Simulation_new.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Welcome to JupyROOT 6.22/02\n"
     ]
    }
   ],
   "source": [
    "import ROOT\n",
    "import numpy as np\n",
    "#from root_numpy import random_sample\n",
    "from scipy.ndimage import uniform_filter\n",
    "import time\n",
    "import matplotlib.pyplot as plt\n",
    "import multiprocessing as mp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Simulation Model</h1>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-17-dda8ac0bd069>:516: MatplotlibDeprecationWarning: Adding an axes using the same arguments as a previous axes currently reuses the earlier instance.  In a future version, a new instance will always be created and returned.  Meanwhile, this warning can be suppressed, and the future behavior ensured, by passing a unique label to each axes instance.\n",
      "  ax = fig.add_subplot(111)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulation took 1.5 seconds\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.000000,1000.000000] using AdaptiveSingular. Result = 0.002373 +/- 0.003932  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.000000,1000.000000] using AdaptiveSingular. Result = 0.002373 +/- 0.003932  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.000303,1000.000000] using AdaptiveSingular. Result = 0.002430 +/- 0.004041  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.000303,1000.000000] using AdaptiveSingular. Result = 0.002430 +/- 0.004041  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.000606,1000.000000] using AdaptiveSingular. Result = 0.002482 +/- 0.004140  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.000606,1000.000000] using AdaptiveSingular. Result = 0.002482 +/- 0.004140  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.000909,1000.000000] using AdaptiveSingular. Result = 0.002523 +/- 0.003799  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.000909,1000.000000] using AdaptiveSingular. Result = 0.002523 +/- 0.003799  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.001212,1000.000000] using AdaptiveSingular. Result = 0.002511 +/- 0.003785  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.001212,1000.000000] using AdaptiveSingular. Result = 0.002511 +/- 0.003785  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.001515,1000.000000] using AdaptiveSingular. Result = 0.002500 +/- 0.003774  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.001515,1000.000000] using AdaptiveSingular. Result = 0.002500 +/- 0.003774  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.001818,1000.000000] using AdaptiveSingular. Result = 0.002493 +/- 0.003767  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.001818,1000.000000] using AdaptiveSingular. Result = 0.002493 +/- 0.003767  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.002121,1000.000000] using AdaptiveSingular. Result = 0.002499 +/- 0.003208  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.002121,1000.000000] using AdaptiveSingular. Result = 0.002499 +/- 0.003208  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.002424,1000.000000] using AdaptiveSingular. Result = 0.002499 +/- 0.003201  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.002424,1000.000000] using AdaptiveSingular. Result = 0.002499 +/- 0.003201  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.002727,1000.000000] using AdaptiveSingular. Result = 0.002500 +/- 0.000579  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.002727,1000.000000] using AdaptiveSingular. Result = 0.002500 +/- 0.000579  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.003333,1000.000000] using AdaptiveSingular. Result = 0.002498 +/- 0.000181  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.003333,1000.000000] using AdaptiveSingular. Result = 0.002498 +/- 0.000181  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.003636,1000.000000] using AdaptiveSingular. Result = 0.002496 +/- 0.000411  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.003636,1000.000000] using AdaptiveSingular. Result = 0.002496 +/- 0.000411  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.003939,1000.000000] using AdaptiveSingular. Result = 0.002493 +/- 0.000517  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.003939,1000.000000] using AdaptiveSingular. Result = 0.002493 +/- 0.000517  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.004242,1000.000000] using AdaptiveSingular. Result = 0.002488 +/- 0.000505  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.004242,1000.000000] using AdaptiveSingular. Result = 0.002488 +/- 0.000505  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.004545,1000.000000] using AdaptiveSingular. Result = 0.002481 +/- 0.000422  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.004545,1000.000000] using AdaptiveSingular. Result = 0.002481 +/- 0.000422  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.004848,1000.000000] using AdaptiveSingular. Result = 0.002471 +/- 0.000313  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.004848,1000.000000] using AdaptiveSingular. Result = 0.002471 +/- 0.000313  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.005152,1000.000000] using AdaptiveSingular. Result = 0.002458 +/- 0.000211  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.005152,1000.000000] using AdaptiveSingular. Result = 0.002458 +/- 0.000211  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.006364,1000.000000] using AdaptiveSingular. Result = 0.002361 +/- 0.003952  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.006364,1000.000000] using AdaptiveSingular. Result = 0.002361 +/- 0.003952  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.006667,1000.000000] using AdaptiveSingular. Result = 0.002326 +/- 0.003891  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.006667,1000.000000] using AdaptiveSingular. Result = 0.002326 +/- 0.003891  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.006970,1000.000000] using AdaptiveSingular. Result = 0.002287 +/- 0.003823  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.006970,1000.000000] using AdaptiveSingular. Result = 0.002287 +/- 0.003823  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.007273,1000.000000] using AdaptiveSingular. Result = 0.002245 +/- 0.003750  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.007273,1000.000000] using AdaptiveSingular. Result = 0.002245 +/- 0.003750  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.007576,1000.000000] using AdaptiveSingular. Result = 0.002200 +/- 0.003670  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.007576,1000.000000] using AdaptiveSingular. Result = 0.002200 +/- 0.003670  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 22 in qags.c at 562 : integral is divergent, or slowly convergent\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.012424,1000.000000] using AdaptiveSingular. Result = 0.000000 +/- 0.000000  - status = 22\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 22 in qags.c at 562 : integral is divergent, or slowly convergent\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [0.012424,1000.000000] using AdaptiveSingular. Result = 0.000000 +/- 0.000000  - status = 22\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n",
      "Error in <GSLError>: Error 18 in qags.c at 557 : roundoff error detected in the extrapolation table\n",
      "Warning in <TF1::IntegralOneDim>: Error found in integrating function sth in [-100.000000,1000.000000] using AdaptiveSingular. Result = 0.002066 +/- 0.003387  - status = 18\n",
      "Info in <TF1::IntegralOneDim>: \t\tFunction Parameters = {\n"
     ]
    }
   ],
   "source": [
    "# the constants of the constants. Pretty much choose once and leave it. Do not change.\n",
    "C_total_channels = int(3.6 * 1e6)\n",
    "C_channels_per_module = int(15*30)\n",
    "C_total_modules = int(C_total_channels/C_channels_per_module)\n",
    "\n",
    "# skip\n",
    "#C_max_radius = 1\n",
    "\n",
    "### Skipping radius dependency for now...\n",
    "\n",
    "\n",
    "#==============================================================================\n",
    "\n",
    "### Code for the simulation:\n",
    "\n",
    "class parameter_object:\n",
    "    # This might look cleaner, but it is less understood exactly what type of parameters and how many each function needs.\n",
    "    # I don't think I will implement the usage of this, (yet at least)\n",
    "    def __init__(self):\n",
    "        pass\n",
    "\n",
    "class noise_generator:\n",
    "    def __init__(self, threshold, channel_count): # channel_count = C_total_channels\n",
    "        global global_counter\n",
    "        low = 0\n",
    "        high = 1000\n",
    "        noise = ROOT.TF1(\"noise_gauss\", \"TMath::Gaus(x, 0, 5)\", low, high)\n",
    "        self._mean = channel_count * noise.Integral(threshold, high)/noise.Integral(low, high)/2\n",
    "        #self._prng = ROOT.TRandom3(time.time_ns())\n",
    "        global_counter += 1\n",
    "        self._prng = ROOT.TRandom3(int(time.time()) + global_counter)\n",
    "\n",
    "    def generate(self):\n",
    "        \"\"\"The first return value is the exact number of noise activated channels in the small window and\n",
    "            the second return value is the estimated number of noise activated channels in the small window. (estimated from large window)\n",
    "            (both results are in small window, both results are noise above threshold)\n",
    "            noise_exact, noise_est = noise.generate()\"\"\"\n",
    "        # Large time window 25ns\n",
    "        # Small time window 3.125ns\n",
    "        prng = self._prng\n",
    "        total = prng.Poisson(self._mean) # number of noise above threshold in large window in this run.\n",
    "        narrow_exact = 0\n",
    "        #for i in range(total):\n",
    "        #    if prng.Uniform(25) < 3.125:\n",
    "        #        narrow_exact += 1\n",
    "        # faster to use numpy\n",
    "        narrow_exact = (np.random.uniform(low=0, high=25, size=total) < 3.125).sum()\n",
    "        \n",
    "        noise_per_time = (total - narrow_exact)/(25 - 3.125)\n",
