{
 "cells": [
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "<script>\n",
    "  function code_toggle() {\n",
    "    if (code_shown){\n",
    "      $('div.input').hide('500');\n",
    "      $('#toggleButton').val('Show Code')\n",
    "    } else {\n",
    "      $('div.input').show('500');\n",
    "      $('#toggleButton').val('Hide Code')\n",
    "    }\n",
    "    code_shown = !code_shown\n",
    "  }\n",
    "\n",
    "  $( document ).ready(function(){\n",
    "    code_shown=false;\n",
    "    $('div.input').hide()\n",
    "    $('div.prompt').hide();\n",
    "    $('div.back-to-top').hide();\n",
    "    $('.breadcrumb').hide();\n",
    "    $('.wrn').hide();\n",
    "  });\n",
    "</script>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class='wrn' style='font-weight:700;font-size:18px;'>This notebook should be viewed on <a href='https://nbviewer.jupyter.org'>nbviewer.jupyter.org</a> to render properly.</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<link href=\"https://fonts.googleapis.com/css2?family=IBM+Plex+Sans:ital,wght@0,400;0,500;0,700;1,400;1,500;1,700&display=swap\" rel=\"stylesheet\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.core.display import HTML\n",
    "HTML('<link href=\"https://fonts.googleapis.com/css2?family=IBM+Plex+Sans:ital,wght@0,400;0,500;0,700;1,400;1,500;1,700&display=swap\" rel=\"stylesheet\">')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type='text/css'>.rendered_html h1,h2,h3 {\n",
       "    font-family: 'IBM Plex Sans', sans-serif !important;\n",
       "}\n",
       ".rendered_html h1 {\n",
       "    font-size: 36px;\n",
       "    font-weight: 700;\n",
       "}\n",
       ".rendered_html h2 {\n",
       "    font-size: 28px;\n",
       "    font-weight: 400;\n",
       "}\n",
       ".rendered_html h3 {\n",
       "    font-size: 20px;\n",
       "    font-weight: 500;\n",
       "}\n",
       ".name {\n",
       "    font-size: 16px;\n",
       "    margin-top: 50px;\n",
       "    text-align: right;\n",
       "    padding-right: 10px;\n",
       "}\n",
       "#notebook a {\n",
       "  font-family: 'IBM Plex Sans', sans-serif !important;\n",
       "  color: #337AB7;\n",
       "  text-decoration: none;\n",
       "}\n",
       "#notebook a:hover{\n",
       "  text-decoration: underline;  \n",
       "  color: #337AB7;\n",
       "}\n",
       "\n",
       "#notebook p {\n",
       "  font-family: 'IBM Plex Sans', sans-serif !important;\n",
       "  font-size: 16px;\n",
       "  line-height: 1.6em;\n",
       "  color: #262730;\n",
       "  font-weight: 400;\n",
       "}\n",
       "\n",
       ".MathJax_Display {\n",
       "    padding-top: 14px;\n",
       "    padding-bottom: 14px;\n",
       "}\n",
       ".hidden-print {\n",
       "    margin-top: 60px;\n",
       "}\n",
       "\n",
       ".container-main {\n",
       "  margin-right: auto;\n",
       "  margin-left: auto;\n",
       "  padding-left: 0px;\n",
       "  padding-right: 0px;\n",
       "  max-width: 724px;\n",
       "  min-width: 340px;\n",
       "}\n",
       "@media (min-width: 724px) {\n",
       "  .container-main {\n",
       "    width: 724px;\n",
       "  }\n",
       "}</style>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import urllib\n",
    "response = urllib.request.urlopen(\"https://gist.githubusercontent.com/sgttwld/9deff60facb16918e54410cca3d65648/raw\")\n",
    "css = str(response.read().decode(\"utf-8\"))\n",
    "HTML(\"<style type='text/css'>\"+css+\"</style>\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%config InlineBackend.figure_format = 'retina'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# imports\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import tensorflow as tf\n",
    "from RD_GD import GD\n",
    "from RD_MA import MA\n",
    "from RD_FC import RDFC\n",
    "import os, time\n",
    "os.environ['TF_CPP_MIN_LOG_LEVEL'] = '2' "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plot settings\n",
    "sns.reset_defaults()\n",
    "sns.set(\n",
    "    rc={\n",
    "        'figure.figsize': (7,3),\n",
    "        'axes.titlesize': 10,\n",
    "        'axes.labelsize': 10,\n",
    "        'legend.fontsize': 9,\n",
    "        'xtick.labelsize': 8,\n",
    "        'ytick.labelsize': 8,\n",
    "        'axes.spines.top': False,\n",
    "        'axes.spines.right': False,\n",
    "        \n",
    "    }, \n",
    "    style=\"white\" \n",
    ")\n",
    "sns.set_palette(sns.cubehelix_palette(5,start=.9,rot=-.1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "lines_to_next_cell": 1
