Chord-diagram.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotly plot of chord diagrams ##"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Circular layout or [Chord diagram](https://en.wikipedia.org/wiki/Chord_diagram) is a method of visualizing  data that describe relationships. It was intensively promoted  through [Circos](http://circos.ca/), a software package in Perl that  was initially designed for displaying genomic data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This 2013  [stackoverflow](http://stackoverflow.com/questions/19105801/chord-diagram-in-python) question, whether there is a Python library for plotting  chord diagrams, was  closed as being  *off topic*.\n",
    "Two years later I presented in the initial version of this Jupyter Notebook a method to generate a chord diagram  via Python Plotly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This Jupyter Notebook is an updated ersion  to be run  using Python 3.7+, and Plotly 4.+."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We illustrate the method of generating a chord diagram from data recorded in a square matrix.  The rows and columns represent  the same entities."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Suppose that for a community of 5 friends on Facebook we record  the number of comments posted by each member on other friends wall. The data table is given in the next cell: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "Image(filename='Data/Data-table.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The aim of our visualization is to illustrate the total number of posts by each community member, and the \n",
    "flows of posts between pairs of friends."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "import platform, plotly\n",
    "import numpy as np\n",
    "from numpy import pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python version: 3.7.3\n",
      "Plotly version: 4.5.4\n"
     ]
    }
   ],
   "source": [
    "print(f'Python version: {platform.python_version()}')\n",
    "print(f'Plotly version: {plotly.__version__}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define the array of data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "matrix = np.array([[16,  3, 28,  0, 18],\n",
    "                   [18,  0, 12,  5, 29],\n",
    "                   [ 9, 11, 17, 27,  0],  \n",
    "                   [19,  0, 31, 11, 12],\n",
    "                   [23, 17, 10,  0, 34]], dtype=int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def check_data(data_matrix):\n",
    "    L, M = data_matrix.shape\n",
    "    if L != M:\n",
    "        raise ValueError('Data array must have a (n,n) shape')\n",
    "    return L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "L = check_data(matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " A chord diagram encodes information in two graphical objects:\n",
    "  - ideograms, represented by   distinctly colored arcs of circles;\n",
    "  - ribbons, that are planar shapes bounded by two quadratic Bezier curves and two arcs of circle, that can degenerate to a point;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ideograms ###"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Summing up the entries on each matrix row, one gets a value (in our example this value is equal to the number of posts by a community member).\n",
    "Let us denote by `total_comments` the total number of posts recorded in this community.\n",
    "\n",
    "Theoretically the interval `[0, total_comments)` is mapped linearly onto the unit circle, identified with the interval $[0,2\\pi)$. \n",
    "\n",
    "For a better looking plot one proceeds as follows: starting from the angular position $0$, in counter-clockwise direction, one draws succesively, around the unit circle,  two parallel arcs of length equal to a mapped row sum value, minus a fixed gap. Click the image below:\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import IFrame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"377\"\n",
       "            height=\"420\"\n",
       "            src=\"https://plot.ly/~empet/12234/\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.IFrame at 0x227dfb1d3c8>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "IFrame('https://plot.ly/~empet/12234/', width=377, height=420)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we are defining  functions that process  data in order to get the ideogram ends.\n",
    "\n",
    "As we pointed out, the unit circle is oriented counter-clockwise.\n",