    "        estimate = 3.125 * noise_per_time\n",
    "        return narrow_exact, estimate\n",
    "\n",
    "    \n",
    "class signal_generator:\n",
    "    def __init__(self, threshold, expected_voltage): # expected_voltage = expected peak voltage  (mu)\n",
    "        global global_counter\n",
    "        low = -100\n",
    "        high = 1000\n",
    "        self._threshold = threshold\n",
    "        self._expected_voltage = expected_voltage\n",
    "        signal_func = ROOT.TF1(\"sth\", \"TMath::Landau(x, %f, %f)\" % (expected_voltage, expected_voltage/4), low, high)\n",
    "        self.fraction_above = signal_func.Integral(threshold, high)/signal_func.Integral(low, high)\n",
    "        #self._prng = ROOT.TRandom3(time.time_ns())\n",
    "        global_counter += 1\n",
    "        self._prng = ROOT.TRandom3(int(time.time()) + global_counter)\n",
    "    \n",
    "    def generate(self, expected_count):\n",
    "        \"\"\"The paramater is the expected number of particles that reach the detector.\n",
    "            The first return value is the number of particles that reached the detector and\n",
    "            the second return value is the number of activated channels.\n",
    "            signal_real_total, signal_above = signal.generate(30)\"\"\"\n",
    "        prng = self._prng\n",
    "        expected_voltage = self._expected_voltage\n",
    "        threshold = self._threshold\n",
    "        \n",
    "        signal_count = prng.Poisson(expected_count)\n",
    "        above_threshold_count = 0\n",
    "        for i in range(signal_count):\n",
    "            if prng.Landau(expected_voltage, expected_voltage/4) > threshold: # 1/4 is just the refernce 25/100\n",
    "                above_threshold_count += 1\n",
    "        return signal_count, above_threshold_count\n",
    "    \n",
    "\n",
    "\n",
    "def simulation_get_counts(bunch_crossing_count , ratio_of_channels_to_sample, signal_to_channel_count_ratio, threshold, signal_mu):\n",
    "    \"\"\"Runs a simulation over specified number of BC, and returns two lists:\n",
    "        total_actual_signal_count and total_estimated_signal_count for each BC\"\"\"\n",
    "\n",
    "    channel_count = get_number_of_channel_readouts(ratio_of_channels_to_sample)\n",
    "    avg_particles_reaching_detector = channel_count * signal_to_channel_count_ratio\n",
    "    peak_signal_voltage = signal_mu\n",
    "    \n",
    "    noise_gen = noise_generator(threshold, channel_count)\n",
    "    signal_gen = signal_generator(threshold, peak_signal_voltage)\n",
    "    \n",
    "    result_actual_signal_count = np.zeros(bunch_crossing_count)\n",
    "    result_estimated_signal_count = np.zeros(bunch_crossing_count)\n",
    "    \n",
    "    for BC in range(bunch_crossing_count):\n",
    "        # The first return value is the exact number of noise activated channels in the small window and\n",
    "        # the second return value is the estimated number of noise activated channels in the small window (estimated from large window).\n",
    "        # (both results are in small window, both results are noise above threshold)\n",
    "        noise_exact, noise_est = noise_gen.generate()\n",
    "        \n",
    "        # The paramater is the expected number of particles that reach the detector.\n",
    "        # The first return value is the number of particles that reached the detector and \n",
    "        # the second return value is the number of activated channels.\n",
    "        total_actual_signal, signal_above = signal_gen.generate(avg_particles_reaching_detector)\n",
    "        \n",
    "        # from the total, estimate how much total signal there was\n",
    "        total_activations = signal_above + noise_exact  # total activations in small window (i.e. above threshold)\n",
    "        total_signal_est = (total_activations - noise_est)/signal_gen.fraction_above\n",
    "\n",
    "        # asign the results\n",
    "        result_actual_signal_count[BC] = total_actual_signal\n",
    "        result_estimated_signal_count[BC] = total_signal_est\n",
    "\n",
    "    return result_actual_signal_count, result_estimated_signal_count\n",
    "# we don't need to know the noise. Therefore not returing the noise values\n",
    "\n",
    "def simulation_parallel_get_counts(number_of_BC, ratio_of_channels_to_sample, signal_to_channel_count_ratio, threshold, signal_mu):\n",
    "    \"\"\"Runs the simulations in parallel inorder to faster simulate. It then combines each result.\n",
    "        and returns two lists: total_actual_signal_count and total_estimated_signal_count for each BC\"\"\"\n",
    "    global global_counter\n",
    "   # parameters for the simulation\n",
    "    bins_of_BC = eq_div_strict(number_of_BC, nprocs)\n",
    "    param_list = [ (bins_of_BC[i],  # number of BC for each parallel simulation\n",
    "                    ratio_of_channels_to_sample,\n",
    "                    signal_to_channel_count_ratio,\n",
    "                    threshold,\n",
    "                    signal_mu)\n",
    "                 for i in range(nprocs)]\n",
    "   # parallel simulation\n",
    "    results = np.asarray(pool.starmap(simulation_get_counts, param_list))\n",
    "    results = np.hstack(results).squeeze() # reshape\n",
    "\n",
    "    result_actual_signal_count = results[0]\n",
    "    result_estimated_signal_count = results[1]\n",
    "\n",
    "   # list of count,  count for each bunch crossing event\n",
    "    return result_actual_signal_count, result_estimated_signal_count\n",
    "\n",
    "\n",
    "\n",
    "def get_listed_deviation_from_expected(result_actual_signal_count, result_estimated_signal_count):\n",
    "    \"\"\"Get the deviation from the simulated signals vs the expected signals as a list for each BC.\n",
    "        Returns the deviation for each BC as a list of positive numbers\"\"\"\n",
    "    deviation_list = np.abs( np.divide(result_estimated_signal_count, result_actual_signal_count) - 1 )\n",
    "    return deviation_list\n",
    "    \n",
    "def get_total_deviation_from_expected(result_actual_signal_count, result_estimated_signal_count):\n",
    "    \"\"\"Get the total deviation from the total simulated signals vs the expected signals.\n",
    "        Returns both the total deviation as a positive number\"\"\"\n",
    "    total_deviation = abs( result_estimated_signal_count.sum() / result_actual_signal_count.sum() - 1 )\n",
    "    return total_deviation\n",
    "    \n",
    "\n",
    "def get_total_deviation_from_expected_with_simulated_results(number_of_BC, ratio_of_channels_to_sample, signal_to_channel_count_ratio, threshold, signal_mu):\n",
    "    \"\"\"Small helper method to pipe the simulation results into the deviation calculation directly.\"\"\"\n",
    "    result_actual_signal_count, result_estimated_signal_count = simulation_parallel_get_counts(number_of_BC, ratio_of_channels_to_sample, signal_to_channel_count_ratio, threshold, signal_mu)\n",
    "    #result_actual_signal_count, result_estimated_signal_count = simulation_get_counts(number_of_BC, ratio_of_channels_to_sample, signal_to_channel_count_ratio, threshold, signal_mu)\n",
    "    return get_total_deviation_from_expected(result_actual_signal_count, result_estimated_signal_count)\n",
    "    \n",
    "\n",
    "def get_the_best_threshold_and_deviation_in_terms_of_least_deviation(list_of_thresholds_to_try, number_of_BC, ratio_of_channels_to_sample, signal_to_channel_count_ratio, signal_mu):\n",
    "    \"\"\"Simulates for each threshold provided in list, tests which threshold has the least deviation in computed vs expected.\n",
    "        and returns the best threshold it has found, also returns the deviation.\"\"\"\n",
    "    # should not contain too large steps.\n",
    "    list_of_thresholds_to_try = list(list_of_thresholds_to_try) # enforce list\n",
    "    # calculate deviation for each simulation for each threshold\n",
    "    deviation_iter = ([\n",
    "        get_total_deviation_from_expected_with_simulated_results(\n",
    "            number_of_BC,\n",
    "            ratio_of_channels_to_sample,\n",
    "            signal_to_channel_count_ratio,\n",
    "            threshold,\n",
    "            signal_mu)\n",
    "        for threshold in list_of_thresholds_to_try])\n",
    "    deviations = np.fromiter(deviation_iter, dtype=np.float, count=len(list_of_thresholds_to_try))\n",
    "    \n",
    "    # Blur the deviations,  assumes deviations follow a smooth curve.\n",
    "    # The actuall minimum should not be discarded because of a random deviation, therefore blur.\n",
    "    size = 5  # default is 3,  might want to change to 3\n",
    "    deviations_blur = uniform_filter(deviations, size=size)#[1:-1] # nah no need to slice, the boundary error doesn't bother us\n",
    "    \n",
    "    # get the minimum\n",
    "    index = np.argmin(deviations_blur)\n",
    "    threshold = list_of_thresholds_to_try[index]\n",
    "    deviation = deviations[index]\n",
    "    \n",
    "    return threshold, deviation\n",
    "\n",
    "def get_the_best_threshold_in_terms_of_least_deviation(list_of_thresholds_to_try, number_of_BC, ratio_of_channels_to_sample, signal_to_channel_count_ratio, signal_mu):\n",
    "    \"\"\"Same as above, except it only returns the threshold\"\"\"\n",
    "    threshold, deviation = get_the_best_threshold_and_deviation_in_terms_of_least_deviation(list_of_thresholds_to_try, number_of_BC, ratio_of_channels_to_sample, signal_to_channel_count_ratio, signal_mu)\n",
    "    return threshold\n",
    "\n",
    "\n",
    "def caluclate_SB(expected_signal_voltage, noise_sigma):\n",
    "    \"\"\"Formula for calculating S/B\"\"\"\n",
    "    return expected_signal_voltage / noise_sigma\n",
    "\n",
    "def calculate_expected_signal_voltage(signal_mu):\n",
    "    \"\"\"Some method to calculate the expected signal voltage for provided signal_mu and sigma\"\"\"\n",
    "    \n",
    "    # INTEGRATION METHOD:  (not used)\n",
    "        # Use the definition:  ∫(x*f(x))dx\n",
    "    \"\"\"\n",
