{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EFM Demo\n",
    "\n",
    "[EnergyFlow website](https://www.energyflow.network)\n",
    "\n",
    "In this tutorial, we demonstrate how to compute the Energy Flow Moments using the EnergyFlow package. We also demonstrate how to speed up collider observbles and verify all of the linear relations among the EFPs discussed in [1911.04491](https://arxiv.org/abs/1911.04491) that arise in the limit of few particles or spacetime dimensions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import time\n",
    "\n",
    "import energyflow as ef"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot Style"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams['figure.figsize'] = (4,4)\n",
    "plt.rcParams['figure.dpi'] = 120\n",
    "plt.rcParams['font.family'] = 'serif'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Energy Flow Moments\n",
    "The Energy Flow Moments (EFMs) were introduced in [1911.04491](https://arxiv.org/abs/1911.04491) as the moments of the radiation pattern. They are fully-symmetric tensors defined as:\n",
    "$$ \\mathcal I^{\\mu_1\\mu_2\\cdots\\mu_v} \\equiv 2^{v/2}\\sum_{i=1}^M E_i n_i^{\\mu_1} n_i^{\\mu_2} \\cdots n_i^{\\mu_v},\\,\\,\\,\\,\\,\\,\\,\\, n_i^\\mu \\equiv p_i^\\mu / E_i$$\n",
    "for an event or jet with $M$ particles.\n",
    "At a hadron collider like the LHC, we use the particle transverse momentum $p_T$ in place of the energy $E$.\n",
    "\n",
    "\n",
    "EFMs provide a $\\mathcal O(M)$ way to compute $\\beta=2$ Energy Flow Polynomials (EFPs) or Energy Correlation Functions (ECFs).\n",
    "For instance, the invariant mass of an event is $\\mathcal O(M^2)$ to compute as an ECF, but can easily be computed in $\\mathcal O(M)$ via:\n",
    "$$ m^2 = \\sum_{i=1}^M \\sum_{j=1}^M p_{i\\mu} p_{i}^{\\mu} = \\left( \\sum_{i=1}^M E_i n_i^\\mu \\right)^2 = \\frac12\\mathcal I_\\mu \\mathcal I^\\mu$$\n",
    "The EFMs provide the natural generalization of this idea to all correlator observables.\n",
    "\n",
    "As a reminder, the EFPs are multiparticle energy correlators with angular monomials specified by multigraphs $G$.\n",
    "They were introduced in [1712.07124](https://arxiv.org/abs/1712.07124) and form a linear basis for all infrared- and collinear-safe (IRC-safe) observables.\n",
    "They are defined as:\n",
    "$$ {\\rm EFP}_G = \\sum_{i_1=1}^M \\sum_{i_2=1}^M \\cdots \\sum_{i_N=1}^M E_{i_1} E_{i_2} \\cdots E_{i_N} \\prod_{(k,\\ell)\\in G} \\theta_{i_k i_\\ell}, $$\n",
    "where $G$ is a multigraph as a list of edges and $\\theta_{ij}$ is an angular distance between particles. Here we use $\\theta_{ij} = (2 n_i^\\mu n_{j\\mu})^{\\beta/2}$.\n",
    "\n",
    "Below, we compute an EFP in the standard way and using contractions of EFMs. EnergyFlow will do this for you automatically if you use EFPs with the `hadrefm` or `eeefm` measure!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 3.36864801 -0.37543981 -0.07672024 -0.01552002]\n",
      " [-0.37543981  0.90235865  0.06150039 -0.12656877]\n",
      " [-0.07672024  0.06150039  1.09764135  0.00562418]\n",
      " [-0.01552002 -0.12656877  0.00562418  1.36864801]]\n"
     ]
    }
   ],
   "source": [
    "# generate a random event\n",
    "event = ef.gen_random_events(1, 25, dim=4)\n",
    "\n",
    "# the metric\n",
    "metric = np.diag([1,-1,-1,-1])\n",
    "\n",
    "# compute several energy flow moments\n",
    "EFM2 = ef.EFM(2, measure='hadrefm', coords='epxpypz')(event)\n",
    "EFM3 = ef.EFM(3, measure='hadrefm', coords='epxpypz')(event)\n",
    "\n",
