Kinematics/Kinematics 64Ni(p,d).ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numpy import *\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [],
   "source": [
    "class StoppingPowerFile:\n",
    "    def __init__(self, filename):\n",
    "        \"\"\"\n",
    "filename: Name of file containing stopping power as a function of energy.\n",
    "Assuming that the first column is energy, second is stopping power.\n",
    "        \"\"\"\n",
    "        infile = open(filename, 'r')\n",
    "        lines = infile.readlines()\n",
    "        infile.close()\n",
    "        data = []\n",
    "        for line in lines: data.append(line.split())\n",
    "\n",
    "        self.x = array([float(data[i][0]) for i in range(len(data))])\n",
    "        self.y = array([float(data[i][1]) for i in range(len(data))])\n",
    "        \n",
    "    def __call__(self, E, factor):\n",
    "        # Interpolates between the points and calculates at energy E.\n",
    "        return factor*interp(E, self.x, self.y, left=1e16, right=self.y[-1])\n",
    "    def Loss(self, E, width, n):\n",
    "        \"\"\"\n",
    "Function to calculate the energy loss experienced by a particle\n",
    "traveling through the material with stopping power extracted from\n",
    "the input file.\n",
    "E: Initial energy of the particle.\n",
    "width: The width of the material.\n",
    "n: Number of point to use in the RK4 algorithm.\n",
    "        \"\"\"\n",
    "        Eafter = 0\n",
    "        try:\n",
    "            if width == 0: return copy(E)\n",
    "\n",
    "            # Making sure we do not overwrite E!\n",
    "            Eafter = copy(E)\n",
    "        except:\n",
    "            if width == 0: return E\n",
    "            \n",
    "            # Making sure we do not owerwrite\n",
    "            Eafter = E\n",
    "        \n",
    "        # Step size.\n",
    "        dx = width/float(n-1)\n",
    "\n",
    "        # Solving the energy loss using Runge-Kutta 4.\n",
    "        for i in range(0, n):\n",
    "            R1 = dx*self(Eafter, -1)\n",
    "            R2 = dx*self(Eafter + 0.5*R1, -1)\n",
    "            R3 = dx*self(Eafter + 0.5*R2, -1)\n",
    "            R4 = dx*self(Eafter + R3, -1)\n",
    "            Eafter += (R1 + 2*R2 + 2*R3 + R4)/6.0\n",
    "        # Negative energy is unphysical, setting all negative\n",
    "        # values to zero.\n",
    "        Eafter[Eafter<0] = 0.\n",
    "        return Eafter\n",
    "    \n",
    "    def Gain(self, E, width, n):\n",
    "        \"\"\"\n",
    "Function to calculate the initial energy that a particle would have\n",
    "if it has energy E after moving through a material with some width.\n",
    "E: Energy after the material.\n",
    "width: The width of the material.\n",
    "n: Number of points to be used in the RK4 algorithm.\n",
    "        \"\"\"\n",
    "        \n",
    "        Eafter = 0\n",
    "        try:\n",
    "            if width == 0: return copy(E)\n",
    "\n",
    "            # Making sure we do not overwrite E!\n",
    "            Eafter = copy(E)\n",
    "        except:\n",
    "            if width == 0: return E\n",
    "            \n",
    "            # Making sure we do not owerwrite\n",
    "            Eafter = E\n",
    "\n",
    "            # Step size.\n",
    "        dx = width/float(n-1)\n",
    "\n",
    "        # Solving the energy using Runge-Kutta 4.\n",
    "        for i in range(0, n):\n",
    "            R1 = dx*self(Eafter, +1)\n",
    "            R2 = dx*self(Eafter + 0.5*R1, +1)\n",
    "            R3 = dx*self(Eafter + 0.5*R2, +1)\n",
    "            R4 = dx*self(Eafter + R3, +1)\n",
    "            Eafter += (R1 + 2*R2 + 2*R3 + R4)/6.0\n",
    "\n",
    "        # Negative energy is unphysical, setting all\n",
    "        # negative values to zero.\n",
    "        try:\n",
    "            Eafter[Eafter<0] = 0.\n",
    "        except:\n",
    "            if Eafter < 0 or Eafter != Eafter: Eafter = 0.\n",
    "        return Eafter\n",
    "    def GainGrid(self, E, width, n):\n",
    "        dx = width/float(n-1)        \n",
    "        for i in range(0, n):\n",
    "            R1 = dx*self(E, +1)\n",
    "            R2 = dx*self(E + 0.5*R1, +1)\n",
    "            R3 = dx*self(E + 0.5*R2, +1)\n",
    "            R4 = dx*self(E + R3, +1)\n",
    "            E += (R1 + 2*R2 + 2*R3 + R4)/6.0\n",
    "        return E\n",
    "    def LossGrid(self, E, width, n):\n",
    "        dx = width/float(n-1)        \n",
    "        for i in range(0, n):\n",
    "            R1 = dx*self(E, -1)\n",
    "            R2 = dx*self(E + 0.5*R1, -1)\n",
    "            R3 = dx*self(E + 0.5*R2, -1)\n",
    "            R4 = dx*self(E + R3, 1)\n",
    "            E += (R1 + 2*R2 + 2*R3 + R4)/6.0\n",
    "        return E\n",
    "    \n",
    "    \n",
    "def Excitation(m1, m2, m3, m4, T2, T3, theta3):\n",
    "    \n",
    "    s = (m1 + m2)**2 + 2*m1*T2\n",
    "    \n",
    "    pcm = sqrt(((s - m1**2 - m2**2)**2 - (2*m1*m2)**2)/(4*s))\n",
    "    \n",
    "    chi = log((pcm + sqrt(m1**2 + pcm**2))/m1)\n",
    "\n",
    "    p3 = sqrt(T3**2 + 2*m3*T3)\n",
    "    \n",
    "    E3cm = sqrt(p3**2 + m3**2)*cosh(chi) - p3*cos(theta3)*sinh(chi)\n",
    "    Ex = sqrt(s - 2*sqrt(s)*E3cm + m3**2) - m4\n",
    "    \n",
    "    return Ex\n",
    "\n",
    "def T3Energy(m1, m2, m3, m4, T2, ex, theta3):\n",
    "    m4eff = m4 + ex\n",
    "    s = (m1 + m2)**2 + 2*m1*T2\n",
    "    \n",
    "    pcm = sqrt(((s - m1**2 - m2**2)**2 - (2*m1*m2)**2)/(4*s))\n",
    "    \n",
    "    chi = log((pcm + sqrt(m1**2 + pcm**2))/m1)\n",
    "\n",
    "    pcmprime = sqrt(((s - m3**2 - m4eff**2)**2 - (2*m3*m4eff)**2)/(4*s))\n",
    "    \n",
    "    E3p = sqrt(pcmprime**2 + m3**2)\n",
    "    p3 = E3p*cos(theta3)*sinh(chi)+sqrt(pcmprime**2 - (m3*sin(theta3)*sinh(chi))**2)\n",
    "    p3 /= (1. + (sin(theta3)*sinh(chi))**2)\n",
    "    \n",
    "    E3lab = sqrt(p3**2 + m3**2)\n",
    "    return E3lab - m3\n",
    "\n",
    "def ScatteringAngle(ringNo, R, innerR, ringPitch, ringWidth):\n",
    "    \n",
    "    # The middle of the ring is at:\n",
    "    rMid = innerR + (ringNo+1)*ringWidth/2.\n",
    "    \n",
    "    # The inner & outer radius of the ring is:\n",
    "    rInn = rMid - ringPitch/2.\n",
    "    rOut = rMid + ringPitch/2.\n",
    "    \n",
    "    # Angles:\n",
    "    \n",
    "    theta = arcsin(rMid/sqrt(R**2 + rMid**2))\n",
    "    thetaInn = arcsin(rInn/sqrt(R**2 + rInn**2))\n",
    "    thetaOut = arcsin(rOut/sqrt(R**2 + rOut**2))\n",
    "    \n",
    "    return theta, thetaInn, thetaOut\n",
    "\n",
    "def ReadStates(filename):\n",
    "    infile = open(filename, \"r\")\n",
    "    lines = infile.readlines()\n",
    "    infile.close()\n",
    "    data = []\n",
    "    for line in lines: data.append(float(line))\n",
    "    return array(data)\n",
    "\n",
    "def SimulateNiPP(Ebeam, Twidth, Fwidth, dEwidth, Ewidth, reactionPoint, ex, theta):\n",
    "    \"\"\"\n",
    "    Ebeam: energy of the incomming beam in MeV\n",
    "    Twidth: Thickness of the target in g/cm2\n",
    "    Fwidth: Thickness of the absorber in um\n",
    "    dEwidth: Thickness of the dE detector in um\n",
    "    Ewidth: Thickness of the E detector in um\n",
    "    reactionPoint: Fraction of target thickness where the reaction will take place.\n",
    "    ex: Array with excitation energy.\n",
    "    theta: Angle of outgoing ion.\n",
    "    \"\"\"\n",
    "    \n",
    "    # Define masses\n",
    "    m1 = 63.9279660*931.494061 # Mass nickel 64\n",
    "    m2 = 1.008*931.494061 # Proton mass\n",
    "    \n",
    "    # Required stopping power\n",
    "    stopTargetP = StoppingPowerFile(\"protonNi.txt\")\n",
    "    stopAbsorberP = StoppingPowerFile(\"SpAl_table_um.txt\")\n",
    "    stopTelescopeP = StoppingPowerFile(\"SpSi_table_um.txt\")\n",
    "    \n",
    "    # First we calculate the point where the interaction will happend.\n",
    "    thick_react = Twidth*reactionPoint # reactionPoint is a number between 0 and 1.\n",
    "    \n",
    "    Ereaction = Ebeam\n",
    "    # Two special cases.\n",
    "    if reactionPoint > 0 and reactionPoint < 1:\n",
    "        Ereaction = stopTargetP.Loss(Ebeam, thick_react, 1001)\n",
    "        Ereaction = T3Energy(m1, m2, m2, m1, Ereaction, ex, theta)\n",
    "        Ereaction = stopTargetP.Loss(Ereaction, (Twidth-thick_react)/cos(theta), 1001)\n",
    "    elif reactionPoint == 1:\n",
    "        Ereaction = stopTargetP.Loss(Ebeam, Twidth, 1001)\n",
    "        Ereaction = T3Energy(m1, m2, m2, m1, Ereaction, ex, theta)\n",
    "    elif reactionPoint == 0:\n",
    "        Ereaction = T3Energy(m1, m2, m2, m1, Ereaction, ex, theta)\n",
    "        Ereaction = stopTargetP.Loss(Ereaction, Twidth/cos(theta), 1001)\n",
    "    else:\n",
    "        print \"Error: reactionPoint is not within range [0, 1]\"\n",
    "        return 0, 0\n",
    "    \n",
    "    EaA = stopAbsorberP.Loss(Ereaction, Fwidth/cos(theta), 1001)\n",
    "    EaDE = stopTelescopeP.Loss(EaA, dEwidth/cos(theta), 1001)\n",
    "    EaE = stopTelescopeP.Loss(EaDE, Ewidth/cos(theta), 1001)\n",
    "    EinDE = EaA - EaDE\n",
    "    EinE = EaDE - EaE\n",
    "    return EinE, EinDE\n",
    "\n",
    "def SimulateNiPD(Ebeam, Twidth, Fwidth, dEwidth, Ewidth, reactionPoint, ex, theta):\n",
    "    \"\"\"\n",
    "    Ebeam: energy of the incomming beam in MeV\n",
    "    Twidth: Thickness of the target in g/cm2\n",
    "    Fwidth: Thickness of the absorber in um\n",
    "    dEwidth: Thickness of the dE detector in um\n",
    "    Ewidth: Thickness of the E detector in um\n",
    "    reactionPoint: Fraction of target thickness where the reaction will take place.\n",
    "    ex: Array with excitation energy.\n",
    "    theta: Angle of outgoing ion.\n",
    "    \"\"\"\n",
    "    \n",
    "    # Define masses\n",
    "    m1 = 63.9279660*931.494061 # Mass nickel 64\n",
    "    m2 = 1.008*931.494061 # Proton mass\n",
    "    m3 = 2.014*931.494061 # Deuteron mass\n",
    "    m4 = 62.9296694*931.494061 # Mass nickel 63\n",
    "    \n",
    "    # Required stopping power\n",
    "    stopTargetP = StoppingPowerFile(\"protonNi.txt\")\n",
    "    stopTargetD = StoppingPowerFile(\"duteronNi.txt\")\n",
    "    stopAbsorberD = StoppingPowerFile(\"SdAl_table_um.txt\")\n",
    "    stopTelescopeD = StoppingPowerFile(\"SdSi_table_um.txt\")\n",
    "    \n",
    "    # First we calculate the point where the interaction will happend.\n",
    "    thick_react = Twidth*reactionPoint # reactionPoint is a number between 0 and 1.\n",
    "    \n",
    "    Ereaction = Ebeam\n",
    "    # Two special cases.\n",
    "    if reactionPoint > 0 and reactionPoint < 1:\n",
    "        Ereaction = stopTargetP.Loss(Ebeam, thick_react, 1001)\n",
    "        Ereaction = T3Energy(m1, m2, m3, m4, Ereaction, ex, theta)\n",
    "        Ereaction = stopTargetD.Loss(Ereaction, (Twidth-thick_react)/cos(theta), 1001)\n",
    "    elif reactionPoint == 1:\n",
    "        Ereaction = stopTargetP.Loss(Ebeam, Twidth, 1001)\n",
    "        Ereaction = T3Energy(m1, m2, m3, m4, Ereaction, ex, theta)\n",
    "    elif reactionPoint == 0:\n",
    "        Ereaction = T3Energy(m1, m2, m3, m4, Ereaction, ex, theta)\n",
    "        Ereaction = stopTargetD.Loss(Ereaction, Twidth/cos(theta), 1001)\n",
    "    else:\n",
    "        print \"Error: reactionPoint is not within range [0, 1]\"\n",
    "        return 0\n",
    "    \n",
    "    EaA = stopAbsorberD.Loss(Ereaction, Fwidth/cos(theta), 1001)\n",
    "    EaDE = stopTelescopeD.Loss(EaA, dEwidth/cos(theta), 1001)\n",
    "    EaE = stopTelescopeD.Loss(EaDE, Ewidth/cos(theta), 1001)\n",
    "    EinDE = EaA - EaDE\n",
    "    EinE = EaDE - EaE\n",
    "    return EinE, EinDE\n",
    "\n",
    "def SimulateNiPT(Ebeam, Twidth, Fwidth, dEwidth, Ewidth, reactionPoint, ex, theta):\n",
    "    \"\"\"\n",
    "    Ebeam: energy of the incomming beam in MeV\n",
    "    Twidth: Thickness of the target in g/cm2\n",
    "    Fwidth: Thickness of the absorber in um\n",
    "    dEwidth: Thickness of the dE detector in um\n",
    "    Ewidth: Thickness of the E detector in um\n",
    "    reactionPoint: Fraction of target thickness where the reaction will take place.\n",
    "    ex: Array with excitation energy.\n",
    "    theta: Angle of outgoing ion.\n",
    "    \"\"\"\n",
    "    \n",
    "    # Define masses\n",
    "    m1 = 63.9279660*931.494061 # Mass nickel 64\n",
    "    m2 = 1.008*931.494061 # Proton mass\n",
    "    m3 = 3.0160492*931.494061 # Deuteron mass\n",
    "    m4 = 61.9283451*931.494061 # Mass nickel 63\n",
    "    \n",
    "    # Required stopping power\n",
    "    stopTargetP = StoppingPowerFile(\"protonNi.txt\")\n",
    "    stopTargetT = StoppingPowerFile(\"tritonNi.txt\")\n",
    "    stopAbsorberT = StoppingPowerFile(\"StAl_table_um.txt\")\n",
    "    stopTelescopeT = StoppingPowerFile(\"StSi_table_um.txt\")\n",
    "    \n",
    "    # First we calculate the point where the interaction will happend.\n",
    "    thick_react = Twidth*reactionPoint # reactionPoint is a number between 0 and 1.\n",
    "    \n",
    "    Ereaction = Ebeam\n",
    "    # Two special cases.\n",
    "    if reactionPoint > 0 and reactionPoint < 1:\n",
    "        Ereaction = stopTargetP.Loss(Ebeam, thick_react, 1001)\n",
    "        Ereaction = T3Energy(m1, m2, m3, m4, Ereaction, ex, theta)\n",
    "        Ereaction = stopTargetT.Loss(Ereaction, (Twidth-thick_react)/cos(theta), 1001)\n",
    "    elif reactionPoint == 1:\n",
    "        Ereaction = stopTargetP.Loss(Ebeam, Twidth, 1001)\n",
    "        Ereaction = T3Energy(m1, m2, m3, m4, Ereaction, ex, theta)\n",
    "    elif reactionPoint == 0:\n",
    "        Ereaction = T3Energy(m1, m2, m3, m4, Ereaction, ex, theta)\n",
    "        Ereaction = stopTargetT.Loss(Ereaction, Twidth/cos(theta), 1001)\n",
    "    else:\n",
    "        print \"Error: reactionPoint is not within range [0, 1]\"\n",
    "        return 0\n",
    "    \n",
    "    EaA = stopAbsorberT.Loss(Ereaction, Fwidth/cos(theta), 1001)\n",
    "    EaDE = stopTelescopeT.Loss(EaA, dEwidth/cos(theta), 1001)\n",
    "    EaE = stopTelescopeT.Loss(EaDE, Ewidth/cos(theta), 1001)\n",
    "    EinDE = EaA - EaDE\n",
    "    EinE = EaDE - EaE\n",
    "    return EinE, EinDE"
   ]
  },
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   "outputs": [
