examples/write_monte_carlo_example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f40b7065-5763-4abc-91ff-40437cf86517",
   "metadata": {},
   "source": [
    "# Simple $e^+e^- \\to \\mu^+ \\mu^- $ Monte Carlo Event Genrator example"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "215df39b-69fc-4f74-b882-3c96f5526783",
   "metadata": {},
   "source": [
    "Differential cross section:\n",
    "$$\n",
    "\\frac{d \\sigma}{ d \\Omega} = \\frac{\\alpha^2}{4 s } ( 1+ \\cos^2(\\theta))\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f7124c5f-9f86-4a0a-ac08-6e30cc55e01d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import random\n",
    "\n",
    "import hist\n",
    "import numpy as np\n",
    "\n",
    "import pylhe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f2553a00-1d72-4d4b-ba6d-c552ca0a7b59",
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 1 / 127.4  # alpha QED\n",
    "aqcd = 0.1075  # alpha QCD\n",
    "EB = 209\n",
    "s = (2 * EB) ** 2\n",
    "theta_min = 0\n",
    "theta_max = math.pi\n",
    "phi_min = 0\n",
    "phi_max = 2 * math.pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7242869e-7fbb-4eee-9d49-8a9d63724e35",
   "metadata": {},
   "outputs": [],
   "source": [
    "# https://equation-database.readthedocs.io/en/latest/_autosummary/equation_database.isbn_9780471887416.html#equation_database.isbn_9780471887416.equation_6_32\n",
    "\n",
    "\n",
    "def dsigma(s, theta, _phi):\n",
    "    return (math.cos(theta) ** 2 + 1) / 4 * alpha**2 / s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "147dfe17-a5d9-4b68-a07f-6f8d8aa390a1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated integral: 1.4735464978545061e-09\n",
      "Real integral:      1.477056777521761e-09\n"
     ]
    }
   ],
   "source": [
    "# Monte Carlo integration\n",
    "\n",
    "\n",
    "def monte_carlo_integration(\n",
    "    func, s, theta_min, theta_max, phi_min, phi_max, num_samples\n",
    "):\n",
    "    theta_samples = [random.uniform(theta_min, theta_max) for _ in range(num_samples)]\n",
    "    phi_samples = [random.uniform(phi_min, phi_max) for _ in range(num_samples)]\n",
    "    func_values = [\n",
    "        (phi_max - phi_min)\n",
    "        * (theta_max - theta_min)\n",
    "        * func(s, theta, phi)\n",
    "        * math.sin(theta)\n",
    "        for theta, phi in zip(theta_samples, phi_samples)\n",
    "    ]\n",
    "    maximum = np.max(func_values)\n",
    "    integral = np.mean(func_values)\n",
    "    return integral, maximum\n",
    "\n",
    "\n",
    "# Parameters\n",
    "\n",
    "num_samples = 100000\n",
    "\n",
    "# Perform integration\n",
    "result, maximum = monte_carlo_integration(\n",
    "    dsigma, s, theta_min, theta_max, phi_min, phi_max, num_samples\n",
    ")\n",
    "print(f\"Estimated integral: {result}\")\n",
    "\n",
    "# https://equation-database.readthedocs.io/en/latest/_autosummary/equation_database.isbn_9780471887416.html#equation_database.isbn_9780471887416.equation_6_33\n",
    "sigma = 4 * math.pi / 3 * alpha**2 / s\n",
    "print(f\"Real integral:      {sigma}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "692b7fad-a519-49b8-9dbc-d7d8c27eaba9",
   "metadata": {},
   "source": [
    "## Weighted Events\n",
    "\n",
    "The information about the distribution is carried by the weights of the events."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5c26e5e3-8e1e-470f-96a6-376a6e294bf9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<LesHouchesEvents version=\"3\">\n",
      "<init>\n",
      "     11    -11  2.0900000e+02  2.0900000e+02     0     0     0     0     3     1\n",
      " 1.4757931e-09  0.0000000e+00  1.0000000e+00     1\n",
      "<initrwgt /></init>\n",
      "<event>\n",
      "  5      0  1.7661008451e-14  1.7472400000e+05  7.8492935636e-03  1.0750000000e-01\n",
