clustering 2.ipynb

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      "choosing gaps :\n",
      "1) total range = (least value greater than cut,greatest value)\n",
      "2) start with the longest gap\n",
      "3) at each step use the longest gap with the center at opposite sign of sum[centers(position from the center of total interval)]\n",
      "4) stop when average of \"var\" starts(?) to increase\n",
      "        var for a bunch = (#gaps)*sum(gap_size**2)/bunch_size**2 (if bunch_size != 0)\n",
      "        ? = when average(var) increases two times in a row\n",
      "        don't stop if number of hits in a bunch is greater than number of layers\n",
      "        I have assumed that each track has at least 2 hits ( to be a track ! )\n",
      "input -> an array of NN output values (sorted ascendingly from cut) + # of layers\n",
      "we also need a matrix for all gaps (may be large though, in the real case)\n",
      "        each row of which is : [length(end-start),center((start+end)/2.0),starting line index]\n",
      "clustering_coefficient (positive) -> greater values for more clusters and 0 for no clustering (one cluster)\n",
      "output -> a matrix -> each row : [starting index of a bunch,ending index of a bunch]"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
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     "input": [
      "in_array = []\n",
      "for i in range (7):\n",
      "    for j in range (int(uniform(2,5))):\n",
      "        in_array.append(numpy.random.normal(10*(i+1),1))\n",
      "in_array = sorted(in_array)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "clustering_coefficient = 1\n",
      "n_layers = 5\n",
      "n_lines = len(in_array)\n",
      "n_gaps = n_lines - 1\n",
      "interval_center = (in_array[n_lines - 1] + in_array[0])/2.0\n",
      "\n",
      "gap_matrix = np.zeros((n_gaps,3),dtype=float32)\n",
      "length_array = np.zeros(n_gaps,dtype=float32)\n",
      "for i in range (n_gaps) :\n",
      "    gap_matrix[i][2] = i\n",
      "    gap_matrix[i][1] = (in_array[i+1] + in_array[i])/2.0 - interval_center\n",
      "    length_array[i] = in_array[i+1] - in_array[i]\n",
      "    if gap_matrix[i][1] < 0 :\n",
      "        gap_matrix[i][0] = in_array[i+1] - in_array[i]\n",
      "    else :\n",
      "        gap_matrix[i][0] = in_array[i] - in_array[i+1]\n",
      "# sorting gap_matrix ascendingly by gap lengths\n",
      "gap_matrix.view('f32,f32,f32').sort(order=['f0'], axis=0)\n",
      "length_array = sorted(length_array)\n",
      "counter = 0\n",
      "for i in range(n_gaps):\n",
      "    if length_array[i] > 0.5*length_array[n_gaps-1] :\n",
      "        counter += 1\n",
      "print \"\\t\" , counter\n",
      "\n",
      "out_matrix = np.zeros((int(n_lines),2),dtype=int32)\n",
      "\n",
      "# var receives indices of first and last line in the bunch and returns val as defined above\n",
      "def var (start1 = 0,end1 = n_gaps) :\n",
      "    start = int(start1)\n",
      "    end = int(end1)\n",
      "    sum_square = 0.0\n",
      "    for i in range (start,end) :\n",
      "        sum_square += (in_array[i+1] - in_array[i])**2\n",
      "    return (end-start) * sum_square / (in_array[end] - in_array[start])\n",
      "\n",
      "sgn = 0\n",
      "# some unreadable code : !!!        (maybe I add some comments later)\n",
      "\n",
      "# finds the interval(start and ending line indices) that we are going to check whether can be separated or not\n",
      "def find_interval (accepted_gaps) :\n",
      "    interval = np.zeros(2,dtype=int8)\n",
      "    interval[1] = n_gaps\n",
      "    Gl_sgn = (-1)**(accepted_gaps%2)\n",
      "    Gl_index = int(Gl_sgn*(accepted_gaps/2) + (accepted_gaps%2)*(n_gaps-1))\n",
      "    for i in range (accepted_gaps) :\n",
      "        sgn = (-1)**(i%2)\n",
      "        index = int(sgn*i + (i%2)*(n_gaps-1))\n",
      "        if gap_matrix[index][1] > gap_matrix[Gl_index][1] and in_array[int(gap_matrix[index][2])] < in_array[interval[1]] :\n",
      "            interval[1] = int(gap_matrix[index][2])\n",
