examples/example_two_circles.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Computing Circular Coordinates\n",
    "This is an example of computing circular coordinates using scikit-tda custom filtration in the package `cechmate` and the original circular coordinates computations in `dionysus`. \n",
    "\n",
    "The original paper describing the computation of circular coordinates can be found here : [Persistent Cohomology and Circular Coordinates](https://link.springer.com/article/10.1007%2Fs00454-011-9344-x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# First import some modules\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "from ripser import ripser\n",
    "import dionysus as dion\n",
    "import cechmate as cm\n",
    "from persim import plot_diagrams"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define a function to generate two circles \n",
    "def generate_twocircles(num_points):\n",
    "    angle = np.linspace(0, np.pi*2, num=num_points)\n",
    "    r = 1\n",
    "    x = np.array([r * np.cos(angle), r*np.sin(angle)])\n",
    "    data = np.concatenate((x,np.array([x[0,:]+4, x[1,:]])), axis=1)\n",
    "    \n",
    "    return data\n",
    "\n",
    "def convert_dionysus_diagram(dgms):\n",
    "    ''' We convert the diagram from dionysus into a numpy array\n",
    "        The format of the array is dimension-birth-death-simplex index\n",
    "    '''\n",
    "    H = np.empty([4,])\n",
    "    for idgm, dgm in enumerate(dgms):\n",
    "        for pt in dgm:\n",
    "            newrow = np.array([idgm, pt.birth, pt.death, pt.data]);\n",
    "            H = np.vstack((H,newrow))\n",
    "    H =  np.delete(H, 0, 0)\n",
    "    return H    \n",
    "\n",
    "def dist2filtration(dist_filtration):\n",
    "    '''\n",
    "        This function converts a filtration as a list from cechmate to \n",
    "        dionysus compatible\n",
    "    '''\n",
    "    ordered_simplices = sorted(dist_filtration, key=lambda x: (x[1], len(x[0])))\n",
    "    f = dion.Filtration()\n",
    "    for vertices, time in ordered_simplices:\n",
    "        f.append(dion.Simplex(vertices, time))\n",
    "        \n",
    "    return f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1800x1200 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate the dataset and plot it\n",
    "number_points = 20;\n",
    "points = generate_twocircles(number_points).T\n",
    "%matplotlib inline\n",
    "mpl.rcParams['figure.dpi']=300\n",
    "plt.scatter(points[:,0], points[:,1])\n",
    "plt.title('Two non-touching circles')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Doing spatial.Delaunay triangulation...\n",
      "Finished spatial.Delaunay triangulation (Elapsed Time 0.000419)\n",
      "Building alpha filtration...\n",
      "Finished building alpha filtration (Elapsed Time 0.0122)\n",
      "Constructing boundary matrix...\n",
      "Finished constructing boundary matrix (Elapsed Time 0.00196)\n",
      "Computing persistence pairs...\n",
      "Finished computing persistence pairs (Elapsed Time 0.000351)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1800x1200 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute apha filtrations using cechmate\n",
    "alpha = cm.Alpha()\n",
    "alpha_filtration = alpha.build(2*points) # Alpha goes by radius instead of diameter\n",
    "dgmsalpha = alpha.diagrams(alpha_filtration)\n",
    "\n",
    "%matplotlib inline\n",
    "mpl.rcParams['figure.dpi']=300\n",
    "plot_diagrams(dgmsalpha, lifetime=True)\n",
    "ax = plt.gca()\n",
    "ax.legend(loc=\"best\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compute the vertex values using alpha filtration\n",
    "prime = 2\n",
    "f = dist2filtration(alpha_filtration)\n",
    "p = dion.cohomology_persistence(f, prime, True)\n",
    "dgms = dion.init_diagrams(p, f)    \n",
    "H = convert_dionysus_diagram(dgms)\n",
    "H1 = H[H[:,0]==1,:] # Collect H1 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "there are 2 circular shapes in the data...\n"
     ]
    }
   ],
   "source": [
    "# Collect the maximum persistence H1 index (You can collect multiple)\n",
    "lifetime_H1 = H1[:, 2] - H1[:, 1]\n",
    "idx = np.where(lifetime_H1>1.5) # collect data above the lifetime\n",
    "num_cocyles = np.shape(idx)[1]\n",
    "print(\"there are %d circular shapes in the data...\"%num_cocyles)\n",
    "vertex_values = np.zeros((num_cocyles,number_points*2))\n",
    "for ind, val in enumerate(idx[0]):\n",
    "    cocycle = p.cocycle(H1[val,3].astype(int))\n",
    "    f_restricted = dion.Filtration([s for s in f if s.data <= (H1[val,1] + H1[val,2])/2])\n",
    "    vertex_values[ind,:] = dion.smooth(f_restricted, cocycle, prime)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3600x1800 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "mpl.rcParams['figure.dpi']=300\n",
    "plt.figure(figsize=(12, 6))\n",
    "plt.subplot(121)\n",
    "plt.scatter(points[:,0], points[:,1], c = vertex_values[0,:], cmap = 'hsv')\n",
    "plt.title('Cocycle 1')\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.scatter(points[:,0], points[:,1], c = vertex_values[1,:], cmap = 'hsv')\n",
    "plt.title('Cocycle 2')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1800x1200 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(vertex_values[0,:], vertex_values[1,:])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}