{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ch-4 : Attenuation and Absorption in Optical Fiber"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:4.1 Pg: 138"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The signal attenuation =16.99 dB\n",
      "\n",
      " The signal attenuation per km =2.83 dB/km\n",
      "\n",
      " The trgth =22.65 km\n",
      "\n",
      " The overall signal attenuation =29.65 dB\n",
      "\n",
      " The i/p o/p power ratio =870.96 \n"
     ]
    }
   ],
   "source": [
    "from math import sqrt,pi,log\n",
    "from __future__ import division\n",
    "Pi=100*10**-6## mean optical power in watt\n",
    "Po=2*10**-6## output mean power in watt\n",
    "L=6## length in km\n",
    "L1=8## length in km\n",
    "As=10*log(Pi/Po)/log(10)## signal attenuation in dB\n",
    "as1=As/L## signal attenuation per km\n",
    "Li=as1*L1## Loss incurred along 8 km\n",
    "Ls=7## Loss due to splice in dB\n",
    "as2=Li+Ls## overall signal attenuation in dB\n",
    "As2=29.4## aprox. overall signal attenuation in dB\n",
    "Pio=10**(As2/10)## i/p o/p power ratio\n",
    "print \"The signal attenuation =%0.2f dB\"%(As)#\n",
    "print \"\\n The signal attenuation per km =%0.2f dB/km\"%( as1)#\n",
    "print \"\\n The trgth =%0.2f km\"%( Li)#\n",
    "print \"\\n The overall signal attenuation =%0.2f dB\"%( as2)#\n",
    "print \"\\n The i/p o/p power ratio =%0.2f \"%( Pio)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:4.2 Pg: 138"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The max possible link Length =57.50 km\n"
     ]
    }
   ],
   "source": [
    "from math import log,pi\n",
    "from __future__ import division\n",
    "Pi=1.5*10**-3## mean optical power in watt\n",
    "Po=2*10**-6## output mean power in watt\n",
    "a=0.5## dB/km\n",
    "L=(10*log(Pi/Po)/log(10))/a## max possible link Length in km\n",
    "print \"The max possible link Length =%0.2f km\"%( L)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:4.3 Pg: 138"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Loss of an optical fiber =1.57 dB/km\n",
      "\n",
      " The Loss of an optical fiber =0.14 dB/km\n",
      "\n",
      " The Loss of an optical fiber =0.29 dB/km\n"
     ]
    }
   ],
   "source": [
    "from math import log,pi\n",
    "from __future__ import division\n",
    "n=1.46## core refractive index\n",
    "p=0.286## photoelastic coeff\n",
    "b=7*10**-11## isothermal compressibility\n",
    "k=1.381*10**-23## boltzmann's constant\n",
    "tf=1400## fictive temperature in k\n",
    "y1=0.85*10**-6## wavelength in m\n",
    "yr=((8*pi**3)*(n**8)*(p**2)*(b*k*tf))/(3*y1**4)#\n",
    "e=2.718281828#\n",
    "akm=e**(-yr*10**3)#\n",
    "at=10*log(1/akm)/log(10)## attenuation at y=0.85 um\n",
    "y2=1.55*10**-6## wavelength in m\n",
    "yr1=((8*pi**3)*(n**8)*(p**2)*(b*k*tf))/(3*y2**4)#\n",
    "akm1=e**(-yr1*10**3)#\n",
    "at1=10*log(1/akm1)/log(10)## attenuation at y=1.55 um\n",
    "y3=1.30*10**-6## wavelength in m\n",
    "yr2=((8*pi**3)*(n**8)*(p**2)*(b*k*tf))/(3*y3**4)#\n",
    "akm2=e**(-yr2*10**3)#\n",
    "at2=10*log(1/akm2)/log(10)## attenuation at y=1.30 um\n",
    "print \"The Loss of an optical fiber =%0.2f dB/km\"%( at)#\n",
    "print \"\\n The Loss of an optical fiber =%0.2f dB/km\"%( at1)#\n",
    "print \"\\n The Loss of an optical fiber =%0.2f dB/km\"%( at2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:4.4 Pg: 139"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The threshold power for SBS =76 mw\n",
      "\n",
      " The threshold power for SRS =1.65 W\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "d=6## core diameter in m\n",
    "y=1.55## wavelength in m\n",
    "a=0.5## attenuation in dB/km\n",
    "v=0.4#\n",
    "Pb=4.4*10**-3*d**2*y**2*a*v## threshold power for SBS\n",
    "Pr=5.9*10**-2*d**2*y*a## threshold power for SRS\n",
    "print \"The threshold power for SBS =%d mw\"%( Pb*10**3)#\n",