    "In order to get  an arc of circle of  end angular\n",
    "coordinates $\\theta_0<\\theta_1$, we define the function, `moduloAB`, that resolves the case when an arc contains\n",
    "the  point of angular coordinate $0$ (for example $\\theta_0=2\\pi-\\pi/12$, $\\theta_1=\\pi/9$). The function corresponding to $a=-\\pi, b=\\pi$  allows to map the interval $[0,2\\pi)$ onto $[-\\pi, \\pi)$. Via this transformation we have:\n",
    "\n",
    "$\\theta_0\\mapsto \\theta'_0=-\\pi/12$, and \n",
    "\n",
    "$ \\theta_1=\\mapsto \\theta'_1=\\pi/9$,\n",
    "\n",
    "and now $\\theta'_0<\\theta'_1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def moduloAB(x, a, b): #maps a real number onto the unit circle identified with \n",
    "                       #the interval [a,b), b-a=2*PI\n",
    "        if a>= b:\n",
    "            raise ValueError('Incorrect interval ends')\n",
    "        y = (x-a) % (b-a)\n",
    "        return y+b if y < 0 else y+a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test_2PI(x):\n",
    "     return 0 <= x < 2*pi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the row sums and the lengths of corresponding ideograms:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "row_sum = [matrix[k,:].sum() for k in range(L)]\n",
    "\n",
    "#set the gap between two consecutive ideograms\n",
    "gap = 2*pi*0.005\n",
    "ideogram_length = 2*pi * np.asarray(row_sum) / sum(row_sum) - gap*np.ones(L)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next function returns the list of  end angular coordinates for each ideogram arc:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_ideogram_ends(ideogram_len, gap):\n",
    "    ideo_ends = []\n",
    "    left = 0\n",
    "    for k in range(len(ideogram_len)):\n",
    "        right = left + ideogram_len[k]\n",
    "        ideo_ends.append([left, right])   \n",
    "        left = right + gap\n",
    "    return ideo_ends "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "ideo_ends = get_ideogram_ends(ideogram_length, gap)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function `make_ideogram_arc` returns equally spaced points on an ideogram arc, expressed as complex\n",
    "numbers in polar form:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_ideogram_arc(R, phi, a=50):\n",
    "    # R is the circle radius\n",
    "    # phi is the list of  angle coordinates of an arc ends\n",
    "    # a is a parameter that controls the number of points to be evaluated on an arc\n",
    "    if not test_2PI(phi[0]) or not test_2PI(phi[1]):\n",
    "        phi = [moduloAB(t, 0, 2*pi) for t in phi]\n",
    "    length = (phi[1]-phi[0]) % 2*pi \n",
    "    nr = 5 if length <= pi/4 else int(a*length/pi)\n",
    "\n",
    "    if phi[0] < phi[1]:   \n",
    "        theta = np.linspace(phi[0], phi[1], nr)\n",
    "    else:\n",
    "        phi = [moduloAB(t, -pi, pi) for t in phi]\n",
    "        theta = np.linspace(phi[0], phi[1], nr)\n",
    "    return R * np.exp(1j*theta)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The real and imaginary parts of these complex numbers will be used to define the ideogram as a [Plotly\n",
    "shape](https://plot.ly/python/shapes/) bounded by a SVG path."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.12583302-0.65j      , 1.14814501-0.60972373j,\n",
       "       1.16901672-0.5686826j , 1.18842197-0.5269281j ,\n",
       "       1.20633642-0.48451259j, 1.22273759-0.44148929j,\n",
       "       1.23760491-0.39791217j, 1.25091973-0.3538359j ,\n",
       "       1.26266534-0.30931575j, 1.27282702-0.26440759j,\n",
       "       1.28139202-0.21916775j, 1.28834958-0.17365297j,\n",
       "       1.29369099-0.12792036j, 1.29740954-0.08202728j,\n",
       "       1.29950058-0.0360313j , 1.29996146+0.01000988j,\n",
       "       1.29879163+0.0560385j , 1.29599253+0.10199682j,\n",
       "       1.2915677 +0.1478272j , 1.28552267+0.19347214j,\n",
       "       1.27786503+0.23887437j])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "make_ideogram_arc(1.3, [11*pi/6, pi/17])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set ideograms labels and colors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "labels=['Emma', 'Isabella', 'Ava', 'Olivia', 'Sophia']\n",
    "ideo_colors=['rgba(244, 109, 67, 0.75)',\n",
    "             'rgba(253, 174, 97, 0.75)',\n",
    "             'rgba(254, 224, 139, 0.75)',\n",
    "             'rgba(217, 239, 139, 0.75)',\n",
