{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy.spatial.distance as spd\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline\n",
      "\n",
      "# used to compare energy before and after a move\n",
      "# we assumed that epsilon and alpha are 1\n",
      "def local_energy(site):\n",
      "    local_sum = 0\n",
      "    for i in xrange(len(system)):\n",
      "        if site != i:\n",
      "            tempx = system[site][0] - system[i][0]\n",
      "            tempy = system[site][1] - system[i][1]\n",
      "            if tempx > 100./2:\n",
      "                tempx = 100. - tempx\n",
      "            if tempy > 100./2:\n",
      "                tempy = 100. - tempy\n",
      "            #r = spd.euclidean(system[i][0],system[j][0])\n",
      "            dist = np.sqrt(tempx**2+tempy**2)\n",
      "            #dist = spd.euclidean(system[site],system[i])\n",
      "            local_sum += -((1/dist)**12-(1/dist)**6)\n",
      "    return local_sum\n",
      "\n",
      "# total energy of the system\n",
      "def system_energy():\n",
      "    total_sum = 0\n",
      "    for i in xrange(len(system)):\n",
      "        total_sum += local_energy(i)\n",
      "    return total_sum\n",
      "\n",
      "def radial_number_density():\n",
      "    rad_dist = []\n",
      "    for i in xrange(len(system)):\n",
      "        for j in xrange(len(system)):\n",
      "            if i != j:\n",
      "                temp = spd.euclidean(system[i],system[j])\n",
      "                rad_dist.append(temp)\n",
      "    return rad_dist\n",
      "\n",
      "n = 100 # number of particles\n",
      "# initializing the system\n",
      "# the atoms occupy a square of size 10X10\n",
      "system = np.zeros([n,2])\n",
      "for i in xrange(len(system)):\n",
      "    system[i][0] = i%10 # np.sqrt(n) wont work as it will return a float\n",
      "    system[i][1] = i/10 # we need an integer denominator for this to work!\n",
      "\n",
      "global_energy = []\n",
      "accepted_moves = 0\n",
      "\n",
      "plt.subplot(131)\n",
      "alist = radial_number_density()\n",
      "anarray = np.asarray(alist)\n",
      "plt.hist(anarray,10);\n",
      "\n",
      "initial_dist = radial_number_density()\n",
      "\n",
      "T = 1.\n",
      "# T = np.array([5.,5./2,1./1./2,1./10])\n",
      "beta = 1./T\n",
      "# B = 1./T\n",
      "#for beta in B:\n",
      "for time in xrange(5000):\n",
      "    site = np.random.choice(np.arange(n)) # atom to be moved\n",
      "    # this atom can now move in the range (-alpha,alpha) in x & y\n",
      "    #xmove = np.random.choice(np.array([-2.,-5./3,-4./3,-1,-2./3,-1./3,0,1./3,2./3,1.,4./3,5./3,2.]))\n",
      "    #ymove = np.random.choice(np.array([-2.,-5./3,-4./3,-1,-2./3,-1./3,0,1./3,2./3,1.,4./3,5./3,2.]))\n",
      "    #xmove = np.random.choice(np.array([0,1./3,2./3,1.,4./3,5./3,2.]))\n",
      "    #ymove = np.random.choice(np.array([0,1./3,2./3,1.,4./3,5./3,2.]))\n",
      "    xmove = np.random.choice(np.array([0.,1.,2.,3.,4.]))\n",
      "    ymove = np.random.choice(np.array([0.,1.,2.,3.,4.]))\n",
      "    pre_move_e = local_energy(site)\n",
      "    system[site] = system[site] + np.array([xmove,ymove])\n",
      "    if system[site][0] > 100 :\n",
      "        system[site][0] = system[site][0]%100\n",
      "    #if system[site][0] < 0 :\n",
      "    #    system[site][0] = system[site][0]%100\n",
      "    if system[site][1] > 100 :\n",
      "        system[site][1] = system[site][1]%100\n",
      "    #if system[site][1] < 0 :\n",
      "    #    system[site][1] = system[site][1]%100\n",
      "    post_move_e = local_energy(site)\n",