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qEqJrkCD3AFsLt3LPqns4UnWEO0bewYxBMzxmVMvJvnnjVTYvX9KhY6V1LkTzJMg9RHl9OX/74W98e/BbxiaM5fGzHic2MNbosjqks90tclFUiBNJkHsQrTWfZn3KP9b/A39vfx4+82GPmnirOTvWrGTpq881O7NiW6TLRQgrGbXiQZRSXNHvCj6a+hEJQQnMWTmHR9Y+QnVDtdGlddjAcedy4aw7UV7t/zjlbN3MvKsultv+hegEaZEbqMHSwMubXuatrW/RI7QHT539FIOiBhldVoftWLOSr//9IpaGhg6fQ/rQRXclXSsebn3+ev7y/V8orinm1hG3cv2g6/H2anPxJrclgS5E+0mQdwFldWU8uvZRlh1YxtDooTx21mOkhaUZXVandGZ0yzES6KK7kCDvIrTWfL3/ax5f9zg1DTXcPvJ2rhl4DSYvk9GldYojAl2ZTFz45zkyykV0WRLkXUxhTSGPrH2E73K+Y0TsCB77zWP0CO1hdFmd5ohAl1EuoquSIO+CtNZ8ufdLnlz/JA2WBuaMmsPVA6722JuImvr4sYfI2bq5U+eQceiiq5Eg78KOVB3h4bUP833u94yKG8XcsXPpFdbL6LIcwhEXRUH60UXX4PQgV0qFA28Ag7Gu1Huj1nptS/tLkDuW1prP93zOMxueodZcy8yhM7lp8E34mHyMLs0hJNCFcE2QvwOs0Vq/oZTyBQK11qUt7S9B7hyFNYU8vf5pvtr/FX3C+zB37FyPneu8OTvWrOSrfz1Po8XSqfNIoAtP5NQgV0qFAZuANG1nP4wEuXOtPrSax356jCNVR7iq/1XcMfIOgn2DjS7LYRxxURQk0IVncXaQDwfmA9uBYcBG4A6tddVJ+80EZgKkpqaOOnDgQEfqEXaqaqjipV9e4v0d7xMTGMNDpz/EhNQJRpflUI7qckEpptx6l1wYFW7N2UE+GvgJ+I3Wep1S6gWgXGv9fy0dIy1y18ksyOThtQ+TVZLFOcnncP9p95MSkmJ0WQ7V2ZkWm5Lx6MJdOTvI44GftNY9bT+PAx7QWl/U0jES5K7V0NjA+zve59VNr2JuNHPTkJu4cfCN+Hv7G12aw0m3i+iqXHGxcw3wR631LqXUw0CQ1vrelvaXIDfGkaojzNs4j6X7lpIUnMQDpz3A+JTxRpflFI7qdpEbjIS7cEWQD8c6/NAX2AvcoLUuaWl/CXJjrc9fz9/X/Z3ssmzOTj6bB8Y8QEpo1+puOWbHmpUsf+MVGmprO3Ue6XIRRpMbgsQpTu5uuX7w9dw0+CYCfQKNLs1pHHHHKEBIdAzjps+QUBcuJUEuWnS0+ijPbniWpfuWEhMQw20jbuOS3pd4/ERcLXHUWPRjIpNTuGHevxxyLiFaI0Eu2rTp6Cae2fAMmQWZDIgcwH1j7mNM/Bijy3K6t+7+M8WHcjp3Ehm+KFxAglzYRWvN0n1LeT7jefKr8pmQMoG7Rt/VJWZWbI0jhy+C9KcL55AgF+1Sa67lve3v8caWN6hvrOfqAVdzy9BbCPMLM7o0p3NUPzpIt4twLAly0SGFNYW8/MvLLMxaSIhvCDcNuYmrB1xNgHeA0aU5nSMDHZDuF9FpEuSiU3YV7+KFjBdYk7uG2IBY/jT8T1zW5zKPXje0vRwV7FNm3y1hLjpEglw4xIbDG3gh4wU2FWyiZ2hPZo+YzaQek7rEYhb2cNRdoyiFydcXS309IVHRMpRR2EWCXDiM1ppVh1bxQsYL7CndQ3pUOneMvIMzE880ujSX2rFmJWs+fJeKwoJOn8vb14/JM2dLmItWSZB3QkVtAyH+XWOBBkeyNFr4377/8covr5BXlcdp8acxa/gsRsWNMro0l3PEEMaQ6BhmvvKWgyoSXZEEeQdtzillxoL1/P2yIVw0NMHoctxSvaWeT3Z/wuuZr1NUW8Tp8afz5+F/7naB7rApdZuQdUdFUxLkHVRcVc/Mdzew4UAJ918wgD+dk4ZSyuiy3FKNuYZPd3/Km1vetAZ6wunMGjaLkXEjjS7N5RzWl96EzMYoJMg7obbBwr2fZrJ4cx5XjErm8csG4+fdNW9fd4Qacw2f7PqEBVsXdPtAd2Q/+slkvpfuR4K8kxobNc99s5uXVuxhdI8IXrt2FNHBfkaX5dZOCfT407l56M2cFn9at/yr5ps3XiXz26/QjY2njFrpTNBL90v3IUHuIIs353HPJ5uJDvbj9RmjSU8MNbokt3cs0N/a9haFNYUMiR7CTUNu4tyUc7vNsMW2zLvq4k4dL6NeugcJcgfKPFTKze9uoLzGzHNXDeeCwfFGl+QR6ix1/HfPf3lr61scqjxE77De3DjkRi7sdSE+Xt17VJAjbjZSXl5orWVcehfmioUl9gMVgAUwt/VinhzkAEfKa5n53kY255Ry16R+3DahT7fsLugIc6OZZfuX8ebWN9ldspvEoESuG3Qdl/W9rFvc+t8SR04JIC30rslVQT5aa11oz0k9PcjBehH0gc8y+XxTHpPT43j2ymGEynhzu2mtWZO7hje2vMEvR38h0j+S3w/4PVf2v5II/wijyzNcZ0e+BEVE86fX3nZcQcJwEuROorXmze/38eTSnaREBPDataMYEC/95u2VcSSDN7a8wZrcNfiZ/Lik9yVck34NaWFpRpdmuM4EesLAv5I2PIa0ETHEpIbIX40ezhVBvg8oATTwb631/Gb2mQnMBEhNTR114MCBjtTjltbvK+bW9zOoqG3gyWlDuGxEstEleaTs0mze2/4ei7MXU99Yz1lJZzEjfQZnJJwhIcSJwxmVlxe6sfH495P5B0eSNHgOeVll6EZNcIQfvYbHkDY8hsQ+Yez6cdUJc7DL6Bf354ogT9Ja5yqlYoHlwG1a69Ut7d9VWuRNHa2oZfb7v7B+XzHXntGDv148UMabd1BxbTEf7/qYD3d+SFFtEX0j+nLtwGu5KO0ifE2+RpfnVnasWcmy+S9jrq87vq1pH3ltZQP7MgvZu6mAnB3FWBoaUeymtnQpWp+43J0siOHeXDpqRSn1MFCptX62pX26YpADNFgaeebrXcxfvZehyWG8OH0EPaODjC7LY9Vb6lmybwnvbX+P3SW7ifSP5Mr+V/K7vr8jLijO6PLcxvGWelFhq6NWGuosHNxexP+ev4uG2tJmz3XsRiN7zidcy6lBrpQKAry01hW2x8uBR7XWX7V0TFcN8mO+3naY+z7NxGxp5InLhvDbEUlGl+TRtNasO7yO97a/x5pDa/BSXkxIncD0/tMZEz9Gul3aad70qdDK/9deJh8aLb/OGSOjYNyDs4M8DVhk+9EbeF9r/URrx3T1IAfILa3hjg9+YcOBEi4fmcyjlw4iyK/7LMTgLDkVOXyy6xMW7llIWV0ZvcN6c9WAq5iaNpVg32Cjy/MI82+9oZW7SRXWS10nCo6K4ZZXZXZGI8kNQQYxWxp58dssXlq5h15RQbx49QgGJ3X9dS9dodZcy9f7v+bDnR+ytWgrgd6BTO09lav6X0XfiL5Gl+fWdqxZyVevvUCj2XzCdmUyoS2WFo6CnqMeocfgKFIHRRKTEoLykr+EXEmC3GA/Zhdy50ebKKlq4O7J/fjjuDRM8j+Bw2wt3MoHOz/gq31fUd9Yz8jYkfyu3++Y2GNit77JqDU71qxsdtRKS5N8+QVFENvndgoOWvf3D/YhZWAkqemRpKRHEhQmcw85mwS5GyiuqueBzzJZtv0IY3pGMO+K4aRGBRpdVpdSWlvKoj2L+HT3pxysOEiwTzAXpV3EtL7TSI9KN7o8j9DWKJjq8npydhRzcHsROduLqamw9qVHJQVbQ31QJIm9wzH5eJ1wTrl42nkS5G5Ca83CjFwe/mIbFq35v4vTmT4mRS7WOZjWmg1HNrAwayHLDyynzlLHgMgBTOs7jSm9phDmJ91brbE3eHWjpvBQ5fFQz88uo9Gi8fb1IqlfBCnpkTRUb+OHj15v8ReDsJ8EuZvJLa3hvk8388OeIs7tH8PTlw8lNtTf6LK6pPL6cpbsXcJnWZ+xs3gnfiY/JvaYyOV9L2d03Gj5JepA9bVm8naXcnC7tcVedrSG2rLXobHilH1labv2kyB3Q42NmnfX7uepr3bi72Ni7tR0fjs8SYLFibYXbWdh1kKW7F1CRUMFScFJTO09lalpU0kNTTW6vC6nvLCG12+9osXnL71vAUn9wwkIlpu87CFB7sayCyq555PN/HKwlPH9Y3j8t4NJjpC+c2eqMdfwzYFv+CL7C9blr0OjGRYzjEt6X8L5Pc+XrhcHammoo/IKxS/sjwBEJQeT3D+C5P4RJPYNxzdAhuk2R4LczVkaNe+t3c8/vt4FwL3n92fG2J4yssUFDlcdZsm+JSzOXsye0j34ePlwTvI5TO09lXFJ4/AxyYyWndHSxdOJf7yVqJRRHNpVQu6uEvKzy6zTB3gpYnuEWEO9XzjxaWH4+kuwgwS5xzhUUs1Di7ayancBI1LDefryofSLCzG6rG5Ba83O4p18kf0FS/Ytobi2mHC/cC7oeQEXpV3EsJhhKKUoW7yYo889jzk/H++EBGLvnEPY1KlGl+/W7Ll4am6wcHhvObm7Sji0s4Sj+8tpbNQoL0VMSjCJfcNJ7BtOQp9w/IO65y9XCXIPorXmv5vyeGTxNirrzPx5fB9mje+Nv49MwOUqDY0NrM1by+Lsxaw4uIL6xnoSghK4IbcPwxb8gKqrP/GAgACorZVgd6D6WjNH9paTt6eUvKxSjuwrx2K2zvIYlRREYp9wEmzhfmwMe1cf5ihB7oGKKut47MvtfL4pj5TIAOZePIiJ6TJRlKtV1leyMmclX+3/iqv+soKY8jYOUIrw6VeRMHeuS+rrLswNFo7uryAvq5S8PaXkZ5dhrrPehRoWG4B/wF4Obf0Mi/nXX7JdbZijBLkH+zG7kLn/3UbW0UrOGxDL3KmD5EYig+wYmN7qZFOnMJnAYsE7MVFa6g5msTRSeLDyeLDv+v4ptOXU37JdaZhjZ4Jcljk32Jm9o1lyxzgemjKQn/YWMfG5VTy3fDe1DS3PiSGcwzshoX0H2OYtMeflkXfvfew8Yyxlixc7obLux2TyIq5XKCMmp3LRrKFoy6lj1QEqiuxatKzLkyB3Az4mL24+O41v7x7P+YPieeHbLCY9t4qvtx3GGX8xiebF3jkHOjHOX5eWknfvfewYMJCsCedJqDtQSHR089ujmt/e3UiQu5H4MH9eunoE7998Ov7eJm55byNXzf+JLYfKjC6tWwibOpXw6Vc55FzmvDzyH3yInWeMZcfAdAn2Tho3fQbevidO3OXt68e46TMMqsi9SB+5mzJbGvng5xyeX76boqp6po1I4t4L+pMQJrP9OVvTIYgqIABdXe2wc6vwcBIeelD60ztARq20cqy9Qa6UMgEbgFyt9cWt7StB7jjltQ28ujKbBT/sw0vBzHFp3HJOb1nEwoWOB3tenkPOp3x8ICgIXVoqF0zFca4K8ruA0UCoBLnr5RRX84+vd7F4cx7RwX7cNqEP009LkQWgXeyEUFeqfaNc2mI7n4R69+T0IFdKJQPvAE8Ad0mQGyfjYAlPL93Jun3FJEcEMGdiPy4bkSS3+xsk/5FHKP3gQ+e9QEAAiY8+IqHeDbgiyD8FngRCgHskyI2ltWZ1ViHPfL2Trbnl9IkN5p7J/Th/ULzMrmiAE1rptq4SU3g4lspKOGm5tc6SPvauy9mLL18MTNFaz1JKjaeFIFdKzQRmAqSmpo46cOBAR+oR7aC1ZunWwzy7bBd7C6oYmhzGXZP6cU6/GAl0N1C2eDFHnvg7ltJS57yAtNa7FGcH+ZPAtYAZ8AdCgYVa62taOkZa5K5ltjSy8JdcXvgmi9zSGoYlh3H7eX2ZMCBWAt0NNB0FYwoLc0pLHQCTifArr5DpAzyUy27Rb61F3pQEuTHqzY18lnGIV1bu4VBJDYMSQ7ltQl8mp8fhJX3obqO5rhinkBa7R5EgFydosDTy+S+5vLJyD/uLqhkQH8LsCX24cHCCXBR1U06/aIr0r7s7mTRLNMvua0nGAAAT2ElEQVRsaeTLzHxeWpFFdkEVadFB/HFcGtNGJsm0uW6obPFi8uc+7NAbkFolMzm6FQly0SpLo2bp1nz+vWovW3LLiA72ZcbYnlx7Rg8igmQ9RXeU/8gjlH78ifO6XZojXTGGkiAXdtFas3ZvEfNX7+W7XQUE+Ji4cnQyfxyXRkqkTJ3rzlzeWj9Gwt1lJMhFu+06XMHra/by3025WBo1Fw5J4KazejEiJVxGurg5pw9rbIX0szuPBLnosMNltbz14z7e/+kgFXVmhiaHMWNsTy4emiD96B7C0XPBtJu02h1Cglx0WmWdmUW/5PLuj/vJOlpJZJAv08ek8IczepAULjMuehLDumFspNXeMRLkwmG01qzNLuKdtftZvv0IAJPT45lxZg/GpkVJt4sHK1u8mLy/POicm5FaIgtX202CXDjFoZJq/rPuIB+uP0hJdQO9Y4KYPiaVaSOTiAr2a/sEwi0ZMiKmKbkDtVkS5MKpahssfJmZzwfrD7LxQAk+JsWk9Dimj0nlrD7RcteohytbvJj8h/6Krq9ve2cnkK4YKwly4TJZRyr48OccFmYcoqS6gaTwAK4cncIVo5NJlL70LmP/DTdQs/Yno8sAuk/QS5ALl6szW1i27Qgf/ZzD93sK8VJwdr8YLhuRxOT0eAJ8ZcRLV2L4yBhvb8Kv+B2Vq1Zjzs/vkn3uEuTCUAeLqvl4Qw6fZRwiv6yWYD9vLhwcz2UjkzijV5R0vXRBRo5lb4mnt9wlyIVbaGzU/LSviEUZuSzdepjKOjOJYf5cOiKJaSOS6BsXYnSJwonyH3mE0g8/cuzyd+3l5YUKDUWXlXlcq12CXLidmnoLy3ccYVHGIVZnFWJp1AxOCuXSYUlMGZogY9O7gabzsKuAAHRNjbEh7+aThEmQC7dWUFHH4s15fL4pl8xDZQCMTA3noqGJTBkST0KYhHp3Yni3TEAA1NQcnwveXRa7liAXHuNAURX/25LP/zLz2ZZXDsDoHhFcPDSBC4ckEBfqb3CFwtXaCnYVHk7YhRdQtuhzdG2tU2pQ/v4kPPaooWHu7KXe/IHVgB/gDXyqtW71bxMJcmGPvQWVLNmSz5eZ+ew8XIFS1lCfnB7PpPQ4ekYHGV2icCPObslbYqOIWfoZsYG/LpHYtHvI2X3uzg5yBQRprSuVUj7A98AdWusWB5lKkIv22nO0kv9l5vPVtsPsyLe21PvGBjMpPY7Jg+IZmhQmo18EcNJQSKWO97urgAB0Q0OHpyBoBKb/xZtgn2DSwtOYsN2b09/LwFT36/mattxP+cViq6WjXTWuXOotEGuQ/1lrva6l/STIRWfkFFezfPsRlm8/wvr9xVgaNbEhfkxMj2NSehxj06JkZkbRrM6Md2+MiyLz37eSXZrN3rK93Pi3dUSVNZ6yX2VkAHnXnEvfV79GmZuf5qAjXTVOD3KllAnYCPQBXtFa39/a/hLkwlFKq+tZsfMoy7cfYdXuAqrrLQT4mBjbO4rx/WM4p18MPaKkC0acqtlZIJu04JtqLnh3DExvdl8NFIZCTHnrr++dmEjfFd/aXa8rW+ThwCLgNq311pOemwnMBEhNTR114MCBjtQjRItqGyyszS7iu11H+W53AQeKrP+D9ooO4px+MYzvH8MZ0loXrTihxd7GqJWsCec127L3TkzEnJ/f9lBKpRi4Y7vdtbl01IpS6m9Atdb62Zb2kRa5cIV9hVWssoX62uwi6syN+Hl7cUaatbV+Vp9o+sQGy9S7okPKFi8m///+dsJImWMtd3u6b1zZIve24+QxQIPWulQpFQBMAp7uyIsJ4Ui9ooPoFd2L63/Ti9oGC+v2FfPdrqOs2l3AI4utLaGYED/O7B3Fb3pHM7Z3lKxNKux2rIXe0qiV/Acfsl5cbYby9yf2zjkuq9WeUStDgXcAE+AFfKy1frS1Y6RFLoyWU1zNj9mF/JhdxA97iiisrAMgNTKQM3tHcWafaMamRRETIvOqi47x2FEr9pIgF+5Ea82eo5X8sKeQH7KL+GlvERW11iFl/eKCGZsWxWm9ohjTK4LYELkhSRhDglyIdrA0arbmlvFDdiE/7ili44ESahqsw8h6RgVyWq9IxvSM5LRekaRGBkofu3AJCXIhOqHB0sjW3DJ+3l/M+n0l/Ly/mLIaa99nXKjf8VA/rVck/WJD5MYk4RQS5EI4UGOjJutoJev3F/PzvmLW7yvmcLl15EJYgA+jekQwMjWckakRDEsJJ8ivzTEDQrTJqaNWhOhuvLwU/eND6B8fwrVn9EBrzaGSGtbbQn3jwRJW7Dxq3VdB//jQ48E+IjWcXtFB0h0jXEpa5EJ0QFl1A7/klJBxsJRfDpaw6WApFbY5OSICfRiRKq120T7SIhfCxcICfRjfP5bx/WMB6wXUPUcryThYQsaBEjJOarX3iwthWHI4Q1PCGJYcTr+4EHy9vYz8TxBdiLTIhXCS0up6NuWUHm+1b8kto7TaehHV19uLgQmhDEsOY0hSGMNSwukdE4xJLqR2W3KxUwgPoLUmp7iGzYdK2ZJbxuacUrbmllFVbx36GOhrYnBiGEOTwxiaEs7QpDB6RMnwx+5CglwID2Vp1OwrrGRzThmZh0rJzC1jW1459Wbr9Kkhft4MTAwlPSGUQYmhpCeG0jdWumW6IukjF8JDmbwUfWJD6BMbwuWjkgHruPZdhyvYklvGtrwytueV89HPOcdvWvIxKfrGhpCeaAv3hFAGJoYS6u9j5H+KMJAEuRBuxsfkxeCkMAYnhR3fZmnU7C+qYnteOdvzy9mWV853u47y6cZDx/dJjQy0hnpCKP3jg+kXF0KPqCDpd+8GJMiF8AAmL0XvmGB6xwQzdVji8e1HK2rZlld+POC355Xz9fbDx6fK9vX2om9sMP3jQugXH0K/OGvAJ4UHSN97FyJBLoQHiw3xJ7a/P+fahkEC1NRb2HO0kl1HKth9pIJdhytYu7eIhb/kHt8n2M+bvnHWgO8bF0Kf2GB6xwSRGBYgUxB4IAlyIbqYAF8TQ5LDGJIcdsL2spoGso5UWAP+sPX719sO8+HPOcf38ffxIi06mN62YD/2V0BaTJCsvOTGJMiF6CbCAnwY3TOS0T0jj2/TWlNYWc/egkqyC6rILqgku6CSTTklfJmZd7yLRilICg84Huy9Y38N+ehgX+mmMZgEuRDdRL25kZoGC3VmC/XmRurMjce/K6VIiQwgLtSPUT0iqDc3Ul7bwM7D1q6Z3YcrOFRSw6GSGlbtLmj2/GEBPnx3z3gignxd/F8m7FnqLQV4F4jDuoD0fK31C84uTAgBdWYL5TVmymsbqKg1U17TQHltw/Ft5TUNVNdbqK43U1VvobrObPvZuq3p4waL4+8ZaaqspoHi6noJcgPY0yI3A3drrTOUUiHARqXUcq21/ctDC9HNaa2pqDNTXFlPcXX98e8lVfUU275Kqq3fy2oaKLeFdp3txqCWeHspAn1NBPl5E+BrIsjX+j062JdA30ACfU3WLz9vAn1MBPia8PMx4Wfyws/HC9/j300n/eyFn48JX5MXPiaFt8kLby+FyUvh7aWkK8XNtBnkWut8IN/2uEIptQNIAiTIRbdXZ7ZwtLyOoxV1FFTUcrSijqPldRwptz2uqKOwso6SqnrMjc23iH29vYgK8iUi0JeIIB8SwgIIDfAm1N+H0AAfQv29bd99Ttrug7+Pl4SqaF8fuVKqJzACWNfMczOBmQCpqakOKE0IY1XXm8krrSG3tJa80hrb4xpbcFuD+tgkWE2ZvBTRwb7EhfqTFO7PsOQwIoN8ibSFdWSwL5GBvse3BfqaJIxFp9gd5EqpYOAzYI7Wuvzk57XW84H5YJ1rxWEVCuEk9eZGckqq2V9Yxf6iag4WVf0a2mU1p4S0yUsRF+JHXJg/vaKDOL1XFHGhfsSG+BMT6kdsiPVxZJCv3E0pXMquIFdK+WAN8f9orRc6tyQhHKfe3MjB4ir2F1azv6iK/UVVHCiyPs4tqaFpb0eInzdJEQEkhgcwskc4ieEBJNm+EsMDiA3xw9skk1UJ92PPqBUFvAns0Fr/0/klCdFE5sfw7aNQdggCIqzbakogLBnO+xsMvRKA2gYL2QWV7DlaSdaRSrKOVpB1tJIDRdVYmqR1qL83vaKDGJESwWXDk+gZHUSPqCB6RQcREegjXRzCI9nTIv8NcC2wRSm1ybbtQa31EueVJbqVzI9h6f1QU2z9OSASBl0G2xb9ug1OfFyWQ8Pnt/H26r38v5rTOVhcffzmFZOXokdUIH1jg5kyOIG0mCB6RgfRKyqIcAlr0QXZM2rle0A++cIxvrwLNrzZ+j41xegNb7b5ofNprOWSojfY1Hcyl41Iom9sCH3jgukRFYift9xOLroPubNTOI89od0Ce1sOcbqQV34/skOvIURXIUEuHKMTod0pYcmuf00h3IwEueiYx+LBUmNsDT4B1gueQnRzEuTCPs8OgMp8Y2vwCQJvv2ZHrQjRnUmQi+ZlfgyL50BDletf2zcIhk6HrGXWYYcS2kK0SoJc/MrI8AbrsMMLn5bAFqKdJMiFVebHsPAWoPXZ9hxKglsIh5Ag786a3jWpvHBqiCsvuOzfEtpCOIEEeXfRNLTDkqHvZNj8PjTYRp5oi2NfL3oAzD5lkkwhhBNIkHcHmR/D4tt/De2yHLvunLSfgmnzpbUthEEkyLuDbx/9NcRtOhXio2+Ci2X+NCHchQR5d1B2qHPHy0VJIdyaBHl3EJYMZTnNPKGwrqdt4xMAU1+UwBbCw8gs+d3BeX+zhnRTPgEw+kYISwGU9buEuBAeSVrk3cGxcG46akXulBSiy7BnhaAFwMXAUa31YOeXJJxi6JUS3EJ0UfZ0rbwNXODkOoQQQnRQm0GutV4NFLe1nxBCCGM47GKnUmqmUmqDUmpDQUGBo04rhBCiDQ4Lcq31fK31aK316JiYGEedVgghRBtk+KEQQng4pww/3LhxY6FS6kAHD48GCh1ZjwtIza4hNbuOJ9bt6TX36OhJlNa69R2U+gAYb3vBI8BcrbXTVtlVSm3QWo921vmdQWp2DanZdTyx7u5cc5stcq311Z19ESGEEM4jfeRCCOHh3DHI5xtdQAdIza4hNbuOJ9bdbWtus49cCCGEe3PHFrkQQoh2MCzIlVIXKKV2KaX2KKUeaOZ5P6XUR7bn1ymlerq+yhPqSVFKrVRKbVdKbVNK3dHMPuOVUmVKqU22r78ZUetJNe1XSm2x1bOhmeeVUupF2/ucqZQaaUSdTerp3+T926SUKldKzTlpH8PfZ6XUAqXUUaXU1ibbIpVSy5VSWbbvES0ce51tnyyl1HWuq7rFup9RSu20/fsvUkqFt3Bsq58lF9f8sFIqt8lnYEoLx7aaMy6u+aMm9e5XSm1q4dj2v89aa5d/ASYgG0gDfIHNQPpJ+8wCXrM9ng58ZEStTepJAEbaHocAu5upeTzwpZF1NlP3fiC6leenAEuxrjJxBrDO6JpP+pwcBnq42/sMnA2MBLY22fYP4AHb4weAp5s5LhLYa/seYXscYXDdkwFv2+Onm6vbns+Si2t+GLjHjs9PqznjyppPen4e8DdHvc9GtchPA/ZorfdqreuBD4FLT9rnUuAd2+NPgfOUUo5bL7idtNb5WusM2+MKYAeQZFQ9DnQp8K62+gkIV0olGF2UzXlAtta6ozeXOY1ufjK5pp/Zd4DfNnPo+cByrXWx1roEWI4LZxdtrm6t9TKttdn2409AsqvqsUcL77U97MkZp2itZluOXQl84KjXMyrIk4Cma48d4tRQPL6P7UNWBkS5pLo22Lp5RgDrmnl6rFJqs1JqqVJqkEsLa54GlimlNiqlZjbzvD3/FkaZTssfdnd7nwHitNb5tseHgbhm9nHn9xvgRqx/oTWnrc+Sq822dQctaKEby13f63HAEa11VgvPt/t9loud7aSUCgY+A+ZorctPejoDazfAMOAl4HNX19eMs7TWI4ELgVuVUmcbXZA9lFK+wCXAJ8087Y7v8wm09W9kjxoSppR6CDAD/2lhF3f6LP0L6A0MB/KxdlV4iqtpvTXe7vfZqCDPBVKa/Jxs29bsPkopbyAMKHJJdS1QSvlgDfH/aK0Xnvy81rpca11pe7wE8FFKRbu4zJNryrV9PwoswvrnZlP2/FsY4UIgQ2t95OQn3PF9tjlyrFvK9v1oM/u45futlLoe60pgf7D9EjqFHZ8ll9FaH9FaW7TWjcDrLdTidu+1LcumAR+1tE9H3mejgvxnoK9Sqpet5TUd+OKkfb4Ajl3R/x2woqUPmCvY+rXeBHZorf/Zwj7xx/rxlVKnYX1/Dfvlo5QKUkqFHHuM9aLW1pN2+wKYYRu9cgZQ1qR7wEgttlrc7X1uouln9jrgv83s8zUwWSkVYesOmGzbZhil1AXAfcAlWuvqFvax57PkMiddx7mshVrsyRlXmwjs1Fofau7JDr/PrriC28KV2SlYR35kAw/Ztj2K9cME4I/1z+o9wHogzahabfWchfVP5Uxgk+1rCvAn4E+2fWYD27BeHf8JONPgmtNstWy21XXsfW5aswJesf07bAFGG1mzraYgrMEc1mSbW73PWH/J5AMNWPteb8J6DedbIAv4Boi07TsaeKPJsTfaPtd7gBvcoO49WPuSj32uj40WSwSWtPZZMrDm92yf10ys4Zxwcs22n0/JGaNqtm1/+9jnuMm+nX6f5c5OIYTwcHKxUwghPJwEuRBCeDgJciGE8HAS5EII4eEkyIUQwsNJkAshhIeTIBdCCA8nQS6EEB7u/wNEiZ8AxBPHNQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1105eb310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ -1.26490183e-03  -9.94635446e-01   1.98367727e+01]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1115b6e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ex_D = linspace(0, 11., 1001)\n",
    "ex_P = linspace(0, 20., 1001)\n",
    "ex_T = linspace(0, 8.5, 1001)\n",
    "\n",
    "# Now we have beam energy:\n",
    "Ebeam = 27.36 # Proton energy [MeV]\n",
    "Twidth = 4.56 # Target thickness [mg/cm^2]\n",
    "\n",
    "Fwidth = 10 # Al-absorber width [um]\n",
    "dEwidth = 309 # delta-E detector width [um]\n",
    "Ewidth = 1041 # E detector width [um] \n",
    "\n",
    "th = ScatteringAngle(0, 22.0, 11.0, 0.491, 0.5)[0]\n",
    "\n",
    "e, de = SimulateNiPP(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, ex_P, th)\n",
    "plt.plot(e, de)\n",
    "\n",
    "e, de = SimulateNiPP(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, ReadStates(\"states64Ni.txt\")*1e-3, th)\n",
    "plt.plot(e, de, \"o\")\n",
    "\n",
    "e, de = SimulateNiPD(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, ex_D, th)\n",
    "plt.plot(e, de)\n",
    "\n",
    "e, de = SimulateNiPD(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, ReadStates(\"states63Ni.txt\")*1e-3, th)\n",
    "plt.plot(e[e>0], de[e>0], \"o\")\n",
    "\n",
    "e, de = SimulateNiPT(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, ex_T, th)\n",
    "plt.plot(e, de)\n",
    "\n",
    "e, de = SimulateNiPT(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, ReadStates(\"states62Ni.txt\")*1e-3, th)\n",
    "plt.plot(e[e>0], de[e>0], \"o\")\n",
    "\n",
    "plt.show()\n",
    "\n",
    "e, de = SimulateNiPD(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, ex_D, th)\n",
    "plt.plot(ex_D, e+de)\n",
    "print polyfit(ex_D, e+de, 2)\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "#for i in range(48):\n",
    "    #th = ScatteringAngle(i, 22.0, 11.0, 0.491, 0.5)[0]\n",
    "    #e, de = SimulateNiPD(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, ex_D, th)\n",
    "    #p = polyfit(e+de, ex_D, 2)\n",
    "    #print \"%i: %1.3f, %2.6f %2.6f %2.6f\" % (i, th*180./pi, p[2], p[1], p[0])\n",
    "    #print \"%2.6f %2.6f %2.6f \\\\\" % (p[2], p[1], p[0])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d6ab1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ex = linspace(0, 11., 1001)\n",
    "\n",
    "# Now we have beam energy:\n",
    "Ebeam = 27.36 # Proton energy [MeV]\n",
    "Twidth = 4.56 # Target thickness [mg/cm^2]\n",
    "\n",
    "Fwidth = 10 # Al-absorber width [um]\n",
    "dEwidth = 309 # delta-E detector width [um]\n",
    "Ewidth = 1041 # E detector width [um] \n",
    "\n",
    "\n",
    "th = ScatteringAngle(0, 22.0, 11.0, 0.491, 0.5)[0]\n",
    "de, e = SimulateNiPD(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, ex, th)\n",
    "plt.plot(e+de, ex, \"r\", label=\"Norm.\")\n",
    "\n",
    "a = de+e\n",
    "\n",
    "th = ScatteringAngle(0, 22.0, 11.0, 0.491, 0.5)[1]\n",
    "de, e = SimulateNiPD(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, ex, th)\n",
    "#plt.plot(ex, e+de, \"g\", label=\"th. min.\")\n",
    "\n",
    "b = de+e\n",
    "\n",
    "#plt.plot(ex, a-b)\n",
    "#plt.show()\n",
    "\n",
    "th = ScatteringAngle(0, 22.0, 11.0, 0.491, 0.5)[2]\n",
    "de, e = SimulateNiPD(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, ex, th)\n",
    "#plt.plot(ex, e+de, \"b\", label=\"th. max.\")\n",
    "\n",
    "plt.legend(loc=\"best\")\n",
    "plt.xlabel(\"Deposited energy [MeV]\")\n",
    "plt.ylabel(\"Excitation energy [MeV]\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11106b350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ex = linspace(0, 11., 1001)\n",
    "\n",
    "# Now we have beam energy:\n",
    "Ebeam = 27.36 # Proton energy [MeV]\n",
    "Twidth = 4.56 # Target thickness [mg/cm^2]\n",
    "\n",
    "Fwidth = 10 # Al-absorber width [um]\n",
    "dEwidth = 309 # delta-E detector width [um]\n",