    "        signal_sigma = signal_mu/4  # get_signal_sigma_for_mu(signal_mu)\n",
    "        low = 0  # There are no particles hitting the detector with negative energies.\n",
    "        high = 500\n",
    "        fSignalEnergy = ROOT.TF1(\"Signal\", \"TMath::Landau(x, %f, %f)*x\" % (signal_mu, signal_sigma), low, high)\n",
    "        scale = 1  # 0.001  # mili, no, sigma is also in mV so it doesn't matter\n",
    "        return fSignalEnergy.Integral(low, high) * scale\n",
    "    \"\"\"\n",
    "    # ASSUME MU IS THE EXPECTED VALUE:  (currently used)\n",
    "    return signal_mu\n",
    "\n",
    "def calculate_list_of_SB_from_list_of_signal_mu(noise_sigma, iterator_mu, steps):\n",
    "    \"\"\"Returns a list of calculated S/B for a list of signal mu.\"\"\"\n",
    "    return np.fromiter(\n",
    "                map(lambda signal_mu : caluclate_SB(\n",
    "                        calculate_expected_signal_voltage(signal_mu),\n",
    "                        noise_sigma) ,\n",
    "                    iterator_mu)\n",
    "             , dtype=np.float, count=steps)\n",
    "\n",
    "def compute_list_of_least_deviation_from_list_of_signal_mu(number_of_BC, ratio_of_channels_to_sample, signal_to_channel_count_ratio, linspace_data_thresholds, linspace_data_signal_mu, number_of_mu_steps):\n",
    "    \"\"\"It will try a lot of thresholds provided for each signal_mu provided,\n",
    "        and get the best result from the threasholds and put that least deviation result in a list for each signal mu.\"\"\"\n",
    "    return np.fromiter(\n",
    "                 map(lambda signal_mu :\n",
    "                         get_the_best_threshold_and_deviation_in_terms_of_least_deviation(\n",
    "                             linspace(*linspace_data_thresholds),  # list_of_thresholds_to_try\n",
    "                             number_of_BC,\n",
    "                             ratio_of_channels_to_sample,\n",
    "                             signal_to_channel_count_ratio,\n",
    "                             signal_mu)[1] ,  # deviation is at index 1\n",
    "                         linspace(*linspace_data_signal_mu))\n",
    "                 , dtype=np.float, count=number_of_mu_steps)\n",
    "\n",
    "def compute_list_of_best_thresholds_from_list_of_signal_mu(number_of_BC, ratio_of_channels_to_sample, signal_to_channel_count_ratio, linspace_data_thresholds, linspace_data_signal_mu, number_of_mu_steps):\n",
    "    \"\"\"It will try a lot of thresholds provided for each signal_mu provided,\n",
    "        and get the best result threasholds from the least deviation,\n",
    "        and put that threasholds in a list for each signal mu.\"\"\"\n",
    "    return np.fromiter(\n",
    "                 map(lambda signal_mu :\n",
    "                         get_the_best_threshold_in_terms_of_least_deviation(\n",
    "                             linspace(*linspace_data_thresholds),  # list_of_thresholds_to_try\n",
    "                             number_of_BC,\n",
    "                             ratio_of_channels_to_sample,\n",
    "                             signal_to_channel_count_ratio,\n",
    "                             signal_mu) ,  \n",
    "                         linspace(*linspace_data_signal_mu))\n",
    "                 , dtype=np.float, count=number_of_mu_steps)\n",
    "\n",
    "\n",
    "\n",
    "# -End of simulation code-\n",
    "\n",
    "#==============================================================================\n",
    "\n",
    "### Code for the plots:\n",
    "\n",
    "def plot_deviation_vs_SB():\n",
    "    \"\"\"Plots deviation vs S/B. See settings below to calibrate the simulation\"\"\"\n",
    "    ## Simulator Settings:\n",
    "    ratio_of_channels_to_sample = 1.0  # scale of simulation,   0.001 = small fast,   1.0 = full scale slow.\n",
    "    number_of_BC = mp.cpu_count() * 4# * 120\n",
    "    \n",
    "    signal_to_channel_count_ratio = get_signal_to_channel_count_ratio()\n",
    "    noise_sigma = 5  #mv\n",
    "    \n",
    "    min_signal_mu = 8  #mv  # cannot be below 0\n",
    "    max_signal_mu = 35 #mv\n",
    "    steps_signal_mu = (max_signal_mu - min_signal_mu) * 2   # resolution\n",
    "    #steps_signal_mu = 20\n",
    "    \n",
    "    min_threshold = 3  #mv  # cannot be below 0\n",
    "    max_threshold = 80 #mv\n",
    "    steps_threshold = (max_threshold - min_threshold) * 2   # resolution\n",
    "\n",
    "    ## Simulate, get data:\n",
    "    #signal_mu_list = list(linspace(min_signal_mu, max_signal_mu, steps_signal_mu)) # can be used to plot\n",
    "    SB = calculate_list_of_SB_from_list_of_signal_mu(\n",
    "            noise_sigma,\n",
    "            linspace(min_signal_mu, max_signal_mu, steps_signal_mu),\n",
    "            steps_signal_mu\n",
    "        )\n",
    "    \n",
    "    linspace_data_signal_mu = (min_signal_mu, max_signal_mu, steps_signal_mu)\n",
    "    linspace_data_thresholds = (min_threshold, max_threshold, steps_threshold)\n",
    "    \n",
    "    deviations = compute_list_of_least_deviation_from_list_of_signal_mu(\n",