      "    if post_move_e - pre_move_e < 0:\n",
      "        global_energy.append(system_energy())\n",
      "        accepted_moves += 1\n",
      "    else :\n",
      "        temp = np.random.random()\n",
      "        if temp < np.exp(-beta*(post_move_e - pre_move_e)):\n",
      "            global_energy.append(system_energy())\n",
      "            accepted_moves += 1\n",
      "        else :\n",
      "            system[site] = system[site] - np.array([xmove,ymove])\n",
      "            global_energy.append(system_energy())\n",
      "# we get global_energy, accepted moves as the outputs here.\n",
      "plt.subplot(132)\n",
      "alist = radial_number_density()\n",
      "anarray = np.asarray(alist)\n",
      "plt.hist(anarray,10);\n",
      "plt.subplot(133)\n",
      "plt.plot(global_energy)\n",
      "print \"accepted_moves\", accepted_moves\n",
      "final_dist = radial_number_density()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "accepted_moves 4438\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "-c:21: RuntimeWarning: divide by zero encountered in double_scalars\n",
        "-c:21: RuntimeWarning: invalid value encountered in double_scalars\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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CfAOfQ3BoGT6H4Mr6+ByCa7miXwGBBx4ALlyQrVpyAp9DICKvwOsIvoOpK4jIabNnAxER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\nmawNLlN+6F0AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb0e1006c>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#print plt.hist(final_dist)[0], plt.hist(final_dist)[1]\n",
      "temp_array_range_initial = plt.hist(initial_dist)[1]\n",
      "temp_array_number_initial = plt.hist(initial_dist)[0]\n",
      "for i in xrange(len(temp_array_range_initial)-1):\n",
      "    denominator = temp_array_range_initial[i+1]**2 - temp_array_range_initial[i]**2\n",
      "    temp_array_number_initial[i] = temp_array_number_initial[i]/denominator\n",
      "#######\n",
      "temp_array_range_final = plt.hist(final_dist)[1]\n",
      "temp_array_number_final = plt.hist(final_dist)[0]\n",
      "for i in xrange(len(temp_array_range_final)-1):\n",
      "    denominator = temp_array_range_final[i+1]**2 - temp_array_range_final[i]**2\n",
      "    temp_array_number_final[i] = temp_array_number_final[i]/denominator\n",
      "plt.cla()\n",
      "#plt.plot(temp_array_number_initial,'o',temp_array_number_final,'.')\n",
      "plt.plot(temp_array_number_final)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "[<matplotlib.lines.Line2D at 0xb0ee022c>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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vvpn58+dbzZSfn8+pU6cAOH36NB9++KH1GULx8fG0a9eOnTt3Aqbf261bN6uZ\nLrVgwQLGjRtnOwZgRqsbN27kzJkzOI7DqlWrPNHKO3ToEAA5OTm8++675beDavI0ctmyZU7nzp2d\njh07OjNnzqzJpVwzduxYp3Xr1k69evWchIQE5/XXX7cdycnMzHR8Pp+TkpLipKamOqmpqc7y5cut\nZvr888+dtLQ0JyUlxenevbvz7LPPWs3zY4FAwBOzOHbv3u2kpKQ4KSkpTrdu3Tzz73zbtm1O7969\nnR49ejgjRozwzCyOvLw8p0WLFs7JkydtR7lg1qxZTlJSkpOcnOxMmjTJKSgosB3J6d+/v5OUlOSk\npKQ4q1evLvd9WqgiIuJR3nlULiIipahAi4h4lAq0iIhHqUCLiHiUCrSIiEepQIuIeJQKtIiIR6lA\ni4h41P8DXLNAvf1OS7UAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb0f91d2c>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = []\n",
      "y = []\n",
      "for i in xrange(len(system)):\n",
      "    x.append(system[i][0])\n",
      "    y.append(system[i][1])\n",
