PySAL-R benchmarking

.gitignore

.ipynb_checkpoints
*.pyc
*.swp

pysal_r_bench.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "PySAL/R Comparison"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**NOTE**: work in progress\n",
      "\n",
      "* The [PySAL](http://pysal.org) team\n",
      "\n",
      "This document presents a comparison between the Python library `PySAL` and different packages of the `R` statistical environment relating to spatial econometric functionality.\n",
      "\n",
      "The following functionality is tested:\n",
      "\n",
      "* Weights creation\n",
      "* OLS\n",
      "* K&P Heteroskedasticity consistent spatial error model\n",
      "* K&P spatial lag model"
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Distribution"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is an IPython notebook hosted on github as a gist. You can see an online rendered version on this link or downloaded on this link. Feel free to fork it and have a go at playing with it. Any change proposal can be issued through a PR following standard [Github procedures](https://help.github.com/articles/using-pull-requests/)."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Dependencies"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import time, seaborn\n",
      "import pandas as pd\n",
      "import numpy as np\n",
      "import pysal as ps\n",
      "import matplotlib.pyplot as plt\n",
      "from scipy.sparse import eye\n",
      "from scipy.sparse.linalg import inv as spinv\n",
      "from scipy.linalg import inv\n",
      "from pysal.spreg.utils import spdot"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%load_ext rpy2.ipython"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "%%R\n",
      "library(spdep)\n",
      "library(sphet)\n",
      "print(sessionInfo())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "Loading required package: sp\n",
        "Loading required package: Matrix\n",
        "R version 3.0.2 (2013-09-25)\n",
        "Platform: x86_64-pc-linux-gnu (64-bit)\n",
        "\n",
        "locale:\n",
        " [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              \n",
        " [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    \n",
        " [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   \n",
        " [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 \n",
        " [9] LC_ADDRESS=C               LC_TELEPHONE=C            \n",
        "[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       \n",
        "\n",
        "attached base packages:\n",
        "[1] tools     stats     graphics  grDevices utils     datasets  methods  \n",
        "[8] base     \n",
        "\n",
        "other attached packages:\n",
        "[1] sphet_1.5    spdep_0.5-77 Matrix_1.1-2 sp_1.0-13   \n",
        "\n",
        "loaded via a namespace (and not attached):\n",
        " [1] boot_1.3-9      coda_0.16-1     deldir_0.0-22   grid_3.0.2     \n",
        " [5] lattice_0.20-24 LearnBayes_2.12 MASS_7.3-29     nlme_3.1-113   \n",
        " [9] parallel_3.0.2  splines_3.0.2  \n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "# Utilities to run tests on the R sides\n",
      "buildW <- function(n){\n",
      "    t0 = Sys.time()\n",
      "    w = cell2nb(sqrt(n), sqrt(n))\n",
      "    we = nb2listw(w)\n",
      "    t1 = Sys.time()\n",
      "    out = list('we'=we, 'tim'=t1-t0)\n",
      "    return(out)\n",
      "}\n",
      "\n",
      "runOLS <- function(y, x){\n",
      "    db <- cbind(data.frame(y=y), data.frame(x))\n",
      "    t0 = Sys.time()\n",
      "    m <- lm('y ~ V1 + V2 + V3', db)\n",
      "    t1 = Sys.time()\n",
      "    return(t1-t0)\n",
      "}\n",
      "\n",
      "runGMERR <- function(y, x, w){\n",
      "    db <- cbind(data.frame(y=y), data.frame(x))\n",
      "    t0 = Sys.time()\n",
      "    m <- spreg(y ~ V1 + V2 + V3, db, listw=w)\n",
      "    t1 = Sys.time()\n",
      "    return(t1-t0)\n",
      "}\n",
      "\n",
      "runMLERR <- function(y, x, w){\n",
      "    db <- cbind(data.frame(y=y), data.frame(x))\n",
      "    t0 = Sys.time()\n",
      "    m <- errorsarlm(y ~ V1 + V2 + V3, db, listw=w)\n",
      "    t1 = Sys.time()\n",
      "    return(t1-t0)\n",
      "}\n",
      "\n",
      "runGMLAG <- function(y, x, w){\n",
      "    db <- cbind(data.frame(y=y), data.frame(x))\n",
      "    t0 = Sys.time()\n",
      "    m <- spreg(y ~ V1 + V2 + V3, db, listw=w, model = \"lag\")\n",
      "    t1 = Sys.time()\n",
      "    return(t1-t0)\n",
      "}\n",
      "\n",
      "runMLLAG <- function(y, x, w){\n",
      "    db <- cbind(data.frame(y=y), data.frame(x))\n",
      "    t0 = Sys.time()\n",
      "    m <- lagsarlm(y ~ V1 + V2 + V3, db, listw=w)\n",
      "    t1 = Sys.time()\n",
      "    return(t1-t0)\n",
      "}"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.random.seed(1234)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def sim(sizes, rho, lamb, ml=False):\n",