    "Ewidth = 1041 # E detector width [um] \n",
    "\n",
    "\n",
    "th = ScatteringAngle(0, 22.0, 11.0, 0.491, 0.5)[0]\n",
    "de, e = SimulateNiPD(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, ex, th)\n",
    "plt.plot(e, de, \"r\", label=\"Norm.\")\n",
    "\n",
    "th = ScatteringAngle(0, 22.0, 11.0, 0.491, 0.5)[1]\n",
    "de, e = SimulateNiPD(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, ex, th)\n",
    "plt.plot(e, de, \"g\", label=\"th. min.\")\n",
    "\n",
    "th = ScatteringAngle(0, 22.0, 11.0, 0.491, 0.5)[2]\n",
    "de, e = SimulateNiPD(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, ex, th)\n",
    "plt.plot(e, de, \"b\", label=\"th. max.\")\n",
    "\n",
    "plt.legend(loc=\"best\")\n",
    "plt.xlabel(\"E detector energy [MeV]\")\n",
    "plt.ylabel(\"dE detector energy [MeV]\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Excitation energy [keV] | dE energy [keV] | E energy [keV] | dE+E energy [keV]\n",
      "0.00 | 1411.125561 | 5314.124550 | 6725.250111\n",
      "1345.75 | 1471.789946 | 5616.112147 | 7087.902094\n",
      "2276.56 | 1522.963433 | 5848.483440 | 7371.446874\n",
      "2485.00 | 1535.066511 | 5903.521377 | 7438.587887\n",
      "2610.10 | 1542.330907 | 5937.352054 | 7479.682960\n",
      "2867.30 | 1557.267277 | 6008.785067 | 7566.052344\n",
      "2972.08 | 1563.352592 | 6038.609707 | 7601.962299\n",
      "3025.83 | 1566.474332 | 6054.071609 | 7620.545941\n",
      "3166.10 | 1574.621369 | 6094.940465 | 7669.561833\n",
      "3275.98 | 1581.003639 | 6127.478108 | 7708.481747\n",
      "3395.70 | 1587.957778 | 6163.452330 | 7751.410107\n",
      "3463.61 | 1591.902595 | 6184.100481 | 7776.003076\n",
      "3482.00 | 1592.970868 | 6189.722115 | 7782.692983\n",
      "3560.40 | 1597.525208 | 6213.832334 | 7811.357542\n",
      "3647.98 | 1602.612997 | 6241.041568 | 7843.654565\n",
      "3749.00 | 1608.481786 | 6272.787592 | 7881.269378\n",
      "3749.40 | 1608.505025 | 6272.914065 | 7881.419089\n",
      "3797.00 | 1611.270447 | 6288.007417 | 7899.277865\n",
      "3808.00 | 1611.909524 | 6291.507604 | 7903.417128\n",
      "3848.90 | 1614.285751 | 6304.562083 | 7918.847834\n",
      "3965.00 | 1621.031205 | 6341.964113 | 7962.995318\n",
      "4085.20 | 1628.015219 | 6381.224602 | 8009.239821\n",
      "4137.00 | 1631.025079 | 6398.357236 | 8029.382315\n",
      "4172.30 | 1633.076239 | 6410.136694 | 8043.212933\n",
      "4174.00 | 1633.175020 | 6410.706137 | 8043.881157\n",
      "4216.00 | 1635.615535 | 6424.836271 | 8060.451806\n",
      "4244.00 | 1637.242570 | 6434.322862 | 8071.565432\n",
      "4263.00 | 1638.346640 | 6440.790473 | 8079.137113\n",
      "4285.00 | 1639.625049 | 6448.309917 | 8087.934966\n",
      "4348.00 | 1643.286014 | 6470.024765 | 8113.310779\n",
      "4369.00 | 1644.506358 | 6477.322974 | 8121.829332\n",
      "4398.00 | 1646.191613 | 6487.450723 | 8133.642335\n",
      "4412.00 | 1647.005192 | 6492.360491 | 8139.365683\n",
      "4455.00 | 1649.504073 | 6507.523797 | 8157.027870\n",
      "4475.00 | 1650.666359 | 6514.619360 | 8165.285719\n",
      "4493.00 | 1651.712426 | 6521.028694 | 8172.741119\n",
      "4521.00 | 1653.339657 | 6531.042566 | 8184.382223\n",
      "4531.70 | 1653.961497 | 6534.883419 | 8188.844916\n",
      "4548.00 | 1654.908791 | 6540.749423 | 8195.658214\n",
      "4573.14 | 1656.369847 | 6549.832268 | 8206.202114\n",
      "4584.00 | 1657.001000 | 6553.769209 | 8210.770208\n",
      "4615.60 | 1658.837521 | 6565.270509 | 8224.108030\n",
      "4640.67 | 1660.294552 | 6574.443590 | 8234.738142\n",
      "4670.00 | 1661.999189 | 6585.229842 | 8247.229031\n",
      "4692.00 | 1663.277826 | 6593.359010 | 8256.636836\n",
      "4704.08 | 1663.979919 | 6597.836757 | 8261.816676\n",
      "4721.00 | 1664.963321 | 6604.125266 | 8269.088587\n",
      "4741.00 | 1666.125745 | 6611.583714 | 8277.709459\n",
      "4762.00 | 1667.346301 | 6619.444542 | 8286.790842\n",
      "4801.00 | 1669.613078 | 6634.123195 | 8303.736273\n",
      "4868.52 | 1673.537603 | 6659.782128 | 8333.319731\n",
      "4889.00 | 1674.728004 | 6667.626651 | 8342.354655\n",
      "4925.00 | 1676.820533 | 6681.485443 | 8358.305976\n",
      "4962.00 | 1678.971223 | 6695.821720 | 8374.792942\n",
      "4991.00 | 1680.656924 | 6707.123926 | 8387.780850\n",
      "5010.00 | 1681.761362 | 6714.560083 | 8396.321445\n",
      "5027.00 | 1682.749551 | 6721.234464 | 8403.984015\n",
      "5065.00 | 1684.958471 | 6736.225433 | 8421.183905\n",
      "5093.00 | 1686.586122 | 6747.334831 | 8433.920953\n",
      "5107.00 | 1687.399955 | 6752.909719 | 8440.309674\n",
      "5123.00 | 1688.330057 | 6759.297540 | 8447.627597\n",
      "5155.51 | 1690.219928 | 6772.330948 | 8462.550876\n",
      "5169.00 | 1691.004137 | 6777.760480 | 8468.764617\n",
      "5188.00 | 1692.108666 | 6785.428914 | 8477.537579\n",
      "5215.00 | 1693.678275 | 6796.368902 | 8490.047177\n",
      "5229.00 | 1694.492154 | 6802.061236 | 8496.553390\n",
      "5264.00 | 1696.526876 | 6816.351130 | 8512.878006\n",
      "5287.00 | 1697.863997 | 6825.787506 | 8523.651504\n",
      "5332.00 | 1700.480146 | 6844.355443 | 8544.835589\n",
      "5354.00 | 1701.759172 | 6853.483889 | 8555.243061\n",
      "5370.00 | 1702.689381 | 6860.143713 | 8562.833094\n",
      "5386.00 | 1703.619630 | 6866.821196 | 8570.440826\n",
      "5408.00 | 1704.902607 | 6876.027647 | 8580.930254\n",
      "5418.21 | 1705.500245 | 6880.309380 | 8585.809625\n",
      "5441.00 | 1706.839321 | 6889.887710 | 8596.727031\n",
      "5484.00 | 1709.384957 | 6908.038578 | 8617.423536\n",
      "5507.00 | 1710.756807 | 6917.789397 | 8628.546204\n",
      "5536.00 | 1712.496690 | 6930.125915 | 8642.622605\n",
      "5567.00 | 1714.369085 | 6943.364963 | 8657.734048\n",
      "5614.00 | 1717.232540 | 6963.539237 | 8680.771777\n",
      "5663.00 | 1720.249461 | 6984.703165 | 8704.952626\n",
      "5734.00 | 1724.678127 | 7015.607214 | 8740.285340\n",
      "5768.66 | 1726.864628 | 7030.796004 | 8757.660632\n",
      "5812.10 | 1729.627744 | 7049.927658 | 8779.555402\n",
      "5817.00 | 1729.941007 | 7052.093758 | 8782.034765\n",
      "5843.00 | 1731.608602 | 7063.630485 | 8795.239087\n",
      "5870.00 | 1733.349910 | 7075.687306 | 8809.037216\n",
      "5902.00 | 1735.426310 | 7090.077818 | 8825.504128\n",
      "5976.00 | 1740.280401 | 7123.776583 | 8864.056984\n",
      "6018.00 | 1743.067952 | 7143.164867 | 8886.232819\n",
      "6030.00 | 1743.868716 | 7148.739294 | 8892.608010\n",
      "6060.00 | 1745.879031 | 7162.743353 | 8908.622385\n",
      "6116.00 | 1749.663704 | 7189.144760 | 8938.808464\n",
      "6182.00 | 1754.177809 | 7220.697337 | 8974.875147\n",
      "6220.00 | 1756.803119 | 7239.078841 | 8995.881959\n",
      "6452.00 | 1773.246960 | 7354.730838 | 9127.977798\n",
      "6512.00 | 1777.615687 | 7385.605258 | 9163.220945\n",
      "6622.00 | 1785.748532 | 7443.245348 | 9228.993880\n",
      "6656.00 | 1788.294616 | 7461.333865 | 9249.628481\n",
      "6687.00 | 1790.629323 | 7477.938832 | 9268.568155\n",
      "6754.00 | 1795.718534 | 7514.194469 | 9309.913003\n",
      "6822.00 | 1800.944080 | 7551.506470 | 9352.450550\n",
      "6838.00 | 1802.182450 | 7560.361364 | 9362.543814\n",
      "6861.00 | 1803.968500 | 7573.140902 | 9377.109402\n",
      "7020.00 | 1816.505332 | 7663.124074 | 9479.629407\n",
      "7130.00 | 1825.358623 | 7727.059587 | 9552.418210\n",
      "7220.00 | 1832.627851 | 7780.381127 | 9613.008978\n",
      "7300.00 | 1839.089803 | 7828.511345 | 9667.601148\n",
      "7730.00 | 1873.831103 | 8102.444254 | 9976.275357\n",
      "7950.00 | 1891.991780 | 8254.471992 | 10146.463772\n",
      "8240.00 | 1916.905468 | 8468.746281 | 10385.651749\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "Excitation energy [keV] | dE energy [keV] | E energy [keV] | dE+E energy [keV]\n",
      "0.00 | 3230.972830 | 16533.058421 | 19764.031252\n",
      "87.15 | 3243.743732 | 16433.357364 | 19677.101096\n",
      "155.55 | 3253.847532 | 16355.021819 | 19608.869351\n",
      "517.55 | 3308.500125 | 15939.195721 | 19247.695846\n",
      "1001.10 | 3385.354330 | 15379.660202 | 18765.014532\n",
      "1068.99 | 3396.490256 | 15300.722089 | 18697.212345\n",
      "1251.10 | 3426.750754 | 15088.566756 | 18515.317510\n",
      "1291.83 | 3433.596113 | 15041.035417 | 18474.631530\n",
      "1324.04 | 3439.029539 | 15003.425732 | 18442.455270\n",
      "1451.70 | 3460.786421 | 14854.133212 | 18314.919633\n",
      "1657.00 | 3496.619353 | 14613.168543 | 18109.787897\n",
      "1677.00 | 3500.165774 | 14589.636399 | 18089.802173\n",
      "1787.00 | 3519.847283 | 14460.026613 | 17979.873896\n",
      "1899.00 | 3540.169256 | 14327.737231 | 17867.906487\n",
      "2149.00 | 3586.455609 | 14031.412516 | 17617.868124\n",
      "2183.50 | 3592.941818 | 13990.416158 | 17583.357976\n",
      "2261.70 | 3607.757879 | 13897.372686 | 17505.130565\n",
      "2297.00 | 3614.504567 | 13855.311611 | 17469.816177\n",
      "2353.10 | 3625.301612 | 13788.389106 | 17413.690718\n",
      "2519.00 | 3657.768701 | 13589.927927 | 17247.696627\n",
      "2573.00 | 3668.509838 | 13525.150041 | 17193.659879\n",
      "2675.00 | 3689.030343 | 13402.551827 | 17091.582170\n",
      "2696.60 | 3693.414697 | 13376.549616 | 17069.964312\n",
      "2814.50 | 3717.582581 | 13234.373553 | 16951.956134\n",
      "2822.00 | 3719.132481 | 13225.315310 | 16944.447791\n",
      "2953.00 | 3746.421123 | 13066.837609 | 16813.258732\n",
      "2980.00 | 3752.095490 | 13034.118787 | 16786.214277\n",
      "3013.00 | 3759.053687 | 12994.105178 | 16753.158865\n",
      "3022.00 | 3760.955804 | 12983.187742 | 16744.143546\n",
      "3075.00 | 3772.212296 | 12918.839240 | 16691.051535\n",
      "3104.00 | 3778.412258 | 12883.587623 | 16661.999882\n",
      "3179.00 | 3794.580140 | 12792.281838 | 16586.861978\n",
      "3237.00 | 3807.215250 | 12721.535789 | 16528.751039\n",
      "3254.00 | 3810.940440 | 12700.777368 | 16511.717808\n",
      "3284.10 | 3817.560440 | 12663.997733 | 16481.558173\n",
      "3292.00 | 3819.303038 | 12654.339314 | 16473.642352\n",
      "3336.00 | 3829.047657 | 12600.505289 | 16429.552946\n",
      "3427.00 | 3849.410890 | 12488.950166 | 16338.361056\n",
      "3471.00 | 3859.358112 | 12434.906766 | 16294.264878\n",
      "3522.00 | 3870.970362 | 12372.180244 | 16243.150607\n",
      "3551.00 | 3877.612896 | 12336.471391 | 16214.084286\n",
      "3594.00 | 3887.514859 | 12283.469290 | 16170.984149\n",
      "3608.00 | 3890.752322 | 12266.198760 | 16156.951081\n",
      "3632.60 | 3896.457148 | 12235.835272 | 16132.292420\n",
      "3680.00 | 3907.507366 | 12177.270020 | 16084.777386\n",
      "3694.00 | 3910.785745 | 12159.957159 | 16070.742904\n",
      "3723.00 | 3917.597844 | 12124.072896 | 16041.670740\n",
      "3739.70 | 3921.533635 | 12103.395095 | 16024.928731\n",
      "3769.00 | 3928.461804 | 12067.092423 | 15995.554227\n",
      "3780.00 | 3931.070342 | 12053.455650 | 15984.525992\n",
      "3792.00 | 3933.920395 | 12038.574281 | 15972.494676\n",
      "3804.00 | 3936.774618 | 12023.687808 | 15960.462426\n",
      "3836.00 | 3944.406407 | 11983.965446 | 15928.371853\n",
      "3889.00 | 3957.133004 | 11918.074209 | 15875.207213\n",
      "3932.00 | 3967.545690 | 11864.515726 | 15832.061416\n",
      "3951.00 | 3972.171024 | 11840.824697 | 15812.995721\n",
      "4022.00 | 3989.586675 | 11752.159660 | 15741.746335\n",
      "4033.00 | 3992.303425 | 11738.403720 | 15730.707144\n",
      "4055.80 | 3997.950356 | 11709.875083 | 15707.825439\n",
      "4074.00 | 4002.473331 | 11687.086425 | 15689.559757\n",
      "4106.00 | 4010.458822 | 11646.984456 | 15657.443278\n",
      "4267.00 | 4051.273765 | 11444.564083 | 15495.837848\n",
      "4313.00 | 4063.130492 | 11386.528375 | 15449.658867\n",
      "4331.00 | 4067.793683 | 11363.794414 | 15431.588098\n",
      "4358.00 | 4074.813357 | 11329.667811 | 15404.481168\n",
      "4387.00 | 4082.386270 | 11292.979006 | 15375.365277\n",
      "4449.00 | 4098.692129 | 11214.421750 | 15313.113879\n",
      "4461.00 | 4101.866276 | 11199.198372 | 15301.064648\n",
      "4488.00 | 4109.029635 | 11164.923559 | 15273.953194\n",
      "4555.00 | 4126.934139 | 11079.738378 | 15206.672517\n",
      "4586.00 | 4135.280394 | 11040.260268 | 15175.540662\n",
      "4622.00 | 4145.022077 | 10994.363875 | 15139.385952\n",
      "4692.00 | 4164.152586 | 10904.927625 | 15069.080211\n",
      "4722.00 | 4172.438086 | 10866.509096 | 15038.947182\n",
      "4799.00 | 4193.940985 | 10767.657688 | 14961.598673\n",
      "4812.00 | 4197.603222 | 10750.933880 | 14948.537102\n",
      "4828.00 | 4202.122666 | 10730.337023 | 14932.459688\n",
      "4876.00 | 4215.761050 | 10668.455588 | 14884.216638\n",
      "4919.00 | 4228.080688 | 10612.904577 | 14840.985265\n",
      "4957.00 | 4239.046471 | 10563.728902 | 14802.775373\n",
      "5026.00 | 4259.144371 | 10474.244779 | 14733.389150\n",
      "5060.00 | 4269.136036 | 10430.060363 | 14699.196399\n",
      "5093.00 | 4278.889593 | 10387.118178 | 14666.007771\n",
      "5123.00 | 4287.804108 | 10348.030856 | 14635.834963\n",
      "5142.00 | 4293.473432 | 10323.251430 | 14616.724862\n",
      "5178.00 | 4304.265201 | 10276.249646 | 14580.514847\n",
      "5240.00 | 4323.004079 | 10195.144750 | 14518.148829\n",
      "5370.00 | 4362.923603 | 10024.439821 | 14387.363424\n",
      "5450.00 | 4387.942956 | 9918.924917 | 14306.867873\n",
      "5600.00 | 4436.075406 | 9719.837810 | 14155.913216\n",
      "5710.00 | 4472.396917 | 9572.794754 | 14045.191671\n",
      "5860.00 | 4523.297091 | 9370.853041 | 13894.150132\n",
      "5930.00 | 4547.557362 | 9276.049751 | 13823.607113\n",
      "6000.00 | 4572.129225 | 9180.917978 | 13753.047203\n",
      "6070.00 | 4597.009368 | 9085.470142 | 13682.479510\n",
      "6160.00 | 4629.457297 | 8962.280753 | 13591.738050\n",
      "6280.00 | 4673.784825 | 8796.944091 | 13470.728916\n",
      "6320.00 | 4688.854271 | 8741.532993 | 13430.387264\n",
      "6440.00 | 4734.944720 | 8574.401554 | 13309.346274\n",
      "6500.00 | 4758.486691 | 8490.329971 | 13248.816663\n",
      "11850.00 | 7791.801851 | 0.000000 | 7791.801851\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Excitation energy [keV] | dE energy [keV] | E energy [keV] | dE+E energy [keV]\n",
      "0.00 | 4699.133007 | 14205.210770 | 18904.343777\n",
      "1172.98 | 4995.281137 | 12746.994991 | 17742.276128\n",
      "2048.68 | 5251.393494 | 11621.576563 | 16872.970056\n",
      "2301.84 | 5332.625770 | 11288.850977 | 16621.476746\n",
      "2336.52 | 5344.040767 | 11242.977684 | 16587.018451\n",
      "2890.63 | 5535.107102 | 10500.702282 | 16035.809384\n",
      "3058.76 | 5596.435586 | 10271.964064 | 15868.399650\n",
      "3157.96 | 5633.673838 | 10135.931505 | 15769.605343\n",
      "3176.70 | 5640.796627 | 10110.143732 | 15750.940359\n",
      "3257.62 | 5671.874910 | 9998.463392 | 15670.338302\n",
      "3262.00 | 5673.572006 | 9992.403227 | 15665.975233\n",
      "3269.97 | 5676.664055 | 9981.371913 | 15658.035969\n",
      "3277.69 | 5679.663944 | 9970.681706 | 15650.345650\n",
      "3369.98 | 5715.895498 | 9842.508051 | 15558.403549\n",
      "3378.00 | 5719.076193 | 9831.336982 | 15550.413175\n",
      "3462.00 | 5752.699607 | 9714.017997 | 15466.717605\n",
      "3486.00 | 5762.410087 | 9680.392521 | 15442.802608\n",
      "3518.23 | 5775.523169 | 9635.162202 | 15410.685370\n",
      "3522.54 | 5777.283062 | 9629.107267 | 15406.390329\n",
      "3524.40 | 5778.043000 | 9626.493775 | 15404.536775\n",
      "3756.50 | 5875.052994 | 9298.146012 | 15173.199007\n",
      "3849.40 | 5915.096654 | 9165.483684 | 15080.580338\n",