    "             'rgba(166, 217, 106, 0.75)']#brewer colors with alpha set on 0.75"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ribbons in a chord diagram ###"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While ideograms illustrate how many comments posted each member of the Facebook community,  ribbons\n",
    "give a comparative information on the flows of comments from one friend to another.\n",
    "\n",
    "To illustrate this flow we map data onto the unit circle. More precisely, for each matrix row, $k$, the application:\n",
    "\n",
    "`t`$\\mapsto$ `t*ideogram_length[k]/row_sum[k]`\n",
    "\n",
    "maps the interval `[0, row_sum[k]]` onto\n",
    "the interval `[0, ideogram_length[k]]. Hence each entry `matrix[k][j]` in the $k^{th}$  row is mapped to `matrix[k][j] * ideogram_length[k] / row_value[k]`.\n",
    "\n",
    "The function `map_data` maps all matrix entries to the corresponding values in the intervals associated to ideograms:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "def map_data(data_matrix, row_value, ideogram_length):\n",
    "    mapped = np.zeros(data_matrix.shape)\n",
    "    for j  in range(L):\n",
    "        mapped[:, j] = ideogram_length * data_matrix[:,j] / row_value\n",
    "    return mapped  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.27949818, 0.05240591, 0.48912181, 0.        , 0.31443545],\n",
       "       [0.31429952, 0.        , 0.20953301, 0.08730542, 0.50637144],\n",
       "       [0.15714976, 0.19207193, 0.29683843, 0.47144927, 0.        ],\n",
       "       [0.33291045, 0.        , 0.54316969, 0.19273763, 0.21025923],\n",
       "       [0.40429305, 0.2988253 , 0.17577959, 0.        , 0.5976506 ]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mapped_data = map_data(matrix, row_sum, ideogram_length)\n",
    "mapped_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- To each pair of values `(mapped_data[k][j], mapped_data[j][k])`, $k<=j$,  one associates a ribbon, that is a curvilinear filled rectangle (that can be degenerate), having as opposite sides two subarcs of the $k^{th}$ ideogram, respectively $j^{th}$ ideogram, and two arcs of quadratic B&eacute;zier curves."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we illustrate the ribbons associated to pairs `(mapped_data[0][j], mapped_data[j][0])`, $j=\\overline{0,4}$,\n",
    "that illustrate the flow of comments between Emma and all other friends, and  herself:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"420\"\n",
       "            height=\"420\"\n",
       "            src=\"https://plot.ly/~empet/12519/\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.IFrame at 0x227dfaf3c18>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "IFrame('https://plot.ly/~empet/12519/', width=420, height=420)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- For a better looking chord diagram, \n",
    "[Circos documentation](http://circos.ca/presentations/articles/vis_tables1/) recommends to sort increasingly each row of the mapped_data. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The  array `idx_sort`, defined below, has on each row the indices that sort the corresponding row in `mapped_data`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 1, 0, 4, 2],\n",
       "       [1, 3, 2, 0, 4],\n",
       "       [4, 0, 1, 2, 3],\n",
       "       [1, 3, 4, 0, 2],\n",
       "       [3, 2, 1, 0, 4]], dtype=int64)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "idx_sort = np.argsort(mapped_data, axis=1)\n",
    "idx_sort"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the following we call ribbon ends, the lists `l=[l[0], l[1]]`, `r=[r[0], r[1]]` having as elements the angular coordinates\n",
    "of the ends of arcs that are opposite sides in a ribbon. These arcs are sub-arcs in the internal boundaries of\n",
    "the ideograms, connected by the ribbon\n",
    "(see the image above)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Compute the ribbon ends  and store them as tuples \n",
    "in a list of lists ($L\\times L$):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_ribbon_ends(mapped_data, ideo_ends,  idx_sort):\n",
    "    L = mapped_data.shape[0]\n",
    "    ribbon_boundary = np.zeros((L,L+1))\n",
    "    for k in range(L):\n",
    "        start = ideo_ends[k][0]\n",
    "        ribbon_boundary[k][0] = start\n",
    "        for j in range(1,L+1):\n",
    "            J = idx_sort[k][j-1]\n",
    "            ribbon_boundary[k][j] = start + mapped_data[k][J]\n",
    "            start = ribbon_boundary[k][j]\n",
