{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "import uproot\t\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits import mplot3d\n",
    "import awkward as ak\n",
    "from scipy.optimize import curve_fit\n",
    "from methods.fit_linear_regression_model import fit_linear_regression_model\n",
    "import sklearn\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40402 10099\n",
      "50501\n"
     ]
    }
   ],
   "source": [
    "file = uproot.open(\n",
    "    \"tracking_losses_ntuple_B_default_radlength_endVelo.root:PrDebugTrackingLosses.PrDebugTrackingTool/Tuple;1\"\n",
    ")\n",
    "\n",
    "# selektiere nur elektronen von B->K*ee\n",
    "allcolumns = file.arrays()\n",
    "found = allcolumns[(allcolumns.isElectron) & (~allcolumns.lost) &\n",
    "                   (allcolumns.fromB)]  # B: 9056\n",
    "lost = allcolumns[(allcolumns.isElectron) & (allcolumns.lost) &\n",
    "                  (allcolumns.fromB)]  # B: 1466\n",
    "\n",
    "electrons = allcolumns[(allcolumns.isElectron) & (allcolumns.fromB)]\n",
    "\n",
    "print(ak.num(found, axis=0), ak.num(lost, axis=0))\n",
    "print(ak.num(electrons, axis=0))\n",
    "# ak.count(found, axis=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "stretch factor:  0.24996287312509283\n"
     ]
    }
   ],
   "source": [
    "rad_length_found = ak.to_numpy(found[\"rad_length_frac\"])\n",
    "eta_found = ak.to_numpy(found[\"eta\"])\n",
    "rad_length_lost = ak.to_numpy(lost[\"rad_length_frac\"])\n",
    "eta_lost = ak.to_numpy(lost[\"eta\"])\n",
    "\n",
    "stretch_factor = ak.num(eta_lost, axis=0) / ak.num(eta_found, axis=0)\n",
    "print(\"stretch factor: \", stretch_factor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(\n",
    "    rad_length_lost,\n",
    "    bins=100,\n",
    "    density=True,\n",
    "    alpha=0.5,\n",
    "    color=\"darkorange\",\n",
    "    histtype=\"bar\",\n",
    "    label=\"lost\",\n",
    "    range=[0, 1],\n",
    ")\n",
    "plt.hist(\n",
    "    rad_length_found,\n",
    "    bins=100,\n",
    "    density=True,\n",
    "    alpha=0.5,\n",
    "    color=\"blue\",\n",
    "    histtype=\"bar\",\n",
    "    label=\"found\",\n",
    "    range=[0, 1],\n",
    ")\n",
    "plt.xlim(0, 1)\n",
    "# plt.yscale(\"log\")\n",
    "plt.title(\"radiation length fraction endVelo\")\n",
    "plt.xlabel(f\"$x/X_0$\")\n",
    "plt.ylabel(\"a.u.\")\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2000x800 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nbins = 100\n",
    "vmax = 80\n",
    "\n",
    "fig, ((ax0, ax1)) = plt.subplots(nrows=1, ncols=2, figsize=(20, 8))\n",
    "\n",
    "a0 = ax0.hist2d(\n",
    "    rad_length_found,\n",
    "    eta_found,\n",
    "    density=False,\n",
    "    bins=nbins,\n",
    "    cmap=plt.cm.jet,\n",
    "    cmin=1,\n",
    "    vmax=vmax,\n",
    "    range=[[0, 0.6], [2, 5]],\n",
    ")\n",
    "ax0.set_xlabel(f\"$x/X_0$\")\n",