    "# take a look at the EFM Imunu\n",
    "print(EFM2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1.1368683772161603e-13\n",
      "-2.8421709430404007e-13\n"
     ]
    }
   ],
   "source": [
    "# compute the EFP corresponding to the \"icecreamcone\" graph in the usual way\n",
    "EFP_correlator = ef.EFP([(0,1),(0,1),(0,2),(1,2)], measure='hadrdot', coords='epxpypz', beta=2)(event)\n",
    "\n",
    "# compute the EFP corresponding to \"icecreamcone\" as a contraction of EFMs with the metric\n",
    "EFP_contraction = np.einsum('abc,def,gh,ad,be,cg,fh->', EFM3, EFM3, EFM2, *([metric]*4))\n",
    "\n",
    "# compute the EFP corresponding to \"icecreamcone\" with explicit sums\n",
    "pTs = np.sqrt(event[:,1]**2 + event[:,2]**2)\n",
    "zs, ns = pTs/np.sum(pTs), (event/pTs[:,np.newaxis])\n",
    "thetas = np.asarray([[np.sum(2*ni*nj*np.asarray([1,-1,-1,-1])) for ni in ns] for nj in ns])\n",
    "\n",
    "EFP_sums = 0\n",
    "for i in range(len(event)):\n",
    "    for j in range(len(event)):\n",
    "        for k in range(len(event)):\n",
    "            EFP_sums += zs[i] * zs[j] * zs[k] * thetas[i,j] * thetas[i,j] * thetas[i,k] * thetas[j,k]\n",
    "\n",
    "# ensure that the two values agree\n",
    "print(EFP_correlator - EFP_contraction)\n",
    "print(EFP_correlator - EFP_sums)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fast Computation of Multi-Prong Taggers\n",
    "The $C_N$ family of $N$-prong taggers was introduced in [1305.0007](https://arxiv.org/abs/1305.0007) built from multiparticle correlators as:\n",
    "$$C_1 = \\sum_{i=1}^M \\sum_{j=1}^M z_i z_j \\theta_{ij}$$\n",
    "$$C_2 = \\frac{\\left(\\sum_{i=1}^M \\sum_{j=1}^M\\sum_{k=1}^M z_i z_j z_k \\theta_{ij}\\theta_{jk}\\theta_{ik}\\right)}{\\left(\\sum_{i=1}^M \\sum_{j=1}^M z_i z_j \\theta_{ij}\\right)^2}$$\n",
    "$$C_3 = \\frac{\\left(\\sum_{i=1}^M \\sum_{j=1}^M\\sum_{k=1}^M \\sum_{\\ell=1}^M z_i z_j z_k z_\\ell \\theta_{ij}\\theta_{ik}\\theta_{i\\ell}\\theta_{jk}\\theta_{j\\ell}\\theta_{k\\ell}\\right)\\left(\\sum_{i=1}^M \\sum_{j=1}^M z_i z_j \\theta_{ij}\\right)}{\\left(\\sum_{i=1}^M \\sum_{j=1}^M\\sum_{k=1}^M z_i z_j z_k \\theta_{ij}\\theta_{jk}\\theta_{ik}\\right)^2}$$\n",
    "where $z_i = p_{T,i}/\\sum_{j=1}^M p_{T,j}$. Here we use $\\theta_{ij} = (2p_i^\\mu p_{j\\mu}/p_{T,i} p_{T,j})^{\\beta/2}$, though the speedups also apply when $\\theta_{ij}$ is the rapidity-azimuth distance (squared).\n",
    "\n",
    "Further, the $D_2$ two-prong tagger was introduced in [1409.6298](https://arxiv.org/abs/1409.6298) and defined as:\n",
    "$$D_2 = \\frac{\\left(\\sum_{i=1}^M \\sum_{j=1}^M\\sum_{k=1}^M z_i z_j z_k \\theta_{ij}\\theta_{jk}\\theta_{ik}\\right)}{\\left(\\sum_{i=1}^M \\sum_{j=1}^M z_i z_j \\theta_{ij}\\right)^3}$$\n",
    "\n",
    "With $\\beta=2$, we will demonstrate that $C_N$, which is naively $\\mathcal O(M^{N+1})$ to compute, can actually be computed in $\\mathcal O(M)$. Similarly, $D_2$, which is naively $\\mathcal O(M^3)$ to compute, can be computed in $\\mathcal O(M)$ as well.\n",
    "\n",
    "Below, we time the $\\mathcal O(M)$ computation of these observables via EFM computation of EFPs using the `hadrdot` measure. You can see the asymptotic linear scaling being achieved, far outpacing the naive computation of these observables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 480x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 434,
       "width": 465
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# specify the relevant graphs and EFPs to compute C1, D2, C3\n",
