Sparse_Linear_Separation_Problem_Solution.ipynb

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      "name": "Sparse Linear Separation Problem Solution",
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        "# Q.2\n",
        " \n",
        "import numpy as np\n",
        "import cvxpy as cp\n",
        "#from numpy import array\n",
        "#from numpy.linalg import norm\n",
        "import matplotlib.pyplot as plt\n",
        " \n",
        "X = np.array([[13.2,    -0.6,   10.9,   10.5,   12.0,   17.3,   18.7,   14.9,   16.9,   14.2,   15.8,   16.4,   6.3,    9.1,    17.2,   11.7,   10.2,   12.2,   8.7,    18.0,   11.8,   21.9,   23.7,   12.5,   14.0,   9.2,    20.3,   19.9,   13.3,   4.5,    22.8,   17.0,   13.4,   18.7,   17.6,   6.3,    12.4,   11.0,   12.6,   15.7,   21.7,   22.3,   18.2,   7.9,    21.3,   9.1,    4.7,    17.9,   18.5,   21.8], [\n",
        "24.1,   14.7,   11.6,   12.2,   -6.4,   16.3,   10.6,   16.3,   9.1,    9.3,    11.0,   18.5,   9.9,    11.2,   11.6,   13.3,   5.8,    6.1,    13.6,   13.3,   -2.8,   3.7,    5.6,    7.4,    7.5,    -2.1,   3.1,    -5.5,   11.3,   11.5,   4.8,    7.9,    10.3,   21.9,   27.0,   3.0,    9.6,    7.1,    7.1,    -4.8,   10.2,   20.9,   10.9,   0.1,    22.2,   3.5,    5.1,    16.4,   13.5,   9.5], [\n",
        "11.3,   5.4,    -0.5,   15.0,   1.7,    6.0,    -6.7,   4.9,    13.4,   0.3,    0.4,    -6.5,   5.2,    12.5,   9.0,    9.9,    11.4,   -2.1,   8.8,    2.3,    0.7,    -4.3,   16.7,   -1.7,   15.0,   8.0,    8.7,    4.6,    5.5,    19.3,   1.6,    1.8,    12.2,   -5.6,   -1.9,   9.4,    4.0,    19.9,   6.8,    -10.2,  9.9,    -4.6,   10.5,   4.0,    4.7,    4.5,    2.2,    4.8,    -0.6,   21.3], [\n",
        "8.7,    0.3,    18.7,   10.5,   16.8,   1.1,    -6.9,   12.9,   10.4,   -0.2,   9.1,    7.2,    11.1,   -6.8,   14.6,   10.8,   14.7,   21.0,   17.5,   0.8,    7.4,    17.6,   3.6,    13.0,   16.5,   12.2,   12.7,   7.6,    18.9,   11.3,   4.3,    8.7,    2.0,    0.3,    6.4,    15.4,   -7.6,   12.2,   9.7,    11.3,   -0.2,   3.8,    12.5,   10.9,   3.0,    25.6,   7.7,    1.0,    5.3,    3.0], [\n",
        "-17.4,  -18.8,  -8.0,   -20.5,  3.2,    -15.0,  -10.1,  -14.5,  -6.3,   -14.7,  -21.2,  -23.8,  -15.7,  -14.6,  -27.6,  -6.2,   -15.0,  -15.5,  -7.6,   -3.6,   -13.7,  -16.0,  -8.0,   -25.7,  -4.8,   -9.6,   -18.0,  -12.5,  -11.1,  -4.9,   -0.4,   -3.4,   -10.4,  -17.3,  -3.4,   -7.7,   -1.5,   -8.4,   4.8,    -27.6,  -13.8,  -5.2,   -11.7,  -10.7,  -9.4,   -18.8,  -15.5,  -16.5,  -13.9,  -1.6], [\n",
        "7.0,    8.3,    9.3,    -7.0,   2.8,    10.8,   -11.0,  -2.8,   -8.1,   -13.6,  -11.4,  10.2,   -10.7,  -0.2,   -1.8,   -6.9,   8.4,    -6.8,   -17.9,  -7.6,   -12.2,  -3.7,   -11.6,  -4.5,   -5.6,   7.7,    10.0,   9.6,    -10.6,  7.0,    0.4,    3.2,    7.5,    2.9,    4.5,    -0.2,   11.4,   -8.9,   -16.1,  14.0,   9.5,    -6.4,   -15.2,  -5.6,   3.7,    5.6,    2.6,    6.3,    3.5,    6.4], [\n",
        "-8.9,   -15.8,  -8.8,   -9.4,   -11.0,  -13.8,  -5.4,   -2.8,   -11.0,  -12.0,  -9.1,   -6.2,   -18.3,  -9.2,   -12.3,  -14.9,  -12.6,  -7.9,   -9.3,   -12.6,  -22.7,  -17.4,  -14.0,  -7.7,   -11.0,  -22.9,  -10.4,  -9.1,   -17.5,  -16.8,  -5.7,   -12.9,  -10.6,  -2.9,   -20.1,  -18.7,  -14.0,  -20.2,  -18.7,  -10.0,  -5.0,   -25.3,  -6.7,   -12.0,  -14.9,  -8.2,   -11.5,  -12.8,  -20.3,  -15.9], [\n",
        "-18.8,  -13.5,  -10.7,  -22.1,  -24.4,  -6.6,   -18.8,  -21.0,  -8.0,   -9.8,   -16.2,  -10.8,  -12.1,  -10.6,  -5.3,   -14.8,  -12.2,  -27.2,  -6.5,   -23.5,  -10.3,  -11.7,  -21.5,  -10.4,  -19.6,  -5.8,   -16.9,  -23.3,  -10.3,  -16.2,  -25.3,  -23.5,  -4.8,   -8.1,   -9.0,   -18.5,  -13.0,  -8.4,   -5.7,   -6.9,   -20.5,  -18.5,  -18.1,  -13.2,  -21.4,  -16.7,  -24.2,  -15.5,  -23.0,  -20.0], [\n",
        "21.3,   5.4,    3.1,    2.0,    5.8,    14.6,   5.9,    -0.0,   6.4,    24.5,   2.6,    3.2,    18.1,   -0.4,   9.4,    18.4,   13.6,   6.1,    32.9,   16.4,   9.3,    15.1,   22.1,   2.1,    30.5,   13.8,   9.8,    8.4,    11.9,   12.1,   10.9,   5.8,    -2.5,   8.2,    13.4,   21.0,   14.8,   4.6,    15.5,   9.5,    9.5,    -2.9,   -9.9,   16.0,   20.5,   14.4,   7.8,    10.2,   3.4,    12.8], [\n",
        "3.8,    11.4,   -7.5,   8.3,    -19.2,  -4.3,   -0.4,   -0.2,   4.7,    -3.5,   -1.9,   -1.5,   -5.3,   -3.5,   2.5,    4.4,    12.1,   1.7,    -0.1,   -1.6,   -4.2,   -4.3,   4.8,    -0.1,   -8.8,   -4.1,   -9.1,   5.8,    4.2,    -2.9,   -3.2,   -3.4,   -1.4,   0.1,    -4.1,   -1.9,   -1.1,   -2.8,   -1.5,   -10.2,  -0.9,   -12.7,  -0.1,   -1.7,   0.9,    4.6,    -11.4,  -2.6,   -7.0,   7.1], [\n",
        "18.2,   1.6,    15.0,   12.8,   9.2,    21.2,   23.8,   15.5,   24.7,   22.7,   20.2,   14.8,   17.1,   18.1,   14.6,   9.8,    11.7,   16.6,   20.8,   17.1,   15.0,   7.6,    12.5,   5.7,    27.3,   23.7,   7.4,    7.9,    14.9,   22.3,   15.8,   -3.8,   13.7,   5.1,    7.0,    9.4,    1.4,    16.0,   19.7,   12.3,   11.6,   12.8,   26.9,   14.2,   6.6,    7.5,    15.2,   7.9,    0.8,    19.5], [\n",
        "11.2,   2.2,    2.6,    17.7,   -1.4,   -2.1,   24.5,   15.9,   15.0,   8.0,    9.2,    12.4,   3.3,    5.1,    4.8,    5.6,    13.7,   10.4,   -0.8,   16.8,   14.5,   4.9,    13.5,   20.9,   -4.8,   9.5,    1.3,    7.9,    -1.0,   10.9,   18.8,   6.3,    9.6,    9.8,    11.7,   0.2,    16.1,   -4.6,   4.7,    10.7,   12.1,   13.3,   8.9,    13.4,   30.2,   8.7,    9.3,    11.3,   -8.1,   16.8], [\n",
        "16.4,   8.5,    10.1,   11.8,   -5.1,   14.3,   7.9,    13.7,   25.5,   15.0,   12.3,   11.8,   12.5,   26.9,   20.5,   4.9,    16.7,   -3.1,   12.2,   11.9,   6.7,    3.7,    8.7,    -5.5,   5.4,    3.2,    15.7,   16.0,   9.3,    17.9,   3.6,    14.1,   25.7,   12.6,   9.1,    12.8,   16.4,   27.1,   12.9,   12.8,   6.4,    8.8,    15.4,   21.0,   11.6,   -10.0,  17.6,   18.4,   11.9,   23.1], [\n",
