\n",
    "The difference in Heun's Method is that it uses the average of the slope at time t and time t+1 to approximate the value of the solution at time t. The recursive equation looks like this:\n",
    "\n",
    "\\begin{equation*}\n",
    "y_{t+1} = y_t + \\frac{(m_t + m_{t+1})}{2} *dt \\\\\n",
    "\\end{equation*}\n",
    "\n",
    "But how do we know what the value of the slope is at time t+1 if we don't yet know the value of the solution at time t? Well, we can use Euler's Method! In this algorithm, we utilize Euler's Method to move one time step forward (t+1), calculate the slope at that time point, and then go back to time t and use the average of our slope at t and T+1 to calculate the value of our solution at time t+1. \n",
    "\n",
    "To paint a better picture of what is going on, I like to use the analogy of the Rectangle Rule vs the Trapazoid Rule for approximating integrals (essentially our whole task is to approximate the integral of a derivative). Euler's Method is analogous to a Rectangle Rule and Heun's Method is analogous to the Trapazoid Rule. For a refresher on what I am referencing here, you can read more on numerical integration techniques [here](https://en.wikipedia.org/wiki/Numerical_integration).\n",
    "\n",
    "I know that can seem confusing. I have outlined the steps below for your reference to hopefully make the process more clear.\n",
    "\n",
    "##### STEPS FOR APPROXIMATING SOLUTION VALUES USING HEUN'S METHOD\n",
    "1. Calculate the value of the slope at time t from the differential equation.\n",
    "2. Use the slope from (1) to calculate the value of the solution at time t+1 using Euler's Method.\n",
    "3. Calculate the value of the slope at time t+1 from the differential equation using the value approximated from (2).\n",
    "4. Go back to time t and approximate the value of the solution at time t+1 using the average of the slopes calculated from (1) and (3).\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "### Heun's Method Function\n",
    "\n",
    "The function for our Heun's Method algorithm is very similar to the function we used for our Euler's Method algorithm, (this makes sense considering the two algorithms are effectively the same sans one term). The additions we have to make are in our *y_approx* function. We add a y_k_m term which is our approximation of the solution at time t+1 using our slope m, the m2 term which is our slope approximated at time t+1, and then we add the average of m and m2 in the returned value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def heun(de, param):\n",
    "    \n",
    "    # size of each time step\n",
    "    dt = (param['t_n']-param['t_0'])/param['n']\n",
    "\n",
    "    # initilize list\n",
    "    y_hat = [param['y_0']]\n",
    "    for k in range(0, param['n']):\n",
    "        t_k = param['t_0'] + k * dt\n",
    "        y_k = y_hat[len(y_hat)-1]\n",
    "        \n",
    "        # calulcate estimated value\n",
    "        m = de.subs([(y,y_k), (t,t_k)])\n",
    "        y_k_m = y_k + m * dt\n",
    "        m2 = de.subs([(y,y_k_m), (t, t_k+dt)])\n",
    "        y_k_hat = y_k + ((m + m2)/2) * dt\n",
    "        \n",
    "        # append estimated value\n",
    "        y_hat.append(y_k_hat)\n",
    "        \n",
    "    return y_hat\n",
    "\n",
    "our_heun_approx = heun(our_ode, our_params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Analyzing the Performance of Heun's Method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00693415601778322\n",
      "Heuns Method Imrovement: 45.78%\n"
     ]
    }
   ],
   "source": [
    "# value of euler's method approximation at the last time_step\n",
    "heun_at_n = our_heun_approx[-1] \n",
    "# value of the solution at the last time step\n",
    "solution_at_n = our_solution.subs([(t,our_params['t_n'])]).evalf()\n",
    "\n",
    "# error\n",
    "heun_error = abs(heun_at_n - solution_at_n)\n",
    "\n",
    "# error comparision\n",
    "print(heun_error)\n",
    "print('Heuns Method Imrovement: ' + str(round(100*(1-heun_error/euler_error),2)) + '%')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we use Heun's method over Euler's method, we decreased our absolute error by over 45 percent!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "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_dpi_ratio', { dpi_ratio: fig.ratio });\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",
       "    if (this.ratio !== 1) {\n",
       "        fig.send_message('set_dpi_ratio', { dpi_ratio: this.ratio });\n",
       "    }\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",
       "    var resizeObserver = new 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 (width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    resizeObserver.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",
       "    // 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",
       "    var cursor = msg['cursor'];\n",
       "    switch (cursor) {\n",
       "        case 0:\n",
       "            cursor = 'pointer';\n",
       "            break;\n",
       "        case 1:\n",
       "            cursor = 'default';\n",
       "            break;\n",
       "        case 2:\n",
       "            cursor = 'crosshair';\n",
       "            break;\n",
       "        case 3:\n",
       "            cursor = 'move';\n",
       "            break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = 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",
       "            /* 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",
       "            evt.data.type = 'image/png';\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",
       "                evt.data\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 http://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",
       " * http://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.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\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",
       "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, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"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.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",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['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.one(\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",
       "\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",
       "    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",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager) {\n",
       "        manager = IPython.keyboard_manager;\n",
       "    }\n",
       "\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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iZXaTmchXMnlK9kCwFU/xRrFB60cGW0vrTbRqgWt2rm2aZILAOqTtBpEq2C0ZJ9acq36uPbq3fOldBFQcgFAMUMxQrxRf3Il1+uwrlU411YMnwHw0uBv0SwLAIvE+WKx1CZqmnhdB3jcBQDt69HgQXu5NHjSciMtO5NooCc+GQKAeKLTwPS0Sfvf9PRIp/tJdNBBQbpVj15zomRUAFBe97cAaLKjlQQ6MEX7tDRJ08BFT7z0FEVbAPQESDzQ2wC0R25GANAeMg3GqR0AowmSnvSITzp4mfwtADrIRwMxDerEqes9b/e3AIgD11sAtG9KbXIt36d1h4PrLQASWHQegEQDTZJ0vsL1FgCJPFq6p2V8OodBp73pdDnxQE+RrtcNU4tp10Ew2kahV9Vo0nXf206+AmCUe6MTYloCgP5Gp9PpkCP5ndpH7aFzFnT+hFa5atasKaog3mkVh14PpLbQPjnt8xO/dgUAnYWhWCa/UZ8i0Un100oLvWlBryVaaa+rTHIBQOc4yB7FHMUmxTr5lXxDZwhI/JGoJ8FHhzbpoCm1n3DRGQ7yoxEBQPZdbwFQXNG5H5rkqS+5vwVAtuk1Wzr3QuKADiDS6gy/BeCLM8V/mFgA+LZ/TKFLTQDQEzOtAtCZgOTLyDQ4Ucd2PUnR4Egd2P2KUzsrAK4G0EBLddPhJhq8aACmLQmamFxPMGYEANVLy6NUJz3d0MBGAxBNiK6T73QHAAkfahudWqd38mkVgNpjRgDQ4EqHwFwHB5M7xXXw0XX7ouseAFqepYmZnpLoND0N1O4nxF280soBTdJ0NsH9HgDXRT+eLnGid7jd7wEgQUc+JFHkegWQXu9yv/KV9ppJJNC2BU1SnhLlpbqI3+SH81I6BGiEeysTYmpXAdOBSXrKJq5pYqPX8GiCpNcVabWIEglbEgm0dUJbG3Smg1Y0KF7sCgCKD/ItiUQ6MEl7/rS1RW+4uJ8ZSanNaZ15SE0A0O9pH54EO72iR/hpj55WuOiwJ/nJde6ABCWtkJAIpnYnvwfAPS5SOitB/ZV8nvweAOpb7odc6a0JOhBIwp6wULtpNZFEGJ8B8NTDvPN3FgDe4Z2tpmMGXAKADsOlldI6oJWO6eGmMQPMgI8wwALARxzBMNIPAywA0o8vuSXMQHpmgAVAevYut80rDLAA8ArtbJQZYAZMMsACwCRhnJ0ZYAaYAWaAGUgPDLAASA9e5DYwA8wAM8AMMAMmGWABYJIwzs4MMAPMADPADKQHBlgApAcvchuYAWaAGWAGmAGTDLAAMEkYZ2cGmAFmgBlgBtIDAywAAHFBht2LKujmK7pkRqfEmNV4i3lmntNigONDn/igS6boQ1vpJbEAAMQVuHYFAN30RnfG65QYsxpvMc/Mc1oMcHzoEx8kAOgrj+klsQBgAaBVLPNgqcZdzLManskKc62Gaxk8swBQ4yulVngFQCndtozJ6MS2AFgozJgtkGahiI48swCw4GiLRWTEBwsAi+T7cjEWAL7snaTYZHRi1a1lzGoY15FnFgBqYkMWzywA1PlLmSUWAMqotm1Ix0GeMdt2u6EKdORZ1sRkiCCJmXTkWgZmFgASg8hXqmIB4Cue8IxDRif2bEVuDsYsl8/UatORZxYAamJDFs8sANT5S5klFgDKqLZtSMdBnjHbdruhCnTkWdbEZIggiZl05FoGZhYAEoPIV6piAeArnvCMQ0Yn9mxFbg7GLJdPXgFQw2daVvw1plkAKI69mTNn4vfff8eFCxcwduxYFCxYMEUE69atw5IlS8T7/A899BC6dOmCwMBAQ2hZABiiyScy+evAo5p85lkd48y1Gq5l8MwCQI2vEq3s27dPvCc7ePBgvPnmmykKALqB791338WoUaOQLVs2jB49GhUqVMCTTz5pCC0LAEM0+UQmGZ1YdUMYsxrGdeSZtwDUxIYsnlkAqPNXEku9evVKVQB8//334hpeeuqntHPnTtDvhgwZYgitXQEw+YfJyBaSDfmRH5lDMiNTpkzImTMn8uTJg9DQUEMYvJFJxwGTMauJFOZZDc+yJiZ1aO9a8tf4YAGgOtL+315aAoC2CXLlyoXmzZuL3CdPnsTIkSMxadIkQ2jtCoCiHxXF7fDbQBSAQwAOAvgHQCyEAKC7o4sWLYpixYqJf0uXLo0yZcoIoeDN5K+dWDXnzLMaxnXk2Z8nUzVR8Z8VGfHBAkC11wwKgNy5c6NZs2Yi94kTJ8R2QEoCYPny5aAfSiEhIRg/fjzi4uIst4rOHIz/bjx+Pv0zdt7YibNxZ0VdQQlBiLgRgbAzYYjdG4tje48hNjY20U5wcDDKli2LqlWrom7duqhTpw6yZ89uGYeVggEBAYiPj7dS1GtlGLMa6plnNTyTFeZaDdeyeDZ6tkxNq+xZ0eZbAL68BeCu4v+5+g/WHF+D1cdWY9vZbYhLuCsuyucpj8rhlVEwuiD+PfQvdu/ajd27d+PSpUvi7xSc5cuXF2KgSZMmKFGihD3PGigtQxEbMCM1C2OWSmeqlTHPanh2HzvUWbRvyV/jg1cA7MeOpRrSEgD0FT46JOh+CJAm06eeesqQLbtbAKl