      "3859.60 | 5919.535648 | 9150.874741 | 15070.410389\n",
      "3967.00 | 5966.784999 | 8996.531468 | 14963.316467\n",
      "3972.90 | 5969.407206 | 8988.025080 | 14957.432286\n",
      "4000.50 | 5981.716312 | 8948.185437 | 14929.901749\n",
      "4011.00 | 5986.419915 | 8933.006298 | 14919.426213\n",
      "4018.88 | 5989.957395 | 8921.606468 | 14911.563863\n",
      "4035.00 | 5997.214149 | 8898.263924 | 14895.478073\n",
      "4055.30 | 6006.391257 | 8868.826271 | 14875.217528\n",
      "4062.40 | 6009.611171 | 8858.519203 | 14868.130374\n",
      "4146.00 | 6047.921119 | 8736.723355 | 14784.644474\n",
      "4151.40 | 6050.420828 | 8728.828743 | 14779.249571\n",
      "4154.20 | 6051.718136 | 8724.734057 | 14776.452193\n",
      "4161.26 | 6054.992745 | 8714.406001 | 14769.398746\n",
      "4179.00 | 6063.243257 | 8688.431589 | 14751.674846\n",
      "4201.00 | 6073.519201 | 8656.174882 | 14729.694083\n",
      "4208.80 | 6077.174306 | 8644.726403 | 14721.900710\n",
      "4230.00 | 6087.139796 | 8613.578409 | 14700.718205\n",
      "4317.20 | 6128.609045 | 8484.973166 | 14613.582211\n",
      "4393.00 | 6165.284091 | 8372.543275 | 14537.827366\n",
      "4407.00 | 6172.121734 | 8351.712896 | 14523.834630\n",
      "4415.90 | 6176.478943 | 8338.460129 | 14514.939073\n",
      "4424.00 | 6180.451441 | 8326.391557 | 14506.842998\n",
      "4437.00 | 6186.841052 | 8307.008009 | 14493.849061\n",
      "4455.00 | 6195.716599 | 8280.140376 | 14475.856975\n",
      "4503.00 | 6219.550122 | 8208.325211 | 14427.875333\n",
      "4623.00 | 6280.407675 | 8027.495949 | 14307.903624\n",
      "4627.50 | 6282.726221 | 8020.677971 | 14303.404192\n",
      "4648.90 | 6293.788265 | 7988.218137 | 14282.006402\n",
      "4655.00 | 6296.952392 | 7978.954491 | 14275.906883\n",
      "4704.00 | 6322.545029 | 7904.363315 | 14226.908344\n",
      "4712.00 | 6326.753172 | 7892.155004 | 14218.908176\n",
      "4719.90 | 6330.916902 | 7880.090995 | 14211.007897\n",
      "4781.00 | 6363.395429 | 7786.506527 | 14149.901957\n",
      "4835.00 | 6392.506622 | 7703.384473 | 14095.891095\n",
      "4847.00 | 6399.027740 | 7684.860221 | 14083.887961\n",
      "4861.00 | 6406.659529 | 7663.224445 | 14069.883974\n",
      "4863.30 | 6407.915810 | 7659.667475 | 14067.583285\n",
      "4882.00 | 6418.155522 | 7630.721802 | 14048.877324\n",
      "4949.00 | 6455.220910 | 7526.629785 | 13981.850696\n",
      "4967.00 | 6465.279518 | 7498.562615 | 13963.842133\n",
      "4981.00 | 6473.133051 | 7476.702006 | 13949.835057\n",
      "4994.00 | 6480.453766 | 7456.374396 | 13936.828162\n",
      "4999.70 | 6483.672534 | 7447.452506 | 13931.125040\n",
      "5016.00 | 6492.907007 | 7421.908771 | 13914.815778\n",
      "5041.00 | 6507.156545 | 7382.644065 | 13889.800610\n",
      "5071.00 | 6524.394029 | 7335.386838 | 13859.780867\n",
      "5121.00 | 6553.458491 | 7256.285715 | 13809.744206\n",
      "5148.00 | 6569.327967 | 7213.394481 | 13782.722448\n",
      "5154.00 | 6572.871143 | 7203.846282 | 13776.717425\n",
      "5203.00 | 6602.034619 | 7125.639227 | 13727.673846\n",
      "5222.00 | 6613.452020 | 7095.203696 | 13708.655716\n",
      "5233.00 | 6620.089980 | 7077.554924 | 13697.644905\n",
      "5280.00 | 6648.683065 | 7001.913029 | 13650.596094\n",
      "5286.00 | 6652.360184 | 6992.229372 | 13644.589556\n",
      "5310.00 | 6667.129885 | 6953.432827 | 13620.562712\n",
      "5331.00 | 6680.133797 | 6919.404512 | 13599.538309\n",
      "5355.00 | 6695.087330 | 6880.422042 | 13575.509372\n",
      "5393.00 | 6718.964676 | 6818.496584 | 13537.461260\n",
      "5420.00 | 6736.080091 | 6774.345268 | 13510.425359\n",
      "5447.00 | 6753.320795 | 6730.067233 | 13483.388027\n",
      "5465.00 | 6764.896193 | 6700.466037 | 13465.362231\n",
      "5488.00 | 6779.788970 | 6662.535630 | 13442.324600\n",
      "5511.00 | 6794.794869 | 6624.485525 | 13419.280393\n",
      "5530.00 | 6807.276838 | 6592.962079 | 13400.238917\n",
      "5541.00 | 6814.538626 | 6574.674228 | 13389.212854\n",
      "5545.00 | 6817.185716 | 6568.017287 | 13385.203004\n",
      "5565.00 | 6830.472894 | 6534.677876 | 13365.150770\n",
      "5574.00 | 6836.480307 | 6519.645338 | 13356.125645\n",
      "5587.00 | 6845.188447 | 6497.899129 | 13343.087575\n",
      "5601.00 | 6854.607410 | 6474.436819 | 13329.044229\n",
      "5628.00 | 6872.892279 | 6429.061480 | 13301.953759\n",
      "5673.00 | 6903.718209 | 6353.065357 | 13256.783565\n",
      "5679.00 | 6907.861088 | 6342.898704 | 13250.759792\n",
      "5709.00 | 6928.689239 | 6291.950586 | 13220.639825\n",
      "5739.00 | 6949.707705 | 6240.810312 | 13190.518017\n",
      "5751.20 | 6958.309667 | 6219.958286 | 13178.267953\n",
      "5772.00 | 6973.048032 | 6184.333859 | 13157.381892\n",
      "5806.10 | 6997.409163 | 6125.729701 | 13123.138865\n",
      "5808.00 | 6998.773667 | 6122.457158 | 13121.230825\n",
      "5834.00 | 7017.524946 | 6077.595101 | 13095.120047\n",
      "5846.00 | 7026.227867 | 6056.840577 | 13083.068443\n",
      "5859.00 | 7035.690726 | 6034.321475 | 13070.012200\n",
      "5870.00 | 7043.725939 | 6015.238395 | 13058.964333\n",
      "5888.00 | 7056.930534 | 5983.954923 | 13040.885458\n",
      "5901.00 | 7066.517886 | 5961.310183 | 13027.828069\n",
      "5912.00 | 7074.666840 | 5942.112391 | 13016.779230\n",
      "5930.00 | 7088.073933 | 5910.624829 | 12998.698762\n",
      "5961.00 | 7111.375657 | 5856.182912 | 12967.558569\n",
      "5979.00 | 7125.028838 | 5824.447391 | 12949.476229\n",
      "5993.00 | 7135.710546 | 5799.701164 | 12935.411710\n",
      "6023.00 | 7158.785135 | 5746.486907 | 12905.272043\n",
      "6026.00 | 7161.106423 | 5741.151547 | 12902.257970\n",
      "6047.00 | 7177.426926 | 5703.731992 | 12881.158918\n",
      "6059.00 | 7186.808596 | 5682.293295 | 12869.101891\n",
      "6073.00 | 7197.805378 | 5657.229588 | 12855.034966\n",
      "6103.00 | 7221.556476 | 5603.333651 | 12824.890126\n",
      "6126.00 | 7239.938323 | 5561.839436 | 12801.777759\n",
      "6133.00 | 7245.562563 | 5549.180768 | 12794.743331\n",
      "6143.00 | 7253.621529 | 5531.072434 | 12784.693963\n",
      "6160.00 | 7267.387012 | 5500.222524 | 12767.609536\n",
      "6170.00 | 7275.522884 | 5482.036693 | 12757.559577\n",
      "6253.00 | 7344.154955 | 5329.981463 | 12674.136418\n",
      "6313.00 | 7395.009716 | 5218.811280 | 12613.820996\n",
      "6354.00 | 7430.491583 | 5142.109236 | 12572.600819\n",
      "6398.00 | 7469.311102 | 5059.049208 | 12528.360310\n",
      "6454.00 | 7519.835628 | 4952.212218 | 12472.047846\n",
      "6520.00 | 7581.004579 | 4824.665782 | 12405.670361\n",
      "6540.00 | 7599.889516 | 4785.664471 | 12385.553987\n",
      "6647.00 | 7703.710758 | 4574.204803 | 12277.915562\n",
      "6680.00 | 7736.685430 | 4508.027810 | 12244.713240\n",
      "6750.00 | 7808.419615 | 4365.855909 | 12174.275524\n",
      "6900.00 | 7971.634401 | 4051.663537 | 12023.297938\n",
      "7030.00 | 8123.817410 | 3768.540875 | 11892.358285\n",
      "7080.00 | 8185.232279 | 3656.700978 | 11841.933257\n",
      "7170.00 | 8301.307012 | 3449.766353 | 11751.073365\n",
      "7260.00 | 8424.638129 | 3235.513314 | 11660.151443\n",
      "7559.40 | 8896.848547 | 2460.683007 | 11357.531555\n",
      "7620.00 | 9008.676825 | 2287.573627 | 11296.250452\n",
      "7645.60 | 9058.090828 | 2212.268859 | 11270.359687\n",
      "7700.00 | 9167.735199 | 2047.600571 | 11215.335770\n",
      "7800.00 | 9387.672366 | 1726.494845 | 11114.167211\n",
      "8130.00 | 10487.415451 | 292.690959 | 10780.106411\n",
      "8460.00 | 10445.708266 | 0.000000 | 10445.708266\n",
      "10596.10 | 8261.135565 | 0.000000 | 8261.135565\n",
      "10597.10 | 8260.105204 | 0.000000 | 8260.105204\n",
      "10598.90 | 8258.250540 | 0.000000 | 8258.250540\n",
      "10599.00 | 8258.147503 | 0.000000 | 8258.147503\n",
      "10602.00 | 8255.056360 | 0.000000 | 8255.056360\n",
      "10602.20 | 8254.850282 | 0.000000 | 8254.850282\n",
      "10602.80 | 8254.232047 | 0.000000 | 8254.232047\n",
      "10603.20 | 8253.819890 | 0.000000 | 8253.819890\n",
      "10604.10 | 8252.892533 | 0.000000 | 8252.892533\n",
      "10605.70 | 8251.243888 | 0.000000 | 8251.243888\n",
      "10608.20 | 8248.667856 | 0.000000 | 8248.667856\n",
      "10608.90 | 8247.946562 | 0.000000 | 8247.946562\n",
      "10609.20 | 8247.637435 | 0.000000 | 8247.637435\n",
      "10609.50 | 8247.328307 | 0.000000 | 8247.328307\n",
      "10609.90 | 8246.916137 | 0.000000 | 8246.916137\n",
      "10612.10 | 8244.649184 | 0.000000 | 8244.649184\n",
      "10613.30 | 8243.412654 | 0.000000 | 8243.412654\n",
      "10614.30 | 8242.382208 | 0.000000 | 8242.382208\n",
      "10616.80 | 8239.806069 | 0.000000 | 8239.806069\n",
      "10616.90 | 8239.703023 | 0.000000 | 8239.703023\n",
      "10619.90 | 8236.611614 | 0.000000 | 8236.611614\n",
      "10623.50 | 8232.901856 | 0.000000 | 8232.901856\n",
      "10624.30 | 8232.077442 | 0.000000 | 8232.077442\n",
      "10624.40 | 8231.974390 | 0.000000 | 8231.974390\n",
      "10625.80 | 8230.531634 | 0.000000 | 8230.531634\n",
      "10626.30 | 8230.016355 | 0.000000 | 8230.016355\n",
      "10627.00 | 8229.294956 | 0.000000 | 8229.294956\n",
      "10627.90 | 8228.367431 | 0.000000 | 8228.367431\n",
      "10628.80 | 8227.439889 | 0.000000 | 8227.439889\n",
      "10629.80 | 8226.409270 | 0.000000 | 8226.409270\n",
      "10632.20 | 8223.935707 | 0.000000 | 8223.935707\n",
      "10632.20 | 8223.935707 | 0.000000 | 8223.935707\n",
      "10632.50 | 8223.626504 | 0.000000 | 8223.626504\n",
      "10636.40 | 8219.606711 | 0.000000 | 8219.606711\n",
      "10638.60 | 8217.339008 | 0.000000 | 8217.339008\n",
      "10640.40 | 8215.483547 | 0.000000 | 8215.483547\n",
      "10640.40 | 8215.483547 | 0.000000 | 8215.483547\n",
      "10641.10 | 8214.761963 | 0.000000 | 8214.761963\n",
      "10641.60 | 8214.246539 | 0.000000 | 8214.246539\n",
      "10645.30 | 8210.432261 | 0.000000 | 8210.432261\n",
      "10645.60 | 8210.122983 | 0.000000 | 8210.122983\n",
      "10646.20 | 8209.504424 | 0.000000 | 8209.504424\n",
      "10646.40 | 8209.298236 | 0.000000 | 8209.298236\n",
      "10647.30 | 8208.370381 | 0.000000 | 8208.370381\n",
      "10648.10 | 8207.545607 | 0.000000 | 8207.545607\n",
      "10649.60 | 8205.999125 | 0.000000 | 8205.999125\n",
      "10651.30 | 8204.246394 | 0.000000 | 8204.246394\n",
      "10652.80 | 8202.699822 | 0.000000 | 8202.699822\n",
      "10653.00 | 8202.493609 | 0.000000 | 8202.493609\n",
      "10654.10 | 8201.359424 | 0.000000 | 8201.359424\n",
      "10655.50 | 8199.915883 | 0.000000 | 8199.915883\n",
      "10655.60 | 8199.812772 | 0.000000 | 8199.812772\n",
      "10658.00 | 8197.338040 | 0.000000 | 8197.338040\n",
      "10658.40 | 8196.925574 | 0.000000 | 8196.925574\n",
      "10658.70 | 8196.616223 | 0.000000 | 8196.616223\n",
      "10660.40 | 8194.863200 | 0.000000 | 8194.863200\n",
      "10663.00 | 8192.182000 | 0.000000 | 8192.182000\n",
      "10664.30 | 8190.841352 | 0.000000 | 8190.841352\n",
      "10664.30 | 8190.841352 | 0.000000 | 8190.841352\n",
      "10665.30 | 8189.810063 | 0.000000 | 8189.810063\n",
      "10667.50 | 8187.541161 | 0.000000 | 8187.541161\n",
      "10671.80 | 8183.106224 | 0.000000 | 8183.106224\n",
      "10671.80 | 8183.106224 | 0.000000 | 8183.106224\n",
      "10673.40 | 8181.455925 | 0.000000 | 8181.455925\n",
      "10673.50 | 8181.352780 | 0.000000 | 8181.352780\n",
      "10674.90 | 8179.908727 | 0.000000 | 8179.908727\n",
      "10677.30 | 8177.433120 | 0.000000 | 8177.433120\n",
      "10677.60 | 8177.123662 | 0.000000 | 8177.123662\n",
      "10678.40 | 8176.298431 | 0.000000 | 8176.298431\n",
      "10681.10 | 8173.513188 | 0.000000 | 8173.513188\n",
      "10682.80 | 8171.759446 | 0.000000 | 8171.759446\n",
      "10688.30 | 8166.085200 | 0.000000 | 8166.085200\n",
      "10690.60 | 8163.712165 | 0.000000 | 8163.712165\n",
      "10690.90 | 8163.402631 | 0.000000 | 8163.402631\n",
      "10691.20 | 8163.093095 | 0.000000 | 8163.093095\n",
      "10692.20 | 8162.061298 | 0.000000 | 8162.061298\n",
      "10692.50 | 8161.751755 | 0.000000 | 8161.751755\n",
      "10695.70 | 8158.449859 | 0.000000 | 8158.449859\n",
      "10698.70 | 8155.354156 | 0.000000 | 8155.354156\n",
      "10699.20 | 8154.838189 | 0.000000 | 8154.838189\n",
      "10700.00 | 8154.012632 | 0.000000 | 8154.012632\n",
      "10702.20 | 8151.742287 | 0.000000 | 8151.742287\n",
      "10703.30 | 8150.607081 | 0.000000 | 8150.607081\n",
      "10703.50 | 8150.400677 | 0.000000 | 8150.400677\n",
      "10704.00 | 8149.884664 | 0.000000 | 8149.884664\n",
      "10704.70 | 8149.162239 | 0.000000 | 8149.162239\n",
      "10706.20 | 8147.614154 | 0.000000 | 8147.614154\n",
      "10708.40 | 8145.343552 | 0.000000 | 8145.343552\n",
      "10711.20 | 8142.453562 | 0.000000 | 8142.453562\n",
      "10712.10 | 8141.524605 | 0.000000 | 8141.524605\n",
      "10712.80 | 8140.802072 | 0.000000 | 8140.802072\n",
      "10714.30 | 8139.253757 | 0.000000 | 8139.253757\n",
      "10715.00 | 8138.531196 | 0.000000 | 8138.531196\n",
      "10716.60 | 8136.879592 | 0.000000 | 8136.879592\n",
      "10719.20 | 8134.195632 | 0.000000 | 8134.195632\n",
      "10720.70 | 8132.647135 | 0.000000 | 8132.647135\n",
      "10721.10 | 8132.234195 | 0.000000 | 8132.234195\n",
      "10721.80 | 8131.511544 | 0.000000 | 8131.511544\n",
      "10723.80 | 8129.446774 | 0.000000 | 8129.446774\n",
      "10724.40 | 8128.827328 | 0.000000 | 8128.827328\n",
      "10724.80 | 8128.414361 | 0.000000 | 8128.414361\n",
      "10729.70 | 8123.355263 | 0.000000 | 8123.355263\n",
      "10730.70 | 8122.322738 | 0.000000 | 8122.322738\n",
      "10731.70 | 8121.290194 | 0.000000 | 8121.290194\n",
      "10734.20 | 8118.708752 | 0.000000 | 8118.708752\n",
      "10735.40 | 8117.469618 | 0.000000 | 8117.469618\n",
      "10736.10 | 8116.746777 | 0.000000 | 8116.746777\n",
      "10736.80 | 8116.023927 | 0.000000 | 8116.023927\n",
      "10738.60 | 8114.165127 | 0.000000 | 8114.165127\n",
      "10740.70 | 8111.996450 | 0.000000 | 8111.996450\n",
      "10741.20 | 8111.480086 | 0.000000 | 8111.480086\n",
      "10742.70 | 8109.930966 | 0.000000 | 8109.930966\n",
      "10746.30 | 8106.212903 | 0.000000 | 8106.212903\n",
      "10747.10 | 8105.386634 | 0.000000 | 8105.386634\n",
      "10748.00 | 8104.457066 | 0.000000 | 8104.457066\n",
      "10748.50 | 8103.940633 | 0.000000 | 8103.940633\n",
      "10749.70 | 8102.701174 | 0.000000 | 8102.701174\n",
      "10752.30 | 8100.015587 | 0.000000 | 8100.015587\n",
      "10753.10 | 8099.189227 | 0.000000 | 8099.189227\n",
      "10754.90 | 8097.329872 | 0.000000 | 8097.329872\n",
      "10757.80 | 8094.334116 | 0.000000 | 8094.334116\n",
      "10759.70 | 8092.371292 | 0.000000 | 8092.371292\n",
      "10760.60 | 8091.441510 | 0.000000 | 8091.441510\n",
      "10763.70 | 8088.238810 | 0.000000 | 8088.238810\n",
      "10766.10 | 8085.759176 | 0.000000 | 8085.759176\n",
      "10767.00 | 8084.829284 | 0.000000 | 8084.829284\n",
      "10769.80 | 8081.936192 | 0.000000 | 8081.936192\n",
      "10772.40 | 8079.249616 | 0.000000 | 8079.249616\n",
      "10774.70 | 8076.872923 | 0.000000 | 8076.872923\n",
      "10776.50 | 8075.012833 | 0.000000 | 8075.012833\n",
      "10778.30 | 8073.152681 | 0.000000 | 8073.152681\n",
      "10781.50 | 8069.845593 | 0.000000 | 8069.845593\n",
      "10786.50 | 8064.677880 | 0.000000 | 8064.677880\n",
      "10787.80 | 8063.334197 | 0.000000 | 8063.334197\n",
      "10790.90 | 8060.129901 | 0.000000 | 8060.129901\n",
      "10793.30 | 8057.649032 | 0.000000 | 8057.649032\n",
      "10796.00 | 8054.857922 | 0.000000 | 8054.857922\n",
      "10798.50 | 8052.273439 | 0.000000 | 8052.273439\n",
