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 },
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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import scipy.sparse as sp\n",
      "import scipy.sparse.linalg as alg\n",
      "import math\n",
      "from time import time\n",
      "\n",
      "import pylab as pl\n",
      "\n",
      "%pylab inline --no-import-all"
     ],
     "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": [
      "# x - bezwymiarowa siatka polozen\n",
      "\n",
      "# Stale 'rho' zadeklerowane dla ponizszych typow potencjalow to bezwymiarowe zmienne\n",
      "# z bezwymiarowego rownania Schrodingera.\n",
      "\n",
      "def rho_harmonic():\n",
      "    return 1.0\n",
      "def harmonic(x):\n",
      "    # potencjal oscylatora harmonicznego:\n",
      "    # v(x) = k * x**2 / 2\n",
      "    return x ** 2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# rozmiar macierzy pieciodiagonalnej:\n",
      "N = 1500\n",
      "    \n",
      "# konce bezwymiarowego przedzialu obustronnie domknietego [x_min,x_max]:\n",
      "x_min = -7.0\n",
      "x_max = 7.0\n",
      "\n",
      "# ilosc wartosci wlasnych i wektorow wlasnych, ktore chcemy wyznaczyc:\n",
      "N_eigvals = 4\n",
      "\n",
      "# wybor potencjalu:\n",
      "potential = harmonic\n",
      "# opcjonalne argumenty wybranego potencjalu:\n",
      "args_potential = ()\n",
      "\n",
      "# wybor parametru rho (odpowiedni dla danego potencjalu):\n",
      "#rho = rho_Konwent\n",
      "rho = rho_harmonic\n",
      "# opcjonalne argumety wejsciowe funkcji zwracajacej wartosc bezwymiarowej zmiennej rho\n",
      "args_rho = ()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def EigenvalEigenvecProblem5(N, x_min, x_max, N_eigvals, potential, *args_potential):\n",
      "    \n",
      "    \"\"\"\n",
      "    funkcja 'EigenvalEigenvecProblem5' rozwiazuje algebraiczne zagadnienie wlasne \n",
      "    wykorzystujac pieciopunktowa metode centralnych roznic skonczonych do przyblizenia \n",
      "    drugiej pochodnej.\n",
      "    \"\"\"\n",
      "    \n",
      "    # dyskretna siatka polozen, gdzie N - ilosc punktow siatki:\n",
      "    x = np.linspace(x_min, x_max, N)\n",
      "    \n",
      "    # krok dyskretnej siatki:\n",
      "    dx = (x_max - x_min) / (N - 1)\n",
      "    \n",
      "    # elementy na glownej diagonali macierzy pentadiagonalnej:\n",
      "    diagonal = 30.0 * np.ones(N) + 12.0 * dx * dx * rho(*args_rho) * potential(x, *args_potential)\n",
      "    # elementy na pierwszych diagonalach macierzy pentadiagonalnej:\n",
      "    diag_edge1 = -16.0 * np.ones(N - 1)\n",
      "    # elementy na drugich diagonalach macierzy pentadiagonalnej:\n",
      "    diag_edge2 = 1.0 * np.ones(N - 2)\n",