    "ax0.set_ylabel(f\"$\\eta$\")\n",
    "ax0.set_title(f\"found $\\eta$ rad_length_frac\")\n",
    "\n",
    "a1 = ax1.hist2d(\n",
    "    rad_length_lost,\n",
    "    eta_lost,\n",
    "    density=False,\n",
    "    bins=nbins,\n",
    "    cmap=plt.cm.jet,\n",
    "    cmin=1,\n",
    "    vmax=vmax * stretch_factor,\n",
    "    range=[[0, 0.6], [2, 5]],\n",
    ")\n",
    "ax1.set_xlabel(f\"$x/X_0$\")\n",
    "ax1.set_ylabel(f\"$\\eta$\")\n",
    "ax1.set_title(f\"lost $\\eta$ rad_length_frac\")\n",
    "# ax1.set(xlim=(0,4000), ylim=(-1000,1000))\n",
    "\n",
    "plt.suptitle(\"radiation length fraction and eta endVelo\")\n",
    "plt.colorbar(a0[3], ax=ax1)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "rad_length_frac = found[\"rad_length_frac\"]\n",
    "# @ z = 9400.mm or 770.mm\n",
    "state = 1\n",
    "\n",
    "if state == 1:\n",
    "    slopex = found[\"ideal_state_770_tx\"]\n",
    "    slopey = found[\"ideal_state_770_ty\"]\n",
    "    x = found[\"ideal_state_770_x\"]\n",
    "    y = found[\"ideal_state_770_y\"]\n",
    "    qop = found[\"ideal_state_770_qop\"]\n",
    "elif state == 2:\n",
    "    slopex = found[\"ideal_state_9410_tx\"]\n",
    "    slopey = found[\"ideal_state_9410_ty\"]\n",
    "    x = found[\"ideal_state_9410_x\"]\n",
    "    y = found[\"ideal_state_9410_y\"]\n",
    "    qop = found[\"ideal_state_9410_qop\"]\n",
    "\n",
    "data = ak.zip({\n",
    "    \"rad_length_frac\": rad_length_frac,\n",
    "    \"x\": x,\n",
    "    \"y\": y,\n",
    "    \"tx\": slopex,\n",
    "    \"ty\": slopey,\n",
    "    \"qop\": qop,\n",
    "})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameterisation for rad_length_frac:\n",
      "intercept= 0.0\n",
      "coef= {'1': 0.19432666451166924, 'x': -0.00010136532791187516, 'y': -0.00022209404990607013, 'tx': 0.058480207541052064, 'ty': 0.18599542917589618, 'qop': -17.657405901936546, 'x^2': 1.2271024867047469e-05, 'x y': 5.376824972059055e-08, 'x tx': -0.025941371835257743, 'x ty': 0.014328015524776564, 'x qop': -0.38410998543244235, 'y^2': -1.8261507968709735e-05, 'y tx': -0.014951077113227147, 'y ty': 0.02154311538810164, 'y qop': -0.008987663050567057, 'tx^2': 9.180854607357592, 'tx ty': 0.1873064867954838, 'tx qop': -0.47120712928737807, 'ty^2': -6.787398610853974, 'ty qop': -0.05031041352613623, 'qop^2': 0.24778641944197533, 'x^3': -5.992321693190818e-09, 'x^2 y': -2.649404482539432e-07, 'x^2 tx': 5.42176741002125e-06, 'x^2 ty': 0.0020253771536145383, 'x^2 qop': 0.003955288970107154, 'x y^2': 2.8906882704270233e-09, 'x y tx': -0.0016493773782229844, 'x y ty': 0.0005067592007986898, 'x y qop': -0.0031813438496783404, 'x tx^2': 0.0022653308811514867, 'x tx ty': -1.5366360302916284, 'x tx qop': -0.47946313010450653, 'x ty^2': -0.16776305178984158, 'x ty qop': 2.1889500302073115, 'x qop^2': 0.008745243979922932, 'y^3': 1.4363120470761714e-08, 'y^2 tx': -0.0005062978553841023, 