pywafo/wafo/doc/tutorial_scripts/WAFO Chapter 2.ipynb

{
 "metadata": {
  "name": "WAFO Chapter 2"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "CHAPTER2 Modelling random loads and stochastic waves\n",
      "====================================================\n",
      "\n",
      "Chapter2 contains the commands used in Chapter 2 of the tutorial and present some tools for analysis of random functions with respect to their correlation, spectral and distributional properties. The presentation is divided into three examples: \n",
      "\n",
      "Example1 is devoted to estimation of different parameters in the model.\n",
      "Example2 deals with spectral densities and\n",
      "Example3 presents the use of WAFO to simulate samples of a Gaussian process.\n",
      "\n",
      "Some of the commands are edited for fast computation. \n",
      "\n",
      "Section 2.1 Introduction and preliminary analysis\n",
      "=================================================\n",
      "\n",
      "Example 1: Sea data\n",
      "-------------------\n",
      "Observed crossings compared to the expected for Gaussian signals\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import wafo\n",
      "import wafo.objects as wo\n",
      "xx = wafo.data.sea()\n",
      "me = xx[:, 1].mean()\n",
      "sa = xx[:, 1].std()\n",
      "xx[:, 1] -= me\n",
      "ts = wo.mat2timeseries(xx)\n",
      "tp = ts.turning_points()\n",
      "\n",
      "cc = tp.cycle_pairs()\n",
      "lc = cc.level_crossings()\n",
      "lc.plot()\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYoAAAEVCAYAAAD+TqKGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEYiOjjZBZEREtiU6OhoRERFF
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Average number of upcrossings per time unit\n",
      "----------------------------------------------\n",
      "Next we compute the mean frequency as the average number of upcrossings per time unit of the mean level (= 0); this may require interpolation in the crossing intensity curve, as follows.  \n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "T = xx[:, 0].max() - xx[:, 0].min()\n",
      "f0 = np.interp(0, lc.args, lc.data, 0) / T  #! zero up-crossing frequency \n",
      "print('f0 = %g' % f0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "f0 = 0.224071\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Turningpoints and irregularity factor\n",
      "----------------------------------------"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fm = len(tp.data) / (2 * T)   # frequency of maxima\n",
      "alfa = f0 / fm                # approx Tm24/Tm02\n",
      "\n",
      "print('fm = %g, alpha = %g, ' % (fm, alfa))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "fm = 0.456159, alpha = 0.491212, \n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Visually examine data\n",
      "------------------------\n",
      "We finish this section with some remarks about the quality of the measured data. Especially sea surface measurements can be of poor quality. We shall now check the  quality of the dataset {\\tt xx}. It is always good practice to visually examine the data before the analysis to get an impression of the quality, \n",
      "non-linearities and narrow-bandedness of the data.First we shall plot the data and zoom in on a specific region. A part of sea data is visualized with the following commands"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "clf()\n",
      "ts.plot_wave('k-', tp, '*', nfig=1, nsub=1)\n",
      "\n",
      "axis([0, 2, -2, 2])\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEXCAYAAACqIS9uAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nvqKiwuY79qJlli5divT0dOTl
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finding possible spurious points\n",
      "------------------------------------\n",
      "However, if the amount of data is too large for visual examinations one could use the following criteria to find possible spurious points. One must be careful using the criteria for extremevalue analysis, because\n",
