returners.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "marco = [\n",
    "    [0.34, 0.34, 0.32], #frequenza\n",
    "    [(0,0), (100,100), (100,100)] #posizioni\n",
    "]\n",
    "\n",
    "laura = [\n",
    "    [0.34, 0.34, 0.32], #frequenza\n",
    "    [(0,0), (0,0), (100,100)] #posizioni\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def f_radius_gyration(positions, frequencies):\n",
    "    frequencies = np.array(frequencies)\n",
    "    s = frequencies.sum()\n",
    "    mass = np.mean(positions)\n",
    "    distances = frequencies*np.array([np.linalg.norm(x-mass) for x in positions])\n",
    "    \n",
    "    return 1/s * distances.sum(axis=-1) \n",
    "\n",
    "def k_radius_gyration(positions, frequencies, k):\n",
    "    return f_radius_gyration(positions[:k], frequencies[:k])\n",
    "\n",
    "is_returner = lambda r_g_ks, k: r_g_ks[k-1]>r_g_ks[-1]/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "63.168205786\n",
      "[70.710678118654755, 63.168205785998246]\n",
      "s2 [ 1.11940299  1.        ]\n",
      "Marco is returner: True\n"
     ]
    }
   ],
   "source": [
    "r_g_marco = f_radius_gyration(marco[1], marco[0])\n",
    "r_ks_marco = [k_radius_gyration(marco[1], marco[0], x) for x in range(2,4)]\n",
    "print(r_g_marco)\n",
    "print(r_ks_marco)\n",
    "print(\"s2\", r_ks_marco/r_g_marco)\n",
    "print(\"Marco is returner:\", is_returner(r_ks_marco, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "62.2253967444\n",
      "[70.710678118654755, 63.168205785998246]\n",
      "s2 [ 1.13636364  1.01515152]\n",
      "Laura is returner: True\n"
     ]
    }
   ],
   "source": [
    "r_g_laura = f_radius_gyration(laura[1], laura[0])\n",
    "r_ks_laura = [k_radius_gyration(marco[1], marco[0], x) for x in range(2,4)]\n",
    "print(r_g_laura)\n",
    "print(r_ks_laura)\n",
    "print(\"s2\", r_ks_laura/r_g_laura)\n",
    "print(\"Laura is returner:\", is_returner(r_ks_laura, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10d7999e8>"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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kWfGATlFxzKknVpVob3md9pad0Oxrz5ckhfl47xOA0GD62e//7s4779RDDz2k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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d6b45f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plt.scatter([r_g_marco, r_g_laura], [k_radius_gyration(marco[1], marco[0], 2), k_radius_gyration(laura[1], laura[0], 2)])\n",
    "plt.plot(r_g_marco, k_radius_gyration(marco[1], marco[0], 2), 'o', c='red')\n",
    "plt.plot(r_g_laura, k_radius_gyration(laura[1], laura[0], 2), 'o', c='green')\n",
    "plt.plot([0,100], [0,100], ls='--')\n",
    "\n",
    "plt.title(r\"$k = 2$\")\n",
    "plt.xlabel(r\"$r_g$\")\n",
    "plt.ylabel(r\"$r_k$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}