14n9v/YtfTv4ixMDPJ35GVCztEQCRWSPxVKGn8GTBJ5HvVj5s2bQFGzZswKZNmxAVdTdPyZIl0bhxY7Rq1UpsGziR/LUTO8FlWnUyz2oY15FnFgBqYkMWzywA1PlLWJo+fTp27NiBK1euICwsTCzbT5w4EVOnTkWlSpXED6WffvoJS5cuTfIaYFBQkCG0TgkAd+MxcTHYenYr1hy7uzpw8vpJ8efwjOGoG1lXiIGaETWxb+c+sUXxww8/JK4OVKtWDW3bthWCIHPmzIbaZCSTjgMmYzbiWft5mGf7HBqtgbk2ypS9fDJ4ZgFgzwc+WVqFAHBvOJ0bOPDvASEESBDsurBL/DkwQyCqRlQVqwOP538cp/acwoIFC7By5UrExMSIVxzbt2+Pzp074/7777fNpYwOYRuEyQoYs0nCLGZnni0SZ6EYc22BNAtFZPDMAsAC8b5eRLUASM7HuZvn8NPxn4QY2HhqI27F3RJZSmYvKcRA1RxV8ff6vzFn9hz8/fffoJWNpk2bokePHuLSI6tJRoewattqOcZslTlz5Zhnc3zZyc1c22HPeFkZPLMAMM63Njm9LQDciYq+Ey1EAK0OkCi4EH1B/Dl35tx4IvIJ5LuSD9u+3oatG7eK3zdo0ACvvfaaJSEgo0OodjJjVsM486yGZ7LCXKvhWgbPLADU+EqpFV8SAO4Nj0+Ix+4LuxO3CmjbgFKmwEwoG1YWN3bewN7Fe8X9Aw0bNhQXJZl5e0BGh1DqKB4sldHNsaGMahYAiqiWEdMsABQ5S6UZXxUAyTk4fu144iuGW89sxZ2EOyJL+PVwXNt2DQGHA9C+Xnv0f70/6F4ET0lGh/BkQ/bfGbNsRlOuj3lWwzOvAOjFMwsAdf5SZkkXAeBOyNXbV5O8Yng15urdP18Fgo8E47kyz2Fo16HImDFjqjzyIK8mxJhn5jktBjg+9IkPFgBqfKXUio4CwJ2g2PhYcekQnRtYsn8JLsZdBBKAXDtzYXL7yahZs2aKfPLAoybMmGfmmQWAmhhwmmcWAN73o3QEugsAd0LoFcNdZ3ah07JOuBRwCdgFNA9qjqHvDhUfJ3JPPDFJDyUWWmooTTc88xaAuoCRMd6xAFDnL2WW0pMAcJF2LeYaXlzxIrZc3AIcB8JXhWP4oOFo0aIFKIh54FEWXnzISxHVMgZ4RVBZiHuBaBnxwQLAC45z2mR6FADEWVx8HIZtG4bP/vwMAdcCEP9VPOqXq48RI0aISUlGh3DaN8nrZ8xqGGee1fDMQlwvnlkAqPOXMkvpVQC4CFxwcAEGbByAhDsJiPs2DtnPZsfo0aPx4osvgr6joFPiiUmNt5hnNTyzANCLZxYA6vylzFJ6FwBE5Paz2/HSmpdw6dYlZN6cGdGro9GtWzcMGDBA6vcFnHYaT0xOM3y3fuZZDc/MtV48swBQ5y9llvxBABCZJ6NOotPqTth/eT9yn8mNizMuomTRkpgyZQoefPBBZXzbMcQTkx32jJdlno1zZTcnc22XQWPlZfDMAsAY11rl8hcBQE65EXsDfX7ugx+O/YD8GfLjzMdnEHwrWHxOuWPHjokHBH3VgTI6seq2MWY1jOvIM68AqIkNWTyzAFDnL2WW/EkAEKl0xfCYHWMwYfcE5AzOieCFwTi365z43PC4ceOQJUsWZdybNaTjIM+YzXrZWn4deZY1MVljzHopHbmWgZkFgPWY8dmS/iYAXI5Yd2EduizrIv639KHS2DVnFx544AHMmDEDRYoU8Ul/yejEqhvGmNUwriPPLADUxIYsnlkAqPOXMkv+KgBowPzhzx/E4UD6JHGNuBrYNGwTwsPCMWnSJDz++OPKfGDUkI6DPGM26l17+XTkWdbEZI8586V15FoGZhYA5mPF50v4swCg1wDP3DiDF1e/iP9d/B8qZ62MQyMP4dqla+INgVdeecWnzgXI6MSqA5Ixq2FcR55ZAKiJDVk8swBQ5y9llvxdABDR0Xei0W99P3x/5HuUCCuBhHkJOPz7YTRq1AgTJkzwmVcFdRzkGbOarqwjz7ImJjUM/2dFR65lYGYBoDrSFNhjAXCXZPqOwPhd4zH297HIFZILpXaXwqb5m1CuXDnMmjXrnm8JKHDNPSZkdGLVuBmzGsZ15JkFgJrYkMUzCwB1/lJmiQVAUqpX/LMCfX/pK64Srh1VG2vGrEFkZCTmzJmDEiVKKPNLSoZ0HOQZs5qQ0ZFnWROTGoZ5BYAFgOpIU2CPBcC9JO+5uAedV3fG6RunUSe4Dja8twFhWcIwbdo0VK9eXYFXUjah4yDPmNWEi448swBQExuyeGYBoM5fyiyxAEiZ6vM3z4s3BHae34nyWcrjr5F/4fa12xg7dixat26tzD/uhnQc5BmzmlDRkWdZE5MahnkFgAWA6khTYI8FQOok37pzC2/++iYW/rUQhUILIXpGNM4fPI+BAweid+/eCryT1ISOgzxjVhMmOvLMAkBNbMjimQWAOn8ps8QCIG2q6XDg1P9NFZ8WDg8OR7Yfs+H4huN4+eWX8fbbbyt9TVDHQZ4xq+nKOvIsa2JSwzCvALAAUB1pCuyxADBG8ppja9Dr5164fec28v+RH8cWHUO7du0wcuRIBAYGGqvEZi4dB3nGbNPpBovryDMLAIPOlZBNRnywAJDgCF+rggWAcY8cuHxAHA48HnUc+U/mx6mZp9CkURNxV0CmTJmMV2Qxp4xObNG05WKM2TJ1pgrqyDMLAFMutpVZRnywALDlAt8szALAnF8u37qMrmu6YuvZrch9NTcufnoRtavWxvTp0xEaGmquMpO5ZXRikyZtZ2fMtik0VIGOPLMAMORaKZlkxAcLACmu8K1KWACY90dMXAwGbRqEeQfnISwmDFGfRaFSkUqYO3cuwsLCzFdosISMTmzQlLRsjFkalWlWpCPPLADUxIYsnlkAqPOXMkssAKxRTYcDZ+6diSFbhyAoLggxc2NQIXsFfPXVVwgPD7dWqYdSOg7yjNmRULinUh15ljUxqWH4Pys6ci0DMwsA1ZGmwB4LAHskrz+5Hj3W9kDU7SgkrEpAudhy+Hre146IABmd2F5rzZdmzOY5s1JCR55ZAFjxtLUyMuKDBYA17n26FAsA++45fOWwOBx45OoRYAfwyKlHMP+r+ciWLZv9yt1qkNGJpQIyUBljNkCShCw68swCQILjDVYhIz5YABgkW6dsLADkeOvK7SvoubYnNpzaABwFSu8pjW9mfYMcOXLIMQBARieWBsZgRYzZIFE2s+nIMwsAm043UVxGfLAAMEG4LllZAMjz1J34O3h/6/uYsXcG8C9QfHtxLPl8iTQRIKMTy2utsZoYszGe7ObSkWcWAHa9bry8jPhgAWCcb21ysgCQ76q5++di4MaBiI+JR9FdRbFy/EopbwfI6MTyW5t2jYxZDeM68swCQCCi4GoAACAASURBVE1syOKZBYA6fymzxALAGao3n96MDss64FaGWyh4oCDWDVuHzJkz2zKm4yDPmG253HBhHXmWNTEZJklSRh25loGZBYCkAPKlalgAOOeNo1ePovFXjXEl+ApKHiiJH4b/YOvGQBmd2LnWplwzY1bDuI48swBQExuyeGYBoM5fyiyxAHCW6os3L6L6rOq4HngdFfdXxHdjvkNwcLAlozoO8ozZkqtNF9KRZ1kTk2mybBbQkWsZmFkA2AwcXyzOAsB5rxy8fBD1v6mP2NhY1DlSB7PHzrb0ASEZndj51ia1wJjVMK4jzywA1MSGLJ5ZAKjzlzJLLADUUL3++Hq0X9UeCdcS0OJiC0waOcn0p4R1HOQZs5r40pFnWROTGob/s6Ij1zIwswBQHWkK7LEAUEDy/5uYu3cu3tz8JnAS6BHSA+8OfNeUcRmd2JRBCZkZswQSDVShI88sAAw4VlIWGfHBAkCSM3ypGhYAar3x/qb38dm+z4C9wODSg9G9W3fDAGR0YsPGJGVkzJKI9FCNjjyzAFATG7J4ZgGgzl/KLLEAUEa1MBSfEI+XVr2E1adWAxuBT5p9gtatWxsCoeMgz5gNudZ2Jh15ljUx2SbPZAU6ci0DMwsAk4GiQ3YWAOq9FH0nGi0Wt8CeK3uQ4fsMmNV3FurVq+cRiIxO7NGI5AyMWTKhqVSnI88sANTEhiyeWQCo85cySywAlFGdxNCFmxfQ4LsGOHvjLIK/Cca3o75F5cqV0wSj4yDPmNXEl448y5qY1DD8nxUduZaBmQWA6khTYI8FgAKSUzFx6N9DaLK4CW7cuIGwBWFY9sUylChRIlVAMjqx6tYyZjWM68gzCwA1sSGLZxYA6vwlLNHkPHnyZERFRSE0NBS9evVCgQIFkqBISEjA3LlzsWvXLgQEBIg757t3746IiAhDaFkAGKLJsUz09cDnVz6PuH/jcP/K+7Hy25XIkydPivZ0HOQZs2Ohk6RiHXmWNTGpYZhXAFgAKI60oUOHonbt2qhTpw62bt2KZcuWYdiwYUlQbN++HYsXL8b777+PoKAgfPfddzh27Bj69etnCC0LAEM0OZpp3oF5eGPjG8AJ4OGdD2PRN4uE4EuedBzkGbOjoZNYuY48swBQExuyeGYBoM5fuHr1Kvr27YsZM2aIW+PoSb9bt25CAOTNmzcRCQmAb775RgiAkJAQfPXVV4iLi0PHjh0NoWUBYIgmxzMN+20YpvxvCrAHqHe1HmbOmHnPbYE6DvKM2fHQEQZ05FlX3DpyLQMzCwA1fVlYOXLkCCZOnIhx48YlWh04cCA6dOiA0qVLJ/4uPj4es2fPxtq1a4UAyJkzJ2jlgP7bSGIBYIQl5/PQ64Hdf+qOlUdXAhuAjpEdhdijTudKMjqx8y1JaoExq2FcR55ZAKiJDVk8swBQ5y8hACZNmoSPP/44TQHw999/Y8GCBWK1gD43O2/ePLF6QOcFkqfly5eDfiiRQBg/frxYLbCb6OwBCRGdki9ivhl7E4/Pfhw7zuwAlgCjnhuF119/PZFWX8TsyeeM2RNDcv6uI8/Uch1x+zNmWo1OLylDAq2r+2iiSbxPnz6YOfPuUnBqWwC0RZA7d240b95ctOTEiRMYMWIEpkyZYqhlvAJgiCZlmc7fPI9GixvhTNQZYA4w9a2paNq0qbCv41MeY1YTOjryzDGtJjZk8cwrAOr8JSwNGTJEHABM6xAgPdH/8ccfePPNN8UhwCVLlmD//v2g7QIjiQWAEZbU5jlw+QCaLW2GmzduImhWEL6Z8g2qVKnCAkCRG3ScTHXELGtiUhQWiWZ05FoGZhYAiiPt9OnT4jXA69evi+V9WtaPjIzE1KlTUalSJfFDn5ilVYADBw4IAZAjRw507do1yUHBtGCzAFDsVIPm1p9cj+dXPY+EKwnijoAV36xAtWrVcO7cOYM1+EY2GQOP6pYwZnWMM9dquJbBMwsANb5SaoUFgFK6TRmbs38O3vr1LfF6YOH1hbF9y3bExMSYqsPbmWUMPKrbwJjVMc5cq+FaBs8sANT4SqkVFgBK6TZt7P2t7+OzPz8D/gTq/lsXX8z8AsHBwabr8VYBGQOPauyMWR3jzLUarmXwzAJAja+UWmEBoJRu08bi4uPQ9aeu+PHYj8B64IXIFzB8+PAkrwearlRhARkDj0K4whRjVsc4c62Gaxk8swBQ4yulVlgAKKXbkjF6PbDVslb489KfwGLgwzYfonPnzpbqUl1IxsDDmD0zoCPPLLY8+1VWDhnxwQJAljd8qB4WAD7kjDSgnLt5Dk2XNsWpq6eQYW4GfDXsK3FNtK8nGQOP6jYyZnWMM9dquJbBMwsANb5SaoUFgFK6bRk7h3OoMbMGom9EI3ReKFbMXpHm1wNtGZNUWMbAIwmK4WoYs2GqbGdkrm1TaKgCGTyzADBEtV6ZWADo4y/qxF/v+Bov/PACEi4loMCPBbDqu1Xi+mdfTTIGHtVtY8zqGGeu1XAtg2cWAGp8pdQKCwCldNsy5urEs/bNwqBNg4BjQJUDVbBg3gJkzJjRVt1OFZYx8DiFLbV6GbM6xplrNVzL4JkFgBpfKbXCAkAp3baMuXfi97a8h+l7pgN/AO1C22HM6DG26naqsIyBxylsLABUM3uvPY4PNT6QwTMLADW+UmqFBYBSum0Zc+/E9HrgS6tfwpoTa4CfgRENRuCFF16wVb8ThWUMPE7gSqtOxqyOceZaDdcyeGYBoMZXSq2wAFBKty1jyTsxvR7YfElz7LuyDwFLArBw8EJUrVrVlg3ZhWUMPLIxeaqPMXtiSN7fmWt5XDotalkAqPGVUissAJTSbctYSoPl2Rtn0WBhA1y4eQHZlmbDmhlrkD9/flt2ZBbmAV4mm6nXpSPP1BodcfsrZhYAavqyUissAJTSbctYagPP3kt70XRxU9y+cRsPbHwAK+asEB+P8oXkr4Olau515JkFgLookREfLADU+UuZJRYAyqi2bSitTrz2+Fp0/KGjeD2wybkmmDpuqk9cFyxj4LFNnMkKGLNJwmxkZ65tkGeiqAyeWQCYIFyXrCwAdPGU5+XSmXtm4t0t7wJHgXcKvYOe3Xp6vXEyBh7VjWDM6hhnrtVwLYNnFgBqfKXUCgsApXTbMmakE7+1/i3MOTRHvB44r808r18XbASzLVIcKMyYHSA1lSqZazVcy+CZBYAaXym1wgJAKd22jBnpxPR64LNLnsWWS1sQsjkE64asQ6FChWzZtVPYCGY79TtRljE7wWrKdTLXariWwTMLADW+UmqFBYBSum0ZM9qJb8TeQL159XA85jju33I/fpn4C7JkyWLLttXCRjFbrd+JcozZCVZZAKhj9V5LMmKaBYA3PeiQbRYADhHrQLVmOvHp66dRd15dXI+7jmp/VcO3H33rlUOBZjA7QJmlKhmzJdosFWKuLdFmupAMnlkAmKbd9wuwAPB9H7kQmu3Ef174E42/a4y4W3HoHtQdg3sPVt5Ys5iVA0zBIGNW5wXmWg3XMnhmAaDGV0qtsABQSrctY1Y68bJDy9Dj5x7AZWDao9PQqG4jWxjMFraC2awN2fkZs2xGU6+PuVbDtQyeWQCo8ZVSKywAlNJty5jVTjxq/ShMODQBQSeC8EuXX1CkYBFbOMwUtorZjA3ZeRmzbEZZAKhjNGVLMmKaBYC3veiAfRYADpDqUJVWO3FCQgJeWPAC1kWtQ45jObB90HZlNwVaxewQhYaqZcyGaJKSibmWQqPHSmTwzALAI836ZWABoI/P7HTiO/F3UOvTWjiW8RjKXiiLlW+vVNJwO5iVAEzBCGNWxzxzrYZrGTyzAFDjK6VWWAAopduWMbud+Oqtq6j8aWXcyHoDnTN1xocvfGgLj5HCdjEbsSE7D2OWzShvAahjlLcAjHKdIYHWRv08sQDQJwBkTEx7TuxBwyUNEY94TK8yHQ2rNnSUABmYHQXIKwCq6U1ij+NDDf0yeOYVADW+UmqFBYBSum0Zk9GJCcAXG77AOwfeQdDlIGx+cTPy53Xu88GyMNsizmRhxmySMBvZmWsb5JkoKoNnFgAmCNclKwsAXTzl+WNAZlrS5csuWBWzCnnP5MX2t7cjKCjITHHDeWUMPIaNScrImCURaaAa5toASRKyyOCZBYAER/haFSwAfM0jqeOR0YldtccnxKPa+Go4mfUkal+vjXmvzXOECJmYHQGYQqWMWRXTckWtKtT+Gh8sAFRFmEI7LAAUkm3TlOyB50LUBVSZXgUxmWPw9v1vo1ezXjYR3ltcNmbpAFkAqKA0VRscH2rol8EzCwA1vlJqhQWAUrptGZPRiZMDWL9/Pdr93A4ZbmXA4oaLUfnByrYwJi/sBGapAFkAOE1nmvVzfKihXwbPLADU+EqpFRYASum2ZUxGJ04JwIjlIzDpzCRkPpcZv/f9HdnCstnC6V7YKczSALIAcJJKj3VzfHikSEoGGTyzAJDiCt+qhAWAb/kjLTQyOnFq9Tef2hw7Aneg2LliWD9ovbQvBzqJ2SnPMWanmL23XuZaDdcyeGYBoMZXSq2wAFBKty1jMjpxagBu37mNChMq4ErYFTyDZzCu6zhbWF2FncQsBSCvADhFo6F6OT4M0WQ7kwyeWQDYdoPvVcACwPd8khoiGZ04rdYePn8Yj89/HHEBcZhYdiJa1WxlmxynMdsGyALACQoN18nxYZgqWxll8MwCwJYLfLMwCwDf9EtKqGR0Yk+tXbB1Afr90Q+BVwOx/vn1KHK/vS8HqsDsqU1m/86YzTJmPT9zbZ07MyVl8MwCwAzjmuRlAaCJo6Dunene83pj8Y3FyHk2J3a+tRPBwcGWSZIx8Fg2brEgY7ZInIVizLUF0iwUkcEzCwALxPt6ERYAvu6h//DJ6MRGWkufyKjxSQ0czXIU1aKqYWG/hUaKpZhHFWbLAFMoyJhlspl2Xcy1Gq5l8MwCQI2vlFphAaCUblvGZHRiowD+vfEvKn1WCbey3MLreV9Hv5b9jBZNkk8lZksAWQDIos1SPRwflmgzXUgGzywATNPu+wVYAPi+j1wIZXRiM63dfGgznlnzDHAH+Lbet6hWppqZ4iKvasymAbIAkEGZ5To4PixTZ6qgDJ5ZAJiiXI/MLAD08JO3JtOPVn6Ej099jJCLIfi99+/IHpbdFGEyBh5TBiVkZswSSDRYBXNtkCib2WTwzALAphN8sTgLAF/0SsqYZHRiK61t9Wkr/Bb0G4peLIoNb20wdUmQtzBbaae3VlrsYNUZs7dErV2+/TWmWQDYjRwfLM8CwAedkgokbw08MXdiUGF8Bfyb7V+0DmyNT178xDBp3sJsGGAKGRmzHfbMlWWuzfFlNbcMnlkAWGXfh8uxAPBh5ySDJqMTW23tkXNHUOfrOojLGIfxD49Hm5ptDFXlTcyGALIAsEqTlHIcH1Jo9FiJDJ5ZAHikWb8MLAD08ZmMTmyntQu3LkTf3X0ReD0Q69uvR5H7PF8S5G3MVtrLmK2wZq0Mc22NN7OlZPDMAsAs6xrkZwGggZP+H6KMTmy3tX3n9sXC6IXIcSEHdg3YheCgtC8J8gXMZtvMmM0yZj0/c22dOzMlZfDMAsAM45rkZQGgiaN85JU6uiSo1rhaOBJ2BFVvVsWivovSJFDGwKPaQ4xZHePMtRquZfDMAkCNrxKt0OQ8efJkREVFITQ0FL169UKBAgXuQXH8+HHMnDkTV69eRXx8PNq1a4eqVasaQssCwBBNPpFJRieW0ZArN66g4qcVcSv8Fvrl64fXm7+earW+gtlMuxmzGbbs5WWu7fFntLQMnlkAGGVbUr6hQ4eidu3aqFOnDrZu3Yply5Zh2LBhSWq/ffs2+vfvL8RBqVKlEBcXhxs3biA8PNwQChYAhmjyiUwyOrGshvx26Dc8/ePTSEACvnniG1QvXT3Fqn0Js9G2M2ajTNnPx1zb59BIDTJ4ZgFghGlJeehpvm/fvpgxYwYCAwNBS6/dunUTAiBv3ryJVtauXYu9e/eiT58+liyzALBEm1cKyejEMoGPXzEeY06PQcjlEOx4eQdyhOW4p3pfw2yk/YzZCEty8jDXcnj0VIsMnlkAeGJZ4t+PHDmCiRMnYty4cYm1Dhw4EB06dEDp0qUTf/fll18iOjoaV65cwaVLl1CoUCG88MILvALgwRcyOoREdxuqyhcxt57cGlsybkHhfwtjY/+NCAgISNIWX8TsiWzG7IkheX9nruVxmVZNMnhmAaDGV8IKCYBJkybh448/TlMA0N7/9u3bxcpAjhw5MH/+fNBTfb9+9368Zfny5aAfSiEhIRg/frzYMrCbaNCnswc6JcYsx1t34u4g8s1IXMh+Ae3C2mF239lJKmae5fDsqRYdeaY26YjbnzHTanR6SRkSaF3dRxNtAdCyPk3waW0BfP/996BDgL179xYtOXnyJEaMGCEODxpJvAVghCXfyCNDxTvRkqPnj6LW3FqIyxyHjx/+GM/WeDbRjK9idvppyQme0xtmag/Hh5pIkcEzrwCo8VWilSFDhogDgGkdArx48aJ4+qcfelOAnvD37duHAQMGGELLAsAQTT6RSUYndqohi7cuRu+dvRF4OxDr2q5D8fuKC1O+jDk1LhizU1Fyb73MtRquZfDMAkCNrxKtnD59WjzJX79+HZkzZxYn/SMjIzF16lRUqlRJ/FBav349li5dKlYKcubMKQ4L5sqVyxBaFgCGaPKJTDI6sZMN6TenHxbcWoDsl7NjV79dyBickQWAk4S71e3rscFiS1EgpGJGRnywAPCuDx2xzgLAEVodqVRGJ3YEmFultcfUxuHsh1H5VmUseWUJCwCnCf//+nWIjZSo0BG3v2JmAaCoM6s0wwJAJdv2bOkw8Fy9cRUVJ1VEdM5o9M3XFx91/Qjnzp2z13DFpXXgOTklOmKmNuiI218xswBQPBCpMMcCQAXLcmzoMvBsO7gNrX5ohYTABKxuvRplIsrIIUBRLbrw7E6HjphZACgKaElCiwWAOn8ps8QCQBnVtg3pNMhPWD4Bo06NQsj1EGzvth05w3Labr+qCnTi2cWJjphZAKiKaDkrLSwA1PlLmSUWAMqotm1It0H+2QnP4tfMv6LgtYLY3G8zaADRIenGs64Tqa64/TU+WADoMHqZxMgCwCRhXsyu28Bz584dVB5bGedznUfzjM0xpeMUL7Jn3LRuPOs6keqK21/jgwWA8TFEm5wsALRxlZYHpm7G3cSDHz+IO2F3MPbhsXiu+nM+T7i/DvDecAxzrYZ1GTyzAFDjK6VWWAAopduWMRmd2BYAC4UJ8+dLPsfLO19GwJ0ArG2zFiXvL2mhJnVFdOVZt7cteAVAr5hmAaDOX8ossQBQRrVtQzpPTP1n9cfXsV8j29Vs2PXqLmQKymSbD6cq0Jlnpzhxql7m2ilmk9Yrg2cWAGp8pdQKCwCldNsyJqMT2wJgobALM312o+6ouvgr11+oGFMR3/f63kJtaorozLMahuRZYa7lcZlWTTJ4ZgGgxldKrbAAUEq3LWMyOrEtABYKu2O+duMaKnxSAdF5otE7ojcGNh1ooUbni+jOs/MMybPAXMvjkgWAOS59+muA5ppiPTcLAOvcqS6ZHgbLHQd3oMXKFkjIlICv636NWg/WUk2jR3vpgWePjfSRDMy1GkfI4JlXAEz46tq1a6Av9cXExCA8PBwRERHi29e+llgA+JpHUscjoxOrbm1KmCd9PwkjTo9AxuiM2NZlG/KE5VENK0176YVnnyI1FTDMtRovyeCZBYAHX124cAFr167F1q1bQROre8qUKRNKly6NunXronLlyj4jBlgAqOmAMqzI6MQycJipIzXMbce3xcYsG1HgegFseXULAjL4jjhOTzyb8ZU38jLXaliXwTMLgDR8NX36dGzevBnlypVDhQoVULRoUeTIkQMZM2YUn/M9efIkDh48iC1btoAuSOnZsydKlvT+61AsANR0QBlWZHRiGTjM1JEaZuoDFUdUxMWIi2icqTE+f+FzM9U6mjc98ewoURIqZ64lkGigChk8swBIg+hFixahQYMGCA0N9eiOAwcO4ObNm0IoeDuxAPC2B4zbl9GJjVuTkzMtzCfOnUCNL2rgTo47+LDMh+hco7McozZrSW8826TD0eLMtaP0JlYug2cWAGp8pdQKCwCldNsyJqMT2wJgobAnzMs3L0f3Hd2RITADljRdgkoFK1mwIreIJ8xyrcmpTUfM1HIdcfsrZhYABvtq7969MWLECISFhSUpcePGDbz55puYNGmSwZqcz8YCwHmOZVlIrwPP4JmDMSNmBkJiQ7DlxS3ImyWvLMos1ZNeebZEhsOFmGuHCf7/6mXwzALAoK+effZZfP7558iWLVuSEpcvX8Yrr7yCr776ymBNzmdjAeA8x7IsyOjEsrAYrccIZrokqOmQpthVYBfyx+fHhpc2ICQoxKgJ6fmMYJZu1GaFOmLmFQCbTjdRXEZ8sADwQPjChQtFjm+//RZNmzZFSMh/g1h8fDz++usvREVFYeTIkSZc52xWFgDO8iuzdhmdWCYeI3UZxUxnYqq+WxWXS11GjfAamP/MfK99PtgoZiPtV5VHR8wsAFRFh5ytFhYAHvw1ePBgkYNO+xcvXhyBgYGJJei/8+TJI4RBZGSkOs97sMQCwGdc4RGIjoO8GcyHDh9Cven1EFcsDi8/8DIG1RrkkRMnMpjB7IR9K3XqiJkFgBVPWysjIz5YABjkfsqUKejUqZOhNwIMVulYNhYAjlErvWIZnVg6KA8VmsW8eMVi9N7ZG4gAJteejBYlW6iGzAfTFDJuNj4UQkvVlL9iZgHgC9EnGQMLAMmEOlidvww8b414C3NC5iAwNBDLWi1D2TxlHWT13qr9hWelpKZijLlW4wUZPLMASMNXH374IVq2bIkyZcqk6VE6A7B69WpkyZJF3Bvg7cQCwNseMG5fRic2bk1OTiuY6ZKgxt0bY0+lPcgWnA1rn1uL+7LcJweQgVqsYDZQraNZdMRMhOiI218xswBIowvT9b8LFizA7du3xW2ARYoUETcBBgUFiUt/Tp06Jc4G0E+tWrXQpk0bZM+e3dFBwUjlLACMsOQbefxp4KFrtWv3qo2rT15F8SzFsarNKoQGe75kS4an/IlnGXzZqYO5tsOe8bIyeGYBYIDvPXv2iG8B0ERPg1hsbCyyZs2KwoUL4+GHH0bNmjXveT3QQLWOZWEB4Bi10iuW0Ymlg/JQoR3M27dvR8sJLZFQKwFPFngSMxvMVPLNADuYVfPrsqcjZl4BUBctMuKDBYBBf+3bt098+EeHxAJABy/dxSijE6turV3M06ZNw5A/hwAPA73L9sbAKgMdb4JdzI4DTMGAjpj9NaZ1jQ8WAAY916FDB/GUT0v99EOfAvbVxALAVz1zLy4dB3m7mOmSoO69umNFnhVAAWBc7XF4puQzjjrNLmZHwaVSuY6YWQCoixQZ8cECwKC/bt26JbYBNmzYAFoNKFGihBACjz32mDj850uJBYAveSNtLDI6serWysBMV2jXf7o+/qn3DwKzB2Jhk4WoElHFsabIwOwYOBYAqqm9x56/xgcLAAuhd/HiRfz6669CDJw7dw4VK1ZEnTp1UL58ea/ddObeDBYAFpzqpSL+OvAQ3YcPH0b9jvVxq90tZM+aHStbrkSh8EKOeMKfeXaE0DQqZa7VMC6DZxYAFn1FqwAkAOiHHEGvAmbKlAndu3fHI488YrFWOcVYAMjhUUUtMjqxCpzuNmRiXrlyJbqO6Qo8BxTLXgzLWyxHeMZw6U2SiVk6OF4BUEVpqnb8NT5YAJgIPZpY169fj40bNyI6Olos/9OTP10RTO85L1q0COvWrcPUqVNN1Co/KwsA+Zw6VaO/DjzufI4dOxbjfhsHPAXULlAbs+vPRlBAkFTKmWepdKZZGXOthmsZPLMAMOirt99+G//884947Y8m/cqVKyM4ODhJ6StXrogVALo7wJuJBYA32TdnW0YnNmfRfm7ZmOmjWl26dsGPGX8EKgAvlnkRHzz2gX2gbjXIxiwVHK8AqKCTRUsKDLAAMBh6S5YsEYf+cubMabCE97KxAPAe92Yt88R0l7Hr16+jaYumOFT1EFAYGFZ9GDqV7mSWzlTzM8/SqPRYEXPtkSIpGWTwzAJAiit8qxIWAL7lj7TQyOjEqlvrFOajR4+i4dMNcf3Z68iQMwPmNpiLWgVqSWmeU5ilgOMVACdpNFS3v8YHCwBD4aFXJhYA+vjLXwee1DxE52va9WkHvARkyZoFy5ovQ4kcJWw7lHm2TaHhCphrw1TZyiiDZxYAtlzgm4VZAPimX1JCJaMTq26t05inT5+O9758Dxk6ZEBkeCRWtFiBnCH2tt6cxuyED3TETDzoiNtfMbMAcKLnerlOFgBedoAJ8/468KRFEd0U+Prrr2PB3wuAJsCjEY/i60ZfI2NgRhPMJs3KPFumznRB5to0ZZYKyOCZBYAl6n27EAsA3/aPOzoZnVh1a1Vgpi9wtm7dGjvz7gQeBZ4t+Sw+qvWR5Yu2VGCW7QcdMfMKgOwoSL0+GfHBAkCdv5RZYgGgjGrbhmR0YtsgTFagCjPdstmwcUNcqHcB8cXiMajKILxc9mWTaO9mV4XZErhUCumImbmWGQFp1yUjPlgAqPOXMkssAJRRbduQjE5sG4TJClRi3r17N1q2bYn4zvGIyxmH6U9OR4PCDUwiZgFgmjAbBVTGhw2YSYr6K2YWALIiyIfqYQHgQ87wAMVfBx4zHqIbNl959xUE9QxCcGgwljRbgodyP2SmCl4BMMWWvcwc0/b4M1paBs8sAIyyrVE+FgD6OEtGJ1bdWm9gHj16ND5Z9AkCOgcgX1g+8WZAvtB8hpvuDcyGwfEWgF2qbJf31/hgAWA7dHyvAhYAvueT1BD568Bj1kN0XXDPnj2x/PhyoBVQLk858QnhzEGZDVXFPBuilplw3QAAIABJREFUSUom5loKjR4rkcEzCwCPNOuXgQWAPj6T0YlVt9ZbmOkDXPRmwO6cu4FaQJMiTfDpE58iIEOARwq8hdkjsDQy6IiZmqMjbn/FzALATg/10bIsAHzUMSnA8teBx6qH6M2ARo0b4Vytc0h4MAGvln8Vb1R6w2N1zLNHiqRlYK6lUZlmRTJ4ZgGgxldKrbAAUEq3LWMyOrEtABYKexvznj170KJNC8S0j0FcvjhMqjsJLYu3dHywtECVrSLe5tkqeB1x+ytmFgBWo9xiOZqcJ0+ejKioKISGhqJXr14oUKBAirXFxMTgzTffRKZMmTBy5EjDFlkAGKbK6xn9deCxS/zq1avRuU9n8WZAQNYAfNvkW1TKVynVaplnu4wbL89cG+fKTk4ZPLMAsOMBC2WHDh2K2rVro06dOti6dSuWLVuGYcOGpVjT7NmzcePGDRw7dowFgAGuZXQIA2akZmHM1umcOnUqPpj+AQK6BCBnlpzizYACYSmLaebZOs9mSzLXZhmzll8GzywArHFvqdTVq1fRt29fzJgxA4GBgaA7z7t16yYEQN68eZPUuX//fnz//fdo0qQJ5syZwwLAAOMyOoQBM1KzMGbrdFL/GTBgAObtnAe0BUrlKIWlzZYia8as91TKPFvn2WxJ5tosY9byy+CZBYA17i2VOnLkCCZOnIhx48Yllh84cCA6dOiA0qVLJ/7u1q1beO+998TyPy3nswAwRreMDmHMkrxcjNkel7RN1r59e2wO2AzUA56IfAJfPPUFAgMCk1TMPNvj2Uxp5toMW9bzyuCZBYB1/k2XJAEwadIkfPzxx2kKAPocatGiRfH4449j7969aQqA5cuXg34ohYSEYPz48YiLizONLXmBgIAA0LvXOiXGrMZbvsbz5cuX8Vj1x3C4zGGgHNC3al989ORHScjwNcxGPKUjZmqXjrj9GTOtRqeXlCGB1gV9NNEWQJ8+fTBz5sw0twD69+8PeueZEj3h0DmAiIiIJMIhrSbyIUAfDYAUYMlQ8apb64uYSVw3a9UMV5tdRXxkPEbXHI32pdonUuOLmD35TUfM1CYdcfsrZl4B8NQLJf99yJAh4gCgkUOAZNrTCkBK8FgASHaag9X568DjBKU7duzAM52eQWynWGTIngHzGs5Djfw1hCnm2QnGU66TuVbDtQyeWQCo8VWildOnT4vXAK9fv47MmTOL1wAjIyNBJ5orVaokftwTCwDjDpLRIYxbk5OTMcvh0VXLqlWr0GVgFwR0DUDWLFmxvMVyFMtejAWAXJrTrI1jWg3ZMnhmAaDGV0qt8AqAUrptGZPRiW0BsFDY1zHTWzaDvxwMPA8UDi8sRECpQqVAtwjqlHyd59S41BG3v2JmAaDTiGAQKwsAg0T5QDZ/HXicpp7u2/h89+dAI+Cx+x7D2k5rcfniZafNSq1fx9jg7RapIeD4SgsLAHX+UmaJBYAyqm0b0nGQ1wEzvcHSo0cPrEhYAVQBupTvgiEVh4AGPF2SDjynxKWOuP0VMwsAXUYDEzhZAJggy8tZ/XXgUUE73afx7HPPYkfJHUBxoOcjPTGoyiBtRICOscErACoi+64NGfHBAkCdv5RZYgGgjGrbhmR0YtsgTFagE2a6I6Bp66Y4Wv0oUBB46aGXMPTRoVqIAJ14dg8hHXH7K2YWACYHPx2yswDQwUvyVLzq1uo2WNK3NFo80wIXnryAhEIJ6PBgBwyvPhwBGQJUU2fKnm48uxqnI25/xcwCwFSX1CMzCwA9/CRrGU91a3UcLM+ePYva9Wojunk04grHoW3JtuKyoORXBqvmMi17OvLMMa0ugmTEBwsAdf5SZokFgDKqbRuS0YltgzBZga6Yly5diuc6PIeEZxIQWzgWrYq3wrja4xAUEGSSATXZdeSZBYCa2JDFMwsAdf5SZokFgDKqbRvScZDXGfOPP/6Il7q/hJDnQxBdKBpNijTBpMcnITgg2LYvZVegI8+yJibZXHqqT0euZWBmAeApMjT8OwsAfZwmoxOrbq3umL/++mv0H9AfYZ3CEFUwCg0KNcCUJ6YgU2Am1VSmaU9HnlkAqAshGfHBAkCdv5RZYgGgjGrbhmR0YtsgTFaQHjDTVzlHjBqBXC/lwqX8l/B45OOYVm8aQoJCTLLhXHYdeWYB4Fw8JK9ZRnywAFDnL2WWWAAoo9q2IRmd2DYIkxWkB8z00VC6LXDa9Gm4v+f9OJ33NGrlr4WZT81E5qDMJhlxJruOPLMAcCYWUqpVRnywAFDnL2WWWAAoo9q2IRmd2DYIkxWkF8x0W2Dfvn2xaPEiFOldBP/k+gfV7quGL+t/iSzBWUyyIj+7jjyzAJAfB6nVKCM+WACo85cySywAlFFt25CMTmwbhMkK0hPm2NhYdO3aFWvWrMEDrz6Ag9kPonK+ypjTYA7CMoaZZEZudh15ZgEgNwbSqk1GfLAAUOcvZZZYACij2rYhGZ3YNgiTFaQ3zHRlcKdOnbBx40Y80v8R/C/r/1A+T3nMbTgX2TNlN8mOvOw68swCQJ7/PdUkIz5YAHhiWcO/swDQx2kyOrHq1qZHzDdv3kS7du2wfft2VHmrCraFbMNDuR7C142+Rs6QnKopFvZ05FlX3DpyLQMzCwCvdG1njbIAcJZfmbXL6MQy8RipK71ivnbtGtq2bYs//vgDtd6thQ2BG/Bgzgcxv9F85M6c2wg1UvPoyDMLAKkhkGZlMuKDBYA6fymzxAJAGdW2DcnoxLZBmKwgPWOmjwe1adMGBw4cQP336+PH+B9RInsJLGi8APlC85lkyl52HXlmAWDP52ZKy4gPFgBmGNckLwsATRyl6TKvjIFHtYfMYD5//jyefvppHDlyBM1HNMfS20tRJLwIvmn8De7Per8y6GYwKwNlwJCOuP0VMwsAAwGtWxYWAPp4zF8HHtUeMsvzqVOn0KpVK5w+fRrPjH4G86/PR8GwgkIERIZFKoFvFrMSUAaM6IjbXzGzADAQ0LplYQGgj8f8deBR7SErPB89elSsBFy4cAFtR7fFvKh5YgVgQaMFKJKtiONNsILZcVAGDOiI218xswAwENC6ZWEBoI/H/HXgUe0hqzzTNgCdCaBtgQ5jO2BO1BzkzZxXnAkonr24o82witlRUAYq1xG3v2JmAWAgoHXLwgJAH4/568Cj2kN2eHYXAZ3GdsKXUV+KVwPp7YBSOUs51hQ7mB0DZaBiHXH7K2YWAAYCWrcsLAD08Zi/DjyqPWSX53/++QetW7cWKwEvjX0Js67PEjcFkggok6uMI82xi9kRUAYq1RG3v2JmAWAgoHXLwgJAH4/568Cj2kMyeCYRQNsB586dQ9exXfHF9S8QGhyKeQ3noWyestKbJAOzdFAGKtQRt79iZgFgIKB1y8ICQB+P+evAo9pDsnimg4G0EkAioMeYHph5cyaCA4LFtcGV8lWS2ixZmKWCMlCZjrj9FTMLAAMBrVsWFgD6eMxfBx7VHpLJM4kAWgk4e/YsXh7zMmZEz0BAhgDMrj8bj973qLSmycQsDZSBinTE7a+YWQAYCGjdsrAA0Mdj/jrwqPaQbJ6PHTsmVgKor3Uf1h1zE+YiLiEOXzz1BWrmrymlebIxSwFloBIdcfsrZhYABgJatywsAPTxmL8OPKo95ATPJ06cEN8OoBWBF999EQszL0RMXAxmPDkDdSLr2G6iE5htgzJQgY64/RUzCwADAa1bFhYA+njMXwce1R5yimc6C/Dcc8/h4MGDaPd6O6zMvRI3Y2/is3qf4alCT9lqplOYbYEyUFhH3P6KmQWAgYDWLQsLAH085q8Dj2oPOckzfUDo+eefF18RbNmzJdYXWo9rt69hyhNT0LhIY8tNdRKzZVAGCuqI218xswAwENC6ZWEBoI/H/HXgUe0hp3mOiopCp06dsHXrVjTq2AjbS2/H5VuXMaHOBLQo3sJSc53GbAmUgUI64vZXzCwADAS0bllYAOjjMX8deFR7SAXP0dHR6Nq1K37++WfUbV0X+6vsx/no8/io1kd4puQzppusArNpUAYK6IjbXzGzADAQ0LplYQGgj8f8deBR7SFVPMfExKB3795YsWIFHm30KI7XPY4zN85gVM1RaF+qvalmq8JsCpSBzDri9lfMLAAMBLRuWVgA6OMxfx14VHtIJc937tzBgAEDsGDBApR5rAyutryKkzdOYthjw9CpTCfDTVeJ2TAoAxl1xO2vmFkAGAho3bKwANDHY/468Kj2kGqeExISMGrUKEycOBGRZSKRoWMGHL95HIOrDkb3R7obar5qzIZAGcikI25/xcwCwEBA65aFBYA+HvPXgUe1h7zF86xZs/DOO+8gR8EcyPpyVhyPPo63Kr+FV8q94pECb2H2CMxDBh1x+ytmFgB2o90Hy7MA8EGnpALJXwce1R7yJs+rVq1Cr169EBgeiNyv5cbxmOPoV6Gf+KEBOLXkTcx2/KMjbn/FzALATqT7aFkWAD7qmBRg+evAo9pD3uZ527Zt6Ny5M6LionDfgPtwMu4kmhVthpE1RiJbpmwp0uFtzFZ9pCNuf8XMAsBqlPtwORYAPuycZND8deBR7SFf4Pmvv/5C+/btcerSKZR4owT+CvwL+bPmx8Q6E1H1vqr3UOILmK34SUfc/oqZBYCVCPfxMiwAfNxBbvD8deBR7SFf4Zm+IEi3Bu7fvx+Ve1TGn/n/REx8DPqU64PXKryGoICgRGp8BbNZX+mI218xswAwG90a5GcBoIGT/h+ivw48qj3kSzxfu3YNPXr0wPr161GuXjncbnIb+6/sR4W8FTCp7iQUCi8k6PElzGb8pSNuf8XMAsBMZGuSlwWAJo7SdJD318FSZlTRXQHvvfce6C2BwsUK49FBj2L+8fnIGpwVw6oPw9PFn0ZERAToY0O6JY4PNR6TwTMLADW+UmqFBYBSum0Zk9GJbQGwUJgxWyAtlSJffPEFBg8ejPDwcPT+uDemXZyGczfPoUWxFpjRcgZuXb0lz5iimjg+1BAtg2cWAGp8pdQKCwCldNsyJqMT2wJgoTBjtkBaGkXo2wG0JXDr1i28/eHb2JpvK1YfW43C2QpjfK3xqBxRWa5Bh2vj+HCY4P+vXgbPLADU+EqpFRYASum2ZUxGJ7YFwEJhxmyBNA9FDh48iI4dO+LEiRN4vsPzKNW+FIbtGIbbcbfxavlX0bd83yQHBOUjkFcjx4c8LtOqSQbPLADU+EqpFRYASum2ZUxGJ7YFwEJhxmyBNANFLl++LFYCNm3ahMqVK2P0zNHo9XMv7Lu8D5XyVRKvCxYML2igJu9m4fhQw78MnlkAqPFVohWanCdPngz6fnhoaKi4IaxAgQJJUOzZswfz5s0DfV40ICAAlSpVQtu2bdO8Ncy9AhYAip1qw5yMTmzDvKWijNkSbYYK0eHAYcOG4fPPP0f+/Pkx6dNJWBW7Cp//+TnCgsMwvMZwtCreylBd3srE8aGGeRk8swBQ46tEK0OHDkXt2rVRp04dbN26FcuWLRMd3j39888/QhyQg+nzoh988AHq16+PGjVqGELLAsAQTT6RSUYnVt0Qxuw844sWLcIbb7yB+Ph4jBw5EhHVI/DqL6/ifPR5IQDoTYHwjOHOA7FggePDAmkWisjgmQWABeKtFrl69Sr69u2LGTNmIDAwEPTFsG7dugkBkDdv3lSrpfzZs2fH008/bcg0CwBDNPlEJhmdWHVDGLMaxk+dOoWWLVuC/m3Xrh36vt0X72x7B2uOr0Fk1khMfHwiKufzvQOCHB9q4kMGzywA1PhKWDly5Ij4POi4ceMSrQ4cOBAdOnRA6dKlU0Ry5coV8SRA+YoWLWoILQsAQzT5RCYZnVh1QxizGsaJ53379qF3797YsGEDypQpg88++wwbojfg/a3vIzY+VhwQ7FO+j08dEOT4UBcfdu+JYAGgxleJAmDSpEn4+OOPDQmAmzdviuX/6tWro0mTJikiXb58OeiHUkhICMaPH4+4uDjbraKzB7T8qFNizGq8xTyr5Zn6M60S0lgQFhYmVhAfqPEAOizpgD/O/YHHCjyG2S1mo3D2wmqAebDC8aHGDbJ4ptXo9JIyJNC6uo8m2gLo06cPZs6c6XELgA4AUqcvV64cWrdubapFvAJgii6vZuanJTX0pweeaRWADg3T2wJdu3ZF/7f6Y+yusZi2Z5o4IDiixgi0LN5SDaFpWEkPXHudRAMAZPDMKwAGiJaZZciQIeIAYFqHAOlCEJr8H3nkEbRp08a0eRYApinzWgEZnVg1eMashvGUeD59+jR69uyJHTt2oHz58qAVxaOBR/Hq+ldxIfqCOCA4vPpwhGUMUwMyBSscH2qol8EzCwA1vkq0Qh2YXgO8fv06MmfOLBR9ZGQkpk6dKl73ox86Afztt98meT2wWrVqaNXK2Os/LAAUO9WGORmd2IZ5S0UZsyXaTBdKjefY2FiMHj0aU6ZMQdasWTF8+HDUaVQH/Tb0w0/Hf0LBsIKYWHeiuDvAG4njQw3rMnhmAaDGV0qtsABQSrctYzI6sS0AFgozZgukWSjiiWfaEqC3is6fPy8eDmjVcNGJRfjgtw/EAUH6vDB9ZjgwQO0eryfcFqhwvIi/YmYB4HhoqTfAAkA951Yt+uvAY5Uvq+XSK8+XLl1Cv3798NNPP6FQoUJidTG0UKi4QXD/5f2okq+KWA0oEJb0sjGrPBopl165NtJ2lXlk8MwCQKXHFNliAaCIaAlmZHRiCTBMVcGYTdFlObNRnuncM31WmN4SoJsE6aBx917dMWb3GMzYM0NcGDSyxkg0L9bcMhYzBY3iNlOn03n9FTMLAKcjywv1swDwAukWTfrrwGORLsvF/IHn/fv3i8mf7g546KGH8Mknn+BMljN4bf1r4oBg6xKtMeyxYciaMatlHo0U9AeujfDgdB4ZPLMAcNpLXqifBYAXSLdoUkYntmjacjHGbJk6UwWt8ExXh9NFY/R2QFBQEAYMGIBWHVqh/6/9se7EOhQKK4RJj09ChbwVTGExk9kKbjP1O5HXXzGzAHAimrxcJwsALzvAhHl/HXhMUCQlq7/xvHPnTrz66qv4+++/UaVKFYwZMwYbb28UBwTvxN/B6xVfR++yvR05IOhvXEsJUAuVyOCZBYAF4n29CAsAX/fQf/hkdGLVrWXMahi3yzNdJjZixAhxc2CmTJnEYcE6z9RB3w19ceDfA3g04lFMqDsB+bPml9ogu7ilgjFYmb9iZgFgMEB0ysYCQB9v+evAo9pD/szzb7/9hv79+4tvkdDZgOGjh2PpjaWYsXcGsmXMJg4INivWTJpL/JlraSQaqEgGzywADBCtWxYWAPp4TEYnVt1axqyGcZk80+2idCiQLg+itwa6d++Ois9WxJtb38TF6It4puQzeLfqu8gZktN242Titg3GYAX+ipkFgMEA0SkbCwB9vOWvA49qDzHPdxnfu3ev+LroH3/8gYIFC6L/kP5YkrBEHBDMHJQZHR7sgO4Pd0dElgjLLmKuLVNnqqAMnlkAmKJcj8wsAPTwE6GU0YlVt5Yxq2HcKZ7prgA6F/DRRx/hxo0beKr+U6jVsxa+Ov6VuDwoY0BGsSLQq2wvFAwvaLqxTuE2DcREAX/FzALARJDokpUFgC6eYgGgylP+OsCnxS+NE0OHDsWyZcvEp8T7vtoXxRsVx5Q9U7Dr/C4EZghEi2It8Eq5V1AiRwnDrmKuDVNlK6MMnlkA2HKBbxZmAeCbfkkJlYxOrLq1jFkN46p4pm8KDBo0SBwSLFasGAYPHoyQB0MwYfcEbDq9CRmQAQ2LNBTfFXg498MeG68Kt0cgJjL4K2YWACaCRJesLAB08RSvAKjylL8O8Eb5vX37Nj777DNMmDAB9Ppg7dq18d577+F69uuYuHsi1hxfI6qqW6Au+pTvgyoRVVKtmrk2yrq9fDJ4ZgFgzwc+WZoFgE+6JUVQMjqx6tYyZjWMe4NnGjtGjhyJhQsXIiAgAM8//7x4hfAczgkhsOzIMiQgAVUjqooVgdoFaoMmEffkDdx2PeKvmFkA2I0cHyzPAsAHnZIKJH8deFR7iHk2x/ju3bsxZMgQbN++HeHh4ejduzdefPFFnL59GlP+mIKFfy3EnYQ7eCT3I0II1C9cHwEZAoQR5toc11Zzy+CZBYBV9n24HAsAH3ZOMmgyOrHq1jJmNYx7m2e6L2D58uUYNmwYTpw4gYiICLz22mto27Ytzt06h0//+BRfH/wat+JuoWT2kuhdrrf44mD++/Lj3LlzakiSZMXbXFtphgzMLACsMO/jZVgA+LiD3ODJ6MSqW8uY1TDuKzzT+YCvvvoK48ePx6VLl1C0aFHxkaHGjRvj0q1LmLZnGr7c9yWux14XHxt6q+ZbqB9RH5kCM6khSoIVX+HaTFNkYGYBYIZxTfKyANDEUbxcqsxRMgZLZWD/35CvYb5+/TqmTZuGqVOngv774YcfFisCTz31FK7GXMUXe7/A9D3TceX2FUSERqD7I93xfKnnERocqpo60/Z8jWsjDZCBmQWAEaY1y5OSAKDlPDrdGx8fb6g19F4wXR+qU2LMEAe3MmfOfM/BLJl+lDHwyMRjpC7GbIQlY3loFWDixImYM2eOGCNKly4tvjzYsGFDRMdFY8nJJRi7aSzOR59Hjkw50OWhLuhcpjOyZcpmzIAXcvlrfLAA8EKwOW0yJQFw8+ZNBAcHix8jib4lTjeG6ZQYMxAbGyt+QkOde+ry18FSdV/wdZ5pn59WA2bPni2EwAMPPIC+ffvipZdewsmzJ7Hg0AJxYPDk9ZMICw5DxzId0fWhrsidObdqKj3a83WuU2qADMwsADyGhn4ZUhIAtGSXNWtWw43hydQwVbYyOsGzWV+bbYCMgcesTbv5GbNdBlMvf/HiRXGHwKxZs0APGqVKlcLLL7+MZs2aAYHAksNLMOmPSTh85TBCAkPQvlR79HikB+7Per9zoEzW7K/xwQLAZKDokJ0FgA5euouRBYAaX/nrAK+G3btWLl++jM8//1wIgaioKNx///1iNaBdu3bIkjULVh1dJe4S2HNpD4IDgtGmRBu8XPZlFMlWRCXMFG35a3ywAPB66MkHoIsAWLlypbh5LC4uDjExMeL94fnz54t97JQSvYpE+4x79uxJ8e/ukykdVmrZsiVy57673OhapuzWrZt8wm3UyALABnkmivrrAG+CImlZaZtxzJgxQghcuHBBrDw+99xzQgwUKFAAP5/8GRN2TcD2c9vF3QHNijYT3xsolbOUNAxmK/LX+GABYDZSNMivgwA4f/486tWrBxIBNChQ+vPPP/HQQw+leoDNjACoWrUqvvzyS7Ec6cuJBYAa7/jrAK+G3aRWXFzT64NLliwRqwIHDhwQwp5eHSQRXr58eWw9uxUTd03E+lPrRQX1C9UXQqB83vLKYftrfLAAUB5qzhvUQQDQU/wLL7yAjRs3IkuWLElIoW+Vv/POO+KthUyZMokbySpXriwuI3FfAcifPz8OHTqUWJ5eSyJBQdeYfvLJJ+J751R+3Lhx+PHHH8WnT+lDJ7TiQJeb/PLLL8LuY489Jn6fMWNGcZqZTtHTh1FOnTolBMSUKVPE35xILACcYPXeOv11gFfDbsoCwPVbegOJ+jmdE3D1uXLlyqFDhw7inMChG4eEEPjh2A+iSM38NcXtgtXuq+bo2yzuqP01PlgAeKOHOGzTkwDo1KkTjh07liYKCgzquGZToUKFxNKfp0SvI3bv3h2bN2/Go48+ikqVKqFFixbIlSsXqlevLpYQ69Spg23btol8mzZtEpeQGBEAkZGRSL4C4Pr2OU30tDJAn0Cly00CAwPRuXNnIQJ69uwpBABN/gsWLBCTfqtWrcTfCZsTiQWAE6yyAFDDaspW0ppMaSVg5syZWLRokRD4dM1w69atxTcHEvIkYPIfk7Hk7yWIT4hHgawFUK9gPfFDYiAkKMSxZrEAcIxapRVnSLAyaymF6LwxHQSAi4XDhw9jy5Yt+Pnnn8W/NDB06dJFTPiuRFsF9IES6qQyBEDXrl3RoEEDPP3008LEqlWrxDvN8+bNEwKAnvp79Ogh/kZfRMuRI4f4vROJBYATrLIAUMOqeQHgKnHt2jXR1+fOnYv9+/eLX1epUkWsCpSpWQbzDs/D6mOrcTzquPhb5qDMqJW/lhADj0c+jogsEVKbyAJAKp1eq4wFAABPAsCId5yYmDzZbd++vVgJoCX85AJg1KhRyJs3bxIBQEv8tJVATxGUSpQogXXr1sHTCgAJjEaNGomne5cAoIGIVgRooi9btqx46qf0/vvviy2G119/3RN8S393gmd+DZAFgKVglFTIzGRKz2s7duwQQoBW5ejcAPXnpk2bCoGeo0QOrD2xFj8d/wnbzm0TKwOU6CNErtWBh3M/nPghIqtNMIPZqg3Z5WRg5i0A2V7xgfp0EACE8eTJk2Jvn9KVK1dEp6e9f/qhffsaNWqIr5HRoaGUtgBq1qyJDz/8UHy7nPb+6cl+69atQgDQqsGIESMS60++BUBP/fRmAB1Moq+c0RYAPfWzAPAcwDIGHs9W5OZgzHL5TKs2q1zTa4Tfffcdvv32W+zdu1eYoC1FEgL0ky0iG9afXC/EAL1JQFcOU8qTOQ+eiHxCCIJaBWohS3DSM0VGWm4Vs5G6ncojAzMLAKe848V6dRAANPnTB0WOHz8uDt3RwTzaZ+/Tpw/oU6Tvvvtu4iFAWoan5cHkhwDpaZ/y0at+NIHTUwQJARIAtJxPh/eobk+HAKtVqyaW+l2HAHkFIO3glTHwqO4ejFkd4zK43rdvnxADixcvTvyyIK0O0qu9tHqXM3dO/H7udyEG6OfQlUOigRkDMorzAq7VgYLhBQ01XAZmQ4YkZpKBmQWARIf4SlU6CAAnuHJiOd0JnO51OoGZtwDu9ZqMwdLpWEhev46YqQ0ycdODwa+//iq2BUnc05XDNGnRwWGp+oUkAAAVSUlEQVR6pZDEANk7du0Y1h6/u1Ww5cwWxMTHCDrpM8UuMVAxX0UEBQSl6EaZmFXFiQzMLABUeUuhHRYACsm2aYoFgE0CDRaXMVgaNCUtm46YZQsAdzJJ2P70009YsWKFOOvjEgO0jdikSRNxPohuH7wecx0bT20UYoDOD1yIviCqyZ4pO+oWqCsEQZ3IOuL/XUlHrmVgZgEgrbv6TkUsAHzHF56QsADwxJCcv8sYLOUgMV6LjpidFADuzNGdHmvXrhVigP6lVwop0UViTzzxhDgDRHcNIAPwv4v/S9wq+PPinyJfYIZAVM5XOXF1oPoD1UGXk+mUZMQHCwCdPG4QKwsAg0T5QDYWAGqcIGOwVIP0Pys6YlYlANx9QR8gohUBuuyL/qUDxZTobFDdunWFGKCDwmFhYThz4wzWnVgnBAGtEkTfuSscimYvirr5764OVL2vKjIFZlLtbtP2ZMQHCwDTtPt+ARYAvu8jF0IWAGp8JWOwVIOUBYAdnunMwM6dO8VWAa0MuO4YoH5G1w/Tm0P0dhH9d1xAnDgv4Hqr4Pi1u3cO0FsEtfPXTrxzIE9oHjuQHCsrI6ZZADjmHu9VzALAe9ybtcwCwCxj1vLLGCytWbZeSkfM3lgBSIthus6bxACtDNArwnSOgFJoaKg4SEhigH5ohWDjof8/N3B8LX4//3vinQPl85THEwWfQMW8FfFAzgeQN3NeZVcUp9U2GfHBAsB6//TZkiwAfNY19wBjAaDGVzIGSzVIeQXAKZ5jY2PFK8b0VgH9/P7776DfUcqePTsqVqwoXjemnwIlC2DLhburA7+c/AXXYq4lwqLDg6VylELJHCWFIKD/fiDHA8gRksMp6CnWKyOmWQAodZkaYywA1PAswwoLABkseq5DxmDp2YrcHDpi9rUVgLQ8QmcH6FsjJAZ27dqVRBDQnSB0HwiJgbIVyiKgYADOJpzFgcsHcPDfg+LHXRSIdofmE0KAfujTxvQviQQrFxMZiSQZ8cECwAjTmuXRQQCk9Lle+igIffjnySeftMS4p8mUPvBDFxCZudaXvjhYunRprFmzJhHT/PnzRR10C6HryuDUAP/www/iPWXac6REHz/64IMPxPcHKHnCnFq91BZa2pw2bdo9WfgegHtZkzFYWgpKG4V0xKyTAHB3DXF99OhRsUJAooBuIKUriqOiohKzRUREiDcLSBjQT0TJCJy+czpREBy8fFcY3Iq7lcTrBcMKCiEgVgpy3hUIxbMXt33QUEZ8sACw0UF9tSgLgJQ9Y1UAPPLII6BvEdC/lOg2MrqzvE2bNh4FQPKrhVkAeKfXyBgsVSPXEbPOAuDcuXNJXEwHCunrhbQ6QJ8op3/p8+P0e1cqXLiweEB48MEHxU/JUiWRIUcG/HXlLxz49/9XCy4fxN9X/0Zs/N3tBkr0GmKRbEXurha4CYPC4YVTvawoefzJiA8WAKp7tQJ76UEA0FPs0KFDQVeC0mRL+3P0xB0cHCw+H+q+UkDfAKBXfehjQr179xbX/9InfekAEH3Zj64EpiW9pUuXig8l0Z3/tP83aNAg0Znpp2PHjuIneaIVgGHDhomOP3z4cPz999/o27cvihcvnvjRINpHpM8X0/cKYmJixN/o64X0BEFXG4eEhCBnzpxCLNCAQdcO07Wm9JRBn0Wmq4rpiYIS3Xj26aefikNG9913H0aPHi3+pXrpGwkkIOhJhGzQ55F5BcBYh5IxWBqzJC+XjpjTkwBIyZN03wB9gIxWCuiHvllAYwL1Y1eij4fRuOMSBfRvwSIFcS3o2n+rBf8eFNsJR68dRQL+++w6vX5YLFuxxC0E13ZC/qz57/ngkYz4YAEgr7/6TE2eBECnHzuJqzPTShQYVr6sXCi8EGbVn+WRC9oCyJQpk/hxJVqCo8matgDoOwG0/0aTPeF44403ULJkSfFhIE8CgCZ/etqnSZ+++EcTL31nwD3R75o1ayae5in9X3tnFhpFs4bhOor5ORiXnERQzHG9iIrxSDiC+4rmRgy4JS4REfcFEXdRMbiLuCWCkQQRlwsD7hci4oLiAuqVCuKGK4oaFcWD6394P+lxJiYz1TPdlerJWzD8/lrd/fVTX1e9VfVVFdYOIxCoOgEA9Y9tRy9cuKC2bNkiZw1AQDhnBuzYsUMqAOfIYDTo7969k5MEqxsBGDNmjDp+/LhcjxMIsZkJzi5Ab6OgoECmB9Dob9++XUQEjirGGeqYhsABRt+/f5f3yszMpACI6Wm/MnhRWWo+yrNsQbS5LrKGKLh3754sOUSHxfk5+xE4DtGkSRPVvn17+UHA478t27RU35t+Vw8+PogQB88/PY/wI8QRhKYREGfwryzVL6uf+vvTb/EQj+NRAMRDzfJrgiIA9u7dK0rZSeENO4bbcfwvHBQJ235iuQ5O+IslAHBP9PKR0NtOS0sLNc7Os9BzRuObl5enevXqJWKjuoQRAPT+MRqBPGjcMa+PQ4gcAQBxgLlCR8xgRACnmOH9qhMA6MljWRLS3bt35TRCjB6gkUflsXnz5pAowcjH/fv35aTD8COMYT/mKjkCoPcxBrExDaLNdVEAVOeB6LRgSgHfM+oPjBI4vzdv3kRcUr9+fRHzON4cP3QwmmU2Uz8zfqqP//yonn19FhIHb/73+9rC7EK1ofsGvQ+ghlwUAAnhs/PiWAJAx+p4g9N07o08sYIAs7Oz1cmTJ6UhrZry8/Ol0czNzZV/mjBhgvTQnSkA3dP8Hj9+LBHAOHUsKytLxEXV5AgA9M4nTpyo+vfvr4qLiyMadjTMy5YtE4FSNcWKAUDPYfz48eratWuqvLxcRgEwnYD04cMHlZOTIwJg8uTJ8o7o+SNRAOh62q98QWxMg2gzWcf2S4wMQAzgu8ZoJf786NEjORkVKxOqJkwpOMIg/d/pqlH7RqrVf1upnNY56j+pv6YO400UAPGSs/i6ZBAAiLKHMsa8O8QIPhoMq7dt21amB9CrX7p0qXw0EAKrVq1yJQDw8WEYDuncuXMyZ4+tRGsSAPgIy8rKVN++fWUqIrxhx6gAAoRKS0sl/gBDgrALosI5rhhxA0hVgwDDBQBGA8aOHStTABj9KCkpkV4+hv337NkjUf8YVcAIA0ZBcPAJRwD0PsQgNqZBtJkCQM8fq8uFUYPKykqpO5wfjkDHn/FfrGDC9B86BSdOnPBE1FIAxF9e1l6ZDAIAQYAIvkPPuF69eiIC0MtGA4ye+4wZM2TeHfNoEAYYynczAoAAQDTGCCqE0MCwPKYCogmA8H8LFwBokBEbcPr06dCUxcyZM6W3jkChefPmif1OEGD4MsBwAYD7V1RUiJBAqikIEH+PQ09QIVAA6H2GQWxMg2gzBYCeP8aTC8HKOLAIowSo97zwDwqAeEoigWvQOO/cuVPmjLEd5axZs2T+p2rCHPHRo0clAA6VPYaA0VDppCAIAJ33cJvH72kLt/bo5PfDZu4D8Cd5LypLnfL0Mk8QbaYA8NIDot/LC/+gADBXXvIkBJNh32nMJWNvagzloKcbnqDyMHSMteeIHMVSMAz76G6QQwFguFATeBwFQALwXFzqRWXp4nGeZA2izRQAnhS91k288A8KAC3U3mRCUBfmghHshd48evdY1gYBgDlfJ2GJGEQAev1ION0Kf4d5bp1EAaBDyY48FABmysGLytKMpb+fEkSbKQDMeYkX/kEBYK68JOITEeQIGnMSAtkKCwtlNyknYTlYenq6zGsjYa4XQWoICtNJFAA6lOzIQwFgphy8qCzNWEoBYJpzXRYtFAAGvQ0CAI04AsZiCYCMjAzZqAYJEaCYDqhOAGCpHH5I2HFu27ZtEVtVOs/Brnj4d90U70ZAuvf3Ix9t/kUVeyZg+aJfCUGZ4Tuf+fUcL+9Lm72kGf1eZG2GtVecdWPLzLxVYk/5x9/xbF+X2DO1r8YUALaGRQ/f9BQAIkcR8Y6fTvKjZ6rz3ETy0GYlSwTxQ4CpX4m9ab/IRt43iJzxBkG0u67azBEAM99y6CmYx0cAYLQgQOwgtXLlyoggQJwmN2TIEC1rq5sCgC7C+nTdnhtGC9CTDFKizUqWTGIvAmcHRT/Kr65Wln6wjHbPIHKmADDnJV74BwWAufKSJ7148UKWAWKpFipqLAPE1o+7du2SA2LwQ8KmLzi8JnwZIHq4Oqk6AaBzXXgeL5zL7TMTzU+bEyWodz0563FKNFcQOVMAJFrq+td74R8UAPq8A5OTAiAwRcXhUkNF5UVlacjU0GOCaDMFgDkv8cI/KADMlZexJ1EAGEOd8IO8+IgTNsLlDWizS2BxZg8iZwqAOAs7jsu88A8KgDjA234JBYDtJfTbPi8+YtNvS5vNEA8iZwoAM77hFWcKAHPlZexJL1++lNiBRBI2JsJmREFKtNlMaZEzOUcjQP8Ijn9AADRv3tyMwQaeYvUyQAPvz0eQAAmQAAmQQJ0kQAHgUbHjtDtsKhSkRJvNlBY5k3M0AvQP+ocZAn8+hQLAI/LTp0+XpYlBSrTZTGmRMzlHI0D/oH+YIUAB4BtnfsS+oY24MTmTc00EgugbeJcg2k2bzXyHfj+FIwAeEcb5AkOHDvXobmZuQ5vJuSYC9A0zvoGnkLUZ1kHk7DcZCgC/CfP+JEACJEACJGAhAQoACwuFJpEACZAACZCA3wQoAPwmzPuTAAmQAAmQgIUEKACiFAp2CMRBRB8/fpTjYnEQUWZm5h9XnD17Vh09ejTiICLnzOgbN26offv2qR8/fqjWrVur2bNnK5zC51fSsfnWrVvq4MGDctohTsPDgUoFBQVyIh42M8IRzDhwyUnz58/3ffMLHbtv376t1q9fr1q0aBGybe3atSolJUX+30bWFy5ckDleJ1VWVqqOHTuqBQsWGGeNY7XB6PXr12rz5s2qVatW1bqhTf6sY7Nt/qxjs22+rGOzTb4Mx/369assvX7+/LnUAU2bNlVTpkxR2FiparLJp/2q++O5LwVAFGpFRUWqX79+UY8iRoO5YsWKiKOIc3Jy1ODBg+V44Dlz5igcadyyZUtVXl4uJxqOHTs2nrLSukbH5kePHomgwdap+IhWr16tcnNzVe/evaVRWrp0qdhqMunYjUoTYmrDhg1/mGYr66qGQkyNGjVKde/e3TjrO3fuSJnj6OzFixdXKwBs82cdm23zZx2bbfNlHZtt8mVHAED84eh3dF5OnTqlrl+/rpYvXx5hqm0+bbJejfUsCoAaCH348EHNnTtXGkL05rFV8NSpUxV6nOEK8/jx41KRT548We508+ZNhb9Do3/lyhV1/vx5aVCRnj17Jj1YjCr4kXRtrvpsvCPU84gRI4w3SrBF1+5olWYQWN+/f1/EC/aLwFHVtSW2MJJVkwCwyZ/D/TSazbb5s2NPNJtt8uV4ONviy+G2P3jwQEYEiouLI1zCVp/2ow1we08KgBqIPXz4UBxp69atoRxoyAsLC1WnTp1Cf4ehs/T0dJWXlxdq5FHJl5SUqBMnTqhXr16FxMGXL1/UxIkT1YEDB2To3euka3P4c9+/f68WLlwoIqVdu3bSKEH4tGnTRv38+VN169ZNDR8+3Bd7HTt07UaluXHjRpkCAL/+/fvLyAVSEFjv3r1bpn8mTJggNtcGazw3WsNkkz/H0zDZ4M+6AsAWX46Hsy2+HG476tzU1FSpY8OTrT7tdf0fz/0oAKIIADjUli1bYgqAjIwMNWzYMMn39OlTaaRqSwDo2Oy80OfPn2X4v1evXqE9DL59+6bw902aNFGfPn0SAdSlS5eQwInHyWJdAwGgYzfsQsL0xdu3b2U0BeKkZ8+etSIAdGx23h3ib9q0aWrNmjWhOJLaYK0jAGzxZ7cNky3+rCMAbPJlt5xt8mXH9sOHD0t8C6a3/vrrrz8EgI0+HateNPHvFAA1UMawNILhoB6DNAWgYzNeGQGAmM7o2rWrGjlyZI2+dunSJYXfkiVLfPNHXdZVDThy5Ih69+6dmjRpUq1Mt+iyht0IoDp9+rQwrymZYB1LANg6XBprCsAmf9YRADb5slsBYJMvw3b47OXLlyUWq2HDhn98Xrb6tG8VqosbUwBEgYV5fAwz43f16lXpZVatwDHED9WJXj96zZs2bZKglCFDhkgjiyBABLg5QYAYAh43bpyLInKXVcdmBMzhPdCzR0BaeEJjjI8Ic9TooWIaBLbn5+e7M8Rlbh270diDMYb/wXbdunVqwIABauDAgdaydjDg/fr06aMGDRoUIlNbrKM1prb5s05jaqM/xxJatvmyDmcbfRkrbC5evCiNP4b/q0u2+rTLKtKX7BQAUbC+ePFCAvYwFI7ofVScWB6HIC4sncMP6cyZM+rYsWMRywDRgCIhKnX//v2yDBDLrnAPDGH7lXRsxnBZRUVFxJLGHj16yHD6tWvX1KFDh6SRhc2dO3eWuIcGDRr4ZbLcV8duRPmiF40RGdiGSHoIGEQA28oadr18+VItWrRIlZaWih85yTTrsrIy8UfMkzdq1EjiESDwbPZnHZtt82cdm23zZR2bbfJl2IJpwBkzZsjKFmdpNeopdAxs9mlfK1KXN6cAcAmM2UmABEiABEggGQhQACRDKfIdSIAESIAESMAlAQoAl8CYnQRIgARIgASSgQAFQDKUIt+BBEiABEiABFwSoABwCYzZSYAESIAESCAZCFAAJEMp8h1IgARIgARIwCUBCgCXwJidBEiABEiABJKBAAVAMpQi34EEPCSATVWys7PV6NGjPbwrb0UCJGAbAQoA20qE9pBALROgAKjlAuDjScAQAQoAQ6D5GBIIAgHsfIm93p3UrFkz346vDgIP2kgCyUyAAiCZS5fvRgIuCeCUOpxY2KFDBznhEltCN27c2OVdmJ0ESCAIBCgAglBKtJEEDBLgFIBB2HwUCdQiAQqAWoTPR5OAjQQoAGwsFdpEAt4ToADwninvSAKBJkABEOjio/EkoE2AAkAbFTOSQN0gUFRUpLKyslRBQUHdeGG+JQnUUQIUAHW04PnaJFATAawEqKysVLNmzVIpKSkqNTWVsEiABJKQAAVAEhYqX4kEEiHw5MkTWfr39OlTlZaWxmWAicDktSRgMQEKAIsLh6aRAAmQAAmQgF8EKAD8Isv7kgAJkAAJkIDFBCgALC4cmkYCJEACJEACfhGgAPCLLO9LAiRAAiRAAhYToACwuHBoGgmQAAmQAAn4RYACwC+yvC8JkAAJkAAJWEyAAsDiwqFpJEACJEACJOAXAQoAv8jyviRAAiRAAiRgMQEKAIsLh6aRAAmQAAmQgF8E/g931AZ84X2NUQAAAABJRU5ErkJggg==\" width=\"639.999990463257\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Heun Plot \n",
    "plot_approx(our_heun_approx, our_params, \"Heun's Method\", 'g')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The improvment in accuracy is even evident in the graph shown above. The green line approximates the black solution line much better than the red line we saw above from our plot of the Euler's Method approximation\n",
    "\n",
    "<hr>\n",
    "\n",
    "## (iii) Runge-Kutta Method\n",
    "\n",
    "Runge-Kutta metheds area  class of approximation methods developed by mathematicians Carl Runge and Wilhelm Kutta. When one refers to the \"Runge-Kutta Method\", they are most likely refereing to the 4th order method, commonly refered to as \"RK4\".\n",
    "\n",
    "The Runge-Kutta method takes a page out of the Heun Method's playbook by again using an average of several slopes, but instead of using an arithmetic average of 2 slopes it uses a weighted average of 4 slopes. The four slopes are calculated as follows:\n",
    "\n",
    "Assume an initial starting point of t_0 and a step size of h.\n",
    "\n",
    "Slope 1: (denoted m)\n",
    "- The first slope is simply the value of the differential equation at t_0 and the value (or approximated value) of the solution at t_0. (Same slope used in Euler's Method)\n",
    "    \n",
    "Slope 2: (denoted n)\n",
    "- The second slope is a little more involved. It uses the slope m, but then uses that slope to approximate the value of the solution at the time point t_0 + h/2 (so halfway between t_0 and t_0 + h). The second slope n is then the value of the differential equation evaluated at t_0 + h/2 and the approximated value of the solution at t_0 + h/2. \n",
    "\n",
    "Slope 3: (denoted q)\n",
    "- The third slope is similar to the second slope in that it is calculated from evaluating the ODE at t_0 + h/2, but it gets there a little bit differently. It uses the slope n (the one calculated in step 2) at the t_0 to project out to t_0 + h/2, where the third slope q is calculated as the value of the differention given the value of the solution just calculated at t_0 + h/2.\n",
    "\n",
    "Slope 4: (denoted p)\n",
    "- The fourth slope is calculated at time t + h (end of the interval). The value of the solution is approximated using the slope q and the time point t_0 to approximate the value of the solution at time t_0 + h. The differential equation is then evaluated at time t_0 + h with the value of the approximated solution to get the final slope, p.\n",
    "\n",
    "Below we will generate a plot to give a visual of what these slopes represent. As a bonus, we can use the code we write below to help create our Runge-Kutta approximation function!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "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_dpi_ratio', { dpi_ratio: fig.ratio });\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",
       "    if (this.ratio !== 1) {\n",
       "        fig.send_message('set_dpi_ratio', { dpi_ratio: this.ratio });\n",
       "    }\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",
       "    var resizeObserver = new 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 (width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    resizeObserver.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",
       "    // 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",
       "    var cursor = msg['cursor'];\n",
       "    switch (cursor) {\n",
       "        case 0:\n",
       "            cursor = 'pointer';\n",
       "            break;\n",
       "        case 1:\n",
       "            cursor = 'default';\n",
       "            break;\n",
       "        case 2:\n",
       "            cursor = 'crosshair';\n",
       "            break;\n",
       "        case 3:\n",
       "            cursor = 'move';\n",
       "            break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = 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",
       "            /* 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",
       "            evt.data.type = 'image/png';\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",
       "                evt.data\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 http://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",
       " * http://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.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\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",
       "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, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"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.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",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['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.one(\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",
       "\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",