    "            number_of_BC,\n",
    "            ratio_of_channels_to_sample,\n",
    "            signal_to_channel_count_ratio,\n",
    "            linspace_data_thresholds,\n",
    "            linspace_data_signal_mu, \n",
    "            steps_signal_mu\n",
    "        )\n",
    "    runs = 10\n",
    "    for _ in range(runs-1):\n",
    "        deviations += compute_list_of_least_deviation_from_list_of_signal_mu(\n",
    "            number_of_BC,\n",
    "            ratio_of_channels_to_sample,\n",
    "            signal_to_channel_count_ratio,\n",
    "            linspace_data_thresholds,\n",
    "            linspace_data_signal_mu, \n",
    "            steps_signal_mu\n",
    "        )\n",
    "    deviations = np.divide(deviations, runs)\n",
    "    \n",
    "    #deviations_log = np.log(deviations)\n",
    "    \n",
    "    # print data\n",
    "    print(deviations)\n",
    "    ## Plot:\n",
    "    x_list = SB\n",
    "    y_list = deviations\n",
    "    title = \"Deviations vs SNR\"\n",
    "    prefix_filename = \"Deviations_vs_SB_with_BC\" + str(number_of_BC)\n",
    "    xlabel = \"SNR\"\n",
    "    ylabel = \"Deviations\"\n",
    "    make_integer_axis = False\n",
    "    make_margin = False\n",
    "    plot_the_data(title, prefix_filename, xlabel, ylabel, make_integer_axis, make_margin, x_list, y_list)\n",
    "    \n",
    "\n",
    "def plot3D_threshold_and_SB_vs_deviation():\n",
    "    \"\"\"Creates a 3D plot of threshold and S/B vs deviaiton\"\"\"\n",
    "    ## Simulator Settings:\n",
    "    ratio_of_channels_to_sample = 0.01  # scale of simulation,   0.001 = small fast,   1.0 = full scale slow.\n",
    "    number_of_BC = mp.cpu_count() * 1\n",
    "    \n",
    "    signal_to_channel_count_ratio = get_signal_to_channel_count_ratio()\n",
    "    noise_sigma = 5  #mv\n",
    "    \n",
    "    min_signal_mu = 15  #mv  # cannot be below 0\n",
    "    max_signal_mu = 40 #mv\n",
    "    steps_signal_mu = (max_signal_mu - min_signal_mu) * 1   # resolution\n",
    "    \n",
    "    min_threshold = 10  #mv  # cannot be below 0\n",
    "    max_threshold = 80 #mv\n",
    "    steps_threshold = (max_threshold - min_threshold) * 1   # resolution\n",
    "\n",
    "    canvas = ROOT.TCanvas(\"c\",\"Graph2D example\",0,0,600,400)\n",
    "    plot_threshold_SB_deviation = ROOT.TGraph2D()\n",
    "    point_index = 0\n",
    "    ## Simulate, get data:\n",
    "    for loop_signal_mu in linspace(min_signal_mu, max_signal_mu, steps_signal_mu):\n",
    "        for loop_treshold in linspace(min_threshold, max_threshold, steps_threshold):\n",
    "            \n",
    "            deviation = get_total_deviation_from_expected_with_simulated_results(\n",
    "                            number_of_BC,\n",
    "                            ratio_of_channels_to_sample,\n",
    "                            signal_to_channel_count_ratio,\n",
    "                            loop_treshold,\n",
    "                            loop_signal_mu\n",
    "                        )\n",
    "            SB = caluclate_SB(calculate_expected_signal_voltage(loop_signal_mu), noise_sigma)\n",
    "            \n",
    "            plot_threshold_SB_deviation.SetPoint(point_index, SB, loop_treshold, deviation) # i, x, y, z\n",
    "            point_index += 1\n",
    "    \n",
    "    \n",
    "    plot_threshold_SB_deviation.SetTitle(\"Graph title; X axis title; Y axis title; Z axis title\");\n",
    "    plot_threshold_SB_deviation.Draw(\"surf1\")\n",
    "    canvas.Draw()\n",
    "    print(\"done\")\n",
    "\n",
    "    \n",
    "def plot_particle_intensity_mu_vs_best_threshold():    \n",
    "    ## Simulator Settings:\n",
    "    ratio_of_channels_to_sample = 1.0  # scale of simulation,   0.001 = small fast,   1.0 = full scale slow.\n",
    "    number_of_BC = mp.cpu_count() * 8\n",
    "    \n",
    "    signal_mu = 50 # mv  # might want to change this\n",
    "    \n",
    "    min_threshold = 2  #mv  # cannot be below 0\n",
    "    max_threshold = 80 #mv\n",
    "    steps_threshold = (max_threshold - min_threshold) * 1   # resolution\n",
    "    \n",
    "    # important setting for this simulation\n",
    "    min_intensity_mu = 0.008\n",
    "    max_intensity_mu = 0.015\n",
    "    steps_intensity_mu = (15-8)*3\n",
    "    \n",
    "    intensity_mu_list = list(linspace(min_intensity_mu, max_intensity_mu, steps_intensity_mu))\n",
    "    threshold_list = np.zeros(len(intensity_mu_list))\n",
    "    \n",
    "    ## Simulate, get data:\n",
    "    for index, collisions_per_BC in enumerate(intensity_mu_list):\n",
    "        signal_to_channel_count_ratio = get_signal_to_channel_count_ratio(collisions_per_BC=collisions_per_BC)\n",
    "        \n",
    "        threshold, deviation = get_the_best_threshold_and_deviation_in_terms_of_least_deviation(\n",
    "                        linspace(min_threshold, max_threshold, steps_threshold), #list_of_thresholds_to_try,\n",
    "                        number_of_BC,\n",
    "                        ratio_of_channels_to_sample,\n",