      "   11  -1   0   0   0   0  0.00000000e+00  0.00000000e+00  2.09000000e+02  2.09000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "  -11  -1   0   0   0   0  0.00000000e+00  0.00000000e+00 -2.09000000e+02  2.09000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "   22   2   1   2   0   0  0.00000000e+00  0.00000000e+00  0.00000000e+00  4.18000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "   13   1   3   3   0   0 -1.81383801e+02 -9.70727770e+01 -3.68482397e+01  2.09000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "  -13   1   3   3   0   0  1.81383801e+02  9.70727770e+01  3.68482397e+01  2.09000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "</event>\n",
      "<event>\n",
      "  5      0  9.7193310495e-15  1.7472400000e+05  7.8492935636e-03  1.0750000000e-01\n",
      "   11  -1   0   0   0   0  0.00000000e+00  0.00000000e+00  2.09000000e+02  2.09000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "  -11  -1   0   0   0   0  0.00000000e+00  0.00000000e+00 -2.09000000e+02  2.09000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "   22   2   1   2   0   0  0.00000000e+00  0.00000000e+00  0.00000000e+00  4.18000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "   13   1   3   3   0   0  6.83511907e+00  6.05767423e+01  1.99911829e+02  2.09000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "  -13   1   3   3   0   0 -6.83511907e+00 -6.05767423e+01 -1.99911829e+02  2.09000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "</event>\n",
      "<event>\n",
      "  5      0  1.8625711578e-14  1.7472400000e+05  7.8492935636e-03  1.0750000000e-01\n",
      "   11  -1   0   0   0   0  0.00000000e+00  0.00000000e+00  2.09000000e+02  2.09000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "  -11  -1   0   0   0   0  0.00000000e+00  0.00000000e+00 -2.09000000e+02  2.09000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "   22   2   1   2   0   0  0.00000000e+00  0.00000000e+00  0.00000000e+00  4.18000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "   13   1   3   3   0   0  1.16076229e+02 -1.48397753e+02 -9.04732882e+01  2.09000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "  -13   1   3   3   0   0 -1.16076229e+02  1.48397753e+02  9.04732882e+01  2.09000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "</event>\n",
      "</LesHouchesEvents>\n"
     ]
    }
   ],
   "source": [
    "num_samples = 100000\n",
    "integ = 0.0\n",
    "lheevents = []\n",
    "for _i in range(num_samples):\n",
    "    theta = random.uniform(theta_min, theta_max)\n",
    "    phi = random.uniform(phi_min, phi_max)\n",
    "    sig = (\n",
    "        (phi_max - phi_min)\n",
    "        * (theta_max - theta_min)\n",
    "        * dsigma(s, theta, phi)\n",
    "        * math.sin(theta)\n",
    "        / num_samples\n",
    "    )\n",
    "    integ += sig\n",
    "    # Fill the LHE event\n",
    "    e = pylhe.LHEEvent(\n",
    "        eventinfo=pylhe.LHEEventInfo(\n",
    "            nparticles=5,\n",
    "            pid=0,\n",
    "            weight=sig,  # The individual weight per event\n",
    "            scale=s,\n",
    "            aqed=alpha,\n",
    "            aqcd=aqcd,\n",
    "        ),\n",
    "        particles=[\n",
    "            pylhe.LHEParticle(\n",
    "                id=11,\n",
    "                status=-1,\n",
    "                mother1=0,\n",
    "                mother2=0,\n",
    "                color1=0,\n",
    "                color2=0,\n",
    "                px=0.0,\n",
    "                py=0.0,\n",
    "                pz=EB,\n",
    "                e=EB,\n",
    "                m=0.0,\n",
    "                lifetime=0,\n",
    "                spin=9.0,\n",
    "            ),\n",
    "            pylhe.LHEParticle(\n",
    "                id=-11,\n",
    "                status=-1,\n",
    "                mother1=0,\n",
    "                mother2=0,\n",
    "                color1=0,\n",
    "                color2=0,\n",
    "                px=0.0,\n",
    "                py=0.0,\n",
    "                pz=-EB,\n",
    "                e=EB,\n",
    "                m=0.0,\n",
    "                lifetime=0,\n",
    "                spin=9.0,\n",
    "            ),\n",
    "            pylhe.LHEParticle(\n",
    "                id=22,\n",
    "                status=2,\n",
    "                mother1=1,\n",
    "                mother2=2,\n",
    "                color1=0,\n",
