tutorial-12-flows.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generating LHC data with Flows"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This week we will use Invertible Neural Networks (INNs) to generate LHC data.  They are a type of normalising flow.  The task this week will be exactly as it was with the GAN, except using the INN.  Instead of doing part of the work for you, I have instead provided some example code for how to define an INN, how to write down it's loss function, and how to sample from it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Background:\n",
    "- Simulations for LHC physics is a major computational task at the experiment, and will become more computationally intensive in the coming years, so if ML techniques can speed up some aspects of this then it would be very useful\n",
    "- As a proof of concept, we will show how a normalising flow, specifically an Invertible Neural Network (INN), can be optimised to generate events simulated by traditional high energy physics simulation software\n",
    "- The process we are studying is Drell-Yan: $pp\\rightarrow Z\\rightarrow \\mu\\mu$\n",
    "- Naively, the dimension of this phase space is 8D, the 4 momentum of the two final state particles\n",
    "- The generative network samples random noise from a unit Normal distribution, passes it through an invertible network to produce an 8D output\n",
    "- **There are detailed notes on this in your lecture notes, please read them!**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Interesting paper:\n",
    "- Invertible Networks or Partons to Detector and Back Again\n",
    "    - Bellagente et al\n",
    "    - https://arxiv.org/abs/2006.06685"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Outline:\n",
    "- Imports and plotting set-up\n",
    "- Study the data\n",
    "- Datasets and dataloaders\n",
    "- Building the INN\n",
    "- Optimising the INN\n",
    "- Study the results - let's generate some events!\n",
    "- Removing redundant degrees of freedom\n",
    "- Optimising the INN on the reduced data\n",
    "- Study the new results\n",
    "- Concluding remarks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You need install the FrEIA package to use the INN modules, you can install it from the terminal with:"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "python3 -m pip install git+https://github.com/VLL-HD/FrEIA.git"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The documentation can be found here:\n",
    "\n",
    "https://github.com/VLL-HD/FrEIA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example code for how to define an INN, how to write it's loss function, and how to sample from it:"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "# FrEIA imports\n",
    "import FrEIA.framework as Ff\n",
    "import FrEIA.modules as Fm\n",
    "\n",
    "BATCHSIZE = 100\n",
    "N_DIM = 8\n",
    "\n",
    "# we define a subnet for use inside an affine coupling block for more detailed information see the full tutorial\n",
    "def subnet_fc(dims_in, dims_out):\n",
    "    return nn.Sequential(nn.Linear(dims_in, 128), nn.ReLU(),\n",
    "                         nn.Linear(128,  dims_out))\n",
    "\n",
    "# a simple chain of operations is collected by ReversibleSequential\n",
    "inn = Ff.SequenceINN(N_DIM)\n",
    "for k in range(8):\n",
    "    inn.append(Fm.AllInOneBlock, subnet_constructor=subnet_fc, permute_soft=True)\n",
    "    \n",
    "# pass to INN and get transformed variable z and log Jacobian determinant\n",
    "z, log_jac_det = inn(x)    \n",
    "    \n",
    "# calculate the negative log-likelihood of the model with a standard normal prior\n",
    "loss = 0.5*torch.sum(z**2, 1) - log_jac_det\n",
    "loss = loss.mean() / N_DIM  \n",
    "  \n",
    "# sample from the INN by sampling from a standard normal and transforming it in the reverse direction\n",
    "z = torch.randn(BATCHSIZE, N_DIM)\n",
    "samples, _ = inn(z, rev=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import sys\n",
    "import random\n",
    "import time\n",
    "import numpy as np\n",
    "import torch\n",
    "from torch.utils.data import Dataset\n",
    "from torch.utils.data import DataLoader\n",
    "from torch import nn\n",
    "from torch.nn import functional as F\n",
    "from torch.nn import Sequential, Linear, ReLU\n",
    "from torch.nn.utils import spectral_norm\n",
    "\n",
    "# FrEIA imports\n",
    "import FrEIA.framework as Ff\n",
    "import FrEIA.modules as Fm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plotting set-up"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import matplotlib\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "from matplotlib.lines import Line2D\n",
    "from matplotlib.font_manager import FontProperties\n",
    "import matplotlib.colors as mcolors\n",
    "import colorsys\n",
    "\n",
    "labelfont = FontProperties()\n",
    "labelfont.set_family('serif')\n",
    "labelfont.set_name('Times New Roman')\n",
    "labelfont.set_size(14)\n",
    "\n",
    "axislabelfont = FontProperties()\n",
    "axislabelfont.set_family('serif')\n",
    "axislabelfont.set_name('Times New Roman')\n",
    "axislabelfont.set_size(22)\n",
    "\n",
    "tickfont = FontProperties()\n",
    "tickfont.set_family('serif')\n",
    "tickfont.set_name('Times New Roman')\n",
    "tickfont.set_size(16)\n",
    "\n",
    "axisfontsize = 16\n",
    "labelfontsize = 16\n",
    "\n",
    "plt.rcParams[\"font.family\"] = \"Times New Roman\"\n",
    "plt.rcParams[\"mathtext.default\"] = \"rm\"\n",
    "plt.rcParams['text.usetex'] = True"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading the data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can load the data from here:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "dy_trn_data = np.load( 'tutorial-11-data/dy_trn_data.npy' )\n",
    "dy_val_data = np.load( 'tutorial-11-data/dy_val_data.npy' )\n",
    "dy_tst_data = np.load( 'tutorial-11-data/dy_tst_data.npy' )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((1384081, 8), (296588, 8), (296588, 8))"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dy_trn_data.shape, dy_val_data.shape, dy_tst_data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each element of the data has 8 entries, corresponding to the 4-momenta of each muon in the process.\n",
    "\n",
    "Each entry has the form $[E_1, p_{x,1}, p_{y,1}, p_{z,1}, E_2, p_{x,2}, p_{y,2}, p_{z,2}]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Study the data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to be able to calculate the invariant mass of each event, and the $p_T$ of the event and the jets.\n",
    "\n",
    "Let's write a function for this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_obs( event ):\n",
    "    \n",
    "    jet1_4m = event[:,0:4]\n",
    "    jet2_4m = event[:,4:]\n",
    "    evnt_4m = np.sum( (jet1_4m,jet2_4m), axis=0 )\n",
    "    \n",
    "    evnt_im = np.sqrt( np.sum( ( evnt_4m[:,0]**2, -evnt_4m[:,1]**2, -evnt_4m[:,2]**2, -evnt_4m[:,3]**2 ), axis=0 ) )\n",
    "    \n",
    "    evnt_pt = np.sqrt( evnt_4m[:,1]**2 + evnt_4m[:,2]**2 )\n",
    "    jet1_pt = np.sqrt( jet1_4m[:,1]**2 + jet1_4m[:,2]**2 )\n",
    "    jet2_pt = np.sqrt( jet2_4m[:,1]**2 + jet2_4m[:,2]**2 )\n",
    "    \n",
    "    return evnt_im, evnt_pt, jet1_pt, jet2_pt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now test it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([90.98955316, 91.3711254 ]),\n",
       " array([0., 0.]),\n",
       " array([44.32344982, 35.10745113]),\n",
       " array([44.32344982, 35.10745113]))"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_obs( dy_trn_data[0:2] )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The $p_T$ of the events will always be zero here due to the fact that the initial incoming protons have no transverse momentum."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's get the observables for the whole dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "trn_evnt_ims, trn_evnt_pts, trn_jet1_pts, trn_jet2_pts = get_obs( dy_trn_data )\n",
    "val_evnt_ims, val_evnt_pts, val_jet1_pts, val_jet2_pts = get_obs( dy_val_data )\n",
    "tst_evnt_ims, tst_evnt_pts, tst_jet1_pts, tst_jet2_pts = get_obs( dy_tst_data )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1384081,)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trn_evnt_ims.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the invariant mass of the events:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots( figsize=(6,5) )\n",
    "\n",
    "axs.hist( trn_evnt_ims, alpha=0.5, density=True, bins=15 )\n",
    "\n",
    "axs.set_xlabel( \"$m_{\\mu\\mu}$ (GeV)\", fontproperties=axislabelfont )\n",
    "axs.set_ylabel( \"\\#events\", fontproperties=axislabelfont )\n",
    "\n",
    "yticks = [  ]\n",
    "axs.set_yticklabels( yticks, fontproperties=tickfont )\n",
    "\n",
    "xticks = [ int(x) for x in axs.get_xticks() ]\n",
    "axs.set_xticklabels( xticks, fontproperties=tickfont )\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we see the clear $Z$ mass peak at $\\simeq 90$ GeV."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's look at $p_T$ distributions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots( figsize=(6,5) )\n",
    "\n",
    "axs.hist( trn_jet1_pts, alpha=0.5, density=True, bins=15 )\n",
    "axs.hist( trn_jet2_pts, alpha=0.5, density=True, bins=15 )\n",
    "\n",
    "axs.set_xlabel( \"$p_{T}$ (GeV)\", fontproperties=axislabelfont )\n",
    "axs.set_ylabel( \"\\#events\", fontproperties=axislabelfont )\n",
    "\n",
    "yticks = [  ]\n",
    "axs.set_yticklabels( yticks, fontproperties=tickfont )\n",
    "\n",
    "xticks = [ int(x) for x in axs.get_xticks() ]\n",
    "axs.set_xticklabels( xticks, fontproperties=tickfont )\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These distributions are completely overlapping with a peak near $m_{\\mu\\mu}/2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Datasets and dataloaders"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This time we only need the dataloader to return the data, no labels, so it's pretty simple."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "class drell_yan_data( Dataset ):\n",
    "    \n",
    "    def __init__( self, data ):\n",
    "        self.data = data\n",
    "\n",
    "    def __len__(self):\n",
    "        return self.data.shape[0]\n",
    "\n",
    "    def __getitem__(self, idx):\n",
    "        return self.data[idx]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's normalise the data a little bit by dividing all dimensionful quantities by $100$ GeV."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "dy_trn_data_p = torch.Tensor( dy_trn_data / 100 )\n",
    "dy_val_data_p = torch.Tensor( dy_val_data / 100 )\n",
    "dy_tst_data_p = torch.Tensor( dy_tst_data / 100 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "trn_dataset = drell_yan_data( dy_trn_data_p )\n",
    "val_dataset = drell_yan_data( dy_val_data_p )\n",
    "tst_dataset = drell_yan_data( dy_tst_data_p )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using a bigger batch size this time, this helps for generative networks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "trn_dataloader = DataLoader( trn_dataset, batch_size=2500, shuffle=True )\n",
    "val_dataloader = DataLoader( val_dataset, batch_size=2500, shuffle=True )\n",
    "tst_dataloader = DataLoader( tst_dataset, batch_size=2500, shuffle=True )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Building the INN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def subnet_fc( dims_in, dims_out ):\n",
    "    return nn.Sequential( nn.Linear(dims_in, 100), \n",
    "                         nn.ReLU(),\n",
    "                         nn.Linear(100,  dims_out) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "ndim = 8\n",
    "inn = Ff.SequenceINN( ndim )\n",
    "for k in range(8):\n",
    "    inn.append( Fm.AllInOneBlock, subnet_constructor=subnet_fc, permute_soft=True )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimising the INN"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we set the device."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using cpu device\n"