    "    return [[(ribbon_boundary[k][j], ribbon_boundary[k][j+1] ) for j in range(L)] for k in range(L)]   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ribbon ends starting from the ideogram[2]\n",
      " [(2.31580258464619, 2.31580258464619), (2.31580258464619, 2.472952342161697), (2.472952342161697, 2.6650242680139837), (2.6650242680139837, 2.9618626988766086), (2.9618626988766086, 3.43331197142313)]\n"
     ]
    }
   ],
   "source": [
    "ribbon_ends = make_ribbon_ends(mapped_data, ideo_ends,  idx_sort)\n",
    "print ('ribbon ends starting from the ideogram[2]\\n', ribbon_ends[2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We note that `ribbon_ends[k][j]` corresponds to `mapped_data[i][idx_sort[k][j]]`, i.e. the length of the arc of ends in `ribbon_ends[k][j]` is equal to `mapped_data[i][idx_sort[k][j]]`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we define a few functions that compute the  control points for B&eacute;zier ribbon sides."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function `control_pts` returns the cartesian coordinates of  the  control points, $b_0, b_1, b_2$, supposed as being  initially located on the unit circle, and thus defined only by their angular coordinate.  The angular coordinate\n",
    "of the point $b_1$ is the mean of angular coordinates of the points $b_0, b_2$.\n",
    "\n",
    "Since for a  B&eacute;zier ribbon side only $b_0, b_2$ are placed on the unit circle, one gives `radius` as a parameter that controls position of $b_1$.  `radius` is the distance  of $b_1$ to the circle center."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "def control_pts(angle, radius):\n",
    "    #angle is a  3-list containing angular coordinates of the control points b0, b1, b2\n",
    "    #radius is the distance from b1 to the  origin O(0,0) \n",
    "\n",
    "    if len(angle) != 3:\n",
    "        raise InvalidInputError('angle must have len =3')\n",
    "    b_cplx = np.array([np.exp(1j*angle[k]) for k in range(3)])\n",
    "    b_cplx[1] = radius * b_cplx[1]\n",
    "    return list(zip(b_cplx.real, b_cplx.imag))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ctrl_rib_chords(l, r, radius):\n",
    "    # this function returns a 2-list containing control poligons of the two quadratic Bezier\n",
    "    #curves that are opposite sides in a ribbon\n",
    "    #l (r) the list of angular variables of the ribbon arc ends defining \n",
    "    #the ribbon starting (ending) arc \n",
    "    # radius is a common parameter for both control polygons\n",
    "    if len(l) != 2 or len(r) != 2:\n",
    "        raise ValueError('the arc ends must be elements in a list of len 2')\n",
    "    return [control_pts([l[j], (l[j]+r[j])/2, r[j]], radius) for j in range(2)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Each ribbon is colored with the color of one of the two  ideograms it connects. \n",
    "We define an L-list of L-lists of colors for ribbons. Denote it by `ribbon_color`.\n",
    "\n",
    "`ribbon_color[k][j]` is the Plotly color string for the ribbon associated to `mapped_data[k][j]` and `mapped_data[j][k]`, i.e. the ribbon connecting two subarcs in the $k^{th}$, respectively, $j^{th}$ ideogram. Hence  this structure is symmetric."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initially we define:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "ribbon_color = [L * [ideo_colors[k]] for k in range(L)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and then eventually we are changing  the color in a few positions.\n",
    "\n",
    "For our example we are perfotming the following color change:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "ribbon_color[0][4]=ideo_colors[4]\n",
    "ribbon_color[1][2]=ideo_colors[2]\n",
    "ribbon_color[2][3]=ideo_colors[3]\n",
    "ribbon_color[2][4]=ideo_colors[4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The symmetric locations are not modified, because  we do not access \n",
    "`ribbon_color[k][j]`, $k>j$, when drawing the ribbons."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Functions that return the Plotly SVG paths that are  ribbon boundaries:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_q_bezier(b):# defines the Plotly SVG path for a quadratic Bezier curve defined by the \n",
    "                     #list of its control points\n",
    "    if len(b) != 3:\n",
    "        raise valueError('control poligon must have 3 points')\n",
    "    A, B, C = b    \n",