      "    timings = pd.DataFrame()\n",
      "    %R timingsR = data.frame()\n",
      "    for n in sizes:\n",
      "            ### Data\n",
      "        print \"Working on Size %i\"%n\n",
      "        timing = {}\n",
      "        # Python\n",
      "        t0 = time.time()\n",
      "        w = ps.lat2W(int(np.sqrt(n)), int(np.sqrt(n)))\n",
      "        t1 = time.time()\n",
      "        w.transform = 'R'\n",
      "        timing['W'] = t1 - t0\n",
      "        x = np.random.random((n, 3))\n",
      "        X = np.hstack((np.ones((n, 1)), x))\n",
      "        eps = np.random.normal(size=(n, 1))\n",
      "        xb =np.dot(X, betas) \n",
      "        spxb_r = ps.spreg.utils.power_expansion(w, xb, rho)\n",
      "        speps_r = ps.spreg.utils.power_expansion(w, eps, rho)\n",
      "        speps_l = ps.spreg.utils.power_expansion(w, eps, lamb)\n",
      "        y = xb + eps\n",
      "        y_lag = spxb_r + speps_r\n",
      "        y_err = xb + speps_l\n",
      "        # R\n",
      "        %Rpush n x y y_lag y_err\n",
      "        %R x = as.data.frame(x)\n",
      "        %R wtw = buildW(n)\n",
      "        %R res = data.frame(W=wtw$tim)\n",
      "        %R w = wtw$we\n",
      "            ### OLS\n",
      "        t0 = time.time()\n",
      "        m = ps.spreg.OLS(y, x)\n",
      "        t1 = time.time()\n",
      "        timing['OLS'] = t1 - t0\n",
      "        %R t = runOLS(y, x)\n",
      "        %R res = cbind(res, data.frame(OLS=t))\n",
      "            ### Spatial Error\n",
      "        t0 = time.time()\n",
      "        m = ps.spreg.GM_Error_Het(y_err, x, w=w)\n",
      "        t1 = time.time()\n",
      "        timing['Err_gm'] = t1 - t0\n",
      "        %R t = runGMERR(y_err, x, w)\n",
      "        %R res = cbind(res, data.frame(Err_gm=t))\n",
      "        if ml:\n",
      "            t0 = time.time()    \n",
      "            m = ps.spreg.ML_Error(y, x, w=w)\n",
      "            t1 = time.time()\n",
      "            timing['Err_ml'] = t1 - t0\n",
      "            %R t = runMLERR(y_err, x, w)\n",
      "            %R res = cbind(res, data.frame(Err_ml=t))\n",
      "        # Spatial lag\n",
      "        t0 = time.time()\n",
      "        m = ps.spreg.GM_Lag(y_lag, x, w=w)\n",
      "        t1 = time.time()\n",
      "        timing['Lag_gm'] = t1 - t0\n",
      "        %R t = runGMLAG(y_lag, x, w)\n",
      "        %R res = cbind(res, data.frame(Lag_gm=t))\n",
      "        if ml:\n",
      "            t0 = time.time()\n",
      "            m = ps.spreg.ML_Lag(y_lag, x, w=w)\n",
      "            t1 = time.time()\n",
      "            timing['Lag_ml'] = t1 - t0\n",
      "            %R t = runMLLAG(y_lag, x, w)\n",
      "            %R res = cbind(res, data.frame(Lag_ml=t))\n",
      "        timings['n%i'%n] = pd.Series(timing)\n",
      "        %R row.names(res) = paste('n', n, sep='')\n",
      "        %R timingsR = rbind(timingsR, res)\n",
      "    timingsPY = timings.T\n",
      "    timingsPY.index = pd.MultiIndex.from_arrays([['Py']*timingsPY.shape[0], \\\n",
      "                                               timingsPY.index])\n",
      "    %Rpull timingsR\n",
      "    ri = %R rownames(timingsR)\n",
      "    timingsR.index = pd.MultiIndex.from_arrays([['R']*ri.shape[0], ri])\n",
      "    timings = timingsPY.T.join(timingsR.T).T\n",
      "    return timings"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Data"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The basic model we are going to test against is a linear regression with four explanatory variables to which, depending on the model, we will be appending terms:\n",
      "\n",
      "$$\n",
      "y = (\\rho W y) + \\alpha + \\beta_1 X_1 + \\beta_2 X_2 + \\beta_3 X_3 + \\beta_4 X_4 + (\\lambda W u) + \\epsilon\n",
      "$$\n",
      "\n",
      "We will record the running time of these models for the following number of observations:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sizes = [100, 625, 900, 3025, 4900, 10000, 25600, 50625, 99225]\n",
      "betas = np.array([[1, 1, 1, 1]]).T\n",
      "rho = 0.5\n",
      "lamb = 0.5"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Running *with* maximum likelihood included"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%time\n",
      "ssizes = sizes[:5]\n",
      "stimings = sim(ssizes, rho, lamb, ml=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/home/dani/code/pysal_darribas/pysal/spreg/user_output.py:349: FutureWarning: comparison to `None` will result in an elementwise object comparison in the future.\n",
        "  if i == None:\n",
        "/home/dani/anaconda/envs/pydata/lib/python2.7/site-packages/scipy/optimize/_minimize.py:570: RuntimeWarning: Method 'bounded' does not support relative tolerance in x; defaulting to absolute tolerance.\n",
        "  \"defaulting to absolute tolerance.\", RuntimeWarning)\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "need more than 0 values to unpack\n",
