OR 7245 Project - Large Example.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 17,
   "outputs": [],
   "source": [
    "from scipy import optimize as opt\n",
    "from scipy.optimize import minimize\n",
    "from scipy.optimize import LinearConstraint\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import math"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Task 2 - Actual Example"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Task 2.1\n",
    "\n",
    "Let's start by loading our matrices as we did for the small example, being sure to enter the correct constants for number of beams, etc. for the actual_example specs:"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Given information\n",
    "num_beams = 126\n",
    "vertical_resolution = 60\n",
    "horizontal_resolution = 80\n",
    "num_pixels = vertical_resolution*horizontal_resolution\n",
    "max_critical_dose = 2\n",
    "min_tumor_dose = 10\n",
    "\n",
    "path_actual = \"task/actualexample/\"\n",
    "tumor_raw = np.loadtxt(path_actual+\"tumor_raw.txt\")\n",
    "critical_raw = np.loadtxt(path_actual+\"critical_raw.txt\")\n",
    "beam_raw = np.loadtxt(path_actual+\"beam_raw.txt\")"
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "Let us take a look at our treatment area (pink denoting tumor area, cyan denoting critical area, and purple denoting non-critical area):"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "outputs": [
    {
     "data": {
      "text/plain": "<matplotlib.colorbar.Colorbar at 0x7fa5dc4d3eb0>"
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 2 Axes>",
      "image/png": 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kbfsF4NJp9h8E1hbrXwKmjcb2VYOWOUizyfV0urZMKdOvMSJiZKYmYyjxwLJxSoUtaRnwH4BPde3u268xImKk6mvzrl3ZZpPfAX4VOK1r36v6NUqatV9jRMQoNDU599O35i3p/cBh2zvmUoCkDVN9J48e/eZcbhERMWev5Zr3xcAHioFSXgf8qKQ/AUr1a7S9EdgIcM45E64o7oiIUpqanPvpW/O2/THby2wvB9YDf2X75ynRrzEiYpRqHJiqdsP08562X2NExNjIZAwdth8BHinWp+3XGBExTppas+4nb1hGRGtlDsuIiIZK8o6IaJoGP5DsJ8k7IlotyTsiomGmxjZpoyTviGi11LwjIpombd4REc2U5B0R0UBJ3hERDdPmB5Yt/WdFRFDbZAySFknaKmlf8XnmDOc9J+lpSTslbR/0+m5J3hHRajWNKjjItJCX2F5pe2KO1wNJ3hHRcjUl72GnhRz4+iTviGitGsfzftW0kMBM00IaeFjSDkkb5nD9cXlgGRGtVjI5L+5ugwY2FrOAHSfpC8CPTXPtrw8QzsW2DxZz/m6V9IztRwe4/rgk74hor/KTMRzpaYM+ge3LZixGKjst5MHi87Ck+4BVwKOUnFayW5pNIqLVamo26TstpKTXSzptah14H7Cr7PW9krwjorVqbPO+BVgtaR+wuthG0jmSthTnLAG+JOlJ4CvAX9h+cLbrZ5Nmk4hotTresJxpWsiimWRtsf4scOEg188myTsi2isDU0VENFOSd0REw7R5bJMk74hotdS8IyKaJm3eERHN9JpO3pKeA74HvAwcsz0haRHwOWA58BzwYdvfnp8wIyLmpq3Je5Cm/N5hDAcewjAiok5TDyz7LU00TNjDDoEYETG/apqMYRTKJu/phjEsNYShpA2StkvafvToN4ePOCJiAG1N3mUfWJ4wjGHZAophFTcCnHPOhOcQY0TEnDU1OfdTqubdPYwhMDWM4aFi6ELKDmEYEVGnGgemql3f5D3LMIYDD2EYEVG3tibvMs0mS4D7JE2d/1nbD0p6HLhH0jXA14Er5i/MiIg5KD8ZQ+P0Td4zDWM4lyEMIyLq1tSadT95wzIiWmuqzbuNkrwjotWSvCMimqbBDyT7aWlTfkRERx29TSQtkrRV0r7i88xpznmLpJ1dy4uSbiiO3STpG13H1vYrM8k7IlqrxrFN+o71ZHtvMT7USuCdwFE6781M+e2p47a39F7fK8k7Ilqtpn7eg471dCnwD7a/NtcCk7wjor3qG5iq1FhPXdYDd/Xsu07SU5LumK7ZpVeSd0S0WsnkvXhqAL1i2dB7H0lfkLRrmmXdIPFIOhX4APCnXbtvA94MrAQmgd/qd5/0NomIVitZsz7SNVfB9PexL5vpmKRDkpbaniwx1tPlwBO2D3Xd+/i6pD8CHugXcGreEdFaNT6wHGSspyvpaTKZGuSv8CE640fNKsk7ItqrvjbvW4DVkvYBq4ttJJ0j6XjPEUkLi+P39lz/G5KelvQUcAnwK/0KTLNJRLRaHS/pzDTWUzGc9tqu7aPAG6c576pBy0zyjohWa+sblkneEdFaGZgqIqKhkrwjIprmtTwZQ0REk6XmHRHRMGnzjohoqCTviIimafFkDEneEdFqeWAZEdEwafOOiGiiNJtERDRTkndERAMleUdENFCSdwUmJ3ccuelmfQ1YDByps+xpjEMMMB5xjEMMMB5xjEMMMB5xjDqGHx/2Bs7r8dWwfRaApO39phyab