     ]
    }
   ],
   "source": [
    "device = \"cuda\" if torch.cuda.is_available() else \"cpu\"\n",
    "print(f\"Using {device} device\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def inn_loss( z, ndim, log_jac_det ):\n",
    "    l = 0.5*torch.sum( z**2, 1 ) - log_jac_det\n",
    "    l = l.mean() / ndim\n",
    "    return l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_epoch( dataloader, model, optimizer ):\n",
    "    \n",
    "    size = len( dataloader.dataset )\n",
    "    \n",
    "    for batch, X in enumerate(dataloader):\n",
    "\n",
    "        # pass data through network\n",
    "        z, log_jac_det = model( X )\n",
    "        \n",
    "        # compute loss\n",
    "        loss = inn_loss( z, ndim, log_jac_det )\n",
    "\n",
    "        # reset gradients in optimizer\n",
    "        optimizer.zero_grad()\n",
    "        \n",
    "        # compute gradients\n",
    "        loss.backward()\n",
    "        \n",
    "        # update weights with optimizer\n",
    "        optimizer.step()\n",
    "        \n",
    "        # print the training loss every 100 updates\n",
    "        if batch % 100 == 0:\n",
    "            loss, current = loss.item(), batch * len(X)\n",
    "            print( f\"current batch loss: {loss:>7f}  [{current:>5d}/{size:>5d}]\" )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def val_pass( dataloader, model ):\n",
    "    \n",
    "    size = len( dataloader.dataset )\n",
    "    num_batches = len( dataloader )\n",
    "    vl = 0.0\n",
    "\n",
    "    # we don't need gradients here since we only use the forward pass\n",
    "    with torch.no_grad():\n",
    "        for X in dataloader:\n",
    "            z, log_jac_det = model( X )\n",
    "            vl += inn_loss( z, ndim, log_jac_det ).item()\n",
    "\n",
    "    vl /= num_batches\n",
    "    print( f\"avg val loss per batch: {vl:>8f}\" )\n",
    "    \n",
    "    return vl\n",
    "\n",
    "def trn_pass( dataloader, model ):\n",
    "    \n",
    "    size = len( dataloader.dataset )\n",
    "    num_batches = len( dataloader )\n",
    "    tl = 0.0\n",
    "\n",
    "    # we don't need gradients here since we only use the forward pass\n",
    "    with torch.no_grad():\n",
    "        for X in dataloader:\n",
    "            z, log_jac_det = model( X )\n",
    "            tl += inn_loss( z, ndim, log_jac_det ).item()\n",
    "\n",
    "    tl /= num_batches\n",
    "    print( f\"avg trn loss per batch: {tl:>8f}\" )\n",
    "    \n",
    "    return tl"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To optimise the network we need separate optimizers for each model, and we also add a learning rate scheduler regulate the training further."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-----------------------------------------------\n",
      "model architecture \n",
      "-----------------------------------------------\n",
      "SequenceINN(\n",
      "  (module_list): ModuleList(\n",
      "    (0): AllInOneBlock(\n",
      "      (softplus): Softplus(beta=0.5, threshold=20)\n",
      "      (subnet): Sequential(\n",
      "        (0): Linear(in_features=4, out_features=128, bias=True)\n",
      "        (1): ReLU()\n",
      "        (2): Linear(in_features=128, out_features=8, bias=True)\n",
      "      )\n",
      "    )\n",
      "    (1): AllInOneBlock(\n",
      "      (softplus): Softplus(beta=0.5, threshold=20)\n",
      "      (subnet): Sequential(\n",
      "        (0): Linear(in_features=4, out_features=128, bias=True)\n",
      "        (1): ReLU()\n",
      "        (2): Linear(in_features=128, out_features=8, bias=True)\n",
      "      )\n",
      "    )\n",
      "    (2): AllInOneBlock(\n",
      "      (softplus): Softplus(beta=0.5, threshold=20)\n",
      "      (subnet): Sequential(\n",
      "        (0): Linear(in_features=4, out_features=128, bias=True)\n",
      "        (1): ReLU()\n",
      "        (2): Linear(in_features=128, out_features=8, bias=True)\n",
      "      )\n",
      "    )\n",
      "    (3): AllInOneBlock(\n",
      "      (softplus): Softplus(beta=0.5, threshold=20)\n",
      "      (subnet): Sequential(\n",
      "        (0): Linear(in_features=4, out_features=128, bias=True)\n",
      "        (1): ReLU()\n",
      "        (2): Linear(in_features=128, out_features=8, bias=True)\n",
      "      )\n",
      "    )\n",
      "    (4): AllInOneBlock(\n",
      "      (softplus): Softplus(beta=0.5, threshold=20)\n",
      "      (subnet): Sequential(\n",
      "        (0): Linear(in_features=4, out_features=128, bias=True)\n",
      "        (1): ReLU()\n",
      "        (2): Linear(in_features=128, out_features=8, bias=True)\n",
      "      )\n",
      "    )\n",
      "    (5): AllInOneBlock(\n",
      "      (softplus): Softplus(beta=0.5, threshold=20)\n",
      "      (subnet): Sequential(\n",
      "        (0): Linear(in_features=4, out_features=128, bias=True)\n",
      "        (1): ReLU()\n",
      "        (2): Linear(in_features=128, out_features=8, bias=True)\n",
      "      )\n",
      "    )\n",
      "    (6): AllInOneBlock(\n",
      "      (softplus): Softplus(beta=0.5, threshold=20)\n",
      "      (subnet): Sequential(\n",
      "        (0): Linear(in_features=4, out_features=128, bias=True)\n",
      "        (1): ReLU()\n",
      "        (2): Linear(in_features=128, out_features=8, bias=True)\n",
      "      )\n",
      "    )\n",
      "    (7): AllInOneBlock(\n",
      "      (softplus): Softplus(beta=0.5, threshold=20)\n",
      "      (subnet): Sequential(\n",
      "        (0): Linear(in_features=4, out_features=128, bias=True)\n",
      "        (1): ReLU()\n",
      "        (2): Linear(in_features=128, out_features=8, bias=True)\n",
      "      )\n",
      "    )\n",
      "  )\n",
      ")\n",
      "-----------------------------------------------\n",
      "Epoch 1\n",
      "-----------------------------------------------\n",
      "current batch loss: 0.231985  [    0/1384081]\n",
      "current batch loss: -1.081748  [250000/1384081]\n",
      "current batch loss: -1.651235  [500000/1384081]\n",
      "current batch loss: -1.902678  [750000/1384081]\n",
      "current batch loss: -2.075740  [1000000/1384081]\n",
      "current batch loss: -2.130662  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -2.183281\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -2.184631\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 2\n",
      "-----------------------------------------------\n",
      "current batch loss: -2.180350  [    0/1384081]\n",
      "current batch loss: -2.256068  [250000/1384081]\n",
      "current batch loss: -2.291788  [500000/1384081]\n",
      "current batch loss: 0.005531  [750000/1384081]\n",
      "current batch loss: -1.345792  [1000000/1384081]\n",
      "current batch loss: -1.561978  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -1.645955\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -1.648267\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 3\n",
      "-----------------------------------------------\n",
      "current batch loss: -1.644407  [    0/1384081]\n",
      "current batch loss: -1.749847  [250000/1384081]\n",
      "current batch loss: -1.820977  [500000/1384081]\n",
      "current batch loss: -1.891027  [750000/1384081]\n",
      "current batch loss: -1.936773  [1000000/1384081]\n",
      "current batch loss: -1.983249  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -2.007133\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -2.008694\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 4\n",
      "-----------------------------------------------\n",
      "current batch loss: -1.999900  [    0/1384081]\n",
      "current batch loss: -2.065438  [250000/1384081]\n",
      "current batch loss: -2.076976  [500000/1384081]\n",
      "current batch loss: -2.128079  [750000/1384081]\n",
      "current batch loss: -2.157328  [1000000/1384081]\n",
      "current batch loss: -2.188247  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -2.208543\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -2.209735\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 5\n",
      "-----------------------------------------------\n",
      "current batch loss: -2.214075  [    0/1384081]\n",
      "current batch loss: -2.238193  [250000/1384081]\n",
      "current batch loss: -2.277580  [500000/1384081]\n",
      "current batch loss: -2.294885  [750000/1384081]\n",
      "current batch loss: -2.314714  [1000000/1384081]\n",
      "current batch loss: -2.305255  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -2.362539\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -2.363808\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 6\n",
      "-----------------------------------------------\n",
      "current batch loss: -2.350904  [    0/1384081]\n",
      "current batch loss: -2.381031  [250000/1384081]\n",
      "current batch loss: -2.410593  [500000/1384081]\n",
      "current batch loss: -2.439334  [750000/1384081]\n",
      "current batch loss: -2.448137  [1000000/1384081]\n",
      "current batch loss: -2.474324  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -2.424583\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -2.426151\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 7\n",
      "-----------------------------------------------\n",
      "current batch loss: -2.420015  [    0/1384081]\n",
      "current batch loss: -2.499391  [250000/1384081]\n",
      "current batch loss: -2.523000  [500000/1384081]\n",
      "current batch loss: -2.529067  [750000/1384081]\n",
      "current batch loss: -2.548295  [1000000/1384081]\n",
      "current batch loss: -2.543315  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -2.568747\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -2.569944\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 8\n",
      "-----------------------------------------------\n",
      "current batch loss: -2.585439  [    0/1384081]\n",
      "current batch loss: -2.572483  [250000/1384081]\n",
      "current batch loss: -2.610960  [500000/1384081]\n",
      "current batch loss: -2.626713  [750000/1384081]\n",
      "current batch loss: -2.631003  [1000000/1384081]\n",
      "current batch loss: -2.624590  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -2.638120\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -2.639258\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 9\n",
      "-----------------------------------------------\n",
      "current batch loss: -2.630212  [    0/1384081]\n",
      "current batch loss: -2.649763  [250000/1384081]\n",
      "current batch loss: -2.689450  [500000/1384081]\n",
      "current batch loss: -2.623234  [750000/1384081]\n",
      "current batch loss: -2.691418  [1000000/1384081]\n",
      "current batch loss: -2.596520  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -2.705959\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -2.707315\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 10\n",
      "-----------------------------------------------\n",
      "current batch loss: -2.706512  [    0/1384081]\n",
      "current batch loss: -2.729004  [250000/1384081]\n",
      "current batch loss: -2.746777  [500000/1384081]\n",
      "current batch loss: -2.523885  [750000/1384081]\n",
      "current batch loss: -2.765216  [1000000/1384081]\n",
      "current batch loss: -2.746091  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -2.773079\n",
      "-----------------------------------------------\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "avg val loss per batch: -2.774229\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 11\n",
      "-----------------------------------------------\n",
      "current batch loss: -2.773338  [    0/1384081]\n",
      "current batch loss: -2.797142  [250000/1384081]\n",
      "current batch loss: -2.747659  [500000/1384081]\n",
      "current batch loss: -2.753408  [750000/1384081]\n",
      "current batch loss: -2.787023  [1000000/1384081]\n",