'y^2 ty': 1.4165440283044409e-05, 'y^2 qop': -0.005787147937546765, 'y tx^2': 1.404047645962725, 'y tx ty': 0.1643910546131908, 'y tx qop': 2.0452379823825813, 'y ty^2': -0.02140660574730952, 'y ty qop': 4.596387657867597, 'y qop^2': -0.00994088354226498, 'tx^3': -0.1303976515212055, 'tx^2 ty': -0.01339610187978276, 'tx^2 qop': -0.0009383144690666937, 'tx ty^2': 0.010330807276347866, 'tx ty qop': 0.00564141621903312, 'tx qop^2': 1.1663926820802422e-05, 'ty^3': 0.00629773549670367, 'ty^2 qop': 0.012052455601588194, 'ty qop^2': -1.60166284721317e-05, 'qop^3': -1.5639205966369518e-06, 'x^4': 1.4244960766518489e-09, 'x^3 y': -3.1096076824610464e-09, 'x^3 tx': -3.587531603760352e-06, 'x^3 ty': 2.4713133050052738e-05, 'x^3 qop': 2.5845963699160437e-05, 'x^2 y^2': -2.0323240867980985e-09, 'x^2 y tx': -1.781414931473213e-05, 'x^2 y ty': -1.0125741814137612e-05, 'x^2 y qop': 0.00010504795400130865, 'x^2 tx^2': 0.00318540624554603, 'x^2 tx ty': -0.019979832566411563, 'x^2 tx qop': 0.006687084675785277, 'x^2 ty^2': 0.01525871952521068, 'x^2 ty qop': 0.5999059816243137, 'x^2 qop^2': 8.117293800523118, 'x y^3': 7.45386197209541e-10, 'x y^2 tx': 1.539536253053475e-05, 'x y^2 ty': -1.089334137566178e-05, 'x y^2 qop': -1.95550966909791e-05, 'x y tx^2': 0.015033712066153922, 'x y tx ty': -0.02448056876178019, 'x y tx qop': -0.6716914089728931, 'x y ty^2': 0.007182752502229531, 'x y ty qop': -0.18936713869537714, 'x y qop^2': 3.611377836849899, 'x tx^3': -0.9115227647899486, 'x tx^2 ty': 0.8829467327098821, 'x tx^2 qop': 0.2695607767961495, 'x tx ty^2': 0.6012451073716732, 'x tx ty qop': -0.00930712726835479, 'x tx qop^2': 0.009680202136377838, 'x ty^3': -0.06079594416933904, 'x ty^2 qop': 0.04029084967629493, 'x ty qop^2': 0.004774793771381167, 'x qop^3': -4.554461348017879e-05, 'y^4': 4.04032363121587e-12, 'y^3 tx': 8.925743423537913e-06, 'y^3 ty': -1.0182095510069544e-06, 'y^3 qop': -2.928516988854517e-05, 'y^2 tx^2': 0.004743417924369025, 'y^2 tx ty': -0.0055290127765494496, 'y^2 tx qop': 0.2133121554871387, 'y^2 ty^2': 0.0017685009285896116, 'y^2 ty qop': 0.020383665461783013, 'y^2 qop^2': -0.90657292007639, 'y tx^3': 0.27175992018246475, 'y tx^2 ty': 0.6761073293647273, 'y tx^2 qop': -0.01248506771745212, 'y tx ty^2': -0.39076013367696105, 'y tx ty qop': 0.04349449144257623, 'y tx qop^2': 0.004752914013263597, 'y ty^3': -0.729116504589348, 'y ty^2 qop': -0.015043560943011547, 'y ty qop^2': -0.001547809754472937, 'y qop^3': -1.316621299355546e-05, 'tx^4': -0.003228436324482351, 'tx^3 ty': 0.0044775047770867545, 'tx^3 qop': 0.001098230908109032, 'tx^2 ty^2': 0.0029303145639830285, 'tx^2 ty qop': -4.337425914757845e-05, 'tx^2 qop^2': 1.134299372765626e-05, 'tx ty^3': -0.0014086661449565522, 'tx ty^2 qop': 0.0001660768862220596, 'tx ty qop^2': 6.3521706353330705e-06, 'tx qop^3': -5.1281203369915226e-08, 'ty^4': -0.0071021220988862245, 'ty^3 qop': -6.713410801676869e-05, 'ty^2 qop^2': -2.7595247487299285e-06, 