   },
   "outputs": [],
   "source": [
    "def legend_string(r):\n",
    "    return ['beta={}\\nN={}\\n{} iterations\\n{:.2f} seconds\\nR={:.3f}\\nD={:.5f}'.format(\n",
    "        r['beta'],len(r['xhat']),r['episodes'],r['elapsed'],r['rate'],r['distortion'])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "lines_to_next_cell": 1
   },
   "outputs": [],
   "source": [
    "def get_source(num):\n",
    "    return tf.constant( np.random.beta(a=1,b=2,size=(num)) ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Rate-distortion with fixed cardinality (RDFC): _a combination of Blahut-Arimoto and the mapping approach_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In [Banerjee et al. (2004)](http://www.cs.utexas.edu/~inderjit/public_papers/icml04breg.pdf) the authors describe a rate-distortion variant they call _rate-distortion with fixed cardinality_ (RTFC), which they define as the optimization problem\n",
    "$$\n",
    "\\min_{\\scriptsize\\begin{array}{c}\\hat{\\mathcal{X}}, q(\\hat{X}|X),\\\\[-2pt] s.t. \\ |\\hat{\\mathcal X}|=N\\end{array}} \\Big[ \\mathbb E[d(X,\\hat X)] + \\tfrac{1}{\\beta} I(X;\\hat X) \\Big]\n",
    "$$\n",
    "which modifies the original Shannon rate-distortion problem by not only optimizing over $q(\\hat X|X)$ but also over the support set $\\hat{\\mathcal X}$ of $\\hat X$, which is constrained to have cardinality $N$, i.e. $|\\hat{\\mathcal{X}}|=N$. \n",
    "\n",
    "We have implemented ([RD_FC.py](https://github.com/sgttwld/rate-distortion-with-fixed-cardinality/blob/master/RD_FC.py)) the alternating optimization algorithm by Banerjee et al., consisting of a combination of the _Blahut-Arimoto algorithm_ and the support reestimation step of the _mapping approach_ by Rose."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "num = 5000\n",
    "beta = 100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Results for a given inverse temperature\n",
    "Here we consider a set of iid samples of a continuous source $X$ distributed according to a Beta distribution, "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 292,
       "width": 615
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = get_source(num)\n",
    "ax = pd.DataFrame(X).plot.hist(bins=20,alpha=.9,fontsize=8,title='Source frequency')\n",
    "ax.legend([r'X ~ Beta(1,2)'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "lines_to_next_cell": 2
   },
   "source": [
    "Before showing at the results of RDFC, it is instructive to have a look at the results of standard rate-distortion algorithms."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### _Optimal reconstruction distribution_ ([RD_GD.py](https://github.com/sgttwld/rate-distortion-with-fixed-cardinality/blob/master/RD_FC.py))\n",
    "Shannon's rate-distortion trade-off \n",
    "$$\n",
    "\\min_{q(\\hat X|X)} \\Big[ \\mathbb E[d(X,\\hat X)] + \\tfrac{1}{\\beta} I(X;\\hat X) \\Big]\n",
    "$$\n",
    "for the above sample set, e.g. calculated using the Blahut-Arimoto algorithm or gradient descent, produces a marginal distribution $q(\\hat X)= E_X[q(\\hat X|X)]$ of the approximate form:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 297,
       "width": 600
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = GD(X,np.array([beta]),N=50)[0]\n",
    "ax = pd.DataFrame(r['q']).plot.bar(title=r'Distribution of reconstruction $\\hat{X}$',rot=0)\n",
    "ax.legend(legend_string(r))\n",
    "xticks = np.arange(0,len(r['q']),8)\n",
    "plt.xticks(xticks,np.round(r['xhat'],2)[xticks])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### _Mapping approach_ ([RD_MA.py](https://github.com/sgttwld/rate-distortion-with-fixed-cardinality/blob/master/RD_MA.py))\n",
    "\n",
    "In the [mapping approach by Rose](https://ieeexplore.ieee.org/document/340468), the rate-distortion Lagrangian is written as an expectation over $q(\\hat X)$, which then is represented by an integral over the unit interval $[0,1]$ (with respect to the Lebesgue measure), and where $\\hat X$ is replaced by the value $y(u)$ of a mapping $y$ at $u\\in[0,1]$. When discretizing $[0,1]$ into $N$ chunks, this results in an optimization over vectors $(y_i)_{i=1}^N$. In some cases (e.g. uniform source) the $y_i$ coincide with the values of $\\hat X$ on which the optimal distribution $q(\\hat X)$ has its support. However, in general, they are not necessarily related to this support set, but should be treated more like _integration points_ in numerical integration, which when $N$ is large enough and the $y_i$ are positioned correctly allows to write the integral (an expectation in this case) as a finite sum (see the [notebook on rate-distortion](https://nbviewer.jupyter.org/github/sgttwld/rate-distortion/blob/master/rate-distortion_nb.ipynb) for more details).\n",