      "current batch loss: -2.823620  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -2.829080\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -2.830124\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 12\n",
      "-----------------------------------------------\n",
      "current batch loss: -2.833019  [    0/1384081]\n",
      "current batch loss: -2.797567  [250000/1384081]\n",
      "current batch loss: -2.842871  [500000/1384081]\n",
      "current batch loss: -2.754305  [750000/1384081]\n",
      "current batch loss: -2.847025  [1000000/1384081]\n",
      "current batch loss: -2.848840  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -2.835865\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -2.836596\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 13\n",
      "-----------------------------------------------\n",
      "current batch loss: -2.842775  [    0/1384081]\n",
      "current batch loss: -2.877844  [250000/1384081]\n",
      "current batch loss: -2.649658  [500000/1384081]\n",
      "current batch loss: -2.772044  [750000/1384081]\n",
      "current batch loss: -2.891755  [1000000/1384081]\n",
      "current batch loss: -2.862111  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -2.320330\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -2.321473\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 14\n",
      "-----------------------------------------------\n",
      "current batch loss: -2.297588  [    0/1384081]\n",
      "current batch loss: -2.878085  [250000/1384081]\n",
      "current batch loss: -2.874412  [500000/1384081]\n",
      "current batch loss: -2.881312  [750000/1384081]\n",
      "current batch loss: -2.841363  [1000000/1384081]\n",
      "current batch loss: -2.940028  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -2.840790\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -2.842104\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 15\n",
      "-----------------------------------------------\n",
      "current batch loss: -2.837676  [    0/1384081]\n",
      "current batch loss: -2.943333  [250000/1384081]\n",
      "current batch loss: -2.609443  [500000/1384081]\n",
      "current batch loss: -2.936083  [750000/1384081]\n",
      "current batch loss: -2.888166  [1000000/1384081]\n",
      "current batch loss: -2.953379  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -2.816975\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -2.818525\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 16\n",
      "-----------------------------------------------\n",
      "current batch loss: -2.829731  [    0/1384081]\n",
      "current batch loss: -2.943568  [250000/1384081]\n",
      "current batch loss: -2.821523  [500000/1384081]\n",
      "current batch loss: -2.886499  [750000/1384081]\n",
      "current batch loss: -2.952999  [1000000/1384081]\n",
      "current batch loss: -2.861999  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -2.784335\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -2.785966\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 17\n",
      "-----------------------------------------------\n",
      "current batch loss: -2.801996  [    0/1384081]\n",
      "current batch loss: -2.985845  [250000/1384081]\n",
      "current batch loss: -2.847946  [500000/1384081]\n",
      "current batch loss: -2.925025  [750000/1384081]\n",
      "current batch loss: -2.972458  [1000000/1384081]\n",
      "current batch loss: -3.011959  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -2.891122\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -2.891984\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 18\n",
      "-----------------------------------------------\n",
      "current batch loss: -2.889470  [    0/1384081]\n",
      "current batch loss: -3.029673  [250000/1384081]\n",
      "current batch loss: -3.040795  [500000/1384081]\n",
      "current batch loss: -2.974699  [750000/1384081]\n",
      "current batch loss: -2.911603  [1000000/1384081]\n",
      "current batch loss: -2.966144  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.047804\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.048690\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 19\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.039985  [    0/1384081]\n",
      "current batch loss: -2.912832  [250000/1384081]\n",
      "current batch loss: -2.773801  [500000/1384081]\n",
      "current batch loss: -3.060719  [750000/1384081]\n",
      "current batch loss: -3.049971  [1000000/1384081]\n",
      "current batch loss: -3.018973  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.017005\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.017932\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 20\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.018724  [    0/1384081]\n",
      "current batch loss: -3.078768  [250000/1384081]\n",
      "current batch loss: -3.009742  [500000/1384081]\n",
      "current batch loss: -2.821416  [750000/1384081]\n",
      "current batch loss: -3.054280  [1000000/1384081]\n",
      "current batch loss: -2.588013  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.044198\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.044942\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 21\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.034838  [    0/1384081]\n",
      "current batch loss: -3.070353  [250000/1384081]\n",
      "current batch loss: -3.044272  [500000/1384081]\n",
      "current batch loss: -2.870930  [750000/1384081]\n",
      "current batch loss: -3.010283  [1000000/1384081]\n",
      "current batch loss: -3.106703  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.013585\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.014776\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 22\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.006684  [    0/1384081]\n",
      "current batch loss: -3.075269  [250000/1384081]\n",
      "current batch loss: -3.115381  [500000/1384081]\n",
      "current batch loss: -3.068620  [750000/1384081]\n",
      "current batch loss: -3.111200  [1000000/1384081]\n",
      "current batch loss: -3.112614  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.053713\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.054540\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 23\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.041779  [    0/1384081]\n",
      "current batch loss: -3.109170  [250000/1384081]\n",
      "current batch loss: -3.025210  [500000/1384081]\n",
      "current batch loss: -3.126895  [750000/1384081]\n",
      "current batch loss: -3.108176  [1000000/1384081]\n",
      "current batch loss: -2.898762  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.098118\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.099005\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 24\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.100769  [    0/1384081]\n",
      "current batch loss: -3.142776  [250000/1384081]\n",
      "current batch loss: -3.071819  [500000/1384081]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "current batch loss: -3.122562  [750000/1384081]\n",
      "current batch loss: -3.127491  [1000000/1384081]\n",
      "current batch loss: -3.056620  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.145842\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.146621\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 25\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.152548  [    0/1384081]\n",
      "current batch loss: -3.108511  [250000/1384081]\n",
      "current batch loss: -3.129835  [500000/1384081]\n",
      "current batch loss: -3.046397  [750000/1384081]\n",
      "current batch loss: -3.128485  [1000000/1384081]\n",
      "current batch loss: -3.171121  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.086923\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.087762\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 26\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.083434  [    0/1384081]\n",
      "current batch loss: -2.645260  [250000/1384081]\n",
      "current batch loss: -2.456795  [500000/1384081]\n",
      "current batch loss: -3.161803  [750000/1384081]\n",
      "current batch loss: -3.091547  [1000000/1384081]\n",
      "current batch loss: -3.063248  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.176998\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.177631\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 27\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.184893  [    0/1384081]\n",
      "current batch loss: -3.163764  [250000/1384081]\n",
      "current batch loss: -3.176748  [500000/1384081]\n",
      "current batch loss: -3.135132  [750000/1384081]\n",
      "current batch loss: -3.141577  [1000000/1384081]\n",
      "current batch loss: -3.075098  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.158617\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.159423\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 28\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.160229  [    0/1384081]\n",
      "current batch loss: -3.159568  [250000/1384081]\n",
      "current batch loss: -3.085428  [500000/1384081]\n",
      "current batch loss: -2.444984  [750000/1384081]\n",
      "current batch loss: -3.186843  [1000000/1384081]\n",
      "current batch loss: -3.183915  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.066812\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.067356\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 29\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.058214  [    0/1384081]\n",
      "current batch loss: -3.129670  [250000/1384081]\n",
      "current batch loss: -2.854055  [500000/1384081]\n",
      "current batch loss: -3.156773  [750000/1384081]\n",
      "current batch loss: -3.106010  [1000000/1384081]\n",
      "current batch loss: -3.116184  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -2.577366\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -2.577878\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 30\n",
      "-----------------------------------------------\n",
      "current batch loss: -2.590313  [    0/1384081]\n",
      "current batch loss: -3.199728  [250000/1384081]\n",
      "current batch loss: -3.202960  [500000/1384081]\n",
      "current batch loss: -3.100303  [750000/1384081]\n",
      "current batch loss: -3.200184  [1000000/1384081]\n",
      "current batch loss: -2.844532  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.208277\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.208985\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 31\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.212491  [    0/1384081]\n",
      "current batch loss: -3.163054  [250000/1384081]\n",
      "current batch loss: -3.139626  [500000/1384081]\n",
      "current batch loss: -3.204505  [750000/1384081]\n",
      "current batch loss: -3.167027  [1000000/1384081]\n",
      "current batch loss: -3.200759  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -2.795880\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -2.797496\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 32\n",
      "-----------------------------------------------\n",
      "current batch loss: -2.799401  [    0/1384081]\n",
      "current batch loss: -3.228410  [250000/1384081]\n",
      "current batch loss: -2.873073  [500000/1384081]\n",
      "current batch loss: -2.950341  [750000/1384081]\n",
      "current batch loss: -3.184716  [1000000/1384081]\n",
      "current batch loss: -3.199275  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.182384\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.182826\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 33\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.182471  [    0/1384081]\n",
      "current batch loss: -2.849362  [250000/1384081]\n",
      "current batch loss: -3.221798  [500000/1384081]\n",
      "current batch loss: -3.153650  [750000/1384081]\n",
      "current batch loss: -3.207535  [1000000/1384081]\n",
