Mochima_2_2LUPM.ipynb 668 KB
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{
 "cells": [
  {
   "cell_type": "code",
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   "execution_count": 1,
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   "metadata": {
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    "collapsed": false
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   },
   "outputs": [],
   "source": [
    "%matplotlib notebook\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 2,
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   "metadata": {
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    "collapsed": true
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   },
   "outputs": [],
   "source": [
    "from scipy.stats import rv_continuous\n",
    "from scipy.special import gamma\n",
    "import numpy as np\n",
    "import emcee\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "from numpy import exp, sqrt\n",
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    "from scipy.integrate import quad, dblquad, simps\n",
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    "from scipy.stats import rv_continuous\n",
    "from scipy.special import gamma\n",
    "from scipy.interpolate import interp1d\n",
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    "from scipy.integrate import quad\n",
    "import scipy.optimize as optimize\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "from sklearn.neighbors import KDTree\n",
    "import sys\n",
    "import lmfit\n",
    "from py_unsio import *\n",
    "import pymc\n",
    "import os\n",
    "from pymodelfit import FunctionModel1DAuto\n",
    "import wkbl\n",
    "from mpl_toolkits.mplot3d import axes3d\n",
    "from matplotlib import cm\n",
    "import wkbl.astro.nbody_essentials as nbe\n",
    "import cfalcon\n",
    "CF =cfalcon.CFalcon()\n",
    "import iminuit\n",
    "from iminuit import Minuit, describe, Struct\n",
    "import probfit\n",
    "import warnings\n",
    "from matplotlib.colors import LogNorm\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# DMO"
   ]
  },
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  {
   "cell_type": "code",
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   "execution_count": 3,
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   "metadata": {
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    "collapsed": false
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loading Dark matter..\n",
      "centering\n",
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      "done r200 = 227.9296875\n"
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     ]
    }
   ],
   "source": [
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    "path = \"/data/OWN/DMO/mochima2_Z5/output_00041\"\n",
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    "#path = \"/media/arturo/ARTUROTECA/OUTPUTS/HaloB/output_00417\"\n",
    "myDMO = wkbl.Galaxy_Hound(path)\n",
    "print \"centering\"\n",
    "zoom_reg = np.where(myDMO.dm.mass == myDMO.dm.mass.min())\n",
    "nucenter = nbe.real_center(myDMO.dm.pos3d[zoom_reg], myDMO.dm.mass[zoom_reg])\n",
    "myDMO.center_shift(nucenter)\n",
    "myDMO.r_virial(600)\n",
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    "print \"done r200 = {0}\".format(myDMO.r200)\n",
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    "myDMO.redefine(2.5)\n",
    "ok,myDMO.dm.rho,_= CF.getDensity(np.array(myDMO.dm.pos3d.reshape(len(myDMO.dm.pos3d)*3),dtype=np.float32), myDMO.dm.mass)\n",
    "\n"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 4,
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   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "3.032886e+16\n",
      "-3.972665162831405e+16\n",
      "0.23656138189405296\n"
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     ]
    }
   ],
   "source": [
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    "\"\"\"\n",
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    "K = np.sum(myDMO.dm.mass*(myDMO.dm.v)**2)\n",
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    "print K\n",
    "myGkm = 6.673e-11*(1e-3**3)*myDMO.p.msuntokg#km^ 3 Msun^-1 s^-2\n",
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    "r_sorted = np.argsort(myDMO.dm.r)\n",
    "M_i = np.cumsum(myDMO.dm.mass[r_sorted]) - myDMO.dm.mass[r_sorted]\n",
    "m_i = myDMO.dm.mass[r_sorted]\n",
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    "r_i = myDMO.dm.r[r_sorted]*(1e-2*myDMO.p.pctocm)# in km\n",
    "U =  np.sum(-myGkm*M_i*m_i/r_i)\n",
    "print U\n",
    "print K/U + 1\n",
    "\"\"\""
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   ]
  },
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  {
   "cell_type": "code",
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   "execution_count": 4,
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   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def abg_logprofile(x,p_s,r_s,al,be,ga):\n",
    "    x = 10**x\n",
    "    power =  (be - ga) / (al)\n",
    "    denominator = ((x/(r_s))**ga) * ((1 + (x / (r_s))**al)**power)\n",
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    "    return np.log10(10**p_s / denominator)\n",
    "\n",
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    "def abg_profile(x,po,r_s,al,be,ga):\n",
    "    power =  (be - ga) / al\n",
    "    denominator = ((x/r_s)**ga) * ((1 + (x / r_s)**al)**power)\n",
    "    return (10**po) / denominator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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    "## Mass fit"
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  },
  {
   "cell_type": "code",
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   "execution_count": 5,
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   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "0.8373210354860829\n"
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     ]
    }
   ],
   "source": [
    "Pcrit = myDMO.dm._p.rho_crit\n",
    "Mdm = myDMO.dm.mass.min()\n",
    "myradiuses = myDMO.dm.r[np.argsort(myDMO.dm.r)]\n",
    "tabN = np.cumsum(np.ones(len(myradiuses)))[1:]\n",
    "myradiuses = myradiuses[1:]\n",
    "Rp03 = np.sqrt(200/64.) * np.sqrt(4 * np.pi * Pcrit * tabN / 3. / Mdm ) * (myradiuses**1.5)/ np.log(tabN) \n",
    "val =0.6\n",
    "R_P03 = myradiuses[ np.where(Rp03 > val) ][0]\n",
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    "\n",
    "\n",
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    "print R_P03\n",
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    "hsml= 0.190# R_P03\n",
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    "# R array logarithmic Bining\n",
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    "r_p = np.logspace(np.log10(0.2*hsml),np.log10(hsml),15)\n",
