usgs.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from collections import deque\n",
    "\n",
    "from statsmodels.tsa.stattools import acf, pacf, ccovf\n",
    "from statsmodels.tsa.ar_model import AR\n",
    "from statsmodels.tsa.arima_model import ARMA\n",
    "\n",
    "from sklearn.metrics import mean_squared_error, r2_score\n",
    "from sklearn.cross_validation import train_test_split\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from statsmodels.tsa.vector_ar.var_model import VAR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from nfn import NFN\n",
    "from helpers import Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "PI = np.pi\n",
    "TAU = 2 * np.pi\n",
    "\n",
    "def get_phase(duration, frequency, phase, sampling_rate):\n",
    "    n = int(duration * sampling_rate)\n",
    "    w = TAU * frequency / sampling_rate\n",
    "    return w, (w * np.arange(n) + phase) % TAU"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-100, 1100)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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KjgNcdP4zAID58wk5YYdtU1m5Mw5bk3hp0WI1TKPADj7HwYbFi/HX7m5SkytJ\nuxhu2gJglBNGXMEZOmxnNPJnvLKTg++jpXdXpVxrfUAyJ2/iU+ESvvk+0D8yg2tm6WfrnzRlOUFE\nWhlJqi7BkufeNdPJYaqRKnkGSekJyMsJceuSHEu7SBykSCtpaFhsIq66QyF9Hys2bsSJ99xDDva/\nPL68UqYbxNEnhhx5El1TZzOS6kvSSdzkvnw2c9gIBGXtusiOjFTKZDtZmkeOk6/bQnZdtBWLmEkk\nfHNdoKAbuGYiNKQzxmORT2l9hjTPVCNV8hSkxF8SXVPD9vZ65PzrvoWvNlxVKccghdIFCfXVq3Rd\nF51796Jr+3ZysO/YnRAlM8H0SWJCLcOoHCPOWvSpJHgrWMszYXJn30+ekzc+9nEcMD2kxJTrZkOD\nJ4mTP2gseaXUeUqpDUqpJ5RSHyGuv0Ip1aeU+kvp718not4XA+U+rdcil7h8gHZsudfMx+MjKyrl\naiTteOXqk5XnxFsmYuieKe2SIGeszCbQkk8S5FZi/nXfwsPq6EqZkjO25Ovl1j0Pe7JZ9K5cSUbJ\nZK3hSpn6RfZgbcP+kyBNDhJdk0S7HPR0jVLKAvBVAOcCOArAW5RSRB5X/E5rfXzp71PjrXdSYWjJ\nS47QpKicJOXDyiXQGfVb8vwO1F3t7dg+Zw452Ge3C2kGxhElYyrHRyXJlrzRikM69EUA51Nxr5mP\n3bqzUo7JiSGUCiGTA93IUeg4eKa9HX+75BIySqa9oa9SJuurr7aKnDHtYqJ0x2PJHyR0zckAntRa\nP6u1LgD4AYDXEd+brBXhxEO0kKPPOeWZdAwcZ1lzjrul8yLl+fWv1y4H38fsdfcDAILnN8evm4RC\nOg42rFyJB048kRzsJx06CWkGAF5ZJwyupMmPvGbIyZuGQgJmFqukBLVWLNXDcfK+D+wcml0p08Jm\nSldKsCfJGU22opxQ3zh22B4s0TUOgOdH/b+n9Fk1TlVKPaiUWq2UOnIC6p08CBZIEl2TJFfPJirH\nAV57WqQ8qTQKrAXiumjY0RvV9x7ikARhxdE/GG03v+ACYsCPx3Ix2dQkccgJ6RcmPE4+SVnX+TnA\nt9PzgNacHJUjcfLk/ohS6uaXMqmbh4OmSrnWdgI19B97lYesrBN+cQqV9f4SJ0+fvzXxuB/AYq31\noFLqfAA/BXAo9+Vrr722Uu7u7kZ3d/dkt28sxJ2PvCUvWcgSXSOe8GSwAvCHZuK7uBgA0DM0E2O4\nM9/HikfTP0qPAAAgAElEQVQfxeJSudr0vu+JqFvWrIkG/OrVY+szjpIxCGkUQ/4kOcAsznoy0gwk\n3R8zuS+esQV/27GSz7bIhF627+yFVVwY71vXRfvICFBO3Ty6YxNgaiEDPCcvyoihnjzG47A1bueL\nZMmvXbsWa9eurem7E6HkfSDSGSUsLH1Wgda6f1T5TqXU15VSM7XWvdQPjlbyLwoMo2QkuSRLXrLM\nxPqYnZZPI7LM3qu+grvGXHTRuWtXpVw92MVXVrDMREeaoUVnDDEkVZYzsjzFnaSCnBjXXX99/j9e\njftHPo/daIf/jy6cu2+rqR2eB6xYMojhoLm+7KoJkA8OT/i9KaZrjFccL5IlX238Xnfddex3J4Ku\nWQdghVJqiVIqB+DNAO4Y/QWl1NxR5ZMBKE7BTwdIM3QgWeSispZXABxMLPnRuyt1Lr7TUsJJy54A\nAJx3HuNENVy2G283N0nFK103jctPGMvGSp69mHCJctg+ciW2Yx5G0BQ/y9TzsLuxETuY1M1zmrZX\nymR9E70pTRIZDy1oaJFP/M7q6YNxK3mtdQDgCgB3AXgUwA+01o8ppS5XSpUZvjcqpR5RSj0A4EsA\nLhpvvZMJJW2mSbDkOZQtci5Khk1PkCDHOWznd0bW+he+EL+4a+ZMbO/sJLV4Uy5KHPWjHxEDfhIs\ns3Iceb0+DrEqw/h609w1YnRNkg/ARLkw/T608iVkGUB0LOKcOfjra19L7zxOrHRqHZrGKZENla7Y\n72LOh4OEk9da/wLAYVWffXNU+WsAvjYRdU0FkvK0j/53DMTt5rycZCmZWPKOA5y4fCN+tv4EfOAD\nwC23jBrXjoPHjz0WvSMjWEUMdjH0Umhn+WOtiYVJDRZyGAJ2lb9QHOwJFrlJdI38BVnQOE7egFbi\nnosatYJTRK4cQOKeJ8FXAUy4USDqW5hz6xNNR00npDteKYhKQpf+Ja4JUStiVI7oeOU5eUlJrHtq\nGQDgN79hjqekON31W3Dv+kMAAM+v30oIJed2odopHQRd/rSeqCOq3jou8L9lGkJpuONVrq/+Ha+N\njXS5IgcpCshU6ZpNYmJVQn1JcsaOUFMuP1Xy+ykkjlzYSSoe5C1ZyKYrB0OHH5v3ftXzeLYY+dDf\n90Y6vj5JCbLKWjjkgpMTOfLyv8xka0qfmE4Oxpx8vZa87+OQLVtwInEIi+cBbdndsFFgHaiUpeuv\n34Id/XMq5XramYSp5rpN6kuyyMUJcD+ga1IlT2Ec8e58VE79UTLR9xnO2vex/L77cPJTT5E7WI5d\n8gwA4Kyz4tR7LdEEVGtkuib6RW7vC/tcIDwXMW6d5/LHFddtGidvOjnUGyJaOoSliziExXGAQ2Y8\niwYrX9cOVHfV8xhAW6VMt2diJ7HElMFTOTmkdM1BiBri1llHYUJ0DSfHgZ1UXBcd27dj7p49JB/T\nmC0CAL79bcaBSgwib80iLLKjQf6F7xNaQnipk3wHtXDysWtAog+A1QUGoYm1rFTIS6YJyrh9Dj7w\n/N75lXI9CIXcNVF7plhZG9Zn1E7D+gCYTyqpJb+fwtSBasitS9E1ewejU+0vvri+AV/+OdKyZiw6\n58T5OO7o5wAAXS+ZG/9CDSsArr4kJVgvJ69L+VlY+otp32gHMQXTeP6JpGtcFxgstlTKY+B56Gtp\nwfYFC8joqFBbCJmJhU2fsWYRWrC3UqaFp5azNubyTTc11S0VIeXk91dIlnWpU6l3SRly65IFct+T\nEUcec6B6HvrmzsW2tjZysAfSpCJa5PXL+T6wfmOUqaKnJy5WyzK67hVAgo+Dz+0y9t8x10SLnPw4\nsZ3GaRQ4OA6eWrgQf2EOYYmyUNKphktfiP/kifMxu+WFSjkm8iJw5BMfBcTD+LhBwxXHVCNV8hRE\nS17mgpN2ytYbXcO+Q46DJ087DX855BB6sEsOTeYnASCQLGSmQa4L7OyPsia+973070509JC4AhDq\nS6J5TLh1sf8MDp72PKCldAYql7tGWuFwFJHxISzMF3wf2DXCJzYbD2c9lVE5MJQzTb8w1UiVPAVx\nU9PYf6vlWGUmWZ6C3PHLIo6ccqCKFrmkBMVsmYIDlatveGhfeWQ4drkWzpo33GQ51scxwXImO1B9\nH3hmN8+tc8/FcYCFbfyJUuK5BdoSOXljxyS1w9YFRkI+sRmAKd+BOhnRPGI++dSS3z9RS7x7vdE1\n5eyO//RP8QGvBLmmXORA/c//ZByoDERlDcGyTuDIqRo97cJBxNN8PvxgXfWVUW+UTPnT+jeX1X9/\nY2skwOQscl2gP99aKY+B72PZxo14GXGcIjC+HcTSsY+8UjK6cxEy153gsDWpDxPrG6lFLuXk91NI\nSld03AkW+X1PRLmC//d/4wNezpVjYFkj2aHJh4jWz8k7Tb3oxloAwNyG3TXL+T7wyJYjK2WynYaO\nVyMfgJieIIGmq3ewuy469u7FPOI4RcA8hW9SSCr7mwZRQN51W9CIgUo53hawz1NydGqlhBOsEmBI\n88j9J9BfKV2zn8IwVFB2pDGvte/jkLvvxkm+T2q6cj3UOy9uopK4Z/H+LL4+gJbzPPQ3z4jkbvg8\n2U6Oy981FHH5HyQWADKHbMblhxJdA2mFA7Y+NiTVA1qzUQLWb34zdrkm8C4CQ/rLhM4ASAejc81l\ncLClUo6BeS6+D+wttlfKVH38ztyEdpoo3SSjgDm74KBJUHZAYhJSDR+3LOJYX/7yKm7dddHu+5g7\nOEhadOVBWyzGf1NMpGYYmpgUlUPW6DjYPm9hJDc3Hp1RSxRJvcoscYetafQQg5FClObp7/4urpg4\ny9pxgKXt0ZfnVz8Wz0PfjBnYRhynCIyj/wxDS0VIk2bS2anM5F7QjZUyKWvKrZuCWWkCwHDQMKEn\nZk01UiVPQLIE9w5Gg/2KK5jBzsiVNyfdeCPjTGMQBDxdIy0zJZpHUrfScl+yXMorgHo4cs8D2huj\nbJk33FBnfQkWuWnoJSf3XG8XAODOOwnFVMOKIzZJOw6eWrkS6046iXwhQmEHsUSDSDRWdH3iooDg\neShadqUcw2TsJE1ygJscNyisNAEgRIacjNIdr/sxJE7+3sfnAQD++Ed6sPNcPjPYPQ+7Fy7E9qYm\n0aIj313TqBUxnl/2ASTRIFw7OUt35ayNAIC5xN4raUfoU7sOrZSrUQvNw0XXmKQ1kOmhaIhRKzE5\nOoqnzUSHO4TJwTQklWun42Aok6uUY