       "    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",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager) {\n",
       "        manager = IPython.keyboard_manager;\n",
       "    }\n",
       "\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=\"639.999990463257\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Initial Conditions\n",
    "t_k = our_params['t_0']\n",
    "y_k = our_params['y_0']\n",
    "\n",
    "# size of each time step\n",
    "dt = (our_params['t_n']-our_params['t_0'])/our_params['n']\n",
    "dt_half = dt/2\n",
    "\n",
    "de = our_ode\n",
    "\n",
    "# Slope 1 (m)\n",
    "m = our_ode.subs([(y,y_k), (t,t_k)])\n",
    "y_k_m = y_k + m * dt_half\n",
    "\n",
    "# Slope 2 (n)\n",
    "n = our_ode.subs([(y,y_k_m), (t, t_k+dt_half)])\n",
    "y_k_n = y_k + n * dt_half\n",
    "\n",
    "# Slope 3 (q)\n",
    "q = our_ode.subs([(y,y_k_n), (t, t_k+dt_half)])\n",
    "y_k_q = y_k + q * dt\n",
    "\n",
    "# Slope 4 (p)\n",
    "p = our_ode.subs([(y,y_k_q), (t, t_k+dt)])\n",
    "y_k_p = y_k + p * dt\n",
    "\n",
    "# approximate value\n",
    "y_k_1 = y_k + ((m + 2 * n + 2 * q + p)/6) * dt\n",
    "\n",
    "# solution (more granular than our time step for plotting purposes)\n",
    "solution_time_stamp = np.arange(t_k,t_k + 1.5*dt,0.01)\n",
    "solution_array = [our_solution.subs(t,x) for x in solution_time_stamp]\n",
    "\n",
    "# plot slopes\n",
    "fig=plt.figure()\n",
    "ax=fig.add_subplot(111)\n",
    "\n",
    "ax.plot(solution_time_stamp, solution_array, c = 'k', label=\"Solution\",fillstyle='none')\n",
    "ax.plot([t_k, t_k+dt/2], [y_k, y_k_m], c = 'r', label=\"Slope 1 (m)\",fillstyle='none')\n",
    "ax.plot([t_k+dt/2, t_k+dt], [y_k_m, y_k_n], c = 'b', label=\"Slope 2 (n)\",fillstyle='none')\n",
    "ax.plot([t_k+dt/2, t_k+dt], [y_k_n, y_k_q], c = 'g', label=\"Slope 3 (q)\",fillstyle='none')\n",
    "ax.plot([t_k+dt, t_k+dt+dt/2], [y_k_q, y_k_p], c = 'y', label=\"Slope 4 (p)\",fillstyle='none')\n",
    "ax.plot([t_k, t_k+dt], [y_k, y_k_1], c = 'c', label=\"Approximated Value\",fillstyle='none')\n",
    "\n",
    "ax.set_title(label = 'RK4 Slopes')\n",
    "ax.set_xlabel(xlabel = 't')\n",
    "ax.set_ylabel(ylabel = 'y(t)')\n",
    "\n",
    "plt.legend(loc=3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Runge-Kutta Function\n",
    "\n",
    "Having already written the code to calculate the four slopes in the RK4 algorithm, we can insert it into our y_approx function to build our RK4 algorithm function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def runge_kutta(de, param):\n",
    "    \n",
    "    # size of each time step\n",
    "    dt = (param['t_n']-param['t_0'])/param['n']\n",
    "    \n",
    "    # initilize list\n",
    "    y_hat = [param['y_0']]\n",
    "    for k in range(0, param['n']):\n",
    "        t_k = param['t_0'] + k * dt\n",
    "        y_k = y_hat[len(y_hat)-1]\n",
    "        \n",
    "        # calculate estimated value\n",
    "        dt_half = dt/2\n",
    "        \n",
    "        m = de.subs([(y,y_k), (t,t_k)])\n",
    "        y_k_m = y_k + m * dt_half\n",
    "        \n",
    "        n = de.subs([(y,y_k_m), (t, t_k+dt_half)])\n",
    "        y_k_n = y_k + n * dt_half\n",
    "        \n",
    "        q = de.subs([(y,y_k_n), (t, t_k+dt_half)])\n",
    "        y_k_q = y_k + q * dt\n",
    "        \n",
    "        p = de.subs([(y,y_k_q), (t, t_k+dt)])\n",
    "        \n",
    "        y_k_hat = y_k + ((m + 2 * n + 2 * q + p)/6) * dt\n",
    "        \n",
    "        # append estimated value\n",
    "        y_hat.append(y_k_hat)\n",
    "        \n",
    "    return y_hat\n",
    "\n",
    "our_rk_approx = runge_kutta(our_ode, our_params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Analyzing the Performance of the Runge-Kutta Method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.000142055256679326\n",
      "Runge-Kutta Improvement Over Eulers Method: 98.89%\n",
      "Runge-Kutta Improvement Over Heun Method: 97.95%\n"
     ]
    }
   ],
   "source": [
    "# value of euler's method approximation at the last time_step\n",
    "rk_at_n = our_rk_approx[-1] \n",
    "# value of the solution at the last time step\n",
    "solution_at_n = our_solution.subs([(t,our_params['t_n'])]).evalf()\n",
    "\n",
    "# error\n",
    "rk_error = abs(rk_at_n - solution_at_n)\n",
    "\n",
    "print(rk_error)\n",
    "print('Runge-Kutta Improvement Over Eulers Method: ' + str(round(100*(1-rk_error/euler_error),2)) + '%')\n",
    "print('Runge-Kutta Improvement Over Heun Method: ' + str(round(100*(1-rk_error/heun_error),2)) + '%')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see from the percent imrpovements in the absolute error that the Runge-Kutta algorithm generates a demonstrably more accurate approximation than our previous two algorithms. (We would certainly hope so given that it is a relatively more complicated algorithm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "            warnings.textContent =\n",
       "                'This browser does not support binary websocket messages. ' +\n",
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       "    this.context = undefined;\n",
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       "            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",
       "    if (this.ratio !== 1) {\n",
       "        fig.send_message('set_dpi_ratio', { dpi_ratio: this.ratio });\n",
       "    }\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",
       "    var resizeObserver = new 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 (width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    resizeObserver.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",
       "    // 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",
       "    var cursor = msg['cursor'];\n",
       "    switch (cursor) {\n",
       "        case 0:\n",
       "            cursor = 'pointer';\n",
       "            break;\n",
       "        case 1:\n",
       "            cursor = 'default';\n",
       "            break;\n",
       "        case 2:\n",
       "            cursor = 'crosshair';\n",
       "            break;\n",
       "        case 3:\n",
       "            cursor = 'move';\n",
       "            break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = 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",
       "            /* 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",
       "            evt.data.type = 'image/png';\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",
       "                evt.data\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 http://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",
       " * http://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.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\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",
       "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, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"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.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",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['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.one(\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",
       "\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",
       "    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",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager) {\n",
       "        manager = IPython.keyboard_manager;\n",
       "    }\n",
       "\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=\"639.999990463257\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Runge-Kutta Plot\n",
    "plot_approx(our_rk_approx, our_params, \"Runge-Kutta Method\", 'b')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "\n",
    "## Improving the Granularity\n",
    "\n",
    "While we have deomonstrated that different approximation algorithms can help us improve accuracy, we haven't tried simply increaseing the number of time points. (Or rather, decreasing the length of the time step)\n",
    "\n",
    "Recall what is [actually happening](https://en.wikipedia.org/wiki/Integral) as the number of time points in our finite interval approaches infintiy. When we increase the number of timesteps, we will approach the integral of our differential equation (the real solution).\n",
    "\n",
    "This will increase the computational cost of running our algorithms, (and improved algorithms were invented for the sole purpose of achieveing better accuracy without having to do this), but we have computers... lets use them!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "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_dpi_ratio', { dpi_ratio: fig.ratio });\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",
       "    if (this.ratio !== 1) {\n",
       "        fig.send_message('set_dpi_ratio', { dpi_ratio: this.ratio });\n",
       "    }\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",
       "    var resizeObserver = new 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 (width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    resizeObserver.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",
       "    // 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",
       "    var cursor = msg['cursor'];\n",