+MQw7jEMQ4xjEsc4xDDuMQxDjFUITXviIgGSvKOiGigJO9qbRxRud3GIQYYjzjGIQYYjzjGIQYYjzjGIYahtPklHdkedQwREfNCExNe8Nj2vue9fLJ2DNO+L+kK4CbgrcAq29MWKmkN8LvAAuBTtqcmKl4EfA5YDjwHfNj2t2crs6XPYSMiOn54Uv+lAruAnwMenekESQuAW4HLgQuAKyVdUBy+EdhmewWwrdieVa3JW9IaSXsl7ZfUN7gKy71D0mFJu7r2LZK0VdK+4vPMeY7hPElflLRH0m5J19cdh6TXSfqKpCeLGG6uO4aeeBZI+jtJD4wiDknPSXpa0k5J20cRQ1HmGZL+TNIzxe/Hu2v+vXhL8TOYWl6UdMOofi+qZvVfhi7D3mN7b5/TVgH7bT9r+yXgbmBdcWwdsKlY3wR8sF+ZtSXvPt868+1OYE3PvoG/6YZ0DPio7bcCFwHXFv/+OuP4F+C9ti8EVgJrJF1Ucwzdrgf2dG2PIo5LbK/s+pN5FDH8LvCg7X8DXEjnZ1JbHLb3Fj+DlcA7gaPAfXXGMG927HgIaUffBV4naXvXsmEeojkXeL5r+0CxD2CJ7UmA4vPsvnezXcsCvBt4qGv7Y8DHaix/ObCra3svsLRYXwrsrSuWosz7gdWjigNYCDwBvGsUMQDL6CSE9wIPjOK/CZ22xcU9++qO4UeBf6R4/jSqOLrKfR/w16OMYVwX4At0mkd6l3Vd5zwCTMxw/RV02rmntq8C/lex/p2ec7/dL546e5tM963zrhrL7/WqbzpJ/b/pKiJpOfB24LG64yj+AtoB/CRwq+3HJI3iZ/E7wK8Cp3XtqzsOAw9LMvCHtjeOIIafAL4J/G9JF9L5b3P9COKYsh64q1gf2f8j48j2ZUPe4gBwXtf2MuBgsX5I0tLi57wUONzvZnW2eU/XsvSa6+oi6Q3A54EbbL9Yd/m2X3bnz+NlwCpJP1V3DJLeDxy2vaPusntcbPsddJryrpX070YQw8nAO4DbbL8d+CdG1Dwh6VTgA8CfjqL814DHgRWSzi9+1uuBzcWxzcDVxfrVdP4yn1WdyXu2b51ROFR8w1H2m25Ykk6hk7g/Y/veUcUBYPs7dP7EWzOCGC4GPiDpOToPbd4r6U/qjsP2weLzMJ023lV1x0Dn/4sDth8rtv+MTjIfxe/F5cATtg8V2yP53WwiSR+SdIBO8/BfSHqo2H+OpC0Ato8B1wEP0XmucY/t3cUtbgFWS9pHpzn1ln5l1pm8Z/vWGYWBv+mGIUnAp4E9tj85ijgknSXpjGL9R4DLgGfqjAHA9sdsL7O9nM7vwV/Z/vk645D0ekmnTa3TaevdVWcMALb/L/C8pLcUuy4Fvlp3HIUreaXJhBHF0Ei27yt+p/+V7SW2/32x/6DttV3nbbH9r22/2fb/6Nr/gu1Lba8oPr9VptA6G/zXAn8P/APw6zWWexcwCfyATk3nGuCNdB6Y7Ss+F81zDD9Np5noKWBnsaytMw7gbcDfFTHsAj5e7K/1Z9ET03t45YFlnT+LnwCeLJbdU7+Po/hZ0On5s7347/LnwJkj+P1cCLwAnN61b2S/F1n6L3nDMiKigfKGZUREAyV5R0Q0UJJ3REQDJXlHRDRQkndERAMleUdENFCSd0REAyV5R0Q00P8HB1sKa+3+JJsAAAAASUVORK5CYII=\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(tumor_raw-critical_raw, cmap='cool')\n",
    "plt.colorbar()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "And, dividing up our beam_raw into a proper set of beams:"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "outputs": [],
   "source": [
    "beam_set = []\n",
    "for i in range(0, num_beams):\n",
    "    temp = beam_raw[i*vertical_resolution : i*vertical_resolution+vertical_resolution]\n",
    "    beam_set.append(temp)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "We can get a general sense of our set of beams by printing them out:"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 1209.6x777.6 with 126 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_rows = 9\n",
    "n_cols = 14\n",
    "plt.figure(figsize=(n_cols * 1.2, n_rows * 1.2))\n",
    "for row in range(n_rows):\n",
    "    for col in range(n_cols):\n",
    "        index = n_cols * row + col\n",
    "        plt.subplot(n_rows, n_cols, index + 1)\n",
    "        plt.imshow(beam_set[index], cmap=\"cool\")\n",
    "        plt.axis('off')\n",
    "plt.subplots_adjust(wspace=0.2, hspace=0.5)\n",
    "\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now, let's make a dosage matrix, where each row i corresponds to the amount of radiation received by a given pixel by the ith beam:"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "outputs": [],
   "source": [
    "dosage_matrix = np.zeros((num_beams,num_pixels))\n",
    "for i in range(0,num_beams):\n",
    "    dosage_matrix[i] = beam_set[i].flatten()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "outputs": [
    {
     "data": {
      "text/plain": "(126, 4800)"