      "plt.scatter(x,y);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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8f/3rX+XYsWOycOHC6LKJ4jVi3okVv5Z5M+1J/2Z//OMf5amnnhIRkY0bN0og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\nIrIRJn0iIhth0icispH/D0F+IBNm4QViAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb31ef86c>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "instead of calling system_energy() at every mcstep, calculating system_energy using system_energy += diff, where diff = post_move_e - pre_move_e"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy.spatial.distance as spd\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline\n",
      "\n",
      "# used to compare energy before and after a move\n",
      "# we assumed that epsilon and alpha are 1\n",
      "def local_energy(site):\n",
      "    local_sum = 0\n",
      "    for i in xrange(len(system)):\n",
      "        if site != i:\n",
      "            dist = spd.euclidean(system[site],system[i])\n",
      "            local_sum += -((1/dist)**12-(1/dist)**6)\n",
      "    return local_sum\n",
      "\n",
      "# total energy of the system\n",
      "def system_energy():\n",
      "    total_sum = 0\n",
      "    for i in xrange(len(system)):\n",
      "        total_sum += local_energy(i)\n",
      "    return total_sum\n",
      "\n",
      "def radial_number_density():\n",
      "    rad_dist = []\n",
      "    for i in xrange(len(system)):\n",
      "        for j in xrange(len(system)):\n",
      "            if i != j:\n",
      "                temp = spd.euclidean(system[i],system[j])\n",
      "                rad_dist.append(temp)\n",
      "    return rad_dist\n",
      "\n",
      "n = 100 # number of particles\n",
      "# initializing the system\n",
      "# the atoms occupy a square of size 10X10\n",
      "system = np.zeros([n,2])\n",
      "for i in xrange(len(system)):\n",
      "    system[i][0] = i%10 # np.sqrt(n) wont work as it will return a float\n",
      "    system[i][1] = i/10 # we need an integer denominator for this to work!\n",
      "\n",
      "global_energy = []\n",
      "global_energy.append(system_energy())\n",
      "energy_now = system_energy() ####\n",
      "accepted_moves = 0\n",
      "\n",
      "plt.subplot(131)\n",
      "alist = radial_number_density()\n",
      "anarray = np.asarray(alist)\n",
      "plt.hist(anarray,10);\n",
      "\n",
      "T = 1.\n",
      "# T = np.array([5.,5./2,1./1./2,1./10])\n",
      "beta = 1./T\n",
      "# B = 1./T\n",
      "#for beta in B:\n",
      "for time in xrange(5000):\n",
      "    site = np.random.choice(np.arange(n)) # atom to be moved\n",
      "    # this atom can now move in the range (-alpha,alpha) in x & y\n",
      "    #xmove = np.random.choice(np.array([-2.,-5./3,-4./3,-1,-2./3,-1./3,0,1./3,2./3,1.,4./3,5./3,2.]))\n",
      "    #ymove = np.random.choice(np.array([-2.,-5./3,-4./3,-1,-2./3,-1./3,0,1./3,2./3,1.,4./3,5./3,2.]))\n",
      "    #xmove = np.random.choice(np.array([0,1./3,2./3,1.,4./3,5./3,2.]))\n",
      "    #ymove = np.random.choice(np.array([0,1./3,2./3,1.,4./3,5./3,2.]))\n",
      "    xmove = np.random.choice(np.array([0.,1.,2.,3.,4.]))\n",
      "    ymove = np.random.choice(np.array([0.,1.,2.,3.,4.]))\n",
      "    pre_move_e = local_energy(site)\n",
      "    system[site] = system[site] + np.array([xmove,ymove])\n",
      "    if system[site][0] > 100 :\n",
      "        system[site][0] = system[site][0]%100\n",
      "    #if system[site][0] < 0 :\n",
      "    #    system[site][0] = system[site][0]%100\n",
      "    if system[site][1] > 100 :\n",
      "        system[site][1] = system[site][1]%100\n",
      "    #if system[site][1] < 0 :\n",
      "    #    system[site][1] = system[site][1]%100\n",
      "    post_move_e = local_energy(site)\n",
      "    diff = post_move_e - pre_move_e ###\n",
      "    if post_move_e - pre_move_e < 0:\n",
      "        energy_now += diff ####\n",
      "        global_energy.append(energy_now) ####\n",