    "\n",
    "Nevertheless, by abusing notiation, we could write $\\hat X \\in \\hat{\\mathcal X}$ with $|\\hat{\\mathcal{X}}|=N$ for the components $y_i\\in \\{y_1,\\dots,y_N\\}$, so that the discretized mapping approach could be written as the optimization problem\n",
    "$$\n",
    "\\min_{\\scriptsize\\begin{array}{c}\\hat{\\mathcal{X}}, s.t.\\\\[-2pt] |\\hat{\\mathcal X}|=N\\end{array}}-\\tfrac{1}{\\beta} \\mathbb E_X\\Bigg[\\log \\tfrac{1}{N} \\sum_{\\hat x\\in\\hat{\\mathcal{X}}} e^{-\\beta d(X,\\hat x)} \\Bigg] =  \\min_{\\scriptsize\\begin{array}{c}\\hat{\\mathcal{X}}, q(\\hat{X}|X),\\\\[-2pt] s.t. \\ |\\hat{\\mathcal X}|=N\\end{array}} \\Big[ \\mathbb E[d(X,\\hat X)] + \\tfrac{1}{\\beta} D_{KL}(q(\\hat{X}|X)\\|\\tfrac{1}{N}) \\Big]\n",
    "$$  \n",
    "In this form, the discretized mapping approach __almost coincides with the RDFC problem__, just that the mutual information between $X$ and $\\hat X$ is replaced by the Kullback-Leibler divergence from the fixed uniform prior $\\frac{1}{N}$ to $q(\\hat X|X)$, i.e. the only difference is the non-optimality of the prior. \n",
    "\n",
    "With the same trade-off parameter as above, the mapping approach with $N=$ 20 discretization points yields:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 293,
       "width": 608
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = MA(X,np.array([beta]),N=20)[0]\n",
    "ax = pd.DataFrame(r['xhat']).plot.hist(bins=100,range=(0,1),title=r'Frequency of $y_i$')\n",
    "ax.legend(legend_string(r))\n",
    "plt.xlim([0,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and with $N=6$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 293,
       "width": 623
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = MA(X,np.array([beta]),N=6)[0]\n",
    "ax = pd.DataFrame(r['xhat']).plot.hist(bins=100,range=(0,1),title=r'Frequency of $y_i$')\n",
    "ax.legend(legend_string(r))\n",
    "plt.xlim([0,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A downside of the mapping approach is that due to the uniform use of the discretization points $y_i$, one requires a relatively high number of them to adjust well to the source distribution. For example, for the trade-off parameter from above, the optimal rate-distortion curve is reached at about N=20:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 296,
       "width": 631
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "MA_points = [MA(X,np.array([100]),N=n) for n in [6,11,20]] \n",
    "df_GD = pd.DataFrame(GD(X,np.linspace(90,110,10),N=100))\n",
    "plt.plot(df_GD['rate'],df_GD['distortion'],label='RD',color='lightgray',ls='--')\n",
    "for r in MA_points:\n",
    "    plt.scatter(r[0]['rate'],r[0]['distortion'],label='MA (N={})'.format(len(r[0]['xhat'])))\n",
    "plt.legend()\n",
    "plt.ylabel('distortion')\n",
    "plt.xlabel('rate')\n",
    "plt.ylim([0.0046,0.0052])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course, this in an improvement over the straightforward discretization of the range of $\\hat X$ that for example yields the \"optimal\" reconstruction distribution shown above ($N=$ 50) and for the reference curve in this plot we used $N=$ 100. However, it turns out that RDFC, which essentially is a combination of these two approaches, can further improve on the number of required parameters in order to to reach the optimality bound given by the rate-distortion curve. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### _RDFC_ ([RD_FC.py](https://github.com/sgttwld/rate-distortion-with-fixed-cardinality/blob/master/RD_FC.py))\n",
    "\n",
    "The RDFC problem formally combines the original rate-distortion problem and the discretized mapping approach in that it optimizes the rate-distortion Lagrangian over the conditional probabilities $q(\\hat X|X)$ which can be rewritten as an optimization over the distribution $q(\\hat X)$ by substituting the Boltzmann distribution, but also optimizes over the support set of $q(\\hat X)$, which in the mapping approach _replaces_ the optimization over $q(\\hat X)$. Here, both are combined which results in an efficient way to calculate the rate-distortion trade-off by making use of the strengths of both approaches:\n",
    "\n",