        "Working on Size 100\n",
        "Working on Size 625"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Working on Size 900"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Working on Size 3025"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Working on Size 4900"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "CPU times: user 45min 17s, sys: 1min 46s, total: 47min 3s"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Wall time: 32min 38s\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/home/dani/code/pysal_darribas/pysal/spreg/twosls.py:139: FutureWarning: comparison to `None` will result in an elementwise object comparison in the future.\n",
        "  if q == None and h == None:\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "stimings"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "      <th>Err_gm</th>\n",
        "      <th>Err_ml</th>\n",
        "      <th>Lag_gm</th>\n",
        "      <th>Lag_ml</th>\n",
        "      <th>OLS</th>\n",
        "      <th>W</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th rowspan=\"5\" valign=\"top\">Py</th>\n",
        "      <th>n100</th>\n",
        "      <td> 0.022200</td>\n",
        "      <td>    0.015826</td>\n",
        "      <td> 0.003856</td>\n",
        "      <td>   0.018613</td>\n",
        "      <td> 0.002736</td>\n",
        "      <td> 0.000991</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n625</th>\n",
        "      <td> 0.025810</td>\n",
        "      <td>    0.594324</td>\n",
        "      <td> 0.003643</td>\n",
        "      <td>   0.635988</td>\n",
        "      <td> 0.002734</td>\n",
        "      <td> 0.063488</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n900</th>\n",
        "      <td> 0.027929</td>\n",
        "      <td>    1.651768</td>\n",
        "      <td> 0.003526</td>\n",
        "      <td>   1.440586</td>\n",
        "      <td> 0.002547</td>\n",
        "      <td> 0.003898</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n3025</th>\n",
        "      <td> 0.040959</td>\n",
        "      <td>   54.081272</td>\n",
        "      <td> 0.004570</td>\n",
        "      <td>  43.543330</td>\n",
        "      <td> 0.003509</td>\n",
        "      <td> 0.014238</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n4900</th>\n",
        "      <td> 0.054737</td>\n",
        "      <td> 1309.297623</td>\n",
        "      <td> 0.007065</td>\n",
        "      <td> 198.539012</td>\n",
        "      <td> 0.004447</td>\n",
        "      <td> 0.026224</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th rowspan=\"5\" valign=\"top\">R</th>\n",
        "      <th>n100</th>\n",
        "      <td> 0.516554</td>\n",
        "      <td>    0.312385</td>\n",
        "      <td> 0.006613</td>\n",
        "      <td>   0.228411</td>\n",
        "      <td> 0.008700</td>\n",
        "      <td> 0.099601</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n625</th>\n",
        "      <td> 1.223979</td>\n",
        "      <td>    1.473421</td>\n",
        "      <td> 0.008109</td>\n",
        "      <td>   0.891190</td>\n",
        "      <td> 0.003769</td>\n",
        "      <td> 0.755120</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n900</th>\n",
        "      <td> 1.265054</td>\n",
        "      <td>    1.841072</td>\n",
        "      <td> 0.008744</td>\n",
        "      <td>   1.767377</td>\n",
        "      <td> 0.003879</td>\n",
        "      <td> 0.812916</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n3025</th>\n",
        "      <td> 3.664639</td>\n",
        "      <td>   32.921955</td>\n",
        "      <td> 0.014100</td>\n",
        "      <td>  32.429866</td>\n",
        "      <td> 0.006280</td>\n",
        "      <td> 2.649967</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n4900</th>\n",
        "      <td> 5.406586</td>\n",
        "      <td>    2.101724</td>\n",
        "      <td> 0.020745</td>\n",
        "      <td>   2.145562</td>\n",
        "      <td> 0.008604</td>\n",
        "      <td> 4.350219</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "            Err_gm       Err_ml    Lag_gm      Lag_ml       OLS         W\n",
        "Py n100   0.022200     0.015826  0.003856    0.018613  0.002736  0.000991\n",
        "   n625   0.025810     0.594324  0.003643    0.635988  0.002734  0.063488\n",
        "   n900   0.027929     1.651768  0.003526    1.440586  0.002547  0.003898\n",
        "   n3025  0.040959    54.081272  0.004570   43.543330  0.003509  0.014238\n",
        "   n4900  0.054737  1309.297623  0.007065  198.539012  0.004447  0.026224\n",
        "R  n100   0.516554     0.312385  0.006613    0.228411  0.008700  0.099601\n",
        "   n625   1.223979     1.473421  0.008109    0.891190  0.003769  0.755120\n",
        "   n900   1.265054     1.841072  0.008744    1.767377  0.003879  0.812916\n",
        "   n3025  3.664639    32.921955  0.014100   32.429866  0.006280  2.649967\n",