      "current batch loss: -3.222010  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.220360\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.221310\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 34\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.209417  [    0/1384081]\n",
      "current batch loss: -3.068606  [250000/1384081]\n",
      "current batch loss: -3.100294  [500000/1384081]\n",
      "current batch loss: -3.227387  [750000/1384081]\n",
      "current batch loss: -3.212973  [1000000/1384081]\n",
      "current batch loss: -3.242828  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.251495\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.252117\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 35\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.240731  [    0/1384081]\n",
      "current batch loss: -3.241776  [250000/1384081]\n",
      "current batch loss: -3.248610  [500000/1384081]\n",
      "current batch loss: -2.987425  [750000/1384081]\n",
      "current batch loss: -3.226950  [1000000/1384081]\n",
      "current batch loss: -3.260057  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.188575\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.189431\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 36\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.190220  [    0/1384081]\n",
      "current batch loss: -3.147385  [250000/1384081]\n",
      "current batch loss: -3.085547  [500000/1384081]\n",
      "current batch loss: -3.235549  [750000/1384081]\n",
      "current batch loss: -3.245234  [1000000/1384081]\n",
      "current batch loss: -3.229799  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.154064\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.155271\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 37\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.153534  [    0/1384081]\n",
      "current batch loss: -3.264748  [250000/1384081]\n",
      "current batch loss: -3.141809  [500000/1384081]\n",
      "current batch loss: -3.148961  [750000/1384081]\n",
      "current batch loss: -3.139947  [1000000/1384081]\n",
      "current batch loss: -3.258090  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -2.872944\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -2.876423\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 38\n",
      "-----------------------------------------------\n",
      "current batch loss: -2.893716  [    0/1384081]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "current batch loss: -3.174422  [250000/1384081]\n",
      "current batch loss: -3.213459  [500000/1384081]\n",
      "current batch loss: -3.241357  [750000/1384081]\n",
      "current batch loss: -2.868732  [1000000/1384081]\n",
      "current batch loss: -2.839727  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.232143\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.232724\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 39\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.219747  [    0/1384081]\n",
      "current batch loss: -3.265328  [250000/1384081]\n",
      "current batch loss: -3.271748  [500000/1384081]\n",
      "current batch loss: -3.211043  [750000/1384081]\n",
      "current batch loss: -3.201252  [1000000/1384081]\n",
      "current batch loss: -3.186126  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.275135\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.275856\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 40\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.274750  [    0/1384081]\n",
      "current batch loss: -3.262087  [250000/1384081]\n",
      "current batch loss: -3.257339  [500000/1384081]\n",
      "current batch loss: -3.238488  [750000/1384081]\n",
      "current batch loss: -3.067486  [1000000/1384081]\n",
      "current batch loss: -3.266923  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.253363\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.254058\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 41\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.262241  [    0/1384081]\n",
      "current batch loss: -2.200576  [250000/1384081]\n",
      "current batch loss: -3.271425  [500000/1384081]\n",
      "current batch loss: -3.264055  [750000/1384081]\n",
      "current batch loss: -2.989060  [1000000/1384081]\n",
      "current batch loss: -3.252657  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -2.944770\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -2.945721\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 42\n",
      "-----------------------------------------------\n",
      "current batch loss: -2.922073  [    0/1384081]\n",
      "current batch loss: -3.267501  [250000/1384081]\n",
      "current batch loss: -3.276243  [500000/1384081]\n",
      "current batch loss: -3.292649  [750000/1384081]\n",
      "current batch loss: -3.259109  [1000000/1384081]\n",
      "current batch loss: -3.250027  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.272828\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.273454\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 43\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.280181  [    0/1384081]\n",
      "current batch loss: -3.203177  [250000/1384081]\n",
      "current batch loss: -3.267819  [500000/1384081]\n",
      "current batch loss: -3.294055  [750000/1384081]\n",
      "current batch loss: -3.300631  [1000000/1384081]\n",
      "current batch loss: -3.269690  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.256012\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.256472\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 44\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.246364  [    0/1384081]\n",
      "current batch loss: -3.263253  [250000/1384081]\n",
      "current batch loss: -3.248559  [500000/1384081]\n",
      "current batch loss: -3.274282  [750000/1384081]\n",
      "current batch loss: -3.301156  [1000000/1384081]\n",
      "current batch loss: -3.306496  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.109776\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.111269\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 45\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.097981  [    0/1384081]\n",
      "current batch loss: -3.309278  [250000/1384081]\n",
      "current batch loss: -3.304300  [500000/1384081]\n",
      "current batch loss: -3.203913  [750000/1384081]\n",
      "current batch loss: -3.304897  [1000000/1384081]\n",
      "current batch loss: -3.179970  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.313447\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.313953\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 46\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.308687  [    0/1384081]\n",
      "current batch loss: -3.038910  [250000/1384081]\n",
      "current batch loss: -1.653113  [500000/1384081]\n",
      "current batch loss: -3.317415  [750000/1384081]\n",
      "current batch loss: -3.307612  [1000000/1384081]\n",
      "current batch loss: -3.320395  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.226677\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.227091\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 47\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.230610  [    0/1384081]\n",
      "current batch loss: -3.315480  [250000/1384081]\n",
      "current batch loss: -3.295780  [500000/1384081]\n",
      "current batch loss: -3.256956  [750000/1384081]\n",
      "current batch loss: -2.308258  [1000000/1384081]\n",
      "current batch loss: -3.154347  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.116252\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.116864\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 48\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.109062  [    0/1384081]\n",
      "current batch loss: -3.312638  [250000/1384081]\n",
      "current batch loss: -3.143602  [500000/1384081]\n",
      "current batch loss: -3.194303  [750000/1384081]\n",
      "current batch loss: -3.299170  [1000000/1384081]\n",
      "current batch loss: -3.313245  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.140806\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.141937\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 49\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.141011  [    0/1384081]\n",
      "current batch loss: -3.226717  [250000/1384081]\n",
      "current batch loss: -3.281295  [500000/1384081]\n",
      "current batch loss: -3.249214  [750000/1384081]\n",
      "current batch loss: -3.131913  [1000000/1384081]\n",
      "current batch loss: -3.194471  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.314853\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.315261\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 50\n",
      "-----------------------------------------------\n",
      "current batch loss: -3.318506  [    0/1384081]\n",
      "current batch loss: -3.285590  [250000/1384081]\n",
      "current batch loss: -3.303375  [500000/1384081]\n",
      "current batch loss: -3.125492  [750000/1384081]\n",
      "current batch loss: -3.306192  [1000000/1384081]\n",
      "current batch loss: -3.303763  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -3.327331\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -3.327979\n",
      "-----------------------------------------------\n",
      "|\n",
      "Done!\n"
     ]
    }
   ],
   "source": [
    "# a useful function to present things clearer\n",
    "def separator():\n",
    "    print( \"-----------------------------------------------\" )\n",
    "\n",
    "epochs = 50\n",
    "\n",
    "# re-initialise the model and the optimizer\n",
    "def subnet_fc( dims_in, dims_out ):\n",
    "    return nn.Sequential( nn.Linear(dims_in, 128), \n",
    "                         nn.ReLU(),\n",
    "                         nn.Linear(128,  dims_out) )\n",
    "ndim = 8\n",
    "inn = Ff.SequenceINN( ndim )\n",
    "for k in range(8):\n",
    "    inn.append( Fm.AllInOneBlock, subnet_constructor=subnet_fc, permute_soft=True )\n",
    "learning_rate = 0.001\n",
    "optimizer = torch.optim.Adam( inn.parameters(), lr=learning_rate )\n",
    "separator()\n",
    "print( \"model architecture \")\n",
    "separator()\n",
    "print( inn )\n",
    "\n",
    "# track train and val losses\n",
    "trn_losses = []\n",
    "val_losses = []\n",
    "\n",
    "for t in range(epochs):\n",
    "    separator()\n",
    "    print( f\"Epoch {t+1}\" )\n",
    "    separator()\n",
    "    train_epoch( trn_dataloader, inn, optimizer )\n",
    "    separator()\n",
    "    trn_loss = trn_pass( trn_dataloader, inn )\n",
    "    trn_losses.append( trn_loss )\n",
    "    separator()\n",
    "    val_loss = val_pass( val_dataloader, inn )\n",
    "    val_losses.append( val_loss )\n",
    "    separator()\n",
    "    print( \"|\" )\n",
    "    \n",
    "print(\"Done!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Study the results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First let's plot the training and validation losses to see how they look."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots( 1, 1, figsize=(7,5) )\n",
    "\n",
    "c1 = 'tab:red'\n",
    "c2 = 'tab:green'\n",
    "\n",
    "axs.plot( trn_losses, label=\"train loss\", color=c1 )\n",
    "axs.plot( val_losses, label=\"val   loss\", color=c2 )\n",
    "\n",
    "#axs.set_yscale('log')\n",
    "\n",
    "axs.set_xlabel( \"epoch\", fontproperties=axislabelfont )\n",
    "axs.set_ylabel( \"Binary CE\", fontproperties=axislabelfont )\n",
    "\n",
    "xticks = [ int(x) for x in axs.get_xticks() ]\n",
    "axs.set_xticklabels( xticks, fontproperties=tickfont )\n",
    "\n",
    "yticks = axs.get_yticks()\n",
    "axs.set_yticklabels( yticks, fontproperties=tickfont )\n",
    "\n",
    "axs.legend( loc='best', prop=tickfont )\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Let's generate some events!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first need to generate random data from the unit normal distribution, the same used during training, with the correct shape.  Here we use $10$k samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "z_gen = torch.randn( (10000, ndim) )\n",