    "# histogram of dm particles per logarithmic bin\n",
    "n_dm,r = np.histogram(myDMO.dm.r,bins=r_p)\n",
    "# edges of bins\n",
    "r1,r2 =r[:-1],r[1:]\n",
    "# shell's volume\n",
    "vol = 4.* np.pi * ((r2**3)-(r1**3)) / 3.\n",
    "r_size = r_p[1:]-r_p[:-1]\n",
    "# density per shell\n",
    "profileDMO_in = n_dm*myDMO.dm.mass.min()/vol\n",
    "# center of bins\n",
    "r_in = (r_p[:-1]+r_p[1:])/2.\n",
    "\n",
    "\n",
    "# R array logarithmic Bining\n",
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    "r_p = np.logspace(np.log10(hsml),np.log10(2.5*myDMO.r200),150)\n",
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    "# histogram of dm particles per logarithmic bin\n",
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    "n_dm,r = np.histogram(myDMO.dm.r,bins=r_p)\n",
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    "# edges of bins\n",
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    "r1,r2 =r[:-1],r[1:]\n",
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    "# shell's volume\n",
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    "vol = 4.* np.pi * ((r2**3)-(r1**3)) / 3.\n",
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    "r_size = r_p[1:]-r_p[:-1]\n",
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    "# density per shell\n",
    "profileDMO = n_dm*myDMO.dm.mass.min()/vol\n",
    "# center of bins\n",
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    "r = (r_p[:-1]+r_p[1:])/2.\n",
    "bin_size= (r_p[:-1]-r_p[1:])/2.\n",
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    "rr = r\n",
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    "\n",
    "\n",
    "Delta_rho = (myDMO.dm.mass.min() /vol) + (4*np.pi*(r**2)* (n_dm*myDMO.dm.mass.min()) * r_size / vol**2)\n",
    "Delta_rho2 = np.sqrt((myDMO.dm.mass.min()/np.sqrt(n_dm) /vol)**2 + (4*np.pi*(r**2)* (n_dm*myDMO.dm.mass.min()) * r_size / vol**2)**2)\n",
    "Delta_rho3 =(4*np.pi*(r**2)* (n_dm*myDMO.dm.mass.min()) * r_size / vol**2)\n",
    "Delta_rho4 =(myDMO.dm.mass.min() /vol)\n",
    "\n",
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    "# extra estatistics from Cfalcon density\n",
    "mean = np.array([])\n",
    "std = np.array([])\n",
    "n=np.array([])\n",
    "for i in range(len(r_p)-1):\n",
    "    shell = np.where((myDMO.dm.r > r_p[i])&(myDMO.dm.r < r_p[i+1])&(myDMO.dm.r > hsml))\n",
    "    n = np.append(n,len(shell[0]))\n",
    "    mean = np.append(mean,np.mean(myDMO.dm.rho[shell]))\n",
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    "    std = np.append(std,np.std(myDMO.dm.rho[shell]))\n",
    "    \n",
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    "\n",
    "m_obs = n_dm*myDMO.dm.mass.min()\n",
    "n = np.array([len(myDMO.dm.mass[myDMO.dm.r<i]) for i in r]) "
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 6,
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   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
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    "def abg_logprofile(x,p_s,r_s,al,be,ga):\n",
    "    x = 10**x\n",
    "    power =  (be - ga) / (al)\n",
    "    denominator = ((x/(r_s))**ga) * ((1 + (x / (r_s))**al)**power)\n",
    "    return np.log10(10**p_s / denominator)\n",
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    "\n",
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    "def abg_profile(x,po,r_s,al,be,ga):\n",
    "    power =  (be - ga) / al\n",
    "    denominator = ((x/r_s)**ga) * ((1 + (x / r_s)**al)**power)\n",
    "    return (10**po) / denominator\n",
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    "\n",
    "def chi2_mass(po,r_s,al,be,ga):\n",
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    "    \"\"\"\n",
    "    logarithmic Chi-square\n",
    "    using the full mass inside a radius R\n",
    "    \"\"\"\n",
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    "    def my_int(R):\n",
    "        r_test = np.logspace(np.log10(hsml),np.log10(R),100)\n",
    "        rho_test = 4* np.pi * (r_test**2) * abg_profile(r_test,po,r_s,al,be,ga)\n",
    "        return simps(rho_test,r_test)\n",
    "    expected = np.array([my_int(i) for i in r])\n",
    "    c = (np.log10(m_obs)- np.log10(expected))/ (np.log10(m_obs)-0.5*np.log10(n))\n",
    "    c = c**2\n",
    "    return np.sum(c)\n",
    "\n",
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    "def chi2_mass_bin(po,r_s,al,be,ga):\n",
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    "    \"\"\"\n",
    "    logarithmic Chi-square\n",
    "    using the full mass inside a shell\n",
    "    between Ri and Rf\n",
    "    \"\"\"\n",
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    "    def my_int(Ri,Rf):\n",
    "        r_test = np.logspace(np.log10(Ri),np.log10(Rf),100)\n",
    "        rho_test =  (r_test**2) * abg_profile(r_test,po,r_s,al,be,ga)\n",
    "        return 4* np.pi * simps(rho_test,r_test)\n",
    "    expected = np.array([my_int(r_p[i],r_p[i+1]) for i in range(len(r))])\n",
    "    c = (np.log10(m_obs)- np.log10(expected))#/ (np.log10(m_obs)-0.5*np.log10(n))\n",
    "    c = c**2\n",
    "    return np.sum(c)\n",
    "\n",
    "\n",
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    "\n",
    "def chi2_rho(po,r_s,al,be,ga):\n",
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    "    \"\"\"\n",
    "    logarithmic Chi-square\n",
    "    using mean of rho per shell\n",
    "    \"\"\"\n",
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    "    rho_obs = profileDMO\n",
    "    rho_the = np.array([abg_profile(i,po,r_s,al,be,ga) for i in r])\n",
    "    c = (np.log10(rho_the) - np.log10(rho_obs))/ np.log10(std)\n",
    "    c = c**2\n",
    "    return np.sum(c)"
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   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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    "collapsed": false
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   "outputs": [],
   "source": []
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  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
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   "execution_count": 7,
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   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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     "data": {
      "text/html": [
       "<hr>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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    },
    {
     "data": {
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      "text/html": [
       "\n",
       "        <table>\n",
       "            <tr>\n",
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       "                <td title=\"Minimum value of function\">FCN = 0.0137883614919</td>\n",