      "    # tablica niezerowych element\u00f3w macierzy pentadiagonalnej:\n",
      "    pentadiagonal = np.array([diag_edge2, diag_edge1, diagonal, diag_edge1, diag_edge2])\n",
      "    \n",
      "    # numery diagonali, gdzie 0 oznacza diagonale glowna, \n",
      "    # -1 -pierwsza diagonale dolna, 1 -pierwsza diagonale gorna,\n",
      "    # -2 -druga diagonale dolna, 2 - druga diagonale gorna:\n",
      "    offsets = [-2, -1, 0, 1, 2]\n",
      "    # macierz trojdiagonalna (hamiltonian) zapisana w postaci macierzy rzadkiej:\n",
      "    hamilton = sp.diags(pentadiagonal, offsets)\n",
      "        \n",
      "    start = time()\n",
      "    \n",
      "    # wyznaczenie N_eigvals wartosci wlasnych i odpowiadajacych im wektorow wlasnych\n",
      "    eigvals, eigvecs = alg.eigsh(hamilton, k = N_eigvals, which = \"SM\", tol = 1.0E-4)\n",
      "    # argument \"SM\" oznacza, \u017ce wyznaczone zostanie N_eigvals najmniejszych wartosci\n",
      "    # wlasnych i odpowiadajacych im wektorow wlasnych, a argument \"tol\" oznacza wzgledna \n",
      "    # dokladnosc, z jaka wyznaczone zostana wartosci wlasne\n",
      "    \n",
      "    # !UWAGA! Argument 'eigvecs' stanowi macierz o 'N' wierszach i 'k' kolumnach,\n",
      "    # wiec i-ty wektor wlasny ma 'i' kolumn o dlugosci 'N'.\n",
      "    \n",
      "    #print \"'alg.eigsh(...)' time: %.2fs\" % (time() - start)\n",
      "    \n",
      "    eigvals = eigvals / (12.0 * dx * dx * rho(*args_rho))\n",
      "    \n",
      "    return eigvals, eigvecs"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "eigvals_a, eigvecs_a = EigenvalEigenvecProblem5(N, x_min, x_max, N_eigvals, potential, *args_potential)\n",
      "print eigvals_a"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 1.          3.          5.          7.00000002]\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# DYSKUSJA BLEDOW\n",
      "N = 1500\n",
      "eigvals_a, eigvecs_a = EigenvalEigenvecProblem5(N, x_min, x_max, N_eigvals, potential, *args_potential)\n",
      "\n",
      "N_max = 1000\n",
      "\n",
      "N_list = range(100, N_max + 50, 50)\n",
      "measures = 5\n",
      "\n",
      "time_list = []\n",
      "digits_list = []\n",
      "\n",
      "for N in N_list:\n",
      "    eigvals_num, eigvecs_num = EigenvalEigenvecProblem5(N, x_min, x_max, N_eigvals, potential, *args_potential)\n",
      "    \n",
      "    time_start = time()\n",
      "    for m in xrange(measures):\n",
      "        EigenvalEigenvecProblem5(N, x_min, x_max, N_eigvals, potential, *args_potential)\n",
      "    exec_time = (time() - time_start) / measures\n",
      "    \n",
      "    time_list.append( exec_time )\n",
      "    digits = [-math.log10( abs( (e_num - e_a) / e_a ) )\n",
