von-Mises.ipynb

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    "# Sampling from the von Mises Distribution  \n",
    "\n",
    "In this notebook we implement functions to calculate and sample from the von Mises distribution [1]. Moreover, we also implement a few simple functions to visualise circular distributions. Strictly speaking one does not need to write their own implementation for calculating the von-Mises probability density function or sampling from it, as it is available in the [scipy statistics package](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.vonmises.html).  Numpy also has an implementation as well, which can be found [here](https://numpy.org/doc/1.16/reference/generated/numpy.random.vonmises.html). However, it is quite easy to write your own implementation (see Refs. [2,3]). However, these libraries don't implement many other functions related to field of directional statistics. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction \n",
    "\n",
    "The von Mises distribution was introduced by Richard von Mises in 1918 [1]. Its probability density function is defined as\n",
    "\\begin{equation}\n",
    "p(\\theta; \\kappa, \\mu) \\equiv \\frac{1}{2\\pi I_{0}(\\kappa)} \\exp\\left( \\kappa \\left[ \\theta - \\mu \\right] \\right)\\  ,\n",
    "\\end{equation}\n",
    "where $\\theta$ is the random angular variable, $\\mu$ is the mean direction such that$-\\pi\\leq \\theta , \\mu < \\pi$, $\\kappa$ is a measure of the \n",
    "concentration of the probability density function and lies in the semi-infinite interval $0\\leq \\kappa < \\infty$. Stricyly speaking the range of $\\theta$ and $\\mu$ can be any interval of length $2\\pi$. The larger the concentration, the more concentrated it is about the mean direction.The function \n",
    "$I_{\\nu}(\\kappa)$ is the modified Bessel function of the first kind,\n",
    "\\begin{equation}\n",
    "I_{\\nu}(\\kappa) \\equiv \\frac{1}{\\pi} \\int_{0}^{\\pi} \\exp\\left( \\kappa \\cos\\theta \\right) \\cos\\left(\\nu\\theta\\right) d\\theta \\  .\n",
    "\\end{equation} \n",
    "\n",
    "Angular random variables are more naturally modelled using circular distributions rather than the almost ubiquitous use of normal distributions. They are more natural  for a number of reasons, a few of which we will now briefly mention:\n",
    "\n",
    "\n",
    "- The von Mises distribution is defined on the correct sample space whereas the normal distribution is not bounded to the interval of length $2\\pi$, e.g., $[-\\pi,\\pi)$ or $[0,2\\pi)$. The normal distribution can be a good approximation away from the boundaries. However, its use can lead to issues near the boundaries.\n",
    "\n",
    "- The von Mises distribution has the correct limiting behaviour as $\\kappa\\to 0$ whereas the normal distribution does not. The von Mises distribution approaches the uniform distribution on the unit circle in this limit, so that all directions are equally likely.\n",
    "\n",
    "- Naive use of normal distributions for circular problems can lead to the incorrect fusion of the prior with the measurement likelihood. Therefore, for example, if you were performing angle of arrival measurements in a tracking application you may be incorrectly fusing measurements when performing a Bayesian update.\n",
    "\n",
    "\n",
    "As the von Mises distribution can be considered a distribution on the unit circle $\\mathbb{S}^{1}$, one can identify the angle $\\theta$ with the unit phasor $e^{i\\theta}$ and the mean direction of the circular random variable $\\alpha$ can be computed as follows\n",
    "\\begin{eqnarray}\n",
    "\\mathbb{E}[\\alpha] & = & \\angle \\int_{-\\pi}^{\\pi} e^{i\\theta} p(\\theta; \\mu, \\kappa) d\\theta \\nonumber\\\\\n",
    "& = & \\angle \\frac{1}{2\\pi I_{0}(\\kappa)} \\int_{-\\pi}^{\\pi} e^{i\\theta} e^{\\kappa \\cos(\\theta -\\mu)} d\\theta \\nonumber\\\\\n",
    "& = & \\angle \\frac{1}{2\\pi I_{0}(\\kappa)} \\int_{-\\pi}^{\\pi} e^{i(\\theta+\\mu)} e^{\\kappa \\cos\\theta} d\\theta \\nonumber\\\\\n",
    "& = & \\angle \\frac{e^{i\\mu}}{2\\pi I_{0}(\\kappa)} \\int_{-\\pi}^{\\pi} e^{i\\theta} e^{\\kappa \\cos\\theta} d\\theta \\nonumber\\\\\n",
    "& = & \\angle \\frac{e^{i\\mu}}{2\\pi I_{0}(\\kappa)} \\int_{-\\pi}^{\\pi} \\left[\\cos\\theta + i \\sin\\theta \\right]e^{\\kappa \\cos\\theta} d\\theta \\nonumber\\\\\n",
    "& = & \\angle \\frac{e^{i\\mu}}{2\\pi I_{0}(\\kappa)} \\int_{-\\pi}^{\\pi} \\cos\\theta e^{\\kappa \\cos\\theta} d\\theta \\nonumber\\\\\n",
    "& = & \\angle \\frac{e^{i\\mu}}{\\pi I_{0}(\\kappa)} \\int_{0}^{\\pi} \\cos\\theta e^{\\kappa \\cos\\theta} d\\theta \\nonumber\\\\\n",
    "& = & \\angle e^{i\\mu} \\frac{I_{1}(\\kappa)}{I_{0}(\\kappa)} \\nonumber \\\\\n",
    "& = & \\mu \\   ,\n",
    "\\end{eqnarray}\n",
    "where $\\angle$ refers to the phase (or angle). The angular distance between two phases can be written as \n",
    "\\begin{equation}\n",
    "d( e^{i\\theta},e^{i\\varphi} )  = \\vert (\\theta - \\varphi)\\ \\ (\\, \\textrm{mod}\\, 2\\pi\\, )\\vert \\   ,\n",
    "\\end{equation}\n",
    "which allows us to calculate the variance of the circular random variable $\\alpha$\n",
    "\\begin{eqnarray}\n",
    "\\sigma_{\\alpha}^{2} & \\equiv &\\mathbb{E}\\left[\\left( d( e^{i\\theta},e^{i\\mu} ) \\right)^{2}\\right] \\nonumber\\\\\n",
    "& = &  \\int_{-\\pi}^{\\pi}  \\vert (\\theta - \\mu)\\ \\ (\\,\\textrm{mod}\\, 2\\pi\\, )\\vert^{2} p(\\theta;\\mu,\\kappa) d\\theta  \\nonumber\\\\\n",