      "        accepted_moves += 1\n",
      "    else :\n",
      "        temp = np.random.random()\n",
      "        if temp < np.exp(-beta*(post_move_e - pre_move_e)):\n",
      "            energy_now += diff ####\n",
      "            global_energy.append(energy_now) ####\n",
      "            accepted_moves += 1\n",
      "        else :\n",
      "            system[site] = system[site] - np.array([xmove,ymove])\n",
      "            global_energy.append(energy_now) ####\n",
      "# we get global_energy, accepted moves as the outputs here.\n",
      "plt.subplot(132)\n",
      "alist = radial_number_density()\n",
      "anarray = np.asarray(alist)\n",
      "plt.hist(anarray,10);\n",
      "plt.subplot(133)\n",
      "plt.plot(global_energy)\n",
      "print \"accepted_moves\", accepted_moves"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "accepted_moves 4390\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Itb74tMvIaDRi6NCheOSRRzB27Fg8+uijuHz5Murr66FQKAAACoUC9fX1AIDa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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb0f9ac0c>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = []\n",
      "y = []\n",
      "for i in xrange(len(system)):\n",
      "    x.append(system[i][0])\n",
      "    y.append(system[i][1])\n",
      "plt.scatter(x,y);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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73/8uDodDuru7ZcuWLdLS0iIiIj6fL/p/MKqdO3fK2rVrZfny5SIipop//fr1\n8uyzz4qIyKVLlyQUCpkm/mAwKAsWLJCLFy+KiEhdXZ3s27fP0PH//ve/l+PHj0t5eXl022TxGjHv\nxIpfy7yZ9qR/rd/+9rfygx/8QEREtm/fLj6fL/qcx+ORt99+W6/QJvXWW2+Jx+OJPh4/Wsnovve9\n70lnZ6eUlJRIf3+/iES+GEpKSnSObHI9PT1SVVUlb7zxhixbtkxExDTxh0IhWbBgwYTtZon//Pnz\n4nA4ZHBwUC5duiTLli2Tjo4Ow8cfDAbHJM3J4jVq3hkf/7XU5k1dF1wz46Suc+fOYd68edHHRo0z\nljNnzuC9997D7bffjoGBAdjtdgCA3W7HwMCAztFN7pFHHsGOHTuiM8ABmCb+YDCIWbNmYcOGDVi0\naBHuv/9+fPHFF6aJPzc3Fw0NDZg/fz5uvvlmzJgxA4qimCb+UZPFa5a8cy21eTMlSV9RFFRUVEz4\neeWVV6KvMeukLiPGFI/PP/8cq1atwq5du3DDDTeMec5msxn2c7366quYPXs2XC4XZJIxB0aO//Ll\nyzh+/Dg2b96M48eP46tf/Sp8Pt+Y1xg5/g8//BBPPvkkzpw5g97eXnz++ed4/vnnx7zGyPHHcr14\njfxZtMibSQ/ZnEpnZ+eUz+/btw+HDh3C66+/Ht02d+5c9PT0RB+fPXsWc+fOTUV4qoyPs6enZ8w3\nrRFdunQJq1atwrp167BixQoAkdpOf38/5syZg76+PsyePVvnKGN766230NbWhkOHDuHixYv47LPP\nsG7dOtPEn5+fj/z8fNx6660AgHvvvRderxdz5swxRfzvvvsu7rrrLsycORMAUFtbi7fffts08Y+a\n7HgxS94BtMubaW/e8fv92LFjBw4ePIivfOUr0e01NTXYv38/wuEwgsEgTp8+jdtuuy3d4V3X4sWL\ncfr0aZw5cwbhcBgHDhxATU2N3mFNSkSwadMmOJ1OPPzww9HtNTU1aG1tBQC0trZGvwyMZvv27ejp\n6UEwGMT+/fvx7W9/G88995xp4p8zZw7mzZuHU6dOAQAOHz6MsrIyLF++3BTxl5aW4ujRoxgaGoKI\n4PDhw3A6naaJf9Rkx4tZ8o6meVOjfoe4FRUVyfz58+WWW26RW265RX74wx9Gn2tubpbCwkIpKSkR\nv9+f7tDidujQIXE4HFJYWCjbt2/XO5wpvfnmm2Kz2aSysjL6N3/ttdfk/PnzUlVVJcXFxaIoily4\ncEHvUK9sB82fAAAAjElEQVQrEAhER++YKf73339fFi9eLN/4xjdk5cqVEgqFTBV/S0uLOJ1OKS8v\nl/Xr10s4HDZ0/KtXr5abbrpJsrKyJD8/X/bs2TNlvEbLO+Pjf/bZZzXNm5ycRURkIbxdIhGRhTDp\nExFZCJM+EZGFMOkTEVkIkz4RkYUw6RMRWQiTPhGRhTDpExFZyP8CE7pUSl9q2CgAAAAASUVORK5C\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb0ef3a6c>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def local_energy(site):\n",
      "    local_sum = 0\n",
      "    for i in xrange(len(system)):\n",
      "        if site != i:\n",
      "            tempx = system[site][0] - system[i][0]\n",
      "            tempy = system[site][1] - system[i][1]\n",
      "            if tempx > 50:\n",
      "                if temp y > 50 :\n",
      "                    \n",
      "            dist = spd.euclidean(system[site],system[i])\n",
      "            local_sum += -((1/dist)**12-(1/dist)**6)\n",
      "    return local_sum"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}