{
 "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": 31
    },
    {
     "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_infWell():\n",
      "    return 1.0\n",
      "def infWell(x):\n",
      "    # potencjal nieskonczonej studni:\n",
      "    # v(x) = 0\n",
      "    return np.zeros_like(x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 32
    },
    {
     "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 = 3.0\n",
      "\n",
      "# ilosc wartosci wlasnych i wektorow wlasnych, ktore chcemy wyznaczyc:\n",
      "N_eigvals = 4\n",
      "\n",
      "# wybor potencjalu:\n",
      "potential = infWell\n",
      "# opcjonalne argumenty wybranego potencjalu:\n",
      "args_potential = ()\n",
      "\n",
      "# wybor parametru rho (odpowiedni dla danego potencjalu):\n",
      "#rho = rho_Konwent\n",
      "rho = rho_infWell\n",
      "# opcjonalne argumety wejsciowe funkcji zwracajacej wartosc bezwymiarowej zmiennej rho\n",
      "args_rho = ()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "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": 34
    },
    {
     "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": [
        "[ 0.27348194  1.09392776  2.46133745  4.37571102]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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7GUkpuFuRSBpPGg/z8x/MpjZtUrw9qIxzCCFgYWGB5OTk6ve0BIAlS5agRYsW8PPzQ+fO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\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xad856cc>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Hx2PixIkPLGQZGRmYNWsW9uzZc18hI/01txWLy9hWJCJZMejMTBAETJkyBY6OjlixYkWL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\nGRERmbz/D8SU686v2TKjAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb55ac0c>"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "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",
      "#plt.savefig(\"num_har_E.png\")\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.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.linspace(x_min, x_max, N)\n",
      "eigvals, eigvecs = EigenvalEigenvecProblem5(N, x_min, x_max, N_eigvals, potential, *args_potential)\n",
      "\n",
      "# WYKRES FUNKCJI FALOWEJ:\n",
      "\n",
      "shift = 0.3\n",
      "\n",
      "fig, ax1 = pl.subplots()\n",
      "\n",
      "#ax1.set_figure(figsize = (10, 6))\n",
      "\n",
      "\n",
      "for idx in range(N_eigvals)[0:4]:\n",
      "    \n",
      "    psi = eigvecs[:,idx]\n",
      "    ax1.plot(x, psi + idx * shift, label = \"$\\psi_{%d}(x)$\" % idx)\n",
      "    \n",
      "#pl.legend(bbox_to_anchor=(1.16, 0.7))\n",
      "ax1.set_xlabel(\"$x$\", {\"fontsize\": \"xx-large\"})\n",
      "ax1.set_ylabel(\"$\\psi_n(x)$\", {\"fontsize\": \"xx-large\", \"rotation\": \"horizontal\"})\n",
      "ax1.set_xlim(x_min, x_max)\n",
      "#pl.ylim(-shift, shift * N_eigvals)\n",
      "ax1.set_xticklabels([x_min, 0.0, x_max], [\"$x_{min}$\", \"$0.0$\", \"$x_{max}$\"], size = 15)\n",
      "ax1.set_yticklabels([])\n",
      "\n",
      "ax2 = ax1.twinx()\n",
      "ax2.set_xticklabels([])\n",
      "ax2.set_yticks(eigvals)\n",
      "ax2.set_yticklabels([\"$n = %d$\" % i for i in range(0,len(eigvals))])\n",
      "\n",
      "#plt.savefig(\"num_harr_psi3.png\")\n",
      "pl.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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+dXS2XVFZGQCodjV/Uj4ltZ0ML1IdvSRhU0oKVl2/jiSdDo+7uWGwiwt87e3LF9O9XlKC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\nRESqw/AiIiLV+X+9N3YvgzXWPwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xc64480c>"
       ]
      }
     ],
     "prompt_number": 109
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.linspace(x_min, x_max, N)\n",
      "eigvals, eigvecs = EigenvalEigenvecProblem5(N, x_min, x_max, N_eigvals, potential, *args_potential)\n",
      "\n",
      "\n",
      "# WYKRES FUNKCJI FALOWEJ:\n",
      "\n",
      "pl.figure(figsize = (10, 6))\n",
      "\n",
      "shift = 0.3\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(\"$\\psi_n(x)$\", {\"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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Us2fPLD+3S5cueuKJJ3J0fgDZk5aeppd/eVlDfh6iBT0WqF/97C9x6Qjda3dX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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xbd75b6c>"
       ]
      }
     ],
     "prompt_number": 90
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pl.figure(figsize = (10, 6))\n",
      "x = np.linspace(-3.0, 9.0, 300)\n",
      "pl.ylim(0.0,2.0)\n",
      "#pl.xlim(0.0, 200.0)\n",
      "pl.plot(x, (1.0 - np.exp(-x)) ** 2)\n",
      "#plt.plot(np.exp(-2.0 * x) - 2.0 * np.exp(-x))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 388,
       "text": [
        "[<matplotlib.lines.Line2D at 0xedf83ac>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0xedf832c>"
       ]
      }
     ],
     "prompt_number": 388
    },
    {
     "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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RokVYv349FH3YmV+zZg1UKhWWLl16znMMvXISColDQ2vXihAwciSweLFoFMeM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\nbkkcohfATfN6Jbd77sPrlYqKph+FhfGXFxSEgzY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       "text": [
        "<matplotlib.figure.Figure at 0xe2af22c>"
       ]
      }
     ],
     "prompt_number": 310
    }
   ],
   "metadata": {}
  }
 ]
}