    "& = &  \\frac{1}{2\\pi I_{0}(\\kappa)} \\int_{-\\pi}^{\\pi}  \\vert (\\theta - \\mu)\\ \\ (\\, \\textrm{mod}\\, 2\\pi\\, )\\vert^{2}e^{\\kappa \\cos(\\theta -\\mu)}d\\theta  \\nonumber\\\\\n",
    "& = &  \\frac{1}{2\\pi I_{0}(\\kappa)} \\int_{-\\pi}^{\\pi}  \\theta^{2}e^{\\kappa \\cos\\theta }d\\theta  \\nonumber\\\\\n",
    "& = & \\frac{1}{\\pi I_{0}(\\kappa)} \\int_{0}^{\\pi}  \\theta^{2}e^{\\kappa \\cos\\theta }d\\theta  \\  .\n",
    "\\label{eq:VMvar1}\n",
    "\\end{eqnarray}\n",
    "\n",
    "The input parameters for the von Mises distribution are the mean direction and the concentration whereas experimental error is commonly given in terms of a variance.\n",
    "Fortunately, it is possible to show that the variance is approximately inversely proportional to the concentration, thus allowing us a way to estimate the concentration  using the variance. We rewrite the equation above as \n",
    "\\begin{eqnarray}\n",
    "\\frac{1}{\\pi I_{0}(\\kappa)} \\int_{0}^{\\pi}  \\theta^{2}e^{\\kappa \\cos\\theta }d\\theta\n",
    "& = & \\frac{1}{\\pi I_{0}(\\kappa)} \\int_{0}^{\\pi}  \\theta^{2}\\left(- \\frac{1}{\\kappa\\sin\\theta}\\right)\\frac{d}{d\\theta}\\left( e^{\\kappa \\cos\\theta }\\right) d\\theta \n",
    "\\end{eqnarray}\n",
    "and we use the expansion for the cosecant function \n",
    "\\begin{eqnarray}\n",
    "\\frac{1}{\\sin x} & = & \\sum_{n=0}^{\\infty} \\frac{(-1)^{n+1}2(2^{2n-1}-1)B_{2n}x^{2n-1}}{(2n)!}  \\\\\n",
    "& = & \\frac{1}{x} + \\frac{x}{6} + \\frac{7}{360}x^{3} +\\frac{31}{15120}x^{5} + \\ldots \\ ,\n",
    "\\end{eqnarray}\n",
    "where the $B_{2n}$ are the Bernoulli numbers. This series converges for $0< \\vert x\\vert <\\pi$. If we keep only the first term\n",
    "\\begin{eqnarray}\n",
    "\\frac{1}{\\pi I_{0}(\\kappa)} \\int_{0}^{\\pi}  \\theta^{2}   \\left(- \\frac{1}{\\kappa\\sin\\theta}\\right)\\frac{d}{d\\theta}\\left( e^{\\kappa \\cos\\theta }\\right) d\\theta & &   \\nonumber\\\\\n",
    "& \\sim &  \\frac{1}{\\pi I_{0}(\\kappa)} \\int_{0}^{\\pi}  \\theta^{2}\\left(- \\frac{1}{\\kappa\\theta}\\right)\\frac{d}{d\\theta}\\left( e^{\\kappa \\cos\\theta }\\right) d\\theta + \\ldots\\nonumber\\\\\n",
    "& = & -\\frac{1}{\\kappa \\pi I_{0}(\\kappa)}  \\int_{0}^{\\pi} \\theta \\frac{d}{d\\theta}  \\left( e^{\\kappa\\cos\\theta} \\right) d\\theta + \\ldots \\nonumber\\\\\n",
    "& = & -\\frac{1}{\\kappa \\pi I_{0}(\\kappa)} \\left[ - \\int_{0}^{\\pi} e^{\\kappa\\cos\\theta} d\\theta + \\left.\\theta e^{\\kappa\\cos\\theta}\\right\\vert_{0}^{\\pi} \\right]+ \\ldots \\nonumber\\\\\n",
    "& = & -\\frac{1}{\\kappa \\pi I_{0}(\\kappa)} \\left[ - \\pi I_{0}(\\kappa) + \\pi e^{-\\kappa} \\right]+ \\ldots \\nonumber\\\\\n",
    "& = & \\frac{1}{\\kappa} - \\frac{1}{\\kappa I_{0}(\\kappa)} e^{-\\kappa} + \\ldots \\ .\n",
    "\\end{eqnarray}\n",
    "One should note that while the regular Bessel functions are oscillatory, the modified Bessel functions are not. The modified Bessel functions of the first kind $I_{n}(\\kappa)$ grow exponentially fast with $\\kappa$. Since the second term is divided by $I_{0}(\\kappa)$ the approximation\n",
    "$\\sigma_{\\alpha}^{2} \\simeq  1/\\kappa$ should be reasonable provided $\\kappa$ is large enough. Vice versa if we have an empirically determined variance we could approximate the concentration by $1/\\sigma_{\\alpha}^{2}$.\n",
    "\n",
    "\n",
    "\n",
    "In this notebook we will be making use of the algorithm by Best and Fisher to sample the von-Mises distribution. This algorithm only requires sampling of a uniform distribution on $[0,1]$ and using some trignometric and logarithmic  functions [2].\n",
    "\n"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation\n",
    "\n",
    "### Imports "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.special import iv # Bessel function of the first kind\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from collections import Counter \n",
    "import matplotlib.cm as cm\n",
    "from mpl_toolkits.mplot3d import axes3d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probability Density Function (PDF)\n",
    "\n",
    "Documentation for the Bessel function of the first kind can be found  [here](https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.iv.html#scipy.special.iv) under the [scipy special functions section.](https://docs.scipy.org/doc/scipy/reference/special.html) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pdf_von_Mises(theta,mu,kappa):\n",
    "    \"\"\"\n",
    "        pdf_von_Mises(theta,mu,kappa)\n",
    "        =============================\n",
    "        \n",
    "        Calculates the von Mises probability density distribution at the angle theta with mean\n",
    "        direction mu and concentration kappa.\n",
    "\n",
    "        INPUT:\n",
    "\n",
    "            * theta - angle at which to evaluate the von Mises distribution (float or numpy array)\n",
    "            * mu - mean direction (float)\n",
    "            * kappa - concentration (float)\n",
    "\n",
    "        OUTPUT:\n",
    "\n",
    "             * pdf - the probability density function is an Nx1 (same size as theta) array of values of a von Mises\n",
    "             distribution with mean direction mu and concentration kappa.\n",
    "\n",
    "        References:\n",
    "        ===========\n",
    "\n",
    "        See the following textbook/monograph\n",
    "\n",
    "        [1] N. I. Fisher, Statistical analysis of circular data, Cambridge University Press, (1993).\n",
    "\n",
    "    \"\"\" \n",
    "    \n",
    "    pdf = np.exp(kappa * np.cos(theta - mu)) / (2.0*np.pi*iv(0,kappa));\n",
    "\n",