    "line = ef.EFP([(0,1)], measure='hadrefm', coords='epxpypz', beta=2)\n",
    "triangle = ef.EFP([(0,1), (0,2), (1,2)], measure='hadrefm', coords='epxpypz', beta=2)\n",
    "kite = ef.EFP([(0,1), (0,2), (0,3), (1,2), (1,3), (2,3)], measure='hadrefm', coords='epxpypz', beta=2)\n",
    "\n",
    "# which numbers of particles to evaluate the observables for\n",
    "Ms = 2**np.arange(8,20)\n",
    "C1_times, D2_times, C3_times = [], [] ,[]\n",
    "\n",
    "# compute the observables for each M. This can be repeated for a more robust estimate\n",
    "for M in Ms:\n",
    "    # generate a random event with M particles\n",
    "    event = ef.gen_random_events(1, M, dim=4)\n",
    "\n",
    "    # time the computation of C1\n",
    "    start = time.time()\n",
    "    C1 = line(event)\n",
    "    C1_times.append(time.time()-start)\n",
    "    \n",
    "    # time the computation of D2\n",
    "    start = time.time()\n",
    "    D2 = triangle(event)/line(event)**3\n",
    "    D2_times.append(time.time()-start)\n",
    "    \n",
    "    # time the comuputation of C3\n",
    "    start = time.time()\n",
    "    C3 = kite(event)*line(event)/triangle(event)**2\n",
    "    C3_times.append(time.time()-start)\n",
    "    \n",
    "\n",
    "# plot the results\n",
    "plt.plot(Ms, C3_times, '-o', label='C3 with EFMs', color='tab:red')\n",
    "plt.plot(Ms, D2_times, '-o', label='D2 with EFMs', color='tab:green')\n",
    "plt.plot(Ms, C1_times, '-o', label='C1 with EFMs', color='tab:blue')\n",
    "\n",
    "# plot settings\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.legend(loc='upper left', frameon=False)\n",
    "plt.xlabel('Number of Particles')\n",
    "plt.ylabel('Computation Time [s]')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Relations\n",
    "When the number of particles or spacetime dimensions is \"small\", linear relationships among the EFPs emerge. These can best be understood in the language of EFMs and other moment structures.\n",
    "\n",
    "Here, we numerically illustrate the identities proved in the paper. To begin, we enumerate every relevant multigraph that we will need."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "graphs ={# d=0\n",
    "        'dot': [],\n",
    "\n",
    "        # d=1\n",
    "        'line': [(0,1)],\n",
    "\n",
    "        # d=2\n",
    "        'dumbbell': [(0,1), (0,1)],\n",
    "        'wedge': [(0,1),(1,2)],\n",
    "        'linesqd' : [(0,1),(2,3)],\n",
    "\n",
    "        # d = 3\n",
    "        'tribell' : [(0,1),(0,1),(0,1)],\n",
    "        'triangle' : [(0,1),(1,2),(2,0)],\n",
    "        'asymwedge' : [(0,1),(0,1),(1,2)],\n",
    "        'birdfoot' : [(0,1),(0,2),(0,3)],\n",
    "        'chain' : [(0,1),(1,2),(2,3)],\n",
    "        'linedumbbell' : [(0,1),(2,3),(2,3)],\n",
    "        'linewedge' : [(0,1),(2,3),(3,4)],\n",
    "        'linecbd'  : [(0,1),(2,3),(4,5)],\n",
    "\n",
    "        # d = 4\n",
    "        'quadbell' : [(0,1),(0,1),(0,1),(0,1)],\n",
    "        'doublewedge' : [(0,1),(0,1),(1,2),(1,2)],\n",
    "        'icecreamcone' : [(0,1),(0,1),(1,2),(2,0)],\n",
    "        'asymwedge2' : [(0,1),(0,1),(0,1),(1,2)],\n",
    "        'square' : [(0,1),(1,2),(2,3),(3,0)],\n",
    "        'flyswatter' : [(0,1),(1,2),(2,3),(3,1)],\n",
    "        'chain2mid' : [(0,1),(1,2),(1,2),(2,3)],\n",
    "        'chain2end' : [(0,1),(1,2),(2,3),(2,3)],\n",
    "        'asymbirdfoot' : [(0,1),(0,1),(1,2),(1,3)],\n",
    "        'bigbirdfoot' : [(0,1),(0,2),(0,3),(0,4)],\n",
    "        'dog' : [(0,1),(1,2),(2,3),(2,4)],\n",