      "10799.10 | 8051.653145 | 0.000000 | 8051.653145\n",
      "10800.60 | 8050.102381 | 0.000000 | 8050.102381\n",
      "10802.20 | 8048.448186 | 0.000000 | 8048.448186\n",
      "10803.00 | 8047.621070 | 0.000000 | 8047.621070\n",
      "10804.60 | 8045.966802 | 0.000000 | 8045.966802\n",
      "10805.90 | 8044.622674 | 0.000000 | 8044.622674\n",
      "10807.10 | 8043.381911 | 0.000000 | 8043.381911\n",
      "10810.30 | 8040.073079 | 0.000000 | 8040.073079\n",
      "10812.40 | 8037.901552 | 0.000000 | 8037.901552\n",
      "10817.10 | 8033.041165 | 0.000000 | 8033.041165\n",
      "10819.20 | 8030.869367 | 0.000000 | 8030.869367\n",
      "10822.70 | 8027.249519 | 0.000000 | 8027.249519\n",
      "10824.30 | 8025.594654 | 0.000000 | 8025.594654\n",
      "10824.40 | 8025.491224 | 0.000000 | 8025.491224\n",
      "10827.80 | 8021.974468 | 0.000000 | 8021.974468\n",
      "10828.50 | 8021.250403 | 0.000000 | 8021.250403\n",
      "10832.20 | 8017.423047 | 0.000000 | 8017.423047\n",
      "10832.30 | 8017.319602 | 0.000000 | 8017.319602\n",
      "10845.60 | 8003.559642 | 0.000000 | 8003.559642\n",
      "10849.80 | 7999.213695 | 0.000000 | 7999.213695\n",
      "10851.40 | 7997.558008 | 0.000000 | 7997.558008\n",
      "10855.30 | 7993.522068 | 0.000000 | 7993.522068\n",
      "10858.70 | 7990.003321 | 0.000000 | 7990.003321\n",
      "10868.70 | 7979.652794 | 0.000000 | 7979.652794\n",
      "10876.10 | 7971.992183 | 0.000000 | 7971.992183\n",
      "10878.90 | 7969.093303 | 0.000000 | 7969.093303\n",
      "10882.50 | 7965.365952 | 0.000000 | 7965.365952\n",
      "10884.40 | 7963.398640 | 0.000000 | 7963.398640\n",
      "10885.70 | 7962.052545 | 0.000000 | 7962.052545\n",
      "10888.20 | 7959.463810 | 0.000000 | 7959.463810\n",
      "10891.20 | 7956.357173 | 0.000000 | 7956.357173\n",
      "10970.00 | 7874.726083 | 0.000000 | 7874.726083\n",
      "11010.00 | 7833.275755 | 0.000000 | 7833.275755\n"
     ]
    }
   ],
   "source": [
    "# Now we will make table of excitation energy, dE energy, E energy and total energy deposited.\n",
    "\n",
    "# Now we have beam energy:\n",
    "Ebeam = 27.36 # Proton energy [MeV]\n",
    "Twidth = 4.56 # Target thickness [mg/cm^2]\n",
    "\n",
    "Fwidth = 10 # Al-absorber width [um]\n",
    "dEwidth = 309 # delta-E detector width [um]\n",
    "Ewidth = 1041 # E detector width [um] \n",
    "\n",
    "th = ScatteringAngle(14, 22.0, 11.0, 0.491, 0.5)[0]\n",
    "\n",
    "e, de = SimulateNiPP(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, ReadStates(\"states64Ni.txt\")*1e-3, th)\n",
    "ex = ReadStates(\"states64Ni.txt\")\n",
    "print \"Excitation energy [keV] | dE energy [keV] | E energy [keV] | dE+E energy [keV]\"\n",
    "for i in range(len(ex)):\n",
    "    print \"%3.2f | %2.6f | %2.6f | %2.6f\" % (ex[i], de[i]*1e3, e[i]*1e3, (de[i]+e[i])*1e3)\n",
    "print \"\\n\\n\\n\\n\"\n",
    "\n",
    "e, de = SimulateNiPD(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, ReadStates(\"states63Ni.txt\")*1e-3, th)\n",
    "ex = ReadStates(\"states63Ni.txt\")\n",
    "print \"Excitation energy [keV] | dE energy [keV] | E energy [keV] | dE+E energy [keV]\"\n",
    "for i in range(len(ex)):\n",
    "    print \"%3.2f | %2.6f | %2.6f | %2.6f\" % (ex[i], de[i]*1e3, e[i]*1e3, (de[i]+e[i])*1e3)\n",
    "print \"\\n\\n\\n\\n\"\n",
    "\n",
    "e, de = SimulateNiPT(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, ReadStates(\"states62Ni.txt\")*1e-3, th)\n",
    "ex = ReadStates(\"states62Ni.txt\")\n",
    "print \"Excitation energy [keV] | dE energy [keV] | E energy [keV] | dE+E energy [keV]\"\n",
    "for i in range(len(ex)):\n",
    "    print \"%3.2f | %2.6f | %2.6f | %2.6f\" % (ex[i], de[i]*1e3, e[i]*1e3, (de[i]+e[i])*1e3)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[    2.69607834  1126.1956859 ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110f71e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x110e54c10>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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TFnge8PyB7f9kZp1yM/vftL1yscz3QXo+H/gOcNyc44fOaffnc19Xm72ReNZC9jznmPt5+qbt2Od5nrl+NzP31GBmeeeBrtdFO9fA3cBru/q5wPbFMNe9/MEtxRf7B/5K4EZgJ/B1Zq6c6f6QPsLMEwA7gYmBz38nMzeNdgPvGFPfF3d93QF8BTitq/8cM1cZu4HbZuvdvsu7/55ddE8V9NjraV1vdwB3AZd39RcAXwbuYeZpjGMXy3wfpOfdXfDc3r2umm9OmXlC43vdvssXuuc5x9zP04E/9nmeZ66fC3wCuBP4FvD6xT7XwKuA7V39VuBli2Gu/U1bSWpE62v4ktQMA1+SGmHgS1IjDHxJaoSBL0mNMPAlqREGviQ1wsCXpEb8P0jJpX3jXdGSAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110e54890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ch = array([5.83E+03,5.03E+03,4.49E+03])\n",
    "ex = array([16851.31101,14670.15238,13241.92612])\n",
    "\n",
    "ch = array([5.86448e+03,5.09801e+03,4.57121e+03])\n",
    "ex = array([16830.569588,14640.032204,13209.962576])\n",
    "\n",
    "p = polyfit(ch, ex, 1)\n",
    "print p\n",
    "\n",
    "plt.plot(ch, ex, \"o\")\n",
    "plt.plot(linspace(3500, 6000, 1001), p[0]*linspace(3500, 6000, 1001)+p[1])\n",
    "plt.plot(linspace(3500, 6000, 1001), 2.71185596591*linspace(3500, 6000, 1001)+143.674174063)\n",
    "plt.show()\n",
    "\n",
    "plt.plot(ch, ex - p[0]*ch - p[1], \"o\")\n",
    "plt.plot(ch, [0,0,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 6014.42  5999.11  5981.23  5964.63  5948.91  5934.    5917.42  5897.86\n",
      "  5873.97  5858.35  5846.12  5825.9   5798.53]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11383f6d0>]"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110554c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = array(range(0, 15))\n",
    "e, de = SimulateNiPD(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, ReadStates(\"states63Ni.txt\")*1e-3, th)\n",
    "\n",
    "n = array([0, 1, 2, 3, 4, 5, 9, 10, 11, 12, 13, 14,15])\n",
    "x = array([5825.9,5858.35,5897.86,5934,5964.63,5999.11,6014.42,5981.23,5948.91,5917.42,5873.97,5846.12,5798.53])\n",
    "\n",
    "y = copy(x[x.argsort()])\n",
    "print y[::-1]\n",
    "\n",
    "plt.plot(n, x, \"o\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3: 28.610 - 16788.106 keV\n",
      "4: 29.110 - 16766.396 keV\n",
      "5: 29.604 - 16744.374 keV\n",
      "6: 30.094 - 16722.046 keV\n",
      "7: 30.579 - 16699.418 keV\n",
      "8: 31.059 - 16676.495 keV\n",
      "9: 31.535 - 16653.282 keV\n",
      "10: 32.005 - 16629.785 keV\n",
      "11: 32.471 - 16606.009 keV\n",
      "12: 32.932 - 16581.959 keV\n",
      "13: 33.389 - 16557.641 keV\n",
      "14: 33.840 - 16533.058 keV\n",
      "15: 34.287 - 16508.217 keV\n",
      "[  1.32135398e+00   8.83899412e+03]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1136e4050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  3.74121237e+00   2.05866189e-01   4.23361458e+00   2.76949199e+00\n",
      "   3.70109507e-02   1.16563421e+01   2.22666939e+01   5.61667437e+00\n",
      "   2.93907150e+01   4.04468325e+00   3.77886663e+01   1.60951245e+01\n",
      "   5.34681854e+01]\n",
      "191.314280843   17.3922073494\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11237a610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e_gs = zeros(16-3)\n",
    "for i in range(3,16):\n",
    "    th = ScatteringAngle(i, 22.0, 11.0, 0.491, 0.5)[0]\n",
    "    e, de = SimulateNiPD(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, 0, th)\n",
    "    e_gs[i-3] = e\n",
    "    print \"%d: %2.3f - %2.3f keV\" % (i, th*180./pi, e*1e3)\n",
    "\n",
    "e_found = y[::-1]\n",
    "p = polyfit(e_found, e_gs*1e3, 1)\n",
    "print p\n",
    "plt.plot(e_found, e_gs*1e3, \"o\")\n",
    "plt.plot(linspace(e_found[0],e_found[-1],1001),p[0]*linspace(e_found[0],e_found[-1],1001)+p[1])\n",
    "plt.show()\n",
    "print ( e_found*p[0]+p[1]-e_gs*1e3 )**2\n",
    "chi2 = sum((e_found*p[0]+p[1]-e_gs*1e3)**2)\n",
    "print chi2, \" \", chi2/(len(e_found)-2)\n",
    "\n",
    "plt.plot(e_found,e_found*p[0]+p[1]-e_gs*1e3,\"o\")\n",
    "#plt.plot(e_found, zeros(len(e_found)))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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S2OdaWLvr0o+zGuWkYmbFbcnipBPjs39PXve6BLofDSs1yDYuq5CTipkVr2nvw2MnwuQ3YP1dkk6MLdbLOiqrgpOKmRWfRfPhpSvgpX9Bk9Vg35th0wPcibEWcFIxs+Iy6Y2kE+P0D2DTA5Ne8au2yjoqy5OTipkVh/lfJ1P6vnEzNGsDhzwEnX+TdVS2jJxUzCx7Hz4NQ0+CuVNg6/+Dnc9JbntZreOkYmbZ+farZOKs9x6CNTeCI5+Gdt2zjspWgJOKmdW8CHj3fnjqzOS2V8+zYPuToGHjrCOzFeSkYmY1a9anMPQvMOF5aNs96cS41kZZR2XVxEnFzGrGksUw8t/w/IWglaD35VByJKxU0xPQWiE5qZhZ4X05NnlMeMpo6Lwb7HkFNG+XdVRWAE4qZlY4C7+Hly6Hl6+ElZvDfrfCL/dzJ8Y6rGDXnZJukzQtnY++rOx8SVMkvZ0uvdPyDpLm5ZTflHPMlpLGSBov6Rop+d8oqaWkZyR9lP7bolB1MbPl8Olr8O8d4MUBSW/440fBpvs7odRxhbyZeQfQq4LyKyOiW7o8mVM+Iaf8mJzyG4E/Ap3Tpew9zwCei4jOwHPpazPL2vdzYehf4fZesOh7OHQw/PYmWKVl1pFZDShYUomIF4GZK/IektYFmkXE6xERwF1A33RzH+DOdP3OnHIzy8q4YXD91jD6duhxHPzpNdhgl6yjshpUaZuKpHz+rFgSEbOX8ZzHSzoMKAVOjohZaXlHSW8Bc4FzIuIloA0wOefYyWkZwNoR8Xm6/gWwdmUnlHQ0cDRA+/btlzFcM1uqb6bBsNNg7COw1ibwu3ug7ZZZR2UZqKqhfmq6VHUDtAGwLN/SNwIXApH++y/gCOBzoH1EzJC0JTBE0ib5vmlEhKSoYvtAYCBASUlJpfuZ2TKKgLf/k0ztu/C7ZHiVbf/sToz1WFVJ5f2I2Lyqg9Mri7xFxJc5x94MDE3L5wPz0/XRkiYAGwJTgLY5b9E2LQP4UtK6EfF5epts2rLEYmYraOYn8Pif4ZMXoP22sPfVsOaGWUdlGauqTaVHHsdvsywnS7/8y/wWeC8tX1NSg3S9E0mD/Mfp7a25knqkT30dBjyaHv8Y0D9d759TbmaFtHgRvHot3LANTHkz6XNy+BNOKAZUfaUyWNJ9wJCI+KaiHSLi+8oOTo/tCbSSNBk4D+gpqRvJ7a+JwP+lu+8IXCBpIbAEOCYiyhr5jyV5kqwpMCxdAC4BHpB0JPApcGCVNTWzFffFmKQT49S3oEvvpFf86m2WfpzVG0oeqqpgg9QH6AfsAowA7gOeiIgFNRZdAZSUlERpaWnWYZjVLgvnwQuXwStXJ48G9x4AXfu6z0k9Iml0RJQsbb9Kr1Qi4lHgUUmrAHuT3Hq6UdIw4D8R8Uy1RWtmxWviy8k88TMnwOaHwm8udJ8Tq9RSh2mJiO+A+4H7Jf2KpE/IYSRPfplZXTVvNjx7Hoy+A1p0gMMehU49s43Jit5Sk4qktUnaK/oB6wIPAIcXNiwzy9T7j8MTp8C302DbE5L5ThqvknVUVgtU1fnxj8BBQBfgYeDUiHi1pgIzswx8/QU8eSq8/xisvSkcPAhaV9mzwOwnqrpS2Qa4mGR8rSU1FI+ZZSEC3robnj4nGVl4l/OSK5QGjbKOzGqZqhrqjwBQ4lCgU0RcIKk9sE5EvFFTQZpZAc2YkHRinPgSrLc97HMNrLF+1lFZLZXPfCo3kPQd2Rm4APia5HbYVgWMy8wKbfEieO1aGHEJNGiS9Ijf/DDPxGgrJJ+ksnVEbFE2JEtEzJLkgX3MarOpbyedGL94FzbaK+nE2GzdpR9nthT5JJWF6RAqAcmQKiRXLmZW2yz4Dl64BF69DlZtBQfeDV33yToqq0PySSrXAI8Aa0n6B7A/8LeCRmVm1e/jF5K2k1mfwBb94TcXQNPmWUdldUw+nR/vlTSaZLgWAX0j4v2CR2Zm1WPerOSprrfugZadoP/j0HHHrKOyOiqfzo9HRsStwAc5ZZdEhKfvNStmEfC/R5N+J9/NgO3+Aj3PgEZNs47M6rB8bn/tJ+n7iLgXQNL1wMqFDcvMVsjcqUky+WAorLsZHPpQ8q9ZgeWVVIDHJC0BegGzI+LIwoZlZstlyRJ48w545jxYvDAZ/LHHsdAgn191sxWX7xz1RwFDgFeAv0tqmTPfiZkVg68+ShriP30laTPZ++qkDcWsBlX158tokseIlfPvnukSgP+3mhWDxQuTeU5euAwarQz7XJcMUe+5TiwDVQ3T0rEmAzGz5TDlzaQT45fvJZNm7XEZrLZ21lFZPVbpeAyStljawVXtI+k2SdMkvZdTdr6kKZLeTpfeOdvOlDRe0jhJu+eU90rLxks6I6e8o6SRafn97uVv9cqCb2H42XDLLsmTXf3+Awfe6YRimatqkJ/bJbWQ1LKyBbi1iuPvIGnYL+/KiOiWLk8CSOpKMl/LJukxN0hqkPbkvx7YA+gKHJTuC3Bp+l4bALMAPzxg9cOE5+GGbeC162DLw+G4kbDRnllHZQZU3aayOkm7SlU3ZqdXtiEiXpTUIc84+gCDImI+8Imk8UD3dNv4iPgYQNIgoI+k90kGuDw43edO4HzgxjzPZ1b7fDczuTp55z+wxgbwh2Gw3rZZR2X2E1W1qXQo0DmPl3QYUAqcHBGzgDbA6zn7TE7LACaVK98aWIPk0eZFFexvVrdEwNjBMOz0pHf8DqfAjqcmjfJmRaamx7i+EVgf6AZ8DvyrJk4q6WhJpZJKp0+v9OLKrPjMmQL39YOHjoDV28LRI2CXvzmhWNGq0R5REfFl2bqkm4Gh6cspQLucXdumZVRSPgNoLqlherWSu39F5x0IDAQoKSmJFayGWeEtWQKlt8Kzf4dYDLv/E7Y+BlZqkHVkZlWq0SsVSbkTNvwWKHsy7DGgn6QmkjoCnYE3gFFA5/RJr8YkjfmPRUQA/yUZMRmgP/BoTdTBrOCmj4Pb94AnT4G2JXDsa7DNcU4oVivkM6DkYJKnvIYty1z1ku4DegKtJE0GzgN6SupG0nlyIvB/ABExVtIDwP+ARcBxEbE4fZ/jgeFAA+C2iBibnuJ0YJCki4C3qPpJNLPit2gBvHIVvDgAGq8KfW+Czfq5E6PVKkr+6K9iB2lX4A9AD+BB4PaIGFcDsRVESUlJlJaWZh2G2U9NGpV0Ypz+PvxyP+h1KfxizayjMvuBpNERUbK0/fKZT+VZ4FlJqwMHpeuTgJuBeyJi4QpHa1Zfzf8Gnr8IRt4EzVrDQfdDl4q6d5nVDnk11EtaAzgU+D3JraZ7ge1J2jJ6Fio4szrto2dh6EkwZxJsdRTsci6s3CzrqMxWSD5tKo8AXYC7gb0j4vN00/2SfB/JbFl9OwOGnwnv3g+tusART0H7HllHZVYt8pqjPiL+W9GGfO6vmVkqAsY8BE+dDt/PhV+fDjucDA2bZB2ZWbXJJ6m0kLRvubI5wJiImFaAmMzqntmfwdC/wvhnoE0J7HMtrN116ceZ1TL5JJUjgW1I+oVA0oYyGugo6YKIuLtAsZnVfksWw6hbkk6MkDzV1f2P7nNidVY+SaURsHFZb3hJawN3kYzB9SJJW4uZlTft/eQx4cmjYINdYa8roXn7rKMyK6h8kkrb3OFVgGlAu4iYKcmPE5uVt2g+vHQFvPQvaLIa7HszbHqAOzFavZBPUhkhaShJx0eA/dKyVYHZBYvMrDb6bGRydfLVONj0QOh1MazaKuuozGpMPknlOGBfkn4pkNz6ejgdf2unQgVmVqvM/xqeuwDeuDkZTfiQh6Dzb7KOyqzGVZlU0pkXn42InYCHayYks1rmw+HJk11zp8DW/wc7/w2a/CLrqMwyUWVSiYjFkpZIWj0i5tRUUGa1wjfT4akz4L2HYM2N4chnoN1WWUdllql8bn99A4yR9AzwbVlhRJxYsKjMilkEvDMo6RW/4FvY6WzY7i/QsHHWkZllLp+kMjhdzGzWxGS8rgnPQ7utYe9rYK2Nso7KrGjkM0rxnZKaAu1r85D3ZitkyeJkJOHnLwKtBL0vh5IjYaWanpHbrLgt9TdC0t7A28BT6etukh4rdGBmReOL9+CWXWH4WdBhB4b3fJTtnl+fjmcNY7tLnmfIW5XOZG1W7+Rz++t8oDswAiAi3pbUqYAxmRWHhd8nszC+chWs3Bz2u5UhC3tw5iPvMW/hYgCmzJ7HmYPHANB38zZZRmtWFPK5dl9YwZNfeU8rbFYrffoq3LQ9vHR50onx+FGw6f4MePrDHxJKmXkLFzNguO8Mm0F+SWWspIOBBpI6S7oWeHVpB0m6TdI0Se9VsO1kSSGpVfq6p6Q5kt5Ol3Nz9u0laZyk8ZLOyCnvKGlkWn6/JD96Yyvu+7lJQ/zte8Di+XDoYPjtjbBKSwCmzp5X4WGVlZvVN/kklROATYD5wH3AXOAveRx3B/CzeVEltQN2Az4rt+mliOiWLhek+zYArgf2ALoCB0kqGy/8UuDKiNgAmEUymrLZ8vvgSbh+axh9B2xzPBz7Omywy092ad28aYWHVlZuVt8sNalExHcRcXZEbBURJen693kc9yIws4JNVwKnAZFHfN2B8RHxcUQsAAYBfSQJ2Bl4KN3vTqBvHu9n9nPfTIMHD4dBB0HTFnDks7D7P6Dxqj/b9dTdu9C00U+HrW/aqAGn7t6lhoI1K275TCe8IXAK0CF3/4jYeVlPJqkPMCUi3tHPR2zdRtI7wFTglIgYC7QBJuXsM5lkyP01gNkRsSinvNJWUklHA0cDtG/vocctFQFv3wvDz4aF85LhVbb7MzRoVOkhZY3xA4aPY+rsebRu3pRTd+/iRnqzVD5Pfz0I3ATcAixeyr6VkrQKcBbJra/y3gTWi4hvJPUGhgCdl/dc5UXEQGAgQElJST5XSFbXzfwYHv8LfPICtN8W9rkGWuX3X67v5m2cRMwqkU9SWRQRN1bDudYHOgJlVyltgTcldY+IL8p2iognJd2QNuJPAdrlvEfbtGwG0FxSw/RqpazcrGqLF8HrN8B//wkrNYQ9r4At/+BOjGbVJJ+k8rikY4FHSBrrAYiIitpLKhURY4C1yl5LmgiURMRXktYBvoyIkNSdpK1nBsl8LZ0ldSRJGv2Ag9P9/gvsT9LO0h94dFnisXro83eTuU4+fxu69IY9/wXNWmcdlVmdkk9S6Z/+e2pOWQBVdoCUdB/JfPatJE0GzouIWyvZfX/gT5IWAfOAful8LYskHQ8MBxoAt6VtLQCnA4MkXQS8BVT23lbfLZwHL1wKr1wDq6wBB9wJXft4JkazAlDy3V1/lJSURGlpadZhWE2Z+DI8diLMnACbHwq/ufCHPidmlj9JoyOiZGn7VXojWdJpOesHlNv2zxULz6zA5s1Okskde0IshsMehT7XO6GYFVhVrZP9ctbPLLftZ50azYrG+48nnRjfuhu2PRH+9Bp06pl1VGb1QlVtKqpkvaLXZtn7+gt48pQkqayzKRw8CFpvnnVUZvVKVUklKlmv6LVZdiLgzbvg6b8l43Xten4yzEoVnRjNrDCqSiqbSZpLclXSNF0nfb1ywSMzy8eMCfD4n2HiS9BhB9j7alhj/ayjMqu3Kk0qEdGgsm1mmVu8EF67DkZcAg2aJNP6bnGYHxM2y1g+/VTMisvUt5NOjF+8CxvvDXsMgGbrZh2VmeGkYrXJgu9gxMXw2vWw6ppw4N3QdZ+sozKzHE4qVjt8/ELSdjLrE9iiP/zmAmjaPOuozKwcJxUrbvNmwdPnwFv3QMtO0H8odNwh66jMrBJOKlacIuB/j8KTp8J3M2D7k+DXp0Mjz7BoVsycVKz4zJ0KT5wC456AdTeDQx+GdX+VdVRmlgcnFSseS5bAm3fAM+cljwz/5kLocSw08H9Ts9rCv61WHL76KBkA8rNXoeOvYe+rkjYUM6tVnFQsW4sXwitXwQsDoNHKyUjC3Q5xJ0azWspJxbIzZTQ8egJMGwtd+8Iel8Fqa2cdlZmtACcVq3kLvk3miH/9BvjF2tDvP7DRnllHZWYaCjugAAAR40lEQVTVwEnFatb452DoX2D2Z1ByJOx6Hqy8etZRmVk1qWqSrhUm6TZJ0yS9V8G2kyWFpFbpa0m6RtJ4Se9K2iJn3/6SPkqX/jnlW0oakx5zjeQb8UXru5nwyJ/gnn2TASD/MAz2usIJxayOKWhSAe6gglkiJbUDdgM+yyneA+icLkcDN6b7tgTOA7YGugPnSWqRHnMj8Mec4zwjZbGJgDEPwXVbwZgHYIdT4JiXYb1ts47MzAqgoEklIl4EZlaw6UrgNH462Vcf4K5IvA40l7QusDvwTETMjIhZwDNAr3Rbs4h4PSICuAvoW8j62DKaMxnu6wcPHwnN28PRL8Auf0ue8jKzOqnG21Qk9QGmRMQ75e5WtQEm5byenJZVVT65gvKKznk0ydUP7du3X8Ea2FItWQKlt8Kzf4dYDLv/E7Y+BlbyFD1mdV2NJhVJqwBnkdz6qjERMRAYCFBSUuKpkAtp+rhkrpNJI2H9nWGvK6FFh6yjMrMaUtNXKusDHYGyq5S2wJuSugNTgHY5+7ZNy6YAPcuVj0jL21awv2Vh0QJ4+Up46XJovCr0vQk26+dOjGb1TKEb6n8iIsZExFoR0SEiOpDcstoiIr4AHgMOS58C6wHMiYjPgeHAbpJapA30uwHD021zJfVIn/o6DHi0JutjqUmj4N87woh/wsb7wHGjoNtBTihm9VBBr1Qk3UdyldFK0mTgvIi4tZLdnwR6A+OB74A/AETETEkXAqPS/S6IiLLG/2NJnjBrCgxLF6sp87+B5y+CkTdBs9Zw0P3QxQ/gmdVnSh6cqj9KSkqitLQ06zBqv4+eTToxzpkM3f8Iu5wLTVbLOiozKxBJoyOiZGn7uUe9LZtvZ8BTZyR9Tlp1gSOGQ/uts47KzIqEk4rlJwLGPJgklO/nwq/PgB3+Cg2bZB2ZmRURJxVbutmfwdC/wvhnoE0J7HMtrN0166jMrAg5qVjlliyGN26G5y5IXu9xGWx1lDsxmlmlnFSsYtPeTzoxTh4FG/wmGfyxuUcjMLOqOanYTy2aDy/9C166AlZuBvveApvu7z4nZpYXJxX70Wcjk6uTr8bBr34Hu18Mq66RdVRmVos4qRjM/zoZ/HHULbB6WzjkYei8a9ZRmVkt5KRS3304HIaeBHOnJiMJ73wONPlF1lGZWS3lpFJffTMdnjod3nsY1uoKB94FbZfaWdbMrEpOKvVNBLwzCIafCQu+hZ3Ohu3+Ag0bZx2ZmdUBTir1yayJya2uCc9Du61h72tgrY2yjsrM6hAnlfpgyeJkJOHnLwKtBL0vh5IjYaUanfnAzOoBJ5W67ov3kseEp74JG/aCPf+VPOFlZlYATip11cLv4cUB8MpVsHJz2P822GRfd2I0s4JyUqmLJr4Cj58IM8bDZgfD7v+AVVpmHZWZ1QNOKnXJ93Pg2fOh9LZknK7fPwLr75x1VGZWjxSspVbSbZKmSXovp+xCSe9KelvS05Jap+U9Jc1Jy9+WdG7OMb0kjZM0XtIZOeUdJY1My++XVL+fif3gSbi+B4y+A7Y5Ho593QnFzGpcIR//uQMoP2H5gIj4VUR0A4YC5+ZseykiuqXLBQCSGgDXA3sAXYGDJJVN5HEpcGVEbADMAo4sXFWK2NdfwgP9YdBByS2uo55Nbnc1XjXryMysHipYUomIF4GZ5crm5rxcFYilvE13YHxEfBwRC4BBQB9JAnYGHkr3uxPoWy2B1xYR8ObdcP1WMG4Y7Pw3OHoEtNky68jMrB6r8TYVSf8ADgPmADvlbNpG0jvAVOCUiBgLtAEm5ewzGdgaWAOYHRGLcsrbFDr2ojHzY3j8z/DJi9B+W9jnGmjVOeuozMwKevurQhFxdkS0A+4Fjk+L3wTWi4jNgGuBIdV5TklHSyqVVDp9+vTqfOuatXgRvHIN3LAtTH0b9roSDn/CCcXMikaWXarvBfaD5LZYRHyTrj8JNJLUCpgCtMs5pm1aNgNoLqlhufIKRcTAiCiJiJI111yz+mtSEz5/F27ZGZ75W9IAf9xIKDnCveLNrKjU6DeSpNw/qfsAH6Tl66TtJEjqnsY1AxgFdE6f9GoM9AMei4gA/gvsn75Xf+DRmqlFDVs4L3lMeGBPmPs5HHAn9LsXmrXOOjIzs58pWJuKpPuAnkArSZOB84DekroAS4BPgWPS3fcH/iRpETAP6JcmjkWSjgeGAw2A29K2FoDTgUGSLgLeAm4tVF0y88lLSSfGmR/D5ofCbhdB0xZZR2VmVikl3931R0lJSZSWlmYdRtXmzU5uc715F7ToAHtfDZ16ZhyUmdVnkkZHxFInXXKP+mLz/uPwxCnw7TTY9kToeSY0XiXrqMzM8uKkUizmfg7DTk2SyjqbwsH3Q+tuWUdlZrZMnFSyFgFv3glPnwuL58Ouf4dtjoMGjbKOzMxsmTmpZGnGhKQT48SXoMMOSdvJGutnHZWZ2XJzUsnC4oXw6rUw4hJouHIyre8Wh3muEzOr9ZxUatrUt5KZGL8YAxvvA70HwGrrZB2VmVm1cFKpKQu+gxH/hNeuh1XXgt/dAxvvnXVUZmbVykmlJnw8Imk7mTURtjw8aYxv2jzjoMzMqp+TSiHNmwXDz4G374GW6yeDP3bYPuuozMwKxkmlECLgf0PgydPguxmw/V/h16dBo6ZZR2ZmVlBOKtVt7tSkR/y4J2DdbnDow7Dur7KOysysRjipVJclS2D07cmIwosXJoM/bv0naOAfsZnVH/7Gy8OQt6YwYPg4ps6eR+vmTTl19y703TxnosmvPoLHToTPXoWOv4a9r4KWnbIL2MwsI04qSzHkrSmcOXgM8xYuBmDK7HmcOXgMAH1/tRa8chW8cBk0WgX6XA/dDnEnRjOrt5xUlmLA8HE/JJQy8xYu5vFhQ+n72p0wbSxs8lvodSmstnZGUZqZFQcnlaWYOnveT1435XtObvggf5j/FMxbF/rdBxv1zig6M7Pi4qSyFK2bN2VKmlh2WOld/tnwVtqtNJ3BDXqx73EDYeXVM47QzKx41Ogc9bXRqbt3oWmjBvyz4S3c3fgSFtCQQxb/nZX2usIJxcysnIImFUm3SZom6b2csgslvSvpbUlPS2qdlkvSNZLGp9u3yDmmv6SP0qV/TvmWksakx1wjVX8Led/N23Dxvpsya+W2XLuoL0c1vYoD9j3gp09/mZkZUOA56iXtCHwD3BURv0zLmkXE3HT9RKBrRBwjqTdwAtAb2Bq4OiK2ltQSKAVKgABGA1tGxCxJbwAnAiOBJ4FrImJYVTHVijnqzcyKTL5z1Bf0SiUiXgRmliubm/NyVZJEAdCHJPlERLwONJe0LrA78ExEzIyIWcAzQK90W7OIeD2SzHgX0LeQ9TEzs6pl0lAv6R/AYcAcYKe0uA0wKWe3yWlZVeWTKyiv6HxHA0cDtG/ffsUrYGZmFcqkoT4izo6IdsC9wPE1cL6BEVESESVrrrlmoU9nZlZvZf30173Afun6FKBdzra2aVlV5W0rKDczs4zUeFKR1DnnZR/gg3T9MeCw9CmwHsCciPgcGA7sJqmFpBbAbsDwdNtcST3Sp74OAx6tuZqYmVl5BW1TkXQf0BNoJWkycB7QW1IXYAnwKXBMuvuTJE9+jQe+A/4AEBEzJV0IjEr3uyAiyhr/jwXuAJoCw9LFzMwyUtBHiouRHyk2M1t2RfFIsZmZ1S/17kpF0nSS224rqhXwVTW8T9Zcj+JRF+oAdaMedaEOUL31WC8ilvr4bL1LKtVFUmk+l4LFzvUoHnWhDlA36lEX6gDZ1MO3v8zMrNo4qZiZWbVxUll+A7MOoJq4HsWjLtQB6kY96kIdIIN6uE3FzMyqja9UzMys2jipmJlZtXFSKUdSA0lvSRqavt5F0pvpTJUvS9ogLW8i6f501smRkjrkvMeZafk4SbtnUIeJ6YyYb0sqTctaSnomnT3zmXQcteWacTPjegyQ9EEa6yOSmufsX+HPXVKvtGy8pDOyrkPOtpMlhaRW6eta9Vmk5Sekn8dYSZfllBfdZ1FZPSR1k/R6WZmk7ml5UX4ekppLeij9ub8vaZui+v2OCC85C/BX4D/A0PT1h8DG6fqxwB056zel6/2A+9P1rsA7QBOgIzABaFDDdZgItCpXdhlwRrp+BnBput6bZMw0AT2AkWl5S+Dj9N8W6XqLIqjHbkDDdP3SnHpU+HNPlwlAJ6Bxuk/XLOuQlrcjGSz107LttfCz2Al4FmiSvl6rmD+LKurxNLBHzmcwopg/D+BO4Kh0vTHQvJh+v32lkkNSW2BP4Jac4gCapeurA1PT9T4kHy7AQ8AukpSWD4qI+RHxCckAmd0LHXsecuO9kx9nyVymGTdrOujyIuLpiFiUvnydH6c/qOzn3h0YHxEfR8QCYFC6b9auBE7jx5lPoZZ9FsCfgEsiYj5ARExLy2vbZ1HV73hRfR6SVgd2BG4FiIgFETGbIvr9dlL5qatIftGX5JQdBTypZJTl3wOXpOU/zEiZfsnNAdag8pkqa1IAT0sarWTWS4C1I5kuAOALYO10fVln3KxJFdUj1xH8ODJ1sdbjZ3WQ1AeYEhHvlNu3WOsAFX8WGwI7KLn9+4KkrdLy2laPvwADJE0CLgfOTMuLsR4dgenA7Upu098iaVWK6Pc7k+mEi5GkvYBpETFaUs+cTScBvSNipKRTgStIEk0x2z4ipkhaC3hG0ge5GyMiJNWGZ8l/Vo+IeBFA0tnAIpKJ3opZRZ/FWSS38WqTiurRkOT2SQ9gK+ABSZ2yDDIPFdVjf+CkiHhY0oEkVwG7Zhpl5RoCWwAnpN9JV5Pc7vpB1r/fvlL50XbAPpImklyW7yzpCWCziBiZ7nM/sG26/sOMlJIaklw2z6DymSprTERMSf+dBjxCctvhy/Syl/TfslsVyzrjZo2ppB5IOhzYCzgk0hvEFGk9KqjDr0n+2nwn/b/WFnhT0jpVxFqsn8VkYHB6a+UNkiv8VlXEW6z16A8MTnd5kB9vVxdjPSYDk3O+kx4iSTLF8/tdU41LtWkhmVhsKMlfBV8BG6blRwIPp+vH8dOG+gfS9U34aSPlx9RgQz2wKrBazvqrJPdKB/DThrzL0vU9+WlD3hvxY0PeJySNeC3S9ZZFUI9ewP+ANcvtX+HPPf0MP07LyhqHN8myDuX2mciPDfW17bM4hmTSPEhuhU1KYy+6z2Ip9Xgf6JmW7wKMLvLP4yWgS7p+fvq7XTS/3zXyQ6htC2lSSdd/C4xJfwFGAJ3S8pVJ/qoZD7xRVp5uO5vkKZdxpE+V1GDsndJY3wHGAmen5WsAzwEfkTyx0zItF3B9Gu8YoCTnvY5I6zce+EOR1GN8+uX1drrctLSfO8kTMB+m287Oug7l9pnIj0mltn0WjYF7gPeAN4Gdi/WzWEo9tgdGp+UjgS2L/PPoBpQC7wJDSJJC0fx+e5gWMzOrNm5TMTOzauOkYmZm1cZJxczMqo2TipmZVRsnFTMzqzZOKmYrQNI6kgZJmpAO/fGkpKOVjnKdUUwjJJVkdX6r35xUzJZTOoDoIySj2q4fEVuSjBu1dtVHmtVdTipmy28nYGFE3FRWEMkgkS8Bv8iZ8+LeNAEh6VxJoyS9J2lgTvkISZdKekPSh5J2SMsPlzRY0lPpvBe5c5bsJuk1JfP9PCjpFzVae7MKOKmYLb9fkvTErsjmJKPfdiXpyb1dWn5dRGwVEb8EmpKMYVamYUR0T487L6e8G/A7YFPgd5LaKZnY6xxg14jYgqSH9V+rp1pmy8+jFJsVxhsRMRlA0ttAB+BlYCdJpwGrkIy/NBZ4PD2mbFDD0en+ZZ6LiDnpe/0PWI9kYqauwCvpxU5j4LXCVccsP04qZstvLMmw6RWZn7O+GGgoaWXgBpLxlyZJOp9kDLnyxyzmp7+bP3svkjGdnomIg5Y/fLPq59tfZsvveaBJ7gRikn4F7FDJ/mUJ5Ku0/aOyhJSP14HtJG2QnndVSRuuwPuZVQsnFbPlFMlorL8Fdk0fKR4LXEwy815F+88GbiYZ1Xc4MGoFzj0dOBy4T9K7JLe+Nlre9zOrLh6l2MzMqo2vVMzMrNo4qZiZWbVxUjEzs2rjpGJmZtXGScXMzKqNk4qZmVUbJxUzM6s2/w/UElSKT4DDXwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110c38750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fa50f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111acd8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111abcf50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1117a2550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1139d8650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111abc0d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112aa6690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113ab1650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111abc150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111c20910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1105efb10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111abc090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gain: 2.891987, Chi2: 0.004283\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111ce8050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gain: -386.885993, Chi2: 322508.928199\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113aacad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  2.82268081 -18.49454202]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112af61d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def CalcGainShift(ringNo,ch):\n",
    "    th=ScatteringAngle(ringNo, 22.0, 11.0, 0.491, 0.5)[0]\n",
    "    energy = array([SimulateNiPD(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, 0, th)[0],\n",
    "                    SimulateNiPT(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, 0, th)[0],\n",
    "                    SimulateNiPT(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, 1172.98*1e-3, th)[0]])*1e3\n",
    "    \n",
    "    p = polyfit(ch, energy, 1)\n",
    "    \n",
    "    plt.title(\"E calibration, ring %i\" % ( ringNo ) )\n",
    "    plt.plot(ch, energy, \"o\")\n",
    "    plt.plot(linspace(ch[0],ch[-1],1001), p[0]*linspace(ch[0],ch[-1],1001)+p[1])\n",
    "    plt.xlabel(\"Channel\")\n",
    "    plt.ylabel(\"Energy [keV]\")\n",
    "    plt.show()\n",
    "    return p[0], p[1], energy, ch\n",
    "\n",
    "gain = []\n",
    "shift = []\n",
    "\n",
    "en = []\n",
    "ch = []\n",
    "\n",
    "# From ring 3:\n",
    "g,s,e,c = CalcGainShift(3, array([6014.42,5319.01,4786.14]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 4:\n",
    "g,s,e,c = CalcGainShift(4, array([5999.11,5299.95,4767.83]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 5:\n",
    "g,s,e,c = CalcGainShift(5, array([5981.23,5262.88,4752.04]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 6:\n",
    "g,s,e,c = CalcGainShift(6, array([5964.63,5233.44,4711.66]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 7:\n",
    "g,s,e,c = CalcGainShift(7, array([5948.91,5218.15,4690.67]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 8:\n",
    "g,s,e,c = CalcGainShift(8, array([5934,5186.98,4671.18]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 9:\n",
    "g,s,e,c = CalcGainShift(9, array([5917.42,5173.78,4641.68]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 10:\n",
    "g,s,e,c = CalcGainShift(10, array([5897.86,5146.37,4616.54]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 11:\n",
    "g,s,e,c = CalcGainShift(11, array([5873.97,5113.79,4596.73]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 12:\n",
    "g,s,e,c = CalcGainShift(12, array([5858.35,5096.29,4564.51]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 13:\n",
    "g,s,e,c = CalcGainShift(13, array([5846.12,5071.68,4541.8]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 14:\n",
    "g,s,e,c = CalcGainShift(14, array([5825.9,5046.41,4506.22]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 15:\n",
    "g,s,e,c = CalcGainShift(15, array([5798.53,5011.39,4492.25]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "gfinal = sum(gain)/float(len(gain))\n",
    "chiGain = sum((gfinal - gain)**2)/float(len(gain)-1)\n",
    "print \"Gain: %2.6f, Chi2: %2.6f\" % ( gfinal, chiGain )\n",
    "plt.plot(range(3,16),gain, \"o\")\n",
    "plt.plot(range(3,16),ones(len(gain))*gfinal)\n",
    "plt.show()\n",
    "\n",
    "sfinal = sum(shift)/float(len(shift))\n",
    "chiShift = sum((sfinal - shift)**2)/float(len(shift)-1)\n",
    "\n",
    "print \"Gain: %2.6f, Chi2: %2.6f\" % ( sfinal, chiShift )\n",
    "plt.plot(range(3,16),shift, \"o\")\n",
    "plt.plot(range(3,16),ones(len(shift))**sfinal)\n",
    "plt.show()\n",
    "\n",
    "p = polyfit(ch, en, 1)\n",
    "print p\n",
    "plt.plot(ch, en,\"o\")\n",
    "plt.plot(linspace(ch[0],ch[-1],1001),p[0]*linspace(ch[0],ch[-1],1001)+p[1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f66dd10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.35082172558 2279.71807455 210136.191827\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11427b8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.36000708746 2245.35927985 201162.032176\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d6bbbd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.33618410618 2397.34772033 226266.16322\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1137da650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.33784591377 2411.86917145 228404.98247\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1124f0e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.32505656098 2503.02025231 216056.035651\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110acde90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.34445144955 2421.22826042 196457.835413\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d6bbe90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.31912421352 2572.045549 206991.526937\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1145168d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.31901515239 2590.93143868 220838.17814\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110ad87d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.30542248496 2700.34658837 212646.032117\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110f38310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.30918059301 2692.35870512 216733.809167\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112790b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.28659441253 2824.90214908 221310.742084\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110f380d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.27825077562 2896.94102847 214795.370117\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112784d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.28874188986 2882.50566137 199379.352021\n",
      "Gain: 2.320054, Chi2: 0.000660\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110ac1cd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gain: 2570.659529, Chi2: 47751.045810\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112d70050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  2.30464486e+00   2.64516135e+03]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112b04cd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def CalcGainShift(ringNo,ch):\n",
    "    th=ScatteringAngle(ringNo, 22.0, 11.0, 0.491, 0.5)[0]\n",
    "    energy = array([SimulateNiPD(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, 0, th)[0],\n",
    "                    SimulateNiPT(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, 0, th)[0],\n",
    "                    SimulateNiPT(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, 1172.98*1e-3, th)[0],\n",
    "                    SimulateNiPT(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, 2048.68*1e-3, th)[0],\n",
    "                    (SimulateNiPT(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, 2301.84*1e-3, th)[0]+\n",
    "                    SimulateNiPT(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, 2336.52*1e-3, th)[0])*0.5\n",
    "                    ])*1e3\n",
    "    \n",
    "    p = polyfit(ch, energy, 1)\n",
    "    \n",
    "    plt.title(\"E calibration, ring %i\" % ( ringNo ) )\n",
    "    plt.plot(ch, energy, \"o\")\n",
    "    plt.plot(linspace(ch[0],ch[-1],1001), p[0]*linspace(ch[0],ch[-1],1001)+p[1])\n",
    "    plt.xlabel(\"Channel\")\n",
    "    plt.ylabel(\"Energy [keV]\")\n",
    "    plt.show()\n",
    "    print p[0], p[1], sum((energy - ch*p[0] - p[1])**2)/(len(energy) - 2)\n",
    "    return p[0], p[1], energy, ch\n",
    "\n",
    "gain = []\n",
    "shift = []\n",
    "\n",
    "en = []\n",
    "ch = []\n",
    "\n",
    "# From ring 3:\n",
    "g,s,e,c = CalcGainShift(3, array([6014.42,5320.45,4785.83,4262.33,3798.61]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 4:\n",
    "g,s,e,c = CalcGainShift(4, array([5999.11,5299.19,4773.43,4231.45,3790.05]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 5:\n",
    "g,s,e,c = CalcGainShift(5, array([5981.23,5265.53,4749.78,4216.06,3732.2]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 6:\n",
    "g,s,e,c = CalcGainShift(6, array([5964.63,5235.59,4722.08,4201.38,3703.22]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 7:\n",
    "g,s,e,c = CalcGainShift(7, array([5948.91,5218.03,4694.27,4152.38,3677.11]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 8:\n",
    "g,s,e,c = CalcGainShift(8, array([5934,5191.19,4671.9,4125.9,3674.49]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 9:\n",
    "g,s,e,c = CalcGainShift(9, array([5917.42,5173.78,4644.72,4092,3628.64]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 10:\n",
    "g,s,e,c = CalcGainShift(10, array([5897.86,5146.37,4620.58,4084.2,3593.46]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 11:\n",
    "g,s,e,c = CalcGainShift(11, array([5873.97,5115.53,4599.44,4016.72,3561.23]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 12:\n",
    "g,s,e,c = CalcGainShift(12, array([5858.35,5095.49,4569.41,4012.18,3534.29]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 13:\n",
    "g,s,e,c = CalcGainShift(13, array([5846.12,5071.68,4543.17,3977.01,3491.29]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 14:\n",
    "g,s,e,c = CalcGainShift(14, array([5825.9,5046.41,4510.02,3934.34,3458.72]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 15:\n",
    "g,s,e,c = CalcGainShift(15, array([5798.53,5012.29,4488.84,3876.61,3445.92]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "gfinal = sum(gain)/float(len(gain))\n",
    "chiGain = sum((gfinal - gain)**2)/float(len(gain)-1)\n",
    "print \"Gain: %2.6f, Chi2: %2.6f\" % ( gfinal, chiGain )\n",
    "plt.plot(range(3,16),gain, \"o\")\n",
    "plt.plot(range(3,16),ones(len(gain))*gfinal)\n",
    "plt.show()\n",
    "\n",
    "sfinal = sum(shift)/float(len(shift))\n",
    "chiShift = sum((sfinal - shift)**2)/float(len(shift)-1)\n",
    "\n",
    "print \"Shift: %2.6f, Chi2: %2.6f\" % ( sfinal, chiShift )\n",
    "plt.plot(range(3,16),shift, \"o\")\n",
    "plt.plot(range(3,16),ones(len(shift))**sfinal)\n",
    "plt.show()\n",
    "\n",
    "p = polyfit(ch, en, 1)\n",
    "print p\n",
    "plt.plot(ch, en,\"o\")\n",
    "plt.plot(linspace(ch[0],ch[-1],1001),p[0]*linspace(ch[0],ch[-1],1001)+p[1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112788e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.91735264655 269.265482626 17297.2796152\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1117eeb50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.91383307678 265.539401586 18832.0525783\n"