    "    return pdf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rand_von_Mises(N,mu,kappa):\n",
    "\n",
    "    \"\"\"\n",
    "        rand_von_Mises(N,mu,kappa)\n",
    "        ==========================\n",
    "        \n",
    "        Generates theta an Nx1 array of samples of a von Mises distribution\n",
    "        with mean direction mu and concentration kappa.\n",
    "\n",
    "        INPUT:\n",
    "         \n",
    "            * N - number of samples to be generated (integer)\n",
    "            * mu - mean direction (float)\n",
    "            * kappa - concentration (float)\n",
    "\n",
    "        OUTPUT:\n",
    "         \n",
    "            * theta - an Nx1 array of samples of a von Mises distribution with mean \n",
    "            direction mu and concentration kappa.\n",
    "\n",
    "         References:\n",
    "         ===========\n",
    "\n",
    "         Algorithm first given in\n",
    "\n",
    "         [1] D. J. Best and N. I. Fisher, Efficient Simulation of the von Mises\n",
    "         Distribution, Applied Statistics, 28, 2, 152--157, (1979).\n",
    "\n",
    "         Also given in the following textbook/monograph\n",
    "\n",
    "         [2] N. I. Fisher, Statistical analysis of circular data, Cambridge University Press, (1993).\n",
    "\n",
    "    \"\"\"\n",
    "    \n",
    "    # Checks \n",
    "    # =======\n",
    "\n",
    "    # N should be a positive non-zero integer scalar \n",
    "    if (type(N) is not int): \n",
    "        raise TypeError(\"N must be a positive non-zero integer.\")\n",
    "    if N <= 0:\n",
    "        raise Exception(\"N must be a positive non-zero integer.\")\n",
    "        \n",
    "    #  mu should be a real scalar. It can wrap around the circle, so it can be negative, positive and also \n",
    "    #  outside the range [0,2*pi].\n",
    "    if (type(mu) is not float) and (type(mu) is not int):\n",
    "        raise TypeError(\"mu must be a real scalar number.\")\n",
    "\n",
    "    # kappa should be positive real scalar \n",
    "    if (type(kappa) is not float) and (type(kappa) is not int): \n",
    "        raise TypeError(\"kappa must be a positive float.\")\n",
    "    if kappa < 0:\n",
    "        raise Exception(\"kappa must be a positive float.\")\n",
    "\n",
    "    #  SPECIAL CASE\n",
    "    # ==============\n",
    "\n",
    "    #  As kappa -> 0 one obtains the uniform distribution on the circle\n",
    "    float_epsilon = np.finfo(float).eps\n",
    "    if kappa <= float_epsilon:\n",
    "        theta = 2.0 * np.pi * np.random.rand(N,1) # [0,1] -> [0,2*pi]\n",
    "        return theta\n",
    "\n",
    "    # MAIN BODY OF ALGORITHM\n",
    "    # =======================\n",
    "    \n",
    "    # Used same notation as Ref.~[2], p49\n",
    "    \n",
    "    a = 1.0 + np.sqrt(1.0 + 4.0 * kappa**2)\n",
    "    b = (a - np.sqrt(2.0 * a)) / (2.0 * kappa)\n",
    "    r = (1.0 + b**2) / (2.0 * b)\n",
    "\n",
    "    counter = 0 \n",
    "    theta = np.zeros((N,1)) \n",
    "\n",
    "    while counter <= N-1:\n",
    "        \n",
    "        # Pseudo-random numbers sampled from a uniform distribution [0,1]\n",
    "        U1 = np.random.rand()\n",
    "        U2 = np.random.rand()\n",
    "        U3 = np.random.rand() \n",
    "        \n",
    "        z = np.cos(np.pi * U1)\n",
    "        f = (1.0 + r *z) / (r + z)\n",
    "        c = kappa * (r - f)\n",
    "        \n",
    "        if ( ((c * (2.0 - c) - U2) > 0.0)  or ((np.log(c/U2) + 1.0 - c) > 0.0) ):\n",
    "        \n",
    "            theta[counter] = np.mod(np.sign(U3 - 0.5) * np.arccos(f) + mu, 2*np.pi)     \n",
    "            counter += 1\n",
    "\n",
    "    return theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2.65622723]\n",
      " [0.70913402]\n",
      " [2.06468918]\n",
      " [1.81297093]\n",
      " [1.34114562]]\n"
     ]
    }
   ],
   "source": [
    "theta = rand_von_Mises(5,2,3)\n",
    "print(theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualisation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x864 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,axes = plt.subplots(2,2,figsize=(15,12))\n",
    "axes = axes.flatten()\n",
    "\n",
    "# Number of samples \n",
    "N = 10000\n",
    "\n",
    "# Number of bins\n",
    "nbins = 100\n",
    "\n",
    "# Fix kappa\n",
    "kappa = 5\n",
    "\n",
    "# Vary mu \n",
    "means = [ (x * np.pi * 0.6) for x in range(4) ] \n",
    "\n",
    "# Full range of theta for calculating the pdf \n",
    "t = np.linspace(0,2*np.pi,1000, endpoint=False)\n",
    "\n",
    "for i in range(4):\n",
    "    \n",
    "    # Probability density line\n",
    "    pdf = pdf_von_Mises(t,means[i],kappa)\n",
    "    \n",
    "    # von-Mises samples\n",
    "    t_samples = rand_von_Mises(N,means[i],kappa)\n",
    "    \n",
    "    # Plot histogram \n",
    "    axes[i].hist(t_samples,bins=nbins,density=True,alpha=0.3,color='black');\n",
    "    \n",
    "    # Plot PDF\n",
    "    axes[i].plot(t,pdf,color='red',lw=2);\n",
    "    \n",
    "    # Layout and labels\n",
    "    axes[i].autoscale(tight=True)\n",
    "    axes[i].set_title('$\\mu$ = '+ str(means[i])[:5] + \", \" + '$\\kappa = $ '+ str(kappa),fontsize=16)\n",
    "    axes[i].set_xlabel(r'$\\theta$ [radians]',fontsize=16)\n",
    "    axes[i].set_ylabel('Probability',fontsize=16)\n",
    "    \n",
    "# More layout and labels\n",
    "fig.suptitle('Fixed $\\kappa$, Varied $\\mu$',fontsize=20)\n",
    "fig.tight_layout()\n",
    "fig.subplots_adjust(top=0.9)\n",