      "it might remove extreme waves that are OK and not spurious."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import wafo.misc as wm\n",
      "dt = ts.sampling_period()\n",
      "# dt = np.diff(xx[:2,0])\n",
      "dcrit = 5 * dt\n",
      "ddcrit = 9.81 / 2 * dt * dt\n",
      "zcrit = 0\n",
      "inds, indg = wm.findoutliers(ts.data, zcrit, dcrit, ddcrit, verbose=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Found 0 spurious positive jumps of Dx\n",
        "Found 0 spurious negative jumps of Dx\n",
        "Found 37 spurious positive jumps of D^2x\n",
        "Found 200 spurious negative jumps of D^2x\n",
        "Found 244 consecutive equal values\n",
        "Found the total of 1152 spurious points\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Section 2.2 Frequency Modeling of Load Histories\n",
      "---------------------------------------------------\n",
      "Periodogram: Raw spectrum"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "clf()\n",
      "Lmax = 9500\n",
      "S = ts.tospecdata(L=Lmax)\n",
      "S.plot()\n",
      "axis([0, 5, 0, 0.7])\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEXCAYAAAC3c9OwAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n9rha4zpBEK4BCYQDcTdH6272
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Calculate moments  \n",
      "-------------------"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mom, text = S.moment(nr=4)\n",
      "print('sigma = %g, m0 = %g' % (sa, sqrt(mom[0])))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "sigma = 0.472955, m0 = 0.472955\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Section 2.2.1 Random functions in Spectral Domain - Gaussian processes\n",
      "--------------------------------------------------------------------------\n",
      "Smoothing of spectral estimate \n",
      "----------------------------------\n",
      "By decreasing Lmax the spectrum estimate becomes smoother."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "clf()\n",
      "Lmax0 = 200; Lmax1 = 50\n",
      "S1 = ts.tospecdata(L=Lmax0)\n",
      "S2 = ts.tospecdata(L=Lmax1)\n",
      "S1.plot('-.')\n",
      "S2.plot()\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAZEAAAEXCAYAAABsyHmSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n88cjhBCWQBrWr3n0UdPO69u3
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      " Estimated autocovariance\n",
      "----------------------------\n",
      "Obviously knowing the spectrum one can compute the covariance\n",
      "function. The following code will compute the covariance for the \n",
      "unimodal spectral density S1 and compare it with estimated \n",
      "covariance of the signal xx."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "clf()\n",
      "Lmax = 85\n",
      "R1 = S1.tocovdata(nr=1)   \n",
      "Rest = ts.tocovdata(lag=Lmax)\n",
      "R1.plot('.')\n",
      "Rest.plot()\n",
      "axis([0, 25, -0.1, 0.25])\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAZAAAAEXCAYAAACDChKsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCwtkZWXB29sbjo6OonmVZNkH
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see in Figure below that the covariance function corresponding to the spectral density S2 significantly differs from the one estimated directly from data. It can be seen in Figure above that the covariance corresponding to S1 agrees much better with the estimated covariance function."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "clf()\n",
      "R2 = S2.tocovdata(nr=1)\n",
      "R2.plot('.')\n",
      "Rest.plot()\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAZAAAAEXCAYAAACDChKsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n4cOHsWnTJhw7dky+7dixY7C1
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Section 2.2.2 Transformed Gaussian models\n",
      "-------------------------------------------\n",
      "We begin with computing skewness and kurtosis for the data set xx and compare it with the second order wave approximation proposed by Winterstein:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import wafo.stats as ws\n",
      "rho3 = ws.skew(xx[:, 1])\n",