    "print \"\\n The threshold power for SRS =%0.2f W\"%( Pr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:4.5 Pg: 139"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The critical radius of curvature for multimode fiber =9.46 um\n",
      "\n",
      " The critical radius of curvature for a single mode fiber =29.26 um\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt,pi\n",
    "from __future__ import division\n",
    "n1=1.46## core refractive index\n",
    "dl=0.03## relative refractive index difference\n",
    "y=0.85*10**-6## operating wavelength in m\n",
    "a=4*10**-6## core radous in m\n",
    "n2=sqrt(n1**2-2*dl*n1**2)## cladding refractive index\n",
    "Rc=(3*n1**2*y)/(4*pi*(n1**2-n2**2)**1.5)## critical radius of curvature for multimode fiber\n",
    "Dl=0.003## relative refractive index difference\n",
    "N2=sqrt(n1**2-2*Dl*n1**2)## \n",
    "yc=(2*pi*a*n1*(2*Dl)**0.5)/2.405## cut off wavelength in m\n",
    "y1=1.55*10**-6## operating wavelength in m\n",
    "Rcs=(20*y1*(2.748-0.996*(y1/yc))**-3)/(0.005)**1.5## critical radius of curvature for a single mode fiber\n",
    "print \"The critical radius of curvature for multimode fiber =%0.2f um\"%( Rc*10**6)##\n",
    "print \"\\n The critical radius of curvature for a single mode fiber =%0.2f um\"%( Rcs*10**3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:4.6 Pg: 139"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The macrobend loss =  14.22 dB\n",
      "\n",
      " The answer is wrong in the textbook\n"
     ]
    }
   ],
   "source": [
    "from sympy import log,N\n",
    "from __future__ import division\n",
    "x=2## index profile\n",
    "dl=0.0126## index difference\n",
    "a=(85/2)*10**-6## core radius\n",
    "R=2*10**-3## curve of radius\n",
    "n1=1.45## core refractive index\n",
    "k=6.28#\n",
    "y=850*10**-9## wavelength in m\n",
    "A=(x+2)/(2*x*dl)#\n",
    "B=(2*a/R)#\n",
    "C=(3*y/(2*k*R*n1))**(2/3)#\n",
    "D=B+C#\n",
    "E=A*D#\n",
    "F=1-E#\n",
    "Lm=-10*log(1-A*(B+C))/log(10)## macrobend loss in dB\n",
    "print \"The macrobend loss = \",abs(N(Lm,4)),\"dB\"#\n",
    "print \"\\n The answer is wrong in the textbook\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:4.7 Pg: 140"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Loss of an optical fiber =22 dB\n"
     ]
    }
   ],
   "source": [
    "from math import log,pi\n",
    "from __future__ import division\n",
    "Pi=15## optical power in uw\n",
    "Po=7## ouput power in uw\n",
    "L=0.15## length in km\n",
    "Ls=(10*log(Pi/Po)/log(10))/L## Loss of an optical fiber in dB\n",
    "print \"The Loss of an optical fiber =%d dB\"%( Ls)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:4.8 Pg: 140"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The signal attenuation per km =0.80 dB/km\n",
      "\n",
      " The overall signal attenuation=14.11 dB \n"
     ]
    }
   ],
   "source": [
    "from math import log,pi\n",
    "from __future__ import division\n",
    "Pi=200*10**-6## average optical power in watt\n",
    "Po=5*10**-6## average output power in watt\n",
    "L=20## in km\n",
    "L1=12## in km\n",
    "ns=5## number of attenuation\n",
    "a=0.9## attenuation in dB\n",
    "sa=10*log(Pi/Po)/log(10)## signal attenuation\n",
    "sp=sa/L## signal attenuation per km\n",
    "sn=sp*L1## signal attenuation for 12 km\n",
    "sn1=ns*a## attenuation in dB\n",
    "sn2=sn+sn1## overall signal attenuation in dB\n",
    "print \"The signal attenuation per km =%0.2f dB/km\"%( sp)#\n",
    "print \"\\n The overall signal attenuation=%0.2f dB \"%( sn2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:4.9 Pg: 141"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The signal attenuation=13.98 dB\n",
      "\n",
      " The signal attenuation per km =2.33 dB/km\n",
      "\n",
      " The overall signal attenuation=32 dB \n"
     ]
    }
   ],
   "source": [
    "from math import log,pi\n",
    "from __future__ import division\n",
    "Pi=100*10**-6## average optical power in watt\n",
    "Po=4*10**-6## average output power in watt\n",