       "                <td title=\"Total number of call to FCN so far\">TOTAL NCALL = 114</td>\n",
       "                <td title=\"Number of call in last migrad\">NCALLS = 114</td>\n",
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       "            </tr>\n",
       "            <tr>\n",
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       "                <td title=\"Estimated distance to minimum\">EDM = 0.000112609340069</td>\n",
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       "                <td title=\"Maximum EDM definition of convergence\">GOAL EDM = 1e-05</td>\n",
       "                <td title=\"Error def. Amount of increase in FCN to be defined as 1 standard deviation\">\n",
       "                UP = 1.0</td>\n",
       "            </tr>\n",
       "        </table>\n",
       "        \n",
       "        <table>\n",
       "            <tr>\n",
       "                <td align=\"center\" title=\"Validity of the migrad call\">Valid</td>\n",
       "                <td align=\"center\" title=\"Validity of parameters\">Valid Param</td>\n",
       "                <td align=\"center\" title=\"Is Covariance matrix accurate?\">Accurate Covar</td>\n",
       "                <td align=\"center\" title=\"Positive definiteness of covariance matrix\">PosDef</td>\n",
       "                <td align=\"center\" title=\"Was covariance matrix made posdef by adding diagonal element\">Made PosDef</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">False</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                <td align=\"center\" title=\"Was last hesse call fail?\">Hesse Fail</td>\n",
       "                <td align=\"center\" title=\"Validity of covariance\">HasCov</td>\n",
       "                <td align=\"center\" title=\"Is EDM above goal EDM?\">Above EDM</td>\n",
       "                <td align=\"center\"></td>\n",
       "                <td align=\"center\" title=\"Did last migrad call reach max call limit?\">Reach calllim</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">False</td>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">False</td>\n",
       "                <td align=\"center\"></td>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">False</td>\n",
       "            </tr>\n",
       "        </table>\n",
       "        "
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      ]
     },
     "metadata": {},
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     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "        <table>\n",
       "            <tr>\n",
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       "                <td><a href=\"#\" onclick=\"$('#JSStBaksGm').toggle()\">+</a></td>\n",
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       "                <td title=\"Variable name\">Name</td>\n",
       "                <td title=\"Value of parameter\">Value</td>\n",
       "                <td title=\"Parabolic error\">Parab Error</td>\n",
       "                <td title=\"Minos lower error\">Minos Error-</td>\n",
       "                <td title=\"Minos upper error\">Minos Error+</td>\n",
       "                <td title=\"Lower limit of the parameter\">Limit-</td>\n",
       "                <td title=\"Upper limit of the parameter\">Limit+</td>\n",
       "                <td title=\"Is the parameter fixed in the fit\">FIXED</td>\n",
       "            </tr>\n",
       "        \n",
       "            <tr>\n",
       "                <td>1</td>\n",
       "                <td>po</td>\n",
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       "                <td>6.50241</td>\n",
       "                <td>2.54847</td>\n",
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       "                <td>0</td>\n",
       "                <td>0</td>\n",
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       "                <td>6.0</td>\n",
       "                <td>11.0</td>\n",
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       "                <td></td>\n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                <td>2</td>\n",
       "                <td>r_s</td>\n",
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       "                <td>32.1969</td>\n",
       "                <td>38.7849</td>\n",
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       "                <td>0</td>\n",
       "                <td>0</td>\n",
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       "                <td>1.0</td>\n",
       "                <td>52.0</td>\n",
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       "                <td></td>\n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                <td>3</td>\n",
       "                <td>al</td>\n",
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       "                <td>1</td>\n",
       "                <td>1</td>\n",
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       "                <td>0</td>\n",
       "                <td>0</td>\n",
       "                <td></td>\n",
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       "                <td></td>\n",
       "                <td>FIXED</td>\n",
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       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                <td>4</td>\n",
       "                <td>be</td>\n",
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       "                <td>3.37526</td>\n",
       "                <td>0.556596</td>\n",
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       "                <td>0</td>\n",
       "                <td>0</td>\n",
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       "                <td>2.5</td>\n",
       "                <td>3.5</td>\n",
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       "                <td></td>\n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                <td>5</td>\n",
       "                <td>ga</td>\n",
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       "                <td>1.29021</td>\n",
       "                <td>0.53755</td>\n",
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       "                <td>0</td>\n",
       "                <td>0</td>\n",
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       "                <td>0.5</td>\n",
       "                <td>1.5</td>\n",
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       "                <td></td>\n",
       "            </tr>\n",
       "            \n",
       "            </table>\n",
       "        \n",
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       "            <pre id=\"JSStBaksGm\" style=\"display:none;\">\n",