      "rho4 = ws.kurtosis(xx[:, 1])\n",
      "\n",
      "sk, ku = S1.stats_nl(moments='sk')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "Comparisons of 3 transformations"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "clf()\n",
      "import wafo.transform.models as wtm\n",
      "gh = wtm.TrHermite(mean=me, sigma=sa, skew=sk, kurt=ku).trdata()\n",
      "g = wtm.TrLinear(mean=me, sigma=sa).trdata() # Linear transformation \n",
      "glc, gemp = lc.trdata(mean=me, sigma=sa)\n",
      "\n",
      "glc.plot('b-') #! Transf. estimated from level-crossings\n",
      "gh.plot('b-.') #! Hermite Transf. estimated from moments\n",
      "g.plot('r')\n",
      "grid('on')\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAETCAYAAADecgZGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ne+2fER0NkybB/PnqLo1ffQWO
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Test Gaussianity of a stochastic process\n",
      "------------------------------------------\n",
      "TESTGAUSSIAN simulates  e(g(u)-u) = int (g(u)-u)^2 du  for Gaussian processes given the spectral density, S. The result is plotted if test0 is given. This is useful for testing if the process X(t) is Gaussian.\n",
      "If 95% of TEST1 is less than TEST0 then X(t) is not Gaussian at a 5% level.\n",
      "\n",
      "As we see from the figure below: none of the simulated values of test1 is above 1.00. Thus the data significantly departs from a Gaussian distribution. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "clf()\n",
      "test0 = glc.dist2gauss()\n",
      "# the following test takes time\n",
      "N = len(xx)\n",
      "test1 = S1.testgaussian(ns=N, cases=50, test0=test0)\n",
      "is_gaussian = sum(test1 > test0) > 5 \n",
      "print(is_gaussian)\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "False\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEKCAYAAAASByJ7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkOCPOhKRSvHyLurSqVlGVVVV
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Normalplot of data xx\n",
      "------------------------\n",
      "indicates that the underlying distribution has a \"heavy\" upper tail and a \"light\" lower tail."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "clf()\n",
      "import pylab\n",
      "ws.probplot(ts.data.ravel(), dist='norm', plot=pylab)\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYcAAAEWCAYAAACNJFuYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\no6wZvYYB7QbUXOF3SQakhRCi
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Section 2.2.3 Spectral densities of sea data\n",
      "-----------------------------------------------\n",
      "Example 2: Different forms of spectra"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import wafo.spectrum.models as wsm\n",
      "clf()\n",
      "Hm0 = 7; Tp = 11;\n",
      "spec = wsm.Jonswap(Hm0=Hm0, Tp=Tp).tospecdata()\n",
      "spec.plot()\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYkAAAEXCAYAAABYsbiOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQPzxxx+V7l86Lrsh/ixatEjx
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Directional spectrum and Encountered directional spectrum\n",
      "=========================================================\n",
      "Directional spectrum\n",
      "---------------------"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "clf()\n",
      "D = wsm.Spreading('cos2s')\n",
      "Sd = D.tospecdata2d(spec)\n",
      "Sd.plot()\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEXCAYAAACtTzM+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nLKKjo5k8eTJ33XVXsc80ZCQi
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Encountered directional spectrum\n",
      "--------------------------------- "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#clf()\n",
      "#Se = spec2spec(Sd,'encdir',0,10);\n",
      "#plotspec(Se), hold on\n",
      "#plotspec(Sd,1,'--'), hold off\n",
      "##!wafostamp('','(ER)')\n",
      "#disp('Block = 17'),pause(pstate)\n",
      "#\n",
      "##!#! Frequency spectra\n",
      "#clf\n",
      "#Sd1 =spec2spec(Sd,'freq');\n",