    "    return f'M {A[0]}, {A[1]} Q {B[0]}, {B[1]} {C[0]}, {C[1]}'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "b=[(1,4), (-0.5, 2.35), (3.745, 1.47)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'M 1, 4 Q -0.5, 2.35 3.745, 1.47'"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "make_q_bezier(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`make_ribbon_arc`  returns the Plotly SVG path corresponding to an arc represented by its end angular coordinates, `theta0, theta1`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_ribbon_arc(theta0, theta1):\n",
    "\n",
    "    if test_2PI(theta0) and test_2PI(theta1):\n",
    "        if theta0 < theta1:\n",
    "            theta0 = moduloAB(theta0, -pi, pi)\n",
    "            theta1 = moduloAB(theta1, -pi, pi)\n",
    "            if theta0  *theta1 > 0:\n",
    "                raise ValueError('incorrect angle coordinates for ribbon')\n",
    "    \n",
    "        nr = int(40 * (theta0 - theta1) / pi)\n",
    "        if nr <= 2: nr = 3\n",
    "        theta = np.linspace(theta0, theta1, nr)\n",
    "        pts=np.exp(1j*theta)# points in polar complex form, on the given arc\n",
    "    \n",
    "        string_arc = ''\n",
    "        for k in range(len(theta)):\n",
    "            string_arc += f'L {pts.real[k]}, {pts.imag[k]} '\n",
    "        return   string_arc \n",
    "    else:\n",
    "        raise ValueError('the angle coordinates for an arc side of a ribbon must be in [0, 2*pi]')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'L 0.5000000000000001, 0.8660254037844386 L 0.5877852522924732, 0.8090169943749473 L 0.6691306063588582, 0.7431448254773941 L 0.7431448254773944, 0.6691306063588581 L 0.8090169943749475, 0.5877852522924731 L 0.8660254037844387, 0.49999999999999994 '"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "make_ribbon_arc(np.pi/3, np.pi/6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Finally we are ready to define data and layout for the Plotly plot of the chord diagram."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "import plotly.graph_objects as go"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_layout(title, plot_size):\n",
    "\n",
    "    return dict(title=title,\n",
    "                xaxis=dict(visible=False),\n",
    "                yaxis=dict(visible=False),\n",
    "                showlegend=False,\n",
    "                width=plot_size,\n",
    "                height=plot_size,\n",
    "                margin=dict(t=25, b=25, l=25, r=25),\n",
    "                hovermode='closest',\n",
    "                 )  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Function that returns the Plotly shape of an ideogram:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_ideo_shape(path, line_color, fill_color):\n",
    "    #line_color is the color of the shape boundary\n",
    "    #fill_collor is the color assigned to an ideogram\n",
    "    \n",
    "    return  dict(line=dict(color=line_color, \n",
    "                           width=0.45),\n",
    "                 path=path,\n",
    "                 layer='below',\n",
    "                 type='path',\n",
    "                 fillcolor=fill_color)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We generate two types of ribbons: a ribbon connecting subarcs in two distinct ideograms, respectively\n",
    "a ribbon from one ideogram to itself (it corresponds to `mapped_data[k][k]`, i.e. it gives the flow of comments\n",
    "from a community member to herself)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_ribbon(l, r, line_color, fill_color, radius=0.2):\n",
    "    #l=[l[0], l[1]], r=[r[0], r[1]]  represent the opposite arcs in the ribbon \n",
    "    #line_color is the color of the shape boundary\n",
    "    #fill_color is the fill color for the ribbon shape\n",
    "    \n",
    "    poligon = ctrl_rib_chords(l,r, radius)\n",
    "    b, c = poligon  \n",
    "           \n",
    "    return  dict(line=dict(color=line_color, \n",
    "                             width=0.5),\n",
    "                 path=make_q_bezier(b) + make_ribbon_arc(r[0], r[1])+\n",
    "                         make_q_bezier(c[::-1]) + make_ribbon_arc(l[1], l[0]),\n",
    "                 type='path',\n",
    "                 layer='below',\n",
    "                 fillcolor = fill_color,    \n",
    "        )\n",
    "\n",
    "def make_self_rel(l, line_color, fill_color, radius):\n",
    "    #radius is the radius of Bezier control point b_1\n",
    "    \n",
    "    b = control_pts([l[0], (l[0]+l[1])/2, l[1]], radius) \n",
    "    \n",
    "    return  dict(line = dict(color=line_color, \n",
    "                             width=0.5),\n",
