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 },
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 "worksheets": [
  {
   "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": 11
    },
    {
     "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_Morse(m, V_c, C, h):\n",
      "    # 1/C - stala o wymiarze dlugosci\n",
      "    # m - masa czastki\n",
      "    # V_c - charakterystyczna energia\n",
      "    # h - stala Diraca\n",
      "    return 2.0 * m * V_c / (C * C * h * h)\n",
      "def rho_Morse2():\n",
      "    return 25.0\n",
      "def Morse(x):\n",
      "    # potencjal Morse'a: v(x) = V_c * ( exp(-2*c*x) - 2*exp(-c*x) )   \n",
      "    # bezwymiarowy potencjal Morse'a: V(x) = exp(-2*x) - 2*exp(-x)   \n",
      "    #return np.exp(-2.0 * x) - 2.0 * np.exp(-x)\n",
      "    return (1.0 - np.exp(-x)) ** 2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "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 = -3.0\n",
      "x_max = 9.0\n",
      "\n",
      "# ilosc wartosci wlasnych i wektorow wlasnych, ktore chcemy wyznaczyc:\n",
      "N_eigvals = 3\n",
      "\n",
      "# wybor potencjalu:\n",
      "potential = Morse\n",
      "# opcjonalne argumenty wybranego potencjalu:\n",
      "args_potential = ()\n",
      "\n",
      "# wybor parametru rho (odpowiedni dla danego potencjalu):\n",
      "#rho = rho_Konwent\n",
      "rho = rho_Morse2\n",
      "# opcjonalne argumety wejsciowe funkcji zwracajacej wartosc bezwymiarowej zmiennej rho\n",
      "args_rho = ()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "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": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "eigvals_a, eigvecs_a = EigenvalEigenvecProblem5(N, x_min, x_max, N_eigvals, potential, *args_potential)\n",
      "\n",
      "print eigvals_a"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.19  0.51  0.75]\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "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(\"morse_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(\"morse_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(\"morse_num_t_N.png\")\n",
      "pl.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "100/1000/0.23\n",
        "150/1000/0.39"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "200/1000/0.44"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "250/1000/0.37"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "300/1000/0.56"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "350/1000/0.68"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "400/1000/1.00"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "450/1000/0.82"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "500/1000/1.10"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "550/1000/1.30"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "600/1000/1.45"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "650/1000/1.22"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "700/1000/2.01"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "750/1000/1.60"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "800/1000/2.03"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "850/1000/2.78"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "900/1000/2.08"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "950/1000/2.66"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1000/1000/2.98"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Kxcc/+LWjVo9SfuP8VLcF3VTImRAVuCZQOU90VoOWDlLBUcHKbDZnvfjECaX+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\ntGjRgp9++olZs2YxZcoUatW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6desASEpKIigoCF9fX4YPH05UVBQbN27k448/zl1Wa7Dq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\nFSgAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb4c2f2c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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UnVS/8QZ07lx1Am595uNcuT6Ph7MH285tK6/4swqzmNRlEg8NfIhvZnyDj6vP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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb32440c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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6vv9+mDgRSvzlPvmJJ+C77/SYkL/uE0Jo0schjPTBB7p/47HHrH3fWrX047qb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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xaf4c12c>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# WYKRES WARTOSCI ENERGII DLA KOLEJNYCH POZIOMOW ENERGETYCZNYCH:\n",
      "\n",
      "N_eigvals = 5\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",
      "\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",
      "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",
      "    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",
      "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] + 0.2)\n",
      "\n",
      "pl.savefig(\"morse_num_all.png\")\n",
      "pl.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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eepzj144TkxZDXEYcakc1DX0bliw+DenXoB/1vOsR5B6Eva0MdhTC1Cz3k0sY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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb87a2ec>"
       ]
      }
     ],
     "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",
      "\n",
      "for idx in range(N_eigvals)[0:5]:\n",
      "    \n",
      "    psi = eigvecs[:,idx]\n",
      "    ax2.plot(x, psi + eigvals[idx], label = \"$\\psi_{%d}(x)$\" % idx, color = \"red\")\n",
      "    \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_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",
      "ax2.set_yticks(eigvals)\n",
      "ax2.set_yticklabels([\"$n = %d$\" % i for i in range(0,len(eigvals))])\n",
      "\n",
      "pl.savefig(\"morse_num_psi.png\")\n",
      "pl.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ffgi8/bZMRDTXL8SUFKmauWgRQ4YaKlWSYmGNGxft9QaDhI3ERNkx986d/I+U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\npB/XAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb2f096c>"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "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)[0:5]:\n",
      "    \n",
      "    psi = 3.0 * 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",
      "\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",
      "plt.savefig(\"morse_num_P.png\")\n",
      "pl.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KiorUvXt3SdLu3bsVHR2t9u3b6+6771ZKSoqfSwegrnm8nDYTgCOX\nX365rrrqKo0fP97fRQHgJ7RoAHCioKBAq1atUv/+/f1dFAB+RNAA4DOFhYVauHChJGnlypXyer2K\niYmRJGVkZGj27Nn+LB4APyBoAPCZGTNmaOjQocrLy9N7772nyMhINWlik9umTZumuLg4P5cQQF1j\njAYAn9m4caOeeuopdenSRUOGDNFHH32knJwcBQcHa/jw4erVq5e/iwigjhE0AACAM3SdAAAAZwga\nAADAGYIGAABwhqABAACcIWgAAABnCBoAAMAZggYAAHCGoAEAAJz5f+PtSjRdnvQZAAAAAElFTkSu\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xc1cb36c>"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}