21h5DwPyGCkUibB0DwjpRVAvf0uYVy5h1JLfj+FYTyxHJoY\n/UtZdJvOPRf3z59PDpSAkys3lWmKiQM1+r5gCY7HkmcGQyDJCRbWnrzA5QOJK4B6J7/57TsAAOec\nQ+QCqmGyZVdipNQ+y5rqd0m5hAmWvBHNI8hJKwDuBx0HaLH7K+XYbwr9Hpayo5Nn0TLtHD0hcLQL\nRQ+V+1khiE9Gvo/FO3fi+J/8pP7cE1OMg1bJ+350WDV5YLXArZ+4fBsA4NRTCStEOvyj9DE5aCFt\n3jGLrjEJhQSAIMmi4+QEhy0r5/to27knqm8zkdoYMFsOC89luBDRC296U30Hlefs6Ma+/31aMfH9\nzitrCDsmkyx5fsVoNklrmMklpURm388k1TOBoZCjJwTuoHJupQkAGRXE+9x1MWNkBF3PPCNsEpge\nOGiVvOtGh1WXD6weDWn51tRQAAD8+7/TcetJO2VJB6qw+SoxhJKB0aYmANrAsgbkSYWVc13Y+aiB\n4cf+tWa5KGolCtXkuHyO5vnb9qUAgF//mu73pPuL9Z/vY8XDD+PkRx4hLboki9yI/gISLeu69w8I\nk4ooV1IhZGhpDfWR14R+VwgqZbI+4saHh+lyRS5hE5WYJmI/wEGr5CVInHwoKGvxIO9JsuSNOVYG\ngWF9YWgbyRVLy28yqRYj5zhAV1MUuveRj9RukbsuUNTCYWhKsQOi/DwLhfiPdvT2Yu6uXaRFl2TJ\nm9A8tUTX1L/yM6TpkqJ5KDnfhxXuK9M/bJBFFCDbOfqjekNnAebdLJ2Z+wJxZu50w0Gr5Mv9snw5\nw7ES8H3gD49FoYJbqvd++D4W3347ju3tpS26hMmBA8vlAwmJ1MbKj2kLYMbJS3ImlrznYTAbbYsP\nr/9UXe3cOhj1w29/S1jkglwZM2fSefY5Tve5XVF0zfNMunUOUgisBFPL2nSTWNlarbe+QNtsfQDN\ndcN1K/QQGTYs0i42J8bKNTXR5SS5ynVKTToONnV14YHXvKa+cLkXAQetki/3y1veEu8jxaQ1cF1g\nW1+0Tf3LX45fnLFxI2bn84xFF/3LKWs+jUICN2vC6Yo5diaHkyfrcxzsbo0cqOGceHgNN9kC+5Qn\nCWFzUkt2EADw05/S/c4pl4F8MwDg6qvjP7pr1ixs6+hgU/8CBpY1+Kgc8blIO14FGFvy4JW8FJdf\nLMldsO6aeCgyYMbJMw2JuiUcVY63k3fY6lFlAml0zfQHF0qXhHr61veB+zdGlue2bUx9CQ5bLiSO\nb5+CjaKBRS5YkCJdY2ZBDheinD7vfCc9kLgsf525KNrlzDMJixx01IrjAAvaegEAs2bV187Kd6ov\nOw6eOP54rD/8cDb1L2DAyUuTJvjnEmoFGwHfD1yUk+kKQMsrANKS9zyMoAEAsOaFk2v2jYxW1tQO\nYi71r+MAdkluwQLyNsh+iNqlRpXj9Y1j+9WUIVXyjJInc3V4wKy2AQAhLqvexe152LN8OXbmcjGt\nE6XijVYAX/0qUx/TvjC0YKPI73gVOF1bMUpeiq4JFWwU2Hz50uRgMcpFWnHsGIrOFv3975lNRgyU\nBWRUEV/+cly3astilVkhsJFBPs6tl9tJfOx5QGNmGIDGv/0bI8dYgtuGZlXKlJzkQLUQGHDrNmyr\nWHdUTggbtmLqA9j6iqEFQOP1r6d9I9wKjqRAxjQo3n+RgraQUQG6umgxqr4wBAJkYKsi2+91T+6Q\nJ83phFTJU33LLIcdBzh60Xa0Yg9mzIhffPbii/FIe3v9HJ2wXHxsywKEUNi+nWg75GySGc6SFycH\nC7ZiLMHoC6TccDELDeCqqxiFxg4iIQQPEOLrM2iyBpHPc8KcUrLRyMhxlrXjAJ1Ne9Gi+jFzZu1y\nrgsMBxEJ/IlPMO0kEOVp74BG/Zt+Qii5/4T4+oyiJ3epviJyABTuuqt230hUh4JCQO87YOorFgEL\nReQyBYyMEPcAeuVQKABZlUfGopU8V9+NN0a/qhCWyrXJTTekSp6ZoTmOvFCw0aQG2JeFswQ7mgeR\nwQje/nbiC4yc6wJ9Q63QsPH1rxNfkBy2pWV7vZtwRooZFLWNq69mLDNGbufgTGjY+NOfmNBEBm3Z\n3cgij1NOofcdkJK+j8xIgLZwL0Z6XohdlgZfIcygUQ3RFh3AywUZNFqDrE9lIlMpuy6Q1w3QsOmV\nA4RNVNpCRljBSRZ5Iczwx0yy9yf4B5j6ggCwUUB7wyC++11iJcbUVyhEq7esVaxrks7ngawqwFaE\nnO9j0datOOWuu2I3PmsW0GwNosHOkzuypUlzOiFV8sS7KyX+GilaaFSDpJJQjEPTcYCls3dijrU1\nvgKIKjSzCJjJyPeBTTvnYUg34oW4DhR35m4bmI0QWdx3X305WhKPuWMGg7KAubltuP56ZrAz0Rlh\naKNN78XIZ79E1sehENhotAbIwb70/vtxxlNPkVquEEQrB3JyZ56n5wG2KiCnhvDRjxKNMZwcuE1U\nvg/0B03YW2zFP/wDnVtJsshDZHD33bXvH4i6JkRW5XH22YxFTvRfsQjYKkDOKrBx69RzKRSiySFr\nB+wKjrLky0o+YwVkCGzb0BDm9/TEbnxkBMha0eRgOrlPBxz0Sp6EYLEWijaaMFC3Iy1fjFYA7MtC\nfOx5QEtuCI0YIFcAkiXYn29BEQ34wAdq33Xt+8BwoYG9Lr3Obbm9aFSDOOEEerDzPoBIeVKDXewH\nZNGCAeTDeNy7Bu+YLIQZNFqEJe+6mPHCC5i/Zw/pZcsHWTSpoboGu+MAGRVifoPP0jy8gzGAQoDh\nYUJZQ3IUZgBY+POfaWdh9fMs7/xOpM0IFIuAjQBzm3fippsYlpJR1haKyNk07QIwtMtzW9Co82ge\n2YORZ+M7pLl25vNApmTJsys4AiMjQE6NwFbE5IA0Qdl+g1gf+T7mfve7OGHPHlI7lpU1a8kz9YwU\nM2hW/XVtinEcoLO5HxYCfOtb9IlSSSB1lpgbJIqWmDGDpk8438HukXbYKOKf/qn20EQgiupotodY\nJc/F1+dVDo32MEYuJw6VTaBrGtQQz+UzyAcZNFp0v3NKXmtgJMxiR74L739/7Y7JsoNRw8a6dXWu\nqCQQK4Dyzm9AwUIRZ5xBHzNZPWn6PvDa10ahnhYCDA0hBolbt1WAnM1b8hQKV30IORTQEAwh/5E4\nj8WtHCJLvogMRfN4HvY0NWGr48RufHi4ZMlbYWrJ78+I9ZHrouWJJ9BVLJKm0MBwBs8Gh+Kmm+jl\nMMflDwxn8XywDDfeWB/X/cLedgxiBv7619rTL0TbvwWusIaXc8kS2jLjLMh82IABPQM33RSXkeKQ\n9+bb8OzwEmzeXIccHOzRbXhMHYkt+XgspOQgLgY2bcl7HnZ3dWFLW1tssIchEOgMnssvx8c+xtAg\nBMoKZSCcwVrWVDuHhuT+4+r70pcAIICNAr2igryzszkzjM9+lqDNiH5wXeCXvwQ0bPSOdGJwkG5n\ndX2+H+UNGgmboKBpJQ+QyrqgM8iigBzyyOssKSdx8iRd4zh4duFC/Pnss2M3PjICKB1gIN+MSy6h\nV1QHDSevlDpPKbVBKfWEUuojzHe+opR6Uin1oFLq2Imodzwod9jtt9dHZ/T0daAPc7BhAzFoBUdo\n70ArduvZePTR+iyzQMjxwVnyjhOF/M22tuCII5gDwAl4HmCpImbbW/GGN5AVsm2ptLeOzVCuCwQ6\ni76gE9/6VlxMoqM0bOwqdtIOYmJFVaYlijqDJ4ePwvXXV8k5Dp455RTcs2zZmMHu+8CqVQCgsTuc\nyVrWFD00NARYCZMthYEBoMUawIzMLpx0Uu0HuLe1AZ3Z3Th+1kP41KeYM4Gr5DwPOPtsIIsRHNL2\nDPr7mbYKk4OlQtKSj8Tik8NvfhP5ALYPzaTpGmZyeOvwTdiO2XgWS/DOoS+SxlI1zeP7wD//M7A9\nPxs7hzpx2WXMeCfkLr8c2JJ3kNcNtK9COi5yGmHcSl4pZQH4KoBzARwF4C1KqcOrvnM+gOVa65UA\nLgdA2HtTi3KHbdpU1Xmeh4HDDsMLmQwZ764FpSs5QvOBkOSIsOQrSilU6LKep9MvIG65lOWGik1i\nXDAl9453lOKsVYDvfa92eiGK/NFoUEMYGWEsHgKjf+qZZ2qvb/RHe/cyoXtVg3YfLQHsCWfjgQfo\nlVF1/5UtVomz5iaVaKIM0ZHZgZe+tLZQQd8HLroIGA5zsBCyHDLVf29+M9BfaMKTe4QVB0OfKAR4\nbmAhPvrR2uQ8LzrlLIdBABof/nAdcfIlDBVypM9Ig54c1v6pEXk0oR9t+OP6hppCNl032oMxgmbk\nwyZyPwblM3Jd4J57gBDxFcOY+vYDSx5a63H9ATgFwJ2j/n81gI9UfecmABeN+v9jAOYyv6cnGz09\nWnd2ah29EfG/ltyQvkRdw17n/ixV1G/Cf9QtBxT1fDwhXjeT4/4Keg42Gsl14RnmWsjK5dSAXmA9\nXbdcBoM6h73114d+vbiBq4//a7L69QJbep5cnQU9m30uUv/l9Szrubrb2YB+PTcr1Uf/ZdGvsxgw\nlBs06Ic9OjPhcvzfQjyql7ZvrluuEXt1V2NP3f0uPZe2Nq3XrZt0VVZBSW+C+lPRdXMopd4A4Fyt\ntVv6/yUATtZav3fUd34G4DNa63tK//81gA9rrf9C/J4eb5uScMEF+6w6Hhqi9TbhcilSpDiQMGcO\nyE2MkwEVOdVJxSPkXX3xcO2111bK3d3d6O7ufhFaYaqoUwWfIkWKycXatWuxdu3a2r7Mmfi1/iGi\na34x6v+10DUb8CLTNWedpXVjY33LuvLSezaeMpLLYI+hHEdZSH8FPR9PGsl1YZOBXKBn4nmz+tSz\nRnKZuqmHUEd7SXdriS7g6rMMqA4gry0D6qEB/borU38/ZDGgs+g3kDOjcoC8EbUC5LU9hXI59Bv1\ng40BDeTrlptOdA35YT1/iBI8PwVgCYAcgAcBHFH1nVUAVpfKpwD4s/B7k/5AOPT0aD1nztjOOuus\nsd954tpr9S9nzYrJrlolyz300Y/q386dK8pZVvzFWHfllfq3ixbF2hnJhXq+vUkvWxZ9Nhp/fPvb\n9doVK2Jy559fkss8q5cvj8v99k1v0r8/6qiY3Lnnag0Eel7meb1yZVxuzetfr+875piY3MtfHtVX\nvsdVq8bK3XHOOXrdy14Wk5s9e+zzrJb7yemn6/u7u8d8dvbZ8cE2ph9GP+xRP5gop7W+56KL9F1V\nz2X0zykUdWtrvP/+9OpX6zWnnFK33B/OOEPfVdWInh6tzzxT6xwGdWd2hz7mmHg//O8JJ+i7L7gg\nJnfGGVo3YEB35Hr1sccS/X7UUfp3F14Ykzv9dK0bsFe35/r08ccT/X744Xr9xReP+WzdOq07OqL3\nheu/NUuW6Addd8xnVD9Uy905b57+27/8S6LcmEfX06N3t7bqzfPmjbmB6jFL9vtRR+lfVT2XsXKB\n7uiYWoVOQVLy446u0VoHAK4AcBeARwH8QGv9mFLqcqWUW/rOGgCblFJPAfgmgHePt97JgOMADzwA\nKLXPYx47ZCCaiGKojk2n5CjJ0elTwxC45ppqsbiU4wCrVwON9jACnUGWCADg5NasARozebys+fdw\nXSLMjmin4wA33xwRUSEsvPnNjFxVSKDjRGF9ZQqrtZUIB2TkTj553/85ueoQxMbGfeUGDOGlbRtx\n222jvuB52DNvHrZU/eCttwLnnQdg1J1X9x8VIul5wKtfDQAhNGz098f7j7o/zwNe+cpkuer7cxzg\ne98DWjKD0FBkv0eNjcvddhvQnt2Dw9ufwic/SfcfFQKcywFa2Vja1oNPf7q2fr/mGqCvD4gyRhbw\nspcxhycJ/WerIn2OckK/lzGm/1wXM/r7MX/r1jGhNZ4HnH46YKFAy5Xvr+q5eF50xrONAgALfX1E\n/00jTEicvNb6F1rrw7TWK7XWN5Q++6bW2hv1nSu01iu01i/VhMN1usBxgMUz+9CBbTj0UPolC4n4\nZscB5nb2oxPb6dh0YjCU5cqHRFNQjBwQbdDZHi7E44/Hw8IUMRiAKFytULTw8z1vxM03E2FvjFwU\nm25he3EBfvITojFCO8s45BBiNyxTn+dFW987M720UgLIwbfq7CEohDjV/hM+9rmOsXKOg2dPPx33\nLF485gfLkyag0G7vJDcScZPRz34me2Go+3Oc6NASS0oUwTyX1lZgd7EdfYWZuP9+ImafkRsYAHYU\nZuHRvsPIDUhcgrzf/hbI6yZs3LMELS3x71hMfWU0ZvL40pdq6/d9MfvDWNq+DTfeGJezgNhk5HnA\nK14BZDGExswIXv7y2k7kc5woL72T7UHOGkZ3d1xOAWT/ffWrQIOitmlPPxz0O14pNDcGWGY/hssu\nI5SLEBfb3FDEcnsD3v3u+uRmt+5Bq9qFl7yEiKVmVg4AYFtCjC6zcnBdIEAWRTTgiSeIyQFIVNY2\nEfIvKeusyqPN6qt5xycQPb+W7ACWN20kD3qgLGvHAVb/pgk5axiDbe3IzaMSxtDttEr56Rc3PEkm\nS0MYks8ll4vs/zarj7ZYmftraoqS2LZYe1iLlZLs65MPluaMgg99KIr53luYgXe8o/bJvYxAK1LJ\nU3LlFY6FImY37iItbQAxZV1eqTRb/QAUGqg0Ssxke8stQLvVi7mte/Ctb1X1n+dhT0sLtsybF3vQ\n5ZXKjIa9+K//IiajMCSfS1MT0JHpRUYV8MpXTu9jXlMlTyBrhxjWLcjliIvM4AOAXDbAkG5FhopZ\nEizd1sY85tk+PvAB2uKh5KJBGkKhiKOOqm1ZWwu4ScXzgJwagirlqCeVBAHHATqa+rAgt4VPYMW0\n01YBhoImcrBTFlYZGRVgKGik+w/8JJa1ixgJm0gahKtPKSBnF7Eg14PPf55J0kXI2TaQVQG6GrbR\nli4j9+53V66is7P2fh/9UV8fk2KBUNbnnw8AGkFok/l3FEAq65/8JEoKpmGR56pyK4BMJjrgIx9k\n2H6ndnrncpFcMbTj/e44eG7hQtzT3R170A0NQEFnEWqbpb+o4xYbG4EQGTRlhvHDH07vY15TJU8g\nmwkwjOZ4p/s+FvzgB2zysoZsgEHdwit54mPfB7bs7sDzxWXYs4cSo5Wn6wLDxSZoZJDL1catA6VT\njuwhKAQ45hhieSrQSpYFaGTw8MM0TcApT1uFGAxayMEuylkBhkJayYuTg1XEUNBEKnnFWOQAkLWK\nGGaUPMKQpOkAIGcXMBQ21zW5+37kjvaHF6K3t3a50Tj6aGZyIBD1M78q5GilMo01Ejbid7+jaUHq\nVzOZaMUxEuRoS57pv+wLm4HQQjhYRMOueKZJ7rlks0BRZ5EPCCUP/r2OlHwOxZBW8twKtbERyOsc\nAm3T/T6NkCp5ArlMiCHdEu9010XL00+jizmsO5sJMQhCDhC57r3DTRhBM77znbgY95KN+Q51mZFz\nHGDpzK1os/bgM59haCWmPqkZUju11thamIvrriMswQRLfjBoZpUEpwQzqoChoJHvBwY5q4gRTU/u\nh95zD07YuJGc3LMWr+S5bf1l2iyvm/DpTzNyDP1lowAbBVx/PfHDQr/nMAxbFXDWWbU5Qvd9lLB1\nn7B0MxmgqG3sGGrHP/9zbSsAAMhcdQWKyEaW/Mc+GK8KgGIcxAXkUAh4i5xbAeTDLIKQDmDg+qG3\nF+grdmCo2DBlG55MkSp5AqySF+D7wFObO7FDd5EWuUTzlMEpa84in9E4AAtFvOc9jByrrDUCbZP5\n1C4zK4sAACAASURBVCROfk7zDlgo0qc4CfXtHulAAQ10JkZOzvfRkh/EcKEBDXviJ5+Ik4MVYDCk\nLXlpBZCxihgKCSXvuujcvh1dRKIc3wcG8k3oLc5iLfKJnqRnZPei0R7B/Pn1/CCQsULkrAJuvZWJ\nruGeJ4pQCPCqV9Xuc4jeLRtFncVvfsOsACiLXBVRQBYjaECDRZ3QQsvlclEgQiHI8DSrZMkzFjnX\nzg9+MPJxaNh4L5HtejohVfIEstmQpms8DwPLlmEbc1h3X38TAuRIi1wKvexs7gcQ4l3vYuSYwX5o\n12bY4A815mApHR1sTPjvJEdvQ6YACyHLPbP0ghJoAoBWLq4LKyhiN2bgQ2/dzh+ETSCjiiwnr5jo\nKCDi1jlOnkM5zXKALGmRc/3neUCDNQwgxCc/yfx4wiRN9Z+krC0VINAZenIXV0YBLKXx3//NRMkQ\nP1jLCoCyrLdd/00EyGAvWrHzE1+OyzBy2WyU2bIYWmy/U8+loaFEu1B0je9jhe/juN/8JrYUGf3s\nDVxfU4pUyRPI2iGGKdrFcbD5DW/Aus7O+j0tAtf90sU+AIs8R1JaAdhWiAIa6MEucM9KaRSFwc5b\nyCGKyNHRNQLNM6c5ssRPP72+FcA2zIOGjT/2HVWzJRi1M+LWqcHOTWK+D7ww1I4R3RS3yD0PfXPm\nYBt5ksqoNnErMabfZzf2ArBYhzTX7wpy/3HPxVIhiiG9govaz9Nm0uTArwAiS/y882r3/Vx+bbQ8\n0bBx5b/TSxVKzraj5zIS5Ori5LdujTwVRZ2N0y6ui47BQXT5fmwpMvp+pnNkDZAq+Rh8H7j/6Ujb\ncrQLZZ94HjCnYwAAcOWVtBwHVbJ0OcddEkdOKt3RX6iCbWkUkaMHu6gkonZychwaMtGxOl/7Wu1x\n8tHIqc9RWEYYRnJXXFG7D8B1o/TMAOJct+PgyZNOwrqVK2M34HlAUyZKpl4Ptw5EShcQQlIZbWyr\nAEWdZfuBU9aWChGCXgFwDtTEdgLs/WWtaP/Hz37GOIiF8xe4n7W0Jjl5ALAQsO2Mfo/u97IafOc7\nxeaMwej7WbiwdrkXA6mSr4LrAtt3RwHB3/wm8QXGYnUc4KQjtgEAb5ELShdgXk5x8PFyEu2iINfH\nQRrs1M7AMuzSYK9rcnAczGrbASDa6FJPiOiufMRfUdEgtUStsO1k+n3BjKid5GCvQXmykzsDJfS7\nAj81lg8wYXVrgvKs2yhAkZXjHNKjd4CzFjITrVQs5Vskqb0a+p1qzO6mJmxfuJBtjK34jYzTBamS\nF1CPIxQAVOlp1hNCGcnJljw7iCxeSciWmWyR85MRrySkwyFsJSsXrr7GbHR+3s031+4D8H1gJOAP\nI5cc2W25aCX2uc/Fr0tcvrQSkyxdaZIG+OeSuKJKWDnUS7uIckCiHKtbuSggNVIpU+2k+u/SS4Gy\nOovKVW0R+r08Lcb0uONg07x5uP+881h6Vjxmc5ogVfJV8DxgTns02ItFetMPr3Sjf2OD3fex9I47\ncPyOHaSZYUuDXbSsIcslTA7soGXrE5S1RCtJ9QlcftlKqkcpRYeRR86UmTNrXwE4DrCwNVqJUacj\nSaGlljHdJkwOUv8lWeSm9FBCP9QrJyl5iY4Sj0wEoIiGPPwwXa6AoXki3a1GleNyEq1kCUEF0wWp\nkq+C4wAZO+o46og4hCFvkZdeZioEb8Zzz6FreJiMrze15KVluywX/Vu/JZhAEwibobj6JDlLoHlq\n2T9w3HG17yAGAL8/onnYkD+mHlZZ+z5W/O1vOOnBB8nJPYn+4qASLHKePjGcHBLkSJrO95ELipVy\nrCqpPoEC4Szyo4+my2PaSXy2r2mapHm4+irXU0t+/4SoOkQLOfq33h1wdkmufovcdAWQIGdA17CW\nru9j1q4ousbaTu9gpBxivg88u3sJAOZ0HSE0sTXbBwD4whdql0uE4HNgLXnXRUdfH+b19pKTu7gC\nAMwm24QQSqD+STNpUiEdva6LjA4q5Vrr831gOGyqlMn2EA257TZAlXwHYzKPjq6PkNvXNMXnVhIs\n+dEZa6crUiVP4JQjI2V02mm1J44CgOF8NOr+5V+qXlDPw57Fi7GtsZF04CQt21luPclhm7ACYDl5\nrr4ki5wScl20jPRH7fzEx2tup+sCe/MdAICrr6bbw4UmLpvxVKVM1kf/HJa0R/1+zjm1h/wBCdFR\nAkzpE1PaTOTywa+oVEKUU9LKgReW6TZK6XIrAMcBMiVHbz1cfhKklSaQkEl0miBV8gTamiOL4Itf\nrC1/dhkPPj4bQHTK+5gX1HHwzHnnYf3cueQbaNu8ktCG9ImxRQ6YrxzYeOmSBUkM+lpoF7KJNVie\n9ewkBYDGbKQkfvxjZkcog2IYPcgLL4xP7n0dHdg6a1bdk7vI5YNX1rU4Qrn+40IvE0+0pBriedBl\nvpq69wQLmYOpHECvAPY1LSQDaJQQsgnse6bTGamSJyBy1gInLw0GKTpDcqCaWvLSuJTi6+U4eQMu\n2PNQbIosM+uznyF/l4t6aG/YBYCmXWQlLyhBwxWOJLd5zxwAwC9+EZ/cNx56KP58wgn05C4pXfCh\nkBJ9Mq7+4+oTrFVLCIEtZO1KOf6bYOk2G/lKuVa5JEiJ94BolzS7AmBoJQAYLDaytNJ0QarkCZQH\nQT07GAHgpKOieGny0AJhB6qV4Hg12QxVywqg7lA6K8FRSA0GOPgjTgMAbFPzaDkm6uHwORsAgMwn\nX0vUSt10VKkfyJ8NQ9aCFFWOlPBN2K8gb4aSQy/ZzVCGjldJyXP95/vAnkJHpUzKMUq32e6vlGNt\nEfpdJE4meMVYnswDZGkufxohVfIEyu9svTs7W1oiWuKmm+pb7g8XIu3+rncxIZtcOxMccEnKrN77\nE2keYTD0DXUCoLl1yULe115CDskcct2hnhINIjzPhZ1R6OWqVfTJQnxOH8jtZJAYXcMK8pOYMW3G\nfO660YlS5TIlxzmyE2FK8wj3x4bym2yimmZIlTyBJCXPW+SKlxMs+fufjrZKxnZo+j6Wr12LE3t6\n6BA8Q448ydJN4uTrfS776iU+M3UU1rDCqXcllnh/jHLJZaLJffXq2rM7+j6wafeiSpmE6XMxVZ5M\ndFRjIV8pT1R9bFROAqTjBhN/TviCltZjApefQSHNXbM/orxztV4loYTJQbawmM9dFx1btqBrYIAO\nwTOMrkmUY5pjErrnecDMZp5br2X7/kSH/PGWfFmekeNbyl8Roof6C62V8hj4PlZu2oQT77mHiTGX\no2Tqb6XwXFwXmVAIhQTYfs+poUq5VrmaMIGcfC1yHK0EAC2ZgWl9KhSQKnkSkkUuDfZELp8Zlacc\n9hwA8Ic5MJA4ednxahCd4fvo6nk2ktu2hZSjnozjAC9d9LdKmayPTYuI+tu5T4wPFaQ/rmxKqzvE\nMMHhXrc2dl109Peja+tWJr7eLPQyMUqGWnEMzYSPBZVyrfU5DtCe3VUp19VOqYlMOwFAa3myNebk\nTVdG0wT7d+snCdKyXRta8tJB3m3NUUrWW26JH0DcN28etrW2ktpfSmwmOV7tJE6eGuz/eDV+N3Aq\nAGD7lUQCdGEwmMflG9JD0iQmOkLL7aXlkrh1Esz9RZu2+ivleqAEbl26kBTvTvpUlIdBtFbKJBIm\naQ6c0SNRJ+NSupOwAhBpnmmCVMkTEGkXIYTSsgU5SNv3GaXkONh4xhm4d+lS0hwaKkShiW99K51S\ndyLTIbiPXInnsQQA8MENl8V/UwrBkyxyw8lBzH0iKUFDS9c0qoNrp+MASzv8SnkMPA99ra3YNm8e\nOQNYSkMhnFAHaiRMyDU20eVyWwzrsww5eWnlV35fyGuTsHLYX5AqeQJluqZeJSHKCQdBW5ISFFYA\nD2xaDIDOtSKGbCZFdVByL3nJvjYdeUTtcpCVvMTJl5Vu3WPMdAUgaXlp0jSW42PMNy5ahHXd3bEZ\nwPeBTXsWQ6O+0MQkSD6VBovn1iNhbvJLaIdpOxkk1WcUJZOwctgf1H+q5AmItIsYmijLcbBs2fI0\n4oL5SyIdxa0AvFub0NW2EwDwFS9u0QESZ53gA0iwyOtPjVv//e1rDAPBpyJQwQkOYlmOTfdQmAHA\nqmvb/76LAhhufWbDjkqZaudkhDSycoC4A1WqT5LjJggr4f4kP8B0QarkCZiGUCZx8hMdennyimcA\nAK9+dZWV5ftYuW4dTnzySTo6w+CEJ8cBTl3+CAD6cAwlbRZKsOR5mscspFFcAZgqF2FFJf6a8L6I\nNI/gOxAhhGxuHlhQKcfqG8cKQNyExMkBxtw6b5HLdI1ROxPlTH51apEqeQJWgpLgOXmerqllJ2m9\nlmdrcxS/fPvtVVaW66Jzxw507d4d43F8H7j36ZUAmOyO3A0gYfITIEWt1BINwq0ATDhdCUk/lzSp\nkJdMLXmAjc9uz/VBIYjTJ76P5Vu34thf/jKmyd1LhzAYtFbK9TVIfjCchZzoQDXl8icwd03lmqSs\nDVYA0wmpkidQVtZ1pdRFMs3D2YJ2Apef5LCtZ6y4lw5h+55oB+rZ3UFdh6IkOmxNo2sMHa+C3cZe\nkS1rQSkJlrxUn+gAT0gXwOVaOWzmU2iyhuL0ieuiY2gIc55/Pu6kSThVQ3QsJ4QmGu8InXAu37yd\nXJ3jcmRPE4xLySulOpVSdymlHldK/VIp1c587xml1ENKqQeUUveNp86pgKiswS/QkmgX1kK2DeLW\nIVjWnoe+WbOwraMj7i0bNcB37rLJwzFMJjE2URX2Wdz1WuRiqKDElUoWskiDJDju2PoSojoSaCxO\njs9fj7oPq7huxW3IoFApUzDxVRhz5IAZlw9MqGM5CUmc/P6A8bb+agC/1lofBuBuAB9lvhcC6NZa\nH6e1PnmcdU46xE1NgmVtulNWjHaRonKE0Msnjz0W9x1xRMxb5h19IxoxQP5euZ0sSvVMdBoFrkZT\ni06UGwcnb7xyqLu2JMdySIcLeh52NzZi++LFscn9mqbPoVjK035NU/wQW8kxmUS7mPTf5GxOSnjS\nhhb5wR4n/zoAt5TKtwD4e+Z7agLqmjIk7nhlLXJZjlXyJaVZN5cvcdbccv+2G3Bh2x0AgHNeMUSH\nxbHKWqCVaogCqj+umx9Acnx2gkXOSQlvqKhckjj5CYzr9n3gbztXYihoilNtjoNNXV144DWviYfC\nJMS7K/DPJUmRGVvyJrQLICj5yZlUTH0A0wXjbX2X1nobAGittwLoYr6nAfxKKbVOKfWOcdY56ZBo\nCWnHq+iYlDZRSTtQGUve94G7/nIYAGDzZkKOa6fjIP/SpQCAn6xpGqsLfB+HP/oojn/oISFrloGy\nTnJkm+yYNOVKpVDIJDnmktgMQ9+BFELZN9KJInJkCCVHL3ge0JQZqJSpdrKW/CRw8hOd9bIWmLZz\nf89CmXhgmVLqVwDmjv4I0Xj4V+Lr3Pt8utZ6i1JqDiJl/5jW+g9cnddee22l3N3dje7u7qRmTigk\nZS3u7JToGkg7XuX6KLgu8PyOyIH6nvcAa9YQ7WRpJWZScV109vXtq2D16sol3wf+sOHoSplMymQS\nKihcS7LoktIa0JfMQt7Go8ySHNl1yQ0PAWiKlxPkHAeY37IFG3evYHMIGYdCmipB0/h6A7pmPJOK\n2O8vUgTl2rVrsXbt2pq+m6jktdav5q4ppbYppeZqrbcppeYBIIPytNZbSv++oJT6CYCTAdSk5F8M\nJO1cZemTjKHj1YTLHz3AR4jBLkblRP9yh05QcF1ga9+sSnmU/t/XToNltGmaAdmSN+XkTduZQBNw\ndA1fGyvnaRcn4Qb0YiY87QK4LSZXdz/4Ppb29mLh7bcDV145Zgb3fWB3ft/hH9UTxHjotsDUKJgE\nuoab+6crXVNt/F533XXsd8fb+jsAvK1UfiuA/6n+glKqWSnVWiq3ADgHwCPjrHdSoaQQSnHHq8zJ\ncw5UW8h5wyl5T7s4DI9F5ZBIAWuyacvzsKujA9tmz647a5bpdnNZKSXUZxIKKdEnCdw6Hwopy/GT\nQ/2WvNPUi7PxW8zBDjhNvXR99dJfrov2fB6znn46FnrpukA+bKyUSZjQX8ABQdeIYbDTBONV8p8F\n8Gql1OMAXgngBgBQSs1XSv289J25AP6glHoAwJ8B/Exrfdc4651UJKYnMLHIpR2TEl3DWOROUy/e\njv8CACxsjg926bg6m6vPcfDkoYdiPXEmqecBczt6K+VYOw0tOunwCJ30epruCDVdcRhEn3CTtO8D\nT+5YXCnHWsI9T89DoakBSoV08jLTFZUhTBOUyRa5IGdoWY9H7qDeDKW17tVav0prfZjW+hytdV/p\n8y1a69eUypu01seWwidforW+YSIaPpkQlTXAWuRKipMHbUn4PvDDX0U7UCkHKmtJeB6GuuZWypQc\n307wWQzDECFxA44DnHbkhkqZArvJKEEJGG83N9lJWkMahXrlkuLIqQa5LrBnpK1SpsA5znvnz0WY\nseiOMFnheB725HLYsWJF7F3yPCCrRiplElMcHWXKyZv6HPZ3x+v0I5umAURlLVjkYgglY5G7LvBU\nT+RAfde7mPqYwb7jjNMr5RikuHWb30wj0iDcy+77OPzpp3EccZKR7wPrnzyyUibrY+mFhBWAoWVt\nSvOYbGoaz/F4bH1WlGqYgtHmHcdBz4wZePiSS2LvkuMAMxp2V8pkOyd4x6sES5RLcONP4QpgOmH/\nbv0kQcwLX8OOUJKnq2Ew1BuVI/VekqXLKnnpcAxuELkuOvv7MWfbNpLT3bG7s1JmG0QgyQFnzIYa\n0koTueLwrtuCmWpnpVyrHBCF3NoI6qoPkJ+XRPOwk5/vY0l/Pw77znfEkFuunVO5czU5Oor3t0jP\n7YCnaw5UJOWT514Wu2zJUwpUGOxHNT5eKVdDPpGI7z5Jzk6w5Pm49Yl/ocWTmhIsZNbCSpAzoXlM\nuXz2eLxrLsPJ+r5KmZQTNlGx/QcYt7PulZHroq1YROeGDWQivL35GZUyWWc94V2j5UzoGmASfDj7\nB/bv1k8SkhyvSZwuNQC5bfHONZfhQ8P/XinH5MQomQTLU1hxWEaWIM/p7mptxXbiJCPPA2a376qU\nY/VB4PKN4+RZscmxBI2jcsziupUCS9cY9R+SHLb1w3WBom6olGP1IVEls1dMD32ZyNw15YlrKGys\ndxEz5UiVPAHTLJRlw+T/b+/sw+woykT/e885M5mZRDKETELohJCFAIFEIbIsIGoICJigG5H1wfWC\neFf7+rGLcn12AdEF1mcf8GNlDXq9ng0XMAi7gChggoSvKCKRYQkkQIRgAmQ6X5DJdyYz56PuH91z\nZuZ0VZ05PTPJzEn9nmeeqdPdb3dVV/dbb731VrXJXWNcbdHWIbQtqGWdpGHz6Sa05E0vkefxxpQp\nvDBnjtane+r0taW0Lp/GJYMTKuvEa9dUsuQNA+dvtLWU0v2+XjZLrrGhlNbKGaOjLJZ8khDKSnKW\nxn1POs32GTMShdwm8XUnXWo4qSVvGzgHKJIxuyGHCU7Ja6gYJaPZFgRw112h73ljoLHkTXHk2Sz7\np04tpbXXG2SffMrmrrG4eYoJLUGbT/eEjRuZ9dhjBg1Z4aUcdN9s9T0j34dde5tK6X5fz/PYfeTE\nUrqcVIWeWDqJJW9ZniBR/Xkem5qa+NOXvqQNuU1LVymtPW+CsQPgwLpdrJMRNelhiFPyGtIJPv7h\n+7B2bWiZ/a+vaCYSW172bZ+8uJTWXc/8slt88hWUvG3gztwDsCiJYrF6JeH7HN7Rwfi2Nq1Pd/Wb\nJ5bS2nwmVNZJLHnjfanwslt95Ekta4tPPqWUeSqz5XopSKQETdfzPGjMdJTSfQgCvP37mXbLLdUP\n2EJyt0vCaB7d2EE425jw4y1qeJvyTslrSPQZvz4ve2d8v82CtPnWrQOvyeQkJdbuvi5OHvqxUJVB\nrpjgO5i+D+177FE5SRc2S+ILNslllU8LW0rp2BmTRCtRoZGu4K4Z7JmdSX35tsZ9dLHI2FWrtI17\nZ6GhlI7lE5IPhNqWNbB8NEQ7lhbNNs5Q0M48Hk44Ja/B6pMH7cOSVT7v5cUwXdQMoNp867aH1ubL\nrzDwmtQnn3i5AGM5DNuzWXY0NPDulCnJfLpJJ9MMoiXvNbZzJitK6WquZ520BcnrL2kUkKkHYHPz\ngFFOqerVi+9DMVr33rTK5mD65LsbEoUYe4zaKKDoeS2SqvrZPdA4Ja+h+1kwLU9gatn/ke+X0jFs\nM1DTdovciK32KrhrjNEZCXsOKYucsQfgeaybMIEXNeufZ7PQPGZHKR3LSkKL1bbMwOo37R+61vYA\nslnyh43uybRGLmmjYlu90uRus02GqhQnn1TO2IOzDNjuE2HnKackU5CDWO8937sV7bdvjdE80fNa\nxDDzeBjhlHwZQQD/5/YjSmkdpmUG8jOOD9O33BLbbZ9EZa8Gs9vFHGdsU7qptNgn05he9gozUJXJ\norM8ZimDnOfBjCnrS+k+BAHHtbdz8gMPWPr05nxqx1Qu76B9z+hSWp9ZTTk8j13T/6In07rrWSxy\nI5bnxTpwbspnz179OROGUNrGAGyN+7b6etZ/4xvaxl2iZ9MUcjuoa94M4Nu30I/1lYYBwz+HBxj/\n8g5e+VNjKV2O0dL1PHZ9MfoeypFHxvfbfMFpczXYLGtrFELFOHnDwF1CH7LVkrdk0zZgWzB1932f\n5s5Oxq1bp/Xpvrbx+FI6nhnDS1vpZe/H0s06BhLNY1vWIJlP3q7kkzYORiVvUS9ppSATD1DwvJ7q\n0TXu43M5jvrWt7SVm2SGdHbmraVebXbmrVo586S06r6ze7BwSr6cCi+77RuopWddd4zVkk/4stsa\nB4tcKm0feDW/tEkHXqu35AEKxepnRPo+7NxnHrA1uV2yM2/lKNpKaZ2cuf6STWqyvX02pVtpMlQS\nt4tgHsiu6Oap1pInUvIGuaIy1Lvv0wiMbm3VNu4FlSmlyzH51r3FN9Mk+0ppnZyxR1Xlx9QPFk7J\nl5GdeSun8VwpHcNS6ZlM9Dro/Og2C8uirK1yFaJrzKtQKjIGd431epUs+QQLhll9uqbGIVo1cdux\nx1bn0w0CxgcB8599NqYJvMU3c27zilJah3GZiApv0WDPlE2lMdZfoslsVPLJ25V1onoHY+MOUCc5\n4z4dl39qP93qLEz3xWTJ43mk6lQpHZOzGUuWxn044ZR8Gd7im7l59t2ltA5T+90dX69T8tZutC3e\n3ba2S8IeQCpjtuRtytraqGCZ3GKLzrC5a0yWvOex4bDDePmyy2Iv5o1f2UKGrlK6D75PY0cHx2ze\nHDfzPY/OU08spctJ+rLb16Cx30/bdwtscfJJ1vRJ3DiAxSKv4K6xKPk0+fjGbJZOYO8ZZ8Qa99XP\nd2jTAAQBDZ2dnLNokdbMr0trrhVhddc4S35kEuDxjfR3SukY/fiMn85dk1RZg3n9elt8vd0nb3fX\nJFpLplhM5OaxumsquHl08fzXX/EWeepL6WqoH2X5sIut/ixepaTRNfYenDKvPUTCxjbhjFBrnHyl\nGbZWS16jeD2PfakUwQ9+EGuIZ45+U5sGwPepUwpvzRqtDy+TNvRqqeCms3x/YDjhlHwZvg/PtUYL\nK32hrBKDgAmrVnHRG29oLYLSOFKV7hqrbz1hfL21u59JNuPVGkJpfdkr+ORN7pqixRIsFrUDd1ay\nWToaGlivWUgtCGD5C1NLaR1JB16TrpdvHlNJFkJpnfGacCzGOsPWIpdRCtHVX3Tz64td+ncMkLq6\n2PbFy45kTuZRLsg8yuJlmsAHC0kt+ZRT8jWAKlPWvk9TezvH7NqltQhK3XbDwKstpBGo3s1j635b\nZ7zaJ9MMdpSMVUkUi3qLLgg4bPO2UjomZ7Dks0uncE7jk1zIUrJLp/Td6XnsHD+eB+fOjVmCvg9t\nW8eW0uV5GbdtGxcuW6bNSzptuTOWqCpbuLd14DVh/dmw+uQtxUsaXWP0yUc3v44uvdVtCrk9bRLz\nzvxXbpt5Dd5pk/ruzGYpAG0nn6xt3LftG1tKl++sKxQ48/vf19a7i64ZoWSzcN55nVzAErILNcsT\nWMhk7Mq64iSOgsY6s3UXE0fXpBKtQml7aa1ySbrtvk96f66ULscYgnfaJC7+yiPcc9in4y87kCoU\nKFTrlvB9Gjs7mbphgzYvtnh3a1x3wh6ApIRUuQHSWy6BZW1z89jkKvnWq5ULOsYBsIPmUjomp7Hk\nAYqplH7yoOehUimeuPJKbeO+P9dYSpfvTAGTXnpJX+/Okh+ZeB7cc89u7pWP4U0oG+HPZulobmZd\nc7PWIvjud5vD9MaylyIImLB2LfNXrdJbpd2+dY2St898TNYDSBwnn2TgLggYt/7NUjp2PYNc0DGO\nVziplC4nbeoBAMV0mpSuwQTShQJF3YJTWTjz1E2cJ0urnoRpbDOCgOZduzjvF78wWIIVlK5pX8Kl\nhq0hlAmVdQpD6GVU3jR5c71rGmlfwpu/n8ZSujcZMLrpCqkUqbzG9aIUmWJRW+8DwblrRjh5gFyZ\nkvc82o87jvtOOklrEaxcGVkE15YpJd+nadcujmlvt3wDD6MlX/FLRlUq+aEKwdPK+T4Nu/eU0jE5\ng5vHlyw7ObyULidtcNdAqOTThuUgUsWi1pL3PPjeN5/l3syCeHBNNktnXR3rp07VNu5/fGFSKd23\nED6j8nmmaCZtgXVJmAprFpnHVFIk+whL0hBKW70D4bcSNGWvA/31Ghr1aeh5zg35zKdS+sa9UAiD\nF3TuvSzMPuYVPjzq8Xjj/pOfoIBNp56qX7LCuWtGLiJCDkBjFaTy+crdfZsTU3u9KFH+gAYBE95+\nm4+uWGFfktXk5kkwGcomV8m3bpIrVljWQGtB2l527AOvxXSatMGSTxkseQAymdAdUI7nsa+piQcX\nLNA27lvfGVNKV4PRkg8C3tPRwZw77tD3ACxK3r5AmRljKGQQkMnlS+mYXAW3S4FUvCdWLFIEX9MN\n/QAAEslJREFU/RK+WThhwvOc2/hkXK/m8+Qx37diKoXo6j2XIy+ilfM8uO4Tt7Ho8MvijXtLC12p\nFH+47rpYvQcB7OtsKqWHM07JGyiAUcnnDRbBOefs4xyWkv321tjOjtGjWTd+vNYS/OlPoy8LbdAM\n9O7bxzFbt9o1SLXumm4lr1Foxo9VBAETXnqpJ9O66+ncLjcu4pn02aW07nraAdQsnDxjHReyROs+\nSSllVNbFdDpsdDTYlLwyKXlCN0+h2u5+NksuleKt444zWIIGOd+nvljEe+01fe+n0jd6ky4ZrJPz\n/Z4P3pTnRSnSoFXy3b0vRTreE8vnTVPx8Dy4/OybuGf8FXGlGylrEwWTJd/VZTXMlKnn19mpfdch\n+rxh0bxa5nDCKXkNIqJ31wCSz2uVhOfB7be/w22Zv8abmI/t3DlpEveefrrWElyzJvqy0NfiFqsN\noy8/CGjZupXzn3hCq5Ab9u4KLcH582P7je4a36dxW3tPpsvzYpDzr5/EtsIRUToe2pYyxNd7Hnz5\nS0tYIh/TLvJnGniFyu4ak5vHaMkT+fI118tm4S/fv5mP6hojz6Orvp6ll1+utQRffsO86qUNSaEf\neA0CGnI5zlq4MH7SIGD07t09Fy8/Z5IQym6LvFq3Sz5PwWBZAxRMYypR42CUS6UQnU8+lwv3mRq/\ndDrskZTT1UXeIjdScEreQE5Ea8mnDZZ8Nwq0lnU6lyNfyRIsf9CyWfY3NLDOENd9//0TwnRbmZzv\n07h/P1ODQKuQp/7qgdASfOSRvvuDgHE7dnDuQw/FFEHQMY7fcEGYjtaG6Y11pqypfJgteeg1oKd5\n4SsNvKaLhp6KzZJPp6u25D0Pbvzn53jI0BhlCgUKugFGH7bvHF1K96E75O+kk+I9gCDg+GefoaGg\niSP3fTLApNWr4yf1fTI5c7SS8YPVNy5iL02ldB8KBeOcz2wWTpiyio/ULYs3ft0+cgOFdFo/gJrP\nJ7PkcznrO1tMpfQ9v64ucga5bBbee8wrzK1/bLgvJ++UvI6SJa950MSi5EWiic465ZLPa5V8Ngsf\n+tBuzmMJ2e/s6LvT89jT3Mz9556r7QGsXx8pibNf7bc5GARwc5vPGmYQUBZi6Ps0dnUx5c03Y4rA\nlywbCCcL+cX/GzuvKVQwm4X3vrctjFv/9/iqnrYQPBEJ73VXV2yfbcakpFIUDI10JZ98nVLa+jNZ\n8t3XM33DN5PPU6yv11/PRLQU4zJNyF9w2TXcteUSfseHCC67pt+nDDrGsYHJpXTPjgDmzycNjNq+\nPSbnXz+JYhjTgn992fMSrY9k8nV/dv5PuL/pU/HGr4JvvWAaU4mUvNEnb+oB9MeSNyh5kyXveXDV\ngkUsHvuZ4b6cvFPyJkzuGpNPvpsi6C15g5L3PPiPG57nYS7C+6fPxJR1JpcjV2lm57Z3+yrlbJau\nTIb1Rx8dswR9H1buncl2xuEf8cv+L/DVu8tdHqccBIzdu5cP//zn8YW/PPj615/k3vpP4I2Lryky\nZv9+zvrpT42NVCGd1ir5dIVp8cV0Wlt/aUN0DQCplL7+lDKGXkIYzaJVH4WC8XOK2Rs3Mfc9vwvd\nPDdu6rszyrc2xPDlf2A172Mjk/Ff/oe+O3/8YxSwURMN4kuWfYwppXt2+LB0KQAzb9UsyGciCGDB\nAtJKUf/OO9pD8uk0aZ1FXiiEjbCBvCkUMmocTNgs+Yo+eV0jbfHJEwSc++CDjNuxY9iPvDolryG1\naROTi0X48pdjFZiyDMClt2zhqHwevvjFmFw6n9d22wEm3XADDQBPPhmzoNO5HAXN5I9sFj7S/Azz\nWEKWL/Td6Xl0NjTwi4svtn+1Ztasvvu7Bwo1qztmszB79mbOTT1C9l/LXmrfp75QwHv9dcOkESGX\nTkNnZ0yuTikmvfqqUU5ryQcBDfk8pxlnIkr4Uusa6UJBqzwBRr37bpi46KK+5y0UwkFJQ703tLeH\nL1L5GEdnJ/l0Wuuz9q7/PE/s/jBLuQjv+rLPRXZ00JVO6y3PWbP0aYDmZvZlMjxz7bXxeq8QrQRo\nR4KzWTjh2NfCnljvR8L34dFHSQPTv/c97enydXVxJR8EcOmljC4UqNu6VStXzGTilnwQwGWX0Vwo\nkNmyRS9nahxyOfMYQBDwwbvv5vDdu+PPUleXuefg+0xZv56GXG7Yj7wOSMmLyCUi8rKIFERktuW4\nC0XkTyLyuohcPZBrHgiavvY1xgI880zMZ920bRt/9/zzWuUy7pprQlvp6ae1ytrk37ORyee1lrzn\nwXcWb+fe1Mfxzo4r5bpcjpzGTZDNwumnv8s5qd+Q/ebbsZMW02l+dcUVMSXhefCtb63gjqZP4Y3d\nU3U58uk07I8vAWujaft2Grq64NJL+95v3ycNTFy5UvuCjdm5M/Q/X3JJj1wQwLx5pJRi9B59/o/7\n7nfDF+I3v+k5bxDARRchSjFm506t3MndFvDSpX3zs38/+f6sr1NuRXZ0GHtv2Z81MmvW22EP4Lay\nY/bupdMkl4UZM9aFcj8p9N0xdy6dIrxy5ZUxOc+Dyy7/L5YwH++o6kKDC+k0mXJl7fvwxBPUA5O/\n/e24UBDw2cceo37v3lid89RTNALjr7tOK/f5P/yBUeXKOhqXau7ooLFd81lO38dbu5ZRhUL8Werq\nCo2TEc5ALfnVwCeA35oOEJEU8CPgAuBk4NMicuIAr3tw8H0yXV3MrBTSWE4QMGrPHv7nb3+rbRy2\n/Mu/sCOVgt5LqEa+0lEdHTQalGN+4kTeaGyEm27qUcrdcp2djNLIeR782/9+ggflIrx//ruYxVqX\nz5MfNUp7vcb2dg7v6IDPf76vXOQmeGvmTK37p2n7dt7T0QGf+1xfuR/9iCIQvO99Wrk5d99NXbEY\n7+FUmIdwwQMPkFEKHn+8R873w4Fm4JOPPqoXNFhsPPooKWD+Qw9Zr9uHIIC/+Rvqcjl945DNsunU\nU8MB/ptv7iv36U8zqquLJo2P3PPgqque4L76i/EO291X7m//lsZcTqvMPA++fuldPCwfw/vCvJ56\n8DxYuJDNTU10tbRoizKmu1Gc10sum4Wzz2ZvKsWfr9bbbaP37SOTz2ujuMAwtc73OamtLXSfGN4x\nk9zMzZvDHkBvOd+Hp5+mMZ/njNtv155PSxDAV7/KkXv26BuHbJY3p08PB4KH+8irUmrAf8BTwGzD\nvjOAR3r9vga42nIudbDZ9dRTqgOUOuwwpVpbw41tbUq1tHQPyyk1b15MbtOvf51Ibt1996n95XJz\n55ZkXps8WZvP1XfcoTpBqbFjtXJ/njZNK7ftlFN68nPOOeHG1laljjhCFUHdeeWVWrktM2ca5Qqg\n7r/2Wq1cMGNGXK6tTam5c1WXiHrg1lu1chumT9fLnXWWKoDaOmtW+LuM9cceG5frdV/WHn209nor\nFy1SOVDq8MO193Od4X4+s3Chylvk3po+XSu37KabQrlx47RywYknauV++c1vWuU2z5yplXtLd19a\nW5VqblZdoJ5ZuFAr9+dp06xyKxct0sqtnTJFLzd2rOoE9drdd8eF5s3rkRk/vqd+e8m1/epX/Zfr\ndV82zpgRl2trU23Tp6siKDVnjlZuy6xZ2