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       "            <textarea rows=\"16\" cols=\"50\" onclick=\"this.select()\" readonly>\\begin{tabular}{|c|r|r|r|r|r|r|r|c|}\n",
       "\\hline\n",
       " & Name & Value & Para Error & Error+ & Error- & Limit+ & Limit- & FIXED\\\\\n",
       "\\hline\n",
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       "1 & po & 6.502e+00 & 2.548e+00 &  &  & 6.000e+00 & 1.100e+01 & \\\\\n",
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       "\\hline\n",
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       "2 & $r_{s}$ & 3.220e+01 & 3.878e+01 &  &  & 1.000e+00 & 5.200e+01 & \\\\\n",
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       "\\hline\n",
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       "3 & al & 1.000e+00 & 1.000e+00 &  &  &  &  & FIXED\\\\\n",
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       "\\hline\n",
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       "4 & be & 3.375e+00 & 5.566e-01 &  &  & 2.500e+00 & 3.500e+00 & \\\\\n",
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       "\\hline\n",
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       "5 & ga & 1.290e+00 & 5.375e-01 &  &  & 5.000e-01 & 1.500e+00 & \\\\\n",
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       "\\hline\n",
       "\\end{tabular}</textarea>\n",
       "            </pre>\n",
       "            "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
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     "metadata": {},
     "output_type": "display_data"
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    }
   ],
   "source": [
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    "\n",
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    "\n",
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    "m_rho = Minuit(chi2_rho, al=1., fix_al=True,\n",
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    "         po=7.0,    error_po=0.01,  limit_po =(6.,11.),\n",
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    "         r_s=19.3,  error_r_s=0.1,   limit_r_s=(1.,52),\n",
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    "         be=3.,     error_be=0.01,   limit_be =(2.5,3.5),\n",
    "         ga=1.,     error_ga=0.01,   limit_ga =(.5,1.5))\n",
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    "m_rho.migrad();"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 8,
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   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
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      "text/html": [
       "<hr>"
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    {
     "data": {
      "text/html": [
       "\n",
       "        <table>\n",
       "            <tr>\n",
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       "                <td title=\"Minimum value of function\">FCN = 0.587861493993</td>\n",
       "                <td title=\"Total number of call to FCN so far\">TOTAL NCALL = 132</td>\n",
       "                <td title=\"Number of call in last migrad\">NCALLS = 132</td>\n",
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       "            </tr>\n",
       "            <tr>\n",
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       "                <td title=\"Estimated distance to minimum\">EDM = 6.79668379773e-07</td>\n",
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       "                <td title=\"Maximum EDM definition of convergence\">GOAL EDM = 1e-05</td>\n",
       "                <td title=\"Error def. Amount of increase in FCN to be defined as 1 standard deviation\">\n",
       "                UP = 1.0</td>\n",
       "            </tr>\n",
       "        </table>\n",
       "        \n",
       "        <table>\n",
       "            <tr>\n",
       "                <td align=\"center\" title=\"Validity of the migrad call\">Valid</td>\n",
       "                <td align=\"center\" title=\"Validity of parameters\">Valid Param</td>\n",
       "                <td align=\"center\" title=\"Is Covariance matrix accurate?\">Accurate Covar</td>\n",
       "                <td align=\"center\" title=\"Positive definiteness of covariance matrix\">PosDef</td>\n",
       "                <td align=\"center\" title=\"Was covariance matrix made posdef by adding diagonal element\">Made PosDef</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">False</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                <td align=\"center\" title=\"Was last hesse call fail?\">Hesse Fail</td>\n",
       "                <td align=\"center\" title=\"Validity of covariance\">HasCov</td>\n",
       "                <td align=\"center\" title=\"Is EDM above goal EDM?\">Above EDM</td>\n",
       "                <td align=\"center\"></td>\n",
       "                <td align=\"center\" title=\"Did last migrad call reach max call limit?\">Reach calllim</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">False</td>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">False</td>\n",
       "                <td align=\"center\"></td>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">False</td>\n",
       "            </tr>\n",
       "        </table>\n",
       "        "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "        <table>\n",
       "            <tr>\n",
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       "                <td><a href=\"#\" onclick=\"$('#fbYfoqComg').toggle()\">+</a></td>\n",
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       "                <td title=\"Variable name\">Name</td>\n",
       "                <td title=\"Value of parameter\">Value</td>\n",
       "                <td title=\"Parabolic error\">Parab Error</td>\n",
       "                <td title=\"Minos lower error\">Minos Error-</td>\n",
       "                <td title=\"Minos upper error\">Minos Error+</td>\n",
       "                <td title=\"Lower limit of the parameter\">Limit-</td>\n",
       "                <td title=\"Upper limit of the parameter\">Limit+</td>\n",
       "                <td title=\"Is the parameter fixed in the fit\">FIXED</td>\n",
       "            </tr>\n",
       "        \n",
       "            <tr>\n",
       "                <td>1</td>\n",
       "                <td>po</td>\n",
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       "                <td>5.85217</td>\n",
       "                <td>0.913094</td>\n",
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       "                <td>0</td>\n",
       "                <td>0</td>\n",
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       "                <td>5.8521658767</td>\n",
       "                <td>7.15264718264</td>\n",