      "        if gap_matrix[index][1] < gap_matrix[Gl_index][1] and in_array[int(gap_matrix[index][2])+1] > in_array[interval[0]] :\n",
      "            interval[0] = int(gap_matrix[index][2] + 1)\n",
      "    return interval\n",
      "\n",
      "def adding_gaps () :\n",
      "    refused_gaps = 0\n",
      "    accepted_gaps = 0\n",
      "    while refused_gaps < 2 and accepted_gaps < n_gaps:\n",
      "        interval = np.zeros(2,dtype=int8)\n",
      "        interval = find_interval(accepted_gaps)\n",
      "        Gl_sgn = (-1)**(accepted_gaps%2)\n",
      "        Gl_index = int(Gl_sgn*(accepted_gaps/2) + (accepted_gaps%2)*(n_gaps-1))\n",
      "        un_spr = var(interval[0],interval[1]) # var for unseperated interval\n",
      "        piece1 = piece2 = 2*un_spr + 1\n",
      "        if in_array[int(interval[0])] != in_array[int(gap_matrix[Gl_index][2])] :\n",
      "            piece1 = var(interval[0],gap_matrix[Gl_index][2])\n",
      "        if in_array[int(gap_matrix[Gl_index][2])+1] != in_array[int(interval[1])] :\n",
      "            piece2 = var(gap_matrix[Gl_index][2]+1,interval[1])\n",
      "        if (piece1+piece2) >= clustering_coefficient * 2 * un_spr and (interval[1] - interval[0]) < n_layers :\n",
      "            refused_gaps += 1\n",
      "            gap_matrix[Gl_index][1] = in_array[n_gaps]\n",
      "            continue\n",
      "        else :\n",
      "            accepted_gaps += 1\n",
      "    return accepted_gaps\n",
      "\n",
      "accepted_gaps = adding_gaps()\n",
      "\n",
      "for i in range (accepted_gaps-1,n_gaps) :\n",
      "    sgn = (-1)**(i%2)\n",
      "    index = sgn*i/2 + (i%2)*(n_gaps-1)\n",
      "    gap_matrix[index][1] = in_array[n_gaps]\n",
      "gap_matrix.view('f32,f32,f32').sort(order=['f1'], axis=0)\n",
      "out_matrix [0] = [0,gap_matrix[0][2]]\n",
      "out_matrix [accepted_gaps] = [gap_matrix[accepted_gaps-1][2]+1,n_gaps]\n",
      "for bunch in range (1,accepted_gaps) :\n",
      "    out_matrix [bunch] = [int(gap_matrix[bunch-1][2]+1),int(gap_matrix[bunch][2])]\n",
      "print \"number of bunches \\t\" , accepted_gaps + 1\n",
      "for i in range (len(out_matrix)) :\n",
      "    for j in range (2) :\n",
      "        if i == 0 or out_matrix[i][j] != 0 :\n",
      "            print in_array[out_matrix[i][j]]\n",
      "    print \"\\t\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\t6\n",
        "number of bunches \t7\n",
        "9.50690843257\n",
        "11.5089097959\n",
        "\t\n",
        "19.9596884015\n",
        "20.2800042505\n",
        "\t\n",
        "29.9421156996\n",
        "31.0790614414\n",
        "\t\n",
        "38.9630906084\n",
        "41.2374877766\n",
        "\t\n",
        "49.4338674217\n",
        "49.6042108866\n",
        "\t\n",
        "58.3844830551\n",
        "60.5672221324\n",
        "\t\n",
        "67.8427220281\n",
        "70.4218320833\n",
        "\t\n",
        "\t\n",
        "\t\n",
        "\t\n",
        "\t\n",
        "\t\n",
        "\t\n",
        "\t\n",
        "\t\n",
        "\t\n",
        "\t\n",
        "\t\n",
        "\t\n",
        "\t\n",
        "\t\n",
        "\t\n"
       ]
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     "prompt_number": 3
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     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.hist([val for val in in_array],bins = 100)"
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        "         67.98523514,  68.59438437,  69.20353361,  69.81268285,  70.42183208]),\n",
        " <a list of 100 Patch objects>)"
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       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7faf34055510>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.hist([val for val in length_array],bins = 100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "(array([ 1.,  1.,  2.,  1.,  3.,  0.,  2.,  1.,  0.,  1.,  0.,  0.,  0.,\n",
        "         1.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