    "        'bigchain' : [(0,1),(1,2),(2,3),(3,4)],\n",
    "\n",
    "        'dumbbellwedge' : [(0,1),(0,1),(2,3),(3,4)],\n",
    "        'triangleline' : [(0,1),(1,2),(2,0),(3,4)],\n",
    "        'dumbbellsqd' : [(0,1),(0,1),(2,3),(2,3)],\n",
    "\n",
    "        # d = 5\n",
    "        'pentagon' : [(0,1),(1,2),(2,3),(3,4),(4,0)],\n",
    "        'triangledumbbell': [(0,1),(0,1),(2,3),(3,4),(4,2)]\n",
    "        }"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Finite Particle Relations\n",
    "\n",
    "When the number of particles in the event is small, a number of linear relations among the EFPs emerge due to the simplified nature of the configuration. The typical example of this is that \"triangle\" or ECF3 vanishes for $M=2$ particles. There is an entire family of these relations, which we check below for $M=2$.\n",
    "\n",
    "These identities hold for EFPs with any choice of $\\beta$ or angular measure $\\theta_{ij}$.\n",
    "Play around with the coefficients to see that these identies are non-trivial!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n",
      "0.0\n",
      "1.7763568394002505e-15\n",
      "0.0\n",
      "0.0\n"
     ]
    }
   ],
   "source": [
    "# pick a random event with 2 particles\n",
    "event = ef.gen_random_events(1, 2, dim=4)\n",
    "\n",
    "# compute the value of all of the EFPs on this event\n",
    "d = {name: ef.EFP(graph, measure='hadr', coords='epxpypz', beta=1)(event) for name,graph in graphs.items()}\n",
    "\n",
    "# check that the identities in the paper are valid (i.e. = 0)\n",
    "print(2 * d['wedge'] - d['dumbbell'])\n",
    "print(2 * d['triangle'])\n",
    "print(d['tribell'] - 2 * d['asymwedge'])\n",
    "print(2 * d['chain'] - d['linedumbbell'] - d['triangle'])\n",
    "print(d['birdfoot'] + d['chain'] - d['asymwedge'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Finite Dimension Relations\n",
    "As the number of spacetime dimensions is finite (e.g. 4), the inner product structure of $\\theta_{ij} = n_i^\\mu n_{j\\mu}$ for $\\beta=2$ EFPs gives rise to additional identities.\n",
    "\n",
    "These identities hold for EFPs with $\\beta=2$ when $\\theta_{ij}$ is an inner product. Play around with the coefficients to see that these identies are non-trivial!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n"
     ]
    }
   ],
   "source": [
    "# Three Dimensions\n",
    "# pick a random event in 3 dimensions\n",
    "event = ef.gen_random_events(1, 25, dim=3)\n",
    "\n",
    "# get the transverse momenta and pairwise distances for the event\n",
    "pTs = np.sqrt(event[:,1]**2 + event[:,2]**2)\n",
    "zs, ns = pTs/np.sum(pTs), (event/pTs[:,np.newaxis])\n",
    "thetas = np.asarray([[np.sum(2*ni*nj*np.asarray([1]+[-1]*(len(ni)-1))) for ni in ns] for nj in ns])\n",
    "\n",
    "# compute the value of all of the EFPs on this event\n",
    "d = {name: ef.EFP(graph)(zs=zs, thetas=thetas) for name,graph in graphs.items()}\n",
    "\n",
    "# check that the identity in the paper is valid (i.e. = 0)\n",
    "print(6*d['bigchain']-12*d['chain']+6*d['linedumbbell']+4*d['triangle']-2*d['triangleline']-3*d['dumbbellwedge'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.7284841053187847e-12\n"
     ]
    }
   ],
   "source": [
    "# Four Dimensions\n",
    "# pick a random event in 4 dimensions\n",
    "event = ef.gen_random_events(1, 25, dim=4)\n",
    "\n",
    "# get the transverse momenta and pairwise distances for the event\n",
    "pTs = np.sqrt(event[:,1]**2 + event[:,2]**2)\n",