        "   n4900  5.406586     2.101724  0.020745    2.145562  0.008604  4.350219"
       ]
      }
     ],
     "prompt_number": 10
    },
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     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for col in stimings:\n",
      "    f, ax = plt.subplots(1)\n",
      "    stimings[col].groupby(level=0).plot(ax=ax)\n",
      "    plt.xlabel('N. Observations')\n",
      "    plt.ylabel('Seconds')\n",
      "    plt.legend()\n",
      "    plt.title(col)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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P8yKiItITCn8R6XMvr3+V5979EyWDx3D7nBsZNED9+kUyicJfRPpUx7a9N6tt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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe04c9be390>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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YJ68oqYGShUzhQURECkJrey/bnz3MmQtqOW9JfdzlyCgUHkREpCA8tLOZdBCw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\nKDyIiIjIhCg8iIiIyIT8/y/gMcfkLaZPAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe04401dcd0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ebYwJAB8MTXkiIonVGenkme0vserD5+iMdjKp6CiumraUiUUT/C5NJCX0FySi\n1tpm7/FZwM8ArLWOMcZJeGUiIgnkOA7v71/HHzauoLqthsLMAq42lzJ/9FyCgaDf5YmkjP6CRNgY\nUwrkA3OAVQDGmKOAziGoTUQkIaqa97Js4+N8ULOBYCDI2RNO48LJ55Cbket3aSIpp78g8X3gHSAT\nuNtau9sYcyXwb8C3h6I4EZHB1BZu4+ltz/L8Ry8TcSJML53KldMuZnT+KL9LE0lZfQYJa+1yY8yr\nuANSvee93ALcaq19YSiKExEZDI7j8EbVOzy66UnqOxopyynl8srFHFc+W6NSinxM/d7+aa3dCeyM\nef5kwisSERlE2xt3sGzDY2yp/5DMYAYXTj6Xc486kyyNSikyKAYyIJWISMpp6mhmxZaVrN71Og4O\nx5fP5rLKxYzILfO7NJG0oiAhImklEo3w8q7XeGLLKlrCrYzOq+DKaUuZXjbV79JE0pKChIikjY21\nW1i28TF2Nu0mJ5TD5ZWLOWP8Qo1KKZJACQsSxpgg8FPgWKAd9yLNzTHLlwDfAMLAvdbau2OWzQe+\nb609y3teCfwKiAJrgM9ZazWWhYgAUNdezyObnuTNqncBWDB6HhcffQHF2YU+VyaS/hI56solQJa1\n9hTgK8APuxYYYzKBO4FzgTOATxtjKrxl/wTcBWTH7OtO4GvW2tOBALA0gXWLSIrojIb547bn+Ze/\n/IA3q95lYuEEvnTC/+NvZl6lECEyRBLZtbEQWAlgrX3NGDMvZtkMYJO1th7AGPMycDqwHNgEXAb8\nNmb9udbal7zHTwOLgEcTWLuIJLk1+z9g+cbH2ddaTUFmPldOvZgFY+ZpVEqRIZbIIFEENMQ8jxhj\ngtbaqLesPmZZI1AMYK192Bgz6aB9xd7o3dS1rogMP3tb9vOHjY+zpno9wUCQM8cv5KLJi8jL1KiU\nIn5IZJBoAGLbFrtCBLghInZZIVDbz76iMY8LgbqBFFBenr5Nm+l8bKDjS3WJOL62zjYe/mAlT9hn\nCUfDzKqYxs1zruKoknGD/l6Hk87nL52PDdL/+PyQyCCxGlgCLDPGLADej1m2HpjqzeXRjNut8YN+\n9vWOMeYMa+2LwAXAswMpYN++xrgKT3bl5YVpe2yg40t1g318juPwVtW7PLL5Kera6ynNLuGyqYuZ\nU34Mgc7AkP8u0/n8pfOxwfA4Pj8kMkg8ApxrjFntPb/ZGHMtUGCtvcsYczvuRGBB4B5r7e6Dto+9\nK+OLwF1D7c4+AAAfoElEQVTGmCxgHe61FCKS5nY07mLZxsfYVLeVjGAGF0z6BOdOPIvsUJbfpYmI\nJ+A4aXsXpZOuyXM4pGodX+oajONr7mzhiS2r+PPOv+DgcOzIWVw+dTEjc0cMUpXxS+fzl87HBsPi\n+HyZOEYDUolI0og6UVbvep0VW1bS3NlCRd5Irpi6lFkjjN+liUgfFCREJClsqd/GQxse46PGnWSH\nsri08iLOHL+QjKD+TIkkM31CRcRX9e0NPLLpKd6oehuAk0bP5ZKjL6Q4u8jnykRkIBQkRMQX4WiY\n5z96mae3PUN7pIMJBWO5ctolHF0yye/SROQIKEiIyJBbV21ZvvFxqlr2kZ+Zx6WVi1k49iSNSimS\nghQkRGTI7G+tZvnGFfx1/zoCBDh93CksnrKI/Mw8v0sTkTgpSIhIwnVEOlj14fM8s/1FwtEwlSWT\nuXLqUsYXjvW7NBH5mBQkRCRhHMfhnX1/5eGNT1DbXkdJdjGXVl7ECRXHEQj4csu7iAwyBQkRSYhd\nTXtYtuExNtRtJiMQYtHEszhv4tnkZGT7XZqIDCIFCREZVM0dLSzb8Bgv7XyVqBNl9ojpXD71Yiry\nRvpdmogkgIKEiBwxx3Foi7TT0tlCc7iFls5WmjtbqGmr5bkdL9HQ3kR57giumHoxs0fO8LtcEUkg\nBQmRYSwSjdAabqMl3EJzZ6v30wsG4RY3KHivx4aGlnArUSfa6z6zM7JZOuUCzjrqNDI1KqVI2tOn\nXCQNdEbD3pd+Cy3hVi8MuI/dANAas7wnHLSG2wb8HsFAkPzMPAoy86nIG0leRh75mXnkZeaSn5FH\nXmYe+Rm5LKg8jnCTxoMQGS4UJESShOM4tEc6er7ou1sADmwh6A4KMYGhI9o54PfJCmaSl5lHWU4p\neRm5bhjIiA0EuV4o8MJBZi55GXlkh7IGdKdFaW4h+5rSd4ZFETmQgoTIIIs6UdrCbQd1FfS0CkR3\nhKluqO9uHegJCa1EnMiA3yc3I4e8jDxG51fEtA64rQJ53uOeoNDzMzOUmcCjF5HhRkFCpA/haLin\na6D7OoFDrx04+JqC1nAbDs6A3iMYCJKXkUteZi4jc8q8L3+vFaC7VaCn1aCrdSA3I4dQMJTg34CI\nyOEpSEhacxyHzmjnIV0BsXca9HUdQXukY8DvkxHMID8jj5LsYsYWjD6oq6AnAORn5jGufCQdTQ55\nmXnkhLI1MJOIpDQFCUkJ7u2GbYdcO9B7q0DsXQathKPhAb9PTiibvMw8KnJHdncPdHcVdHUPxLzW\n1VKQdQTdBeVlheyL6BoCEUkPChLiu45IJ1Ut+9jTXMWe5iqaNjdR01TvBgIvNLSG2/q83fBgAQLd\n3QUlOSW9dA/EhoLcA15Td4GIyJFRkJAh0x7poKp5L7ubq9jT4v7c3VxFdWtNr9cUhAIh8jPzKMwq\nZFRexQHdA/1dR5CTka3pqEVEhoiChAy6tnCbFxT2sscLC3uaq6huqz1k3fzMPI4umcTo/FGMyRvF\n6PwKpo+fSHuje5uirh8QEUluChISt5bOVi8w7GFPV0tD815q2+sOWbcwq4BpJUczpmAUo/NGMSa/\ngtH5oyjMKjhk3fL8Qva16BoCEZFUoCAhh9XU2RwTFKq6H9d3NByybkl2MdNLpzIm321dGO39LMjM\n96FyERFJNAUJAdy7Ipo6m7vDQmy3RGNn0yHrl2aXMLPMMDq/wgsNoxidV0FeZq4P1YuIiF8UJIYZ\nx3Fo6Gjs7obY3bzHDQ0tVTR3thyy/oicMmYXTXevYfD+G5VXTk5Gjg/Vi4hIslGQSFOO41DXXn9g\nC0OL+7M13HrAugECjMwt4+jiyTEtDBWMyqsgO5Tl0xGIiEgqUJBIcVEnSm1b3QG3VO7xuiXaIu0H\nrBsMBCnPHYkpPdq7S8K9hqEir/yIBlQSERHpoiCRIqJOlOrWWva0VNGwv47Nez/qvlvi4JkfQ4EQ\nFXkjDwgLY/JHUZE3koygTrmIiAwefaskmUg0wv62mpguCbeFoaplL50HDfWcEQgxKr+C0XkVjMkf\n3X1LZXnuCI3QKCIiQ0JBwifhaJh9rdWH3FK5t2Uf4YOmks4MZnp3RbjjL5ixk8gLFzIip0yBQURE\nfKUgkWCd0TB7vXkkum+pbNnL3pZ9h8wdkRXKYlzB2AMueByTP4qynNIDhnwuLy9k3z4N2CQiIv5T\nkBgksRNPdXdLtFSxv7XmkMCQE8phYuH47sGaurolSrKLNUeEiIgMiOM47KlpYe3WGtZtq+Vf/36h\nL3UoSByh2Imn3Dsl3JaG3iaeysvIZVLRUd3jL3S1MBRnFWkOCREROWLNbZ18sK2WNVurWbu1huqG\n9sNvlGAKEn1oDbd130a5u6XnlsreJp4qyMynsmRyTwtDnjvSY1FWgQKDiIjELRyJsnV3A2u21LB2\nWw1bdzfgeP9mzc/JYN70