    "                color2=0,\n",
    "                px=0.0,\n",
    "                py=0.0,\n",
    "                pz=EB - EB,\n",
    "                e=EB + EB,\n",
    "                m=0.0,\n",
    "                lifetime=0,\n",
    "                spin=9.0,\n",
    "            ),\n",
    "            pylhe.LHEParticle(\n",
    "                id=13,\n",
    "                status=1,\n",
    "                mother1=3,\n",
    "                mother2=3,\n",
    "                color1=0,\n",
    "                color2=0,\n",
    "                px=EB * math.sin(theta) * math.cos(phi),\n",
    "                py=EB * math.sin(theta) * math.sin(phi),\n",
    "                pz=EB * math.cos(theta),\n",
    "                e=EB,\n",
    "                m=0,\n",
    "                lifetime=0,\n",
    "                spin=9.0,\n",
    "            ),\n",
    "            pylhe.LHEParticle(\n",
    "                id=-13,\n",
    "                status=1,\n",
    "                mother1=3,\n",
    "                mother2=3,\n",
    "                color1=0,\n",
    "                color2=0,\n",
    "                px=-EB * math.sin(theta) * math.cos(phi),\n",
    "                py=-EB * math.sin(theta) * math.sin(phi),\n",
    "                pz=-EB * math.cos(theta),\n",
    "                e=EB,\n",
    "                m=0,\n",
    "                lifetime=0,\n",
    "                spin=9.0,\n",
    "            ),\n",
    "        ],\n",
    "    )\n",
    "    lheevents.append(e)\n",
    "# Fill the LHE init\n",
    "lheinit = pylhe.LHEInit(\n",
    "    initInfo=pylhe.LHEInitInfo(\n",
    "        beamA=11,\n",
    "        beamB=-11,\n",
    "        energyA=EB,\n",
    "        energyB=EB,\n",
    "        PDFgroupA=0,\n",
    "        PDFgroupB=0,\n",
    "        PDFsetA=0,\n",
    "        PDFsetB=0,\n",
    "        weightingStrategy=3,\n",
    "        numProcesses=1,\n",
    "    ),\n",
    "    procInfo=[\n",
    "        pylhe.LHEProcInfo(\n",
    "            xSection=integ,\n",
    "            error=0,\n",
    "            unitWeight=1,\n",
    "            procId=1,\n",
    "        )\n",
    "    ],\n",
    "    weightgroup={},\n",
    "    LHEVersion=3,\n",
    ")\n",
    "print(pylhe.write_lhe_string(lheinit, lheevents[0:3], rwgt=False, weights=False))\n",
    "pylhe.write_lhe_file(\n",
    "    lheinit, lheevents, filepath=\"weighted.lhe.gz\", rwgt=False, weights=False\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2fca49b0-2d93-476a-9b6b-835b72a24bb0",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c94b9451-e7cc-4f40-9c1e-63dd8e180595",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html>\n",
       "<div style=\"display:flex; align-items:center;\">\n",
       "<div style=\"width:290px;\">\n",
       "<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"-10 -105 270 120\">\n",
       "<line x1=\"-5\" y1=\"0\" x2=\"255\" y2=\"0\" style=\"fill:none;stroke-width:2;stroke:currentColor\"/>\n",
       "<text text-anchor=\"middle\" x=\"0\" y=\"15\" style=\"fill:currentColor;\">\n",
       "0\n",
       "</text>\n",
       "<text text-anchor=\"middle\" x=\"250\" y=\"15\" style=\"fill:currentColor;\">\n",
       "3.14\n",
       "</text>\n",
       "<text text-anchor=\"middle\" x=\"125.0\" y=\"15\" style=\"fill:currentColor;\">\n",
       "Axis 0\n",
       "</text>\n",
       "<polyline points=\"  0,0   0,-14.6 12.5,-14.6 12.5,-41.6  25,-41.6  25,-63.3 37.5,-63.3 37.5,-83.6  50,-83.6  50,-92.3 62.5,-92.3 62.5,-100  75,-100  75,-98.4 87.5,-98.4 87.5,-95.8 100,-95.8 100,-95.5 112.5,-95.5 112.5,-91.5 125,-91.5 125,-93 137.5,-93 137.5,-93.6 150,-93.6 150,-97.6 162.5,-97.6 162.5,-97.7 175,-97.7 175,-97.4 187.5,-97.4 187.5,-92.7 200,-92.7 200,-84.1 212.5,-84.1 212.5,-65 225,-65 225,-41.9 237.5,-41.9 237.5,-14 250,-14 250,0\" style=\"fill:none; stroke:currentColor;\"/>\n",
       "</svg>\n",
       "</div>\n",
       "<div style=\"flex=grow:1;\">\n",
       "Regular(20, 0, 3.14159, label='Axis 0')<br/>\n",
       "<hr style=\"margin-top:.2em; margin-bottom:.2em;\"/>\n",
       "Weight() Σ=WeightedSum(value=1.47579e-09, variance=2.45707e-23)\n",
