{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "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": 38
    },
    {
     "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_Konwent():\n",
      "    k = 1.0\n",
      "    return 0.25 * (2 * k + 1)**2\n",
      "def Konwent(x):\n",
      "    # potencjal Konwenta: v(x) = V_c * (alpha * cosh(C*x) - 1)**2\n",
      "    # bezwymiarowy potencjal Konwenta: V(x) = ( (b / (2*k+1)) * cosh(x) - 1 ) ** 2\n",
      "    k = 1.0\n",
      "    b = 0.03   \n",
      "    return  ( (b / (2.0 * k + 1.0)) * np.cosh(x) - 1) ** 2 \n",
      "\n",
      "\n",
      "def rho_Konwent2(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 Konwent2(x):\n",
      "    # potencjal Konwenta: v(x) = V_c * (alpha * cosh(C*x) - 1)**2\n",
      "    # bezwymiarowy potencjal Konwenta: V(x) = (apha*cosh(x) - 1)**2\n",
      "    return  (c * np.cosh(x) - 1) ** 2   "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.linspace(-8.0, 8.0, 300)\n",
      "pl.ylim(0.0,5.0)\n",
      "#pl.xlim(-8.0, 8.0)\n",
      "plt.plot(x, ( (0.03 / (2.0 * 1.0 + 1.0)) * np.cosh(x) - 1) ** 2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 40,
       "text": [
        "[<matplotlib.lines.Line2D at 0xb33b12c>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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fbm4uqqqqUFZWhrKyMmRkZKCkpATp6em6S7tIcXExFi5ciNWrVyOhPVc5iCKr\nrN9XSmH69OnIycnBjBkzdJfTqnnz5qGiogJlZWVYsWIFxo4di6VLl+ou6yI9e/ZEZmYmvv32WwDA\n+vXrMWjQIM1VXWzgwIHYunUrvF4vlFJYv349cnJy2rx/yCOOQF555RU8/PDDOHv2LBITE/HKK69E\n4mkjatq0aZg2bRry8vLQqVMnU36TXcjML9UfeeQR+Hw+FBYWAgBGjhyJ3/3ud5qrElZZv79lyxYs\nW7YMgwcPRkFBAQBZgnWjiXfhMvP35OLFizF58mT4fD70798fS5Ys0V3SRfLz8zFlyhRcddVViImJ\nwdChQ3H//fe3ef8OXfKKiIiix7yHZYmIHI4BTURkUgxoIiKTYkATEZkUA5qIyKQY0EREJvX/HOH3\n4AqXMGYAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb33b04c>"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "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 = -8.0\n",
      "x_max = 8.0\n",
      "\n",
      "# ilosc wartosci wlasnych i wektorow wlasnych, ktore chcemy wyznaczyc:\n",
      "N_eigvals = 3\n",
      "\n",
      "# wybor potencjalu:\n",
      "potential = Konwent\n",
      "# opcjonalne argumenty wybranego potencjalu:\n",
      "args_potential = ()\n",
      "\n",
      "# wybor parametru rho (odpowiedni dla danego potencjalu):\n",
      "rho = rho_Konwent\n",
      "# opcjonalne argumety wejsciowe funkcji zwracajacej wartosc bezwymiarowej zmiennej rho\n",
      "args_rho = ()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 41
    },
    {
     "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": 44
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# DYSKUSJA BLEDOW:\n",
      "\n",
      "eigvals_a, eigvecs_a = EigenvalEigenvecProblem5(N, x_min, x_max, N_eigvals, potential, *args_potential)\n",
      "\n",
      "print eigvals_a\n",
      "\n",
      "N_list = range(100, 800, 200)\n",
      "measures = 5\n",
      "\n",
      "# blad wzgledny:\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",
      "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)\n",
      "    \n",
      "pl.legend(bbox_to_anchor=(1.16, 0.7))\n",
      "pl.xlabel(\"$N^2$\", {\"fontsize\": \"xx-large\"})\n",
      "pl.ylabel(\"$l_n$\", {\"fontsize\": \"xx-large\", \"rotation\": \"horizontal\"})\n",
      "pl.xlim(None,1000)\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)\n",
      "    \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.xlim(None,1000)\n",
      "pl.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.55525592  0.55565556  1.00049965]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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AdnZ22NraAuDl5UVmZiY3btwwd4nCFDIyYMECcHXVPj9+XOt5FPHgyFE5/Bj3I8+ueZYe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\nN2FlQghRdBlzn0ex32F+ISm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       "text": [