    "fig.subplots_adjust(wspace=0.3, hspace=0.3)\n",
    "\n",
    "# Save it\n",
    "plt.savefig(\"vm-fix-k-vary-mu.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x864 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,axes = plt.subplots(2,2,figsize=(15,12))\n",
    "axes = axes.flatten()\n",
    "\n",
    "# Number of samples \n",
    "N = 10000\n",
    "\n",
    "# Number of bins\n",
    "nbins = 100\n",
    "\n",
    "# Vary kappa\n",
    "kappas = [x*0.6 for x in range(4)]\n",
    "\n",
    "# fix mu \n",
    "mu = np.pi\n",
    "\n",
    "for i in range(4):\n",
    "    \n",
    "    # Probability density line\n",
    "    pdf = pdf_von_Mises(t,mu,kappas[i])\n",
    "    \n",
    "    # von-Mises samples\n",
    "    t_samples = rand_von_Mises(N,mu,kappas[i])\n",
    "    \n",
    "    # Plot histogram \n",
    "    axes[i].hist(t_samples,bins=nbins,density=True,alpha=0.3,color='black');\n",
    "    \n",
    "    # Plot PDF\n",
    "    axes[i].plot(t,pdf,color='red',lw=2);\n",
    "    \n",
    "    # Layout and labels\n",
    "    axes[i].autoscale(tight=True)\n",
    "    axes[i].set_title('$\\mu$ = '+ str(mu)[:5] + \", \" + '$\\kappa = $ '+ str(kappas[i])[:5],fontsize=16)\n",
    "    axes[i].set_xlabel(r'$\\theta$ [radians]',fontsize=16)\n",
    "    axes[i].set_ylabel('Probability',fontsize=16)\n",
    "    \n",
    "# More layout and labels\n",
    "fig.suptitle('Fixed $\\mu$, Varied $\\kappa$',fontsize=20)\n",
    "fig.tight_layout()\n",
    "fig.subplots_adjust(top=0.9)\n",
    "fig.subplots_adjust(wspace=0.3, hspace=0.3)\n",
    "\n",
    "# Save it\n",
    "plt.savefig(\"vm-fix-mu-vary-k.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def polar2cartesian(r,theta):\n",
    "    \n",
    "    \"\"\"\n",
    "        polar22cartesian(r,theta)\n",
    "        =========================\n",
    "    \n",
    "        This function converts polar coordinates to cartesian coordinates. Note that \n",
    "        we allow r to be scalar, it will broadcast to the correct size if theta is \n",
    "        an array.\n",
    "        \n",
    "        INPUT: \n",
    "        \n",
    "            * r - radial coordinate - float scalar or array the same size as theta. \n",
    "            * theta - angular coordinate - float scalar or array.\n",
    "        \n",
    "        OUTPUT: \n",
    "        \n",
    "            * x, y - Cartesian coordinates - these are arrays of floats the same size as theta.\n",
    "        \n",
    "    \"\"\"\n",
    "    \n",
    "    x = r * np.cos(theta)\n",
    "    y = r * np.sin(theta)\n",
    "    \n",
    "    return x,y\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_label_colours(labels):\n",
    "    \n",
    "    \"\"\"\n",
    "        get_label_colours(labels)\n",
    "        =========================\n",
    "\n",
    "        Creates an array of distinct colours for the distinct classes in the array labels. This \n",
    "        array is the same size as labels. \n",
    "        \n",
    "        INPUT: \n",
    "        \n",
    "            * labels - an array of labels. \n",
    "            \n",
    "        OUTPUT: \n",
    "        \n",
    "            * colours - an array of colours of the same size as labels with distinct colours for \n",
    "            distinct classes in labels.\n",
    "    \"\"\"\n",
    "    \n",
    "    # Assigns a unique colour to each distinct label. A dictionary is returned from distinct_colours() \n",
    "    # with keys equal to the distinct classes in labels and the values are the distinct colours.\n",
    "    dic = distinct_colours(labels)\n",
    "        \n",
    "    # Create an array of the same length as labels containing distinct colours for each distinct label   \n",
    "    colours = [dic[l] for l in labels]\n",
    "\n",
    "    return colours"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def distinct_colours(labels):\n",
    "    \n",
    "    \"\"\"\n",
    "        distinct_colours(labels)\n",
    "        ========================\n",
    "        \n",
    "        INPUT: \n",
    "        \n",
    "            * labels - an array of labels. \n",
    "            \n",
    "        OUTPUT: \n",
    "        \n",
    "            * dic - a dictionary with keys equal to the distinct classes in\n",
    "            labels and the values are the distinct colours.\n",
    "            \n",
    "        NOTES: requires \"from collections import Counter\"\n",
    "          \n",
    "    \"\"\"\n",
    "    \n",
    "    # keys = labels, values = counts\n",
    "    dic = dict(Counter(labels)) \n",
    "    \n",
    "    # list of distinct labels\n",
    "    distinct_labels = list(dic.keys()) \n",
    "    \n",
    "    # number of distinct labels \n",
    "    num_labels = len(distinct_labels) \n",
    "    \n",
    "    # distinct colours, length is num_labels\n",
    "    distinct_colours = cm.rainbow(np.linspace(0, 1, num_labels)) \n",
    "    \n",
    "    # Replace counts with colours in the dictionary\n",
    "    for i,l in enumerate(dic): \n",
    "        dic[l] = distinct_colours[i] \n",
    "    \n",
    "    return dic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_angular_scatter(samples,labels=None,ms=100):\n",
    "    \n",
    "    \"\"\"\n",
    "        plot_angular_scatter(samples,labels=None,ms=100)\n",
    "        ================================================\n",
    "        \n",
    "        Creates a scatter plot on a circle of samples from a circular distribution. \n",
    "        \n",
    "        INPUT: \n",
    "        \n",