CmZPLmPmpFLfahz2QcKdeKoqZqTHvieeKsoqZFpppXt3xGEmnhIREYnH\n3rpW1m6tYc2WatZvr6W13b0APxgIUDmumFmTy5g1uYzJo4sIBv3/x+qwCRKxE0/13ClRRX3HoRct\nlmQXM6Ns2gGtC6PzK8jPzPOhchERSWet7WHWf1jLmq01rN1aw966ntGHK0pyWTDTDQ7TjyolLyf5\nvraTr6JBsnLjC2yq2t7dwtDbxFNlOaXMHGG6w4LbwlBBboYmnhIRkcSIRh227Wnsvs5h884Gol5/\nRU5WiDlTRzLba3WoKE3+f8CmbZC49+3fA+48EiNySplYNOOACx5H5VWQk5Htc5UiIjIcVNe3sXZb\nDWu21vDBthqa29wBBgMBmDymiFmTypg9pYzJY4rICKXW3XtpGyT+3/ybKIgWMyqvnCxNPCUiIkOo\nvSPC+u21rN3qXiS5u7pnduWyomxOMOXMnjyC6RNLKchN7bmO0jZInD5pvgZtEhGRIRF1HD6qauru\nrti4o55I1O2uyMoMcuzRI5g1uYzZk8sYXZaXVnf0pW2QEBERSaTaxnbWbavpbnVobOmZQHHiqMLu\n4HD0uGIyM1Kru+JIKEiIiIgMQEdnhA076tzgsLWGHfuau5cVF2SxcPZoZk0pY+akMoryhk+XuoKE\niIhILxzHYee+Zve2zG01bPiojs6wO+VBZkawu8Vh1uQyxo3MT6vuiiOhICEiIuJpaO7o7q5Ys62G\n+qaO7mXjy/OZPdm91mHq+GKyMjX7MihIiIjIMNYZjrJpZ70bHLZWs72qZ8yhwrxMFswaxaxJbqtD\nSYGGDOiNgoSIiAwbXTNmdo0iuX57LR2dbndFRijAjIml7hDUk8qYMKqA4DDtrjgSChIiIpLWmlo7\n+eDDWjY/v5m3PthzwIyZY0bkdV/rYCaUkp2l7oojpSAhIiJpJRyJsmVXg9ddUcO23Q14E2aSn5PB\nidMrulsdRhTn+FprOlCQEBGRlLe3tqU7OHzwYS1tHe6MmaFggKnj3RkzT507geLsUFLMmJlOFCRE\nRCTltLSFWb+9a8bMavbVtXUvqyjN5eTZZcyeVMb0iaXkZrtfdeXlhRrxOAEUJEREJOlFow5b9zSw\ndot7W+aWmBkzc7NDzJ1W7nZXTC6jokQzOA8lBQkREUlK1fVt3XNXrNtWS0t7z4yZU8YUdQeHKWOL\nCAXTdwjqZKcgISIiSaGtI8z67T1DUO+p6Zkxc0RRNvOmVzB7chkzJpWSn5PaM2amk4QFCWNMEPgp\ncCzQDtxqrd0cs3wJ8A0gDNxrrb27r22MMXOAFcBGb/OfWWsfSlTtIiKSeFHHYXtVY3dwiJ0xMzsz\nxHFdM2ZOGcGo0txhOwR1sktki8QlQJa19hRjzHzgh95rGGMygTuBeUALsNoY8zhwKpDdyzYnAHda\na+9MYL0iIpJgtY3t3bNlrt1aQ1OrO2NmADhqdCGzY2bMzAipuyIVJDJILARWAlhrXzPGzItZNgPY\nZK2tBzDGvAycDpwMPN3LNicA04wxS3FbJW6z1jYhIiJJraMzwoaP6ronvtoZM2NmSUEWC48ZzezJ\nI5gxqXRYzZiZThIZJIqAhpjnEWNM0Fob9ZbVxyxrBIr72CYEvAb8n7X2HWPM14BvAv+YwNpFRCQO\njuOwY1+z111Rjf2onnCkZ8bM2TEzZo4dxjNmppNEBokGoDDmeVeIADdExC4rBOr62CZijHnUWlvn\nvfYo8KOBFFBeXnj4lVJUOh8b6PhSnY4vdcVzbHWN7by7YS/vbNjHO3YvtY09Q1BPGlPEXFPBHFPO\nzMkjfJ8xM53PnV8SGSRWA0uAZcaYBcD7McvWA1ONMaVAM263xg8Ap49tnjbGfN5a+wbwCeDNgRSQ\nrgOPpPugKjq+1KbjS10DPbbOcJRNO+pY413nEDtjZlFeJifPGsWsyWXMnHTgjJn1dS297W7IpPO5\nA/9CUiKDxCPAucaY1d7zm40x1wIF1tq7jDG3A6uAIHCPtXa3MeaQbbyfnwF+YozpBHYDn05g3SIi\nEsNxHHZXt3RfJNnbjJld3RXjKzRj5nATcBzn8GulJiddk+dwSNU6vtSl40tdscfW1NrJOq/FYe22\nGmoOmjFz9mT31kwzoSRlZsxM53MHUF5e6EuC04BUIiLDnOM4NLZ2UrV5P6vf3cnardVs2914wIyZ\nJ82oYNYkt9WhrEgzZkoPBQkRkTTX2h6mprGd2oY2qhvaqGlop6ahjZrGnp+d4Wj3+qFggKkTStzB\noCaXMXFUoWbMlD4pSIiIpLBwJEptVyBoaHeDQvdz97WuOSp6U5SXydiR+YwoymHC6CKOKs9j+lE9\nM2aKHI7+TxERSVJRx6GhuaOnBcELCd2tCo1tNDR10NeVbjlZIUYU5TBlXBFlhTmMKMqmrCjH+y+b\nssJsMjN6rm9I92sIJDEUJEREfOA4jtvl0EcrQnVDG7WN7d1zTxwsIxSgtDCbaRNKuoPBiO6A4IaF\nvBz9iZfE0/9lIiIJ0BmOdLckVHutB7HXJlQ3tNHeEel12wBQVJDFxNGFlBXGtCIUZjOi2P1ZmJ+l\n2ywlKShIiIgcoWjUoa6pPaYVoau7oafLobGls8/t83MyKC/OjelqyO4JCkU5lBRma8IqSRkKEiIi\nMRzHobktTHV9W6+tCPXNHVTXtRHtYwyezIwgZUU5jC8viOluiO1yyCYnS396JX3o/2YRGVbaOyLU\nNB50G6TXilDd4N4i2RFzK2SsYCBAWXEOU8YWdbcijPBaErrCQkFupiaikmElbYPEqr9so7Wlg1Ao\nQEYwSEYoSEYoQMj7mREKEgoGul/PCAV7lgWDhEIBQsGA/iCIpJBwJEpdY0+XQ/dFjPU9FzM2t/V9\nK2RBbiZjRuT3dDV4rQhdFzEWF2QxelSx7mwQiZG2QeJ/l703KPvpDh8xocMNHO5rBwST7tAS8zwU\n7A4mh4SZYG/hpufxwet27SOYlUFDS8cB76XBYiTdOY5DQ0vnIXc2xA60VN/PrZDZWSHKCrOZPKbo\ngDsburofSguzfZ+ZUiQVpW2QuP26udTWtRCJOIQjUcIRh0jU/RmORHtej3Y9j1kWjdmm6/Voz/OO\nzggtbeGe/YWjff7xGiqBAD3hI9h7K0t/LTKx4eiAEHTI/rpeP4IgFfNeoVBAV5pLr1rbwweMj1Bz\nSNdDO+FI710OoaB7K+TUCSU91yUUHjhmQl52hloYRRIgbYPEWSdMGNLmx2hM+AhHY4JKV2iJHhRM\nDgg3fYeWA4KPt25GRgbNLe29vJe3TUw4amsPdwemrv35LRQMHBA6Dm6RyckOEYk4hIIBggEIBgPu\nf4GDfx60rOv1rmUHPD9wm5D3WsB7veu9AsEAoYPfZwD767OGmP0FAu77ZOd10NLW2f082F0LaftF\n1xmOUtvY28iLPaGhtb33WyEBivOzmFBRENPVcGBIKNKtkCK+SdsgMdSCwQBZwRBZmYl/r48z+pzj\nOESiTi/h5jAtMpFov6Hl4CB0SAg6KMz0FqTaOzrd1xy3vq5ahxM3iNBvMIkNVF3X8QSD9DyPWdZb\nOArEBKfew1HP/noNVL2EOrcOdxsnWMX23fXUxoSGhuaOPo85Lzsj5s6Gnlsgy4qyKS3KobQgm8wM\n3QopkqwUJIaZQCDg/esfsknO/uCDg1LUcYhGvf8ch2g05rWDlzkQiTo43vOI99Pxtul53vM4Gu0J\nWL3t78Dnscu99/Je6/e9nJ5tMjNDtLZ29rq/A47JOej1mBo6O6PeMbrLIs6Bx9zHnYlDLiMUpKwo\nm3EjSw+4syE2NGhOB5HUpk+wJL1gIEAwFCBJc88RG4r5DBzHDROx4agnLPUfjnoNM13LuoJKL0Gt\n6/HYUUVkEKWsMIfCPN0KKZLuFCRE0lDAu+bCj7t5NPGTyPCijkcRERGJm4KEiIiIxE1BQkREROKm\nICEiIiJxU5AQERGRuClIiIiISNwUJERERCRuChIiIiISNwUJERERiZuChIiIiMRNQUJERETipiAh\nIiIicVOQEBERkbgpSIiIiEjcFCREREQkbgoSIiIiEjcFCREREYmbgoSIiIjETUFCRERE4qYgISIi\nInFTkBAREZG4KUiIiIhI3BQkREREJG4KEiIiIhI3BQkRERGJm4KEiIiIxE1BQkREROKmICEiIiJx\nU5AQERGRuClIiIiISNwUJERERCRuChIiIiISNwUJERERiZuChIiIiMRNQUJERETipiAhIiIicVOQ\nEBERkbhlJGrHxpgg8FPgWKAduNVauzlm+RLgG0AYuNdae3df2xhjKoFfAVFgDfA5a62TqNpFRERk\nYBLZInEJkGWtPQX4CvDDrgXGmEzgTuBc4Azg08aYCm+b7F62uRP4mrX2dCAALE1g3SIiIjJAiQwS\nC4GVANba14B5MctmAJustfXW2k7gZeB0b5une9lmrrX2Je/x08A5CaxbREREBiiRQaIIaIh5HvG6\nLrqW1ccsawSK+9gmhNsK0aXJW1dERER8lrBrJHADQWHM86C1Nuo9rj9oWSFQ18c2EWNMtJd1DydQ\nXl54+LVSVDofG+j4Up2OL3Wl87FB+h+fHxLZIrEauBDAGLMAeD9m2XpgqjGm1BiThdut8Uo/27xj\njDnDe3wB8BIiIiLiu4DjJObmB2NMgJ47MABuBk4ACqy1dxljFgN34IaZe6y1P+ttG2vtBmPMVOAu\nIAtYB/yt7toQERHxX8KChIiIiKQ/DUglIiIicVOQEBERkbgpSIiIiEjcEnn75xExxowAvmut/Ywx\nZhvwIe6Q2CGgAPcCy7fi3Pd/Aeuttb/wnv8t8Gnc4bm/Y6190hiTC/wOKMcd1+KT1tr9xphvAb+3\n1n7wcY4vnSXi3Hkjnd4FlOCOI3KjtXabMeYLwNXeak9Za7/tXaS7A9jgvf6Ktfafde4GJkHn7zjg\n57ifsY3AZ6y1HfrsDY4EnbOZwP95TzfiTlEQ6eOcFeOes0Lci+Bvt9b+xRhzKfAD4CNvP3cAbwA/\nt9beFO/xppMEf9ddB/w/b3RojDG3AzcAbcCPrbUP9PN5WwD8N+55/qP3tzUX+Nnhzl0ytUh8B/hf\n77EDnGutPcsbFvsrwLeOdIfGmHJjzNPAEm+fGGNGA/8AnAKcB/ybdwvq3wPvee/3G+Dr3m7+C/jP\neA9qmBj0cwf8B/Bba+0ZuH+MZhtjJgPXASdbaxcAi4wxxwBHA29573mWtfafvX3o3A1MIs7f3cAX\nrLWnATuBz+qzN6gScc6+C3zFWnuq93xJP+fsC8CfrLVnAjcBP/G2OQH4p5jP4p+ttW3AK8aYG+Oo\nKR0l4txhjJkD3BLzfDZwI7AAOAv4Z2PMKPr+vP0cuNY7//ONMcdba1sZwLlLihYJY0wRMM9auybm\n5djRLCcBNf1sfxPu+BO5uF8q/26t/TWQD3wTd+yJrv2dBKz2hubuNMZswr3ddCHw7946K3EnFMNa\nW2+MaTXGHGOt/evHOc50lMBzdwrwnjHmT8A24P8DOoDzYm79zQRacf94jTPGPOc9/4K1doPO3eEl\n8PyNt9b+xVvtFdx/0W5Gn72PLYHn7HJrbdQLCqNxB/7r6+/lf+FOrAg9n0NwP4vHG2NuA14Hvmyt\njQAP4Z7b38R73OkgUeeuq5UDuA23JRdgJvCCtbbD23YNbqg45PNmjCnEnRtrq/f6KtypKN5lAOcu\nWVokFgD2oNf+aIx5zRjzEXAi8KXD7KPIWrsEuBg31WGt3Watff2g9Qo5/PDcXa91eR84c2CHMuwk\n5NzhfaCstecC23H/IIWttTXGmIAx5j+Bt621m4BdwPestWcD38Nttuuic9e/RJ2/LcaY073HS3BD\n/UCGxtdn7/AS9fcyaow5ClgLjMD93ff699KbJ6nNa7H4LfDVrjpwm9ZPx22m/4y37zpgpPeFNZwN\n+rnzpp64B7gddwqJLu8DpxtjCrygcQo9n8ODP28HT0/R/TkcyLlLliAxAqg66LVzrbXzcVNQvrV2\nXz/bO7jJCdy+8px+1j14GO7ehuc+eBju3V6NcqhEnbtq4HHv8Qq8CdyMMTnAfbgfiM96y9/sWtda\nuxoYG7N/nbv+Jer83Qx81RjzjLf//eizN1gS9vfSWrvdWjsV+AXurMu9nbNaAK9b8Rngq9baP3vL\n77XWbvMePwbMidm2CigbyAGmsUScuxOASuBnwAPATGPMndba9bhdKCuBHwOvcejnsK/pKYo48HPY\n77lLliCxF/eiut58HRhrjPlsH8u7DHRkrTeA04wx2d4FQzOANcQMz82hw3CXcujJF1eizt3LwEXe\n4zNwzxG4f5zetdb+fUwXxx24TXpdF/ltj9mPzl3/EnX+FgPXW2vPwf3juQq3qVufvY8vIefMGPO4\nMabSe9oEROjjnHkXZi7D7VNf5W0fwO2OHOft4xzckN+lBOjvS3I4GPRzZ619w1o721p7FnANsM5a\ne7sxZiRu68WpuNdFzARepZfPm7W2EegwxkzxzuMiDvwc9nvukiVI/AU4LuZ59y/K+7K4Ffi6MWaM\nMebLxpjzetmH08fjA16z1u4BfgT8GXgW+Jq1th03zc0yxvzZe79/idl2vreuHCpR5+6LwI3GmNW4\n/1N/z7si/HTgfGPM895/84Hv4zbhPY97cd5NMfvTuetfos7fBuAZY8yr3mu/sdZWoc/eYEjUOfs3\n4FfetUY34J6f3s5ZB24XYhbwI+9z+Ij33p8C/mCMeQHIxuuvN8aUAHXW2paPeeypLtHfdQF6vuv2\nA8YY8zpukP8nLzD09Xn7DG5r72u43cZvwMDOXdIMkW2M+RnwC2vtu4dZbwnQZK19fojqKgN+Za29\neCjeLxXp3KU2nb/Uk6znrJ86Pov7ZXS/n3Ukg3Q8d8nSIgFu8/ThmnTAbdYeyl/sbfRcSCS907lL\nbTp/qSdZz9khjDsWwSkKEd3S7twlTYuEiIiIpJ5kapEQERGRFKMgISIiInFTkBAREZG4KUiIiIhI\n3JJirg0RGThjzCRgC7DIWvtMzOvbgNOttdt73xKMMZm4889chTs/Qhvwn9baZd7yXwErrLV/SFD5\nh2WMOQm4zFr7Fe8WuHnW2m/6VY+I9E8tEiKpqRO4yxhTEPPaQG7BuguYAsyx1h6HOxLet40xNxzB\nPhJtJjAKwFq7QiFCJLmpRUIkNe3CnSDph8DfDWQD407DfhkwypseGGvtVmPM7bhj8XdNdnaFMeZr\nuLM6fsta+7Ax5ljc+RcycFsxbrbWbjLGnI87Ml4msBX4W29itW24o/gdjzsk7zpr7Q+9OpbjjqC3\n0XvffKDCO5bfAN8G8r0adgFnWGtvNsYsAP4bd36B/cDfWWs3e6MovgacBpQD/2CtXWmMuQ74R9yh\nnrcCN3gjaYrIIFKLhEjq+hJwnjHmnAGuPw/4oCtExPgzMMUYU4o7xG62t+75uEMgj8QdHOqH1toT\ncb/85xtjynGHVV5krZ2LG2y6pid2gKestdO99a8B8GYQPBl4Enc45W9ba08Czga+a62tx51G/DFr\n7fe69uV1yTwIfM5aezzwc9wJirreK9NaewrwBeA73uv/ijsh0jxgPTB9gL8nETkCChIiKcobN/9v\nObSLoy8OvbdCZh20zi+ttY61dhfuv/S7vvj/1xhzN9CB+yU+HzgKeMEY8w7wOdxZCLu85tX5LpBj\njDkauBT3GowO3PlU8owxXwG+i9syAW6YCcTsJwBMw51W/i1vn8uBSmNMkbfOSu/nWnpmKVwBvGKM\n+Q/gCWvtewP4HYnIEVKQEElh1to/AX/CnfL5cF4HpnmT8MQ6Gdhsra31nkdilgWATu/iy7nePm7D\nbREIAi9ba+dYa+cAJ+FexNkltuXjd7itElfR04WyDFiK++X/VQ4MDwfr7W9VAAh5j9u8n07Xfqy1\ntwGXAzXA74wx1/ezfxGJk4KESOr7Iu4MqWP7W8m7m+N3wD3GmHwAr5Xgh8C3vNUCwHXesonAicAb\nxpj7gZOstf+HO1fAHLzWCmPMVG/br9PTtXGw+4CrgUpr7cvea+cA37TWrgDO9N4zCIQ5tOXEAiOM\nMfO89a4CtsWEnwMYY4LGGAvst9Z+H/fai+P7+/2ISHwUJERSU+z0w11dHN1fvsaYd4wxo3vZ7nPA\n27jhYA3we+Ab1tr7Yvbbbox5G3gc+LS1thp3qvavGWPeAn4A3O5NMX0L8JAx5n3ccPHF3oq11u4A\n9gHLY17+FvCyN1X8dOADYBJuQFlgjPk3rx7H6wq5Grd75a+4kx5d3dfvxv7/7d0xDcAwDADBsDH/\nvQyKIGSqDiHQ/nyH4mXZ8t7POmeu18zc6yxifpnaAD952gUAZCYSAEAmJACATEgAAJmQAAAyIQEA\nZEICAMiEBACQCQkAIHsBz2nPBjEZTioAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe038827050>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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OxK/WhLimoCAiIte43N7Nxn11ZGemsOjefK/LEY8pKIiIyDU2vFlLV3eAlQtL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\noBQUREREZFD/F4w9MdhnMH6jAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe0387bb650>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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HEZEg4/P5+LhgMX9tXjfj6eFPkJnQ0+lYEsRUJILQ+Kzr6RbblXUlGzlx9qTT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\nEiIiIpI3BRIiIiKSt/8HfEAjyW0htwIAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe0386fcad0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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K84DPj7Zia21ZdB25OEHhlzGz2wOxv3ooBTocS+EiIm3BP7Z9yIKvF9Ijuzu3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\nAWB32R7nFwcxowSm00DG549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Az40x70bXvxe991qKa5+X1tqt1tpBwMM4V8JtaJvtB4ju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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe038689690>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Running *without* maximum likelihood"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%time\n",
      "timings = sim(sizes, rho, lamb)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "need more than 0 values to unpack\n",