    "                        signal_to_channel_count_ratio,\n",
    "                        signal_mu\n",
    "                    )\n",
    "        threshold_list[index] = threshold\n",
    "    \n",
    "    # print result in list form\n",
    "    print(threshold_list)\n",
    "    \n",
    "    ## Plot:\n",
    "    x_list = intensity_mu_list\n",
    "    y_list = threshold_list\n",
    "    title = \"threshold vs intensity_mu\"\n",
    "    prefix_filename = \"threshold_vs_intensity_mu_with_BC\" + str(number_of_BC)\n",
    "    xlabel = \"intensity_mu\"\n",
    "    ylabel = \"threshold\"\n",
    "    make_integer_axis = True\n",
    "    make_margin = False\n",
    "    plot_the_data(title, prefix_filename, xlabel, ylabel, make_integer_axis, make_margin, x_list, y_list)\n",
    "    \n",
    "\n",
    "def plot_signal_mu_vs_best_threshold():\n",
    "    ## Simulator Settings:\n",
    "    ratio_of_channels_to_sample = 1.0  # scale of simulation,   0.001 = small fast,   1.0 = full scale slow.\n",
    "    number_of_BC = mp.cpu_count() * 4\n",
    "    \n",
    "    signal_to_channel_count_ratio = get_signal_to_channel_count_ratio()\n",
    "    \n",
    "    noise_sigma = 5  #mv\n",
    "    \n",
    "    min_threshold = 2  #mv  # cannot be below 0\n",
    "    max_threshold = 80 #mv\n",
    "    steps_threshold = (max_threshold - min_threshold) * 1   # resolution\n",
    "    \n",
    "    min_signal_mu = 12  #mv  # cannot be below 0\n",
    "    max_signal_mu = 40 #mv\n",
    "    steps_signal_mu = (max_signal_mu - min_signal_mu) * 2   # resolution\n",
    "    \n",
    "    linspace_data_thresholds = (min_threshold, max_threshold, steps_threshold)\n",
    "    linspace_data_signal_mu = (min_signal_mu, max_signal_mu, steps_signal_mu)\n",
    "    \n",
    "    ## Simulate, get data:\n",
    "    signal_mu_list = list(linspace(*linspace_data_signal_mu))\n",
    "    \n",
    "    threshold_list = compute_list_of_best_thresholds_from_list_of_signal_mu(\n",
    "        number_of_BC,\n",
    "        ratio_of_channels_to_sample,\n",
    "        signal_to_channel_count_ratio,\n",
    "        noise_sigma,\n",
    "        linspace_data_thresholds,\n",
    "        linspace_data_signal_mu,\n",
    "        steps_signal_mu\n",
    "    )\n",
    "    \n",
    "    ## Plot:\n",
    "    x_list = signal_mu_list\n",
    "    y_list = threshold_list\n",
    "    title = \"threshold vs signal_mu\"\n",
    "    prefix_filename = \"threshold_vs_signal_mu_with_BC\" + str(number_of_BC)\n",
    "    xlabel = \"signal_mu\"\n",
    "    ylabel = \"threshold\"\n",
    "    make_integer_axis = False\n",
    "    make_margin = False\n",
    "    plot_the_data(title, prefix_filename, xlabel, ylabel, make_integer_axis, make_margin, x_list, y_list)\n",
    "\n",
    "    \n",
    "def plot_deviation_vs_threshold(signal_mu, min_threshold, max_threshold, number_of_thresholds_to_try):\n",
    "    \"\"\"Plots deviation vs threshold for given mu.\"\"\"\n",
    "    ## Simulator Settings:\n",
    "    ratio_of_channels_to_sample = 0.001  # scale of simulation,   0.001 = small fast,   1.0 = full scale slow.\n",
    "    number_of_BC = mp.cpu_count() * 4\n",
    "    \n",
    "    signal_to_channel_count_ratio = get_signal_to_channel_count_ratio()\n",
    "\n",
    "    steps_threshold = number_of_thresholds_to_try  # resolution, number of steps\n",
    "    \n",
    "    linspace_data_thresholds = np.linspace(min_threshold, max_threshold, steps_threshold)\n",
    "    deviation_list = []    # Är append ett ineffektivt sätt att koda på?\n",
    "    \n",
    "    for threshold in linspace_data_thresholds:\n",
    "        deviation_list.append(get_total_deviation_from_expected_with_simulated_results(\n",
    "            number_of_BC, \n",
    "            ratio_of_channels_to_sample, \n",
    "            signal_to_channel_count_ratio, \n",
    "            threshold, \n",
    "            signal_mu\n",
    "        ))\n",
    "    \n",
    "#     print(linspace_data_thresholds, deviation_list)\n",
    "    \n",
    "    ## Plot:\n",
    "    x_list = linspace_data_thresholds\n",
    "    y_list = deviation_list\n",
    "    title = \"deviation vs threshold for mu=\"+str(signal_mu)\n",
    "    prefix_filename = \"deviation_vs_threshold_with_BC\" + str(number_of_BC)+\"_mu\"+str(signal_mu)\n",
    "    xlabel = \"threshold\"\n",
    "    ylabel = \"deviation\"\n",
    "    make_integer_axis = True\n",
    "    make_margin = False\n",
    "    plot_the_data(title, prefix_filename, xlabel, ylabel, make_integer_axis, make_margin, x_list, y_list)\n",
    "    \n",
    "\n",
    "def plot_the_data(title, prefix_filename, xlabel, ylabel, make_integer_axis, make_margin, x_list, y_list):\n",
    "    timestr = time.strftime(\"%Y%m%d-%H%M%S\")\n",
    "    FILENAME = prefix_filename + \"_(\" + timestr + \").pdf\"\n",
    "    \n",
    "    fig = plt.figure()\n",
    "    plt.title(title)\n",
    "    plt.xlabel(xlabel)\n",
    "    plt.ylabel(ylabel)\n",
    "    if make_integer_axis:\n",