    "            * samples - samples of a circular distribution - either a scalar or array of floats.\n",
    "            * labels - an optional argument containing class labels, default is None. \n",
    "            * ms - an optional argument markersize, default is 100.\n",
    "            \n",
    "        OUTPUT: \n",
    "        \n",
    "            * Scatter plot on a circle of samples from a circular distribution.\n",
    "            * ax (axes) - axes on which the plot is constructed.\n",
    "    \n",
    "    \"\"\"\n",
    "    \n",
    "    # Plot the unit circle S^{1}\n",
    "    # ==========================\n",
    "    \n",
    "    # Radius\n",
    "    r = 1.0\n",
    "    \n",
    "    # Angular grid \n",
    "    theta = np.linspace(0,2*np.pi,500, endpoint=False)\n",
    "    \n",
    "    # Convert polar coordinates to cartesian coordinates\n",
    "    [x,y] = polar2cartesian(r,theta)\n",
    "    \n",
    "    # Plot the circle \n",
    "    plt.plot(x,y,color='black',lw=2,zorder=0) # zorder=0 puts the circle behind all the data\n",
    "    \n",
    "    # Make aspect square\n",
    "    ax = plt.gca() \n",
    "    ax.set_aspect('equal')\n",
    "    \n",
    "    # Make the scatter plot of samples \n",
    "    # ================================\n",
    "    \n",
    "    # Convert polar coordinates to cartesian coordinates\n",
    "    [xi,yi] = polar2cartesian(r,samples)\n",
    "    \n",
    "    if labels is None:\n",
    "        \n",
    "        # if there are no labels plot every point a different colour\n",
    "        colors = cm.rainbow(np.linspace(0, 1, len(xi)))\n",
    "        scatter = plt.scatter(xi,yi,color=colors,label=labels)\n",
    "        \n",
    "    else:\n",
    "        \n",
    "        # if labels are given create a dictionary were the keys are \n",
    "        # the distinct labels and the values are distinct colours\n",
    "        dic = distinct_colours(labels)        \n",
    "        \n",
    "        # Loop over each distinct class (label)\n",
    "        for k in dic.keys():\n",
    "            \n",
    "            # Get indices for this distinct class\n",
    "            indices = [i for i, l in enumerate(labels) if l == k]\n",
    "            \n",
    "            # Get coordinates for this distinct class\n",
    "            x = [xi[i] for i in indices]\n",
    "            y = [yi[i] for i in indices]\n",
    "            \n",
    "            # Plot this class\n",
    "            plt.scatter(x,y,color=dic[k],label=k,s=ms)   \n",
    "        \n",
    "        # Turn axes off\n",
    "        ax = plt.gca()\n",
    "        ax.axis('off')  \n",
    "        \n",
    "    return ax "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Mock data \n",
    "t_samples = rand_von_Mises(25,mu,kappa=5)\n",
    "labels = ['small']*10 + ['medium']*4 + ['large']*6 + ['x-large']*5\n",
    "\n",
    "# Plot the angular scatter plot\n",
    "fig = plt.figure(figsize=(8,4))\n",
    "plot_angular_scatter(t_samples,labels)\n",
    "\n",
    "# Legend\n",
    "plt.legend(frameon=False,loc=\"center left\", bbox_to_anchor=(1,0.5), ncol=1,  fontsize=16)\n",
    "\n",
    "# Save it\n",
    "plt.savefig(\"vm-ang-scatter.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_angular_density(theta,pdf,colour=\"blue\",maxline=False,axes=\"off\",fs=16):\n",
    "    \n",
    "    \"\"\"\n",
    "        plot_angular_density(theta,pdf,colour=\"blue\",maxline=False,axes=\"off\",fs=16)\n",
    "        ============================================================================\n",
    "        \n",
    "        Plots the probability density function of a circular distribution on the unit \n",
    "        circle.\n",
    "        \n",
    "        INPUT: \n",
    "        \n",
    "            * theta - angular grid - an array of floats. \n",
    "            * pdf - the values of the probability density function on the angular grid theta. \n",
    "            * colour - an optional argument, the colour of the pdf curve, a string. \n",
    "            * maxline - an optional argument, whether or not to include a line connecting the \n",
    "            centre of the circle with the maximum value of pdf, boolean. \n",
    "            * axes - an optional argument, whether or not to include the axes, boolean.\n",
    "            * fs - an optional argument, the fontsize.\n",
    "        \n",
    "        OUTPUT: \n",
    "        \n",
    "            * A plot on a circle of a circular distribution.\n",
    "            * ax (axes) - axes on which the plot is constructed.\n",
    "    \n",
    "    \"\"\"\n",
    "    \n",
    "    # Draw the unit circle \n",
    "    # ====================\n",
    "    \n",
    "    # Radius\n",
    "    r = 1.0\n",
    "    \n",
    "    # Angular grid \n",
    "    ctheta = np.linspace(0,2*np.pi,500, endpoint=False)\n",
    "    \n",
    "    # Convert polar coordinates to cartesian coordinates\n",
    "    [x,y] = polar2cartesian(r,ctheta)\n",
    "    \n",
    "    # Plot the unit circle \n",
    "    plt.plot(x,y,color='black',lw=2,zorder=0)\n",
    "    \n",
    "    # Draw angular probability density \n",
    "    # ================================\n",
    "    \n",
    "    # PDF will be drawn on the circle, so we need to account for the radius of the unit circle \n",
    "    d = r + pdf\n",
    "    \n",
    "    # Convert polar coordinates of the pdf to cartesian coordinates\n",
    "    [xi,yi] = polar2cartesian(d,theta)\n",
    "    \n",
    "    # Plot the PDF\n",
    "    plt.plot(xi,yi,color=colour,lw=2)\n",