       "    switch (cursor) {\n",
       "        case 0:\n",
       "            cursor = 'pointer';\n",
       "            break;\n",
       "        case 1:\n",
       "            cursor = 'default';\n",
       "            break;\n",
       "        case 2:\n",
       "            cursor = 'crosshair';\n",
       "            break;\n",
       "        case 3:\n",
       "            cursor = 'move';\n",
       "            break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = 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",
       "            /* 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",
       "            evt.data.type = 'image/png';\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",
       "                evt.data\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 http://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",
       " * http://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.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\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",
       "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, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"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.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",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['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.one(\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",
       "\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",
       "    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",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager) {\n",
       "        manager = IPython.keyboard_manager;\n",
       "    }\n",
       "\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=\"639.999990463257\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_list = np.arange(10,100,10)\n",
    "\n",
    "euler_error_list = []\n",
    "heun_error_list = []\n",
    "rk_error_list = []\n",
    "for n in n_list:\n",
    "    # define paramaters\n",
    "    n_params = {'t_0': 0., 't_n': 2., 'n': n, 'y_0': 1.}\n",
    "    \n",
    "    # ground truth value\n",
    "    solution_at_n = our_solution.subs([(t,our_params['t_n'])]).evalf()\n",
    "\n",
    "    \n",
    "    # approximation values\n",
    "    euler_approx = euler(our_ode, n_params)\n",
    "    heun_approx = heun(our_ode, n_params)\n",
    "    rk_approx = runge_kutta(our_ode, n_params)\n",
    "   \n",
    "    # append errors to list\n",
    "    # euler_error_list.append(rmse(euler_approx, solution_values, n_params))\n",
    "    # heun_error_list.append(rmse(heun_approx, solution_values, n_params))\n",
    "    # rk_error_list.append(rmse(rk_approx, solution_values, n_params))\n",
    "    euler_error_list.append(abs(solution_at_n - euler_approx[-1]))\n",
    "    heun_error_list.append(abs(solution_at_n - heun_approx[-1]))\n",
    "    rk_error_list.append(abs(solution_at_n - rk_approx[-1]))\n",
    "    \n",
    "# plot errors\n",
    "fig=plt.figure()\n",
    "ax=fig.add_subplot(111)\n",
    "\n",
    "ax.plot(n_list, euler_error_list, color = 'r', label=\"Euler's Method\",fillstyle='none')\n",
    "ax.plot(n_list, heun_error_list, color = 'g', label=\"Heun's Method\",fillstyle='none')\n",
    "ax.plot(n_list, rk_error_list, color = 'b', label=\"Runge-Kutta Method\",fillstyle='none')\n",
    "ax.set_title(label = 'Comparison of Errors')\n",
    "ax.set_xlabel(xlabel = 'Number of Timesteps')\n",
    "ax.set_ylabel(ylabel = 'RMSE')\n",
    "\n",
    "plt.legend(loc=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is cool to see how the errors converge for each respective algorithm. It is apparent that Euler's method is limited in its potential, while Heun's Method and the RK4 algorithms converge to much smaller errors much faster.\n",
    "\n",
    "There are several interesting features of this plot, for example if you zoom into the range between 10 and 100 you can see that Heun's Method seems to approach a similar error to that of the RK4 method, but never quite reaches it.\n",
    "\n",
    "There is an interesting observation to be made about how the Euler's Method error is related to the number of timesteps, we shall explore further.\n",
    "\n",
    "***\n",
    "\n",
    "## Global Truncation Error of Euler's Method\n",
    "\n",
    "Global truncation error is defined as the error at a the final time point. In our case, it is the error at time 2. Consider our approximation for the solution's value using Euler's Method. At time 0 we have our initial conditions so there is no error. When we project out to the next time step, we are approximating the value of the solution using the slope at time 0 and introduce error (called the *Local Truncation Error*). Then on top of that, we use this approximation to calculate the slope at the this time step (more local truncation error) and approximate the solution's value at the next time step (add on some more local truncation error for good measure). The additive result of all these compounding errors is called the \"Global Truncation Error\".\n",
    "\n",
    "To analyze the effect that the number of steps has on the global trunction error, let's loop over different step counts from 10 to 500 by 10 and calculate the error at each number. Let's make a simple plot to help us think about what is really happening."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "\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",
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       "};\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",
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       "    x0 = Math.floor(x0) + 0.5;\n",
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       "    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",
       "    var cursor = msg['cursor'];\n",
       "    switch (cursor) {\n",
       "        case 0:\n",
       "            cursor = 'pointer';\n",
       "            break;\n",
       "        case 1:\n",
       "            cursor = 'default';\n",
       "            break;\n",
       "        case 2:\n",
       "            cursor = 'crosshair';\n",
       "            break;\n",
       "        case 3:\n",
       "            cursor = 'move';\n",
       "            break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = 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",
       "            /* 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",
       "            evt.data.type = 'image/png';\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",
       "                evt.data\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 http://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",
       " * http://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.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\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",
       "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, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"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.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",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['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.one(\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",
       "\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",
       "    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",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager) {\n",
       "        manager = IPython.keyboard_manager;\n",
       "    }\n",
       "\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=\"639.999990463257\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# list of step counts to loop over\n",
    "n_list = np.arange(10,500,10)\n",
    "\n",
    "# initialize list\n",
    "error_list = []\n",
    "for n in n_list:\n",
    "    # insert the number of steps into our parameters\n",
    "    n_params = {'t_0': 0., 't_n': 2., 'n': n, 'y_0': 1.}\n",
    "    \n",
    "    # ground truth value\n",
    "    solution_at_n = our_solution.subs([(t,our_params['t_n'])]).evalf()\n",
    "    # approximation values\n",
    "    approx = euler(our_ode, n_params)[-1]\n",
    "    # append the error to list\n",
    "    error_list.append(abs(approx - solution_at_n))\n",
    "    \n",
    "# Plot of errors v step count\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(n_list, error_list)\n",
    "ax.set(xlabel='Number of Steps', ylabel='Abolute Error',\n",
    "       title='Error by Number of Steps')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluating the Error Relationship\n",
    "\n",
    "If we can remember back to our algebra days, we might recognize the shape of the curve above as being similar to the function\n",
    "\n",
    "\\begin{equation*}\n",
    "f(x) = \\frac{1}{x}\\\\\n",
    "\\end{equation*}\n",
    "\n",
    "Well, that is because it is very similar. In fact, the error with respect to step count can be modeled with a function of the same form.\n",
    "\n",
    "Let x be the number of time steps in our approximation algorithm and let f(x) be the global truncation error, then:\n",
    "\n",
    "\\begin{equation*}\n",
    "f(x) = \\frac{K}{x}\\\\\n",
    "\\end{equation*}\n",
    "For some constant K.\n",
    "\n",