    "zs, ns = pTs/np.sum(pTs), (event/pTs[:,np.newaxis])\n",
    "thetas = np.asarray([[np.sum(2*ni*nj*np.asarray([1]+[-1]*(len(ni)-1))) for ni in ns] for nj in ns])\n",
    "\n",
    "# compute the value of all of the EFPs on this event\n",
    "d = {name: ef.EFP(graph)(zs=zs, thetas=thetas) for name,graph in graphs.items()}\n",
    "\n",
    "# check that the identity in the paper is valid (i.e. = 0)\n",
    "print(6*d['pentagon']-5*d['triangledumbbell'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Center of Momentum Relations\n",
    "\n",
    "For kinematic polynomials or $\\beta=2$ EFPs in $e^+e^-$ collisions, additional relations emerge when working in the center of momentum.\n",
    "\n",
    "Correlators which correspond to multigraphs with \"leaves\", i.e valency-1 vertices, are no longer independent. Further, counting the number of leafless multigraphs also counts the number of independent kinematic polynomials.\n",
    "\n",
    "Here we count the multigraphs with up to 10 edges for connected and all multigraphs. Going further requires specialized graph packages such as Nauty. The sequences up to 16 edges have been added to the Online-Encyclopedia of Integer Sequences as [A307316](https://oeis.org/A307316) and [A307317](https://oeis.org/A307317)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# function to check if a graph is leafless (i.e. has no valency-1 vertices)\n",
    "def leafless(graph):\n",
    "    return not 1 in np.unique(graph, return_counts=True)[1]\n",
    "\n",
    "# count the number of leafless multigraphs (all or just connected) with degree d\n",
    "ds = np.arange(11)\n",
    "counts_all, counts_con = [], []\n",
    "\n",
    "# for each degree, get the graphs with edges<=d and check whether they are leafless\n",
    "for d in ds:\n",
    "    counts_all.append(np.sum([leafless(graph) for graph in ef.EFPSet(('d<=',d)).graphs()]))\n",
    "    counts_con.append(np.sum([leafless(graph) for graph in ef.EFPSet(('d<=',d), ('p==',1)).graphs()]))\n",
    "\n",
    "# note: computed counts are cumulative, must take the difference to get individual d    \n",
    "counts_all = np.asarray(counts_all[1:]) - np.asarray(counts_all[:-1])\n",
    "counts_con = np.asarray(counts_con[1:]) - np.asarray(counts_con[:-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Counting Multigraphs\n",
      "Edges   Num. Connected & Leafless   Num. Leafless\n",
      "   1       0                           0\n",
      "   2       1                           1\n",
      "   3       2                           2\n",
      "   4       4                           5\n",
      "   5       9                          11\n",
      "   6      26                          34\n",
      "   7      68                          87\n",
      "   8     217                         279\n",
      "   9     718                         897\n",
      "  10    2553                        3129\n"
     ]
    }
   ],
   "source": [
    "# display the results in a table\n",
    "print(\"Counting Multigraphs\")\n",
    "print(\"Edges\", \"  Num. Connected & Leafless\", \"  Num. Leafless\")\n",
    "for d, count_con, count_all in zip(ds[1:], counts_con, counts_all):\n",
    "    print(\"{:4g}    {:4g}                        {:4g}\".format(d, count_con, count_all))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Euclidean Slicing Relations\n",
    "When using the $\\beta=2$ EFPs for $e^+e^-$ collisions, there is an interesting correspondence between the EFMs and generalized sphericity tensors:\n",