    "    \n",
    "    # Layout\n",
    "    ax = plt.gca() \n",
    "    ax.set_aspect('equal')\n",
    "    ax.axis(axes)\n",
    "    \n",
    "    #  Add axes angles in radians\n",
    "    plt.text(0.8, -0.05, r\"$0$\", fontsize=fs)\n",
    "    plt.text(-0.17, 0.77, r\"$\\pi/2$\", fontsize=fs)\n",
    "    plt.text(-0.87, -0.05, r\"$\\pi$\", fontsize=fs)\n",
    "    plt.text(-0.17, -0.85, r\"$\\pi/2$\", fontsize=fs)\n",
    "    \n",
    "    # Add axes tick marks\n",
    "    plt.scatter(0,0,marker=\"+\",s=50,color='black')\n",
    "    plt.scatter(1,0,marker=\"+\",s=50,color='black')\n",
    "    plt.scatter(0,1,marker=\"+\",s=50,color='black')\n",
    "    plt.scatter(-1,0,marker=\"+\",s=50,color='black')\n",
    "    plt.scatter(0,-1,marker=\"+\",s=50,color='black')\n",
    "    \n",
    "    if maxline: \n",
    "        # Add a line from the origin to the maximum of the pdf\n",
    "        idx = np.argmax(pdf)\n",
    "        lx = [0,xi[idx]]\n",
    "        ly = [0,yi[idx]]  \n",
    "        plt.plot(lx,ly,color=\"black\",alpha=0.3)\n",
    "    \n",
    "    return ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# PDF grid \n",
    "t = np.linspace(0,2*np.pi,1000, endpoint=False)\n",
    "# PDF parameters \n",
    "mu = 2.\n",
    "kappa = 20\n",
    "\n",
    "# The PDF \n",
    "pdf = pdf_von_Mises(t,mu,kappa)\n",
    "\n",
    "# Plot the PDF on a circle \n",
    "fig = plt.figure(figsize=(8,6))\n",
    "plot_angular_density(t,pdf,colour=\"green\",maxline=True)\n",
    "\n",
    "# Save it\n",
    "plt.savefig(\"vm-ang-density.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Use the two plots together \n",
    "fig = plt.figure(figsize=(8,6))\n",
    "plot_angular_density(t,pdf,colour=\"green\",maxline=True)\n",
    "plot_angular_scatter(t_samples,labels)\n",
    "\n",
    "# Legend\n",
    "plt.legend(frameon=False,loc=\"center left\", bbox_to_anchor=(1,0.5), ncol=1,  fontsize=16)\n",
    "\n",
    "# Save it\n",
    "plt.savefig(\"vm-ang-scatter-density.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def polar_hist(samples, nbins,colour=\"blue\",ax=None,label=None,grid=True,circle_radius=1,density=True):\n",
    "    \n",
    "    \"\"\"\n",
    "        polar_hist(samples, nbins,colour=\"blue\",ax=None,label=None,grid=True,circle_radius=1,density=True)\n",
    "        ==================================================================================================\n",
    "        \n",
    "        Creates a histogram of samples from a circular distribution and plots in on a circle.\n",
    "        \n",
    "        INPUT: \n",
    "        \n",
    "            * samples - samples from a circular distribution, a scalar or array of floats. \n",
    "            * nbins - number of histogram bins. \n",
    "            * colour - an optional argument, the colour of the histogram. \n",
    "            * ax - an optional argument, ax is an axes object. Use ax to plot multiple polar histograms\n",
    "            on the same set of axes.\n",
    "            * label - an optional argument to pass a label for the data.\n",
    "            * grid - an optional argument, whether or not to show the polar grid.\n",
    "            * circle_radius - an optional argument, it is the radius on which the histogram is plotted. \n",
    "            If you choose density=True, you should accept the default of 1. However, if you set \n",
    "            density=False, you should manually select the radius depending on your data count. \n",
    "            * density - an optional argument, if true the normalised histogram is plotted, else the \n",
    "            count is used. \n",
    "            \n",
    "        OUTPUT: \n",
    "        \n",
    "            * A polar histogram plot is created. \n",
    "            * ax - the axes object on which the polar histogram was plotted. Use ax to plot multiple \n",
    "            polar histograms on the same set of axes.\n",
    "            \n",
    "    \"\"\"\n",
    "    \n",
    "    # The polar axis\n",
    "    if ax is None:\n",
    "        ax = plt.axes(polar=True, frameon=False)\n",
    "\n",
    "    # radius of inner circle\n",
    "    bottom = circle_radius\n",
    "\n",
    "    # theta grid\n",
    "    theta = np.linspace(0.0, 2*np.pi, nbins, endpoint=False)\n",
    "\n",
    "    # histogram bin heights and edges\n",
    "    bin_heights, bin_edges = np.histogram(samples,bins=nbins,range=(0,2*np.pi),density=density)\n",
    "    \n",
    "    # height of radial bins \n",
    "    radii = bin_heights\n",
    "\n",
    "    # bin width\n",
    "    width = bin_edges[1] - bin_edges[0]\n",
    "\n",
    "    # bar plot on polar axes \n",
    "    bars = ax.bar(theta, radii, width=width, bottom=bottom,color=colour, edgecolor='k',alpha=0.5,label=label)\n",
    "    \n",
    "    # polar grid\n",
    "    if not grid:\n",
    "        \n",
    "        ax.grid(linewidth=2,color=\"black\",alpha=0.5)\n",
    "        ax.set_rgrids([0,bottom], angle=222,labels=[])\n",
    "        ax.set_thetagrids([])\n",
    "        \n",
    "    else: \n",
    "        \n",
    "        if density:\n",
    "           \n",
    "            radial = [0,0.5,1,1.5,2,2.5]\n",
    "            radial_labels = [x - bottom for x in radial]    \n",
    "            \n",
    "        else: \n",
    "            \n",
    "            mx = max(bin_heights)      \n",
    "            radial = range(0,mx+int(bottom*2),int(bottom/2))\n",
    "            radial_labels = [x - bottom for x in radial]\n",
    "\n",