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dosage_matrix.shape"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now let's add our non-critical matrix. As with the small example, this will be the compliment of (tumor_raw+critical_raw)."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "outputs": [],
   "source": [
    "non_critical_raw = 1-(tumor_raw+critical_raw)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "For convenience, let us create flattened, vector versions of our various matrices:"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "outputs": [],
   "source": [
    "tumor_flat = tumor_raw.flatten()\n",
    "critical_flat = critical_raw.flatten()\n",
    "non_critical_flat = non_critical_raw.flatten()\n",
    "#print(\"Tumor locations:\", tumor_flat,\n",
    "#      \"\\nCritical locations:\",critical_flat,\n",
    "#     \"\\nNon-critical locations:\",non_critical_flat)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now we can go on to making the various components of our cost vector. Since to start, we want to minimize critical radiation and maximize tumor radiation, let’s make those two components of the cost vector first:"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "outputs": [],
   "source": [
    "cost_tumor = dosage_matrix @ tumor_flat\n",
    "cost_critical = dosage_matrix @ critical_flat\n",
    "#cost_non_critical = dosage_matrix @ non_critical_flat"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now we can go ahead defining our objective function and constraints. But first, we need to make vectors representative of the right-hand sides of our constraints. For our minimum tumor dosage vector, this will be a vector of all zeros, except for 10 at entries corresponding to pixels with values of 1 in our (flattened) tumor_raw. For our maximum critical dosage vector, it will be essentially the same—the only difference being for implementation purposes, instead of values of zeros in areas that aren’t critical, we’ll use an arbitrarily large value. This way we can use the vector in a less than or equal constraint and not be mistakenly constrained to be less than or equal to zero where we don’t need to be."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tumor dosage constraint: [0. 0. 0. ... 0. 0. 0.] \n",
      "Critical dosage constraint: [999. 999. 999. ... 999. 999. 999.]\n"
     ]
    }
   ],
   "source": [
    "min_tumor_dose_vector = min_tumor_dose * tumor_flat\n",
    "max_critical_dose_vector = max_critical_dose * critical_flat\n",
    "max_critical_dose_vector[max_critical_dose_vector==0] = 999\n",
    "\n",
    "print(\"Tumor dosage constraint:\",min_tumor_dose_vector,\n",
    "      \"\\nCritical dosage constraint:\",max_critical_dose_vector)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "We want to ultimately produce a weight vector, with each entry corresponding to a weight on a given beam. So, let us make an initial weight vector of zeros:"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "outputs": [
    {
     "data": {
      "text/plain": "array([0., 0., 0., 0., 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., 0., 0., 0., 0.,\n       0., 0., 0., 0., 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., 0., 0., 0., 0.,\n       0., 0., 0., 0., 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., 0., 0., 0., 0.,\n       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n       0., 0., 0., 0., 0., 0., 0.])"