        "15.3,   19.0,   -5.9,   13.0,   -4.6,   8.9,    -12.1,  -5.3,   7.8,    1.2,    1.1,    -7.0,   -0.4,   -2.8,   -9.0,   2.4,    -15.0,  -0.0,   -5.3,   3.2,    -0.3,   -9.4,   -1.5,   -1.8,   -4.4,   -5.9,   1.4,    -0.2,   2.7,    3.9,    -6.4,   5.4,    -15.8,  -13.9,  4.7,    8.1,    6.5,    -20.5,  -8.2,   -23.4,  2.5,    4.6,    -14.9,  -7.9,   8.1,    -0.2,   7.8,    1.4,    -8.1,   0.7], [\n",
        "3.6,    8.2,    18.4,   2.9,    -3.8,   13.7,   10.1,   -8.8,   -2.2,   4.7,    12.6,   11.8,   9.3,    4.1,    22.5,   -6.7,   0.7,    7.3,    -3.5,   7.6,    -1.5,   11.0,   4.9,    14.0,   -0.2,   -4.0,   14.1,   -3.5,   -4.8,   -3.2,   5.1,    2.7,    9.5,    23.9,   7.9,    -1.3,   5.1,    4.2,    5.0,    11.7,   12.7,   5.7,    17.8,   -2.2,   19.4,   5.8,    -1.5,   24.7,   9.3,    0.8], [\n",
        "-9.1,   -3.0,   5.5,    -3.0,   11.6,   6.9,    -24.6,  -12.6,  -11.8,  -5.5,   -16.8,  -9.3,   -4.9,   -6.2,   -8.9,   -7.3,   -12.9,  -11.0,  -16.3,  -8.6,   -15.8,  -4.5,   -1.7,   -4.7,   4.5,    1.4,    3.0,    -10.4,  1.8,    -3.9,   -5.1,   -19.8,  -14.3,  -22.1,  -13.5,  -1.8,   1.1,    -9.6,   -10.4,  -20.3,  -12.6,  -2.9,   -3.9,   -17.9,  -19.1,  -9.2,   -1.2,   -2.0,   -5.6,   2.1], [\n",
        "-12.9,  7.6,    -5.6,   2.8,    -1.8,   0.8,    -17.3,  0.6,    0.5,    -16.2,  -7.4,   -2.2,   -2.3,   -10.9,  -8.4,   -12.3,  -7.3,   -13.1,  -7.6,   -10.3,  -11.2,  -9.2,   -5.5,   -6.0,   11.6,   1.3,    5.1,    -3.4,   -1.9,   3.9,    -0.2,   2.6,    -14.3,  2.8,    -6.4,   -6.6,   -10.6,  0.0,    -17.4,  8.2,    12.6,   -8.1,   -0.8,   -21.0,  -9.7,   14.6,   4.6,    -6.1,   4.3,    -9.8], [\n",
        "-14.8,  -19.4,  -16.1,  -13.4,  -28.5,  -22.5,  -7.7,   -15.5,  -23.0,  -18.8,  -18.9,  -3.1,   -17.6,  -22.7,  -8.2,   -15.0,  -2.8,   -1.8,   -11.6,  -3.5,   -5.0,   -7.8,   -17.1,  0.7,    -20.7,  2.0,    -21.7,  -8.9,   -14.3,  -25.4,  -12.3,  -28.7,  -20.4,  -9.0,   -12.9,  -21.8,  -27.4,  -16.0,  -17.6,  -15.8,  -7.5,   2.3,    -3.9,   -15.0,  -4.7,   -14.8,  -21.3,  -16.9,  -23.3,  -7.8], [\n",
        "-15.4,  -3.6,   -5.4,   -15.7,  -7.6,   -18.5,  -6.2,   -15.5,  -19.8,  -7.2,   -21.3,  -16.8,  -16.7,  -14.9,  -21.5,  -17.1,  -18.1,  -0.1,   -13.6,  -11.8,  -9.8,   -16.1,  -15.6,  -19.2,  2.8,    -19.6,  -11.9,  -23.7,  -17.5,  -11.1,  -13.7,  -9.2,   -23.1,  -14.1,  -17.5,  -2.4,   -23.0,  -8.4,   -9.3,   -17.2,  -20.6,  -24.1,  -10.8,  -9.6,   -20.8,  -9.9,   -14.9,  -18.4,  -10.5,  -18.2], [\n",
        "3.3,    26.0,   11.4,   13.6,   5.8,    5.2,    11.8,   5.0,    2.0,    6.8,    -2.1,   21.7,   3.6,    2.5,    19.2,   7.9,    0.8,    17.0,   -0.3,   8.9,    1.9,    14.4,   6.2,    16.3,   -0.5,   -2.7,   17.0,   -2.4,   -4.1,   0.9,    3.5,    10.1,   7.7,    18.8,   17.1,   7.6,    5.2,    8.0,    5.9,    17.8,   -1.8,   10.6,   15.2,   8.2,    9.0,    22.0,   3.8,    15.4,   16.2,   -6.4], [\n",
        "-17.0,  -19.2,  -15.9,  -20.9,  -14.1,  -7.5,   -41.9,  -11.0,  -26.3,  -27.6,  -12.2,  -23.8,  -19.5,  -18.3,  -8.0,   -20.2,  -18.6,  -27.9,  -11.5,  -22.6,  -21.2,  -13.4,  -16.0,  -24.4,  -7.6,   -19.2,  0.8,    -11.1,  -11.2,  -14.2,  -19.8,  -17.4,  -22.0,  -18.1,  -11.6,  -14.8,  -22.0,  2.3,    -20.1,  -23.6,  -15.0,  -16.0,  -7.0,   -20.0,  -38.6,  -28.2,  -18.7,  -17.8,  -13.3,  -20.1], [\n",
        "-2.3,   -4.9,   -8.6,   -8.6,   -15.1,  -16.0,  8.4,    -7.4,   13.0,   -4.7,   -2.4,   -0.5,   1.5,    4.5,    2.5,    4.2,    2.1,    -1.7,   5.0,    -3.0,   0.7,    4.4,    -9.2,   2.1,    -3.3,   -6.1,   -12.1,  -4.9,   -5.2,   -9.3,   -3.0,   0.5,    5.0,    1.9,    -4.7,   -4.6,   -7.5,   1.7,    1.1,    -2.5,   1.4,    -8.1,   -1.5,   5.0,    -6.9,   7.6,    0.9,    2.3,    -6.4,   -4.6], [\n",
        "-14.7,  -3.4,   -18.6,  -13.9,  -14.9,  -12.2,  -22.3,  -13.6,  -12.9,  -9.8,   -17.9,  -11.8,  -22.6,  -7.6,   -21.6,  -8.8,   -16.3,  -14.9,  -22.5,  -22.5,  -18.2,  -12.1,  -5.7,   -24.5,  -28.2,  -20.0,  -1.9,   -5.5,   -15.9,  -19.2,  -12.6,  0.8,    -10.1,  -24.7,  -11.3,  -15.1,  1.6,    -17.3,  -22.2,  -32.5,  -16.2,  -15.4,  -25.6,  0.4,    0.9,    -24.6,  -6.6,   -9.8,   -11.4,  -0.6], [\n",
        "-2.4,   -34.1,  -22.2,  -21.1,  -30.5,  -16.5,  -11.6,  -19.1,  -6.4,   -9.5,   -14.7,  -9.1,   3.9,    -0.6,   -8.1,   -11.3,  -2.3,   -19.2,  -13.8,  -15.8,  -7.6,   -5.0,   -18.8,  -14.5,  -10.9,  -13.6,  -15.2,  -8.0,   -14.6,  -10.3,  -13.1,  -12.9,  4.4,    -12.4,  -15.8,  -9.8,   -12.0,  -23.6,  -14.4,  -6.0,   -4.1,   -14.7,  -18.8,  10.1,   -8.0,   -11.1,  -3.8,   -2.0,   -14.1,  -8.7], [\n",
        "16.3,   20.2,   -8.5,   -0.9,   -10.2,  2.8,    16.1,   9.3,    10.0,   3.3,    16.1,   6.4,    10.7,   15.0,   0.2,    -1.8,   18.7,   7.8,    1.4,    -0.4,   20.0,   3.2,    8.7,    2.0,    8.6,    -10.8,  7.2,    14.3,   2.0,    3.4,    12.7,   18.7,   4.4,    14.8,   8.0,    6.8,    4.4,    5.6,    -4.7,   16.7,   20.8,   8.1,    -8.4,   9.1,    -1.7,   4.9,    5.7,    9.8,    15.2,   -2.0], [\n",
        "-8.8,   3.5,    -11.9,  11.7,   -9.7,   -18.9,  2.0,    -9.7,   -10.7,  -4.0,   -14.4,  -7.8,   -14.9,  -10.5,  -9.0,   -1.8,   -21.6,  1.6,    -10.0,  -1.9,   -14.0,  -4.8,   -16.8,  1.0,    -7.8,   -14.7,  -16.9,  -5.0,   -15.1,  -13.7,  -10.8,  -8.8,   -21.3,  -11.4,  -16.0,  -6.2,   -15.1,  -23.6,  -8.3,   -11.4,  -12.0,  -12.3,  -8.9,   -4.4,   -16.8,  -1.4,   -2.8,   -10.8,  -15.3,  -8.2], [\n",
        "-36.7,  -19.5,  -24.9,  -21.7,  -9.6,   -16.9,  -11.4,  -31.7,  -13.7,  -14.5,  -9.3,   -17.6,  -7.2,   -19.8,  -18.4,  -17.9,  -12.4,  -21.7,  -21.2,  -24.5,  1.6,    -11.2,  -0.3,   -27.1,  -11.7,  -4.9,   -19.3,  -11.7,  -8.6,   -33.9,  -12.6,  -6.8,   -20.9,  -12.3,  -25.5,  -9.7,   -21.1,  -8.8,   -12.3,  -1.7,   -6.7,   -17.3,  -7.5,   -18.9,  -15.4,  -27.7,  -22.3,  -27.7,  -16.2,  -19.8], [\n",