      "                  for e_num, e_a in zip(eigvals_num, eigvals_a) ]\n",
      "    digits_list.append(digits)\n",
      "    \n",
      "    print \"%d/%d/%.2f\" % (N, N_max,exec_time)\n",
      "    \n",
      "for idx in xrange(N_eigvals):\n",
      "    \n",
      "    digit_data = [digit[idx] for digit in digits_list]\n",
      "    pl.plot(N_list, digit_data, \".-\", label = \"$\\widetilde{E}_{%d}$\" % (idx+1))\n",
      "    \n",
      "pl.grid()\n",
      "pl.legend(loc = \"lower right\")\n",
      "pl.xlabel(\"$N$\", {\"fontsize\": \"xx-large\"})\n",
      "pl.ylabel(\"$l_n$\", {\"fontsize\": \"xx-large\", \"rotation\": \"horizontal\"})\n",
      "pl.savefig(\"harmonic_num_l_N.png\")\n",
      "pl.show()\n",
      "\n",
      "for idx in xrange(N_eigvals):\n",
      "    \n",
      "    digit_data = [digit[idx] for digit in digits_list]\n",
      "    pl.plot(time_list, digit_data, \".-\", label = \"$\\widetilde{E}_{%d}$\" % (idx+1))\n",
      "\n",
      "pl.grid()\n",
      "pl.legend(loc = \"lower right\")\n",
      "#pl.legend(bbox_to_anchor=(1.16, 0.7))    \n",
      "pl.xlabel(\"$t$\", {\"fontsize\": \"xx-large\"})\n",
      "pl.ylabel(\"$l_n$\", {\"fontsize\": \"xx-large\", \"rotation\": \"horizontal\"})\n",
      "pl.savefig(\"harmonic_num_l_t.png\")\n",
      "pl.show()\n",
      "\n",
      "pl.grid()\n",
      "pl.plot(N_list, [t**0.33 for t in time_list], \".-\") \n",
      "pl.xlabel(\"$N$\", {\"fontsize\": \"xx-large\"})\n",
      "pl.ylabel(\"$t^3$\", {\"fontsize\": \"xx-large\", \"rotation\": \"horizontal\"})\n",
      "pl.savefig(\"harmonic_num_t_N.png\")\n",
      "pl.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "100/1000/0.03\n",
        "150/1000/0.06"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "200/1000/0.10"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "250/1000/0.14"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "300/1000/0.23"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "350/1000/0.34"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "400/1000/0.36"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "450/1000/0.53"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "500/1000/0.65"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "550/1000/1.03"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "600/1000/0.90"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "650/1000/0.99"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "700/1000/1.14"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "750/1000/1.74"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "800/1000/1.68"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "850/1000/2.34"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "900/1000/2.74"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "950/1000/2.38"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1000/1000/2.60"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