    "L=6## in km\n",
    "L1=10## in km\n",
    "sa=10*log(Pi/Po)/log(10)## signal attenuation\n",
    "sp=sa/L## signal attenuation per km\n",
    "sn=sp*L1## signal attenuation for 12 km\n",
    "sn1=sn+9## overall signal attenuation in dB\n",
    "print \"The signal attenuation=%0.2f dB\"%( sa)#\n",
    "print \"\\n The signal attenuation per km =%0.2f dB/km\"%( sp)#\n",
    "print \"\\n The overall signal attenuation=%d dB \"%( sn1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:4.10 Pg: 141"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The signal Loss =4.26 dB\n",
      "\n",
      " The signal Loss per km=0.28 dB/km\n",
      "\n",
      " The overall signal attenuation=37.52 dB\n",
      "\n",
      " The input output power ratio=75.16\n"
     ]
    }
   ],
   "source": [
    "from math import log,pi\n",
    "from __future__ import division\n",
    "Pi=20*10**-6## average optical power in watt\n",
    "Po=7.5*10**-6## average output power in watt\n",
    "sl=10*log(Pi/Po)/log(10)## signal Loss in dB\n",
    "L=15## in km\n",
    "L1=30## in km\n",
    "ns=29## number of attenuation\n",
    "sp=sl/L## signal Loss per km\n",
    "sn=sp*L1## signal attenuation for 30 km\n",
    "sn1=sn+ns## overall signal attenuation in dB\n",
    "i_o=10**(sn1/20)## input output power ratio\n",
    "print \"The signal Loss =%0.2f dB\"%( sl)#\n",
    "print \"\\n The signal Loss per km=%0.2f dB/km\"%( sp)#\n",
    "print \"\\n The overall signal attenuation=%0.2f dB\"%( sn1)#\n",
    "print \"\\n The input output power ratio=%0.2f\"%( i_o)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:4.11 Pg: 142"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Attenuation=0.82 dB/km\n"
     ]
    }
   ],
   "source": [
    "from math import log,pi\n",
    "from __future__ import division\n",
    "Tf=1400## temperature in k\n",
    "Bc=7*10**-11## in m**2/N\n",
    "n=1.38## \n",
    "P=0.29## Photoelastic coefficient\n",
    "y=0.9*10**-6## wavelength in m\n",
    "K=1.38*10**-23## boltzman's constant\n",
    "Rrs=((8*pi**3)*(n**8)*(P**2)*(Bc*Tf*K))/(3*y**4)#\n",
    "Rrs1=Rrs/10**-3## per km\n",
    "e=2.718281828## Exponential term\n",
    "Lkm=e**(-Rrs1)## transmission loss facter\n",
    "At=10*log(1/Lkm)/log(10)## Attenuation in dB/km\n",
    "print \"The Attenuation=%0.2f dB/km\"%( At)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:4.12 Pg: 142"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The ratio of threshold power level=4.53 %\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "y=1.35## wavelength in um\n",
    "d=5## core diamater in um\n",
    "a=0.75## attenuation in dB/km\n",
    "v=0.45## bandwidth in GHz\n",
    "Pb=4.4*10**-3*(d**2)*(y**2)*(a*v)## threshold optical power for sbs\n",
    "Pr=5.9*10**-2*(d**2)*(y)*(a)## threshold optical power for sbr\n",
    "Pbr=Pb/Pr## the ratio of threshold power level\n",
    "print \"The ratio of threshold power level=%0.2f %%\"%( Pbr*100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:4.13 Pg: 143"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The critical radius of curvature =11.21 um\n"
     ]
    }
   ],
   "source": [
    "from math import log,pi,sqrt\n",
    "from __future__ import division\n",
    "n1=1.5## core refractive index\n",
    "y=0.85*10**-6## wavelength in m\n",
    "dl=0.024## relative refractive index difference\n",
    "N2=sqrt(n1**2-2*dl*n1**2)## cladding refractive index\n",
    "n2=1.46#\n",
    "Rcs=(3*n1**2*y)/((4*pi)*(n1**2-n2**2)**1.5)## critical radius of curvature for multimode fiber\n",
    "print \"The critical radius of curvature =%0.2f um\"%( Rcs*10**6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:4.14 Pg: 143"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The critical radius of curvature for single mode fiber =46.89 um\n",
      "\n",
      " The answer is wrong in the textbook\n",
      "\n",
      " The critical radius of curvature for multimode fiber =16.80 um\n"
     ]
    }
   ],
   "source": [