vL97O//PpRraen7vs+bF/5pns2hItKbep1q2lHNXwUl\n/0kg2+v3/wAWWs41pDejEm1tberZpqZSBRd7/XVv2wbq8TvvjMs1NlrlFKgtp50Wk9vWa7/peq3d\nD9FBkmttbVXvDJHc70W0ciuGSO6Phvvyx7q6RHIrMpkhuS/vDLLcu5XqT0S1lSmmoZRrbWiIyT1+\n551DJve04b78boju546yd30oGZCSBx4DVvX6Wx39/1ivY2pGyc+bN09t7lVRur8OUPX19VXL5UFN\nzWRich39uF5LS8ugyW3tRz7L5VpaWoZMTpfPlpaWROVLKneg66E/+dw6yHL7+5HPeWU9zQMtV19f\n36/7mURu8yDfz3wlORF1oLAp+YqjQkqpjyR1BUUEwNG9fk+Othm54YYbSuk5c+YwZ86cAWahOlYD\nEy37dxu2V5JrBzZpBl9bgQ8muF5SuZeA8yxyOwzbh0rOlM/dEEYd1ahcpfp7aZDldgF6r3vIcwdY\n7kDXw+qEcqb7uROIr4/aw5p02lr+gbB8+XKWL1/ev4NN2r+aP0JL/v2GfWngDWAqUA+8CMywnGto\nm7wKtLW1qfNnzlTP07cL1v23HdRpoJYsWTJocuccf7x6ltAS1sl9oKFB6yawybVXkDPl0yTX2tqq\njm1oGHS57aA+2NiolfurTEZtGwI50325ZNo0o5ztfl4ybZpqH+T78t+gThgzZlDlbPflv0Gde+KJ\nWreLSa4AakUFOdt9+dSxx8bklixZok6J9g+mnO2+nFlfn0jOdj9fBPVi2bs+lER6U6tTJdyfDBFZ\nANwKjCc05F5USn1URCYB/6GUuig67kLgh4TRPLcppfRfyA6PVQPJk8PhcBxqiAjK8HWeASn5ocAp\neYfD4agOm5J3M14dDoejhnFK3uFwOGoYp+QdDoejhnFK3uFwOGoYp+QdDoejhnFK3uFwOGoYp+Qd\nDoejhnFK3uFwOGoYp+QdDoejhnFK3uFwOGoYp+QdDoejhnFK3uFwOGoYp+QdDoejhnFK3uFwOGoY\np+QdDoejhnFK3uFwOGoYp+QdDoejhnFK3uFwOGoYp+QdDoejhnFK3uFwOGoYp+QdDoejhnFK3uFw\nOGoYp+QdDoejhnFK3uFwOGoYp+QdDoejhnFK3uFwOGoYp+QdDoejhnFK3uFwOGqYASl5EblERF4W\nkYKIzLYc96aIvCQiK0XkuYFc0+FwOBz9Z6CW/GrgE8BvKxxXBOYopU5VSp0+wGsOGsuXLz/YWRhS\nXPlGNq58I5fhVLYBKXml1GtKqbWAVDhUBnqtoWA4VcRQ4Mo3snHlG7kMp7IdKMWrgMdEpFVEvnCA\nrulwOByHPJlKB4jIY8DE3psIlfZ1SqmH+3mdDyilNolIC6GyX6OU+n312XU4HA5HNYhSauAnEXkK\n+LpS6oV+HHs9sFsp9QPD/oFnyOFwOA4xlFJat3lFS74KtBcQkSYgpZTaIyKjgfOBG00nMWXU4XA4\nHNUz0BDKBSKyATgD+LWIPBJtnyQiv44Omwj8XkRWAiuAh5VSywZyXYfD4XD0j0Fx1zgcDodjeDLs\nwhoPFCJyoYj8SUReF5GrD3Z+qkVEJovIkyLyioisFpEro+2Hi8gyEXlNRB4VkbG9ZK4VkbUiskZE\nzj94ue8/IpISkRdE5KHod82UT0TGish9UX5fEZG/qrHyXRVNllwlIj8XkfqRXD4RuU1EtojIql7b\nqi6PiMyO7snrIvLvQ55xpdQh90fYuL0BTAXqgBeBEw92vqosw5HAKVF6DPAacCLwHeCfou1XAzdH\n6ZOAlYTjMMdE5ZeDXY5+lPMq4C7goeh3zZQPuAP4XJTOAGNrpXzAUcA6oD76/V/AZ0dy+YCzgVOA\nVb22VV0e4I/AX0bppcAFQ5nvQ9WSPx1Yq5R6SymVA/4T+OuDnKeqUEptVkq9GKX3AGuAyYTluDM6\n7E5gQZT+OPCfSqm8UupNYC3hfRi2iMhkYB6wqNfmmiifiBwGfFApdTtAlO+d1Ej5ItLAaBHJAI1A\nwAgunwrDvreXba6qPCJyJPAepVRrdNzPeskMCYeqkveADb1+t0XbRiQicgyhhbECmKiU2gJhQwBM\niA4rL3PA8C/zLcA/Es7L6KZWyjcNeFdEbo/cUdkoEq0myqeU2gj8G/A2YV53KqUep0bK14sJVZbH\nI9Q33Qy57jlUlXzNICJjgPuBr0YWfflI+ogcWReR+cCWqLdiC6sdkeUj7MbPBn6slJoN7AWuoXbq\nr5nQyp1K6LoZLSKfoUbKZ2HYledQVfIBcHSv35OjbSOKqBt8P7BYKfVgtHmLiEyM9h8JbI22B8CU\nXuLDvcwfAD4uIuuAe4C5IrIY2Fwj5WsDNiilno9+/4JQ6ddK/Z0HrFNKtSulCsAvgbOonfJ1U215\nDng5D1Ul3wocJyJTRaQeuBR46CDnKQn/D3hVKfXDXtseAq6I0p8FHuy1/dIowmEacBwwbJd9Vkp9\nQyl1tFLqLwjr50ml1GXAw9RG+bYAG0Tk+GjTucAr1Ej9EbppzhCRBhERwvK9ysgvn9C3Z1lVeSKX\nzk4ROT26L5f3khkaDvaI9cH6Ay4kjEhZC1xzsPOTIP8fAAqEkUErgReiMo0DHo/Ktgxo7iVzLeEo\n/xrg/INdhirK+mF6omtqpnzA+wgNjheBBwija2qpfNdHeV1FOChZN5LLB9wNbAQ6CRuxzwGHV1se\n4P2Ey7SvBX441Pl2k6EcDoejhjlU3TUOh8NxSOCUvMPhcNQwTsk7HA5HDeOUvMPhcNQwTsk7HA5H\nDeOUvMPhcNQwTsk7HA5HDeOUvMPhcNQw/x8XiQLoYjF98QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f570c1fd6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w, t = get_phase(1, 880, 0, 44100)\n",
    "c = 1.0\n",
    "\n",
    "k = 1000\n",
    "y = np.sign(np.sin(t[1:k]))\n",
    "z = np.tanh(c / w * np.sin(t[1:k]))\n",
    "dz = np.hstack([0, z[1:] - z[:-1]])\n",
    "plt.plot(y, 'k.-') \n",
    "plt.plot(z, 'r.-')\n",
    "plt.plot(dz, 'b.-')\n",
    "plt.ylim(-1.5, 1.5)\n",
    "plt.xlim(-k // 10, k + k // 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = pd.read_csv('data.csv')\n",
    "data.drop('Unnamed: 0', axis=1, inplace=True)\n",
    "weather = pd.read_csv('weather.csv')\n",
    "weather.replace({'Precipitat': {'T': 0}}, inplace=True)\n",
    "data['precipitation'] = np.repeat(weather.Precipitat.values.astype(float), 96, axis=0)[20:20+data.shape[0]]\n",
    "data['temperature'] = np.repeat(weather.Temperat.values.astype(float), 96, axis=0)[20:20+data.shape[0]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "g = data.groupby('day_id')['gh'].mean().values\n",
    "u = data.groupby('day_id')['precipitation'].mean().values\n",
    "t = data.groupby('day_id')['temperature'].mean().values\n",
    "\n",
    "#y = data.gh.values\n",
    "#u = data.precipitation.values\n",
    "#t = data.temperature.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "DG = Dataset(g, range(1,11))\n",
    "DU = Dataset(u, range(1,3))\n",
    "DT = Dataset(t, range(1,5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X, y, x_ranges = DG.get_scaled()\n",
    "U, _, u_ranges = DU.get_scaled()\n",
    "T, _, t_ranges = DT.get_scaled()\n",
    "k = np.min([X.shape[0], U.shape[0], T.shape[0]])\n",
    "\n",
    "X = np.hstack([X[-k:], U[-k:], T[-k:]])\n",
    "ranges = np.vstack([x_ranges, u_ranges, t_ranges])\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "y = np.array(data.gh.values)\n",
    "\"\"\"for i in range(y.size - 1000):\n",
    "    p = np.random.rand()\n",
    "    if p < 0.0005:\n",
    "        b = 2*np.round(np.random.rand()) - 1\n",
    "        y[i] += b * (2 + np.random.rand())\n",
    "        k = 1\n",
    "        while np.random.rand() < 0.99:\n",
    "            y[i+k] += b *(1 + 0.3*np.random.randn())\n",
    "            k += 1\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "k = 128\n",
    "m = k // 2 + 1\n",
    "n = y.size // k\n",
    "\n",
    "spectrogram = np.zeros((n, m))\n",
    "for i in range(n):\n",
    "    spectrogram[i] = np.abs(np.fft.rfft(y[k*i:k*(i+1)])[::-1])\n",
    "    \n",
    "avg_spectrum = spectrogram.mean(axis=1)\n",
    "energy = np.square(spectrogram).sum(axis=1) / np.square(avg_spectrum).sum()\n",
    "    \n",
    "j = 128\n",
    "plt.figure(figsize=(16,4))\n",
    "plt.plot(y[:j*k])\n",
    "plt.xlim(0,j*k)\n",
    "\n",
    "plt.figure(figsize=(16,4))\n",
    "plt.imshow(np.log(1 + spectrogram.T[:,:j]), aspect='auto', interpolation='nearest')\n",
    "\n",
    "plt.figure(figsize=(16,4))\n",
    "plt.plot(energy[:j])\n",
    "plt.xlim(0,j)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.semilogy(1 + spectrogram[78])\n",
    "plt.grid(which='both')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X = np.vstack([g, u, t]).T\n",
    "\n",
    "var = VAR(X)\n",
    "var_res = var.fit(maxlags=15, ic='aic', trend='c')\n",
    "\n",
    "plt.plot(X[15:,0])\n",
    "plt.plot(var_res.fittedvalues[:,0])\n",
    "plt.xlim(0,300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "r2_score(X[15:,0], var_res.fittedvalues[:,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X.shape, ranges.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "nfn = NFN(16, 32, ranges, init_X=X, init_y=y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "i, best, train_error, test_error, steps = nfn.train(X, y, X_test, y_test, \n",
    "                                                    n_epochs=10000, max_no_best=32, tol=1e-7, is_adaptive=True,\n",
    "                                                    verbose=100, return_errors=True, return_steps=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "r2_score(y, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "y_out = g.copy()\n",
    "y_out[500:600]   -= 0.02*np.arange(100)\n",
    "y_out[1000:1200] += 0.01*np.arange(200)\n",
    "y_out[1500:1800] += 0.01*np.arange(300)\n",
    "DO = Dataset(y_out, range(1,11))\n",
    "X, y_out, x_ranges = DO.get_scaled()\n",
    "\n",
    "k = np.min([X.shape[0], U.shape[0], T.shape[0]])\n",
    "\n",
    "X = np.hstack([X[-k:], U[-k:], T[-k:]])\n",
    "ranges = np.vstack([x_ranges, u_ranges, t_ranges])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.plot(nfn._W[:,10])\n",
    "plt.plot(nfn._W[:,11])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.hist(u[u>0], bins=100);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.figure(figsize=(16,4))\n",
    "plt.plot(g[1:] - g[:-1])\n",
    "plt.plot(0.05*u - 4)\n",
    "plt.xlim(0,500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.figure(figsize=(16,4))\n",
    "e = y_out - y_pred\n",
    "plt.plot(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.imshow(nfn._W, interpolation='nearest')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.plot(nfn._W[:,9])\n",
    "plt.plot(nfn._W[:,8])\n",
    "plt.plot(nfn._W[:,7])\n",
    "plt.plot(nfn._W[:,10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def wiener_process(n, mu=0.0, sigma=1.0):\n",
    "    y = np.zeros(n)\n",
    "    for i in range(1,n):\n",
    "        y[i] = mu + y[i-1] + sigma*np.random.randn()\n",
    "    return y\n",
    "\n",
    "\n",
    "def ARMAX_sim(ar_params=list(), \n",
    "              ma_params=list(), \n",
    "              ex_params=list(), \n",
    "              c=0, \n",
    "              u=np.zeros(1), \n",
    "              init=None, \n",
    "              n=100, \n",
    "              sigma=1.0):\n",
    "    \n",
    "    p = len(ar_params)\n",
    "    q = len(ma_params)\n",
    "    r = len(ex_params)\n",
    "    k = np.max(p, q, r)\n",
    "    \n",
    "    if init is None:\n",
    "        y = np.zeros(n)\n",
    "        y[:k] = np.random.randn(k)\n",
    "    elif len(init) == k:\n",
    "        y = np.zeros(n)\n",
    "        y[:k] = init\n",
    "    else:\n",
    "        raise Exception('Bad initials')\n",
    "        \n",
    "    e = sigma*np.random.randn(n)\n",
    "    for i in range(k, n):\n",
    "        y[i] = c + np.dot(ar_params, y[i-p:i]) + np.dot(ma_params, e[i-q:i]) + np.dot(ex_params, u[i-r:i]) + e[i]\n",
    "    return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f6ccca9df60>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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jEJmgneqxlYmh4W8PYBbn/A3O+WIAEwAcGCHdyhPimtdKA+bTT5P3WJvJ54nP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\nCKJN+H9FD58RHHW4lAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6cccb38080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 2000\n",
    "y = np.random.randn(n) #ARMAX_sim([0.8, 0.1], n=1000, sigma=0.1)\n",
    "plt.plot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X = np.zeros((n-1,n-1))\n",
    "for i in range(n-1):\n",
    "    X[i,:i+1] = y[:i+1][::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p, r, R, S = np.linalg.lstsq(X, y[1:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "y_pred = np.dot(X, p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.017468842198428286, 1.86657151124125)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.square(y[1:] - y_pred).mean(), np.square(y[1:] - y[:-1]).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.98187107816885288"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import r2_score\n",
    "\n",
    "r2_score(y_pred, y[1:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 200)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ib8VZp0TjPWM5wy0Vc8FpcVYxj2x9hO+c/U7Ccwb0tpgZz/374cQJ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6cc7202390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16,4))\n",
    "plt.plot(y_pred)\n",
    "plt.plot(y[1:])\n",
    "plt.xlim(0,200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.plot(y_pred - y[1:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n = 1000\n",
    "q = 3\n",
    "p = 3\n",
    "\n",
    "# y = ARMA_simulation(np.array([0.6, -0.4, 0.3]), 1, n = n, sigma=0.5) \n",
    "# y = np.random.randn(n) + 0.005*np.arange(n) \n",
    "# y = wiener_process(n)\n",
    "y = ARMA_simulation([0.45, 0.3, -0.2], [0.1, -0.2, 0.05], init=[4, 4, 4], n = n, sigma=0.1)\n",