'ty qop^3': -1.972159538523153e-08, 'qop^4': 3.222747801976328e-10, 'x^5': -3.2453151277422876e-11, 'x^4 y': -7.538414337204813e-13, 'x^4 tx': 9.439335535432747e-08, 'x^4 ty': 1.5053041968471348e-07, 'x^4 qop': 2.0621745686622006e-06, 'x^3 y^2': -6.107114813858061e-12, 'x^3 y tx': -1.4186378294311908e-07, 'x^3 y ty': 9.335861888004615e-07, 'x^3 y qop': 4.389303884896889e-06, 'x^3 tx^2': -0.00010056331721829473, 'x^3 tx ty': -0.000368816675172811, 'x^3 tx qop': -0.0031371932512015794, 'x^3 ty^2': -0.0006215843383633401, 'x^3 ty qop': -0.0040682949745989485, 'x^3 qop^2': -0.01783210821802376, 'x^2 y^3': -2.1280754936015e-12, 'x^2 y^2 tx': -9.287590581052996e-07, 'x^2 y^2 ty': -4.159245552415314e-07, 'x^2 y^2 qop': -3.762232883230965e-06, 'x^2 y tx^2': 0.0003560931930516667, 'x^2 y tx ty': -0.00014974182212146823, 'x^2 y tx qop': -0.002168783048351754, 'x^2 y ty^2': 0.0005557263565684947, 'x^2 y ty qop': -0.0027368181509398255, 'x^2 y qop^2': -0.021251765155328187, 'x^2 tx^3': 0.04636097936049924, 'x^2 tx^2 ty': 0.19264721978393362, 'x^2 tx^2 qop': 1.1201214250508411, 'x^2 tx ty^2': 0.2717131602944406, 'x^2 tx ty qop': 1.0069243735131281, 'x^2 tx qop^2': 0.0017781753799746996, 'x^2 ty^3': -0.17716467804753896, 'x^2 ty^2 qop': -0.7967627886628681, 'x^2 ty qop^2': -0.020752836202331357, 'x^2 qop^3': -0.0003102149541338055, 'x y^4': -3.716849050761084e-11, 'x y^3 tx': 4.2096182362172385e-07, 'x y^3 ty': 9.343710843934261e-08, 'x y^3 qop': -4.85417695898771e-06, 'x y^2 tx^2': 0.0007723490259714336, 'x y^2 tx ty': -0.000465174042059667, 'x y^2 tx qop': 0.0083072051829175, 'x y^2 ty^2': -0.0001514875700367028, 'x y^2 ty qop': 0.0033210944559410355, 'x y^2 qop^2': -0.0016097785846472324, 'x y tx^3': -0.18644890104309755, 'x y tx^2 ty': -0.04212197105444866, 'x y tx^2 qop': 1.0626013948995083, 'x y tx ty^2': 0.09950829907042329, 'x y tx ty qop': -0.7011822284857461, 'x y tx qop^2': -0.02153879411999937, 'x y ty^3': 0.07920758108734982, 'x y ty^2 qop': -1.3677505196768507, 'x y ty qop^2': 0.005572049947548557, 'x y qop^3': 0.0003625259165958029, 'x tx^4': -7.806580145878633, 'x tx^3 ty': -0.48543671938056426, 'x tx^3 qop': 0.01223464815691587, 'x tx^2 ty^2': -0.7759844557140754, 'x tx^2 ty qop': 0.004830189695310542, 'x tx^2 qop^2': 6.943806457826217e-06, 'x tx ty^3': -0.2626842333297885, 'x tx ty^2 qop': -0.002218311914437031, 'x tx ty qop^2': -5.935445430100284e-05, 'x tx qop^3': -4.652385512477656e-07, 'x ty^4': -0.13391527053501218, 'x ty^3 qop': -0.004907072655857102, 'x ty^2 qop^2': 1.6619362532345914e-05, 'x ty qop^3': 8.142368541762968e-07, 'x qop^4': 4.653376619669799e-09, 'y^5': 3.825384453648439e-12, 'y^4 tx': -4.679158727149968e-10, 'y^4 ty': -5.908476596871992e-09, 'y^4 qop': 2.1690478767266708e-08, 'y^3 tx^2': -9.496214334184586e-05, 'y^3 tx ty': 7.42067773199526e-05, 'y^3 tx qop': 0.004042069781436391, 'y^3 ty^2': 1.3648094370263125e-06, 'y^3 ty qop': -9.095584346929984e-05, 