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       "                <td></td>\n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                <td>2</td>\n",
       "                <td>r_s</td>\n",
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       "                <td>28.9772</td>\n",
       "                <td>6.43401</td>\n",
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       "                <td>0</td>\n",
       "                <td>0</td>\n",
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       "                <td>28.9771730865</td>\n",
       "                <td>35.4165448835</td>\n",
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       "                <td></td>\n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                <td>3</td>\n",
       "                <td>al</td>\n",
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       "                <td>1</td>\n",
       "                <td>1</td>\n",
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       "                <td>0</td>\n",
       "                <td>0</td>\n",
       "                <td></td>\n",
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       "                <td></td>\n",
       "                <td>FIXED</td>\n",
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       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                <td>4</td>\n",
       "                <td>be</td>\n",
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       "                <td>3.71279</td>\n",
       "                <td>0.675052</td>\n",
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       "                <td>0</td>\n",
       "                <td>0</td>\n",
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       "                <td>3.03773495566</td>\n",
       "                <td>3.71278716803</td>\n",
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       "                <td></td>\n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                <td>5</td>\n",
       "                <td>ga</td>\n",
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       "                <td>1.16119</td>\n",
       "                <td>0.13827</td>\n",
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       "                <td>0</td>\n",
       "                <td>0</td>\n",
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       "                <td>1.16118809445</td>\n",
       "                <td>1.41922989322</td>\n",
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       "                <td></td>\n",
       "            </tr>\n",
       "            \n",
       "            </table>\n",
       "        \n",
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       "            <pre id=\"fbYfoqComg\" style=\"display:none;\">\n",
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       "            <textarea rows=\"16\" cols=\"50\" onclick=\"this.select()\" readonly>\\begin{tabular}{|c|r|r|r|r|r|r|r|c|}\n",
       "\\hline\n",
       " & Name & Value & Para Error & Error+ & Error- & Limit+ & Limit- & FIXED\\\\\n",
       "\\hline\n",
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       "1 & po & 5.852e+00 & 9.131e-01 &  &  & 5.852e+00 & 7.153e+00 & \\\\\n",
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       "\\hline\n",
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       "2 & $r_{s}$ & 2.898e+01 & 6.434e+00 &  &  & 2.898e+01 & 3.542e+01 & \\\\\n",
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       "\\hline\n",
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       "3 & al & 1.000e+00 & 1.000e+00 &  &  &  &  & FIXED\\\\\n",
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       "\\hline\n",
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       "4 & be & 3.713e+00 & 6.751e-01 &  &  & 3.038e+00 & 3.713e+00 & \\\\\n",
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       "\\hline\n",
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       "5 & ga & 1.161e+00 & 1.383e-01 &  &  & 1.161e+00 & 1.419e+00 & \\\\\n",
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       "\\hline\n",
       "\\end{tabular}</textarea>\n",
       "            </pre>\n",
       "            "
      ]
     },
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     "output_type": "display_data"
    },
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     "data": {
      "text/html": [
       "<hr>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "low = 0.9\n",
    "upp = 1.1\n",
    "po,r_s,al,be,ga = m_rho.values['po'] ,m_rho.values['r_s'],m_rho.values['al'],m_rho.values['be'],m_rho.values['ga']\n",
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    "m_SC = Minuit(chi2_mass, al=1., fix_al=True,\n",
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    "         po=po,    error_po=0.01,  limit_po =(po*low,po*upp),\n",
    "         r_s=r_s,  error_r_s=1.,   limit_r_s=(r_s*low,r_s*upp),\n",
    "         be=be,     error_be=0.1,   limit_be =(be*low,be*upp),\n",
    "         ga=ga,     error_ga=0.1,   limit_ga =(ga*low,ga*upp))\n",
    "m_SC.migrad();"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 9,
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   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<hr>"
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    {
     "data": {
      "text/html": [
       "\n",
       "        <table>\n",
       "            <tr>\n",
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       "                <td title=\"Minimum value of function\">FCN = 0.870010738122</td>\n",
       "                <td title=\"Total number of call to FCN so far\">TOTAL NCALL = 404</td>\n",
       "                <td title=\"Number of call in last migrad\">NCALLS = 404</td>\n",
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       "            </tr>\n",
       "            <tr>\n",
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       "                <td title=\"Estimated distance to minimum\">EDM = 1.34288676412e-06</td>\n",
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       "                <td title=\"Maximum EDM definition of convergence\">GOAL EDM = 1e-05</td>\n",
       "                <td title=\"Error def. Amount of increase in FCN to be defined as 1 standard deviation\">\n",
       "                UP = 1.0</td>\n",
       "            </tr>\n",
       "        </table>\n",
       "        \n",
       "        <table>\n",
       "            <tr>\n",
       "                <td align=\"center\" title=\"Validity of the migrad call\">Valid</td>\n",
       "                <td align=\"center\" title=\"Validity of parameters\">Valid Param</td>\n",
       "                <td align=\"center\" title=\"Is Covariance matrix accurate?\">Accurate Covar</td>\n",