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WA6rMQNwSVeSDWr5cZi4VGIhr12TxyOOPw9Kl4OhYaTLic3L4+epVVsXFcSI9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\nxsziYsEYY8wsLhaMMcbM+j9LUgezoNezwgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa69a0ec>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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o1vY4Vp+Ct7e0rJVboHWftZRP3ciYgwm5PonXykr0R/73v0Uyb2QkxMdD164d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\nACjEAYBCHAAoxAGAQhwAKMQBgOIPk2Em1I8zLr8AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xacef16c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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kCQMGDPD8dyr/s0qS4ZprruHKK68kJSUFYwxz5swp+JnzcqNB46Z+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\nESmR/w+07BMvlwq6xAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa6b804c>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# WYKRES WARTOSCI ENERGII DLA KOLEJNYCH POZIOMOW ENERGETYCZNYCH:\n",
      "\n",
      "N_eigvals = 4\n",
      "\n",
      "eigvals, eigvecs = EigenvalEigenvecProblem5(N, x_min, x_max, N_eigvals, potential, *args_potential)\n",
      "\n",
      "fig, ax1 = pl.subplots(figsize = (8, 5))\n",
      "ax1.set_yticklabels([])\n",
      "ax1.set_ylabel(\"$\\psi_n$\", {\"fontsize\": \"xx-large\", \"rotation\": \"horizontal\"})\n",
      "\n",
      "ax2 = ax1.twinx()\n",
      "\n",
      "num_x = len(eigvecs)\n",
      "dx = (x_max - x_min) / (num_x - 1) \n",
      "x_list = [x_min + i * dx for i in xrange(num_x)]\n",
      "print len(x_list)\n",
      "h_list = [potential(x_i) for x_i in x_list]\n",
      "ax2.plot(x_list, h_list, color = \"black\")\n",
      "\n",
      "for i in xrange(N_eigvals):\n",
      "    \n",
      "    ax2.plot([x_min, x_max], [eigvals[i],eigvals[i]], color = \"orange\")\n",
      "    ax2.plot(x_list, eigvecs[:,i] + eigvals[i], color = \"green\")\n",
      "\n",
      "\n",
      "ax2.set_xticks([x_min, x_max])\n",
      "ax2.set_xticklabels([\"$x_{min}$\", \"$x_{max}$\"])\n",
      "ax2.set_xlim(x_min, x_max)\n",
      "ax2.set_yticks(eigvals)\n",
      "ax2.set_yticklabels([\"$n = %d$\" % i for i in range(0,len(eigvals))])\n",
      "ax2.set_ylim(None, eigvals[-1] + 1)\n",
      "\n",
      "plt.savefig(\"harmonic_num_all.png\")\n",
      "pl.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1000\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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XQUOksbERJ0+exIwZM0SXQiRcv+cUeJtSxlXIf9lsNkRGRuKnn35CRESE6HLI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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa8d97ec>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# WYKRES FUNKCJI FALOWEJ:\n",