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weights = np.zeros(num_beams)\n",
    "weights"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now we can write out our objective function and constraints. We want to minimize critical dosage and maximize tumor dosage, so formulating this for a minimization problem we want our objective function to be:\n",
    "$$Z = c_{c}^Tx - c_{t}^Tx$$"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "outputs": [],
   "source": [
    "def objective(x):\n",
    "#    return (cost_critical + cost_non_critical - cost_tumor) @ x\n",
    "    return (cost_critical - cost_tumor) @ x\n",
    "\n",
    "# the constraint is \"Ax <= b\"\n",
    "# For minimize() formulation, we have to return\n",
    "# \"Ax - b\" in preparation for saying\n",
    "# \"Ax - b >= 0\"\n",
    "def tumor_radiation_constraint(x):\n",
    "    return (dosage_matrix.T @ x) - min_tumor_dose_vector\n",
    "# Same for our critical constraint\n",
    "# But, it will be a <= constraint.\n",
    "# However, minimize() uses >= for its inequalities\n",
    "# So, we flip the signs.\n",
    "def critical_radiation_constraint(x):\n",
    "    return -(dosage_matrix.T @ x) + max_critical_dose_vector\n",
    "\n",
    "# the bounds parameter takes a list of doubles\n",
    "# where each double is an upper and lower bound for a decision variable.\n",
    "# So, for a non-negativity constraint on all variables,\n",
    "# we make a list with (0, 1e99) for each weight:\n",
    "non_neg_bounds = (0.0, 1e99)\n",
    "non_negativity_constraint = []\n",
    "for i in range(0, len(weights)):\n",
    "    non_negativity_constraint.append(non_neg_bounds)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "And now, solving:"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "outputs": [
    {
     "data": {
      "text/plain": "array([6.13300569e-07, 3.35575757e-10, 1.95356560e-09, 1.54469654e-07,\n       8.74570505e-10, 0.00000000e+00, 4.31488905e-09, 0.00000000e+00,\n       3.13401857e-09, 2.95086674e-03, 2.13207929e-09, 3.18752392e-07,\n       4.04753406e-07, 7.53025329e-01, 4.15600902e-09, 2.37594522e-01,\n       3.40849743e-09, 4.50731857e-01, 1.67584056e-06, 1.81558546e-08,\n       1.12600119e+02, 5.65602545e-07, 1.29579958e+02, 3.26687994e-01,\n       5.66881949e-02, 4.67204408e-09, 2.83468305e+02, 7.59114801e-04,\n       3.45076492e+02, 8.04166249e-01, 9.14507602e-03, 3.61406721e-01,\n       1.23887801e+01, 6.14522102e-02, 1.04381368e+02, 2.72119685e-02,\n       4.08157129e-01, 1.02985018e-07, 7.34436320e+01, 4.12987120e-01,\n       1.34934523e+02, 7.31520492e-03, 8.88352277e-03, 3.29756047e-01,\n       4.69941502e+01, 5.49088548e-03, 1.19030683e+02, 9.43743851e-11,\n       1.96885012e-01, 0.00000000e+00, 2.12095281e+02, 4.17490270e-01,\n       1.01900815e+02, 1.10154996e+00, 1.12682907e-07, 3.71840355e-08,\n       3.84809911e-09, 5.03106659e-03, 1.73393026e+02, 6.48364089e-07,\n       4.08148374e-04, 2.40853591e-09, 2.60726551e-09, 2.05432171e-04,\n       3.68204775e+02, 1.09956401e+02, 2.49906434e-06, 3.94363885e-10,\n       1.95392141e-09, 1.20659052e-06, 1.23766530e-06, 5.34734416e+02,\n       6.36484823e-07, 4.28451050e-10, 2.30992470e-09, 5.49662886e-03,\n       2.32118081e+02, 2.84444446e-09, 3.58191685e-09, 2.74438474e-07,\n       2.57279910e-09, 4.22910886e-01, 3.22066525e-09, 3.13854089e-09,\n       9.42584366e-10, 4.73082384e-07, 3.59729810e-09, 1.62662251e-06,\n       1.46406590e+01, 1.23161484e+02, 0.00000000e+00, 2.32558142e+00,\n       3.19789506e+02, 1.25120299e-07, 1.81218675e-07, 1.13742245e+02,\n       0.00000000e+00, 4.37459541e+02, 2.32558203e+00, 1.07601229e-07,\n       1.20626502e+02, 3.26429696e-10, 6.32187357e-10, 1.10524430e+01,\n       4.29276568e-07, 5.49495706e-03, 1.93852793e+02, 2.11741537e-06,\n       3.93819883e-09, 0.00000000e+00, 1.34923854e+00, 1.20915094e-07,\n       4.09573877e-09, 2.15202349e-10, 5.50594500e-07, 5.48542235e-10,\n       1.83342296e-07, 4.22911863e-01, 2.84136541e-03, 9.93057765e-10,\n       4.87108597e-07, 8.77011385e-10, 0.00000000e+00, 6.97831305e-07,\n       3.73116004e-09, 1.48251614e-09])"
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cons = [{'type':'ineq','fun':tumor_radiation_constraint},\n",
    "        {'type':'ineq','fun':critical_radiation_constraint}]\n",
    "\n",
    "actual_solution = minimize(objective, x0=weights, constraints=cons, bounds=non_negativity_constraint)\n",