    "x_gen, _ = inn( z_gen, rev=True )\n",
    "x_gen = x_gen*100.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([10000, 8])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_gen.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the energy distribution of the first jet, for both real and generated data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots( figsize=(6,5) )\n",
    "\n",
    "bins = np.arange( 0, 350, step=20 )\n",
    "axs.hist( x_gen.detach().numpy()[:,0], alpha=0.5, density=True, bins=bins, label='gen' )\n",
    "axs.hist( dy_trn_data[:,0], alpha=0.5, density=True, bins=bins, label='real' )\n",
    "\n",
    "axs.set_xlabel( \"$E_{1}$ (GeV)\", fontproperties=axislabelfont )\n",
    "axs.set_ylabel( \"\\#events\", fontproperties=axislabelfont )\n",
    "\n",
    "yticks = [  ]\n",
    "axs.set_yticklabels( yticks, fontproperties=tickfont )\n",
    "\n",
    "xticks = [ int(x) for x in axs.get_xticks() ]\n",
    "axs.set_xticklabels( xticks, fontproperties=tickfont )\n",
    "\n",
    "axs.legend( loc='best', prop=tickfont )\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks good!!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can do the same for $p_y$ of the first jet:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots( figsize=(6,5) )\n",
    "\n",
    "bins = np.arange( -100, +100, step=10 )\n",
    "axs.hist( x_gen.detach().numpy()[:,2], alpha=0.5, density=True, bins=bins, label='gen' )\n",
    "axs.hist( dy_trn_data[:,2], alpha=0.5, density=True, bins=bins, label='real' )\n",
    "\n",
    "axs.set_xlabel( \"$p_{y,1}$ (GeV)\", fontproperties=axislabelfont )\n",
    "axs.set_ylabel( \"\\#events\", fontproperties=axislabelfont )\n",
    "\n",
    "yticks = [  ]\n",
    "axs.set_yticklabels( yticks, fontproperties=tickfont )\n",
    "\n",
    "xticks = [ int(x) for x in axs.get_xticks() ]\n",
    "axs.set_xticklabels( xticks, fontproperties=tickfont )\n",
    "\n",
    "axs.legend( loc='best', prop=tickfont )\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_gen_evnt_ims, x_gen_evnt_pts, x_gen_jet1_pts, x_gen_jet2_pts = get_obs( x_gen.detach().numpy() )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The $p_T$ of the first jet:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots( figsize=(6,5) )\n",
    "\n",
    "bins = np.arange( 5, 85, step=5 )\n",
    "axs.hist( x_gen_jet1_pts, alpha=0.5, density=True, bins=bins, label='gen' )\n",
    "axs.hist( trn_jet1_pts, alpha=0.5, density=True, bins=bins, label='real' )\n",
    "\n",
    "axs.set_xlabel( \"$p_{T,1}$ (GeV)\", fontproperties=axislabelfont )\n",
    "axs.set_ylabel( \"\\#events\", fontproperties=axislabelfont )\n",
    "\n",
    "yticks = [  ]\n",
    "axs.set_yticklabels( yticks, fontproperties=tickfont )\n",
    "\n",
    "xticks = [ int(x) for x in axs.get_xticks() ]\n",
    "axs.set_xticklabels( xticks, fontproperties=tickfont )\n",
    "\n",
    "axs.legend( loc='best', prop=tickfont )\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks good!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the invariant mass of the whole event:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots( figsize=(6,5) )\n",
    "\n",
    "bins = np.arange( 5, 165, step=10 )\n",
    "axs.hist( np.nan_to_num( x_gen_evnt_ims ), alpha=0.5, density=True, bins=bins, label='gen' )\n",
    "axs.hist( np.nan_to_num( trn_evnt_ims ), alpha=0.5, density=True, bins=bins, label='real' )\n",
    "\n",
    "axs.set_xlabel( \"$m_{\\mu\\mu}$ (GeV)\", fontproperties=axislabelfont )\n",
    "axs.set_ylabel( \"\\#events\", fontproperties=axislabelfont )\n",
    "\n",
    "yticks = [  ]\n",
    "axs.set_yticklabels( yticks, fontproperties=tickfont )\n",
    "\n",
    "xticks = [ int(x) for x in axs.get_xticks() ]\n",
    "axs.set_xticklabels( xticks, fontproperties=tickfont )\n",
    "\n",
    "axs.legend( loc='best', prop=tickfont )\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Removing redundant degrees of freedom"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the collider the incoming particles have no momentum in the $x$ or $y$ directions, therefore momentum conservation means that the final state should also not have any momentum in these directions.  This means that we have redundant degrees of freedom that can be removed from the data.\n",
    "\n",
    "We can check this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots( figsize=(6,5) )\n",
    "\n",
    "bins = np.arange( -5, 5, step=0.1 )\n",
    "axs.hist( dy_trn_data[:,1]+dy_trn_data[:,5], alpha=0.5, density=True, bins=bins, label='$p_{x,1}+p_{x_2}$' )\n",
    "axs.hist( dy_trn_data[:,2]+dy_trn_data[:,6], alpha=0.5, density=True, bins=bins, label='$p_{y,1}+p_{y_2}$' )\n",
    "\n",
    "axs.set_xlabel( \"$p_T$ (GeV)\", fontproperties=axislabelfont )\n",
    "axs.set_ylabel( \"\\#events\", fontproperties=axislabelfont )\n",
    "\n",
    "yticks = [  ]\n",
    "axs.set_yticklabels( yticks, fontproperties=tickfont )\n",
    "\n",
    "xticks = [ int(x) for x in axs.get_xticks() ]\n",
    "axs.set_xticklabels( xticks, fontproperties=tickfont )\n",
    "\n",
    "axs.legend( loc='best', prop=tickfont )\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Muons have a mass of about $106$ MeV.  This is much smaller than the typical energy scales involved in the Drell-Yan process we are studying, so we can assume to a good approximation that the mass of the final state particles are zero.  These final state particles are on-shell, i.e. $p^2=m^2=0$, so we can also use this as a constraint.  We can check that this approximately holds:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAFgCAYAAADuCe0ZAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/Il7ecAAAACXBIWXMAAAsTAAALEwEAmpwYAAAWhklEQVR4nO3dT28j933H8c+3WcdOEG8oeZVT4K65TXttZBlojo6p9J6K8gNoVnKOBZIo+wTqyDbQY0vJfQC7knMvSCPHHJaUc23R5aZGEiCQreU6QGxkE3x7mCGXokiKHA7F73LeL2CxIjkc/khQ89Hvv7m7AACI5q8WXQAAAIYhoAAAIRFQAICQCCgAQEgEFAAgpGuLLsAoN27c8Js3by66GACAOWu1Wp+4+9rg/WED6ubNm2o2m4suBgBgzszs/4bdTxMfACAkAgoAEBIBBQAIiYACAIREQAEAQiKgAAAhhR1mDgBRPX78WJ988on+9Kc/LbooYX3pS1/Siy++qNXVVT3//POZzkFAAcAUvvjiC/3+97/XN7/5TX3lK1+RmS26SOG4u548eaLPPvtMH3/8sV5++eVMIUUTHwBM4fT0VGtra/rqV79KOI1gZvryl7+sGzduaGVlRWdnZ5nOQ0ABwBS++OILfe1rX1t0MZ4Z169f1x/+8IdMzyWgAGAKf/7zn3XtGr0jk3ruuef0l7/8JdNzCSgAmBJNe5Ob5bPizwAgmH+r/8+52/+y+bcLKgmwWAQUEMBgKAHRHRwcSJJarZb29vZULpdzfw0CCgjgHz4+GPPoe1dWDmASJycn2tjY0Pr6uhqNhnZ3d1Wv13N/HQIKAHKw6FrwVTYFt9tt1et11Wo1bWxszG3vPgIKADCVra0tbW1tSZKazaY2Njbm8jqM4gMAZFar1XR0dDSXcxNQAIBMDg4OtL+/r1KpNJfzE1AAgKk1Gg1VKhWVy2U1Go25vAZ9UABQYAcHB2q1Wtrf3+8Fzf379/Xmm29Kks7OztRutyVJOzs7kpJRfNVqVaurq5Kk9fV1VSqV3MtGQAFAQTUaDW1vb6vVaqlarfaGipdKJd2+fVtHR0daX1+XJK2srPQCan19XY8ePZp7+QgoACiocrmsUqmkZrOpw8PD3v3deU7dybftdrtXW7pK9EEBQEH1B1C3piRJ9Xpd1Wq1d7vb39Sv0+lob29PJycncysfAQUABdZoNC7MY2o2m+cCqVaraXd3V51O59wx3b6peSGgAKDA6vW6Njc3e7dPTk4urKvXrWHdu3evd1+lUpl7sx99UACQg2d11fl2u63d3d1zt7sj+Lq2t7d1fHw8l5F64xBQAFBgg6tAdJcw6ler1a6qOOfQxAcACImAAgCERBMfAGBqjUZDzWaztw5f/zD1vBBQAICpVSoVtVqtub4GTXwAgJAIKABASAQUACAkAgoAEBIBBQAIiYACAITEMHMAwNQODg4kSa1WS3t7excWmM0DNSgAwFS6Gxru7OyoWq2eW2w2T9SgACAPv3h7sa//+p0re6l2u616va5araaNjQ01m825vA4BBQCYytbWVm/V82azeWHDw7zQxAcAyKxWq13YsiMvoQLKzHbMrGlmzdPT00UXBwAwxsHBgfb393sLxuYtVEC5+4G7b7j7xtra2qKLAwAYodFoqFKpqFwuq9FozOU16IMCgAI7ODhQq9XS/v5+L2ju37/f2/b97OxM7XZbkrSzsyMpGcVXrVa1uroqKdlqYx7bwRNQAFBQjUZD29vbarVaqlarqtfrkqRSqaTbt2/r6Oiot8/TyspKL6DW19f16NGjuZePgAKAgiqXyyqVSmo2mzo8POzd353n1J182263e7Wlq0RAAUBB9QdQ/4649Xpde3t7vdvd/qZ+rCQBAJirRqNxYR5Ts9k8F0i1Wk27u7vqdDqSrm4lCQIKAAqsXq9rc3Ozd/vk5ORCbahbw7p3717vdq1WkyRWkgCA8K5wqaE8tdvtczWgdrvdG8HXtb29rePj416t6qpWkiCgAKDABleB6AZPv25taZjCrCQBAHh2FGolCQDAs4GVJAAA4bCSBAAgpKtaSYImPgBASAQUAEzJ3RddhGfGLJ8VAQUAU3juuef0+eefL7oYz4zPP/9czz//fKbnElAAMIVvfOMb+u1vf6s//vGP1KRGcHc9efJEZ2dn+s1vfqOXXnop03kYJAEAU7h+/bok6Xe/+52ePHmy4NLEde3aNb3wwgt6+eWX9cILL2Q7R85lAoCld/369V5QYX5o4gMAhERAAQBCIqAAACERUACAkAgoAEBIBBQAICQCCgAQEgEFAAiJgAIAhERAAQBCIqAAACERUACAkAgoAEBIBBQAICQCCgAQEgEFAAiJgAIAhERAAQBCIqAAACERUACAkAgoAEBIBBQAICQCCgAQEgEFAAiJgAIAhERAAQBCIqAAACERUACAkAgoAEBIBBQAICQCCgAQEgEFAAiJgAIAhERAAQBCIqAAACERUACAkAgoAEBIBBQAICQCCgAQEgEFAAiJgAIAhBQqoMxsx8yaZtY8PT1ddHEAAAsUKqDc/cDdN9x9Y21tbdHFAQAsUKiAAgCgi4ACAIREQAEAQiKgAAAh5RZQZnbdzG7mdT4AQLFdm/YJZvYzSd+WdCKp5u6/NrO7ktYlfWhmK5L23P3XuZYUAFAoUweUpPtKgumhJJnZjyWtu/u3ugeY2Y8kvZdPEQEARZSliW+lG06pXUm1gWMeCgCAGWQJqEfdH8zs65LKkhoDx/gshQIAIEtA9YfPjqSOu/9q4JiXMpcIAABl64N6nPYxPZa0L2mr+4CZ/ZOkn0qq5lM8AEBRTV2DcvcPJX2Q3nzV3X8u9QZLlCXdk1TJrYQAgELKUoNSOkjicOC+d3MpEQAAyjYP6ubgHKd0sMS2kv6ps26tCgCArLIMktgbvMPdH7v7obu/7+4/N7Mf5FA2AECBZQkoy70UAAAMuLSJz8ze0Pmh5a+Y2XdHHF6S9Fr6//uzFg4AUFyT9EG1lYzOqyqZ9+SSbo05vu7uP8yhbACAArs0oNIRew+VLAR7LGnL3d+ae8kAAIU2VR+Uuzck1S87bkwTIAAAE8kyUfeDy4/SboayAADQk2Ue1HVJx5LeGHWIWCwWADCjLCtJvC/pSMl8qM6Qx03Sf8xQJgAAMgVU3d0Pxx1gZoP7QwEAMJUsE3XPLjtgwn4qAABGyhJQHTO7Oe6AdDsOAAAyy9LE55K2zOyWpJaG16jelPTeLAUDABRbloA6Tv8/U7Ks0aCSpFeyFggAAClbQDXd/XvjDjAzRvEBAGaSpQ9qkkm4+xnOCwBAT5aVJB5KyYRdM/tuOnFX6X1/338MAABZZalBdZvwOpJqkirnH2IEHwBgdlMHlJn9WNIDd/8rd/+W+jYwdPeP3P09M/t+noUEABRPlkESnYGVJFh3DwCQuyxNfJ9OcEw5w3kBAOjJElCDu+nauRvJKhM3shYIAAApW0A1zOy/zOz1dASfS0kwpf1TdUn/mmchAQDFM3UflLt/ZGbvSjpUumKEWa8SdSzpe+7+WW4lBAAUUpYNC2+mW7//jZl9W0l/U0fJChOPcy4fAKCgsoziO1K6Bp+7fyTpo1xLBACAsvVBvZr2QTHXCQAwN1kCas/d/1HSR2Z228x+dNn+UAAATCvLIIl30/8fKhkoITN7w8w2lYzou8cgCQDArDKtxTfI3T9MV5d4JOmhmd3N47wAgOLKMkjinLR5b1fSTnrXoZJFZAEAyCzLYrF3zexFM/uBmTUlPVAy1Hzb3V9y95+y3QYAYFZZalBVSVuSTpTUlO4x/wkAkLcsAdWWVE3nQAEAMBdZBknUCCcAwLxl2fL9XWn8lu8AAMyKLd8BACGx5TsAICS2fAcAhMSW7wCAkNjyHQAQElu+AwBCYst3AEBImRaLZct3AMC8zbSaOVu+AwDmJfN+UMMm5M46SdfMdsysaWbN09PTWU4FAHjGzbJh4eaQ+96c4Xxy9wN333D3jbW1tVlOBQB4xo0NKDP7/pj19WzC+wAAmNplfVCPJb1lZhtKNiasS2q4+681fAUJVpUAAORibEC5+4eSPpQkM/u6koVh3zGzsqRXzOwHSkbv/WreBQUAFMvEo/jSIeQfpP+UbvduSmpYZUmrSkLr+0pqWcyFAgBkNssw87N00djewrFm9r9KlkJ6y8xWJDX1tFmQwAIATGxsQJnZzyR9oiRgfjXw8LD+pkfphobdTQ2/raRZ8C0ze+DuP5y9yACAIrisD+qnZvaGng6U+FRpjUhJk95YfRN5382hrACAArm0iW/EQIm3JL1qZncl3Zd0Iqk1x3ICAApmqom67v7Y3T9w97eU1KJ2lNSQXlXSF7VuZv+ezp+6nn9xAQBFMcsgCU9H9vXXsJqS3lFSy3rfzF4RAyUAABnMtFjsEO7uD5XUpg6lcwMlXpN0J+fXAwAsqbwD6gJWPAcAZDHLYrHD9n56OMP5AADoyRxQ7r49yX0AAGQxSw0KAIC5IaAAACERUACAkAgoAEBIBBQAICQCCgAQEgEFAAiJgAIAhERAAQBCIqAAACERUACAkAgoAEBIBBQAICQCCgAQEgEFAAiJgAIAhERAAQBCIqAAACERUACAkAgoAEBIBBQAICQCCgAQEgEFAAiJgAIAhERAAQBCIqAAACERUACAkAgoAEBIBBQAICQCCgAQEgEFAAiJgAIAhERAAQBCIqAAACERUACAkAgoAEBIBBQAICQCCgAQEgEFAAiJgAIAhERAAQBCIqAAACERUACAkAgoAEBIBBQAICQCCgAQUqiAMrMdM2uaWfP09HTRxQEALFCogHL3A3ffcPeNtbW1RRcHALBAoQIKAIAuAgoAEBIBBQAIiYACAIREQAEAQiKgAAAhEVAAgJAIKABASAQUACAkAgoAEBIBBQAIiYACAIREQAEAQiKgAAAhEVAAgJAIKABASAQUACAkAgoAEBIBBQAIiYACAIREQAEAQiKgAAAhEVAAgJAIKABASAQUACAkAgoAEBIBBQAIiYACAIREQAEAQiKgAAAhEVAAgJAIKABASAQUACAkAgoAEBIBBQAIiYACAIR0bdEFAArpF29nO/b1O/mXBQiKgAIW4JftTzMd+53X51EaICaa+AAAIRFQAICQCCgAQEgEFAAgJAIKABASAQUACImAAgCEREABAEIioAAAIRFQAICQCCgAQEgEFAAgJAIKABASAQUACIntNoAr8sv//FHu5/jOP7838zmBqKhBAQBCIqAAACERUACAkAgoAEBIBBQAICRG8QFzkseovWlegxF9WDbm7osuQ4+Z7UjaSW/+naT/XmBx8nZD0ieLLkRAfC4X8ZkMx+cy3DJ8Ln/t7muDd4YKqGVmZk1331h0OaLhc7mIz2Q4PpfhlvlzoQ8KABASAQUACImAujoHiy5AUHwuF/GZDMfnMtzSfi70QQEAQqIGBQAIiYACAITERN0FMLOau+8uuhyLZmYlPZ339pqkursvbXv6ZczsJ5LaklYlqcifRRffkcks6zWFgLpiZrYvqbzocgRxx933ujfM7IGZFfLCnH4v7rv7cfe2mW11bxcY35FLLPM1hSa+K2Rm64suQxTpX8aDv1Q1SXsXjy6EnYEwuitp6f4ingbfkcst+zWFgLpaG5Lqiy5EIBUz678AdbSkfwmOM+Ii05FUueKiRMR3ZLylvqYQUFfEzLYk3Vt0OaJw9467r7h7u+/uTUmNRZVpgVYlnQ3cN3i7cPiOjFeEawp9UFcgbarouHvHzBZdnJDSz6gi6Y0FF2URSqMeMLOSu3eurihxFfw7ck5RrinUoK7GtrvzV994h5Kq7n6y6IIsQEfpyL0+g7dR7O/IoEJcU6hB5cjM6jrfPr6rpKlm6b9I4wz7XPp/udLh1bUi/MKNcKaLtaiSlDRzXXFZQuI78lTaZ1mIz4GljubMzCqS+jvBX0tv1yQdD7SvF07ajt7pXnjMrFLEi5CZPXL3lb7bFUl77r65wGKFwHfkvCJdU6hBzVn6i9RfW9iRVHb3dxZXqhjSX7RVSY20TX1VyS9aES8+9wbmPW0queAUGt+Ri4p0TaEGdYXSL1JVydDQtyUdFLUJJ73YPBry0LG7V6+4OCGkzVgnSptDiz4Zle/I5Zb9mkJAAQBCYhQfACAkAgoAEBIBBQAIiYACAIREQAEAQmIeFDBCOsx5W8mqDq+pICsZFPV9Ix6GmQMjmNl+d7O8vjk5t5Zppv4wRX3fiIcmPmCIdA+iUvd2OvnxWBk3yxvY0yisSd73s/Je8OwjoIDRttMaRL+pVxlPV4h4lvZ3uux9r6dLEAFzRUABQ7h7O90sr9N397qk+9OcJ12KpjFu+Rkz2zGzupkdmVkt/VdJHyul55jmNX9iZi0zczN7lAbkuGO7x+1P8r7T9QI3qUlh3uiDAiaQbnFw5O63pnhOSdK+u++OeLws6UhJgO0NPFZR0tS2KelBloVAzeyRkrXZxjZLmlktLeeFPqZR7zt9b4esiYd5ogYFTOZQSVhMYz/9d0EaTi0lW2pcCJB01Fxb0lS1pwH3Jnz+gzEDIIa+77SG1aapD/NEQAGXMLN9SbczjGIrj3nOkZLazcjh2+nOsbOsaF6TVBoXIuljQ8swwfuuKdmUE5gLAgoYI+3/udvdZjxt8prkeVuS6mPOua5ke4TLHE1Y1AvSMp9ofIisD9tCfZL3nQbXRJ8HkAUTdbFU0gtpRUmz1K67t/sGCdyStNrtN0nvf0lPt1ffHThXRcnou3bfqLYNJRf9y2xqdLhUJbUn2bfH3Rt2cURd//tsKxlhVxrRT1WTVDOz0uDrpee9UIYp33fDzIaGHDArAgrL5k133zOzW0ouzCf9fTxm9qAbWP0X9HQUW6u7SWDaRzSsBjRpk9aGRs+Z2pDUnPA83VFzPcO2g09H49WGDMi4pySkdiQNBth2+nj/uad93w+UBCUBhdwRUFgaaa2iOxy6rCQIBkeZdZTUrAZH450pqWFJ6jVf2QzFuVBj6X9MQ2ouU7jQ9+Pu76TDxff6X9fdO2Z2nB4/GFAXypjhfbc1/eARYCL0QWGp9NU2NiS9PSQk1pVc4AeVNeUcp0uMm9DbUd9qDdNIQ7is4TWwtpL3Pagmqdzfj5T+nEetp6MMk5eBSVCDwtLo69DvLtdzbnRa3wV6WJOZBo+fo6aSkBkqLU81Pabbz3ScNlV2n1cxu1DR2dOQ4Er7sdqS7uhpjbKSZW7VCKWczgOcQ0BhGVWkp4E1cH9nyLDpqqSTSQYtTKE05rGapCMzGzoMPR163pAkM3M9DScpbRoc7JeaQE0j5mTlgEVkMRc08WEZbWp4bWjU/duS7kqTDyOfQGfUA2m4NDT5wrOf9v3clDIt2Nod/LGTDoGfNuBGKWm2/jRgJAIKy6ii4SPRLtyfBlJJTyfE5rUywtmw4eF9diXtXDKJ9kII9a0uvjXk+PVRAZs+r5G+7rgJxNMq63yAArkhoLBUJuh/GqxBrSqdk5Q+N68Ld0PDByxI6o2WuyVp38z2R4TZroavJLEnaXdIgFUumY+0r2SQSJ5NcrfEEHPMCYvFYqmkNZLakMVNK0oWRH11yHPqSmpWne48qBzKsaWkpnLpQIR01YaqkqaytpK5RSUlSyF1zKwyuCRSGmh3lNRe2tJk/VLpXK8Ln0FWeZ8P6EdAAXNiZvX+ybTLhhXNMW808QHz017yPZN2NHxOGZALAgqYnz1l3CI+urT29Nq41diBWRFQwJykI+daOQ5dj+SOljR8EQcBBcxROuiicsmQ82dKOuCknuNQdWAoBkkAV2DUqhHPomV6L4iNgAIAhEQTHwAgJAIKABASAQUACImAAgCEREABAEL6f6DdPxL9528sAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots( figsize=(6,5) )\n",