    "$$\\Theta^{j_1j_2\\cdots j_v} \\equiv \\sum_{i=1}^M E_i \\hat n_i^{j_1}\\hat n_i^{j_2}\\cdots \\hat n_i^{j_v},\\,\\,\\,\\,\\,\\,\\, \\hat n_i \\equiv \\vec p/E.$$\n",
    "\n",
    "In particular, the spatial components of the EFMs are precisely the sphericity tensors. For instance:\n",
    "$$\\mathcal I^{j_1j_2} = 2\\Theta^{j_1j_2}.$$\n",
    "\n",
    "Polynomials obtained by contracting the generalized sphericity tensors are interesting objects, closely related to famous event shapes such as the $C$ and $D$ parameters. The relationship between $\\Theta$ and $\\mathcal I$ induces a close relationship between these polynomials and the EFPs.\n",
    "\n",
    "Here, we showcase a translation table between the sphericity polynomials and EFPs for graphs of degree up to 4. Play with the coefficients in the table to see that these relationships are nontrivial!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# function to compute the \"euclidean\" (i.e. sphericity) polynomial of a graph using EFPs\n",
    "def euc(efp, event):\n",
    "    l = list(range(event.shape[1])) + [0]\n",
    "    return (-1)**efp.d * efp(event[:,l])\n",
    "\n",
    "# specify the desired graphs, here all graphs up to d<=3 and all connected graphs with d=4\n",
    "gnames = [# d=0\n",
    "          'dot',\n",
    "          # d = 1\n",
    "          'line',\n",
    "          # d = 2\n",
    "          'dumbbell', 'wedge', 'linesqd',\n",
    "          # d = 3\n",
    "          'tribell', 'triangle', 'asymwedge', 'birdfoot', 'chain', 'linedumbbell', 'linewedge', 'linecbd',\n",
    "          # d = 4 (connected)\n",
    "          'quadbell', 'doublewedge', 'icecreamcone', 'asymwedge2', 'square', 'flyswatter',\n",
    "          'chain2mid', 'chain2end', 'asymbirdfoot', 'bigbirdfoot', 'dog', 'bigchain']\n",
    "\n",
    "# take the entire translation matrix from sphericity polynomials to EFPs from the paepr\n",
    "M = np.asarray([\n",
    "    [1,   0,  0, 0,   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [2,  -1,  0, 0,   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [4,  -4,  1, 0,   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [4,  -4,  0, 1,   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [4,  -4,  0, 0,   1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [8, -12,  6, 0,   0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [8, -12,  0, 6,   0, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [8, -12,  2, 4,   0, 0, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [8, -12,  0, 6,   0, 0, 0, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [8, -12,  0, 4,   2, 0, 0, 0, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [8, -12,  2, 0,   4, 0, 0, 0, 0, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [8, -12,  0, 2,   4, 0, 0, 0, 0, 0, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [8, -12,  0, 0,   6, 0, 0, 0, 0, 0, 0, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [16,-32, 24, 0,   0,-8, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [16,-32,  8, 16,  0, 0, 0,-8, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [16,-32,  4, 20,  0, 0,-4,-4, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [16,-32, 12, 12,  0,-2, 0,-6, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [16,-32,  0, 16,  8, 0, 0, 0, 0,-8, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],\n",
    "    [16,-32,  0, 20,  4, 0,-2, 0,-2,-4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0],\n",
    "    [16,-32,  4, 16,  4, 0, 0,-4, 0,-4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],\n",