    "#actual_solution = minimize(objective, x0=weights, constraints=cons, bounds=non_negativity_constraint)\n",
    "actual_solution.x"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Our problem in its current form is infeasible. This is a flaw with scipy.optimize.minimize(), in that if given an infeasible problem, it will ignore the constraints in order to give an approximation of our objective function. Special formulation is required of our constraints if we want minimize() to explicitly adhere to constraints (as it should). In particular, one can make their constraints instantiations of the LinearConstraint() class, where we can explicitly \"True\" for a \"keep_feasible\" field. However, this requires a matrix as input, and currently our constraints are in the form of functions. In implementation later on in this notebook, we will address this infeasibility. In the meantime, we will have to manually keep an eye out for when our model produces a result in which constraints (namely, our minimum tumor radiation constraint) is not adhered to."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "To illustrate our infeasibility, let us take a look at which pixels are being radiated to at least a value of 10, and which are not:"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "outputs": [
    {
     "data": {
      "text/plain": "<matplotlib.colorbar.Colorbar at 0x7fa5b9a4c460>"
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 2 Axes>",
      "image/png": "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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "radiation_area = np.zeros(beam_set[0].shape)\n",
    "\n",
    "for i in range(0, num_beams):\n",
    "    radiation_area = radiation_area + (actual_solution.x[i] * beam_set[i])\n",
    "\n",
    "radiation_area[radiation_area<9.9]=0\n",
    "radiation_area[radiation_area>10]=10\n",
    "plt.imshow(radiation_area, cmap='cool')\n",
    "plt.colorbar()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Indeed, while our radiation beams did not all manage to satisfy the minimum tumor radiation constraints, we see that the program did successfully avoid using beams which cross over the critical region. While this formulation may be infeasible, it appears we are on the right track. In order to get a feasible result, let us now relax our constraints to allow for some wiggle room:"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Task 2.2\n",
    "\n",
    "We will now implement our relaxed threshold model. Let us create these in the straightforward manner as with the small example."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "outputs": [],
   "source": [
    "delta_tumor_dose = 3\n",
    "delta_critical_dose = 3\n",
    "\n",
    "delta_tumor_dose_vector = delta_tumor_dose * tumor_flat\n",
    "delta_critical_dose_vector = delta_critical_dose * critical_flat\n",
    "\n",
    "def relaxed_tumor_radiation_constraint(x):\n",
    "    normal_bound = tumor_radiation_constraint(x)\n",
    "    result = normal_bound - delta_tumor_dose_vector\n",
    "    return result\n",
    "\n",
    "def relaxed_critical_radiation_constraint(x):\n",
    "    normal_bound = critical_radiation_constraint(x)\n",
    "    result = normal_bound + delta_critical_dose_vector\n",
    "    return result"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "For implementation purposes, we will add a maximum weight constraint as well. This is to ensure that the algorithm terminates once minimize() decides to violate the inequality constraints.\n",
    "\n",
    "And now, redefining our constraints and re-optimizing:"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "outputs": [],
   "source": [
    "#Weight limit constraint:\n",
    "WT_LIMIT = 100 #An arbitrary weight limit we would like to impose\n",
    "#Must return -total+limit\n",
    "#Since minimize() uses >=0 for its inequalities\n",
    "def max_radiation_constraint(x):\n",
    "    total_weight = np.sum(x)\n",
    "    return -total_weight + WT_LIMIT"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "outputs": [],
   "source": [
    "#WT_LIMIT is remaining 100, from last time\n",
    "cons = [{'type':'ineq','fun':relaxed_tumor_radiation_constraint},\n",
    "        {'type':'ineq','fun':relaxed_critical_radiation_constraint},\n",
    "        {'type':'ineq','fun':max_radiation_constraint}]\n",
    "\n",