    "But how do we find K? We will demonstrate one method of approximating this value using ordinary least squares.\n",
    "\n",
    "Consider in the case of linear regression, if we simply rewrite the function as \n",
    "\n",
    "\\begin{equation*}\n",
    "y = K * \\frac{1}{x}\\\\\n",
    "\\end{equation*}\n",
    "\n",
    "and regress y (the error) onto 1/k (1 divided by the step count) to estimate the parameter K."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create an array of 1/(step count)\n",
    "n_list_transformed = np.array([float(1/i) for i in n_list]).reshape(-1,1)\n",
    "error_list = np.array(error_list)\n",
    "\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "regressor = LinearRegression()\n",
    "regressor.fit(n_list_transformed, error_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get our value of K, we will grab the first value in the coef_ attribute of the regressor class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "K Estimate: 0.12733495937131162\n"
     ]
    }
   ],
   "source": [
    "K = regressor.coef_[0]\n",
    "print('K Estimate: ' + str(K))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To analyze the quality of the fit, let's look at the r-squared value of our model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r-squared: 0.9998653418287083\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import r2_score\n",
    "predicted = regressor.predict(n_list_transformed)\n",
    "\n",
    "print('r-squared: ' + str(r2_score(error_list, predicted)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see our model is able to explain nearly all of the variance in our data. Let's plot our model against the observed errors to visually inspect our model's fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function () {\n",
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       "        return MozWebSocket;\n",
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       "        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",
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       "    this.supports_binary = this.ws.binaryType !== undefined;\n",
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       "    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",
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       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
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       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
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       "        fig.send_message('supports_binary', { value: fig.supports_binary });\n",
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       "mpl.figure.prototype._init_header = function () {\n",
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       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
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       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
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       "\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",
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       "    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",
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       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
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       "        '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",
       "    if (this.ratio !== 1) {\n",
       "        fig.send_message('set_dpi_ratio', { dpi_ratio: this.ratio });\n",
       "    }\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
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       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
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       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
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       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
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       "                width = entry.contentRect.width;\n",
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       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
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       "                    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",
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       "                '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 (width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    resizeObserver.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
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       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
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       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
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       "        on_mouse_event_closure('motion_notify')\n",
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       "        on_mouse_event_closure('scroll')(event);\n",
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       "\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",
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       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\n",
       "        return false;\n",
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       "\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",
       "    var cursor = msg['cursor'];\n",
       "    switch (cursor) {\n",
       "        case 0:\n",
       "            cursor = 'pointer';\n",
       "            break;\n",
       "        case 1:\n",
       "            cursor = 'default';\n",
       "            break;\n",
       "        case 2:\n",
       "            cursor = 'crosshair';\n",
       "            break;\n",
       "        case 3:\n",
       "            cursor = 'move';\n",
       "            break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = 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",
       "            /* 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",
       "            evt.data.type = 'image/png';\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",
       "                evt.data\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 http://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",
       " * http://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.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\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",
       "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, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"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.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",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['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.one(\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",
       "\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",
       "    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",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager) {\n",
       "        manager = IPython.keyboard_manager;\n",
       "    }\n",
       "\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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\" 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       "<IPython.core.display.HTML object>"
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   ],
   "source": [
    "# Plot of errors and K\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(n_list, error_list, label = 'Observed Error', c = 'k')\n",
    "ax.plot(n_list, [K/i for i in n_list], label = 'Modeled Error: K = ' + str(round(K,5)), c = 'm')\n",
    "ax.set(xlabel='Number of Steps', ylabel='Abolute Error',title='Error by Number of Steps')\n",
    "plt.legend(loc=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Yep. It looks like we got it. *chef's kiss*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As I am sure you can imagine, this is barely scratching the surface on numerical techniques to evaluate ODE's, let alone all the other interesting topics surrounding ODE's (my personal favorite is the application of the Laplace Transform to solve ODE's). If you found this work interesting, I highly encourage you to dive into other recourses on the topic. I used Blanchard's text book (ISBN-13: [978-0495561989](https://www.chegg.com/textbooks/differential-equations-with-de-tools-printed-access-card-4th-edition-9781133109037-1133109039)) as my primary recourse to learn about differential equations. The text is very well written and easy to follow. Other recourses that I have found useful include online courses on Udemy, such as [this one](https://www.udemy.com/course/a-complete-first-course-in-differential-equations/). I encourage anyone to defer to the recources that are more alinged with their learning style.\n",
    "\n",
    "Lastly, I want to sincerely thank you for taking the time to read through my small project on numerical approximations for solutions of first order ODE's. I found the process of investigating these techniques and creating a practical demonstration to be incredibly rewarding. If you have any questions, comments, or suggested improvements, please don't hesitate to reach out to me at yahr.mason@gmail.com"
   ]
  }
 ],
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