    "    [16,-32,  4, 12,  8, 0, 0,-2, 0,-4,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0],\n",
    "    [16,-32,  4, 20,  0, 0, 0,-4,-4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0],\n",
    "    [16,-32,  0, 24,  0, 0, 0, 0,-8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0],\n",
    "    [16,-32,  0, 16,  8, 0, 0, 0,-2,-4, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0],\n",
    "    [16,-32,  0, 12, 12, 0, 0, 0, 0,-4, 0,-4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.00000000e+00  4.44089210e-16  1.77635684e-15  8.88178420e-16\n",
      "  1.77635684e-15  1.06581410e-14  8.88178420e-16  3.55271368e-15\n",
      "  4.44089210e-15  1.77635684e-15  5.32907052e-15  3.55271368e-15\n",
      "  4.44089210e-15 -2.13162821e-14  1.42108547e-14  1.59872116e-14\n",
      "  2.84217094e-14  3.55271368e-15  8.88178420e-15  7.10542736e-15\n",
      "  1.77635684e-14  2.13162821e-14  8.88178420e-15  1.59872116e-14\n",
      "  5.32907052e-15]\n",
      "2.842170943040401e-14\n"
     ]
    }
   ],
   "source": [
    "# generate a random event\n",
    "event = ef.gen_random_events(1, 25, dim=4)\n",
    "\n",
    "# compute the EFPs and Sphericity polynomials\n",
    "efps = [ef.EFP(graphs[name], coords='epxpypz', measure='eeefm', beta=2)(event) for name in gnames]\n",
    "eucs = [euc(ef.EFP(graphs[name], coords='epxpypz', measure='eeefm', beta=2),event) for name in gnames]\n",
    "\n",
    "# convert the results to numpy arrays\n",
    "efps, eucs = np.asarray(efps), np.asarray(eucs)\n",
    "\n",
    "# check that all of the relationships are valid (i.e. = 0)\n",
    "print(efps - np.dot(M,eucs))\n",
    "print(np.max(efps - np.dot(M,eucs)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's explore the relationship between the $C$ and $D$ parameters, sphericity polynomials, and the EFPs. We can write the $C$ and $D$ parameters as contractions of the sphericity tensors.\n",
    "\n",
    "We also use our table above to translate these into linear combinations of EFPs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n",
      "-1.6653345369377348e-15\n",
      "[ 1.5   -0.375] ['line' 'dumbbell']\n",
      "[-3.375  6.75  -1.125] ['dumbbell' 'wedge' 'triangle']\n"
     ]
    }
   ],
   "source": [
    "# generate a random event\n",
    "event = ef.gen_random_events(1, 25, dim=4)\n",
    "\n",
    "# get the theta matrix\n",
    "theta = ef.EFM(2, measure='eeefm')(event)[1:,1:]/2\n",
    "\n",
    "# compute the C and D parameters\n",
    "C = 3/2 * (np.trace(theta)**2 - np.trace(np.dot(theta,theta)))\n",
    "D = 27 * np.linalg.det(theta)\n",
    "\n",
    "# compute some sphericity polynomials\n",
    "euc_dumbbell = euc(ef.EFP(graphs['dumbbell'], coords='epxpypz', measure='eeefm', beta=2),event)\n",
    "euc_triangle = euc(ef.EFP(graphs['triangle'], coords='epxpypz', measure='eeefm', beta=2),event)\n",
    "\n",
    "# check the graphical expressions for the C and D parameters (i.e. difference = 0)\n",
    "print(-3/8 * euc_dumbbell + 3/2 - C)\n",
    "print(9/8 * euc_triangle - 27/8 * euc_dumbbell + 9/2 - D)\n",
    "\n",
    "# we can also translate these into linear combinations of EFPs as follows\n",
    "vec = np.dot(M[:3,:3].T, np.asarray([3/2, 0, -3/8]))\n",
    "print(vec[vec!=0], np.asarray(gnames[:3])[vec!=0])\n",
    "\n",
    "vec = np.dot(M[:7,:7].T, np.asarray([9/2, 0, -27/8, 0, 0, 0, 9/8]))\n",
    "print(vec[vec!=0], np.asarray(gnames[:7])[vec!=0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, since the generalized sphericity tensors live in 3 spacetime dimensions, they are sensitive to three-dimensional finite dimension identities. These can be obtained using our usual techniques and then translated to relations among EFPs using our table."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n",