    "from math import log,pi,sqrt\n",
    "from __future__ import division\n",
    "n1=1.45## core refractive index\n",
    "y=1.5*10**-6## wavelength in m\n",
    "dl=0.03## relative refractive index difference\n",
    "a=5*10**-6## core radius\n",
    "n2=sqrt(n1**2-2*dl*n1**2)## cladding refractive index\n",
    "yc=(2*pi*a*n1*sqrt(2*dl))/(2.405)#\n",
    "Rcs=(20*y*(2.748-0.996*(y/yc))**-3)/(n1**2-n2**2)**1.5## critical radius of curvature for single mode fiber\n",
    "Rcs1=(3*n1**2*y)/((4*pi)*(n1**2-n2**2)**1.5)## critical radius of curvature for multimode fiber\n",
    "print \"The critical radius of curvature for single mode fiber =%0.2f um\"%( Rcs*10**6)#\n",
    "print \"\\n The answer is wrong in the textbook\"#\n",
    "print \"\\n The critical radius of curvature for multimode fiber =%0.2f um\"%( Rcs1*10**6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:4.15 Pg: 144"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Loss =12.04 dB/km\n"
     ]
    }
   ],
   "source": [
    "from math import log,pi\n",
    "from __future__ import division\n",
    "L=500/1000## distance in km\n",
    "Pio=(1/(1-0.75))#\n",
    "Ls=10*log(Pio)/log(10)/L## Loss in dB/km\n",
    "print \"The Loss =%0.2f dB/km\"%( Ls)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:4.16 Pg: 144"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The power level =0.56 mW\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "L=5## length in km\n",
    "a=0.5## attenuaion loss in dB/km\n",
    "Po=10**-3*10**(-(a*L)/10)## power level in mW\n",
    "print \"The power level =%0.2f mW\"%( Po*10**3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:4.17 Pg: 144"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Loss =2.22 dB/km\n"
     ]
    }
   ],
   "source": [
    "from math import log,pi\n",
    "from __future__ import division\n",
    "L=1## distance in km\n",
    "Pio=(1/(1-0.40))#\n",
    "Ls=10*log(Pio)/log(10)/L## Loss in dB/km\n",
    "print \"The Loss =%0.2f dB/km\"%( Ls)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:4.18 Pg: 145"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The transmission length =2.50 km\n"
     ]
    }
   ],
   "source": [
    "from math import log,pi\n",
    "from __future__ import division\n",
    "Pi=1*10**-3## input power in watt\n",
    "Po=0.75*10**-3## output power in watt\n",
    "a=0.5## in dB/km\n",
    "L=(10*log(Pi/Po)/log(10))/a## transmission length in km\n",
    "print \"The transmission length =%0.2f km\"%( L)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:4.19 Pg: 145"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mode field diameter =11.63 um\n",
      "\n",
      " The macrobend loss =127.25 dB\n",
      "\n",
      " The answer is wrong in the textbook\n"
     ]
    }
   ],
   "source": [
    "from math import pi\n",
    "from sympy import log,N\n",
    "from __future__ import division\n",
    "y=1300*10**-9## wavelemgth in m\n",
    "yc=1200*10**-9## cut off wavelength in m\n",
    "rc=5*10**-6## core diameter in m\n",
    "n=1.5## refractive index\n",
    "R=1.2/100## curve of radius in m\n",
    "dmf=2*rc*((0.65)+0.434*(y/yc)**1.5+0.0149*(y/yc)**6)## mode field diameter\n",
    "K=(2*pi)/y#\n",
    "Lm=-10*log(1-(K**4)*(n**4)*((3.95*10**-6)/(8*R**2))**6)/log(10)## macrobend loss\n",
    "print \"The mode field diameter =%0.2f um\"%( dmf*10**6)#\n",
    "print \"\\n The macrobend loss =%0.2f dB\"%abs(N(Lm,4))\n",
    "print \"\\n The answer is wrong in the textbook\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:4.20 Pg: 146"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The transmission length =-6.46 km\n"
     ]
    }
   ],
   "source": [
    "from math import log,pi\n",
    "from __future__ import division\n",
    "Pi=10*10**-3## input power in watt\n",
    "Po=8*10**-3## output power in watt\n",
    "L=0.150## length in km\n",
    "Ls=(10*log(Po/Pi)/log(10))/L#\n",
    "print \"The transmission length =%0.2f km\"%( Ls)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}