    "                 path =  make_q_bezier(b)+make_ribbon_arc(l[1], l[0]),\n",
    "                 type = 'path',\n",
    "                 layer = 'below',\n",
    "                 fillcolor = fill_color   \n",
    "                )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "def invPerm(perm):\n",
    "    # function that returns the inverse of a permutation, perm\n",
    "    inv = [0] * len(perm)\n",
    "    for i, s in enumerate(perm):\n",
    "        inv[s] = i\n",
    "    return inv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "layout=plot_layout('Chord diagram', 400)    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us explain the key point of associating  ribbons  to right data:\n",
    "    \n",
    "From the definition of `ribbon_ends` we notice that `ribbon_ends[k][j]` corresponds to data stored in\n",
    "`matrix[k][sigma[j]]`, where `sigma` is the permutation of indices $0, 1, \\ldots L-1$, that sort the row k in `mapped_data`.\n",
    "If `sigma_inv` is the inverse permutation of `sigma`, we get that to `matrix[k][j]` corresponds the\n",
    "`ribbon_ends[k][sigma_inv[j]]`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`ribbon_info` is a list of dicts setting the information that is displayed when hovering the mouse over the  ribbon ends."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the radius of B&eacute;zier control point, $b_1$, for each ribbon associated to a diagonal data entry:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "radii_sribb = [0.4, 0.30, 0.35, 0.39, 0.12]# these value are set after a few trials "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "ribbon_info = []\n",
    "shapes = []\n",
    "for k in range(L):\n",
    "    \n",
    "    sigma = idx_sort[k]\n",
    "    sigma_inv = invPerm(sigma)\n",
    "    for j in range(k, L):\n",
    "        if matrix[k][j] == 0 and matrix[j][k]==0: continue\n",
    "        eta = idx_sort[j]\n",
    "        eta_inv = invPerm(eta)\n",
    "        l = ribbon_ends[k][sigma_inv[j]]  \n",
    "        \n",
    "        if j == k:\n",
    "            shapes.append(make_self_rel(l, 'rgb(175,175,175)' ,\n",
    "                                    ideo_colors[k], radius=radii_sribb[k])) \n",
    "            z = 0.9*np.exp(1j*(l[0]+l[1])/2)\n",
    "            \n",
    "            #the text below will be displayed when hovering the mouse over the ribbon\n",
    "            text = f'{labels[k]} commented on {int(matrix[k][k])} of herself Fb posts'\n",
    "\n",
    "            ribbon_info.append(go.Scatter(x=[z.real],\n",
    "                                       y=[z.imag],\n",
    "                                       mode='markers',\n",
    "                                       marker=dict(size=0.5, color=ideo_colors[k]),\n",
    "                                       text=text,\n",
    "                                       hoverinfo='text'\n",
    "                                       )\n",
    "                              )\n",
    "        else:\n",
    "            r = ribbon_ends[j][eta_inv[k]]\n",
    "            zi = 0.9 * np.exp(1j*(l[0]+l[1])/2)\n",
    "            zf = 0.9 * np.exp(1j*(r[0]+r[1])/2)\n",
    "            #texti and textf are the strings that will be displayed when hovering the mouse \n",
    "            #over the two ribbon ends\n",
    "            texti = f'{labels[k]} commented on {int(matrix[k][j])} of {labels[j]} Fb posts'\n",
    "            textf = f'{labels[j]} commented on {int(matrix[j][k])} of {labels[k]} Fb posts'\n",
    "            \n",
    "            ribbon_info.append(go.Scatter(x=[zi.real],\n",
    "                                          y=[zi.imag],\n",
    "                                          mode='markers',\n",
    "                                          marker=dict(size=0.5, color=ribbon_color[k][j]),\n",
    "                                          text=texti,\n",
    "                                          hoverinfo='text'\n",
    "                                       )\n",
    "                              ),\n",
    "            ribbon_info.append(go.Scatter(x=[zf.real],\n",
    "                                          y=[zf.imag],\n",
    "                                          mode='markers',\n",
    "                                          marker=dict(size=0.5, color=ribbon_color[k][j]),\n",
    "                                          text=textf,\n",
    "                                          hoverinfo='text'\n",
    "                                       )\n",
    "                              )\n",