       "\n",
       "</div>\n",
       "</div>\n",
       "</html>"
      ],
      "text/plain": [
       "Hist(Regular(20, 0, 3.14159, label='Axis 0'), storage=Weight()) # Sum: WeightedSum(value=1.47579e-09, variance=2.45707e-23)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = pylhe.to_awkward(pylhe.read_lhe_with_attributes(\"weighted.lhe.gz\"))\n",
    "hist1 = hist.Hist.new.Reg(20, 0, math.pi).Weight()\n",
    "hist1.fill(arr.particles.vector[:, -1].theta, weight=arr.eventinfo.weight)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b43498cd-1fe7-49c1-a24c-5b66cf4e257f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[StairsArtists(stairs=<matplotlib.patches.StepPatch object at 0x7f3afb8169c0>, errorbar=<ErrorbarContainer object of 3 artists>, legend_artist=<ErrorbarContainer object of 3 artists>)]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist1.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77d19d7a-07c7-4da3-81c6-31e716f3b15d",
   "metadata": {},
   "source": [
    "## Unweighted Events\n",
    "\n",
    "The information about the distribution is carried by the distribution/number of the events."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a43da3e7-5263-4557-8024-cb08ae00f01b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<LesHouchesEvents version=\"3\">\n",
      "<init>\n",
      "     11    -11  2.0900000e+02  2.0900000e+02     0     0     0     0     3     1\n",
      " 1.4735465e-09  0.0000000e+00  1.0000000e+00     1\n",
      "<initrwgt /></init>\n",
      "<event>\n",
      "  5      0  1.4735464979e-14  1.7472400000e+05  7.8492935636e-03  1.0750000000e-01\n",
      "   11  -1   0   0   0   0  0.00000000e+00  0.00000000e+00  2.09000000e+02  2.09000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "  -11  -1   0   0   0   0  0.00000000e+00  0.00000000e+00 -2.09000000e+02  2.09000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "   22   2   1   2   0   0  0.00000000e+00  0.00000000e+00  0.00000000e+00  4.18000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "   13   1   3   3   0   0 -9.71832976e+01 -1.05925675e+02 -1.51710771e+02  2.09000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "  -13   1   3   3   0   0  9.71832976e+01  1.05925675e+02  1.51710771e+02  2.09000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "</event>\n",
      "<event>\n",
      "  5      0  1.4735464979e-14  1.7472400000e+05  7.8492935636e-03  1.0750000000e-01\n",
      "   11  -1   0   0   0   0  0.00000000e+00  0.00000000e+00  2.09000000e+02  2.09000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "  -11  -1   0   0   0   0  0.00000000e+00  0.00000000e+00 -2.09000000e+02  2.09000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "   22   2   1   2   0   0  0.00000000e+00  0.00000000e+00  0.00000000e+00  4.18000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "   13   1   3   3   0   0 -1.95033954e+02 -5.97356676e+01 -4.55456570e+01  2.09000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "  -13   1   3   3   0   0  1.95033954e+02  5.97356676e+01  4.55456570e+01  2.09000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "</event>\n",
      "<event>\n",
      "  5      0  1.4735464979e-14  1.7472400000e+05  7.8492935636e-03  1.0750000000e-01\n",
      "   11  -1   0   0   0   0  0.00000000e+00  0.00000000e+00  2.09000000e+02  2.09000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "  -11  -1   0   0   0   0  0.00000000e+00  0.00000000e+00 -2.09000000e+02  2.09000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "   22   2   1   2   0   0  0.00000000e+00  0.00000000e+00  0.00000000e+00  4.18000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "   13   1   3   3   0   0  1.16000482e+02 -9.74154245e+01  1.43996956e+02  2.09000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "  -13   1   3   3   0   0 -1.16000482e+02  9.74154245e+01 -1.43996956e+02  2.09000000e+02  0.00000000e+00  0.0000e+00  9.0000e+00\n",
      "</event>\n",
      "</LesHouchesEvents>\n"
     ]
    }
   ],
   "source": [
    "num_samples = 100000\n",
    "integ = 0.0\n",
    "lheevents = []\n",
    "while len(lheevents) < num_samples:\n",