    "\n",
    "bins = np.arange( -5, 5, step=0.1 )\n",
    "axs.hist( dy_trn_data[:,0]**2-dy_trn_data[:,1]**2-dy_trn_data[:,2]**2-dy_trn_data[:,3]**2, \n",
    "         alpha=0.5, density=True, bins=bins, label='$m_1^2$' )\n",
    "axs.hist( dy_trn_data[:,4]**2-dy_trn_data[:,5]**2-dy_trn_data[:,6]**2-dy_trn_data[:,7]**2, \n",
    "         alpha=0.5, density=True, bins=bins, label='$m_2^2$' )\n",
    "\n",
    "axs.set_xlabel( \"$m^2$ (GeV$^2$)\", fontproperties=axislabelfont )\n",
    "axs.set_ylabel( \"\\#events\", fontproperties=axislabelfont )\n",
    "\n",
    "yticks = [  ]\n",
    "axs.set_yticklabels( yticks, fontproperties=tickfont )\n",
    "\n",
    "xticks = [ int(x) for x in axs.get_xticks() ]\n",
    "axs.set_xticklabels( xticks, fontproperties=tickfont )\n",
    "\n",
    "axs.legend( loc='best', prop=tickfont )\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can remove $p_{x,2}$, $p_{y,2}$, $E_{1}$, and $E_{2}$ by simply removing these from the data.  They can be calculated and re-introduced from:\n",
    "- $p_{x,2}=-p_{x,1}$\n",
    "- $p_{y,2}=-p_{y,1}$\n",
    "- $E_{1}=\\sqrt{p_{x,1}^2+p_{y,1}^2+p_{z,1}^2}$\n",
    "- $E_{2}=\\sqrt{p_{x,2}^2+p_{y,2}^2+p_{z,2}^2}=\\sqrt{p_{x,1}^2+p_{y,1}^2+p_{z,2}^2}$\n",
    "\n",
    "So we are left with $4$ degrees of freedom."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's re-do the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "dy_trn_data_nr = np.delete( dy_trn_data, (0,1,2,4), axis=1 )\n",
    "dy_val_data_nr = np.delete( dy_val_data, (0,1,2,4), axis=1 )\n",
    "dy_tst_data_nr = np.delete( dy_tst_data, (0,1,2,4), axis=1 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((1384081, 4), (296588, 4), (296588, 4))"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dy_trn_data_nr.shape, dy_val_data_nr.shape, dy_tst_data_nr.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "dy_trn_data_nr_p = torch.Tensor( dy_trn_data_nr / 100 )\n",
    "dy_val_data_nr_p = torch.Tensor( dy_val_data_nr / 100 )\n",
    "dy_tst_data_nr_p = torch.Tensor( dy_tst_data_nr / 100 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "trn_dataset_nr = drell_yan_data( dy_trn_data_nr_p )\n",
    "val_dataset_nr = drell_yan_data( dy_val_data_nr_p )\n",
    "tst_dataset_nr = drell_yan_data( dy_tst_data_nr_p )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "trn_dataloader_nr = DataLoader( trn_dataset_nr, batch_size=2500, shuffle=True )\n",
    "val_dataloader_nr = DataLoader( val_dataset_nr, batch_size=2500, shuffle=True )\n",
    "tst_dataloader_nr = DataLoader( tst_dataset_nr, batch_size=2500, shuffle=True )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we need a new get_obs function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_events_nr( event ):\n",
    "    \n",
    "    pz1 = event[:,0]\n",
    "    px2 = event[:,1]\n",
    "    py2 = event[:,2]\n",
    "    pz2 = event[:,3]\n",
    "    px1 = -px2\n",
    "    py1 = -py2\n",
    "    E1 = np.sqrt( px1**2 + py1**2 + pz1**2 )\n",
    "    E2 = np.sqrt( px2**2 + py2**2 + pz2**2 )\n",
    "    \n",
    "    events = np.stack( ( E1,px1,py1,pz1,E2,px2,py2,pz2 ), axis=-1 )\n",
    "    \n",
    "    return events\n",
    "\n",
    "def get_obs_nr( event ):\n",
    "    \n",
    "    pz1 = event[:,0]\n",
    "    px2 = event[:,1]\n",
    "    py2 = event[:,2]\n",
    "    pz2 = event[:,3]\n",
    "    px1 = -px2\n",
    "    py1 = -py2\n",
    "    E1 = np.sqrt( px1**2 + py1**2 + pz1**2 )\n",
    "    E2 = np.sqrt( px2**2 + py2**2 + pz2**2 )\n",
    "    \n",
    "    jet1_4m = np.stack( ( E1,px1,py1,pz1 ), axis=-1 )\n",
    "    jet2_4m = np.stack( ( E2,px2,py2,pz2 ), axis=-1 )\n",
    "    \n",
    "    evnt_4m = np.sum( (jet1_4m,jet2_4m), axis=0 )\n",
    "    \n",
    "    evnt_im = np.sqrt( np.sum( ( evnt_4m[:,0]**2, -evnt_4m[:,1]**2, -evnt_4m[:,2]**2, -evnt_4m[:,3]**2 ), axis=0 ) )\n",
    "    \n",
    "    evnt_pt = np.sqrt( evnt_4m[:,1]**2 + evnt_4m[:,2]**2 )\n",
    "    jet1_pt = np.sqrt( jet1_4m[:,1]**2 + jet1_4m[:,2]**2 )\n",
    "    jet2_pt = np.sqrt( jet2_4m[:,1]**2 + jet2_4m[:,2]**2 )\n",
    "    \n",
    "    return evnt_im, evnt_pt, jet1_pt, jet2_pt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's double check it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "trn_evnt_nr_ims, trn_evnt_nr_pts, trn_jet1_nr_pts, trn_jet2_nr_pts = get_obs_nr( dy_trn_data_nr )\n",
    "val_evnt_nr_ims, val_evnt_nr_pts, val_jet1_nr_pts, val_jet2_nr_pts = get_obs_nr( dy_val_data_nr )\n",
    "tst_evnt_nr_ims, tst_evnt_nr_pts, tst_jet1_nr_pts, tst_jet2_nr_pts = get_obs_nr( dy_tst_data_nr )\n",
    "trn_events_nr = get_events_nr( dy_trn_data_nr )\n",
    "val_events_nr = get_events_nr( dy_val_data_nr )\n",
    "tst_events_nr = get_events_nr( dy_tst_data_nr )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot $p_{y,1}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots( figsize=(6,5) )\n",
    "\n",
    "bins = np.arange( -100, +100, step=10 )\n",
    "axs.hist( trn_events_nr[:,2], alpha=0.5, density=True, bins=bins, label='gen' )\n",
    "axs.hist( dy_trn_data[:,2], alpha=0.5, density=True, bins=bins, label='real' )\n",
    "\n",
    "axs.set_xlabel( \"$p_{y,1}$ (GeV)\", fontproperties=axislabelfont )\n",
    "axs.set_ylabel( \"\\#events\", fontproperties=axislabelfont )\n",
    "\n",
    "yticks = [  ]\n",
    "axs.set_yticklabels( yticks, fontproperties=tickfont )\n",
    "\n",
    "xticks = [ int(x) for x in axs.get_xticks() ]\n",
    "axs.set_xticklabels( xticks, fontproperties=tickfont )\n",
    "\n",
    "axs.legend( loc='best', prop=tickfont )\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the invariant mass of the events:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAFgCAYAAADuCe0ZAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/Il7ecAAAACXBIWXMAAAsTAAALEwEAmpwYAAAVOElEQVR4nO3dz3IbV3bH8d+Z8jYemDa2igRlnG1MQQ+QETnZO5T8Ag6pWbpqRrReIB5arpplQsovIFGefYr0ExiUvY0rpJw1LQrKC5ws+jbZbDb+NUD2afH7qWJZ6G6ABzCBH+7t2/eauwsAgGh+03QBAABUIaAAACERUACAkAgoAEBIBBQAIKT3mi5glI8++shv3rzZdBkAgAU5ODj41d270x4fNqBu3rypwWDQdBkAgAUxs/+d5Xi6+AAAIRFQAICQCCgAQEgEFAAgJAIKABASAQUACImAAgCEREABAEIioAAAIRFQAICQCCgAQEgEFAAgpLCTxQJt9de9ny/tsb9Y/fjSHhuIhhYUACAkAgoAEBIBBQAIiYACAIREQAEAQiKgAAAhEVAAgJAIKABASAQUACAkAgoAEBIBBQAIiYACAIREQAEAQgoVUGa2bmYDMxscHx83XQ4AoEGhAsrdd9y97+79brfbdDkAgAaFCigAAHIEFAAgJAIKABASAQUACImAAgCEREABAEIioAAAIRFQAICQCCgAQEgEFAAgJAIKABASAQUACImAAgCEREABAEIioAAAIRFQAICQCCgAQEgEFAAgJAIKABASAQUACImAAgCEREABAEIioAAAIRFQAICQCCgAQEgEFAAgJAIKABASAQUACImAAgCEREABAEIioAAAIRFQAICQCCgAQEgEFAAgJAIKABASAQUACClUQJnZupkNzGxwfHzcdDkAgAaFCih333H3vrv3u91u0+UAABoUKqAAAMgRUACAkAgoAEBIBBQAICQCCgAQEgEFAAiJgAIAhERAAQBCIqAAACERUACAkAgoAEBIBBQAICQCCgAQEgEFAAiJgAIAhERAAQBCIqAAACERUACAkAgoAEBIBBQAICQCCgAQEgEFAAiJgAIAhERAAQBCIqAAACERUACAkAgoAEBIBBQAICQCCgAQEgEFAAiJgAIAhERAAQBCIqAAACERUACAkAgoAEBIoQLKzNbNbGBmg+Pj46bLAQA0KFRAufuOu/fdvd/tdpsuBwDQoFABBQBAjoACAIREQAEAQiKgAAAhEVAAgJAIKABASAQUACCkhQWUmb1vZjcX9XgAgOvtvVnvYGZ/kfSJpJeStt39FzN7JmlZ0vdm9oGkTXf/ZaGVAgCulZkDStIPyoLplSSZ2Z8lLbv77/IDzOxPkr5ZTIkAgOuoThffB3k4JRuStkvHvBIAAHOoE1Bv8n+Y2W8l9STtl47xeYoCAKBOQBXDZ13S0N1/Kh3zYe2KAABQvXNQb9M5preStiSt5TvM7F8lfSnp/mLKAwBcVzO3oNz9e0nfpZt33P1v0ulgiZ6k55JWFlYhAOBaqtOCUhok8bS07clCKgIAQPWug7pZvsYpDZZ4oOz81EneqgIAoK46gyQ2yxvc/a27P3X3b939b2b2+QJqAwBcY3UCyhZeBQAAJRO7+Mzsns4PLb9lZr8fcXhH0t3032/nLQ4AcH1Ncw7qSNnovPvKrntySbfHHL/n7n9cQG0AgGtsYkClEXuvlE0E+0LSmrs/vPTKAADX2kznoNx9X9LepOPGdAECADCVOhfqfjf5KG3UqAUAgFN1roN6X9ILSfdGHSImiwUAzKnOTBLfStpVdj3UsGK/SfrPOWoCAKBWQO25+9NxB5hZeX0oAABmUudC3ZNJB0x5ngoAgJHqBNTQzG6OOyAtxwEAQG11uvhc0pqZ3ZZ0oOoW1WeSvpmnMADA9VYnoF6k/54om9aorCPpVt2CAACQ6gXUwN3/MO4AM2MUHwBgLnXOQU1zEe5WjccFAOBUnZkkXknZBbtm9vt04a7Stn8qHgMAQF11WlB5F95Q0raklfO7GMEHAJjfzAFlZn+WdOjuv3H336mwgKG7/+ju35jZp4ssEgBw/dS6DsrdnxRuL2zePTNbN7OBmQ2Oj48X9bAAgBaqE1CvpzimV+Nx5e477t539363263zEACAd0SdgCqvpmvnbmSzTHxUtyAAAKR6AbVvZv9lZv+cRvC5lAVTOj+1J+nfF1kkAOD6mflCXXf/0cyeSHqqNGOE2Wkj6oWkP7j7/y2sQgDAtVRnwcKbaen3fzCzT5Sdbxoqm2Hi7YLrAwBcU3WmOtpVmoPP3X+U9ONCKwIAQPXOQd1J56C41gkAcGnqBNSmu/+LpB/N7N/M7E+T1ocCAGBWdQZJPEn/faVsoITM7J6ZrSob0fecQRIAgHnVmouvzN2/d/enkt5IemVmzxbxuACA66vOIIlzUvfehqT1tOmpsklkAQCorc5ksc/M7O/M7HMzG0g6VDbU/IG7f+juX7LcBgBgXnVaUPclrUl6qayl9JzrnwAAi1YnoI4k3U/XQAEAcCnqDJLYJpwAAJetzpLvT6TxS74DADAvlnwHAITEku8AgJDqDJIYpotycwtb8h0AgFyoJd8BAMix5DsAICSWfAcAhMSS7wCAkGpNFsuS7wCAyzbXbOYs+Q4AuCy114OquiCXi3QBAIsyz4KFqxXbPpvj8QAAODU2oMzs0zHz69mU2wAAmNmkc1BvJT00s76yhQn3JO27+y+qnkGCWSUAAAsxNqDc/XtJ30uSmf1W2cSwX5tZT9ItM/tc2ei9ny67UADA9TL1KL40hPy79KO03Lspa2H1JC0pC61PlbWyuBYKAFDbPMPMT9KksacTx5rZ/yibCumhmX0gaaCzbkECCwAwtbEBZWZ/kfSrsoD5qbS76nzTm7SgYb6o4SfKugUfmtmhu/9x/pIBANfBpHNQX5rZPZ0NlHit1CJS1qU3VuFC3icLqBUAcI1M7OIbMVDioaQ7ZvZM0g+SXko6uMQ6AQDXzEwX6rr7W3f/zt0fKmtFrStrId1Rdi5q2cz+I10/9f7iywUAXBfzDJLwNLKv2MIaSPpaWSvrWzO7pRkGSpjZurLQ040bN+YoDQDQdvNMdVTF3f2Vuz919wfuflfSjrKRfY+nuPOOu/fdvd/tdhdcGgCgTeaazXwazHgOAKhjnhZU1dpPr+Z4PAAATtUOKHd/MM02AADqWPQ5KAAAFoKAAgCEREABAEIioAAAIRFQAICQCCgAQEgEFAAgJAIKABASAQUACImAAgCEREABAEIioAAAIRFQAICQCCgAQEgEFAAgJAIKABASAQUACImAAgCEREABAEIioAAAIRFQAICQCCgAQEgEFAAgJAIKABASAQUACImAAgCEREABAEIioAAAIRFQAICQCCgAQEgEFAAgJAIKABASAQUACClUQJnZupkNzGxwfHzcdDkAgAaFCih333H3vrv3u91u0+UAABoUKqAAAMgRUACAkAgoAEBIBBQAICQCCgAQEgEFAAiJgAIAhERAAQBCIqAAACERUACAkAgoAEBIBBQAICQCCgAQEgEFAAiJgAIAhERAAQBCIqAAACERUACAkAgoAEBIBBQAICQCCgAQEgEFAAiJgAIAhERAAQBCIqAAACERUACAkAgoAEBIBBQAICQCCgAQEgEFAAiJgAIAhERAAQBCIqAAACERUACAkAgoAEBI7zVdQJGZrUtal6QbN240XA3edX/d+7npEgCMEaoF5e477t5393632226HABAg0K1oACMd5mtvi9WP760xwbqCNWCAgAgR0ABAEIioAAAIRFQAICQCCgAQEgEFAAgJAIKABASAQUACImAAgCEREABAEIioAAAIRFQAICQCCgAQEgEFAAgJAIKABASAQUACImAAgCEREABAEIioAAAIRFQAICQCCgAQEgEFAAgJAIKABASAQUACImAAgCEREABAEJ6r+kCgHH+uvdz0yUAaAgBBUDS5X4Z+GL140t7bLy76OIDAIREQAEAQiKgAAAhcQ4Kc2MgA4DLQEABuHSX9SWGwRfvNgIqGFojwPQYefhue6cDig97AHXx+XFeE4Ft7n7lv3QUM1uXtJ5u/qOk/26wnGl9JOnXpouooa11S+2tva11S+2tva11S+2tfVzdf+/u3WkfKFRAtZGZDdy933Qds2pr3VJ7a29r3VJ7a29r3VJ7a19k3QwzBwCEREABAEIioOa303QBNbW1bqm9tbe1bqm9tbe1bqm9tS+sbs5BAQBCogUFAAiJgAIAhPROX6i7SGbWkfRY0mHaNHD3l4X9jyQdSVqSJHcP0X9sZruStpXVdlLc5+7DdEzU2h9JGqabHXf/umJ/uLolycy2lP2t3JZ0WK4tQu3pb3pd0ofuvlmxf2yNTT6HKWqftL+R2sfVVdgnSXcl7UV5zaeo+0G6eTvVVT6mXt3uzs+EH0kdZX8s+e11SbuF21uS1kbdbrj2Q0le8bMWuXZJj0q3l4vbotadatmTtFK4vV263XjtklYkraXativ2j62xyecwRe1zPbcmX/PS7UNJ6y2oe1vZF8j89sGi3quX/sf0LvxI2i29wB1JvcLtN6Xjl4uB1nDtj8Zti1q7pIOq/w8tqLsnyUvb1nT+C06Y2tOHRdWHztgaIzyHUbXP+9yaqDt9puyWtj1S1voOW3faflD6fNxd1HuVc1DTWZO0b2Y9M1t296G7H0mSmS1XHD9U9q0jggtdBJ66yoLXfpK6JyWdToP1LP07ct1VtR0p1Ra8dkmTa2zDcxgleO0rZtYr3B4q+8ITum53v+PuLwqblpX1IsxdNwE1QeEF7he27aZ+VynrUz0p3a18uzGezjNJkpmtSNov7I5c+4ayN+yb1H99UngTRK77pXTaL59bKmyLXHtuUo1teA6jhKw9fen9IP/im6zq7P0asu6y9F7d97NzTHPVTUBNdvqNxt2PPBsY8UzS07S5M+qOpQ+pCO57YWCHAtee3qhfSRoo61q4W9jdGXW/IHW/VOHvRudbVZ1R92269oLOqB2pxkn7I+uM2hGp9lTLiqR8sEFnwrGNMrNO6uWQzgaSSXPWzSi+yYbpv4PCtiNl3X75/qXSfcq3G2dma8r6iouGClq7meUnZL9OLb9dM+u5+30Frju5J+mxmfWVfVs8krJvyWY2VOzapcmv76T9kQ3Vjtqf6vwXyqEC1516anYkycz2zOzuIt6rtKAmO/1wKWwbSqffAE508VtCp+I+TdtQei4FIWtP3arD/M3p7vuSbums3zpk3bnUXbPp7jupW3Ko1PWn4LUnk2psw3MYJXztqZtsO/3d50LWnVpOj0qb93T2BX6uugmoCVKXzbDUHO0o+wDNP0SHpbst6fy5nghWdPE6qKi1L0l6XdyQ/pj307+j1i1JKp3olqT7yobihq9dmlxjG57DKNFrTz0dL/NwSr0HkevuS9oa1V03b90E1HS+0tmFaJL0WdqWe57+sHKrSh9IERT+eIYVu8PVnt6cq8Vt6TkUW4Dh6i44yAfXpLr7fv7CxMi15ybV2IbnMErI2lMYLUkapJZJT+fPX4arO71XN0utoVVJxYvqa9fNZLFTKjdjvXpWg9OT4x5rVoOOsvNPd6qa1RFrT2/ODRVOuJbrili3dPotWMo+bG776JkMGqs9BeiKstdYyj4w9v3i7Cgja2zqOUyqfRHP7arrTu/RNxV3e5HO5eSPEarutL+nsy69DyW9XtTnIwEFAAiJLj4AQEgEFAAgJAIKABASAQUACImAAgCEREABDau4sDesNtWK9iOggAblM7U3XccMlvPZDYDLRkABDUmzP++Pm5PMzNbT5Ju7ZradfvJ1mYozSE/7Ox+Z2YGZeWEpk3HH5sdtSVKaW3CVlhSuAhfqAg1IMwdsufvGiP09ZSuT7pdnokgB1VE2Zcxh+ar9KX//G0k7VbNclI7bTnUeFbZ1JD0tznAAXAZaUEAzttLPBSmcDpTNcXYhQNL8Z0eSZmo9lTyf8v6HpUX08ol7j+jqw2UjoIBm9Mof/AW7ylo3I2d8TvOgzTMP27akzriQqViBuXz/ytYfsCgEFHDF0mSyeyP2rSubwfqrqv0lu3VrSAH3UuNDZrm0AnPx/kc6P9M2sHCsqItWK8y0vCppw92PCif+b0tays+VpO0f6mzBtKZaAKsaHS73JR1Ns5ibu+9XrcNTeE2OlM2o3hlxnmpb0raZdcq/Lz3upBr2zWxkiAHzYpAEWs3Mttx9M53M7ylb7G2zsP9QZ4sFfl3Y/kbZOZ4rX6LDzA4k3Rux9MkbSQN3X71wx+kee0XZ81otbHukbNmPjdKxHWVLPGxWLI+wLun5hBGGj6SLS88Ai0IXH1ortRR+SDd7ylb3LHeNDZW1rMofoifKWlhNuNBiKe7T5JbLONsqDb5Iz3293NpKNbxQdTffuBpzR2ruNcQ1QECh1dJ1OVIKp4oP1WVVr97Z01m4XbWlMfuGSl2Qs0qB3ZM0qNh9pOw1KtuW1MtXAC48zjTddkONfy7AXDgHhdYqrejZUWnEWeFD90Vpez5ybeQouQYNlFYdrZJqv5+Oyc8zvUjdmvn9VsysfNdNVQRXOo91JOlxelxJWpmh264z5XHAzAgovAtWpLPAKm0fVgznvq/sXNXwCmqr0hmzb1vSrplVDkNPQ8/3JcnMXGfhJKWuwUKrcloXugVnMGqoPDA3uvjwLlhVdWto1PYHkp5J51pZV2k4akcKl31lLZ5pvC78eyDVmtB1J91vPQ2BnzbgOprvfBkwFgGFd8GKqq8rurA9BVJHZxe5rpT35/POpds9M9ud9ZgJTqqGhxdsKBvUMO4i2gshVBj0sFZx/PKoME7320+/d9wFxGU9nQ9IYKEIKLTaFOefyi2oJaXrjNJ9yx/Gn0k6LNxeqXnMOPuqHrAg6fQi2NuStsxsa0SYbah6JolNSRsVAbYy4XqlLWUDSmZ5Hrc13WAKoBbOQaHtesoCp/xBuaTsPFN5Hrl9M8sv5h1WXAe1ovOj/lZ1cRTgNMeMs6csDMZNZXQk6U66HmnXzIbKwuNQWSB/lUJ2pXw/M7sj6bGZvU73mXitUnpdXs54/qrf4MXOuAa4UBdIUkvllbt/UNj2RtKtfEDFNMdM+bv26l6MGwEzmuMq0MUHnOmrMBQ7dZOdFLoDpz1mGkctX1NpXbO1GoGZEVDAmVWdH5W2Iellai30ZjhmGpuafqReKOm53h032zqwCAQUcGZF2RIU+XDrbWVTIj0ofBhPc8xEqTvwoKFh7vN6rJaGK9qFc1CAqs8t1Tmmxu99pGztp+GiHvMy5YMyaD3hKtCCAjJ9TZ76aJpjZpJG17VpPrsjwglXhYACMstKs0vMeczMZrgwtnFtqhXtRxcfACAkWlAAgJAIKABASAQUACAkAgoAEBIBBQAI6f8B4sWDZ3CMJ80AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots( figsize=(6,5) )\n",
    "\n",
    "axs.hist( trn_evnt_nr_ims, alpha=0.5, density=True, bins=15 )\n",
    "\n",
    "axs.set_xlabel( \"$m_{\\mu\\mu}$ (GeV)\", fontproperties=axislabelfont )\n",
    "axs.set_ylabel( \"\\#events\", fontproperties=axislabelfont )\n",
    "\n",
    "yticks = [  ]\n",
    "axs.set_yticklabels( yticks, fontproperties=tickfont )\n",
    "\n",
    "xticks = [ int(x) for x in axs.get_xticks() ]\n",
    "axs.set_xticklabels( xticks, fontproperties=tickfont )\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we see the clear $Z$ mass peak at $\\simeq 90$ GeV."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's look at $p_T$ distributions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots( figsize=(6,5) )\n",
    "\n",
    "axs.hist( trn_jet1_nr_pts, alpha=0.5, density=True, bins=15 )\n",
    "axs.hist( trn_jet2_nr_pts, alpha=0.5, density=True, bins=15 )\n",
    "\n",
    "axs.set_xlabel( \"$p_{T}$ (GeV)\", fontproperties=axislabelfont )\n",
    "axs.set_ylabel( \"\\#events\", fontproperties=axislabelfont )\n",
    "\n",
    "yticks = [  ]\n",
    "axs.set_yticklabels( yticks, fontproperties=tickfont )\n",
    "\n",
    "xticks = [ int(x) for x in axs.get_xticks() ]\n",
    "axs.set_xticklabels( xticks, fontproperties=tickfont )\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we can recover the original distributions.  Let's move on."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimising the INN on the reduced data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-----------------------------------------------\n",
      "model architecture \n",
      "-----------------------------------------------\n",
      "SequenceINN(\n",
      "  (module_list): ModuleList(\n",
      "    (0): AllInOneBlock(\n",
      "      (softplus): Softplus(beta=0.5, threshold=20)\n",
      "      (subnet): Sequential(\n",
      "        (0): Linear(in_features=2, out_features=128, bias=True)\n",
      "        (1): ReLU()\n",
      "        (2): Linear(in_features=128, out_features=4, bias=True)\n",
      "      )\n",
      "    )\n",
      "    (1): AllInOneBlock(\n",
      "      (softplus): Softplus(beta=0.5, threshold=20)\n",
      "      (subnet): Sequential(\n",
      "        (0): Linear(in_features=2, out_features=128, bias=True)\n",
      "        (1): ReLU()\n",
      "        (2): Linear(in_features=128, out_features=4, bias=True)\n",
      "      )\n",
      "    )\n",
      "    (2): AllInOneBlock(\n",
      "      (softplus): Softplus(beta=0.5, threshold=20)\n",
      "      (subnet): Sequential(\n",
      "        (0): Linear(in_features=2, out_features=128, bias=True)\n",
      "        (1): ReLU()\n",
      "        (2): Linear(in_features=128, out_features=4, bias=True)\n",
      "      )\n",
      "    )\n",
      "    (3): AllInOneBlock(\n",
      "      (softplus): Softplus(beta=0.5, threshold=20)\n",
      "      (subnet): Sequential(\n",
      "        (0): Linear(in_features=2, out_features=128, bias=True)\n",
      "        (1): ReLU()\n",
      "        (2): Linear(in_features=128, out_features=4, bias=True)\n",
      "      )\n",
      "    )\n",
      "    (4): AllInOneBlock(\n",
      "      (softplus): Softplus(beta=0.5, threshold=20)\n",
      "      (subnet): Sequential(\n",
      "        (0): Linear(in_features=2, out_features=128, bias=True)\n",
      "        (1): ReLU()\n",
      "        (2): Linear(in_features=128, out_features=4, bias=True)\n",
      "      )\n",
      "    )\n",
      "    (5): AllInOneBlock(\n",
      "      (softplus): Softplus(beta=0.5, threshold=20)\n",
      "      (subnet): Sequential(\n",
      "        (0): Linear(in_features=2, out_features=128, bias=True)\n",
      "        (1): ReLU()\n",
      "        (2): Linear(in_features=128, out_features=4, bias=True)\n",
      "      )\n",
      "    )\n",
      "    (6): AllInOneBlock(\n",
      "      (softplus): Softplus(beta=0.5, threshold=20)\n",
      "      (subnet): Sequential(\n",
      "        (0): Linear(in_features=2, out_features=128, bias=True)\n",
      "        (1): ReLU()\n",
      "        (2): Linear(in_features=128, out_features=4, bias=True)\n",
      "      )\n",
      "    )\n",
      "    (7): AllInOneBlock(\n",
      "      (softplus): Softplus(beta=0.5, threshold=20)\n",
      "      (subnet): Sequential(\n",
      "        (0): Linear(in_features=2, out_features=128, bias=True)\n",
      "        (1): ReLU()\n",
      "        (2): Linear(in_features=128, out_features=4, bias=True)\n",
      "      )\n",
      "    )\n",
      "  )\n",
      ")\n",
      "-----------------------------------------------\n",
      "Epoch 1\n",
      "-----------------------------------------------\n",
      "current batch loss: 0.108974  [    0/1384081]\n",
      "current batch loss: -0.157473  [250000/1384081]\n",
      "current batch loss: -0.197659  [500000/1384081]\n",
      "current batch loss: -0.210336  [750000/1384081]\n",
      "current batch loss: -0.221443  [1000000/1384081]\n",
      "current batch loss: -0.238656  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -0.236689\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -0.236994\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 2\n",
      "-----------------------------------------------\n",
      "current batch loss: -0.237469  [    0/1384081]\n",
      "current batch loss: -0.242861  [250000/1384081]\n",
      "current batch loss: -0.251201  [500000/1384081]\n",
      "current batch loss: -0.258773  [750000/1384081]\n",
      "current batch loss: -0.258000  [1000000/1384081]\n",
      "current batch loss: -0.258712  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -0.261473\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -0.261525\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 3\n",
      "-----------------------------------------------\n",
      "current batch loss: -0.264261  [    0/1384081]\n",
      "current batch loss: -0.266487  [250000/1384081]\n",
      "current batch loss: -0.270700  [500000/1384081]\n",
      "current batch loss: -0.273941  [750000/1384081]\n",
      "current batch loss: -0.278399  [1000000/1384081]\n",
      "current batch loss: -0.287050  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -0.285278\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -0.285226\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 4\n",
      "-----------------------------------------------\n",
      "current batch loss: -0.282615  [    0/1384081]\n",
      "current batch loss: -0.294237  [250000/1384081]\n",
      "current batch loss: -0.293141  [500000/1384081]\n",
      "current batch loss: -0.300909  [750000/1384081]\n",
      "current batch loss: -0.309025  [1000000/1384081]\n",
      "current batch loss: -0.313688  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -0.313368\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -0.313907\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 5\n",
      "-----------------------------------------------\n",
      "current batch loss: -0.303022  [    0/1384081]\n",
      "current batch loss: -0.318081  [250000/1384081]\n",
      "current batch loss: -0.322462  [500000/1384081]\n",
      "current batch loss: -0.319980  [750000/1384081]\n",
      "current batch loss: -0.324892  [1000000/1384081]\n",
      "current batch loss: -0.332659  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -0.331971\n",
      "-----------------------------------------------\n",
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      "Epoch 6\n",
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      "Epoch 7\n",
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      "Epoch 8\n",
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      "Epoch 9\n",
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      "Epoch 10\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "avg val loss per batch: -0.355529\n",
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      "Epoch 11\n",
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      "Epoch 13\n",
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      "Epoch 14\n",
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      "Epoch 15\n",
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    },
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     "output_type": "stream",
     "text": [
      "current batch loss: -0.388538  [750000/1384081]\n",
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      "Epoch 25\n",
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     ]
    },
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      "-----------------------------------------------\n",
      "avg val loss per batch: -0.389952\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 39\n",
      "-----------------------------------------------\n",
      "current batch loss: -0.396029  [    0/1384081]\n",
      "current batch loss: -0.390531  [250000/1384081]\n",
      "current batch loss: -0.394067  [500000/1384081]\n",
      "current batch loss: -0.393951  [750000/1384081]\n",
      "current batch loss: -0.393287  [1000000/1384081]\n",
      "current batch loss: -0.399321  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -0.396799\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -0.390676\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 40\n",
      "-----------------------------------------------\n",
      "current batch loss: -0.398299  [    0/1384081]\n",
      "current batch loss: -0.396054  [250000/1384081]\n",
      "current batch loss: -0.398049  [500000/1384081]\n",
      "current batch loss: -0.386783  [750000/1384081]\n",
      "current batch loss: -0.396360  [1000000/1384081]\n",
      "current batch loss: -0.394653  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -0.396706\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -0.393947\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 41\n",