        "-9.9,   -4.4,   -0.4,   -10.4,  -13.7,  5.2,    -11.5,  -2.1,   -5.7,   -14.2,  -4.3,   -9.6,   -9.9,   3.8,    -11.9,  -13.7,  -15.4,  -14.9,  -23.0,  -10.6,  -7.7,   -6.4,   -20.5,  0.4,    -17.5,  -6.8,   -4.8,   -2.5,   -16.5,  -8.0,   -14.1,  -2.9,   -4.1,   -11.2,  -7.0,   -20.2,  -7.1,   -12.6,  -18.8,  2.8,    -10.4,  -8.6,   -11.3,  -5.0,   -10.8,  -8.5,   -2.3,   -5.9,   -13.2,  -18.3], [\n",
        "-2.6,   -4.6,   -2.2,   -7.5,   -2.7,   -1.0,   10.7,   2.2,    -11.9,  -0.8,   -1.4,   -1.1,   -6.1,   -8.1,   -12.2,  -5.3,   0.7,    -8.3,   11.0,   -2.9,   -2.7,   -6.1,   8.4,    -22.1,  5.3,    -10.1,  -6.9,   2.9,    -1.0,   -0.5,   -7.2,   -1.2,   -13.1,  2.2,    3.3,    -8.9,   -5.9,   -0.2,   -0.5,   -10.3,  -0.9,   -5.4,   -7.0,   1.2,    -3.0,   -20.2,  0.2,    -7.6,   -11.3,  5.9], [\n",
        "-10.2,  -5.1,   6.0,    -9.7,   -7.6,   4.3,    -0.6,   -9.1,   -2.4,   -9.2,   -24.7,  -3.3,   -11.3,  12.3,   -11.2,  -8.0,   -10.2,  -12.9,  -9.0,   -8.2,   -4.8,   11.5,   -2.7,   -9.4,   5.7,    -11.4,  0.4,    -11.0,  -2.3,   -13.1,  -0.2,   -4.4,   -6.9,   -13.8,  0.8,    -4.2,   -9.6,   0.6,    -3.6,   -7.5,   -9.0,   -4.3,   -9.2,   4.3,    -16.4,  -18.3,  -3.6,   -1.5,   -8.5,   -11.6], [\n",
        "1.8,    -5.1,   1.8,    4.9,    5.0,    8.7,    10.2,   18.9,   7.5,    8.6,    10.2,   10.5,   5.1,    16.7,   -4.1,   5.9,    5.6,    3.5,    -3.9,   7.2,    7.4,    3.5,    3.5,    3.6,    -19.9,  11.3,   1.4,    14.5,   -3.1,   10.2,   9.3,    3.6,    6.9,    -3.7,   8.8,    -10.7,  -2.1,   4.4,    1.1,    -5.5,   16.2,   9.3,    0.5,    15.7,   15.8,   -15.5,  15.3,   4.7,    -2.4,   12.7], [\n",
        "4.2,    -18.0,  -3.4,   -0.4,   -10.9,  3.3,    -27.1,  -6.3,   2.0,    -9.8,   -7.3,   -8.4,   -20.6,  -5.4,   -6.7,   -13.5,  -18.4,  -7.7,   -6.9,   -11.6,  -14.5,  -2.4,   -10.2,  -5.3,   -12.6,  -10.0,  -1.5,   -11.3,  3.1,    -8.9,   -5.0,   -11.3,  -18.0,  -15.4,  -4.5,   -4.0,   -7.0,   -13.8,  -16.7,  -22.2,  -8.9,   7.0,    -3.9,   -9.1,   -9.2,   -11.7,  -10.3,  -9.0,   -14.6,  -7.1], [\n",
        "-8.1,   0.1,    -7.2,   9.5,    6.5,    1.5,    12.4,   4.1,    -7.2,   9.2,    7.4,    2.5,    -0.9,   -10.8,  7.6,    20.0,   9.3,    8.8,    5.2,    2.6,    -0.4,   19.0,   16.0,   15.8,   -2.4,   6.9,    7.6,    12.3,   21.7,   0.3,    -2.8,   1.8,    4.8,    17.8,   3.7,    -12.4,  6.9,    1.2,    -0.8,   -4.7,   15.6,   -8.4,   1.9,    16.7,   -0.1,   23.9,   -0.9,   9.5,    17.0,   2.7], [\n",
        "18.8,   13.8,   15.7,   10.7,   -0.1,   10.3,   23.7,   4.0,    15.5,   16.6,   8.4,    16.5,   4.1,    16.0,   1.1,    7.6,    3.3,    6.3,    -5.4,   9.4,    16.2,   2.9,    8.9,    13.4,   10.4,   10.6,   -1.8,   -4.6,   6.1,    2.0,    17.5,   12.3,   9.4,    8.4,    11.9,   14.0,   20.8,   -9.0,   4.6,    9.3,    0.3,    15.2,   9.6,    8.1,    18.6,   8.7,    4.7,    12.3,   7.9,    8.8], [\n",
        "-12.1,  -27.4,  3.0,    -2.1,   -20.8,  -14.3,  -1.6,   -1.3,   -1.5,   -21.6,  0.7,    -14.5,  -9.5,   4.1,    -1.8,   -5.8,   -13.0,  -12.2,  -2.5,   3.0,    -14.9,  -4.8,   -9.9,   1.6,    -24.7,  -15.5,  -23.5,  -5.1,   -0.7,   -16.0,  -12.8,  -5.9,   -6.1,   -16.3,  -12.8,  -17.2,  -13.3,  5.5,    -8.0,   -11.0,  -20.7,  -4.8,   1.2,    -4.6,   -10.0,  -14.1,  -8.7,   -11.9,  -14.4,  -9.4], [\n",
        "-1.1,   17.6,   -6.8,   8.5,    2.4,    0.7,    4.5,    3.5,    11.8,   6.1,    -0.9,   0.7,    1.7,    0.9,    -4.0,   3.1,    -13.9,  3.4,    8.3,    11.0,   6.5,    -7.5,   16.0,   0.3,    14.8,   5.1,    2.4,    -10.3,  0.4,    -0.9,   -9.4,   -7.1,   4.4,    -0.3,   -0.0,   -0.0,   11.5,   6.3,    3.7,    6.6,    -1.1,   18.0,   1.8,    -11.3,  12.1,   7.4,    -2.9,   -7.8,   -4.9,   0.3], [\n",
        "3.6,    -17.1,  14.7,   4.7,    11.2,   10.5,   9.0,    5.2,    13.2,   3.2,    8.5,    6.8,    9.3,    7.1,    5.4,    9.4,    10.4,   -0.1,   -7.2,   2.7,    11.8,   8.0,    13.7,   13.9,   4.2,    19.9,   0.5,    2.8,    15.6,   3.5,    10.2,   1.3,    6.9,    -2.9,   1.0,    1.1,    4.7,    1.6,    -2.7,   2.9,    0.5,    16.0,   13.9,   9.5,    11.3,   2.4,    4.1,    7.3,    -5.3,   15.9], [\n",
        "11.6,   3.7,    12.3,   15.0,   10.0,   8.5,    -1.8,   14.0,   11.4,   4.1,    10.7,   10.0,   6.8,    11.1,   13.6,   18.2,   6.8,    14.2,   10.2,   7.6,    10.4,   17.0,   2.6,    19.4,   -2.9,   1.7,    11.5,   8.3,    7.6,    9.1,    6.6,    16.5,   16.9,   -7.4,   10.4,   5.9,    10.0,   8.5,    10.6,   3.3,    1.7,    15.5,   17.6,   19.5,   5.9,    11.6,   7.4,    6.2,    -0.3,   11.0], [\n",
        "15.8,   22.8,   3.0,    12.2,   0.4,    3.9,    6.7,    -3.8,   -1.0,   2.1,    5.8,    18.0,   -7.8,   -6.8,   1.1,    9.7,    6.3,    13.9,   -2.3,   6.8,    3.7,    -8.8,   -20.3,  15.8,   0.5,    12.2,   -6.1,   -7.5,   -10.7,  -3.7,   5.8,    -2.7,   1.8,    5.5,    13.4,   9.0,    6.0,    -17.0,  -1.8,   2.7,    0.2,    1.9,    1.4,    -12.0,  12.5,   25.2,   6.4,    11.6,   -0.2,   5.5], [\n",
        "-2.6,   -8.4,   -10.7,  -8.1,   -10.9,  -6.1,   -14.5,  -15.4,  -9.3,   -10.4,  -13.6,  -7.0,   -21.7,  0.3,    -8.4,   -8.1,   -13.0,  -16.7,  -14.6,  -6.0,   -3.7,   -7.2,   -10.9,  -12.9,  -17.4,  -16.4,  -0.3,   -2.6,   -10.1,  -15.5,  -13.0,  -10.0,  -12.0,  -13.6,  -7.6,   2.6,    -2.5,   -3.4,   -4.9,   -16.1,  -10.2,  0.9,    -13.2,  -8.1,   -10.7,  -22.6,  -7.4,   -10.9,  -11.2,  -4.4], [\n",
        "-6.4,   1.1,    -7.0,   -13.4,  5.2,    7.9,    -0.3,   -11.0,  -11.0,  5.5,    -2.4,   -7.5,   -8.3,   -3.1,   -9.9,   -5.1,   -1.4,   -7.0,   -3.5,   -7.9,   2.0,    -1.8,   4.1,    -15.6,  -6.2,   0.1,    0.6,    -3.6,   -1.6,   -7.8,   -5.5,   -9.6,   -1.2,   -3.2,   -5.1,   3.9,    8.1,    -1.3,   -3.0,   -9.9,   -10.9,  -7.6,   -10.1,  -4.0,   -9.6,   -19.6,  -8.3,   -8.4,   -2.8,   -0.8], [\n",