    "            r = (r[1], r[0]) # IMPORTANT!!!  Reverse these arc ends because otherwise you get\n",
    "                          # a twisted ribbon\n",
    "            #append the ribbon shape\n",
    "            shapes.append(make_ribbon(l, r, 'rgb(175,175,175)' , ribbon_color[k][j]))\n",
    "           \n",
    "                                    \n",
    "            "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`ideograms` is a list of dicts that set the position, and color of ideograms, as well as the information associated to each ideogram.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "ideograms = []\n",
    "for k in range(len(ideo_ends)):\n",
    "    z =  make_ideogram_arc(1.1, ideo_ends[k])\n",
    "    zi = make_ideogram_arc(1.0, ideo_ends[k])\n",
    "    m = len(z)\n",
    "    n = len(zi)\n",
    "    ideograms.append(go.Scatter(x=z.real,\n",
    "                                y=z.imag,\n",
    "                                mode='lines',\n",
    "                                line=dict(color=ideo_colors[k], shape='spline', width=0.25),\n",
    "                                text=f'{labels[k]} <br>{int(row_sum[k])} comments', \n",
    "                                hoverinfo='text'\n",
    "                             )\n",
    "                     )\n",
    "    \n",
    "       \n",
    "    path = 'M '\n",
    "    for s in range(m):\n",
    "        path += f'{z.real[s]}, {z.imag[s]} L '\n",
    "        \n",
    "    Zi = np.array(zi.tolist()[::-1]) \n",
    "\n",
    "    for s in range(m):\n",
    "        path += f'{Zi.real[s]}, {Zi.imag[s]} L '\n",
    "    path += f'{z.real[0]} ,{z.imag[0]}' \n",
    "   \n",
    "    shapes.append(make_ideo_shape(path,'rgb(150,150,150)' , ideo_colors[k]))\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
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[0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]]}, \"colorway\": [\"#636efa\", \"#EF553B\", \"#00cc96\", \"#ab63fa\", \"#FFA15A\", \"#19d3f3\", \"#FF6692\", \"#B6E880\", \"#FF97FF\", \"#FECB52\"], \"font\": {\"color\": \"#2a3f5f\"}, \"geo\": {\"bgcolor\": \"white\", \"lakecolor\": \"white\", \"landcolor\": \"#E5ECF6\", \"showlakes\": true, \"showland\": true, \"subunitcolor\": \"white\"}, \"hoverlabel\": {\"align\": \"left\"}, \"hovermode\": \"closest\", \"mapbox\": {\"style\": \"light\"}, \"paper_bgcolor\": \"white\", \"plot_bgcolor\": \"#E5ECF6\", \"polar\": {\"angularaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"radialaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"scene\": {\"xaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"yaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"zaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}}, \"shapedefaults\": {\"line\": {\"color\": \"#2a3f5f\"}}, \"ternary\": {\"aaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"baxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"caxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"title\": {\"x\": 0.05}, \"xaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}, \"yaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}}}, \"title\": {\"text\": \"Chord diagram\"}, \"width\": 400, \"xaxis\": {\"visible\": false}, \"yaxis\": {\"visible\": false}},\n",
       "                        {\"responsive\": true}\n",
       "                    ).then(function(){\n",
       "                            \n",
       "var gd = document.getElementById('9d8ca46c-0d98-47eb-bea7-f01cbe1abd13');\n",
       "var x = new MutationObserver(function (mutations, observer) {{\n",
       "        var display = window.getComputedStyle(gd).display;\n",
       "        if (!display || display === 'none') {{\n",
       "            console.log([gd, 'removed!']);\n",
       "            Plotly.purge(gd);\n",
       "            observer.disconnect();\n",
       "        }}\n",
       "}});\n",
       "\n",
       "// Listen for the removal of the full notebook cells\n",
       "var notebookContainer = gd.closest('#notebook-container');\n",
       "if (notebookContainer) {{\n",
       "    x.observe(notebookContainer, {childList: true});\n",
       "}}\n",
       "\n",
       "// Listen for the clearing of the current output cell\n",
       "var outputEl = gd.closest('.output');\n",
       "if (outputEl) {{\n",
       "    x.observe(outputEl, {childList: true});\n",
       "}}\n",
       "\n",
       "                        })\n",
       "                };\n",
       "                });\n",
       "            </script>\n",