    "        # First two labels are inside the inner circle (bottom),\n",
    "        # so remove them\n",
    "        radial_labels[0] = \"\"\n",
    "        radial_labels[1] = \"\"\n",
    "        \n",
    "        # Update to correct labels\n",
    "        ax.set_rgrids(radial,labels=radial_labels)\n",
    "        \n",
    "\n",
    "    return ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Mock Data\n",
    "# Number of data points\n",
    "N = 1000\n",
    "\n",
    "# Three sets of data\n",
    "t_samples_1 = rand_von_Mises(N,mu=2,kappa=20)\n",
    "t_samples_2 = rand_von_Mises(N,mu=4,kappa=30)\n",
    "t_samples_3 = rand_von_Mises(N,mu=5,kappa=4)\n",
    "\n",
    "# Plot the NORMALISED polar histograms of the three sets of data on the same set of axes\n",
    "fig = plt.figure(figsize=(14,8))\n",
    "\n",
    "# Set 1\n",
    "ax=polar_hist(t_samples_1,nbins=100,colour=\"blue\",label=\"Set 1\",grid=True)\n",
    "\n",
    "# Set 2\n",
    "ax=polar_hist(t_samples_2,nbins=100,colour=\"green\",ax=ax,label=\"Set 2\",grid=True)\n",
    "\n",
    "# Set 3\n",
    "ax = polar_hist(t_samples_3,nbins=100,colour=\"orange\",ax=ax,label=\"Set 3\",grid=True)\n",
    "\n",
    "# Legend    \n",
    "plt.legend(frameon=False,loc=\"center left\", bbox_to_anchor=(1.1, 0.8), ncol=1,  fontsize=20)  \n",
    "\n",
    "# Save it\n",
    "plt.savefig(\"vm-polar-hist-normalised.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the polar histograms of the three sets of data on the same set of axes\n",
    "fig = plt.figure(figsize=(14,8))\n",
    "\n",
    "# Circle radius\n",
    "cr = 50\n",
    "\n",
    "# Set 1\n",
    "ax=polar_hist(t_samples_1,nbins=100,colour=\"blue\",label=\"Set 1\",grid=True,density=False,circle_radius=cr)\n",
    "\n",
    "# Set 2\n",
    "ax=polar_hist(t_samples_2,nbins=100,colour=\"green\",ax=ax,label=\"Set 2\",grid=True,density=False,circle_radius=cr)\n",
    "\n",
    "# Set 3\n",
    "ax=polar_hist(t_samples_3,nbins=100,colour=\"orange\",ax=ax,label=\"Set 3\",grid=True,density=False,circle_radius=cr)\n",
    "\n",
    "# Legend    \n",
    "plt.legend(frameon=False,loc=\"center left\", bbox_to_anchor=(1.1, 0.8), ncol=1,  fontsize=20)  \n",
    "\n",
    "# Save it\n",
    "plt.savefig(\"vm-polar-hist.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_angular_density_3d(theta,pdf,colour=\"blue\",axes=\"off\",fs=16,label=None):\n",
    "    \n",
    "    \"\"\"\n",
    "        plot_angular_density_3d(theta,pdf,colour=\"blue\",axes=\"off\",fs=16)\n",
    "        ============================================================================\n",
    "        \n",
    "        Plots the probability density function of a circular distribution on the unit \n",
    "        circle.\n",
    "        \n",
    "        INPUT: \n",
    "        \n",
    "            * theta - angular grid - an array of floats. \n",
    "            * pdf - the values of the probability density function on the angular grid theta. \n",
    "            * colour - an optional argument, the colour of the pdf curve, a string. \n",
    "            * axes - an optional argument, whether or not to include the axes, boolean.\n",
    "            * fs - an optional argument, the fontsize.\n",
    "        \n",
    "        OUTPUT: \n",
    "            \n",
    "            * ax (axes) - Return axes of plot \n",
    "            * A plot on a circle of a circular distribution.\n",
    "    \n",
    "    \"\"\"\n",
    "    \n",
    "    # Set projection\n",
    "    ax = plt.axes(projection='3d')\n",
    "    \n",
    "    # Draw the unit circle \n",
    "    # ====================\n",
    "    \n",
    "    # Radius\n",
    "    r = 1.0\n",
    "    \n",
    "    # Angular grid \n",
    "    ctheta = np.linspace(0,2*np.pi,500, endpoint=False)\n",
    "    \n",
    "    # Convert polar coordinates to cartesian coordinates\n",
    "    [x,y] = polar2cartesian(r,ctheta)\n",
    "    \n",
    "    # Plot the unit circle \n",
    "    plt.plot(x,y,0,color='black',lw=2,zorder=0)\n",
    "    \n",
    "    # Draw angular probability density \n",
    "    # ================================\n",
    "        \n",
    "    # Convert polar coordinates to cartesian coordinates\n",
    "    [xi,yi] = polar2cartesian(r,theta)\n",
    "    \n",
    "    z = pdf\n",
    "    \n",
    "    # Plot the PDF\n",
    "    ax.plot(xi,yi,z,color=colour,lw=2,label=label)\n",
    "    \n",
    "    # Limits\n",
    "    ax.set_xlim((-1,1))\n",
    "    ax.set_ylim((-1,1))\n",
    "    \n",
    "    # Turn off grid \n",
    "    ax.grid(False)\n",
    "    \n",
    "    # Labels \n",
    "    ax.set_xlabel('x',fontsize=fs)\n",
    "    ax.set_ylabel('y',fontsize=fs)\n",
    "    ax.set_zlabel('z',fontsize=fs)\n",
    "    ax.zaxis.set_rotate_label(False)\n",
    "    \n",
    "    # Ticks \n",
    "    ax.set_xticks([-1,0,1])\n",
    "    ax.set_yticks([-1,0,1])\n",
    "    \n",
    "    return ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\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('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",
       "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 = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(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 (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.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 = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\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 nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\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",