        "20.9,   18.3,   6.3,    15.5,   5.4,    10.2,   2.0,    23.4,   6.7,    1.3,    26.7,   10.4,   -6.9,   -0.4,   16.6,   9.1,    3.4,    5.7,    5.3,    5.0,    11.4,   4.5,    -4.4,   12.1,   4.4,    15.8,   15.6,   8.6,    6.3,    22.4,   10.9,   4.4,    11.2,   10.2,   28.7,   9.4,    15.8,   8.6,    10.0,   9.1,    4.1,    20.1,   10.1,   -5.5,   12.9,   21.6,   10.1,   13.7,   17.9,   14.5], [\n",
        "-29.6,  0.8,    -9.5,   -10.0,  -18.0,  -4.0,   1.3,    -8.7,   -0.9,   -12.6,  10.6,   -15.5,  -11.1,  -9.8,   -4.1,   -2.4,   -24.0,  3.4,    -12.1,  -8.6,   -8.6,   -12.0,  -3.9,   -20.2,  -8.7,   -23.3,  -8.0,   -11.1,  -8.4,   -8.0,   -8.0,   -8.7,   -20.7,  -17.5,  -6.7,   6.3,    -12.6,  -4.2,   -3.5,   -28.6,  -1.4,   -21.1,  2.4,    -6.1,   -28.5,  -3.2,   -13.2,  -14.5,  -12.9,  -21.5], [\n",
        "-0.5,   -10.1,  -9.6,   -3.5,   -11.1,  -5.0,   -29.0,  -2.8,   -11.9,  0.3,    -7.7,   -2.5,   -13.9,  -11.5,  -13.2,  -7.9,   -2.0,   -18.9,  -5.0,   -23.6,  9.6,    11.4,   -15.5,  3.8,    -10.6,  -5.3,   -3.9,   -6.2,   11.4,   -5.8,   -16.7,  1.2,    -11.0,  4.5,    1.0,    -12.3,  -10.1,  -7.4,   -20.8,  -8.1,   -10.4,  1.0,    -10.6,  -3.2,   -10.6,  -6.0,   1.3,    -15.6,  3.3,    -9.1], [\n",
        "1.9,    23.2,   7.7,    4.0,    19.0,   6.7,    23.8,   9.1,    10.8,   17.2,   5.9,    8.1,    3.6,    4.3,    4.0,    13.6,   -1.2,   19.4,   7.4,    16.0,   22.1,   14.8,   13.1,   3.8,    9.9,    11.2,   7.2,    7.1,    9.5,    9.6,    9.1,    9.9,    -1.9,   4.5,    10.6,   12.8,   13.4,   2.7,    16.6,   -1.1,   4.3,    11.2,   6.0,    7.6,    16.6,   10.1,   9.6,    2.2,    11.6,   10.0], [\n",
        "-19.2,  -25.6,  -9.1,   -18.9,  -1.5,   -14.3,  -28.8,  -21.6,  -15.3,  -20.0,  -11.2,  -25.0,  -15.4,  -21.6,  -17.3,  -16.7,  -20.8,  -26.9,  -8.5,   -14.1,  -21.2,  -9.8,   -21.7,  -2.2,   -27.3,  -16.9,  -25.9,  -9.0,   -11.4,  -14.1,  -13.1,  -7.9,   -6.2,   -14.6,  -19.2,  -19.3,  12.5,   -35.7,  -6.8,   -16.0,  -12.1,  -26.2,  -29.8,  -29.5,  -9.7,   0.8,    -19.1,  -18.6,  -8.1,   -19.2], [\n",
        "16.5,   21.5,   -7.3,   11.0,   -12.0,  8.3,    20.2,   22.0,   7.6,    -1.9,   19.0,   2.2,    5.0,    8.5,    0.4,    8.1,    8.8,    5.3,    -8.3,   -0.3,   11.4,   -8.8,   8.2,    10.5,   5.7,    1.0,    8.1,    2.4,    2.6,    9.3,    6.6,    4.9,    -6.2,   9.5,    10.7,   -5.2,   -0.8,   2.9,    -5.4,   1.4,    11.5,   10.2,   11.0,   2.4,    5.7,    5.0,    6.2,    11.1,   -5.6,   0.7], [\n",
        "3.8,    -1.1,   -14.2,  -5.7,   -2.9,   -11.0,  -13.8,  -5.6,   -12.6,  -8.4,   -21.0,  -3.1,   -9.5,   -2.4,   -5.2,   -3.4,   -5.2,   -17.3,  -7.3,   -18.4,  -14.9,  -14.7,  -4.1,   -21.2,  4.6,    -11.2,  -0.3,   -11.6,  -5.8,   -5.3,   -15.7,  -4.0,   -1.9,   9.5,    -15.4,  -11.3,  -3.6,   -1.1,   -10.8,  -0.7,   -2.2,   -12.3,  0.6,    -1.8,   -4.1,   -9.3,   -6.4,   -2.0,   -5.2,   -7.6], [\n",
        "17.3,   12.6,   0.8,    -5.7,   -3.9,   10.4,   12.6,   7.8,    6.3,    13.9,   8.9,    11.7,   -1.8,   11.4,   3.1,    -5.3,   6.6,    9.5,    -3.1,   9.7,    8.1,    1.1,    -5.4,   -0.7,   -3.5,   7.6,    15.5,   4.0,    3.0,    5.5,    6.9,    0.6,    0.9,    14.0,   10.1,   6.2,    0.9,    9.9,    -6.4,   -4.7,   6.5,    1.7,    1.7,    2.2,    10.9,   -10.8,  17.9,   11.1,   3.9,    11.3], [\n",
        "6.4,    15.3,   4.9,    -4.3,   5.3,    17.9,   5.8,    6.3,    -0.5,   10.5,   4.2,    3.4,    6.6,    4.3,    7.8,    3.9,    -4.0,   1.0,    3.9,    1.7,    13.9,   13.7,   8.1,    1.2,    13.3,   8.1,    19.3,   -5.4,   -0.2,   16.5,   -0.1,   3.8,    -4.8,   18.6,   17.2,   13.0,   7.3,    8.3,    7.9,    1.2,    10.4,   12.2,   10.5,   3.9,    0.3,    3.5,    2.3,    7.1,    11.0,   1.4 ]])\n",
        " \n",
        "Y = np.array([[-21.5,   -24.4,  -24.2,  -19.1,  -32.8,  -9.5,   -25.4,  -29.0,  -30.2,  -14.7,  -15.8,  -23.9,  -21.8,  -12.8,  -11.8,  -27.8,  -24.2,  -14.6,  -12.2,  -18.0,  -14.9,  -11.4,  -12.5,  -21.2,  -19.3,  -24.5,  -21.4,  -12.4,  -16.0,  -15.9,  -18.8,  -14.8,  -17.5,  -18.8,  -22.8,  -19.2,  -11.3,  -3.4,   -23.5,  -23.8,  -19.8,  -18.0,  -14.1,  -8.0,   -22.2,  -26.7,  -19.1,  -21.8,  -27.0,  -18.3], [\n",
        "-15.2,  -13.9,  -18.4,  -32.8,  -7.6,   -9.6,   -17.6,  -10.6,  -10.2,  -17.1,  -17.4,  -14.8,  -19.5,  -21.3,  -22.6,  -10.2,  -13.2,  -28.5,  -13.9,  -9.5,   -2.7,   -4.6,   -4.2,   -15.5,  -18.8,  -10.5,  -4.9,   -6.1,   -14.4,  -10.5,  -5.3,   -0.8,   -10.7,  -0.6,   -12.8,  -7.7,   -5.3,   -8.9,   -6.1,   -7.4,   -2.5,   -2.7,   -8.1,   -12.1,  -9.5,   -18.4,  -13.8,  -21.6,  -18.7,  -9.2], [\n",
        "-1.8,   -11.4,  -19.5,  -0.2,   -15.3,  9.0,    -0.2,   -6.8,   -2.6,   -16.6,  7.0,    -16.9,  -6.4,   -10.8,  -0.3,   3.1,    -4.0,   -16.7,  -13.3,  -3.7,   -8.9,   -8.4,   1.5,    -17.0,  -4.7,   -9.7,   -2.2,   -3.8,   -5.1,   0.5,    0.8,    3.6,    -5.3,   -10.1,  -10.5,  -13.1,  0.1,    -3.2,   -18.4,  -7.3,   -4.2,   -3.5,   -9.1,   1.3,    9.0,    -1.2,   -6.1,   3.5,    -12.5,  -10.2], [\n",
        "-9.6,   -9.4,   -10.4,  -13.9,  -18.4,  -5.3,   -16.6,  -5.6,   -3.0,   -13.7,  0.3,    -9.1,   -5.8,   -2.9,   -4.8,   -0.2,   7.5,    -15.9,  -15.0,  -7.8,   -20.4,  -7.6,   -10.7,  -0.2,   9.0,    -15.1,  -5.1,   -15.9,  1.5,    -7.1,   -5.3,   -4.8,   -0.2,   1.2,    -1.4,   -16.7,  -1.3,   -2.7,   1.8,    -1.2,   -9.1,   -4.4,   -2.9,   -0.1,   -7.2,   -2.4,   -7.9,   2.3,    -15.2,  -10.9], [\n",
        "10.3,   8.8,    7.7,    7.0,    9.9,    12.7,   11.1,   21.5,   7.9,    9.1,    11.8,   9.1,    12.1,   22.0,   12.9,   5.0,    7.6,    13.1,   3.1,    15.3,   24.4,   8.7,    7.7,    -1.6,   19.9,   14.2,   1.1,    17.1,   12.5,   10.3,   17.5,   12.1,   -4.6,   17.1,   15.5,   15.8,   8.2,    13.4,   18.6,   0.7,    15.5,   14.2,   25.3,   5.1,    19.6,   21.0,   9.0,    9.5,    12.9,   5.2], [\n",
        "6.1,    0.7,    2.5,    2.9,    9.4,    -1.1,   12.6,   9.1,    3.1,    0.2,    9.3,    0.4,    -5.9,   -2.9,   7.4,    3.0,    8.3,    -1.2,   -8.5,   -10.0,  -5.0,   2.9,    -0.1,   -2.0,   8.0,    2.1,    6.2,    11.5,   -2.1,   10.7,   11.9,   8.9,    5.6,    8.8,    -6.7,   -2.0,   4.8,    -5.1,   -8.3,   9.0,    -4.3,   15.3,   8.1,    10.0,   12.5,   18.0,   8.1,    1.7,    8.3,    8.2], [\n",