        "<matplotlib.figure.Figure at 0xb863f0c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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gX79+ePXVVzFo0CAAQGpqKuLi4pCUlITBgwejvLwcmzdvRmRk5D3f8LPPPsPE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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb346fcc>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.55525591  0.55565555  1.00049964]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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92LrVnJcA+PprePBBmzexcnMsoUtHci3/QV4LnMG4ru21ulpEHE7F4m6cPg0v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\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb45538c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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pnw6+5NMwYO2Ph/l8bQxxR2M44b6Gkpl3E1A6hLDGIQzr2BYPd3erY4o4FQ0N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\nFQIRESf3/3ZpnEda9719AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xad16b6c>"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# WYKRES ZALEZNOSCI ENERGII DLA KOLEJNYCH POZIOMOW ENERGETYCZNYCH:\n",
      "\n",
      "eigvals, eigvecs = EigenvalEigenvecProblem5(N, x_min, x_max, N_eigvals, potential, *args_potential)\n",
      "\n",
      "\n",
      "\n",
      "fig, ax1 = pl.subplots()\n",
      "ax1.set_xticklabels([])\n",
      "ax1.set_yticklabels([])\n",
      "ax1.set_xlabel(\"\")\n",
      "ax1.set_ylabel(\"$E_n$\", {\"fontsize\": \"xx-large\", \"rotation\": \"horizontal\"})\n",
      "ax1.set_xlim(x_min, x_max)\n",
      "\n",
      "ax2 = ax1.twinx()\n",
      "ax2.set_xticklabels([])\n",
      "#ax2.plot((eigvals), \"o-\")\n",
      "for eigval in eigvals:\n",
      "    ax2.plot([eigvals[0],eigvals[-1]], [eigval,eigval], \"b\")\n",
      "ax2.set_yticks(eigvals)\n",
      "ax2.set_yticklabels([\"$n = %d$\" % i for i in range(0,len(eigvals))])\n",
      "\n",
      "#pl.plot(x, x ** 2)\n",
      "\n",
      "#pl.savefig(\"num_har_E.png\")\n",
      "pl.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAADtCAYAAABzqDgeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nFwDSiQsA6f4D5GgnfZXYQBkAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xabb9ccc>"
       ]
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.linspace(x_min, x_max, N)\n",
      "\n",
      "# WYKRES FUNKCJI FALOWEJ:\n",
      "\n",
      "pl.figure(figsize = (10, 6))\n",
      "\n",
      "shift = 0.24\n",
      "\n",
      "for idx in range(N_eigvals)[0:3]:\n",
      "    \n",
      "    psi = eigvecs[:,idx]\n",
      "    pl.plot(x, psi + idx * shift, label = \"$\\psi_{%d}(x)$\" % idx)\n",
      "    \n",
      "pl.legend(bbox_to_anchor=(1.16, 0.7))\n",
      "pl.xlabel(\"$x$\", {\"fontsize\": \"xx-large\"})\n",
      "pl.ylabel(\"$\\psi_i(x)$\", {\"fontsize\": \"xx-large\", \"rotation\": \"horizontal\"})\n",
      "pl.xlim(x_min, x_max)\n",
      "#pl.ylim(-shift, shift * N_eigvals)\n",
      "pl.xticks([x_min, 0.0, x_max], [\"$x_{min}$\", \"$0.0$\", \"$x_{max}$\"], size = 15)\n",
      "pl.yticks([])\n",
      "#plt.savefig(\"num_harr_psi3.png\")\n",
      "pl.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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hIOQW1yH0Au5o1y5pwQLpp59Md4gaNUwAvukmqXNnqUwZuysEci8z0/RrX7bMhNzly6V6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\nvZ+Xl1jy86/dv+MOUwiycLNQSNq/31wkCgRMAN6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       "text": [
        "<matplotlib.figure.Figure at 0xa86274c>"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# WYKRES GESTOSCI PRAWDOPODOBIENSTWA:\n",
      "\n",
      "pl.figure(figsize = (10, 6))\n",
      "\n",
      "#shift2 = shift**2\n",
      "shift2 = 0.012\n",
      "\n",
      "for idx in range(N_eigvals)[0:4]:\n",
      "    \n",
      "    psi = eigvecs[:,idx]\n",
      "    pl.plot(x, psi**2 + idx * shift2, label = \"$P_{%d}(x)$\" % idx)\n",
      "    \n",
      "pl.legend(bbox_to_anchor=(1.16, 0.7))\n",
      "pl.xlabel(\"$x$\", {\"fontsize\": \"xx-large\"})\n",
      "pl.ylabel(\"$P_i(x)$\", {\"fontsize\": \"xx-large\", \"rotation\": \"horizontal\"})\n",
      "#pl.xlim(x_min, x_max)\n",
      "#pl.ylim(-shift2, shift2 * N_eigvals)\n",
      "pl.xticks([x_min, 0.0, x_max], [\"$x_{min}$\", \"$0.0$\", \"$x_{max}$\"], size = 15)\n",
      "pl.yticks([])\n",
      "#pl.savefig(\"num_harr_P3.png\")\n",
      "pl.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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x0vh14K/ouKYj3Cq7oXH5xrJLIiJ6Lr2ix6ido+BVzwv96/WXXU6mIpoi8O3m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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xac66cac>"
       ]
      }
     ],
     "prompt_number": 49
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}