      "\n",
      "x = np.linspace(x_min, x_max, N)\n",
      "eigvals, eigvecs = EigenvalEigenvecProblem5(N, x_min, x_max, N_eigvals, potential, *args_potential)\n",
      "\n",
      "fig, ax1 = pl.subplots(figsize = (8, 5))\n",
      "ax2 = ax1.twinx()\n",
      "\n",
      "for idx in range(N_eigvals)[0:4]:\n",
      "    \n",
      "    psi = 9.0 * eigvecs[:,idx]\n",
      "    ax2.plot(x, psi + eigvals[idx], label = \"$\\psi_{%d}(x)$\" % idx, color = \"red\")\n",
      "    \n",
      "ax1.set_ylabel(\"$\\psi_n(x)$\", {\"fontsize\": \"xx-large\", \"rotation\": \"horizontal\"})\n",
      "ax1.set_yticks([])\n",
      "ax1.set_xticks([])\n",
      "ax1.set_xlabel(\"$x$\", {\"fontsize\": \"xx-large\"})\n",
      "\n",
      "ax2.set_xlim(x_min, x_max)\n",
      "ax2.set_xticklabels([x_min, x_max], [\"$x_{min}$\", \"$x_{max}$\"], size = 15)\n",
      "ax2.set_yticks(eigvals)\n",
      "ax2.set_yticklabels([\"$n = %d$\" % i for i in range(0,len(eigvals))])\n",
      "\n",
      "pl.savefig(\"harmonic_num_psi.png\")\n",
      "pl.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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zhlWrVtGnTx/Gjh2Lz+fj2LFj9O/f/y9fe/PNN9OvX790P7eIiIgERpojGnv2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\niIiIOOb/AReXOfBbz1DCAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xc0efd6c>"
       ]
      }
     ],
     "prompt_number": 50
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# WYKRES GESTOSCI PRAWDOPODOBIENSTWA: \n",
      "\n",
      "x = np.linspace(x_min, x_max, N)\n",
      "eigvals, eigvecs = EigenvalEigenvecProblem5(N, x_min, x_max, N_eigvals, potential, *args_potential)\n",
      "\n",
      "fig, ax1 = pl.subplots(figsize = (8, 5))\n",
      "ax2 = ax1.twinx()\n",
      "\n",
      "for idx in range(N_eigvals)[0:4]:\n",
      "    \n",
      "    psi = 9.0 * eigvecs[:,idx]\n",
      "    ax2.plot(x, psi ** 2 + eigvals[idx], label = \"$P_{%d}(x)$\" % idx, color = \"red\")\n",
      "    \n",
      "ax1.set_ylabel(\"$P_n(x)$\", {\"fontsize\": \"xx-large\", \"rotation\": \"horizontal\"})\n",
      "ax1.set_yticks([])\n",
      "ax1.set_xticks([])\n",
      "ax1.set_xlabel(\"$x$\", {\"fontsize\": \"xx-large\"})\n",
      "ax2.set_xlim(x_min, x_max)\n",
      "ax2.set_xticklabels([x_min, x_max], [\"$x_{min}$\", \"$x_{max}$\"], size = 15)\n",
      "\n",
      "ax2.set_yticks(eigvals)\n",
      "ax2.set_yticklabels([\"$n = %d$\" % i for i in range(0,len(eigvals))])\n",
      "\n",
      "pl.savefig(\"harmonic_num_P.png\")\n",