        "19.8,   22.1,   28.6,   11.5,   15.9,   -0.0,   6.8,    7.7,    18.7,   18.2,   14.0,   23.4,   10.2,   17.1,   14.0,   22.6,   14.9,   23.8,   18.0,   17.3,   11.9,   17.1,   12.4,   11.9,   17.2,   7.6,    18.5,   -2.2,   11.2,   2.4,    14.2,   8.2,    22.6,   6.0,    17.1,   23.9,   5.3,    10.6,   10.9,   24.4,   16.9,   7.7,    15.7,   5.6,    7.3,    4.5,    13.9,   13.8,   21.8,   13.0], [\n",
        "14.1,   13.2,   16.7,   15.9,   7.5,    18.2,   26.5,   22.3,   13.1,   11.4,   14.6,   22.3,   24.7,   14.1,   24.2,   11.6,   15.0,   9.8,    9.4,    20.7,   9.5,    20.2,   20.9,   23.6,   23.0,   22.6,   6.3,    8.0,    13.6,   27.3,   17.9,   27.8,   9.1,    23.3,   21.4,   14.1,   22.0,   11.2,   7.2,    17.4,   19.1,   9.2,    10.2,   18.1,   21.4,   20.4,   19.6,   19.0,   9.6,    19.0], [\n",
        "-8.9,   -20.6,  -12.7,  -8.1,   -13.8,  -15.0,  -19.1,  -4.9,   -9.5,   -13.6,  -6.5,   -11.5,  -12.5,  -13.7,  -5.2,   -6.3,   -15.9,  -6.6,   -12.3,  -10.1,  6.5,    -26.9,  -5.4,   -9.1,   -15.2,  -13.9,  -17.4,  -2.9,   -12.8,  -11.3,  -9.4,   -16.0,  -11.7,  -2.8,   -10.7,  -10.3,  -2.3,   1.7,    -24.6,  0.7,    1.6,    -9.0,   -7.8,   -14.9,  -6.9,   -13.1,  -12.6,  -10.0,  -6.9,   -11.7], [\n",
        "-0.1,   3.2,    7.1,    5.4,    2.0,    -0.6,   -8.2,   1.6,    7.9,    -2.1,   1.6,    10.5,   -11.2,  11.7,   -2.4,   -8.1,   6.5,    11.5,   2.4,    -2.3,   2.9,    1.8,    -6.7,   9.2,    12.8,   -2.8,   -3.9,   -5.5,   3.5,    -7.7,   10.1,   -5.5,   -2.9,   6.5,    16.0,   -0.8,   -4.7,   2.2,    -2.5,   9.2,    6.2,    12.1,   14.5,   -8.2,   -2.9,   -0.0,   3.4,    4.6,    0.6,    6.2], [\n",
        "-3.5,   -6.7,   -14.2,  -10.4,  -15.5,  -10.4,  -11.6,  -20.9,  -24.1,  -13.1,  -13.5,  -5.4,   -10.0,  -14.2,  -10.7,  -25.6,  -17.5,  -4.6,   -14.5,  -8.4,   1.1,    -10.5,  -19.7,  -10.2,  -17.9,  -10.2,  -23.0,  -13.8,  -17.3,  -13.9,  -16.9,  0.3,    -18.7,  -10.3,  -10.1,  -9.6,   -15.4,  -15.9,  -12.6,  -18.5,  -16.2,  -11.2,  -31.7,  -13.6,  0.1,    -15.7,  -13.1,  -17.2,  -12.2,  -13.0], [\n",
        "-15.9,  -6.5,   1.3,    -20.8,  -14.1,  -18.6,  -2.5,   -11.4,  -7.3,   -2.3,   -10.3,  -29.3,  -11.9,  -3.8,   -14.3,  -2.5,   -12.1,  -12.4,  -18.4,  -10.0,  -20.6,  -0.3,   -14.8,  -21.2,  -22.7,  -3.7,   -15.7,  -6.3,   -0.2,   -13.4,  -19.5,  -19.1,  -8.6,   -28.4,  1.1,    -2.3,   -19.3,  -11.2,  -3.7,   -24.6,  -5.8,   -13.6,  -1.8,   -6.9,   -13.7,  -14.6,  -2.1,   -3.6,   -10.0,  -11.4], [\n",
        "-6.7,   -9.9,   -11.7,  -7.7,   -5.7,   -6.6,   -12.2,  -11.0,  -12.1,  -13.1,  6.3,    -19.8,  -2.5,   -25.1,  -13.0,  -11.6,  -15.3,  -15.6,  -4.9,   -18.9,  -20.5,  -0.5,   -30.0,  -3.6,   -5.4,   -17.8,  -24.6,  -17.0,  -19.0,  -4.8,   -19.0,  -8.0,   -15.6,  -10.9,  -7.9,   -11.3,  -19.6,  -20.5,  -10.8,  -11.7,  -12.5,  -22.4,  -21.0,  -4.3,   -5.7,   2.6,    -1.2,   -12.7,  -1.3,   -11.8], [\n",
        "4.1,    -4.3,   -12.2,  -2.9,   11.7,   19.9,   3.2,    9.5,    1.3,    -2.0,   2.4,    -8.0,   1.6,    6.4,    3.8,    -8.0,   2.7,    0.9,    4.7,    -9.0,   17.8,   -0.4,   -7.2,   4.6,    6.7,    -2.3,   -10.2,  10.0,   -3.8,   6.9,    -7.2,   9.4,    -4.1,   9.3,    -1.2,   -1.6,   -12.2,  -1.9,   -1.2,   1.0,    9.5,    12.0,   -0.6,   11.1,   16.7,   8.6,    7.2,    -0.7,   2.7,    -10.2], [\n",
        "-1.3,   3.4,    4.0,    -20.9,  -7.6,   -13.3,  -3.8,   -24.7,  -10.3,  -4.2,   1.3,    7.9,    -0.2,   7.4,    -1.0,   -24.8,  -1.0,   0.6,    -6.6,   -16.0,  -18.3,  -14.5,  -11.4,  -25.5,  -19.7,  3.7,    -0.5,   -16.0,  -13.6,  -8.8,   -1.0,   -9.7,   -12.0,  -2.0,   -2.8,   -6.4,   -6.3,   -6.1,   -1.3,   -13.3,  -12.4,  -8.3,   -6.5,   -17.4,  -2.5,   -22.2,  -14.1,  0.3,    -0.4,   1.4], [\n",
        "6.8,    16.4,   9.7,    6.6,    7.1,    11.4,   -2.5,   -0.6,   12.7,   16.7,   -2.3,   4.4,    -1.7,   -0.4,   7.5,    7.1,    7.6,    7.7,    13.5,   13.9,   7.9,    9.5,    3.9,    8.9,    0.1,    2.3,    11.4,   -1.9,   19.6,   -0.9,   7.5,    4.9,    5.0,    -0.1,   17.8,   16.6,   -3.1,   1.0,    7.2,    9.6,    4.7,    -4.0,   2.4,    1.7,    3.8,    15.3,   8.3,    12.5,   6.2,    29.3], [\n",
        "10.4,   4.2,    6.4,    -0.8,   -3.7,   1.1,    6.9,    0.7,    7.2,    6.3,    -4.5,   -7.1,   -0.3,   9.4,    -8.4,   -0.9,   1.3,    4.5,    3.2,    14.2,   6.7,    25.3,   -3.1,   16.3,   13.7,   -7.7,   -9.2,   -0.6,   11.6,   9.0,    -7.3,   7.3,    -3.4,   15.9,   11.2,   -13.8,  -7.7,   14.8,   4.2,    0.4,    3.0,    -2.5,   3.7,    -7.1,   -6.1,   9.1,    4.3,    -0.5,   -0.7,   9.7], [\n",
        "19.0,   22.0,   10.5,   -15.4,  12.1,   27.5,   5.8,    9.3,    6.0,    18.4,   4.0,    5.9,    5.8,    7.0,    11.4,   16.2,   14.4,   10.7,   12.4,   20.0,   23.8,   18.4,   11.0,   6.7,    28.8,   0.7,    9.4,    13.8,   13.7,   15.7,   17.0,   19.4,   18.0,   21.1,   10.3,   4.1,    23.6,   14.9,   16.2,   7.0,    14.0,   6.4,    14.6,   4.4,    17.3,   16.3,   -0.1,   6.6,    10.4,   16.2], [\n",
        "11.5,   12.8,   15.4,   15.6,   17.8,   13.2,   19.9,   24.2,   14.5,   13.2,   9.2,    9.7,    16.0,   -0.8,   19.4,   10.3,   12.7,   12.4,   18.8,   24.1,   13.3,   2.3,    19.5,   9.1,    9.1,    6.5,    15.3,   6.0,    9.1,    10.0,   29.6,   12.0,   17.4,   21.2,   8.7,    14.8,   19.9,   8.5,    18.2,   14.1,   7.1,    28.0,   8.4,    14.8,   12.9,   12.3,   15.4,   14.7,   6.3,    14.3], [\n",
        "-6.9,   -5.5,   -8.1,   -3.4,   -6.9,   -7.0,   -1.3,   -1.8,   -18.8,  -11.0,  -13.5,  3.0,    -3.3,   -4.7,   -13.7,  -14.6,  -7.4,   -1.1,   -10.9,  -11.7,  -1.1,   -13.4,  -8.4,   2.6,    -9.8,   -12.3,  -17.0,  -13.0,  -4.1,   -4.2,   -15.1,  -12.2,  -1.8,   -9.2,   -9.8,   -10.6,  -8.3,   -5.0,   -4.3,   -12.2,  -15.5,  -7.1,   -20.2,  -9.3,   -16.0,  -11.3,  -10.8,  -7.3,   -2.8,   -18.3], [\n",