    "* __adaptive grid__: it allows to freely adapt the reconstruction points $\\hat X\\in \\hat{\\mathcal{X}}$ (strength of the mapping approach that allows to obtain optimal solutions despite of a finite number $N$ of discretization intervals)\n",
    "\n",
    "* __adaptive distribution__: a non-uniform distribution $q(\\hat X)$ over the reconstruction points allows that the reconstruction points can be used according to the source distribution (strength of the original rate-distortion problem)\n",
    "\n",
    "One can also use a combination of the respective iterative solution algorithms to solve the RDFC problem (Algorithm 1 in [Banerjee et al. (2004)](http://www.cs.utexas.edu/~inderjit/public_papers/icml04breg.pdf)), consisting of (i) a _Blahut-Arimoto step_, which consists of calculating the Boltzmann distribution $q^\\ast(\\hat X|X)$ and the marginal $q^\\ast(\\hat X) = E_X[q(\\hat X|X)]$, and (ii) of a _support re-estimation step_ which just like in the iterative mapping approach consists in a nearest-neighbour approximation (minimizing average distortion). In the case of the squared distance $d(s,t) = (t-s)^2$ (or any other Bregman divergence) this optimum is simply the conditional expectation of $X$ given the reconstruction point.  \n",
    "\n",
    "With the same trade-off parameter as above and the low number of reconstruction points $N=$ 6, we obtain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 297,
       "width": 600
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = RDFC(X,np.array([beta]),N=6)[0]\n",
    "ax = pd.DataFrame(r['q']).plot.bar(\n",
    "    title=r'Distribution of reconstruction $\\hat X$',rot=0,fontsize=8)\n",
    "ax.legend(legend_string(r))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 299,
       "width": 617
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.DataFrame(r['xhat']).plot.hist(bins=100,range=(0,1),title=r'Frequency of reconstruction $\\hat X$')\n",
    "plt.xlim([0,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see how the work, which in the mapping approach has to be done solely by the position of the reconstruction points, is now spread over the choice of the reconstruction points _and_ their distribution. This way, we only need 11 independent parameters (6 positions and 5 independent probability values) to reach optimal rate-distortion performance: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 296,
       "width": 631
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "RDFC_points = [RDFC(X,np.array([100]),N=n) for n in [6,11,20]]\n",
    "plt.plot(df_GD['rate'],df_GD['distortion'],label='RD',color='lightgray',ls='--')\n",
    "for r in RDFC_points:\n",
    "    plt.scatter(r[0]['rate'],r[0]['distortion'],label='RDFC (N={})'.format(len(r[0]['q'])))\n",
    "plt.legend()\n",
    "plt.ylabel('distortion')\n",
    "plt.xlabel('rate')\n",
    "plt.ylim([0.0046,0.0052])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rate-distortion curves for non-optimal cardinality\n",
    "When constraining the cardinality of the reproduction support to a low number (here $N=$ 5), then RDFC can achieve optimality for longer (i.e. higher $\\beta$) than the mapping approach, since it has the extra degrees of freedom given by the distribution $q(\\hat X)$, which allows to make up for the lack of reproduction points by choosing them probabilistically: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "betas = np.linspace(60,400,20)\n",
    "df_MA = pd.DataFrame(MA(X,betas,N=5))\n",
    "df_RDFC = pd.DataFrame(RDFC(X,betas,N=5))\n",
    "df_GD = pd.DataFrame(GD(X,betas,N=50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 295,
       "width": 629
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(df_GD['rate'],df_GD['distortion'],label='RD',color='lightgray',ls='--')\n",
    "plt.scatter(df_MA['rate'],df_MA['distortion'],label='MA',marker='.')\n",
    "plt.scatter(df_RDFC['rate'],df_RDFC['distortion'],label='RDFC',marker='.')\n",
    "plt.legend()\n",
    "plt.ylabel('distortion')\n",
    "plt.xlabel('rate')\n",
    "plt.xlim([1.3,2.2])\n",
    "plt.ylim([0.0015,0.0075])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class='name'>2020-05-28<br> <a href='https://gttwld.de'><i>Sebastian Gottwald</i></a></div>"
   ]
  }
 ],
 "metadata": {
  "jupytext": {
   "cell_metadata_filter": "-all"
  },
  "kernelspec": {
   "display_name": "Python 3.7.5 64-bit",
   "language": "python",
   "name": "python37564bitd6d03e7a62f8431181f582755adfdb3f"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}