      "-----------------------------------------------\n",
      "current batch loss: -0.392079  [    0/1384081]\n",
      "current batch loss: -0.396633  [250000/1384081]\n",
      "current batch loss: -0.390924  [500000/1384081]\n",
      "current batch loss: -0.396543  [750000/1384081]\n",
      "current batch loss: -0.394816  [1000000/1384081]\n",
      "current batch loss: -0.400415  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -0.396292\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -0.396031\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 42\n",
      "-----------------------------------------------\n",
      "current batch loss: -0.400820  [    0/1384081]\n",
      "current batch loss: -0.401008  [250000/1384081]\n",
      "current batch loss: -0.393114  [500000/1384081]\n",
      "current batch loss: -0.394089  [750000/1384081]\n",
      "current batch loss: -0.389497  [1000000/1384081]\n",
      "current batch loss: -0.400597  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -0.396153\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -0.390700\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 43\n",
      "-----------------------------------------------\n",
      "current batch loss: -0.403169  [    0/1384081]\n",
      "current batch loss: -0.395387  [250000/1384081]\n",
      "current batch loss: -0.402243  [500000/1384081]\n",
      "current batch loss: -0.392138  [750000/1384081]\n",
      "current batch loss: -0.406464  [1000000/1384081]\n",
      "current batch loss: -0.404012  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -0.397776\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -0.397638\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 44\n",
      "-----------------------------------------------\n",
      "current batch loss: -0.398947  [    0/1384081]\n",
      "current batch loss: -0.397014  [250000/1384081]\n",
      "current batch loss: -0.401115  [500000/1384081]\n",
      "current batch loss: -0.401878  [750000/1384081]\n",
      "current batch loss: -0.400889  [1000000/1384081]\n",
      "current batch loss: -0.405692  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -0.397502\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -0.393271\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 45\n",
      "-----------------------------------------------\n",
      "current batch loss: -0.394301  [    0/1384081]\n",
      "current batch loss: -0.394642  [250000/1384081]\n",
      "current batch loss: -0.403895  [500000/1384081]\n",
      "current batch loss: -0.397062  [750000/1384081]\n",
      "current batch loss: -0.397684  [1000000/1384081]\n",
      "current batch loss: -0.405385  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -0.397662\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -0.397568\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 46\n",
      "-----------------------------------------------\n",
      "current batch loss: -0.400071  [    0/1384081]\n",
      "current batch loss: -0.398985  [250000/1384081]\n",
      "current batch loss: -0.402716  [500000/1384081]\n",
      "current batch loss: -0.400045  [750000/1384081]\n",
      "current batch loss: -0.394820  [1000000/1384081]\n",
      "current batch loss: -0.399884  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -0.399134\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -0.398774\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 47\n",
      "-----------------------------------------------\n",
      "current batch loss: -0.386752  [    0/1384081]\n",
      "current batch loss: -0.401114  [250000/1384081]\n",
      "current batch loss: -0.400853  [500000/1384081]\n",
      "current batch loss: -0.397388  [750000/1384081]\n",
      "current batch loss: -0.392258  [1000000/1384081]\n",
      "current batch loss: -0.395346  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -0.397149\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -0.397075\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 48\n",
      "-----------------------------------------------\n",
      "current batch loss: -0.394420  [    0/1384081]\n",
      "current batch loss: -0.403277  [250000/1384081]\n",
      "current batch loss: -0.402587  [500000/1384081]\n",
      "current batch loss: -0.397314  [750000/1384081]\n",
      "current batch loss: -0.407241  [1000000/1384081]\n",
      "current batch loss: -0.398615  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -0.399153\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -0.399085\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 49\n",
      "-----------------------------------------------\n",
      "current batch loss: -0.399075  [    0/1384081]\n",
      "current batch loss: -0.409186  [250000/1384081]\n",
      "current batch loss: -0.401461  [500000/1384081]\n",
      "current batch loss: -0.402980  [750000/1384081]\n",
      "current batch loss: -0.407409  [1000000/1384081]\n",
      "current batch loss: -0.398784  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -0.399259\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -0.399219\n",
      "-----------------------------------------------\n",
      "|\n",
      "-----------------------------------------------\n",
      "Epoch 50\n",
      "-----------------------------------------------\n",
      "current batch loss: -0.401206  [    0/1384081]\n",
      "current batch loss: -0.400816  [250000/1384081]\n",
      "current batch loss: -0.394532  [500000/1384081]\n",
      "current batch loss: -0.407213  [750000/1384081]\n",
      "current batch loss: -0.395978  [1000000/1384081]\n",
      "current batch loss: -0.389401  [1250000/1384081]\n",
      "-----------------------------------------------\n",
      "avg trn loss per batch: -0.400013\n",
      "-----------------------------------------------\n",
      "avg val loss per batch: -0.399934\n",
      "-----------------------------------------------\n",
      "|\n",
      "Done!\n"
     ]
    }
   ],
   "source": [
    "# a useful function to present things clearer\n",
    "def separator():\n",
    "    print( \"-----------------------------------------------\" )\n",
    "\n",
    "epochs = 50\n",
    "\n",
    "# re-initialise the model and the optimizer\n",
    "def subnet_fc( dims_in, dims_out ):\n",
    "    return nn.Sequential( nn.Linear(dims_in, 128), \n",
    "                         nn.ReLU(),\n",
    "                         nn.Linear(128,  dims_out) )\n",
    "ndim_nr = 4\n",
    "inn_nr = Ff.SequenceINN( ndim_nr )\n",
    "for k in range(8):\n",
    "    inn_nr.append( Fm.AllInOneBlock, subnet_constructor=subnet_fc, permute_soft=True )\n",
    "learning_rate = 0.001\n",
    "optimizer_nr = torch.optim.Adam( inn_nr.parameters(), lr=learning_rate )\n",
    "separator()\n",
    "print( \"model architecture \")\n",
    "separator()\n",
    "print( inn_nr )\n",
    "\n",
    "# track train and val losses\n",
    "trn_losses_nr = []\n",
    "val_losses_nr = []\n",
    "\n",
    "for t in range(epochs):\n",
    "    separator()\n",
    "    print( f\"Epoch {t+1}\" )\n",
    "    separator()\n",
    "    train_epoch( trn_dataloader_nr, inn_nr, optimizer_nr )\n",
    "    separator()\n",
    "    trn_loss = trn_pass( trn_dataloader_nr, inn_nr )\n",
    "    trn_losses_nr.append( trn_loss )\n",
    "    separator()\n",
    "    val_loss = val_pass( val_dataloader_nr, inn_nr )\n",
    "    val_losses_nr.append( val_loss )\n",
    "    separator()\n",
    "    print( \"|\" )\n",
    "    \n",
    "print(\"Done!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Study the new results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now generate data and recover the original observables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "z_gen_nr = torch.randn( (10000, ndim_nr) )\n",
    "x_gen_nr, _ = inn_nr( z_gen_nr, rev=True )\n",
    "x_gen_nr = x_gen_nr*100.0\n",
    "x_gen_nr = get_events_nr( x_gen_nr.detach().numpy() )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the energy distribution of the first jet, for both real and generated data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots( figsize=(6,5) )\n",
    "\n",
    "bins = np.arange( 0, 350, step=20 )\n",
    "axs.hist( x_gen_nr[:,0], alpha=0.5, density=True, bins=bins, label='gen' )\n",
    "axs.hist( dy_trn_data[:,0], alpha=0.5, density=True, bins=bins, label='real' )\n",
    "\n",
    "axs.set_xlabel( \"$E_{1}$ (GeV)\", fontproperties=axislabelfont )\n",
    "axs.set_ylabel( \"\\#events\", fontproperties=axislabelfont )\n",
    "\n",
    "yticks = [  ]\n",
    "axs.set_yticklabels( yticks, fontproperties=tickfont )\n",
    "\n",
    "xticks = [ int(x) for x in axs.get_xticks() ]\n",
    "axs.set_xticklabels( xticks, fontproperties=tickfont )\n",
    "\n",
    "axs.legend( loc='best', prop=tickfont )\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can do the same for $p_y$ of the first jet:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots( figsize=(6,5) )\n",
    "\n",
    "bins = np.arange( -100, +100, step=10 )\n",
    "axs.hist( x_gen_nr[:,6], alpha=0.5, density=True, bins=bins, label='gen' )\n",
    "axs.hist( dy_trn_data[:,6], alpha=0.5, density=True, bins=bins, label='real' )\n",
    "\n",
    "axs.set_xlabel( \"$p_{y,1}$ (GeV)\", fontproperties=axislabelfont )\n",
    "axs.set_ylabel( \"\\#events\", fontproperties=axislabelfont )\n",
    "\n",
    "yticks = [  ]\n",
    "axs.set_yticklabels( yticks, fontproperties=tickfont )\n",
    "\n",
    "xticks = [ int(x) for x in axs.get_xticks() ]\n",
    "axs.set_xticklabels( xticks, fontproperties=tickfont )\n",
    "\n",
    "axs.legend( loc='best', prop=tickfont )\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can look at more complicated observables which involve correlations between the different inputs.\n",
    "\n",
    "first we need to calucate them from the generated data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_gen_evnt_nr_ims, x_gen_evnt_nr_pts, x_gen_jet1_nr_pts, x_gen_jet2_nr_pts = get_obs_nr( x_gen.detach().numpy() )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The $p_T$ of the first jet:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots( figsize=(6,5) )\n",
    "\n",
    "bins = np.arange( 5, 85, step=5 )\n",
    "axs.hist( x_gen_jet1_nr_pts, alpha=0.5, density=True, bins=bins, label='gen' )\n",
    "axs.hist( trn_jet1_nr_pts, alpha=0.5, density=True, bins=bins, label='real' )\n",
    "\n",
    "axs.set_xlabel( \"$p_{T,1}$ (GeV)\", fontproperties=axislabelfont )\n",
    "axs.set_ylabel( \"\\#events\", fontproperties=axislabelfont )\n",
    "\n",
    "yticks = [  ]\n",
    "axs.set_yticklabels( yticks, fontproperties=tickfont )\n",
    "\n",
    "xticks = [ int(x) for x in axs.get_xticks() ]\n",
    "axs.set_xticklabels( xticks, fontproperties=tickfont )\n",
    "\n",
    "axs.legend( loc='best', prop=tickfont )\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks good!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the invariant mass of the whole event:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots( figsize=(6,5) )\n",
    "\n",
    "bins = np.arange( 5, 165, step=10 )\n",
    "axs.hist( np.nan_to_num( x_gen_evnt_nr_ims ), alpha=0.5, density=True, bins=bins, label='gen' )\n",
    "axs.hist( np.nan_to_num( trn_evnt_ims ), alpha=0.5, density=True, bins=bins, label='real' )\n",
    "\n",
    "axs.set_xlabel( \"$m_{\\mu\\mu}$ (GeV)\", fontproperties=axislabelfont )\n",
    "axs.set_ylabel( \"\\#events\", fontproperties=axislabelfont )\n",
    "\n",
    "yticks = [  ]\n",
    "axs.set_yticklabels( yticks, fontproperties=tickfont )\n",
    "\n",
    "xticks = [ int(x) for x in axs.get_xticks() ]\n",
    "axs.set_xticklabels( xticks, fontproperties=tickfont )\n",
    "\n",
    "axs.legend( loc='best', prop=tickfont )\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again this is not perfect, but the peak of the generated distribution is at the correct place."
   ]
  }
 ],
 "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": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}