       "                <td align=\"center\" title=\"Positive definiteness of covariance matrix\">PosDef</td>\n",
       "                <td align=\"center\" title=\"Was covariance matrix made posdef by adding diagonal element\">Made PosDef</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">False</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                <td align=\"center\" title=\"Was last hesse call fail?\">Hesse Fail</td>\n",
       "                <td align=\"center\" title=\"Validity of covariance\">HasCov</td>\n",
       "                <td align=\"center\" title=\"Is EDM above goal EDM?\">Above EDM</td>\n",
       "                <td align=\"center\"></td>\n",
       "                <td align=\"center\" title=\"Did last migrad call reach max call limit?\">Reach calllim</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">False</td>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">False</td>\n",
       "                <td align=\"center\"></td>\n",
       "                <td align=\"center\" style=\"background-color:#92CCA6\">False</td>\n",
       "            </tr>\n",
       "        </table>\n",
       "        "
      ]
     },
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     "output_type": "display_data"
    },
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     "data": {
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       "\n",
       "        <table>\n",
       "            <tr>\n",
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       "                <td><a href=\"#\" onclick=\"$('#lGUYdvpgdq').toggle()\">+</a></td>\n",
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       "                <td title=\"Variable name\">Name</td>\n",
       "                <td title=\"Value of parameter\">Value</td>\n",
       "                <td title=\"Parabolic error\">Parab Error</td>\n",
       "                <td title=\"Minos lower error\">Minos Error-</td>\n",
       "                <td title=\"Minos upper error\">Minos Error+</td>\n",
       "                <td title=\"Lower limit of the parameter\">Limit-</td>\n",
       "                <td title=\"Upper limit of the parameter\">Limit+</td>\n",
       "                <td title=\"Is the parameter fixed in the fit\">FIXED</td>\n",
       "            </tr>\n",
       "        \n",
       "            <tr>\n",
       "                <td>1</td>\n",
       "                <td>po</td>\n",
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       "                <td>6.93319</td>\n",
       "                <td>0.782943</td>\n",
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       "                <td>0</td>\n",
       "                <td>0</td>\n",
       "                <td>2.0</td>\n",
       "                <td>15.0</td>\n",
       "                <td></td>\n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                <td>2</td>\n",
       "                <td>r_s</td>\n",
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       "                <td>19.0938</td>\n",
       "                <td>12.0441</td>\n",
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       "                <td>0</td>\n",
       "                <td>0</td>\n",
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       "                <td>10.0</td>\n",
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       "                <td>25.0</td>\n",
       "                <td></td>\n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                <td>3</td>\n",
       "                <td>al</td>\n",
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       "                <td>1</td>\n",
       "                <td>1</td>\n",
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       "                <td>0</td>\n",
       "                <td>0</td>\n",
       "                <td></td>\n",
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       "                <td></td>\n",
       "                <td>FIXED</td>\n",
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       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                <td>4</td>\n",
       "                <td>be</td>\n",
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       "                <td>3.1</td>\n",
       "                <td>0.147596</td>\n",
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       "                <td>0</td>\n",
       "                <td>0</td>\n",
       "                <td>2.9</td>\n",
       "                <td>3.1</td>\n",
       "                <td></td>\n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                <td>5</td>\n",
       "                <td>ga</td>\n",
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       "                <td>1.20283</td>\n",
       "                <td>0.30994</td>\n",
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       "                <td>0</td>\n",
       "                <td>0</td>\n",
       "                <td>0.01</td>\n",
       "                <td>2.0</td>\n",
       "                <td></td>\n",
       "            </tr>\n",
       "            \n",
       "            </table>\n",
       "        \n",
862
       "            <pre id=\"lGUYdvpgdq\" style=\"display:none;\">\n",
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       "            <textarea rows=\"16\" cols=\"50\" onclick=\"this.select()\" readonly>\\begin{tabular}{|c|r|r|r|r|r|r|r|c|}\n",
       "\\hline\n",
       " & Name & Value & Para Error & Error+ & Error- & Limit+ & Limit- & FIXED\\\\\n",
       "\\hline\n",
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       "1 & po & 6.933e+00 & 7.829e-01 &  &  & 2.000e+00 & 1.500e+01 & \\\\\n",
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       "\\hline\n",
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       "2 & $r_{s}$ & 1.909e+01 & 1.204e+01 &  &  & 1.000e+01 & 2.500e+01 & \\\\\n",
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       "\\hline\n",
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       "3 & al & 1.000e+00 & 1.000e+00 &  &  &  &  & FIXED\\\\\n",
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       "\\hline\n",
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       "4 & be & 3.100e+00 & 1.476e-01 &  &  & 2.900e+00 & 3.100e+00 & \\\\\n",
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       "\\hline\n",
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       "5 & ga & 1.203e+00 & 3.099e-01 &  &  & 1.000e-02 & 2.000e+00 & \\\\\n",
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       "\\hline\n",
       "\\end{tabular}</textarea>\n",
       "            </pre>\n",
       "            "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<hr>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