    "    theta = random.uniform(theta_min, theta_max)\n",
    "    phi = random.uniform(phi_min, phi_max)\n",
    "    sig = (\n",
    "        (phi_max - phi_min)\n",
    "        * (theta_max - theta_min)\n",
    "        * dsigma(s, theta, phi)\n",
    "        * math.sin(theta)\n",
    "    )\n",
    "    if sig / maximum > random.uniform(\n",
    "        0, 1\n",
    "    ):  # Pick events randomly according to their contribution\n",
    "        e = pylhe.LHEEvent(\n",
    "            eventinfo=pylhe.LHEEventInfo(\n",
    "                nparticles=5,\n",
    "                pid=0,\n",
    "                weight=result / num_samples,  # The same weight per event\n",
    "                scale=s,\n",
    "                aqed=alpha,\n",
    "                aqcd=aqcd,\n",
    "            ),\n",
    "            particles=[\n",
    "                pylhe.LHEParticle(\n",
    "                    id=11,\n",
    "                    status=-1,\n",
    "                    mother1=0,\n",
    "                    mother2=0,\n",
    "                    color1=0,\n",
    "                    color2=0,\n",
    "                    px=0.0,\n",
    "                    py=0.0,\n",
    "                    pz=EB,\n",
    "                    e=EB,\n",
    "                    m=0.0,\n",
    "                    lifetime=0,\n",
    "                    spin=9.0,\n",
    "                ),\n",
    "                pylhe.LHEParticle(\n",
    "                    id=-11,\n",
    "                    status=-1,\n",
    "                    mother1=0,\n",
    "                    mother2=0,\n",
    "                    color1=0,\n",
    "                    color2=0,\n",
    "                    px=0.0,\n",
    "                    py=0.0,\n",
    "                    pz=-EB,\n",
    "                    e=EB,\n",
    "                    m=0.0,\n",
    "                    lifetime=0,\n",
    "                    spin=9.0,\n",
    "                ),\n",
    "                pylhe.LHEParticle(\n",
    "                    id=22,\n",
    "                    status=2,\n",
    "                    mother1=1,\n",
    "                    mother2=2,\n",
    "                    color1=0,\n",
    "                    color2=0,\n",
    "                    px=0.0,\n",
    "                    py=0.0,\n",
    "                    pz=EB - EB,\n",
    "                    e=EB + EB,\n",
    "                    m=0.0,\n",
    "                    lifetime=0,\n",
    "                    spin=9.0,\n",
    "                ),\n",
    "                pylhe.LHEParticle(\n",
    "                    id=13,\n",
    "                    status=1,\n",
    "                    mother1=3,\n",
    "                    mother2=3,\n",
    "                    color1=0,\n",
    "                    color2=0,\n",
    "                    px=EB * math.sin(theta) * math.cos(phi),\n",
    "                    py=EB * math.sin(theta) * math.sin(phi),\n",
    "                    pz=EB * math.cos(theta),\n",
    "                    e=EB,\n",
    "                    m=0,\n",
    "                    lifetime=0,\n",
    "                    spin=9.0,\n",
    "                ),\n",
    "                pylhe.LHEParticle(\n",
    "                    id=-13,\n",
    "                    status=1,\n",
    "                    mother1=3,\n",
    "                    mother2=3,\n",
    "                    color1=0,\n",
    "                    color2=0,\n",
    "                    px=-EB * math.sin(theta) * math.cos(phi),\n",
    "                    py=-EB * math.sin(theta) * math.sin(phi),\n",
    "                    pz=-EB * math.cos(theta),\n",
    "                    e=EB,\n",
    "                    m=0,\n",
    "                    lifetime=0,\n",
    "                    spin=9.0,\n",
    "                ),\n",
    "            ],\n",
    "        )\n",
    "        lheevents.append(e)\n",
    "lheinit = pylhe.LHEInit(\n",
    "    initInfo=pylhe.LHEInitInfo(\n",
    "        beamA=11,\n",
    "        beamB=-11,\n",
    "        energyA=EB,\n",
    "        energyB=EB,\n",
    "        PDFgroupA=0,\n",
    "        PDFgroupB=0,\n",
    "        PDFsetA=0,\n",