        "Working on Size 100\n",
        "Working on Size 625"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Working on Size 900"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Working on Size 3025"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Working on Size 4900"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Working on Size 10000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Working on Size 25600"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Error: cannot allocate vector of size 4.9 Gb\n",
        "In addition: There were 50 or more warnings (use warnings() to see the first 50)\n",
        "Error: cannot allocate vector of size 4.9 Gb"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Working on Size 50625"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Error: cannot allocate vector of size 19.1 Gb\n",
        "In addition: Warning messages:\n",
        "1: In if (!(model %in% c(\"ols\", \"ols.end\"))) { :\n",
        "  the condition has length > 1 and only the first element will be used\n",
        "2: In if (model %in% c(\"sarar\", \"lag\", \"ivhac\")) { :\n",
        "  the condition has length > 1 and only the first element will be used\n",
        "3: In if (model == \"error\") { :\n",
        "  the condition has length > 1 and only the first element will be used\n",
        "4: In if (model == \"ols.end\") { :\n",
        "  the condition has length > 1 and only the first element will be used\n",
        "5: In if (model %in% c(\"sarar\", \"error\")) { :\n",
        "  the condition has length > 1 and only the first element will be used\n",
        "Error: cannot allocate vector of size 19.1 Gb\n",
        "Working on Size 99225"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Error: cannot allocate vector of size 73.4 Gb\n",
        "In addition: Warning messages:\n",
        "1: In if (!(model %in% c(\"ols\", \"ols.end\"))) { :\n",
        "  the condition has length > 1 and only the first element will be used\n",
        "2: In if (model %in% c(\"sarar\", \"lag\", \"ivhac\")) { :\n",
        "  the condition has length > 1 and only the first element will be used\n",
        "3: In if (model == \"error\") { :\n",
        "  the condition has length > 1 and only the first element will be used\n",
        "4: In if (model == \"ols.end\") { :\n",
        "  the condition has length > 1 and only the first element will be used\n",
        "5: In if (model %in% c(\"sarar\", \"error\")) { :\n",
        "  the condition has length > 1 and only the first element will be used\n",
        "Error: cannot allocate vector of size 73.4 Gb\n",
        "CPU times: user 3min 45s, sys: 30 s, total: 4min 15s"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Wall time: 22min 13s\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "timings"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "      <th>Err_gm</th>\n",
        "      <th>Lag_gm</th>\n",
        "      <th>OLS</th>\n",
        "      <th>W</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th rowspan=\"9\" valign=\"top\">Py</th>\n",
        "      <th>n100</th>\n",
        "      <td>  0.020799</td>\n",
        "      <td> 0.003664</td>\n",
        "      <td> 0.002098</td>\n",
        "      <td>  0.000670</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n625</th>\n",
        "      <td>  0.026594</td>\n",
        "      <td> 0.002983</td>\n",
        "      <td> 0.002443</td>\n",
        "      <td>  0.005336</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n900</th>\n",
        "      <td>  0.027249</td>\n",
        "      <td> 0.003719</td>\n",
        "      <td> 0.002479</td>\n",
        "      <td>  0.006735</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n3025</th>\n",
        "      <td>  0.041921</td>\n",
        "      <td> 0.005710</td>\n",
        "      <td> 0.003510</td>\n",
        "      <td>  0.029185</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n4900</th>\n",
        "      <td>  0.054417</td>\n",
        "      <td> 0.006932</td>\n",
        "      <td> 0.004522</td>\n",
        "      <td>  0.045991</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n10000</th>\n",
        "      <td>  0.088830</td>\n",
        "      <td> 0.205651</td>\n",
        "      <td> 0.006430</td>\n",
        "      <td>  0.084250</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n25600</th>\n",
        "      <td>  0.194143</td>\n",
        "      <td> 6.968898</td>\n",
        "      <td> 0.136538</td>\n",
        "      <td>  0.785413</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n50625</th>\n",
        "      <td>  0.491060</td>\n",
        "      <td> 0.061421</td>\n",
        "      <td> 0.348023</td>\n",
        "      <td> 49.088749</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n99225</th>\n",
        "      <td>  0.687504</td>\n",
        "      <td> 0.123573</td>\n",
        "      <td> 0.056800</td>\n",