    "z = np.zeros(:max(p,q))\n",
    "\n",
    "a = 0.01*np.random.randn(p)\n",
    "b = 0.01*np.random.randn(q)\n",
    "c = 0\n",
    "\n",
    "e = 0\n",
    "cache_a = np.zeros(p)\n",
    "cache_b = np.zeros(q)\n",
    "cache_c = 0\n",
    "alpha = 0.98"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "arma = ARMA(y, (3, 3))\n",
    "arma_res = arma.fit(maxiter=1000)\n",
    "arma_res.arparams, arma_res.maparams"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "e = np.mean(e) + np.zeros(n)\n",
    "e_max = 100\n",
    "step = 0.05\n",
    "\n",
    "for i in range(max(p,q),n):\n",
    "    z[i] = np.dot(a, y[i-p:i]) + np.dot(b, e[i-q:i]) + c\n",
    "    e[i] = z[i] - y[i]\n",
    "    \n",
    "    cache_a = alpha*cache_a + (1 - alpha)*np.square(y[i-p:i]*e[i])\n",
    "    cache_b = alpha*cache_b + (1 - alpha)*np.square(e[i-q:i]*e[i])\n",
    "    cache_c = alpha*cache_c + (1 - alpha)*np.square(e[i])    \n",
    "    \n",
    "    a -= (step / (1 + np.sqrt(cache_a))) * y[i-p:i]*e[i]\n",
    "    b -= (step / (1 + np.sqrt(cache_b))) * e[i-q:i]*e[i]\n",
    "    c -= (step / (1 + np.sqrt(cache_c))) * e[i]\n",
    "\n",
    "z = np.zeros(n)\n",
    "for i in range(max(p,q),n):\n",
    "    z[i] = np.dot(a, y[i-p:i]) + np.dot(b, e[i-q:i]) \n",
    "\n",
    "print(cache_a, cache_b, cache_c)\n",
    "print(a, b, c)\n",
    "print(mean_squared_error(y, z))\n",
    "print(r2_score(y, z))\n",
    "\n",
    "plt.figure(figsize=(16,3))\n",
    "plt.plot(y)\n",
    "plt.plot(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "z = np.zeros(n)\n",
    "for i in range(max(p,q),n):\n",
    "    z[i] = np.dot(a, y[i-p:i])\n",
    "\n",
    "plt.figure(figsize=(16,3))\n",
    "plt.plot(y)\n",
    "plt.plot(z)\n",
    "plt.xlim(0,200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error, r2_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.plot(acf(y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "a, b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.figure(figsize=(16,3))\n",
    "plt.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "z = ARMA_simulation(0.5*np.random.randn(2), np.random.rand(5), n=1000, sigma=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.figure(figsize=(16,4))\n",
    "plt.plot(z)\n",
    "plt.xlim(0,100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "y = 2.5*np.sin(0.0172*t + 50)\n",
    "\n",
    "Z = np.zeros((100, 100))\n",
    "i = 0\n",
    "for w in np.linspace(0.01, 0.025, 100):\n",
    "    for f in range(100):\n",
    "        z = 2.5*np.sin(w*t + f)\n",
    "        Z[i,f] = mean_squared_error(y, z)\n",
    "    i += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "best_score = 1e+27\n",
    "best_phi = 0\n",
    "\n",
    "omega = 2 * np.pi / 365.25\n",
    "\n",
    "for omega in range(1,730):\n",
    "    \n",
    "\n",
    "for phi in range(365):\n",
    "    X = np.vstack([np.ones(t.size), t, np.sin(omega*t + phi)]).T\n",
    "    theta = np.linalg.lstsq(X, g)[0]\n",
    "    y = theta[0] + theta[1]*t + theta[2]*np.sin(omega*t + phi)\n",
    "    r = mean_squared_error(g, y)\n",
    "    if r < best_score:\n",
    "        best_score = r\n",
    "        best_phi = phi\n",
    "\n",
    "omega = 2 * np.pi / 365.25\n",
    "phi = best_phi\n",
    "X = np.vstack([np.ones(t.size), t, np.sin(omega*t + phi)]).T\n",
    "theta = np.linalg.lstsq(X, g)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def periodicity(y):\n",
    "    cf = acf(y, unbiased=True, nlags=g.size // 2)\n",
    "    idx = list()\n",
    "    for i in range(1,cf.size):\n",
    "        if cf[i] * cf[i-1] < 0:\n",
    "            idx.append(i)\n",
    "    T = [idx[i] - idx[i-2] for i in range(2,len(idx))]\n",
    "    return np.mean(T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.figure(figsize=(16,4))\n",
    "for k in range(20):\n",
    "    r = np.zeros(401)\n",
    "    r[191:210] = 1 / 19\n",
    "    p = r.copy()\n",
    "    for i in range(k):\n",
    "        p = np.convolve(p,r, mode='same')\n",
    "    plt.plot(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy import signal\n",
    "import pywt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "cA, cD = pywt.dwt(t, wavelet='haar')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.plot(cA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n = 6000\n",
    "z = np.zeros(n)\n",
    "for i in range(1,n):\n",
    "    z[i] = z[i-1] + np.random.randn()\n",
    "\n",
    "k_max = 500\n",
    "cwmat = np.zeros((k_max,z.size))\n",
    "for k in range(1,k_max+1):\n",
    "    kernel = np.ones(2*k)\n",
    "    kernel[k:] = -1\n",
    "    kernel /= np.sqrt(kernel.size)\n",
    "    cwmat[k-1] = np.convolve(z, kernel, mode='same')\n",
    "    \n",
    "plt.figure(figsize=(16,4))\n",
    "plt.imshow(cwmat, aspect='auto', interpolation='nearest')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.plot(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n = 6000\n",
    "z = np.zeros(n)\n",
    "for i in range(1,n):\n",
    "    z[i] = z[i-1] + np.random.randn()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "widths = np.arange(1, 256)\n",
    "cwtmatr = signal.cwt(t, signal.ricker, widths)\n",
    "plt.figure(figsize=(16,4))\n",
    "plt.imshow(cwtmatr, aspect='auto') #, vmax = abs(cwtmatr).max(), vmin = -abs(cwtmatr).max())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.figure(figsize=(16,4))\n",
    "plt.plot(g)\n",
    "plt.xlim(0,g.size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.figure(figsize=(16,4))\n",
    "plt.plot(cwmat[6])\n",
    "plt.xlim(0,g.size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
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