        "26.7,   17.1,   11.1,   2.3,    13.2,   25.0,   7.8,    12.3,   16.6,   15.6,   11.9,   5.2,    10.8,   11.4,   18.2,   11.6,   29.3,   10.8,   9.5,    22.9,   10.6,   17.6,   15.0,   17.4,   16.2,   15.5,   11.2,   12.2,   17.0,   15.7,   15.7,   22.2,   16.2,   20.0,   21.7,   10.8,   15.1,   8.7,    20.7,   8.9,    10.5,   24.2,   18.4,   23.1,   20.0,   12.5,   14.2,   20.5,   11.1,   15.8], [\n",
        "10.3,   -1.7,   4.5,    -6.8,   -9.5,   -3.2,   3.0,    -4.0,   9.4,    5.1,    1.7,    9.0,    -2.4,   9.4,    8.8,    0.5,    8.6,    -2.0,   -0.5,   6.3,    -7.6,   3.6,    -2.5,   3.4,    10.2,   8.3,    2.0,    10.9,   5.9,    4.8,    6.7,    3.9,    0.8,    7.5,    5.9,    -6.7,   4.3,    5.4,    -8.2,   1.8,    -1.9,   9.6,    -1.9,   2.9,    3.2,    4.6,    -4.0,   3.0,    -0.2,   19.0], [\n",
        "7.5,    5.5,    6.6,    25.5,   9.6,    2.9,    17.0,   7.0,    3.1,    14.3,   18.4,   20.7,   5.0,    13.0,   22.9,   13.6,   -2.9,   23.9,   6.4,    9.6,    8.9,    14.1,   19.9,   9.2,    23.8,   5.1,    12.8,   14.6,   -2.8,   0.2,    7.6,    16.6,   16.7,   16.1,   8.8,    5.9,    14.9,   21.6,   0.0,    9.7,    4.9,    15.0,   26.1,   14.7,   15.1,   10.9,   7.1,    13.8,   13.0,   2.5], [\n",
        "24.6,   18.5,   19.6,   11.7,   3.8,    8.7,    3.0,    -3.6,   19.0,   14.1,   19.2,   3.8,    -4.5,   0.8,    15.0,   17.3,   15.9,   21.2,   10.5,   12.7,   17.3,   21.7,   3.9,    21.0,   12.6,   10.0,   13.9,   13.9,   24.0,   14.1,   18.3,   16.2,   12.4,   15.5,   25.4,   20.1,   6.3,    4.1,    18.7,   15.1,   5.4,    13.6,   7.0,    20.5,   13.2,   16.3,   21.8,   14.9,   7.2,    16.9], [\n",
        "-0.6,   -10.2,  -12.5,  -18.1,  -10.3,  8.7,    -14.9,  -11.3,  -3.7,   -13.7,  0.0,    -12.8,  2.7,    -2.7,   -15.5,  -20.0,  -5.9,   -7.7,   4.7,    -2.6,   -13.3,  -4.2,   -12.9,  -9.7,   -0.1,   -11.0,  -7.7,   -9.2,   -15.2,  -6.5,   -12.3,  -6.0,   -7.0,   -6.6,   -15.0,  -10.8,  0.3,    3.3,    0.4,    -12.3,  -11.8,  -13.9,  -11.4,  -2.8,   -10.8,  -16.5,  -15.0,  -23.1,  -11.9,  -26.5], [\n",
        "9.9,    1.7,    6.7,    -0.2,   4.2,    3.5,    -4.0,   1.2,    1.8,    4.2,    12.2,   6.3,    22.4,   2.2,    7.5,    10.7,   6.9,    12.8,   10.1,   12.3,   7.2,    -3.1,   10.8,   7.5,    -0.6,   -5.2,   18.6,   3.9,    7.5,    -0.0,   4.0,    2.3,    14.1,   10.3,   5.5,    7.3,    16.3,   16.0,   11.2,   0.9,    12.0,   10.1,   6.8,    8.3,    -1.5,   1.3,    9.9,    6.7,    11.4,   -5.1], [\n",
        "25.1,   25.1,   20.8,   22.4,   14.9,   15.0,   16.6,   4.7,    25.6,   10.5,   26.1,   16.5,   7.5,    24.3,   16.9,   17.9,   19.0,   25.6,   31.7,   13.4,   14.6,   27.5,   13.7,   11.0,   27.7,   21.6,   18.8,   19.4,   13.5,   21.9,   25.3,   18.7,   16.2,   18.9,   17.9,   19.9,   12.9,   13.6,   16.6,   28.3,   10.3,   14.1,   17.4,   14.4,   20.5,   19.8,   14.8,   5.8,    11.2,   24.6], [\n",
        "4.0,    11.9,   8.3,    4.3,    11.0,   13.2,   15.9,   -1.7,   7.7,    9.3,    7.6,    0.5,    3.9,    10.7,   8.1,    13.4,   1.0,    17.2,   -7.3,   19.2,   18.8,   8.2,    11.9,   6.3,    6.7,    13.8,   15.1,   12.2,   20.0,   17.2,   6.2,    16.9,   7.1,    6.5,    15.9,   -1.8,   11.4,   6.1,    2.4,    -4.3,   9.3,    -3.9,   11.2,   13.3,   11.5,   7.2,    0.4,    8.8,    20.5,   7.8], [\n",
        "2.9,    -1.5,   3.4,    1.5,    -3.5,   13.4,   19.1,   4.7,    6.9,    5.2,    -2.1,   2.3,    12.4,   10.1,   -0.1,   10.5,   5.3,    -1.1,   -4.3,   6.6,    -4.3,   1.6,    5.7,    3.6,    1.7,    5.3,    16.9,   2.7,    13.4,   6.2,    3.5,    10.9,   3.6,    2.8,    2.2,    -7.9,   7.0,    10.1,   -1.3,   -5.2,   -0.4,   -0.4,   -0.2,   7.7,    2.5,    11.4,   -2.7,   11.9,   2.3,    6.2], [\n",
        "11.9,   -0.9,   4.2,    -1.0,   -0.1,   11.7,   -4.4,   -4.2,   7.0,    9.6,    0.8,    10.2,   3.7,    2.3,    8.8,    8.2,    7.1,    0.2,    12.6,   6.1,    1.7,    5.4,    4.6,    1.4,    11.8,   4.7,    14.0,   2.9,    15.8,   10.8,   19.6,   11.8,   -0.4,   5.0,    1.9,    6.0,    4.1,    10.5,   -3.5,   11.0,   7.0,    -3.2,   1.0,    13.7,   13.2,   22.9,   6.1,    2.7,    9.5,    14.0], [\n",
        "-1.0,   5.8,    8.3,    -13.6,  -4.3,   -9.1,   -0.5,   -15.7,  -2.0,   -1.7,   -8.3,   -3.4,   -4.4,   -4.6,   -3.8,   -12.3,  0.7,    11.8,   -4.7,   5.6,    -3.3,   -4.1,   -15.3,  6.7,    -4.2,   -2.0,   -17.8,  -8.3,   -14.4,  4.2,    -7.1,   -2.8,   -4.2,   -3.0,   14.5,   3.1,    -2.5,   -10.9,  -2.8,   -6.4,   -8.6,   -5.5,   -9.6,   -10.2,  -1.8,   -0.6,   0.1,    -9.6,   -6.7,   -10.3], [\n",
        "-1.1,   6.8,    10.4,   7.2,    11.4,   19.4,   5.8,    10.1,   17.7,   8.9,    4.9,    10.5,   18.7,   11.3,   4.9,    7.0,    8.5,    2.0,    15.7,   0.2,    -1.5,   9.3,    9.6,    16.5,   -1.7,   20.3,   20.8,   10.7,   12.3,   8.6,    -0.2,   7.0,    5.1,    1.4,    14.0,   8.1,    10.7,   10.9,   14.9,   6.0,    14.5,   -3.7,   6.4,    5.7,    5.0,    11.6,   7.6,    13.3,   8.9,    17.1], [\n",
        "-7.7,   -9.0,   -6.9,   0.6,    -9.0,   -14.2,  -2.6,   -8.8,   -12.2,  -12.8,  -5.4,   3.9,    -9.3,   -2.6,   -6.0,   -5.9,   -4.2,   -4.6,   -15.3,  -1.8,   -5.8,   -16.6,  5.2,    1.9,    -7.1,   0.9,    -3.6,   4.1,    0.6,    -5.5,   -0.3,   -7.5,   -8.9,   1.7,    -9.4,   4.7,    -1.5,   3.4,    -3.5,   -0.8,   -23.8,  3.5,    -2.9,   -8.0,   -8.2,   -19.3,  -6.1,   -1.1,   -23.4,  0.6], [\n",
        "-22.0,  -11.9,  -6.8,   -9.1,   -0.4,   -1.7,   -15.7,  -9.4,   -6.9,   -4.4,   -20.3,  -7.8,   -15.6,  -21.6,  -7.8,   -1.3,   -20.2,  -14.3,  -1.7,   -18.0,  -10.1,  -5.2,   -11.6,  -15.6,  -13.8,  -19.0,  -6.5,   -9.7,   -7.9,   -18.5,  -4.5,   -17.7,  -0.3,   -20.5,  -4.2,   -13.4,  -7.8,   -5.5,   -19.5,  -9.7,   -5.0,   -8.8,   -5.5,   -12.1,  -10.8,  -8.1,   -11.7,  -6.4,   -6.6,   -8.7], [\n",