        "      <td>  0.789296</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th rowspan=\"9\" valign=\"top\">R</th>\n",
        "      <th>n100</th>\n",
        "      <td>  0.372393</td>\n",
        "      <td> 0.006577</td>\n",
        "      <td> 0.002660</td>\n",
        "      <td>  0.087507</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n625</th>\n",
        "      <td>  0.356954</td>\n",
        "      <td> 0.007866</td>\n",
        "      <td> 0.003204</td>\n",
        "      <td>  0.546080</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n900</th>\n",
        "      <td>  0.413155</td>\n",
        "      <td> 0.008901</td>\n",
        "      <td> 0.003610</td>\n",
        "      <td>  0.772779</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n3025</th>\n",
        "      <td>  1.610812</td>\n",
        "      <td> 0.014108</td>\n",
        "      <td> 0.006154</td>\n",
        "      <td>  2.663630</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n4900</th>\n",
        "      <td>  3.627312</td>\n",
        "      <td> 0.019419</td>\n",
        "      <td> 0.008348</td>\n",
        "      <td>  4.076419</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n10000</th>\n",
        "      <td> 20.597504</td>\n",
        "      <td> 0.076775</td>\n",
        "      <td> 0.015285</td>\n",
        "      <td>  8.635177</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n25600</th>\n",
        "      <td>  0.056522</td>\n",
        "      <td> 2.104784</td>\n",
        "      <td> 0.056522</td>\n",
        "      <td> 22.532605</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n50625</th>\n",
        "      <td>  0.161837</td>\n",
        "      <td> 0.203868</td>\n",
        "      <td> 0.161837</td>\n",
        "      <td> 47.339219</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n99225</th>\n",
        "      <td>  0.393457</td>\n",
        "      <td> 0.421947</td>\n",
        "      <td> 0.393457</td>\n",
        "      <td>  1.564577</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "              Err_gm    Lag_gm       OLS          W\n",
        "Py n100     0.020799  0.003664  0.002098   0.000670\n",
        "   n625     0.026594  0.002983  0.002443   0.005336\n",
        "   n900     0.027249  0.003719  0.002479   0.006735\n",
        "   n3025    0.041921  0.005710  0.003510   0.029185\n",
        "   n4900    0.054417  0.006932  0.004522   0.045991\n",
        "   n10000   0.088830  0.205651  0.006430   0.084250\n",
        "   n25600   0.194143  6.968898  0.136538   0.785413\n",
        "   n50625   0.491060  0.061421  0.348023  49.088749\n",
        "   n99225   0.687504  0.123573  0.056800   0.789296\n",
        "R  n100     0.372393  0.006577  0.002660   0.087507\n",
        "   n625     0.356954  0.007866  0.003204   0.546080\n",
        "   n900     0.413155  0.008901  0.003610   0.772779\n",
        "   n3025    1.610812  0.014108  0.006154   2.663630\n",
        "   n4900    3.627312  0.019419  0.008348   4.076419\n",
        "   n10000  20.597504  0.076775  0.015285   8.635177\n",
        "   n25600   0.056522  2.104784  0.056522  22.532605\n",
        "   n50625   0.161837  0.203868  0.161837  47.339219\n",
        "   n99225   0.393457  0.421947  0.393457   1.564577"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for col in timings:\n",
      "    f, ax = plt.subplots(1)\n",
      "    timings[col].groupby(level=0).plot(ax=ax)\n",
      "    plt.xlabel('N. Observations')\n",
      "    plt.ylabel('Seconds')\n",
      "    plt.legend()\n",
      "    plt.title(col)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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aKurpGx3QYEhSkJQciEhO2VgP0VCE8xo7gw6lYDmOQ1djB6Nz48RmR4IOR+QM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\nOoItWybjdV78Cl577rf91zt4TUk7/X3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       "text": [
        "<matplotlib.figure.Figure at 0x7fe064a39150>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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YR5TR8RlGxqaLXRRZJQUCIiIrkEyl6R0cY1NHFL+/ehMFs7LdA9nuEik/CgRE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\nZlZjLgTMzMxq7BtONLt4bSshkgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe038756050>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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8BFN1D+e7Z+d8DxOpeXgGuGPUuf7rmxIRkSn1/sEI8YTjyxU0ARrPHyKaiLJh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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe038500310>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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eRbMVRETa1umFN5hdmefIwG0EvYGG7HMnFCPW1FZoJLzI+Zmcu8G45IojB2v8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\n9ltdfVV623MwEnCnZbdJWijpWWAP4MSV1LGx7fG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       "text": [
        "<matplotlib.figure.Figure at 0x7fe038578e10>"
       ]
      }
     ],
     "prompt_number": 14
    }
   ],
   "metadata": {}
  }
 ]
}