'y^3 qop^2': 0.0026650743754950902, 'y^2 tx^3': -0.22830126100028328, 'y^2 tx^2 ty': 0.07976968562385643, 'y^2 tx^2 qop': -0.569375473311322, 'y^2 tx ty^2': -0.05752462027849215, 'y^2 tx ty qop': -1.3821142344540522, 'y^2 tx qop^2': 0.0030041051075548795, 'y^2 ty^3': 0.0007092199317686958, 'y^2 ty^2 qop': 0.08213843039582976, 'y^2 ty qop^2': -0.009533342523832138, 'y^2 qop^3': -4.410702217968634e-05, 'y tx^4': -0.4617640318570093, 'y tx^3 ty': -0.7726015660797079, 'y tx^3 qop': 0.004989400779050441, 'y tx^2 ty^2': -0.2543425991684884, 'y tx^2 ty qop': -0.001971807200332014, 'y tx^2 qop^2': -6.047144105356334e-05, 'y tx ty^3': -0.14996432803062354, 'y tx ty^2 qop': -0.00494485016520198, 'y tx ty qop^2': 1.250565568496303e-05, 'y tx qop^3': 7.906173456988411e-07, 'y ty^4': 0.023264047526106668, 'y ty^3 qop': 0.0014038996016424031, 'y ty^2 qop^2': -2.8280611787753928e-05, 'y ty qop^3': 3.0725068466100624e-07, 'y qop^4': -4.09432863754477e-09, 'tx^5': -0.052446331725343374, 'tx^4 ty': -0.0031642363210890884, 'tx^4 qop': 5.831594421042545e-05, 'tx^3 ty^2': -0.005193740457310502, 'tx^3 ty qop': 1.5211405438268112e-05, 'tx^3 qop^2': 7.987434860389955e-09, 'tx^2 ty^3': -0.0017266713029734364, 'tx^2 ty^2 qop': -3.2665518364513855e-06, 'tx^2 ty qop^2': -1.2886641260179494e-07, 'tx^2 qop^3': -7.431322766916425e-10, 'tx ty^4': -0.0009711418007784676, 'tx ty^3 qop': -1.1566774851255521e-05, 'tx ty^2 qop^2': 3.07405227672554e-08, 'tx ty qop^3': 1.5258831556369568e-09, 'tx qop^4': 6.567772758657935e-12, 'ty^5': 0.00011456709116180268, 'ty^4 qop': 6.736678103390532e-06, 'ty^3 qop^2': -6.391677860197088e-08, 'ty^2 qop^3': 8.915568061124554e-10, 'ty qop^4': -6.626331897050053e-12, 'qop^5': -2.2660425734485018e-13}\n",
      "r2 score= 0.04993524171391073\n",
      "RMSE = 0.12351226258714283\n",
      "Type  <class 'numpy.ndarray'>\n"
     ]
    }
   ],
   "source": [
    "lin_reg, features, xx0_test, xx0_predicted = fit_linear_regression_model(\n",
    "    data,\n",
    "    \"rad_length_frac\",\n",
    "    [\"x\", \"y\", \"tx\", \"ty\", \"qop\"],\n",
    "    5,\n",
    "    include_bias=True,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nbins = 100\n",
    "vmax = 50\n",
    "\n",
    "a0 = plt.hist2d(\n",
    "    xx0_test,\n",
    "    xx0_predicted,\n",
    "    density=False,\n",
    "    bins=nbins,\n",
    "    cmap=plt.cm.jet,\n",
    "    cmin=1,\n",
    "    vmax=vmax,\n",
    "    range=[[-0.1, 0.6], [-0.1, 0.6]],\n",
    ")\n",
    "plt.plot([-0.1, 0.6], [-0.1, 0.6], marker=\"\", alpha=0.8)\n",
    "plt.xlabel(f\"True $x/X_0$\")\n",
    "plt.ylabel(f\"Predicted $x/X_0$\")\n",
    "plt.title(f\"found rad_length_frac\")\n",
    "# ax1.set(xlim=(0,4000), ylim=(-1000,1000))\n",
    "\n",
    "plt.colorbar(a0[3])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "tuner",
   "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": "3.10.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}