      "0.0\n",
      "5.684341886080802e-14\n",
      "-1.4210854715202004e-14\n"
     ]
    }
   ],
   "source": [
    "# generate a random event\n",
    "event = ef.gen_random_events(1, 25, dim=4)\n",
    "\n",
    "# compute some sphericity polynomials\n",
    "euc_line          = euc(ef.EFP(graphs['line'],          coords='epxpypz', measure='eeefm', beta=2),event)\n",
    "euc_dumbbell      = euc(ef.EFP(graphs['dumbbell'],      coords='epxpypz', measure='eeefm', beta=2),event)\n",
    "euc_wedge         = euc(ef.EFP(graphs['wedge'],         coords='epxpypz', measure='eeefm', beta=2),event)\n",
    "euc_triangle      = euc(ef.EFP(graphs['triangle'],      coords='epxpypz', measure='eeefm', beta=2),event)\n",
    "euc_linedumbbell  = euc(ef.EFP(graphs['linedumbbell'],  coords='epxpypz', measure='eeefm', beta=2),event)\n",
    "euc_square        = euc(ef.EFP(graphs['square'],        coords='epxpypz', measure='eeefm', beta=2),event)\n",
    "euc_dumbbellsqd   = euc(ef.EFP(graphs['dumbbellsqd'],   coords='epxpypz', measure='eeefm', beta=2),event)\n",
    "euc_dumbbellwedge = euc(ef.EFP(graphs['dumbbellwedge'], coords='epxpypz', measure='eeefm', beta=2),event)\n",
    "euc_triangleline  = euc(ef.EFP(graphs['triangleline'],  coords='epxpypz', measure='eeefm', beta=2),event)\n",
    "euc_chain         = euc(ef.EFP(graphs['chain'],         coords='epxpypz', measure='eeefm', beta=2),event)\n",
    "euc_bigchain      = euc(ef.EFP(graphs['bigchain'],      coords='epxpypz', measure='eeefm', beta=2),event)\n",
    "\n",
    "# verify the euclidean finite dimension (= 3) relations\n",
    "print(6*euc_square - 16*euc_triangle - 3*euc_dumbbellsqd + 24*euc_dumbbell - 16)\n",
    "print(6*euc_bigchain - 12*euc_chain - 3*euc_dumbbellwedge - 2*euc_triangleline\n",
    "      + 12*euc_wedge + 6*euc_linedumbbell - 8*euc_line)\n",
    "\n",
    "\n",
    "# compute some EFPs\n",
    "line          = ef.EFP(graphs['line'],          coords='epxpypz', measure='eeefm', beta=2)(event)\n",
    "dumbbell      = ef.EFP(graphs['dumbbell'],      coords='epxpypz', measure='eeefm', beta=2)(event)\n",
    "wedge         = ef.EFP(graphs['wedge'],         coords='epxpypz', measure='eeefm', beta=2)(event)\n",
    "triangle      = ef.EFP(graphs['triangle'],      coords='epxpypz', measure='eeefm', beta=2)(event)\n",
    "linedumbbell  = ef.EFP(graphs['linedumbbell'],  coords='epxpypz', measure='eeefm', beta=2)(event)\n",
    "square        = ef.EFP(graphs['square'],        coords='epxpypz', measure='eeefm', beta=2)(event)\n",
    "dumbbellsqd   = ef.EFP(graphs['dumbbellsqd'],   coords='epxpypz', measure='eeefm', beta=2)(event)\n",
    "dumbbellwedge = ef.EFP(graphs['dumbbellwedge'], coords='epxpypz', measure='eeefm', beta=2)(event)\n",
    "triangleline  = ef.EFP(graphs['triangleline'],  coords='epxpypz', measure='eeefm', beta=2)(event)\n",
    "chain         = ef.EFP(graphs['chain'],         coords='epxpypz', measure='eeefm', beta=2)(event)\n",
    "bigchain      = ef.EFP(graphs['bigchain'],      coords='epxpypz', measure='eeefm', beta=2)(event)\n",
    "\n",
    "# verify the induced EFP subslicing relations\n",
    "print(6*square + 16*triangle - 3*dumbbellsqd - 48*chain + 24*linedumbbell)\n",
    "print(6*bigchain - 12*chain - 3*dumbbellwedge - 2*triangleline + 4*triangle + 6*linedumbbell)"
   ]
  }
 ],
 "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}