        "2.3,    1.7,    22.9,   16.8,   -3.4,   7.5,    -14.6,  7.5,    3.8,    21.3,   5.2,    14.9,   10.3,   -3.1,   9.4,    16.4,   3.3,    6.7,    12.0,   3.4,    3.0,    23.2,   10.4,   21.4,   3.5,    0.3,    19.1,   4.6,    15.5,   7.0,    10.1,   14.3,   12.0,   14.0,   -0.0,   10.6,   8.4,    6.2,    -3.1,   5.7,    7.4,    2.2,    8.8,    14.3,   6.3,    10.6,   8.0,    18.7,   5.9,    20.1], [\n",
        "10.2,   1.2,    -3.9,   -6.1,   -0.2,   18.7,   -7.3,   0.9,    -10.0,  -5.3,   -0.9,   5.0,    17.9,   4.1,    4.9,    -19.9,  2.1,    2.7,    7.9,    0.5,    -3.5,   -6.3,   -0.9,   -4.9,   6.5,    2.1,    -3.4,   -4.3,   -7.8,   -4.3,   1.1,    -0.9,   -17.8,  5.8,    -4.8,   -0.5,   7.0,    -5.8,   13.2,   -11.3,  -8.2,   -4.6,   7.1,    -7.9,   -0.2,   -7.2,   -9.1,   -5.3,   -5.0,   -9.4], [\n",
        "4.3,    -0.1,   -11.0,  -10.4,  -2.3,   -21.1,  2.7,    -6.3,   -0.7,   -9.7,   -6.8,   1.1,    -9.3,   -2.7,   -20.5,  -7.1,   13.6,   -1.5,   -6.0,   -7.2,   -2.6,   -7.9,   -9.0,   -12.3,  0.8,    -20.6,  -6.8,   -4.5,   -11.3,  -17.6,  -4.9,   -9.5,   0.7,    3.4,    -0.5,   -16.2,  -5.0,   9.8,    -2.0,   5.5,    -3.7,   3.0,    1.8,    -28.4,  -7.1,   8.8,    -4.5,   -9.2,   -4.2,   3.4], [\n",
        "-1.2,   -10.5,  -10.1,  -9.9,   -10.1,  -17.2,  -17.6,  -30.6,  -8.5,   0.1,    -11.1,  -6.7,   -26.9,  -15.1,  -14.7,  -4.6,   -4.1,   -9.4,   -14.8,  -18.0,  -14.2,  -6.8,   -8.2,   -16.2,  -13.9,  -0.4,   4.3,    -7.1,   -9.5,   -5.4,   2.8,    -5.7,   -12.2,  -0.7,   -21.1,  -11.2,  -15.4,  -11.3,  -13.5,  -8.0,   -16.9,  0.6,    -1.5,   -2.5,   -5.6,   -17.3,  -12.4,  -5.9,   -11.2,  -9.1], [\n",
        "0.6,    2.4,    -10.7,  -4.0,   -10.9,  7.3,    10.0,   -10.6,  0.8,    -8.1,   1.9,    -6.7,   -8.0,   4.2,    7.2,    -6.9,   -9.6,   10.7,   -14.6,  -4.9,   2.5,    -1.9,   -4.2,   -5.1,   2.5,    -1.5,   -0.2,   -1.5,   0.4,    0.4,    -5.7,   3.9,    -9.5,   -14.2,  3.2,    -0.9,   -9.1,   5.5,    -7.8,   2.4,    -0.1,   -10.4,  -6.8,   6.0,    0.4,    9.4,    3.3,    -1.0,   -1.4,   -5.9], [\n",
        "19.1,   12.0,   8.5,    7.9,    5.7,    9.1,    16.6,   1.0,    9.5,    11.7,   10.8,   8.9,    13.8,   3.9,    12.5,   11.3,   18.1,   7.5,    -5.9,   21.8,   10.3,   1.6,    1.5,    10.0,   -3.6,   8.8,    17.1,   4.3,    28.4,   14.7,   18.2,   6.3,    4.8,    7.1,    9.0,    15.6,   11.5,   15.8,   15.5,   6.2,    -0.7,   5.2,    1.3,    13.8,   0.8,    17.5,   18.1,   22.3,   8.1,    19.4], [\n",
        "6.2,    -6.6,   -0.2,   9.0,    0.2,    -2.1,   -3.2,   4.1,    -0.9,   -4.3,   16.5,   16.6,   -2.3,   7.7,    12.2,   17.3,   7.3,    4.1,    -8.5,   5.1,    9.4,    -5.2,   12.2,   9.1,    20.2,   6.9,    0.5,    13.1,   8.0,    2.2,    8.3,    9.0,    8.2,    11.3,   0.3,    9.5,    13.5,   -2.1,   -16.9,  15.5,   9.7,    2.6,    4.5,    5.5,    10.3,   0.8,    1.3,    13.9,   4.1,    9.0], [\n",
        "-7.9,   -4.9,   -9.0,   -3.3,   12.5,   -3.2,   16.8,   11.6,   -3.8,   -9.5,   -3.9,   -4.0,   -16.2,  2.7,    -7.7,   -7.6,   -4.4,   -7.4,   -16.6,  -17.7,  -1.3,   -13.0,  -22.2,  -14.5,  4.6,    -4.4,   -8.8,   0.4,    -15.1,  -4.9,   -13.1,  -15.6,  1.3,    -16.6,  -26.7,  -11.9,  -6.2,   -7.0,   -10.9,  -6.6,   -14.6,  4.8,    -10.0,  -14.2,  -6.6,   -14.9,  -12.8,  -13.7,  -6.0,   -17.0], [\n",
        "7.4,    18.6,   19.0,   13.6,   16.8,   12.4,   20.1,   10.2,   18.0,   9.3,    14.5,   10.8,   0.7,    3.5,    7.5,    19.4,   -0.9,   18.8,   0.1,    0.3,    -11.6,  17.1,   13.1,   3.9,    6.7,    16.5,   35.1,   10.9,   9.7,    11.1,   10.5,   8.4,    14.9,   -8.5,   -1.1,   10.9,   3.4,    6.9,    15.5,   8.4,    -12.3,  2.9,    17.3,   20.1,   0.1,    17.0,   5.5,    11.7,   21.3,   9.5], [\n",
        "7.2,    12.2,   0.4,    4.3,    -4.4,   9.5,    6.7,    17.1,   4.1,    -0.8,   2.4,    11.0,   11.4,   11.3,   8.9,    11.0,   7.6,    -2.2,   -2.8,   5.4,    20.2,   9.1,    15.1,   1.3,    12.5,   23.5,   16.1,   6.0,    20.5,   6.5,    11.0,   20.4,   2.4,    16.2,   8.1,    12.4,   14.1,   -5.0,   12.3,   3.3,    24.5,   11.1,   -1.4,   7.3,    14.3,   12.9,   7.3,    8.7,    6.7,    11.0], [\n",
        "-7.3,   -9.5,   -6.8,   -13.6,  -6.1,   -1.3,   -16.7,  -10.9,  -9.5,   -4.9,   -5.2,   -3.1,   -9.0,   -11.0,  -6.6,   -6.5,   -2.4,   -13.3,  -2.8,   -5.5,   -12.5,  -5.0,   -20.0,  -13.0,  -3.4,   -11.0,  -8.5,   -15.2,  -9.2,   -1.9,   2.2,    -10.0,  -13.8,  -8.3,   -10.1,  -16.3,  -10.0,  -14.0,  -8.5,   -11.7,  -16.5,  -9.2,   -3.5,   -2.8,   -6.7,   -1.4,   -13.1,  -1.5,   4.9,    -11.1], [\n",
        "9.3,    13.9,   16.8,   27.5,   11.5,   18.4,   23.5,   14.6,   18.7,   17.9,   14.3,   17.2,   10.1,   17.4,   18.2,   31.4,   15.0,   12.8,   13.3,   16.7,   29.4,   27.4,   17.7,   19.6,   18.9,   13.6,   14.1,   24.1,   23.4,   20.3,   11.4,   20.6,   19.5,   16.6,   14.3,   12.6,   20.1,   23.1,   2.4,    12.3,   16.7,   5.4,    8.1,    17.4,   26.3,   15.4,   14.5,   21.5,   8.6,    17.6], [\n",
        "-1.2,   -8.0,   -8.8,   -13.4,  -13.3,  4.6,    -11.3,  -12.9,  -2.1,   -1.8,   -19.2,  -8.9,   -1.1,   -9.2,   -7.6,   -8.8,   3.5,    -9.9,   -2.7,   -2.6,   -1.6,   -18.2,  -14.7,  -3.3,   -21.1,  -20.6,  -4.6,   -11.3,  1.2,    -6.1,   -6.1,   -6.8,   -9.8,   -15.1,  5.6,    -13.4,  -9.3,   -2.3,   -12.4,  -3.6,   -1.1,   -0.1,   -17.2,  -6.5,   -1.2,   -6.4,   -12.9,  -8.4,   -5.5,   -0.4], [\n",
        "-5.1,   4.9,    8.6,    -6.7,   16.3,   -1.4,   1.2,    2.8,    5.9,    15.7,   2.0,    5.3,    1.1,    8.3,    0.1,    23.9,   10.1,   -5.4,   10.8,   -3.2,   7.2,    -4.5,   6.2,    -1.9,   -2.9,   5.4,    20.1,   17.8,   3.8,    -1.8,   5.6,    -1.1,   21.3,   6.1,    0.4,    4.2,    9.8,    14.8,   -0.2,   18.5,   16.6,   10.9,   9.8,    5.3,    13.1,   1.8,    -0.4,   5.1,    13.1,   14.6], [\n",