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    "m_bin = Minuit(chi2_mass_bin,  al=1., fix_al=True,\n",
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    "          po=8.0,    error_po=0.01,  limit_po =(2.,15.),\n",
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    "         r_s=20.3,  error_r_s=0.1,   limit_r_s=(10,25),\n",
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    "         be=3.,     error_be=0.01,   limit_be =(2.9,3.1),\n",
    "         ga=1.,     error_ga=0.01,   limit_ga =(0.01,2.))\n",
    "m_bin.migrad();"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 11,
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   "metadata": {
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    "collapsed": false,
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    "hide_input": false
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   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
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       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width);\n",
       "        canvas.attr('height', height);\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
       "    var y1 = fig.canvas.height - msg['y1'];\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x;\n",
       "    var y = canvas_pos.y;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
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\">"
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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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    }
   ],
   "source": [
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    "fig, [ax,ax1] = plt.subplots(2,1,gridspec_kw = {'height_ratios':[3.5, 1]},figsize=[6,7],sharex=True)\n",
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    "ax.set_xlim([0.2*hsml,600])\n",
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    "ax1.set_xlim([0.2*hsml,600])\n",
    "ax1.set_ylim([.5,1.5])\n",
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    "ax.set_ylim([2e2,2e10])\n",
    "ax.set_xscale('log')\n",
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    "ax1.set_xscale('log')\n",
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    "ax.set_yscale('log')\n",
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    "ax1.set_xlabel('R [kpc]',fontsize=15)\n",
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    "ax.set_ylabel(r'$\\rho(r)$ [M$_{\\odot}$ kpc $^{-3}$]',fontsize=15)\n",
    "ax.set_title(\"Mochima 2 DM\",fontsize=17)\n",
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    "\n",
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    "#define sigma pluss and sigma minus lines\n",
    "mean_plus = profileDMO+std\n",
    "mean_minu = profileDMO-std\n",
    "\n",
    "#  plot things\n",
    "#ax.scatter(myDMO.dm.r,myDMO.dm.rho,s=0.02,lw=0,alpha=0.6,c='#FF9100')\n",
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    "mean_minu[np.isnan(np.log10(mean_minu))] = 0\n",
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    "ax.plot(r[~np.isnan(np.log10(mean_plus))],mean_plus[~np.isnan(np.log10(mean_plus))],\n",
    "        c='g')\n",
    "ax.plot(r[~np.isnan(np.log10(mean_minu))],mean_minu[~np.isnan(np.log10(mean_minu))],\n",
    "        c='g')\n",
    "\n",
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    "ax.fill_between(r,mean_plus,mean_minu,color=\"g\",alpha=0.3)\n",
    "#ax.errorbar(r,profileDMO,xerr=bin_size,yerr=std,alpha=0.5)\n",
    "\n",
    "#ax.scatter(myDMO.dm.r,myDMO.dm.rho,s=0.2,lw=0,alpha=0.2,c='gray')\n",
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    "\n",
    "#plot means\n",
    "#ax.plot(r_p[:-1],mean,lw=1.5)\n",
    "ax.plot(r_p[:-1],profileDMO,lw=1.5)\n",
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    "## rho fit\n",
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    "ax.plot(r,(abg_profile(r,m_rho.values['po'] ,m_rho.values['r_s'],m_rho.values['al'],m_rho.values['be'],m_rho.values['ga'])),\n",
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    "        \"k\",lw=2,label=r\"$\\chi^2(\\rho) \")\n",
    "## spehere mass\n",
    "#ax.plot(r,(abg_profile(r,m_SC.values['po'] ,m_SC.values['r_s'],m_SC.values['al'],m_SC.values['be'],m_SC.values['ga'])),\n",
    "#        \"r-\",lw=2)\n",
    "## shell mass\n",
    "ax.plot(r[1:],(abg_profile(r[:-1],m_bin.values['po'] ,m_bin.values['r_s'],m_bin.values['al'],m_bin.values['be'],m_bin.values['ga'])),\n",
    "        \"r--\",lw=2)\n",
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    "\n",
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    "texto = \"fit results: \\n\"\n",
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    "texto += r\"$\\rho_0$ = {0:.3f} $\\pm$ {1:.3f}\".format(m_bin.values[\"po\"],m_bin.errors[\"po\"])+\"\\n\"\n",
    "texto += r\"$r_s$ = {0:.3f} $\\pm$ {1:.3f}\".format(m_bin.values[\"r_s\"],m_bin.errors[\"r_s\"])+\"\\n\"\n",
    "texto += r\"$\\alpha$ = {0:.3f} $\\pm$ {1:.3f}\".format(m_bin.values[\"al\"],m_bin.errors[\"al\"])+\"\\n\"\n",
    "texto += r\"$\\beta$ = {0:.3f} $\\pm$ {1:.3f}\".format(m_bin.values[\"be\"],m_bin.errors[\"be\"])+\"\\n\"\n",
    "texto += r\"$\\gamma$ = {0:.3f} $\\pm$ {1:.3f}\".format(m_bin.values[\"ga\"],m_bin.errors[\"ga\"])+\"\\n\"\n",
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    "\n",
    "fig.text(0.25,0.3,texto,fontsize=12)\n",
    "ax.text(3*hsml*1.1,1e8,\"3hsml\",color='gray',fontsize=14)\n",
    "ax.text(8*1.1,1e8,\"Sun\",color='y',fontsize=14)\n",
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    "ax.text(myDMO.r200*1.01,1e8,r\"R$_{200}$\",color='k',fontsize=14)\n",
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    "r_dm = r\n",
    "\n",
    "\n",
    "#horizontal lines\n",
    "ax.axvline(x=hsml,c='gray',alpha=0.5,linestyle='--',lw=1.5)\n",
    "ax.axvline(x=3*hsml,c='gray',alpha=0.5,linestyle='--',lw=1.5)\n",
    "ax.axvline(x=8,c='y',linestyle='--',lw=1.5) #Sun\n",
    "ax.axvline(x=myDMO.r200,c='k',linestyle='--',lw=1.5) #r200\n",
    "\n",
    "#########33\n",
    "\n",
    "##\n",
    "ax1.axhline(y=1.,color=\"g\",linestyle=\"--\")\n",
    "## rho fit\n",
    "r_local = np.logspace(np.log10(hsml),np.log10(2.5*myDMO.r200),100)\n",
    "ax1.plot(r,(abg_profile(r,m_rho.values['po'] ,m_rho.values['r_s'],m_rho.values['al'],m_rho.values['be'],m_rho.values['ga']))/profileDMO,\n",
    "        \"k\",lw=1.5,label=r\"$\\chi^2(\\rho) \")\n",
    "\n",
    "ax1.plot(r_in,(abg_profile(r_in,m_rho.values['po'] ,m_rho.values['r_s'],m_rho.values['al'],m_rho.values['be'],m_rho.values['ga']))/profileDMO_in,\n",
    "        \"k--\",lw=1.5,label=r\"$\\chi^2(\\rho) \")\n",
    "## spehere mass\n",
    "#ax.plot(r,(abg_profile(r,m_SC.values['po'] ,m_SC.values['r_s'],m_SC.values['al'],m_SC.values['be'],m_SC.values['ga'])),\n",