      "pl.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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A0SpVpPfek845x/05C1Km7t2l+vWl8eOls892f85Vq6SBA20Q6dChdn6fz/15\ngQAJl7ovjC5XAEiy7oG5c6UrrpBGjJDeekuaPz84IUOSzj/fpog2amSzV776Kjjn/T2LF0stW0q3\n3ip98EFwQoZk51ywwMawPP+8tSYtWhSccwPFCC0aQDhZtMhaMBITbSZIt26hvYqeMUO67z7pxRel\ne+8N7rk9Txo92loT3ntP6tgxuOc/3tHWpdhYG8Px4os20wcIY+FS9xE0gHAQH28BY9cu6ZlnpNtv\nD5+1Hb791roNWre2ij8iwv0509JsrMj69dLHH0sXXuj+nAVx5Ij09tvWwtG+vc3SueiiUJcKyFW4\n1H10nQCh4vdL//mP1KGDTS2NicmZRREuIUOSLr3UxiukpNiaGzt3uj3f9u0WarKzpeXLwydkSFLZ\nsjat9n//swG5rVpJt90W+u4lIIwRNIBgO3jQ1sCIirJWjLvvlr77TrrrrvCd3VCpknUd9OplYxfm\nzXNznv/8x8ZCxMRIkyeH75oeZ58tDRokbdtmYaN7d2vhmD7dWj0AHEPXCRAMfr8NsJwwQZo92yql\nRx+Vrr226M1kWLLEZqU88ID01FOBmQKbmSk9+6w0aZIFmmuuOfNjBlNmpjRtmnWrJCRId9xhwbFJ\nk6L3+0WxES51H0EDcOXwYZu1MHu29Omndt+Ru+6yVoGaNUNdujOze7f0l7/Yct/jx5/Z+9m40Vow\natSwoFHUP5vvv5fefVeaMsVaqG6+2Qb1tmxpXS9AkLiq+/x+v/7xj3/o1VdfLVg5CBpAAHieDeRc\nu9YGdsbH2w3MrrrKKpmuXc9sBc9wdOSIdR+88459feCBwnX9pKRIw4ZZUBk2zGa1FKerf8+T1q2T\nZs2yoLlli4WNtm2tu6VpUwtXgCMu6r6kpCS9++67mjJlitasWVOwchA0gAI6csSW/v7xR1uq+scf\nrY8+IcGuysuXt6byNm2sS6RlS3uuuEtIsJuSbdsm9e9v3QZ53dht1y5p7FjrZrjpJpu5Ubt28Mob\nKsnJ0tKl1oW2erX0zTc2BqVJE5u5cuGFOVutWlL16rSA4Iy4rPvat2+vRQVcV6ZEBI3zfD7tnjbt\nxCdze9snP1eQ13Cs8DpWQffz++326hkZtrT10e3o92lpVjEkJkpJSfY1I8MqgLp1bVGr88+3FTsb\nN7bFrUr61eny5dJrr9lA0ZYt7R4iF11kt2k/eNC6FBYvlrZutZk1Dz4oXXJJqEsdOp5ngXX9egtp\n27bZjJsR+vL2AAALsElEQVQdO6RffpH277cgUqOGrc5aqZJ9X7HiiVvZstaSdPxWuvSJ35cqldNa\n5OorQi4uIUFxCQnHvn/uo49OCRrx8fGaMWOG2rZtK0lKSEhQbGxsoc9VmKARpkPcA+s8yVYUPFlu\n/0FOfq4gr+FY4XWsgr6mXDlbE6JyZftjHhFhW7ly1hIRGWljEKpWta9nn80f1bxcc41thw5JCxda\nt8HSpdYSVLGidR0NH26vOeusUJc29Hw+qV4923Lj91v30r59FjoOHbJxP0e31FT7mplp4Tgr68Qt\nO/vEx1JO6A70V4SFdr9tRz2Xy2t8v/0Nq1OnjqKjozVr1qxjP9u0aZPmz5+f67FjYmIUGRl5WuUq\nES0adJ0AAEqa36v7unbtqjlz5iglJUX9+/fX+PHjC31sWjQAAMAp0tLSFPHb6r5z585Vx44dtWLF\nCrVq1SrPFo0+ffqoal5jr/JA0AAAoIRISEg4Nj6jUqVK2rp1q1q3bi1JioqKUlRUVJ77Hz58WOPG\njdPmzZs1YsQI9e3bVxUrVsxzH7pOAAAohsKl7mMJcgAA4AxBAwAAOEPQAAAAzhA0AACAMwQNAADg\nDEEDAAA4Q9AAAADOEDQAAIAzBA0AAOAMQQMAADhD0AAAAM4QNAAAgDMEDQAA4AxBAwAAOEPQAAAA\nzhA0AACAMwQNAADgDEEDAAA4Q9AAAADOEDQAAIAzBA0AAOAMQQMAADhD0AAAAM4QNAAAgDMEDQAA\n4AxBAwAAOEPQAAAAzhA0AACAMwQNAADgDEEDAAA4Q9AAAADOEDQAAIAzBA0AAOAMQQMAADhD0AAA\nAM4QNAAAgDMEDQAA4AxBAwAAOEPQAAAAzhA0AACAMwQNAADgDEEDAAA4UybUBQBQDHietGWLFB8v\nbdwoffuttGePdOCAlJEhVaggVa4sXXCBdNFFUosW0jXXSHXqhLrkABzzeZ7nhboQrvl8PpWAtwkE\nl98vLV0qffih9PHHUpkyUtu2UrNm0iWXWIioUkUqW1ZKS5OSk6Xt2y2QfPmltHy5VLOm1L271KOH\n1LRpqN8RUKyES91H0ABQOL/+Kv3739Kbb0qRkdJtt1lQuPhiyecr+HH8fgscM2ZI06ZJNWpI998v\n9expLSAAzki41H0EDQAFs2uXNGyYNHWqdPPN0kMPSVdcEZhjZ2dL8+ZZePnyS+nvf5cefFCqVCkw\nxwdKoHCp+xgMCiBve/ZIjzwiNWliLQ3ffSe9+27gQoYklS4tdekizZkjxcVJCQlSgwbSCy9Ihw8H\n7jwAgo6gASB3qanS4MFS48ZSqVLSpk3SK6/YuAqXLrtMmjzZxn9s2GDjPSZOtK4WAEUOXScATuR5\nNmbi8celli2ll1+22SKhsnKl1L+/lJ4uDR8utW8furIARUi41H0EDQA51q2zbpKUFGnkSJtFEg48\nT5o+XXriCal5c+lf/5Lq1w91qYCwFi51H10nAGwmyX33SZ07S716SWvWhE/IkGw2y1/+Im3ebGtw\nREdLTz0lHTwY6pIByAdBAyjJsrOlN96QoqJsvYvNm6V+/WxwZjiKiLCAsX69zYK59FJp0iTGbwBh\njK4ToKRautSmqFapIo0eLV1+eahLVHirVkkPP2yPR46Urr46tOUBwki41H0EDaCk2bPHxjrExdlY\nh1tvLdxCW+HG75emTJEGDrSBoi++KNWuHepSASEXLnUfXSdASXH4sDRkiLVcnH++dZPcdlvRDhmS\nTb298067v0q9eraU+Qsv2LLnAEKOoAEUd1lZ0ltv2RLhmzfbyptDh0pnnx3qkgXW2WdLzz8vrV4t\nrV1r405mzLAZKwBChq4ToLjKyrIbng0ZIp13nq2H0aJFqEsVPIsW2VLmVapIzz5r3SpFvfUGKIRw\nqfsIGkBxc+SIzcQYNszuoBobK11/fcmsZLOzbZXRYcOkqlXts+jSpWR+FihxwqXuI2gAxcVPP0nj\nxklvv23LhsfGSn/8Y6hLFR6ys60b5YUXrKXngQdsXEflyqEuGeBMuNR9jNEAirIjR6RPP7XFrC6/\n3Bbe+u9/bSNk5Chd2mbXrFsnjRljM24uuMBuS798OeM4AIdo0QCKmowMKT5e+ugjaeZMW7Tqjjts\n4wq94H76ye5CO3Wq3UCuZ0+pRw+7K20prsFQ9IVL3UfQAMJddrbdOXXJEunzz6XFi21GxS232PTU\nunVDXcKizfPsLrHvvy998om1CnXsKN1wg3TttdbywZgOFEGu6r4hQ4aoadOm2rhxo5566qn8y0HQ\nAMJIaqq0ZYutCfHNN3bn0jVrpHPPlVq3tnuRXH+9dM45oS5p8bVzpzRvnm3Ll9uCYFdfbTN2GjWy\nkNeggXTWWaEuKZAnF3XfF198oeXLl+vpp5/Wc889p+uuu07XXntt3uUgaACO+f3SgQN2R9TkZNt+\n/dWa7o/ftm+Xfv5Zuugi6w5p1Mhu037VVQSLUPE86ccfcwLf5s227dpli4Odf/6JW40aNrulWrWc\nLSIi1O8CJZSLum/w4MG64oordNNNN2n27Nlau3atnnnmmTz3KRPQEoSpxpL04IOn/iC3X0BBnytK\n+wfzXKHeP5jn8jybwZCebuMmMjJOfZyWJh06ZItJRUbmbNWq2TLZtWtboKhd2yquCy8M3xualUQ+\nn3VN1a1rg0mPSk+Xtm2zEHJ0W75c2r9fSkw8cfM8qXz53LeICPt957WVKWNfTx43cnJ3zvHfu/gZ\nwl7cTz8p7qef8nxNfHy8ZsyYoba/3Z05ISFBsbGxBT7HL7/8ogoVKkiSKlasqL179+a7T4kIGock\nu0LMTW7/kQr6XFHaP5jnCvX+wTzXWWdJ5crlbBERJz6OiLABmoSH4iUiwrpQoqLyfp3n2cygtLTc\nt/R0G4OT15aVZV+PD7snB1/XP0OR0K5hQ7U77vvnvvzylNf4fvs7VqdOHUVHR2vWrFnHfrZp0ybN\nnz8/12PHxMQoMjJSfr9fpX/7e5adnX3scV5KRNDYIeXeogEALvl8OcEzMjLUpUFJc/TOxsdp06aN\nXnrpJUVHRyslJUVlyuTEgKioKEXlE55r1aqlw4cPS5IOHDigGjVq5FuMEhE0AACAlJaWpojfxg3N\nnTtXHTt21IoVK9SqVas8WzT69OmjqlWrqk2bNlq9erW6dOmi1atXq0OHDvmek6ABAEAJkZCQcGx8\nRqVKlbR161a1bt1aUsFaNK677jrNnTtX06dPl8/nU6dOnfI9J7NOAAAohsKl7mP5OwAA4AxBAwAA\nOEPQAAAAzhA0AACAMwQNAADgDEEDAAA4Q9AAAADOEDQAAIAzBA0AAOAMQQMAADhD0AAAAM4QNAAA\ngDMEDQAA4AxBAwAAOEPQAAAAzhA0AACAMwQNAADgDEEDAAA4Q9AAAADOEDQAAIAzBA0AAOAMQQMA\nADhD0AAAAM4QNAAAgDMEDQAA4AxBAwAAOEPQAAAAzhA0AACAMwQNAADgTJlQFyBYfD5fqIsAAECJ\nUyKChud5oS4CAAAlEl0nAADAGYIGAABwhqABAACcIWgAAABnCBoAAMAZggYAAHCmRExvBRBcI0eO\nVGpqqr7++msNHjxYM2fOlOd5SkpK0vDhw0NdPABBRIsGgIAaNWqUOnfurIEDB6pTp05q166d7r77\nbmVkZGjy5MmhLh6AICNoAAiorKwsXXLJJZKkXbt2qXnz5jrvvPPUr18/xcfHh7h0AILN57FsJgBH\n2rdvrxtuuEEDBgwIdVEAhAgtGgCcyMjI0KpVq9S2bdtQFwVACBE0AARMZmamFi5cKElauXKlPM9T\ndHS0JGn//v2aOHFiKIsHIAQIGgACZty4cerSpYvS0tI0e/ZsVa9eXWXK2OS2MWPGqGvXriEuIYBg\nY4wGgIDZuHGjhg4dqgYNGqhz586aN2+eDh8+rPLly6tHjx5q1qxZqIsIIMgIGgAAwBm6TgAAgDME\nDQAA4AxBAwAAOEPQAAAAzhA0AACAMwQNAADgDEEDAAA4Q9AAAADO/D/z3/bXRSh8JAAAAABJRU5E\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb72870c>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}