     ]
    },
    {
     "data": {
      "image/png": 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ppcQhJZMZHHoyXPkBnHp/0HHiE93h6bPgmyWRhDSwaxMyM9J3KsvMSGdg1yaRxCMSFSUOKdnSy0GrC4MK9M63wcpZwSBS46+ADf8t1lB6tqzLkF7NqJuViQF1szIZ0quZWlVJmaPmuJJaflofjIE++xHAofVlcMyfgk4WRWSPqDmulE6VqkGX2+Ha+XDEWTD7IRjeAt79B/zyY9TRiZQJShySmqrUgx4j4Mp/Q4OjYdrtMLwl5DwOO7ZFHZ1IqabEIalt30PhnGfhkslQtSFM/D8Y0RaWTCgRTXhFSiMlDikd9m8Hl7wJvZ8NhrV9sQ881ikY0lZEipQSh5QeZnBI9+DxVY8RsOlrGHMKPHU6fL046uhESg0lDil90tKh5flBE94TboevcuDhY+Dly+D7FVFHJ5LylDik9MrIhPbXwoCF0H4ALH0V7s+GN26CH7+NOjqRlKXEIaVfZlU44W9wzXxocQ7MeSTohfede2Dr5qijE0k5ShxSdlSpG3RfctUsOPBYmD44aMI751E14RVJQNITh5mlm9kCM5sYLj9hZl+Y2cJwahGWm5kNN7PlZvahmbWKOUYfM/s0nPokO2Yp5Wo2gd5PQ98pUP0gmHQ9jGgDH42DX3+NOjqREq/AxGFm1eKYsuI4xwBgaZ6yge7eIpwWhmUnAo3DqR/wUG4cwK1AW6ANcKuZVU3sY4rko34buHgSnPsClKsIL10Mj3WEz2dEHZlIiVZuF+tWh5PtYpt0YP+CVppZPeAkYDBwXSGx9ADGetB51iwzyzKz2sBxwBR3Xx8ecwrQDXi2kOOJFM4MDu4KB3WGD5+HaYNhbA9o1DHoVLF286gjFClxdvWoaqm7H+juDQuagO8KOf59wA1A3vv/weHjqHvNrEJYVhdYGbPNV2FZQeUiRSctHVqcGzTh7TIYVi+ARzrAS31h/RdRRydSouwqcbSLY/+jClphZicDa919Xp5Vg4BDgNZANeDGOM5TKDPrZ2Y5Zpazbt26ojiklEUZFeEPV8O1C+Ho6+Dj1+GB1jDpBtis75UI7DpxjDOz882sckEbuPvPu9i/PXCqma0AngM6mtlT7r7GA1uB0QT1FgCrgPox+9cLywoqzxvLSHfPdvfsmjVr7iIskThkZkHnW+HaBdDyPJj7WNAL74y7YOumqKMTidSuEsdIgvqJz83sBTM7zczKx3tgdx/k7vXcvQHQG5jm7ueH9RaYmQE9gY/CXV4FLgxbV7UDNrr7GmAy0MXMqoaV4l3CMpHk26c2nDIM+s8O6j1mDAma8M4eCdt/iTo6kUgUmDjc/RV3PwdoALwMXAj818xGm9kJe3DOp81sMbAYqAHcEZZPAj4HlgOPAleFcawHbgfmhtPfcyvKRYpNjcZw9pPQdyrUaAJvDIQRrWHxS2rCC0xYsIr2d02j4U2v0/6uaUxY8LuHAlKKJDQCoJkdAYwBjnD39MK2j4pGAJSkcoflU2HqbfDNR7DfEcGb6Y06Rh1ZJCYsWMWgcYvZsm3Hb2WZGekaVjcFFdkIgGZWy8yuMbOZwASCx0StCtlNpPQyg8YnwOXvwWkjYcsGePK0oBnv6gVRR1fshk5etlPSANiybQdDJy+LKCJJtl29AHiZmU0D5hO8lDcwbJ57k7svKrYIRUqqtDRofjZckwNdh8CaD2HkcfDixfDdZ1FHV2xWb9iSULmkvl3dcRwFDAHqu/u17v7vYopJJLWUqwBHXRX0wtthIHzyZtCFyet/gs1ro44u6epkZSZULqlvV5Xjl7j7FMDDZrm3AJjZ/mbWpqD9RMqsilWg41+DJryt+kDO6KAX3ul3ws8/RB1d0gzs2oTMjJ2rPDMz0hnYtUlEEUmyxdPJ4YMEdx/nhMubgBFJi0gk1e29H5z8L+g/J6gLeefu4B2QWQ/D9q1RR1fkerasy5BezaiblYkBdbMyVTFeyhXaqsrM5rt7KzNb4O4tw7JF7l5iO/FRqyopUVbNgym3wor3IOsA6HgzHH56UEciUoIUWasqYJuZpQMeHrgmv+97SkQKUvdI6PManP8yVNwHxl0KIzsETXoTaA4vUlLEkziGA+OBfc1sMPA+QaW5iMTLLOiBt9+70OuxoM7jqdNh7KnBHYlIConrBUAzOwToRNDF+tvunnd8jRJFj6qkxNv+C8wbHdR//PQdNO0JnW6B6o2ijkzKsKJ8AbCvu3/s7iPc/QF3X2pmdxVNmCJlVLny0PbyoBfeY2+ET6cEvfBO/D/Y9HXU0YnsUjyPqk43s/NyF8xsBKDuZ0WKQsV94Pg/B++AZF8C88cGnShOu6NUN+GV1BZX4gAuMrNzzGwMsN3d+yY5LpGypfK+cNI/gia8TU6Ed4fCsObwwYOlsgmvpLZCxxwHMoFLCUby2wT8LSwXkaJWvRGc8Tj0mwG1j4DJg+D+bFj0HPy6o7C9RYpFgZXjZvYFQRNci/mZy939wOSHt3tUOS6lxmfTgl541yyCWocH46Af1DlopSVSxOKtHC9X0IpwTHERiVKjjtDwOFgyDqbdDk+fAQccHXTjXq/Q32+RpNjVo6pCu06PZxsR2UNpadDsDOg/F7r/A75dBo91gufPh28/jTo6KYN2VTk+OhyutVpBEzCquAIVKfPKlYc2lwWdKB43CD6bDiPawmsD4Ic1UUcnZUiBj6qAKsA8dq7byGtd0YYjIoWqsDccdxNk9w1aX+U8Doueh3ZXQvsBkJkVdYRSyiU0dGyqUOW4lCnrv4Dpg2Hxi5BZFY75E7S+DDIqRh2ZpJii7ORQREqyag3h9Mfg8nehTkt4669w/5Gw8Bk14ZWkUOIQKS1qN4cLxsOFr8BeNWDClfDw0bDsTfXCK0VKiUOktDnwOLhsOpwxGrb/DM+eDaO7w8o5UUcmpUQ8nRyOM7OTzExJRiRVpKXB4b2CLkxO+id8txxGnQDPnQfrlkUdnaS4eIeOPRf41MzuMjMNJCySKtIzoPWlQRPe4/8Kn78DD7aDV66Gjauijk5SVKGJw92nuvt5QCtgBTDVzP5tZhebWUayAxSRIlChMhw7MOiFt+0VQd9X97cKhrTd8n3U0UmKievxk5lVBy4i6OxwATCMIJFMSVpkIlL09qoB3YbANTnQtAfMHAbDWgQ/t22JOjpJEfHUcYwH3gMqAae4+6nu/ry7XwNUTnaAIpIEVRtAr5FwxXtQrzVMuSVowrvgKTXhlULFNea4uzd19yHuvlO/BvG8KCIiJdh+zeD8l6DPRNh7P3ilPzz0B/h4kprwSoF21eVIrqpm1itP2UZgsbuvTUJMIlLcGh4Dl74NS1+Ft/8Oz50D9dsFvfDu3y7q6KSEieeOoy/wGHBeOD0K3AjMNLMLkhibiBQns6De46pZcPJ98P0KeLwrPHsOrF0adXRSgsSTODKAQ939dHc/HWhKMLBTW4IEIiKlSXoGZF8M186HjjfDiveDx1cT+sPGr6KOTkqAeBJHPXf/JmZ5LVDf3dcD25ITlohErvxe0OF6GLAI2l0Fi1+A4a3grZvhp/VRRycRiidxzDCziWbWx8z6AK+EZXsBG5IbnohErlI16DoYrpkHh58O/74fhreA9+9VE94yqtBu1c3MgF7A0WHRTOBlL8H9satbdZEk+mYJTP0bfDoZ9q4TjA3S4jxIj6etjZRk8XarvsvEYWbpwFR3P74og0s2JQ6RYrBiJky9Fb6aCzUOhk63wiEnBZXskpKKZDwOd98B/GpmVfYgkHQzW2BmE8PlhmY228yWm9nzZlY+LK8QLi8P1zeIOcagsHyZmXXd3VhEpAg1aA99p8DZTwXvfDx/HozqAl/+O+rIJMniqePYDCw2s1FmNjx3SuAcA4DYtnx3A/e6+0HA9wTNfQl/fh+W3xtuh5k1BXoDhwHdgAfDOyERiZoZHHpK0IT3lOGwcSWMPhGeORu++U/U0UmSxJM4xgE3A+8SjEGeOxXKzOoBJxG8B5JbX9IReCncZAzQM5zvES4Tru8Ubt8DeM7dt7r7F8ByoE085xeRYpJeDo7sA9fMDx5ZfflB0IR3/JWwYWXU0UkRK7Q2y93HmFkmsL+7J9qR/33ADcDe4XJ1YIO7bw+XvwLqhvN1gZXhObeb2cZw+7rArJhjxu4jIiVJ+UpwzHVw5EXw/r9g9kj46GVoc1kwFnqlalFHKEUgnk4OTwEWAm+Gyy3M7NU49jsZWOvucd2d7Ckz62dmOWaWs27duuI4pYgUpFI16HJH0IS32Zkw60EY1hze+yf88lPU0ckeiudR1W0Ej4Y2ALj7QuDAOPZrD5xqZiuA5wgeUQ0Dssws906nHpA7mswqoD5AuL4K8F1seT77/MbdR7p7trtn16xZM47wRCTpsupDzxFwxUw4oH3QD9bwlpAzGnZsL3x/KZHiSRzb3H1jnrJfC9vJ3Qe5ez13b0BQuT0tHBBqOnBGuFnuC4UAr4bLhOunhe+KvAr0DltdNQQaAxo8WSSV1GoK5z4HF78JVQ+AiX8MRiL8z6vqhTcFxZM4lpjZuUC6mTU2s/uBPWlvdyNwnZktJ6jDGBWWjwKqh+XXATcBuPsS4AXgPwSPy/qHzYRFJNUccBRcMhl6PwOWBi9cAI91DvrDkpQRz5vjlYC/AF0AAyYDt7v7z8kPb/foBUCRFLBjOyx6FqbfCZtWQ+MuQYus/Q6POrIyq0jeHE9VShwiKWTbFpgzMqg4//kHOOJsOP7PwSMtKVbxJo5Cm+Oa2cHA9UCD2O3dveOeBCgiAkBGJrQfAK0uDDpOnP0ILBkHrS+FY66HvapHHaHkEc+jqkXAwwQv/f1Wt1BczWx3h+44RFLYxlUwYwgsfBrKV4b21wbdupffK+rISr0ie1QVHujIIousGChxiJQCaz+GabfDxxOhci049sbgriQ9I+rISq0i6eQw9JqZXWVmtc2sWu5UBDGKiBRs30Og99NwyVtQ7UB4/ToY0RaWjFcT3ojFc8fxRT7F7u7xvAQYCd1xiJQy7vDJZJh6G6xbCnVaQefb4MBjIw6sdCmyynF3b1g0IYmI7CYzaNINGp8AHz4P0wbD2FOhUacggdQ+IuoIy5QCH1WZ2Q0x82fmWXdnMoMSEclXWjq0ODfoA6vLHbB6PjxyDLx8KazP7+GIJMOu6jh6x8wPyrOuWxJiERGJT0ZF+MM1cO1COPo6WDoRHmgNb9wIP34bdXSl3q4ShxUwn9+yiEjxy8yCzrfCtQug5Xkw59GgF94Zd8PWzVFHV2rtKnF4AfP5LYuIRGef2nDKsGAkwkbHw4w7YXiLIJFs/yXq6EqdXSWO5mb2g5ltAo4I53OXmxVTfCIi8at5cDAGet+pUONgmHQ9jGgTDCb1a6GdekucCkwc7p7u7vu4+97uXi6cz13WGzgiUnLVbw0XvQ7nvggZleClS+DR4+Cz6VFHVirE8wKgiEjqMYODu8AV78Fpj8BP6+HJnjC2J6xeGHV0KU2JQ0RKt7R0aN4brs6BrnfCmkUw8tjgLmT951FHl5KUOESkbMioCEf1hwELg153P54UNOGdNBA2r406upSixCEiZUvFKtDp5iCBtLoQ5o6CYS1g+hDYuinq6FKCEoeIlE177wcn3wv950DjzvDOXUECmf2ImvAWQolDRMq2GgfBWWPh0mmw76Hwxg0wojUsfklNeAugxCEiAlDvSOjzGpz3MpTfG17uG1SiL39b3bjnocQhIpLLLHhsdfm70OtR+HkDPNULxvaAVfOjjq7EUOIQEckrLQ2OOCtowtvtbvjmI3j0eHjxIvjus6iji5wSh4hIQcpVgHZXBL3wdrgBPnkr6MJk4nWw6Zuoo4uMEoeISGEq7gMd/xL0wnvkRTB/TNCJ4rTB8PMPUUdX7JQ4RETitXctOOmfQRPeg7vCu/cECWTWQ7B9a9TRFRslDhGRRFVvBGc+AZdNh1qHwZs3wQPZsOj5MtGEV4lDRGR31W0FF74K54+Dilkwvh880gE+nVqqm/AqcYiI7AkzOKgT9HsHTh8Fv2yCp0+HMafAV/Oiji4plDhERIpCWho0OwP6z4UTh8LapfAxOVH6AAAMQUlEQVRYR3jhQvh2edTRFSklDhGRolSuPLTtF3SieNyg4M3zEW3gtT/Cpq+jjq5IKHGIiCRDhb3huJuCd0BaXwoLnoLhLeHt2+HnjVFHt0eUOEREkqlyTeh+D1w9B5p0h/f+EfTC+8GIlG3Cq8QhIlIcqh0IZ4wKKtHrtIDJf4b7s2Hhs/DrjqijS4gSh4hIcarTAi4YDxdMgErVYMIV8PAxQXcmKdKEV4lDRCQKjY4PXiA8YzRs+wmeOROeOAlWzo06skIlLXGYWUUzm2Nmi8xsiZn9LSx/wsy+MLOF4dQiLDczG25my83sQzNrFXOsPmb2aTj1SVbMIiLFKi0NDu8FV8+F7v+Abz+FUZ3h+fNh3SdRR1egckk89lago7tvNrMM4H0zeyNcN9DdX8qz/YlA43BqCzwEtDWzasCtQDbgwDwze9Xdv09i7CIixSc9A9pcBs3PgVkPwsxh8PEkaHl+0DJrnzpRR7iTpN1xeGBzuJgRTrt6gNcDGBvuNwvIMrPaQFdgiruvD5PFFKBbsuIWEYlMhcpw7A0wYBG06QcLnwma8E69DbZsiDq63yS1jsPM0s1sIbCW4D//2eGqweHjqHvNrEJYVhdYGbP7V2FZQeUiIqXTXjXgxLvgmhw49FR4/z4Y1hxmDodtP0cdXXITh7vvcPcWQD2gjZkdDgwCDgFaA9WAG4viXGbWz8xyzCxn3bp1RXFIEZFoVW0Apz8aDGVbLxum3Az3HwkLno60CW+xtKpy9w3AdKCbu68JH0dtBUYDbcLNVgH1Y3arF5YVVJ73HCPdPdvds2vWrJmMjyEiEo3aR8D5L0Of16DyvvDKVfBQe1j2RiRNeJPZqqqmmWWF85nACcDHYb0FZmZAT+CjcJdXgQvD1lXtgI3uvgaYDHQxs6pmVhXoEpaJiJQtDTvAZdPgzDGw4xd4tjeMPhH+O7vwfYtQMltV1QbGmFk6QYJ6wd0nmtk0M6sJGLAQuCLcfhLQHVgO/ARcDODu683sdiC3cfPf3X19EuMWESm5zOCwnnDISbDgSZhxFzzeBZqcBJ1ugX0PSX4IniJvKiYiOzvbc3Jyog5DRCT5fvkxaML7/jDY9iMc1R+63LFbhzKzee6eXdh2enNcRCSVld8LOgwMmvC2vRKq1C98nz2UzEdVIiJSXPaqDt3uLJZT6Y5DREQSosQhIiIJUeIQEZGEKHGIiEhClDhERCQhShwiIpIQJQ4REUmIEoeIiCREiUNERBKixCEiIglR4hARkYQocYiISEKUOEREJCFKHCIikhAlDhERSYgSh4iIJESJQ0REEqLEISIiCVHiEBGRhChxiIhIQpQ4REQkIUocIiKSECUOERFJiBKHiIgkRIlDREQSosQhIiIJUeIQEZGEKHGIiEhClDhERCQh5aIOQERE9tyEBasYOnkZqzdsoU5WJgO7NqFny7pJOZcSh4hIipuwYBWDxi1my7YdAKzasIVB4xYDJCV56FGViEiKGzp52W9JI9eWbTsYOnlZUs6nxCEikuJWb9iSUPmeSlriMLOKZjbHzBaZ2RIz+1tY3tDMZpvZcjN73szKh+UVwuXl4foGMccaFJYvM7OuyYpZRCQV1cnKTKh8TyXzjmMr0NHdmwMtgG5m1g64G7jX3Q8Cvgf6htv3Bb4Py+8Nt8PMmgK9gcOAbsCDZpaexLhFRFLKwK5NyMzY+b/FzIx0BnZtkpTzJS1xeGBzuJgRTg50BF4Ky8cAPcP5HuEy4fpOZmZh+XPuvtXdvwCWA22SFbeISKrp2bIuQ3o1o25WJgbUzcpkSK9mqdmqKrwzmAccBIwAPgM2uPv2cJOvgNxPVhdYCeDu281sI1A9LJ8Vc9jYfUREhCB5JCtR5JXUynF33+HuLYB6BHcJhyTrXGbWz8xyzCxn3bp1yTqNiEiZVyytqtx9AzAdOArIMrPcO516wKpwfhVQHyBcXwX4LrY8n31izzHS3bPdPbtmzZpJ+RwiIpLcVlU1zSwrnM8ETgCWEiSQM8LN+gCvhPOvhsuE66e5u4flvcNWVw2BxsCcZMUtIiK7lsw6jtrAmLCeIw14wd0nmtl/gOfM7A5gATAq3H4U8KSZLQfWE7Skwt2XmNkLwH+A7UB/d9+BiIhEwoI/6kuX7Oxsz8nJiToMEZGUYmbz3D270O1KY+Iws3XAl1HHUYRqAN9GHUQJoWuxM12Pnel6/M/uXIsD3L3QSuJSmThKGzPLieevgLJA12Jnuh470/X4n2ReC/VVJSIiCVHiEBGRhChxpIaRUQdQguha7EzXY2e6Hv+TtGuhOg4REUmI7jhERCQhShwiIpIQJY4ImVm6mS0ws4nhcpkd5Cqfa/GEmX1hZgvDqUVYbmY2PPzMH5pZq5hj9DGzT8OpT0HnKunMbIWZLQ4/d05YVs3MpoSfbYqZVQ3Ly+r1uM3MVsV8P7rHbJ/v74SZdQvLlpvZTVF8lqJgZllm9pKZfWxmS83sqGL/fri7pogm4DrgGWBiuPwC0Ducfxi4Mpy/Cng4nO8NPB/ONwUWARWAhgTd1qdH/bmK6Fo8AZyRz3bdgTcAA9oBs8PyasDn4c+q4XzVqD/Xbl6LFUCNPGX3ADeF8zcBd5fx63EbcH0+2+b7OxFOnwEHAuXDbZpG/dl283qMAS4N58sDWcX9/dAdR0TMrB5wEvBYuGyU0UGu8l6LQvQAxnpgFkFvy7WBrsAUd1/v7t8DUwhGjCwtYr8Deb8bZfF6FKSg34k2wHJ3/9zdfwGeC7dNKWZWBehA2Mefu//iQe/jxfr9UOKIzn3ADcCv4XJ14hzkCogd5GplzDFTdZCrvNci1+Dw9vpeM6sQlhX0mUvLtYBgpMy3zGyemfULy2q5+5pw/mugVjhfVq8HwNXh9+Px3EczlP7r0RBYB4wOH+0+ZmZ7UczfDyWOCJjZycBad58XdSxR28W1GEQw8FdrgtvpG4s7tggd7e6tgBOB/mbWIXalB88aylI7+vyux0NAI6AFsAb4Z4TxFadyQCvgIXdvCfxI8GjqN8Xx/VDiiEZ74FQzW0Fwy9wRGEaSBrkq4X53LczsKXdfE95ebwVG879HcAV95tJwLQBw91Xhz7XAeILP/k34iIHw59pw8zJ5Pdz9Gw9GGP0VeJSy8/34CvjK3WeHyy8RJJJi/X4ocUTA3Qe5ez13b0BQ2T3N3c+jDA5yVcC1OD/ml8AIntd+FO7yKnBh2FqkHbAxvEWfDHQxs6rhY4suYVlKMbO9zGzv3HmCz/ERO38H8n43ytz1yP1+hE5j5+9Hfr8Tc4HGFrRcLE/wXXu1uD5HUXH3r4GVZtYkLOpEMFZRsX4/kjmQkyTuRjTIVa6nzawmQWuQhcAVYfkkgpYiy4GfgIsB3H29md1O8B8EwN/dfX3xhlwkagHjg3xJOeAZd3/TzOYCL5hZX4IhA84Kty+r1+NJC5poO0Grq8th178TZnY1wX+O6cDj7r6kuD9MEbmG4PejPEFrqIsJB8srru+HuhwREZGE6FGViIgkRIlDREQSosQhIiIJUeIQEZGEKHGIiEhClDhE4mBm+5nZc2b2Wdj1xSQz62dhb74RxTTDzLKjOr+UXUocIoUIX0IcD8xw90bufiRBlyi1dr2nSOmkxCFSuOOBbe7+cG6Buy8C3gMqx4yN8HSYZDCzW8xsrpl9ZGYjY8pnmNndZjbHzD4xs2PC8ovMbJyZvRmOj3BP7rnMrIuZfWBm883sRTOrXKyfXiQPJQ6Rwh0OFNQhZUvgjwTjQBxI0PcWwAPu3trdDwcygZNj9inn7m3C/W6NKW8BnA00A842s/pmVgP4K9A57Ogvh2DsEpHIqMsRkT0zx92/AjCzhUAD4H3geDO7AahE0LvvEuC1cJ9x4c954fa53nb3jeGx/gMcQDBIT1NgZnjTUh74IHkfR6RwShwihVvC/zqfzGtrzPwOoJyZVQQeBLLdfaWZ3QZUzGefHez8O/i7YxH01TXF3c/Z/fBFipYeVYkUbhpQIXYQITM7AjimgO1zk8S3YX1EQUknHrOA9mZ2UHjevczs4D04nsgeU+IQKUTYhf1pQOewOe4SYAjBSGv5bb+BYIyIjwh6Y52b33ZxnnsdcBHwrJl9SPCY6pDdPZ5IUVDvuCIikhDdcYiISEKUOEREJCFKHCIikhAlDhERSYgSh4iIJESJQ0REEqLEISIiCfl/RCRMfPosvK4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113b82e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.827096810117 8386.69600754 148912.693517\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112b0e090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.832589725755 8419.19263571 148333.450425\n"
     ]
    },
    {
     "data": {
      "image/png": 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TWUZ6Gn2zGhZ7LCKpQMlDUtsuNeGUe+Ha2XDI6fDO/2BAY3jvYdiyqdjC6NSkLvecdQR1q2VgQN1qGdxz1hF0alK32GIQSSXmKdaqJREyMzM9Ozs76jAkGVZ8CNNugy+mQ9W9oe1NcMS5wWBVIrJTzGyOu2fGsq3uPKRk2asRXDwOLh4fvHQ47ip4tA0snppyzXtFSjMlDymZ9j8BrpwB5zwBv/0Cz54Dw0+HZXOijkykTFDykJKrXDk4/GzoORtO/U/QY+/jbWH0JbD6i6ijEynVlDyk5CtfAVpcGbTMOu5GWDwNHm4OE6+Dn7+POjqRUknJQ0qPirvCCf2CJJJ5OcwdHrTMmn43/PpT1NGJlCpKHlL6VNkDTvsP9JwFB7WHt+4PksgHQ4q1ea9IaabkIaXX7vvDuU8GFeu1D4NJNwSPsz56AbZtizo6kRJNyUNKv7pN4ZIJcNFYqLQbjL0Chh4XvCsiIjtEyUPKBjM44ETo/hac9Rj8uhaePhNGdITl86KOTqTEUfKQsqVcOTjyPLg2G9rfCys+gqHHw5jLYc2XUUcnUmKUL2yFmdWIYf9t7l78vdSJ7KzyFaHV1dD4QnhvILw/CD55KWil1eZ6qFIr6ghFUlqhfVuZ2a/AcsC2s3+au++djMB2hvq2krj9/B28eR/MGQ7pGXB0LziqZ9D8V6SMSFTfVp+6+37uvm9hE7A6MSGLRGzXPaHDA8FgVAecCG/cE3QBP+sx2Lo56uhEUs72kkerGPY/KlGBiKSEmgfCeSOCYXFrHgSv/hMGtYCFY9Xxokge20seY83sIjOrUtgG7v5rUScwszQzm2dmE8Plp8zsKzObH06Nw3IzswFmtsTMPjKzpnmO0dXMFodT1zg+n8iOqZcJl74CF74A5TNgzGXw2AnByIYist3kMRQ4DfjSzEab2ZlmVmEHztEH+DRfWV93bxxO88OyU4ADw6k7MBh+r7i/FWgJtABuNbPqOxCHSHzM4KB20ONt6DQE1v8AI86Ap8+C7xZEHZ1IpApNHu7+krtfADQAXgQuAb4xsyfN7ORYDm5m9QgS0OMxbN4RGOGBD4BqZrYXkAVMdfc17v4jMBVoH8v5RRKiXBo0viBo3tvuLsiZA0OOhbHd4cevo44ucuPn5dD63unse+MrtL53OuPn5UQdkhSDIt/zcPcN7j7K3c8E2gGNgUkxHv9B4Hogf18Qd4ePph4ws4phWV3g2zzbLAvLCiv/EzPrbmbZZpa9atWqGMMTiUN6paAVVp8P4Zi/BU17H86ESf1gfdlsOzJ+Xg79xi4gZ+1GHMhZu5F+YxcogZQBRSYPM6ttZr3M7F1gPDAZaFrEbphZB2Clu+cfnacfcDDQHKgB3BB31AVw96HununumbVqqY2+JFFGNTjpNug9Dxp1hplDgo4X3+oPv62POrpi1X/yIjZu3vqnso2bt9J/8qKIIpLiUmjyMLMrzWw6MJegHqJv2HT3Rnf/MIZjtwbOMLOlwPNAWzN7xt1XhI+mNgFPEtRjAOQA9fPsXy8sK6xcJFq71YEzBsI1H8C+bWD6XUHz3uwnYOuWqKMrFsvXboyrXEqP7d15HAXcA9R3997u/l48B3b3fu5ez90bAJ2B6e5+UViPgZkZ0AlYGO4yAbgkbHXVCljn7isI7nTamVn1sKK8XVgmkhpqNYTOz8LlU6D6vjDx7/BIS/hkQqlv3lunWkZc5VJ6bK/C/HJ3nwp42GT3FgAz29vMWhS2XwyeNbMFwAKgJnBXWP4q8CWwBHgMuCaMYw1wJzA7nO4Iy0RSy94t4fJJ0Pk5KFceRl8Mj58ES9+NOrKk6ZvVkIz0tD+VZaSn0TerYUQRSXEptHuS3zcwG0xQ4d3W3Q8J//qf4u7NiyPAHaHuSSRyW7fAh8/BjH/Dz8vhwCw46dZgXJFSZvy8HPpPXsTytRupUy2DvlkN6dTkL21apASIp3uSWJLHXHdvambz3L1JWPahuzdKQKxJoeQhKWPzRpj5KLzzv2Ao3EYXwAn/gmr1i95XpJglqm+rXJvNLA3w8OC1+GvTWxEpSHpG0Ky39/ygme/CF2FgM5h8E2zQ01cpuWJJHgOAccAeZnY38A5BRbqIxKpyDWh3J/SaA0ecE3QB/1BjeOeB4O5EpIQp8rEVgJkdDJxI0D376+6ev7uRlKLHVpLyvv8EXr8dPp8Eu9aBE/pBowshrdAhdkSSLqGPrcysm7t/5u6D3P1hd//UzO7d+TBFyrDah8KFo+DSV6FqXZjQCwYfDZ+9Uuqb90rpEMtjq7PNrEvugpkNAvQKt0giNGgN3abC+c+Ab4PnL4QnsuCbD6KOTGS7YkoewKVmdoGZDQe2uHu3JMclUnaYwSGnB2+qn/5Q0NniE1nw3AWw8rOooxMp0Pa6J6kRdoeeAVxB0MHhz8DtMY5vLiLxSCsPzS4N+sxq+3+w9B0YfBS8dC2sU488klq2N4b5VwTNcy3Pz1zu7vslP7wdowpzKRXWr4a3/wuzHwMrBy17BM1+MzScjSRHQl8SLImUPKRU+fHr4E31j0ZBpapw7D+gRfegi3iRBEpIa6u8w8DuzDYispOq7wNnPRqMaFivOUz9v+BFw3nPwratRe8vkgTbqzB/MuzJtkZhEzCsuAIVKfP2PAIuGgNdX4Yqe8BL18CQY+DzyWreK8Vue28kVQXm8Oe6jvw0ZJ9Icdu3DVw5HT4ZD6/fASPPg31aw0m3Q/2U7a9USplCk0c4DoeIpCIzOOxMOLgDzB0Ob9wHw04KmvyeeCvUPDDqCKWUi+U9DxFJVWnp0PyKoHnvCTfBFzNgUEt4uQ/8tCLq6KQUU/IQKQ0qVoHjrg96721xZVCZPqBJ8Fjr13VRRyelkJKHSGlSpRacch9cOwsOPi14T+ShxvD+I7BlU9TRSSkSS8eIY83sNDNTohEpKWrsB+cMg+5vwl6NYHI/GJgJH46CbRqOR3ZeLAnhEeBCYLGZ3WtmGpxYpKSo0xguGQ8Xj4PK1WFcd3i0DSyepua9slOKTB7uPs3duwBNgaXANDN7z8wuM7P0ZAcoIgmwf1u48g04exj89jM8ezYMPx1y5kQdmZRQMT2KMrPdgUsJOkicBzxEkEymJi0yEUmscuWCUQx7zoZT+sPKT+GxtjC6K6z+IuropISJpc5jHPA2UBk43d3PcPdR7t4LqJLsAEUkwcpXgJbdoc98OO4GWDwVBrWAV/4BP38fdXRSQhTZMaKZneDuM4opnoRQx4gicfj5e3jrfpjzFKRVhKOvhaN7QcVdo45MillCe9U1s7MKKF4HLHD3lTsQX9IpeYjsgNVfwPQ74eNxULlm8N5Is8uCOxUpExI6hjnQDXgc6BJOjwE3AO+a2cU7HKWIpJbd94dznwr6zdrjEHjtehjUHBaMUfNe+YtYkkc6cIi7n+3uZwOHEgwO1ZIgiYhIaVK3WdBz70UvQoVd4cVu8NjxQdcnIqFYkkc9d89bi7YSqO/ua4DNyQlLRCJlBgecBFe9BWcOhQ0/wtOdYEQnWD4/6ugkBcSSPN4ws4lm1tXMugIvhWW7AGuTG56IRKpcOWh0PvTKhqx7YMWHMPQ4GNMN1nwVdXQSoVgqzA04CzgmLHoXeNFTePxaVZiLJMmv6+DdAfD+INi2BZp3gzZ9YZeaUUcmCZCw1lZmlgZMc/cTEhVccVDyEEmyn1bAm/fC3KchPQNa94FW1wS9+0qJlbDWVu6+FdhmZlUTEpmIlA677QWnPwTXfAD7nwAz7g66gJ/9OGxVVWhZEEudxy/AAjMbZmYDcqdkByYiJUCtg+D8Z6DbNNj9gOAt9UEtgndFUvfJtiTA9sYwzzU2nERECla/OVz2KiyeAtNugxcuhTpN4eTbgzHXpdQpssIcwMwygL3dfVHyQ9p5qvMQidC2rfDRKJh+N/y0LGjye9JtsOcRUUcmRUjoG+ZmdjowH5gULjc2swlxBJNmZvPMbGK4vK+ZzTSzJWY2yswqhOUVw+Ul4foGeY7RLyxfZGZZsZ5bRCJQLg0aXwi95sDJd8KybBhyLIy9Cn78OuroJEFiqfO4DWhB+E6Hu88H9ovjHH2AT/Ms3wc84O4HAD8SdH9C+PPHsPyBcDvM7FCgM3AY0B54JGwFJiKpLL0StO4d9N7bug98Mh4ezoRJ/4L1q6OOTnZSLMljs7uvy1cWU0c3ZlYPOI2gb6zcd0baAmPCTYYDncL5juEy4foTw+07As+7+yZ3/wpYQpDMRKQkyKge1H30mgtHng8zB8OAxvDWf+C39VFHJzsoluTxsZldCKSZ2YFmNhB4L8bjPwhczx/JZndgrbtvCZeXAXXD+brAtwDh+nXh9r+XF7DP78ysu5llm1n2qlWrYgxPRIpN1brQ8WG4+n1ocGzQg++AppD9JGzdUvT+klJiSR69CB4ZbQKeA34C/lbUTmbWAVjp7sUyzqW7D3X3THfPrFWrVnGcUkR2xB4HwwUj4bJJUH0fmPg3eKQVfPqymveWILGMYb7B3W9y9+bhf843ufuvMRy7NXCGmS0Fnid4XPUQUM3McpsI1wNywvkcoD5AuL4qsDpveQH7iEhJtc9RcPlk6DwSrByMugiGnQxfx/pgQ6IUS2urg8xsqJlNMbPpuVNR+7l7P3ev5+4NCCq8p7t7F2AGcE64WW5HiwATwmXC9dPD/rMmAJ3D1lj7AgcCs+L4jCKSqszg4NPg6vfgjIGwbhk8eQqMPB++/yTq6GQ7YnlJ8AVgCEGl99YEnPMG4HkzuwuYBwwLy4cBT5vZEmANQcLB3T82s9HAJ8AWoGfYbYqIlBZp5aHpJXD4OTDrUXj7ARh8dNDk9/h+UK1+0ceQYhVLr7pz3L1ZMcWTEHpJUKSE27AG3v4vzBoKGLS8Co75O1SuEXVkpVqih6F92cyuMbO9zKxG7rSTMYqIFK5yDci6O3jR8PCz4b2BQfPedx6EzRujjk6I7c6joBFf3N3jeVGwWOnOQ6SU+f5jmHY7LJ4Mu9aBE/4FjS4IHndJwiT0zsPd9y1gStnEISKlUO3DoMtouPQV2K0OTLgWhrSGz15V896IFJo8zOz6PPPn5lv372QGJSJSoAbHwBXT4Lyng5EMn78AnmgP33wQdWRlzvbuPDrnme+Xb137JMQiIlI0Mzj0jGAgqg4Pwo9fwRNZ8NyFsKpEdPxdKmwveVgh8wUti4gUr7R0yLwMes+DtjfDV28Fb6pP6AU/LY86ulJve8nDC5kvaFlEJBoVdoE2faHPh9CyB8x/LhgSd9ptsHFt1NGVWoW2tjKzrcB6gruMDGBD7iqgkrunF0uEO0CtrUTKsB+Xwox/w0ejoVJVaPNPaH5l0EW8bFdCWlu5e5q77+buu7p7+XA+dzllE4eIlHHVG8BZQ+Gqt6BeJky5GQY2g/kjg1EOJSFieUlQRKTk2etIuOhFuGQC7FITxl8djGj4+RQ1700AJQ8RKd32Ow6unAHnPAmbN8DIc+GpDsHwuLLDlDxEpPQrVw4OPwuunQ2n/gd+WASPnwijLoYfFkcdXYmk5CEiZUdaOrS4EnrPh+P/BV9Mh0Et4eW/wc/fRR1diaLkISJlT8UqcPwNQRJp3g3mPR00751+F/z6U9TRlQhKHiJSdlWpBaf2Dx5nNTwF3uoPDzWCDwbDlk1RR5fSlDxERGrsB+c8Ad3fgD2PgEk3wsOZwbsi27ZFHV1KUvIQEclVpwl0nQAXj4NK1WDslfBoG1gyTc1781HyEBHJb/+20P1NOHsYbPoJnjkbRpwBOXOjjixlKHmIiBSkXDk44hy4NhtOuT8YkOqxE+CFS2H1F1FHFzklDxGR7SlfIRhDvfd8aHM9fD4ZBrWAV/4Jv6yMOrrIKHmIiMSi0m7Q9qYgiTTtCtlPwEONYcY9sOnnqKMrdkoeIiLx2LU2dPgf9JwFB54Mb94bJJGZQ2HLb1FHV2yUPEREdkTNA+C84XDFdKh1MLzWN3ictfDFMtG8V8lDRGRn1GsGl06ELmMgvTKMuTyoWP/yjagjSyolDxGRnWUWPMLq8Tac+ShsWA3tkM3BAAAMeElEQVQjOsLTZ8KKD6OOLimUPEREEqVcGjTqHDTvzfo3LJ8XvGT44hXBCIeliJKHiEiipVeCo3oG46ofcx18OhEGZsJrN8L6H6KOLiGUPEREkqVSVTjpVug9FxpfCLMeDVpmvdkfflsfdXQ7RclDRCTZdqsDZwyAa2YGIxvOuCvoAn72MNi6OerodoiSh4hIcal1EHR+FrpNDXryfeW6YDCqj8eXuI4XlTxERIpb/RZw2WtwwShIqwAvdA2Gxf3q7agji5mSh4hIFMygYXu4+l3oOCgYBnd4B3jmHPhuYdTRFUnJQ0QkSuXSoMlF0GsOnHwHLJsFQ46BcT1g7TdRR1coJQ8RkVSQngGt+wTNe1v3hoVjYWAzmHwTbFgTdXR/oeQhIpJKMqoHdyC958KR58EHjwTjqr/9X/htQ9TR/S5pycPMKpnZLDP70Mw+NrPbw/KnzOwrM5sfTo3DcjOzAWa2xMw+MrOmeY7V1cwWh1PXZMUsIpIyqtYL6kKufg8aHAOv3wEDm8Kcp2DrlqijS+qdxyagrbs3AhoD7c2sVbiur7s3Dqf5YdkpwIHh1B0YDGBmNYBbgZZAC+BWM6uexLhFRFLHHofABc8FrbOq1oeX+8Dgo4K31iNs3pu05OGBX8LF9HDa3iftCIwI9/sAqGZmewFZwFR3X+PuPwJTgfbJiltEJCXtczR0mwLnPxssj+oCw9rB1+9HEk5S6zzMLM3M5gMrCRLAzHDV3eGjqQfMrGJYVhf4Ns/uy8Kywsrzn6u7mWWbWfaqVasS/llERCJnBod0gKvfh9MHwLpv4cn2MLIzrPy0WENJavJw963u3hioB7Qws8OBfsDBQHOgBnBDgs411N0z3T2zVq1aiTikiEhqSisPzbpCr7lw4q3w9Xsw+GgY3xPWLSuWEIqltZW7rwVmAO3dfUX4aGoT8CRBPQZADlA/z271wrLCykVEyrYKleHY66DPfGh1DSwYDRP/XiynTmZrq1pmVi2czwBOBj4L6zEwMwM6AbmvUk4ALglbXbUC1rn7CmAy0M7MqocV5e3CMhERAahcA7LuDl40zLqnWE5ZPonH3gsYbmZpBElqtLtPNLPpZlYLMGA+0CPc/lXgVGAJsAG4DMDd15jZncDscLs73D313pgREYlatb2L7VTmJawnx1hkZmZ6dnZ21GGIiJQoZjbH3TNj2VZvmIuISNyUPEREJG5KHiIiEjclDxERiZuSh4iIxE3JQ0RE4qbkISIicVPyEBGRuCl5iIhI3JQ8REQkbkoeIiISNyUPERGJm5KHiIjETclDRETipuQhIiJxU/IQEZG4KXmIiEjclDxERCRuSh4iIhI3JQ8REYmbkoeIiMRNyUNEROKm5CEiInFT8hARkbgpeYiISNyUPEREJG5KHiIiErfyUQcgIiI7b/y8HPpPXsTytRupUy2DvlkN6dSkbtLOp+QhIlLCjZ+XQ7+xC9i4eSsAOWs30m/sAoCkJRA9thIRKeH6T170e+LItXHzVvpPXpS0cyp5iIiUcMvXboyrPBGUPERESrg61TLiKk8EJQ8RkRKub1ZDMtLT/lSWkZ5G36yGSTunKsxFREq43ErxUtHayswqAW8BFcPzjHH3W81sX+B5YHdgDnCxu/9mZhWBEUAzYDVwvrsvDY/VD+gGbAV6u/vkZMUtIlISdWpSN6nJIr9kPrbaBLR190ZAY6C9mbUC7gMecPcDgB8JkgLhzx/D8gfC7TCzQ4HOwGFAe+ARM/vz/ZmIiBSrpCUPD/wSLqaHkwNtgTFh+XCgUzjfMVwmXH+imVlY/ry7b3L3r4AlQItkxS0iIkVLaoW5maWZ2XxgJTAV+AJY6+5bwk2WAbn3WXWBbwHC9esIHm39Xl7APnnP1d3Mss0se9WqVcn4OCIiEkpq8nD3re7eGKhHcLdwcBLPNdTdM909s1atWsk6jYiIUExNdd19LTADOAqoZma5FfX1gJxwPgeoDxCur0pQcf57eQH7iIhIBJLZ2qoWsNnd15pZBnAyQSX4DOAcghZXXYGXwl0mhMvvh+unu7ub2QRgpJn9D6gDHAjM2t6558yZ84OZfZ2Ej5WKagI/RB1EitC1+IOuxR90Lf5Q1LXYJ9YDJfM9j72A4WHLqHLAaHefaGafAM+b2V3APGBYuP0w4GkzWwKsIWhhhbt/bGajgU+ALUBPd9/Kdrh7mXluZWbZ7p4ZdRypQNfiD7oWf9C1+EMir0XSkoe7fwQ0KaD8SwpoLeXuvwLnFnKsu4G7Ex2jiIjsGHVPIiIicVPyKPmGRh1ACtG1+IOuxR90Lf6QsGth7p6oY4mISBmhOw8REYmbkoeIiMRNySNFhV27zDOzieHyvmY208yWmNkoM6sQllcMl5eE6xvkOUa/sHyRmWVF80l2XgHX4ikz+8rM5odT47DczGxA+Jk/MrOmeY7R1cwWh1PXqD7LzjCzpWa2IPzM2WFZDTObGn6uqWZWPSwvi9fiNjPLyfO9ODXP9gX+LphZ+7BsiZndGMVn2VlmVs3MxpjZZ2b2qZkdVSzfC3fXlIITcB0wEpgYLo8GOofzQ4Crw/lrgCHhfGdgVDh/KPAhQZf4+xL0K5YW9edK0LV4CjingO1OBV4DDGgFzAzLawBfhj+rh/PVo/5cO3AdlgI185XdD9wYzt8I3FeGr8VtwD8L2LbA34Vw+gLYD6gQbnNo1J9tB67FcOCKcL4CUK04vhe680hBZlYPOA14PFw2ymhvxPmvRRE6AiM88AFBVzh7AVnAVHdf4+4/EnTS2T5pQRevvP/++b8XZe1aFKaw34UWwBJ3/9LdfyPo9aJjhHHGzcyqAm0IX7Z299886A4q6d8LJY/U9CBwPbAtXN6dJPVGXALkvxa57g5vux+wYCAxKPwzl5Zr4cAUM5tjZt3DstruviKc/w6oHc6XxWsBcG34vXgi91ENpfta7AusAp4MH+0+bma7UAzfCyWPFGNmHYCV7j4n6liitp1r0Y+gh+bmBLfZNxR3bBE5xt2bAqcAPc2sTd6VHjx/KCtt7wu6FoOB/QkGn1sB/DfC+IpLeaApMNjdmwDrCR5T/S5Z3wslj9TTGjjDzJYS3Ea3BR6ibPZG/JdrYWbPuPuK8LZ7E/AkfzyOK+wzl4ZrgbvnhD9XAuMIPvf34WMHwp8rw83L3LVw9+89GAZiG/AYZeN7sQxY5u4zw+UxBMkk6d8LJY8U4+793L2euzcgqACf7u5d+KM3Yii4N2LI0xtxWN45bI21LzH0RpxqCrkWF+X5pTCCZ7kLw10mAJeELUpaAevCW/fJQDszqx4+ymgXlpUYZraLme2aO0/wGRby53///N+LMnUtcr8XoTP58/eioN+F2cCBFrRkrEDwHZtQXJ8jEdz9O+BbM2sYFp1I0Ils0r8XyexVVxLrBpLcG3EJ8qwFXf4bMB/oEZa/StCaZAmwAbgMwN3XmNmdBP9ZANzh7muKN+SdVhsYF+RLygMj3X2Smc0GRptZN+Br4Lxw+7J4LZ62oNm2E7TGugq2/7tgZtcS/CeZBjzh7h8X94dJgF4EvxMVCFpJXUbYk3kyvxfqnkREROKmx1YiIhI3JQ8REYmbkoeIiMRNyUNEROKm5CEiInFT8hCJgZntaWbPm9kXYZcYr5pZdwt7+o0opjfMLDOq80vZpuQhUoTwZcRxwBvuvr+7NyPoIqX29vcUKb2UPESKdgKw2d2H5Ba4+4fA20CVPGMpPBsmGszsFjObbWYLzWxonvI3zOw+M5tlZp+b2bFh+aVmNtbMJoXjKdyfey4za2dm75vZXDN7wcyqFOunFymAkodI0Q4HCuuosgnwN4IxI/Yj6I8L4GF3b+7uhwMZQIc8+5R39xbhfrfmKW8MnA8cAZxvZvXNrCZwM3BS2BFgNsH4JiKRUvckIjtnlrsvAzCz+UAD4B3gBDO7HqhM0PPvx8DL4T5jw59zwu1zve7u68JjfQLsQzCwz6HAu+HNSwXg/eR9HJHYKHmIFO1j/uiUMr9Neea3AuXNrBLwCJDp7t+a2W1ApQL22cqffwf/ciyC/rumuvsFOx6+SOLpsZVI0aYDFfMOOmRmRwLHFrJ9bqL4IayfKCzxxOIDoLWZHRCedxczO2gnjieSEEoeIkUIu7g/EzgpbKr7MXAPwQhtBW2/lmA8iYUEPbbOLmi7GM+9CrgUeM7MPiJ4ZHXwjh5PJFHUq66IiMRNdx4iIhI3JQ8REYmbkoeIiMRNyUNEROKm5CEiInFT8hARkbgpeYiISNz+H+Z2+SRXbxpoAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110ad87d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.83112469678 8415.83839992 149111.156184\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1137cd6d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.843386538099 8484.92018026 145161.756368\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110a4d110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.836978810858 8458.23415313 149779.697572\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11454b450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.841303367667 8486.90339767 151988.463411\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1103cdd10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.839592460461 8477.44139626 153463.884668\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1137cd6d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.84545754241 8516.62122546 154331.030953\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112fef090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.841078223996 8501.64819368 156432.902623\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110acdb10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.841860430414 8508.60510208 157190.061124\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112af8f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.850010698517 8549.38164507 156027.308938\n",
      "Gain: -0.415330, Chi2: 1.070214\n"
     ]
    },
    {
     "data": {
      "image/png": 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KcvZIu+qT4X+GqurKqtpYVZuZvaH4xapakWeYVfUo8HCSE/9D9BuBB0bY0iC+Abw2yfOThNm5rMib13PsBS7tLV8KfG6EvQwkyQXMXiq9qKq+O+p++lFVB6rqh6tqc+/7/zDw6t730Ypj+Ou3gM8kuQ94FfD7I+6nL71/vdwM3AUcYPbv9or5ScwkNwL/BGxNcjjJu4CrgDcneYjZf9lcNcoeT9cp5vJx4IXA7UnuSXL1SJs8DaeYx9jwJ3wlqUGe+UtSgwx/SWqQ4S9JDTL8JalBhr8kNcjwl6QGGf6S1CDDX5Ia9H8eq8v9FRezigAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1132d2a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shift: 7210.791325, Chi2: 9498038.292216\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112ae4710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ -2.66707149e-01   5.67515041e+03]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11470ea90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def CalcGainShift(ringNo,ch):\n",
    "    th=ScatteringAngle(ringNo, 22.0, 11.0, 0.491, 0.5)[1]\n",
    "    energy = array([SimulateNiPD(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, 0, th)[1],\n",
    "                    SimulateNiPT(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, 0, th)[1],\n",
    "                    SimulateNiPT(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, 1172.98*1e-3, th)[1],\n",
    "                    SimulateNiPT(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, 2048.68*1e-3, th)[1],\n",
    "                    (SimulateNiPT(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, 2301.84*1e-3, th)[1]+\n",
    "                    SimulateNiPT(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 0.5, 2336.52*1e-3, th)[1])*0.5\n",
    "                    ])*1e3\n",
    "    \n",
    "    p = polyfit(ch, energy, 1)\n",
    "    \n",
    "    plt.title(\"E calibration, ring %i\" % ( ringNo ) )\n",
    "    plt.plot(ch, energy, \"o\")\n",
    "    plt.plot(linspace(ch[0],ch[-1],1001), p[0]*linspace(ch[0],ch[-1],1001)+p[1])\n",
    "    plt.xlabel(\"Channel\")\n",
    "    plt.ylabel(\"Energy [keV]\")\n",
    "    plt.show()\n",
    "    print p[0], p[1], sum((energy - ch*p[0] - p[1])**2)/(len(energy) - 2)\n",
    "    return p[0], p[1], energy, ch\n",
    "\n",
    "gain = []\n",
    "shift = []\n",
    "\n",
    "en = []\n",
    "ch = []\n",
    "\n",
    "# From ring 3:\n",
    "g,s,e,c = CalcGainShift(3, array([1472.99,2092.6,2232.06,2381.77,2528.54]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 4:\n",
    "g,s,e,c = CalcGainShift(4, array([1486.03,2118.76,2247.58,2394,2556.15]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 5:\n",
    "g,s,e,c = CalcGainShift(5, array([5981.23,5265.53,4749.78,4216.06,3732.2]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 6:\n",
    "g,s,e,c = CalcGainShift(6, array([5964.63,5235.59,4722.08,4201.38,3703.22]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 7:\n",
    "g,s,e,c = CalcGainShift(7, array([5948.91,5218.03,4694.27,4152.38,3677.11]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 8:\n",
    "g,s,e,c = CalcGainShift(8, array([5934,5191.19,4671.9,4125.9,3674.49]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 9:\n",
    "g,s,e,c = CalcGainShift(9, array([5917.42,5173.78,4644.72,4092,3628.64]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 10:\n",
    "g,s,e,c = CalcGainShift(10, array([5897.86,5146.37,4620.58,4084.2,3593.46]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 11:\n",
    "g,s,e,c = CalcGainShift(11, array([5873.97,5115.53,4599.44,4016.72,3561.23]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 12:\n",
    "g,s,e,c = CalcGainShift(12, array([5858.35,5095.49,4569.41,4012.18,3534.29]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 13:\n",
    "g,s,e,c = CalcGainShift(13, array([5846.12,5071.68,4543.17,3977.01,3491.29]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 14:\n",
    "g,s,e,c = CalcGainShift(14, array([5825.9,5046.41,4510.02,3934.34,3458.72]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "# From ring 15:\n",
    "g,s,e,c = CalcGainShift(15, array([5798.53,5012.29,4488.84,3876.61,3445.92]))\n",
    "for i in range(len(e)):\n",
    "    en.append(e[i])\n",
    "    ch.append(c[i])\n",
    "gain.append(g)\n",
    "shift.append(s)\n",
    "\n",
    "gfinal = sum(gain)/float(len(gain))\n",
    "chiGain = sum((gfinal - gain)**2)/float(len(gain)-1)\n",
    "print \"Gain: %2.6f, Chi2: %2.6f\" % ( gfinal, chiGain )\n",
    "plt.plot(range(3,16),gain, \"o\")\n",
    "plt.plot(range(3,16),ones(len(gain))*gfinal)\n",
    "plt.show()\n",
    "\n",
    "sfinal = sum(shift)/float(len(shift))\n",
    "chiShift = sum((sfinal - shift)**2)/float(len(shift)-1)\n",
    "\n",
    "print \"Shift: %2.6f, Chi2: %2.6f\" % ( sfinal, chiShift )\n",
    "plt.plot(range(3,16),shift, \"o\")\n",
    "plt.plot(range(3,16),ones(len(shift))**sfinal)\n",
    "plt.show()\n",
    "\n",
    "p = polyfit(ch, en, 1)\n",
    "print p\n",
    "plt.plot(ch, en,\"o\")\n",
    "plt.plot(linspace(ch[0],ch[-1],1001),p[0]*linspace(ch[0],ch[-1],1001)+p[1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.590620398615 0.582882080776 0.598279246898\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f5ef8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.7848743028 12.7086683858\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111f5e650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def SimulateNiPT(Ebeam, Twidth, Fwidth, dEwidth, Ewidth, ex, theta):\n",
    "    \"\"\"\n",
    "    Ebeam: energy of the incomming beam in MeV\n",
    "    Twidth: Thickness of the target in g/cm2\n",
    "    Fwidth: Thickness of the absorber in um\n",
    "    dEwidth: Thickness of the dE detector in um\n",
    "    Ewidth: Thickness of the E detector in um\n",
    "    reactionPoint: Fraction of target thickness where the reaction will take place.\n",
    "    ex: Array with excitation energy.\n",
    "    theta: Angle of outgoing ion.\n",
    "    \"\"\"\n",
    "    \n",
    "    # Define masses\n",
    "    m1 = 63.9279660*931.494061 # Mass nickel 64\n",
    "    m2 = 1.008*931.494061 # Proton mass\n",
    "    m3 = 3.0160492*931.494061 # Deuteron mass\n",
    "    m4 = 61.9283451*931.494061 # Mass nickel 63\n",
    "    \n",
    "    # Required stopping power\n",
    "    stopTargetP = StoppingPowerFile(\"protonNi.txt\")\n",
    "    stopTargetT = StoppingPowerFile(\"tritonNi.txt\")\n",
    "    stopAbsorberT = StoppingPowerFile(\"StAl_table_um.txt\")\n",
    "    stopTelescopeT = StoppingPowerFile(\"StSi_table_um.txt\")\n",
    "    \n",
    "    # First we calculate the point where the interaction will happend.\n",
    "    thick_react = Twidth*0.5 # reactionPoint is a number between 0 and 1.\n",
    "    \n",
    "    Ereaction = Ebeam\n",
    "    Ereaction = stopTargetP.Loss(Ereaction, thick_react, 1001)\n",
    "    Ereaction = T3Energy(m1, m2, m3, m4, Ereaction, ex, theta)\n",
    "    Ereaction = stopTargetT.Loss(Ereaction, (Twidth-thick_react)/cos(theta), 1001)\n",
    "        \n",
    "    EaA = stopAbsorberT.Loss(Ereaction, Fwidth/cos(theta), 1001)\n",
    "    EaDE = stopTelescopeT.Loss(EaA, dEwidth/cos(theta), 1001)\n",
    "    EaE = stopTelescopeT.Loss(EaDE, Ewidth/cos(theta), 1001)\n",
    "    EinDE = EaA - EaDE\n",
    "    EinE = EaDE - EaE\n",
    "    return EinE, EinDE\n",
    "\n",
    "# Now we have beam energy:\n",
    "Ebeam = 27.36 # Proton energy [MeV]\n",
    "Twidth = 4.56 # Target thickness [mg/cm^2]\n",
    "\n",
    "Fwidth = 10 # Al-absorber width [um]\n",
    "dEwidth = 309 # delta-E detector width [um]\n",
    "Ewidth = 1041 # E detector width [um] \n",
    "\n",
    "th, th_min, th_max = ScatteringAngle(14, 22.0, 11.0, 0.491, 0.5)\n",
    "print th, th_min, th_max\n",
    "th_r = linspace(th_min, th_max, 11)\n",
    "e = zeros(len(th_r))\n",
    "de = zeros(len(th_r))\n",
    "for i in range(len(th_r)):\n",
    "    e[i], de[i] = SimulateNiPT(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, 1172.98*1e-3, th_r[i])\n",
    "    #print e[i], de[i]\n",
    "plt.plot(e, de,\"o\")\n",
    "e_a,de_a = SimulateNiPT(Ebeam, Twidth*1e-3, Fwidth, dEwidth, Ewidth, linspace(0, 2.,1001), th)\n",
    "plt.plot(e_a,de_a)\n",
    "plt.show()\n",
    "print e[0], e[-1]\n",
    "plt.plot(e+de,e)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  2.21013644e+01  -9.77446996e+04]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1104ea950>]"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112774b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p=polyfit([4900,5150,4450.5,4590.5],[14169,14240,1270.86,1278.49],1)\n",
    "print p\n",
    "plt.plot([4900,5150,4450.5,4590.5],[14169,14240,1270.86,1278.49],\"o\")\n",
    "plt.plot([4900,5150,4450.5,4590.5],p[0]*array([4900,5150,4450.5,4590.5])+p[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}