    "#        \"r-\",lw=2)\n",
    "## shell mass\n",
    "ax1.plot(r,(abg_profile(r,m_bin.values['po'] ,m_bin.values['r_s'],m_bin.values['al'],m_bin.values['be'],m_bin.values['ga']))/profileDMO,\n",
    "        \"r-\",lw=1.5)\n",
    "ax1.plot(r_in,(abg_profile(r_in,m_bin.values['po'] ,m_bin.values['r_s'],m_bin.values['al'],m_bin.values['be'],m_bin.values['ga']))/profileDMO_in,\n",
    "        \"r--\",lw=1.5)\n",
    "\n",
    "#horizontal lines\n",
    "ax1.axvline(x=hsml,c='gray',alpha=0.5,linestyle='--',lw=1.5)\n",
    "ax1.axvline(x=3*hsml,c='gray',alpha=0.5,linestyle='--',lw=1.5)\n",
    "ax1.axvline(x=8,c='y',linestyle='--',lw=1.5) #Sun\n",
    "ax1.axvline(x=myDMO.r200,c='k',linestyle='--',lw=1.5) #r200\n",
    "\n",
    "\n",
    "\n",
    "# layout\n",
    "fig.tight_layout(h_pad=-1.65)\n",
    "ax.tick_params(axis='both', which='major', labelsize=15, size=5,width=1.2)\n",
    "ax.tick_params(axis='both', which='minor', labelsize=15, size=3,width=1.2)\n",
    "ax1.tick_params(axis='both', which='major', labelsize=15, size=5,width=1.2)\n",
    "ax1.tick_params(axis='both', which='minor', labelsize=15, size=3,width=1.2)"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 12,
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   "metadata": {
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    "collapsed": false,
    "hide_input": true
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "###################################################\n",
      "##################### LUPM ########################\n",
      "################## Mochima DMO ####################\n",
      "fit results: \n",
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      "$\\rho_0$ = 6.933 $\\pm$ 0.783\n",
      "$r_s$ = 19.094 $\\pm$ 12.044\n",
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      "$\\alpha$ = 1.000 $\\pm$ 1.000\n",
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      "$\\beta$ = 3.100 $\\pm$ 0.148\n",
      "$\\gamma$ = 1.203 $\\pm$ 0.310\n",
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      "\n"
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     ]
    }
   ],
   "source": [
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    "print \"###################################################\"\n",
    "print \"##################### LUPM ########################\"\n",
    "print \"################## Mochima DMO ####################\"\n",
    "print texto"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": null,
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   "metadata": {
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    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#### TAKES TIME ####\n",
    "\n",
    "myGkpc = 6.673e-11*((1e-3/myDMO.p.kpctokm)**3)*myDMO.p.msuntokg#kpc^ 3 Msun^-1 s^-2\n",
    "pos = np.array(myDMO.dm.pos3d.reshape(len(myDMO.dm.pos3d)*3),dtype=np.float32)#*myDMO.p.kpctokm\n",
    "#ok, acc, Phy = CF.getGravity(pos,myDMO.dm.mass,0.190,G=myGkpc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\nbin_num = 512\\n\\npot_sph, bins_pot = np.histogram(r2,bins=bin_num,\\n                                 weights=Phy)\\nn, _ = np.histogram(r2,bins=bin_num)\\n\\nbin_num = 512\\nbins_pot = np.linspace(0.,myDMO.dm.r.max(),512)\\npot_sph_vesc, bins_pot_vesc = np.histogram(r2[(r2<myDMO.r200**2)], bins=bin_num, weights=Phy[(r2<myDMO.r200**2)])\\nrmax = np.sqrt(bins_pot[(pot_sph/n)==(pot_sph/n)[(bins_pot<503.**2)].max()])[0]\\npot_max = (pot_sph/n)[(pot_sph/n)==(pot_sph/n)[(bins_pot<503.**2)].max()][0]\\n'"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "bin_num = 512\n",
    "\n",
    "pot_sph, bins_pot = np.histogram(r2,bins=bin_num,\n",
    "                                 weights=Phy)\n",
    "n, _ = np.histogram(r2,bins=bin_num)\n",
    "\n",
    "bin_num = 512\n",
    "bins_pot = np.linspace(0.,myDMO.dm.r.max(),512)\n",
    "pot_sph_vesc, bins_pot_vesc = np.histogram(r2[(r2<myDMO.r200**2)], bins=bin_num, weights=Phy[(r2<myDMO.r200**2)])\n",
    "rmax = np.sqrt(bins_pot[(pot_sph/n)==(pot_sph/n)[(bins_pot<503.**2)].max()])[0]\n",
    "pot_max = (pot_sph/n)[(pot_sph/n)==(pot_sph/n)[(bins_pot<503.**2)].max()][0]\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "hide_input": false
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   },
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   "outputs": [],
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   "source": [
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    "\n",
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    "mass = myDMO.dm.mass\n",
    "v = myDMO.dm.v\n",
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    "\n",
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    "pos3d = pos.reshape(len(pos)/3,3)\n",
    "r2 = pos3d[:,0]**2 + pos3d[:,1]**2 +pos3d[:,2]**2\n",
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    "\n",
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    "def vesc_from_pot(limmin, limmax):\n",
    "    \"\"\"\n",
    "    a function calculating the vesc from potential inside interval\n",
    "    \"\"\"\n",
    "    contidion = (r2>limmin**2)&(r2<limmax**2)\n",
    "    mean = np.average(Phy[contidion])\n",
    "    sigma = np.std((Phy[contidion]))\n",
    "    v_esc = np.sqrt(2*np.abs(mean - pot_max))\n",
    "    sig_vesc = sigma / v_esc \n",
    "    return v_esc, sig_vesc \n",
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    "\n",
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    "def maxw(v,sigma):\n",
    "    N = np.sqrt(32 * np.pi) * v**2 / sigma**3\n",
    "    return N * np.exp(- v**2 / 2. / sigma**2)\n",
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    "\n",
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    "get_maxw = np.vectorize(maxw)\n",
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    "\n",
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    "def eddingtong_from_file(path):\n",
    "    v = np.array([])\n",
    "    fv = np.array([])\n",
    "    files = open(path)\n",
    "    for line in files:\n",
    "        row = line.split(' ')\n",
    "        if row[0][0]==\"#\":continue\n",
    "        if np.isnan(float(row[1][:-1])):\n",
    "            continue\n",
    "        \n",
    "        v = np.append(v,float(row[0]))\n",
    "        \n",
    "        fv = np.append(fv,float(row[1][:-1]))\n",
    "        \n",
    "    return v,fv\n",
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    "\n",
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    "\n",
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    "def fdv_plot_chi2_max_edd(ax,sim,path, limmin, limmax,dmo=True,save=False,outname=\"/home/arturo/Pictures/ploto\",width=None):\n",
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