        "         1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
        "         0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
        "         0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
        "         0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,\n",
        "         0.,  0.,  0.,  1.,  0.,  0.,  1.,  0.,  0.,  1.,  0.,  0.,  1.,\n",
        "         0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.]),\n",
        " array([ 0.00992372,  0.1064456 ,  0.20296747,  0.29948935,  0.39601122,\n",
        "         0.4925331 ,  0.58905497,  0.68557685,  0.78209872,  0.8786206 ,\n",
        "         0.97514248,  1.07166435,  1.16818623,  1.2647081 ,  1.36122998,\n",
        "         1.45775185,  1.55427373,  1.65079561,  1.74731748,  1.84383936,\n",
        "         1.94036123,  2.03688311,  2.13340498,  2.22992686,  2.32644873,\n",
        "         2.42297061,  2.51949249,  2.61601436,  2.71253624,  2.80905811,\n",
        "         2.90557999,  3.00210186,  3.09862374,  3.19514562,  3.29166749,\n",
        "         3.38818937,  3.48471124,  3.58123312,  3.67775499,  3.77427687,\n",
        "         3.87079874,  3.96732062,  4.0638425 ,  4.16036437,  4.25688625,\n",
        "         4.35340812,  4.44993   ,  4.54645187,  4.64297375,  4.73949563,\n",
        "         4.8360175 ,  4.93253938,  5.02906125,  5.12558313,  5.222105  ,\n",
        "         5.31862688,  5.41514875,  5.51167063,  5.60819251,  5.70471438,\n",
        "         5.80123626,  5.89775813,  5.99428001,  6.09080188,  6.18732376,\n",
        "         6.28384564,  6.38036751,  6.47688939,  6.57341126,  6.66993314,\n",
        "         6.76645501,  6.86297689,  6.95949876,  7.05602064,  7.15254252,\n",
        "         7.24906439,  7.34558627,  7.44210814,  7.53863002,  7.63515189,\n",
        "         7.73167377,  7.82819565,  7.92471752,  8.0212394 ,  8.11776127,\n",
        "         8.21428315,  8.31080502,  8.4073269 ,  8.50384877,  8.60037065,\n",
        "         8.69689253,  8.7934144 ,  8.88993628,  8.98645815,  9.08298003,\n",
        "         9.1795019 ,  9.27602378,  9.37254566,  9.46906753,  9.56558941,\n",
        "         9.66211128]),\n",
        " <a list of 100 Patch objects>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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LDvW9wOZl65s5dOS+riQ5Afg08Kmquqnvfnr0UuDiJP8FXAf8dpJre+6pL3uA+6vqrm79\nRuCcHvvp028BX62qR7rp2s8AL++5p749nGQjQJLnsPS80ESLDvWnHl7qAu3NLE32rzvdX3J2NXBv\nVV3Rdz99qqoPVdXmqnoe8PvAv1XVH/TdVx+qag/w/SS/1m16NfDNHlvq038CL0nytO798upu23p2\n4OFOuv/eNu2AaU+UHpaVHl5a5DWPYi9j6X/KPUl2dNv+vKo+32NPR4v1Pk33DuCT3df3vgOsyymH\nqroryY0sfYngSWAH8Hf9dnXkJLkOuADYmGQP8JfAFuD6JG8HHmRpYDz5PD58JEnt8J+zk6SGGOqS\n1BBDXZIaYqhLUkMMdUlqiKEuSQ0x1CWpIYa6JDXk/wGIMKUPvG1TVQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7faf340557d0>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def separating_point (length_array,x1,x2) :\n",
      "    for i in range (len(length_array)):\n",
      "        if abs(length_array[i] - x1) > abs(x2 - length_array[i]) :\n",
      "            return i\n",
      "mean1 = length_array[0]\n",
      "mean2 = length_array[len(length_array)-1]\n",
      "everything_is_ok = True\n",
      "def accepted_gaps (length_array) :\n",
      "    while everything_is_ok :\n",
      "        sum1 = 0\n",
      "        sum2 = 0\n",
      "        s = separating_point(length_array,mean1,mean2)\n",
      "        for i in range (s) :\n",
      "            sum1 += length_array[i]\n",
      "        x1 = sum1 / float(s)\n",
      "        for i in range (s,len(length_array)) :\n",
      "            sum2 += length_array[i]\n",
      "        x2 = sum2 / float(len(length_array)-s)\n",
      "        if mean1 != x1 or mean2 != x2 :\n",
      "            mean1 = x1\n",
      "            mean2 = x2\n",
      "        else :\n",
      "            everything_is_ok = False\n",
      "    return len(length_array)-separating_point(length_array,mean1,mean2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "6\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}