      "#Sd2 = spec2spec(Se,'enc');\n",
      "#plotspec(spec), hold on\n",
      "#plotspec(Sd1,1,'.'),\n",
      "#plotspec(Sd2),\n",
      "##!wafostamp('','(ER)')\n",
      "#hold off\n",
      "#disp('Block = 18'),pause(pstate)\n",
      "#\n",
      "##!#! Wave number spectrum\n",
      "#clf\n",
      "#Sk = spec2spec(spec,'k1d')\n",
      "#Skd = spec2spec(Sd,'k1d')\n",
      "#plotspec(Sk), hold on\n",
      "#plotspec(Skd,1,'--'), hold off\n",
      "##!wafostamp('','(ER)')\n",
      "#disp('Block = 19'),pause(pstate)\n",
      "#\n",
      "##!#! Effect of waterdepth on spectrum\n",
      "#clf\n",
      "#plotspec(spec,1,'--'), hold on\n",
      "#S20 = spec;\n",
      "#S20.S = S20.S.*phi1(S20.w,20);\n",
      "#S20.h = 20;\n",
      "#plotspec(S20),  hold off\n",
      "##!wafostamp('','(ER)')\n",
      "#disp('Block = 20'),pause(pstate)\n",
      "#\n",
      "##!#! Section 2.3 Simulation of transformed Gaussian process\n",
      "##!#! Example 3: Simulation of random sea    \n",
      "##! The reconstruct function replaces the spurious points of seasurface by\n",
      "##! simulated data on the basis of the remaining data and a transformed Gaussian\n",
      "##! process. As noted previously one must be careful using the criteria \n",
      "##! for finding spurious points when reconstructing a dataset, because\n",
      "##! these criteria might remove the highest and steepest waves as we can see\n",
      "##! in this plot where the spurious points is indicated with a '+' sign:\n",
      "##!\n",
      "#clf\n",
      "#[y, grec] = reconstruct(xx,inds);\n",
      "#waveplot(y,'-',xx(inds,:),'+',1,1)\n",
      "#axis([0 inf -inf inf])\n",
      "##!wafostamp('','(ER)')\n",
      "#disp('Block = 21'),pause(pstate)\n",
      "#\n",
      "##! Compare transformation (grec) from reconstructed (y) \n",
      "##! with original (glc) from (xx)\n",
      "#clf\n",
      "#trplot(g), hold on\n",
      "#plot(gemp(:,1),gemp(:,2))\n",
      "#plot(glc(:,1),glc(:,2),'-.')\n",
      "#plot(grec(:,1),grec(:,2)), hold off \n",
      "#disp('Block = 22'),pause(pstate)\n",
      "#\n",
      "##!#!\n",
      "#clf\n",
      "#L = 200;\n",
      "#x = dat2gaus(y,grec);\n",
      "#Sx = dat2spec(x,L);\n",
      "#disp('Block = 23'),pause(pstate)\n",
      "#      \n",
      "##!#!\n",
      "#clf\n",
      "#dt = spec2dt(Sx)\n",
      "#Ny = fix(2*60/dt) #! = 2 minutes\n",
      "#Sx.tr = grec;\n",
      "#ysim = spec2sdat(Sx,Ny);\n",
      "#waveplot(ysim,'-')\n",
      "##!wafostamp('','(CR)')\n",
      "#disp('Block = 24'),pause(pstate)\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Estimated spectrum compared to Torsethaugen spectrum\n",
      "-------------------------------------------------------"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "clf()\n",
      "fp = 1.1;dw = 0.01\n",
      "H0 = S1.characteristic('Hm0')[0]\n",
      "St = wsm.Torsethaugen(Hm0=H0,Tp=2*pi/fp).tospecdata(np.arange(0,5+dw/2,dw))  \n",
      "S1.plot()\n",
      "St.plot('-.')\n",
      "axis([0, 6, 0, 0.4])\n",
      "show()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEXCAYAAAC6baP3AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nNRqNTJ8+nQ0bNuDn50ePHj2I
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Transformed Gaussian model compared to Gaussian model\n",
      "-------------------------------------------------------\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dt = St.sampling_period()\n",
      "va, sk, ku = St.stats_nl(moments='vsk' )\n",
      "#sa = sqrt(va)\n",
      "gh = wtm.TrHermite(mean=me, sigma=sa, skew=sk, kurt=ku, ysigma=sa)\n",
      " \n",
      "ysim_t = St.sim(ns=240, dt=0.5)\n",
      "xsim_t = ysim_t.copy()\n",
      "xsim_t[:,1] = gh.gauss2dat(ysim_t[:,1])\n",
      "\n",
      "ts_y = wo.mat2timeseries(ysim_t)\n",
      "ts_x = wo.mat2timeseries(xsim_t)\n",
      "ts_y.plot_wave(sym1='r.', ts=ts_x, sym2='b', sigma=sa, nsub=5, nfig=1)\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
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      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}