       "\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",
       "\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]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.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, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\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",
       "    {\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.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",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\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(\"No handler for the '\" + msg_type + \"' message type: \", msg);\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(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\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",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\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",
       "    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",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\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",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\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,\n",
       "                             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\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";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 = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\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.get(0);\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",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\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).html('<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/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<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 () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('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",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\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",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\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('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"800\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# PDF grid \n",
    "%matplotlib notebook\n",
    "t = np.linspace(0,2*np.pi,1000, endpoint=False)\n",
    "# PDF parameters \n",
    "mu = 2.\n",
    "kappa = 20\n",
    "\n",
    "# The PDF \n",
    "pdf = pdf_von_Mises(t,mu,kappa)\n",
    "\n",
    "# Plot the PDF on a circle \n",
    "fig = plt.figure(figsize=(8,6))\n",
    "ax=plot_angular_density_3d(t,pdf,colour=\"green\",label='pdf curve on the circle')\n",
    "ax.legend()\n",
    "\n",
    "# # Draw a centre point\n",
    "# ax.scatter([0], [0], [0], color=\"k\", s=10)\n",
    "# # Draw line in the mean direction \n",
    "# ax.plot([0,np.cos(mu)],[0,np.sin(mu)],0,color=\"k\")\n",
    "# ax.scatter( [np.cos(mu)], [np.sin(mu)], [0], color=\"k\", s=10)\n",
    "\n",
    "# View \n",
    "ax.view_init(30,80)\n",
    "\n",
    "# Save it\n",
    "plt.savefig(\"vm-ang-density_3d.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "   1. Von Mises, R., Uber die 'Ganzzahligkeit' der Atomgewichte und verwandte Fragen, Physikalische Zeitschrift, 19, 490--500, (1918).\n",
    " \n",
    "<!-- @Article{ja:VonMises1918,\n",
    "  author  = {Von Mises, R.},\n",
    "  title   = {{Uber die 'Ganzzahligkeit' der Atomgewichte und verwandte Fragen}},\n",
    "  journal = {Physikalische Zeitschrift},\n",
    "  year    = {1918},\n",
    "  volume  = {19},\n",
    "  pages   = {490-500},\n",
    "  note    = {cited By 158},\n",
    "  source  = {Scopus},\n",
    "} -->\n",
    " \n",
    "\n",
    "   2. Best, D. J.  and Fisher, N. I. , Efficient Simulation of the von-Mises Distribution, J. Appl. Stat.,28, 152--157, (1979).\n",
    "\n",
    "<!-- @Article{Best:1979:ESM,\n",
    "  author          = {D. J. Best and N. I. Fisher},\n",
    "  title           = {Efficient Simulation of the {von Mises} Distribution},\n",
    "  journal         = j-APPL-STAT,\n",
    "  year            = {1979},\n",
    "  volume          = {28},\n",
    "  number          = {2},\n",
    "  pages           = {152--157},\n",
    "  issn            = {0035-9254 (print), 1467-9876 (electronic)},\n",
    "  acknowledgement = {#ack-nhfb#},\n",
    "  bibdate         = {Sat Apr 21 10:22:32 MDT 2001},\n",
    "  bibsource       = {http://www.math.utah.edu/pub/tex/bib/as1970.bib; JSTOR database},\n",
    "  classcodes      = {C1140Z (Other topics in statistics)},\n",
    "  coden           = {APSTAG},\n",
    "  corpsource      = {CSIRO Div. of Math. and Statistics, North Ryde, NSW, Australia},\n",
    "  fjournal        = {Applied Statistics},\n",
    "  journal-url     = {http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues},\n",
    "  keywords        = {simulation; statistical analysis; von Mises distribution},\n",
    "  treatment       = {A Application; T Theoretical or Mathematical},\n",
    "} -->\n",
    "    \n",
    "   3. Fisher, N. I., Statistical Analysis of Circular Data, , Cambridge University Press, (1993)\n",
    "    \n",
    "<!-- @Book{fisher_1993,\n",
    "  title     = {Statistical Analysis of Circular Data}\n",
    "  publisher = {Cambridge University Press},\n",
    "  year      = {1993},\n",
    "  author    = {Fisher, N. I.},\n",
    "  doi       = {10.1017/CBO9780511564345},\n",
    "  place     = {Cambridge},\n",
    "} -->\n",
    " \n",
    "\n"
   ]
  }
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