    "        PDFsetB=0,\n",
    "        weightingStrategy=3,\n",
    "        numProcesses=1,\n",
    "    ),\n",
    "    procInfo=[\n",
    "        pylhe.LHEProcInfo(\n",
    "            xSection=result,\n",
    "            error=0,\n",
    "            unitWeight=1,\n",
    "            procId=1,\n",
    "        )\n",
    "    ],\n",
    "    weightgroup={},\n",
    "    LHEVersion=3,\n",
    ")\n",
    "print(pylhe.write_lhe_string(lheinit, lheevents[0:3], rwgt=False, weights=False))\n",
    "pylhe.write_lhe_file(\n",
    "    lheinit, lheevents, filepath=\"unweighted.lhe\", rwgt=False, weights=False\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e840fba3-e797-497c-9ad8-e48451928614",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html>\n",
       "<div style=\"display:flex; align-items:center;\">\n",
       "<div style=\"width:290px;\">\n",
       "<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"-10 -105 270 120\">\n",
       "<line x1=\"-5\" y1=\"0\" x2=\"255\" y2=\"0\" style=\"fill:none;stroke-width:2;stroke:currentColor\"/>\n",
       "<text text-anchor=\"middle\" x=\"0\" y=\"15\" style=\"fill:currentColor;\">\n",
       "0\n",
       "</text>\n",
       "<text text-anchor=\"middle\" x=\"250\" y=\"15\" style=\"fill:currentColor;\">\n",
       "3.14\n",
       "</text>\n",
       "<text text-anchor=\"middle\" x=\"125.0\" y=\"15\" style=\"fill:currentColor;\">\n",
       "Axis 0\n",
       "</text>\n",
       "<polyline points=\"  0,0   0,-13.5 12.5,-13.5 12.5,-40.5  25,-40.5  25,-66.2 37.5,-66.2 37.5,-82.2  50,-82.2  50,-93.7 62.5,-93.7 62.5,-99.6  75,-99.6  75,-98.3 87.5,-98.3 87.5,-100 100,-100 100,-93.4 112.5,-93.4 112.5,-92.1 125,-92.1 125,-94.5 137.5,-94.5 137.5,-92.5 150,-92.5 150,-99.2 162.5,-99.2 162.5,-99.8 175,-99.8 175,-99.9 187.5,-99.9 187.5,-93.5 200,-93.5 200,-83.8 212.5,-83.8 212.5,-66 225,-66 225,-40.6 237.5,-40.6 237.5,-14.1 250,-14.1 250,0\" style=\"fill:none; stroke:currentColor;\"/>\n",
       "</svg>\n",
       "</div>\n",
       "<div style=\"flex=grow:1;\">\n",
       "Regular(20, 0, 3.14159, label='Axis 0')<br/>\n",
       "<hr style=\"margin-top:.2em; margin-bottom:.2em;\"/>\n",
       "Weight() Σ=WeightedSum(value=1.47355e-09, variance=2.17134e-23)\n",
       "\n",
       "</div>\n",
       "</div>\n",
       "</html>"
      ],
      "text/plain": [
       "Hist(Regular(20, 0, 3.14159, label='Axis 0'), storage=Weight()) # Sum: WeightedSum(value=1.47355e-09, variance=2.17134e-23)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = pylhe.to_awkward(pylhe.read_lhe_with_attributes(\"unweighted.lhe\"))\n",
    "hist2 = hist.Hist.new.Reg(20, 0, math.pi).Weight()\n",
    "hist2.fill(arr.particles.vector[:, -1].theta, weight=arr.eventinfo.weight)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c9ab56a1-50bc-405a-b7e5-c7d6b61881de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[StairsArtists(stairs=<matplotlib.patches.StepPatch object at 0x7f3afebe3e30>, errorbar=<ErrorbarContainer object of 3 artists>, legend_artist=<ErrorbarContainer object of 3 artists>)]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist2.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c9be8352-6ab8-45c2-a4ac-fa458ee41652",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(([StairsArtists(stairs=<matplotlib.patches.StepPatch object at 0x7f3afd6c34a0>, errorbar=<ErrorbarContainer object of 3 artists>, legend_artist=<ErrorbarContainer object of 3 artists>)],\n",
       "  [StairsArtists(stairs=<matplotlib.patches.StepPatch object at 0x7f3afd6acef0>, errorbar=<ErrorbarContainer object of 3 artists>, legend_artist=<ErrorbarContainer object of 3 artists>)]),\n",
       " RatioErrorbarArtists(line=<matplotlib.lines.Line2D object at 0x7f3afdb733e0>, errorbar=<ErrorbarContainer object of 3 artists>))"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist1.plot_ratio(hist2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f964bc54-a958-4b2f-b3de-7f142d878472",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "651a1ba9-727e-4533-8186-a5e46fb08a87",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.12.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}