        "-3.4,   -9.5,   -0.1,   -5.2,   -3.0,   -1.8,   -14.4,  -2.8,   -4.9,   -4.4,   -2.3,   7.9,    -6.4,   -3.8,   -2.5,   -3.1,   -1.1,   -6.4,   -9.2,   -7.9,   0.6,    0.8,    -12.4,  8.6,    -0.9,   -16.0,  -8.3,   0.5,    -5.0,   2.3,    -9.4,   -7.5,   4.5,    -7.6,   -11.3,  -25.6,  3.5,    -0.9,   -18.3,  -0.0,   -11.3,  -10.0,  -8.3,   -0.4,   -8.1,   -10.2,  -17.6,  -0.7,   10.0,   -8.4], [\n",
        "-12.8,  -10.1,  -4.1,   -2.3,   -5.2,   -5.2,   -3.8,   -3.8,   -1.8,   -13.7,  -8.7,   -14.3,  -5.2,   2.0,    -9.8,   -5.8,   -5.4,   -9.4,   3.3,    -15.6,  -15.3,  -10.9,  -4.5,   -5.1,   -1.9,   -2.4,   4.1,    -7.9,   6.4,    -8.3,   -2.9,   -12.4,  -9.3,   -10.0,  -4.8,   -16.2,  -10.3,  -21.3,  -11.1,  -5.2,   2.1,    -10.4,  -7.2,   -10.0,  -17.6,  -6.2,   -6.8,   -13.4,  -2.7,   6.7 ]])\n",
        " \n",
        "n = 50\n",
        "lamda = np.logspace(-2, 5, num=100)\n",
        "thickness = np.empty(99)\n",
        "card_a = np.empty(99)\n",
        " \n",
        "# Minimizing only 2-norm of a\n",
        " \n",
        "a = cp.Variable(n)\n",
        "b = cp.Variable(1)\n",
        "objective = cp.Minimize(cp.norm(a,2))\n",
        "constraints = [a.T@X - b >= 1, a.T@Y - b <= -1]\n",
        "prob = cp.Problem(objective, constraints)\n",
        "prob.solve()\n",
        " \n",
        "print(\"i. Max thickness using only L2 norm:\", 2.0/cp.norm(a,2).value)\n",
        "print(\"Cardinality for the above max thickness:\", (cp.abs(a).value >= 0.0001).sum())\n",
        " \n",
        "# Standard heuristic method using L1 norm\n",
        "print(\"ii. Cardinality curve:\", )\n",
        "for i in range(0,99):\n",
        "  a = cp.Variable(n)\n",
        "  b = cp.Variable(1)\n",
        "  fcn = cp.norm(a,2) + lamda[i]*cp.norm(a,1)\n",
        "  objective = cp.Minimize(fcn)\n",
        "  constraints = [a.T@X - b >= 1, a.T@Y - b <= -1]\n",
        "  prob = cp.Problem(objective, constraints)\n",
        "  prob.solve()\n",
        " \n",
        "  thickness[i] = 2.0/cp.norm(a,2).value\n",
        "  card_a[i] = (cp.abs(a).value >= 0.0001).sum()\n",
        " \n",
        "plt.figure()\n",
        "plt.plot(card_a, thickness, '*')\n",
        "plt.xlabel('Cardinality of a, card(a)')\n",
        "plt.ylabel('Slab thickness') \n",
        "plt.title('Slab thickness vs Cardinality')\n",
        "plt.show()\n",
        " \n",
        "# Choosing min cardinality for feature selection\n",
        "print(\"iii. Feature selection:\", )\n",
        "for i in range(0,99):\n",
        "  min_card_a = cp.min(card_a[i])\n",
        "  min_thickness = thickness[i]\n",
        "#  if card_a[i] == 10.0:\n",
        "#    print(\"index:\", i)\n",
        "#    print(\"lamda:\", lamda[i])\n",
        " \n",
        "print(\"Minimum cardinality:\", min_card_a.value)\n",
        "print(\"Thickness corresponding to the above min cardinality:\", min_thickness)\n",
        " \n",
        "a = cp.Variable(n)\n",
        "b = cp.Variable(1)\n",
        "fcn = cp.norm(a,2) + 24.77076355991709*cp.norm(a,1)\n",
        "objective = cp.Minimize(fcn)\n",
        "constraints = [a.T@X - b >= 1, a.T@Y - b <= -1]\n",
        "prob = cp.Problem(objective, constraints)\n",
        "prob.solve()\n",
        " \n",
        "# Choosing indices of a for which a>=0.0001 and card(a)=10\n",
        "print(\"Indices of a for which a>=0.0001 and card(a)=10:\", )\n",
        "for i in range(0,n-1):\n",
        "  if cp.abs(a[i]).value >= 0.0001:\n",
        "    print(\"i:\", i) # printing indices of a that result in a.value>0.0001\n",
        "#    index[i] = i\n",
        " \n",
        "# Solving the problem with 10 feature selection using the above indices of a (0,6,7,17,18,20,22,25,26,45):\n",
        "print(\"Resolving the problem using the above 10 features selection:\", )\n",
        " \n",
        "a = cp.Variable(10)\n",
        "b = cp.Variable(1)\n",
        "Xn = np.empty([10,49])\n",
        "Yn = np.empty([10,49])\n",
        " \n",
        "for i in range(0,n-1):\n",
        "  Xn[0][i] = X[0][i]\n",
        "  Yn[0][i] = Y[0][i]\n",
        "  Xn[1][i] = X[6][i]\n",
        "  Yn[1][i] = Y[6][i]\n",
        "  Xn[2][i] = X[7][i]\n",
        "  Yn[2][i] = Y[7][i]\n",
        "  Xn[3][i] = X[17][i]\n",
        "  Yn[3][i] = Y[17][i]\n",
        "  Xn[4][i] = X[18][i]\n",
        "  Yn[4][i] = Y[18][i]\n",
        "  Xn[5][i] = X[20][i]\n",
        "  Yn[5][i] = Y[20][i]\n",
        "  Xn[6][i] = X[22][i]\n",
        "  Yn[6][i] = Y[22][i]\n",
        "  Xn[7][i] = X[25][i]\n",
        "  Yn[7][i] = Y[25][i]\n",
        "  Xn[8][i] = X[26][i]\n",
        "  Yn[8][i] = Y[26][i]\n",
        "  Xn[9][i] = X[45][i]\n",
        "  Yn[9][i] = Y[45][i]\n",
        " \n",
        "obj = cp.Minimize(cp.norm(a,2))\n",
        "constr = [a.T@Xn - b >= 1, a.T@Yn - b <= -1]\n",
        "prob = cp.Problem(obj, constr)\n",
        "prob.solve()\n",
        " \n",
        "print(\"Max thickness using features selection:\", 2.0/cp.norm(a,2).value)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "i. Max thickness using only L2 norm: 116.42440493435046\n",
            "Cardinality for the above max thickness: 49\n",
            "ii. Cardinality curve:\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "iii. Feature selection:\n",
            "Minimum cardinality: 10.0\n",
            "Thickness corresponding to the above min cardinality: 77.02461436795765\n",
            "Indices of a for which a>=0.0001 and card(a)=10:\n",
            "i: 0\n",
            "i: 6\n",
            "i: 7\n",
            "i: 17\n",
            "i: 18\n",
            "i: 20\n",
            "i: 22\n",
            "i: 25\n",
            "i: 26\n",
            "i: 45\n",
            "Resolving the problem using the above 10 features selection:\n",
            "Max thickness using features selection: 78.46967629614345\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}