    "        plt.locator_params(axis=\"both\", integer=True) # integer axis\n",
    "    if make_margin:\n",
    "        plt.margins(y=1)  # add margin to y\n",
    "    \n",
    "    plt.plot(x_list, y_list)\n",
    "    plt.show()\n",
    "    ax = fig.add_subplot(111)\n",
    "    fig.savefig(FILENAME)\n",
    "    #fig.savefig(FILENAME, dpi=200)  # use for png\n",
    "    \n",
    "\n",
    "    \n",
    "# -End of plot code-\n",
    "    \n",
    "#==============================================================================\n",
    "\n",
    "### Helper functions:\n",
    "\n",
    "def eq_div(N, i):\n",
    "    return int([N // i + 1] * (N % i) + [N // i] * (i - N % i))\n",
    "def eq_div_strict(N, i):\n",
    "    return [N // i] * i\n",
    "def np_stats(np_list):\n",
    "    \"\"\"Use a list from e.g. simulaiton_combined_get_counts and get statistics about that list\"\"\"\n",
    "    return np.mean(np_list), np.var(np_list), np.std(np_list)\n",
    "def print_count_statistics(np_list):\n",
    "    \"\"\"Use a list from e.g. simulaiton_combined_get_counts and get statistics about that list\"\"\"\n",
    "    mean, variance, standard_deviation = np_stats(np_list)\n",
    "    print(\"mean:\", mean)\n",
    "    print(\"variance:\", variance)\n",
    "    print(\"standard_deviation:\", standard_deviation)\n",
    "def get_signal_sigma_for_mu(signal_mu):\n",
    "    \"\"\"Using references from the short paper, to calculate sigma\"\"\"\n",
    "    reference_singal_mu = 100  # from s.15  (at threshold 40)\n",
    "    reference_signal_sigma = 25  #mv  25 from reference for signal_mu = 100 (s.24)\n",
    "    minimum = 0.01\n",
    "    signal_sigma = minimum + reference_signal_sigma * (signal_mu/reference_singal_mu) \n",
    "    return signal_sigma\n",
    "def get_signal_to_channel_count_ratio(collisions_per_BC = 50, particles_per_collision = 500, ratio_of_particles_reaching_HGTD=0.1):\n",
    "    \"\"\"Determines how many signals there will be,\n",
    "        based from  collisions_per_BC,  particles_per_collision,  ratio_of_particles_reaching_HGTD\"\"\"\n",
    "    #collisions_per_BC = 50\n",
    "    #particles_per_collision = 500\n",
    "    #ratio_of_particles_reaching_HGTD = 0.1\n",
    "    signal_to_channel_count_ratio = collisions_per_BC * particles_per_collision * ratio_of_particles_reaching_HGTD / C_total_channels\n",
    "    return signal_to_channel_count_ratio\n",
    "def get_number_of_channel_readouts(ratio_of_channels_to_sample):\n",
    "    \"\"\"Returns the number of channels to read from - used to downscale simulation\"\"\"\n",
    "    return int(C_total_channels * ratio_of_channels_to_sample)\n",
    "\n",
    "def linspace(start, end, steps):\n",
    "    scale = (end-start)/(steps)\n",
    "    return map(lambda x : start + x*scale, range(steps)) # does not include the last value, since steps = length\n",
    "\n",
    "\n",
    "# -End of helper functions-\n",
    "\n",
    "#==============================================================================\n",
    "\n",
    "###  Main code - what to run, what to plot, what do calculate\n",
    "\n",
    "def main():\n",
    "    # code... what to plot, what do calculate, ...\n",
    "    \n",
    "#     plot_deviation_vs_SB()\n",
    "#     plot3D_threshold_and_SB_vs_deviation()\n",
    "#     plot_particle_intensity_mu_vs_best_threshold()\n",
    "#     plot_signal_mu_vs_best_threshold()\n",
    "    plot_deviation_vs_threshold(0.01,0,0.03,100)\n",
    "    \n",
    "    # -code end-\n",
    "    return\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "### Not important to understand ... it's just a startup script, see main() above instead.\n",
    "if __name__ == '__main__':\n",
    "    mp.freeze_support()\n",
    "    \n",
    "    # profiles to determine compute resources\n",
    "    profiles = {\"normal\": 2, \"fast\": 4, \"fastest\": 99}\n",
    "    max_processes = profiles[\"fastest\"]  # edit this\n",
    "    \n",
    "    # setup pool\n",
    "    nprocs = min(mp.cpu_count(), max_processes)\n",
    "    pool = mp.Pool(processes=nprocs)\n",
    "    \n",
    "    global_counter = 0\n",
    "    \n",
    "    # run code\n",
    "    t0 = time.time()\n",
    "    main()\n",
    "    t1 = time.time()\n",
    "    print(\"Simulation took\", round(t1-t0, 1), \"seconds\") # real time not the actuall process_time()\n",
    "    \n",
    "    # clean up\n",
    "    pool.close()\n",
    "    pool.join()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "====================================================\n",
    "\n",
    "# Notes\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "====================================================\n",
    "\n",
    "\n",
    "<h1>Testing</h1>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(signal_count):\n",
    "            if prng.Landau(expected_voltage, expected_voltage/4) > threshold: # 1/4 is just the refernce 25/100\n",
    "                above_threshold_count += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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