       "        </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = ideograms + ribbon_info\n",
    "layout['shapes'] = shapes\n",
    "fig = go.Figure(data=data, layout=layout)\n",
    "from plotly.offline import download_plotlyjs, init_notebook_mode,  iplot, plot\n",
    "init_notebook_mode(connected=True)\n",
    "iplot(fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a chord diagram associated to a community of 8 Facebook friends:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"500\"\n",
       "            height=\"500\"\n",
       "            src=\"https://plot.ly/~empet/12148/chord-diagram-of-facebook-comments-in-a-community/\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.IFrame at 0x227e41b7e80>"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "IFrame('https://plot.ly/~empet/12148/chord-diagram-of-facebook-comments-in-a-community/',\n",
    "     width=500, height=500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "        margin-left: 13% !important;\n",
       "        margin-right: auto;\n",
       "    }\n",
       "    #notebook li { /* More space between bullet points */\n",
       "    margin-top:0.8em;\n",
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       "    .text_cell_render h4 {\n",
       "        font-weight: 300;\n",
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       "        color: rgb(8, 66, 133);\n",
       "        margin-bottom: 0.5em;\n",
       "        margin-top: 0.5em;\n",
       "        display: block;\n",
       "    }\n",
       "    h5 {\n",
       "        font-family: 'Alegreya Sans', sans-serif;\n",
       "    }\n",
       "    .text_cell_render h5 {\n",
       "        font-weight: 300;\n",
       "        font-style: normal;\n",
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       "        margin-bottom: 0em;\n",
       "        margin-top: 1.5em;\n",
       "        display: block;\n",
       "        }\n",
       "    div.text_cell_render{\n",
       "        font-family: 'Alegreya Sans',Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n",
       "        line-height: 145%;\n",
       "        font-size: 130%;\n",
       "        width:900px;\n",
       "        margin-left:auto;\n",
       "        margin-right:auto;\n",
       "        %text-align:justify;\n",
       "        %text-justify:inter-word;\n",
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       "    \n",
       "    \n",
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       "    .rendered_html code{\n",
       "        background-color: transparent;\n",
       "        white-space: inherit;   \n",
       "    }\n",
       "    .prompt{\n",
       "        display: None;\n",
       "     }\n",
       "    .rendered_html code{\n",
       "    background-color: transparent;\n",
       "    }\n",
       "\n",
       "    blockquote{\n",
       "      display:block;\n",
       "      background: #f3f3f3;\n",
       "      font-family: \"Open sans\",verdana,arial,sans-serif;\n",
       "      width:610px;\n",
       "      padding: 15px 15px 15px 15px;\n",
       "      text-align:justify;\n",
       "      text-justify:inter-word;\n",
       "      }\n",
       "      blockquote p {\n",
       "        margin-bottom: 0;\n",
       "        line-height: 125%;\n",
       "        font-size: 100%;\n",
       "      }\n",
       "   /* element.style {\n",
       "    } */\n",
       "</style>\n",
       "<script>\n",
       "    MathJax.Hub.Config({\n",
       "                        TeX: {\n",
       "                           extensions: [\"AMSmath.js\"]\n",
       "                           },\n",
       "                tex2jax: {\n",
       "                    inlineMath: [ [\"$\",\"$\"], [\"\\\\(\",\"\\\\)\"] ],\n",
       "                    displayMath: [ [\"$$\",\"$$\"], [\"\\\\[\",\"\\\\]\"] ]\n",
       "                },\n",
       "                displayAlign: \"center\", // Change this to \"center\" to center equations.\n",
       "                \"HTML-CSS\": {\n",
       "                    styles: {\".MathJax_Display\": {\"margin\": 4}}\n",
       "                }\n",
       "        });\n",
       "</script>\n"
      ],
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       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.core.display import HTML\n",
    "def  css_styling():\n",
    "    styles = open(\"./custom.css\", \"r\").read()\n",
    "    return HTML(styles)\n",
    "css_styling()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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