    "actual_solution = minimize(objective, x0=weights, constraints=cons, bounds=non_negativity_constraint)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "And, plotting our radiation pattern:"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "outputs": [
    {
     "data": {
      "text/plain": "<matplotlib.colorbar.Colorbar at 0x7fa5b98c46a0>"
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 2 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "radiation_area = np.zeros(beam_set[0].shape)\n",
    "\n",
    "for i in range(0, num_beams):\n",
    "    radiation_area = radiation_area + (actual_solution.x[i] * beam_set[i])\n",
    "\n",
    "plt.imshow(radiation_area, cmap='cool')\n",
    "plt.colorbar()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "We see that we have achieved a similar result to the previous iteration of our problem, this time yielding a slightly lower total tumor radiation received, reflecting the decreased constraint boundary. Similarly, there is a minor increase in critical area radiation compared to our previous result.\n",
    "\n",
    "In both instances, the solution follows the pattern of heavily weighting only a handful of beams, and using small fractional weights for the remaining beams."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Task 2.3"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "As in the analysis for the small example, we must create and load a border_raw.txt file to indicate where the border of the critical region is. We must then create an associated cost vector for radiating the border region, in preparation for creating a modified cost function."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "outputs": [],
   "source": [
    "border_raw = np.loadtxt(path_actual+\"border_raw.txt\")\n",
    "border_flat = border_raw.flatten()\n",
    "cost_border = dosage_matrix @ border_flat"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now, we can create a modified cost function as follows:\n",
    "$$Z = c_B + c_C - c_T$$\n",
    "For some border region $c_B$."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "outputs": [],
   "source": [
    "def objective_border(x):\n",
    "    return (cost_critical + cost_border - cost_tumor) @ x"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now, let us re-optimize and plot:"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Objective Function Value:  -5809.026206772727\n",
      "Tumor radiation received: 5853.405075969319\n",
      "Critical radiation received: 44.37886919659177\n"
     ]
    }
   ],
   "source": [
    "cons = [{'type':'ineq','fun':tumor_radiation_constraint},\n",
    "        {'type':'ineq','fun':critical_radiation_constraint},\n",
    "        {'type':'ineq','fun':max_radiation_constraint}]\n",
    "\n",
    "actual_solution = minimize(objective_border, x0=weights, constraints=cons, bounds=non_negativity_constraint)\n",
    "\n",
    "print(\"Objective Function Value: \",objective(actual_solution.x))\n",
    "print(\"Tumor radiation received:\",(cost_tumor @ actual_solution.x))\n",
    "print(\"Critical radiation received:\",(cost_critical @ actual_solution.x))"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Plotting:"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "outputs": [
    {
     "data": {
      "text/plain": "<matplotlib.colorbar.Colorbar at 0x7fa5b8f30a90>"
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 2 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "radiation_area = np.zeros(beam_set[0].shape)\n",
    "\n",
    "for i in range(0, num_beams):\n",
    "    radiation_area = radiation_area + (actual_solution.x[i] * beam_set[i])\n",
    "\n",
    "plt.imshow(radiation_area, cmap='cool')\n",
    "plt.colorbar()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Task 2.4"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now we must implement our enhanced model. Given what we have observed in our infeasible formulations up to now, it is not clear that a single decision variable for upper and lower bounds on critical and tumor areas (respectively) will yield a feasible result. So, for this problem we will be formulating a version of our enhanced model (as discussed in the paper) which:\n",
    "* uses a decision variable for the lower bound on each pixel in the tumor region; and\n",
    "* does not include a decision variable or variables for our critical region, as we appear to be able to avoid it relatively easily.\n",
    "\n",
    "As our problem is infeasible, we cannot hope to radiate each pixel of the tumor region with the recommended 10 units of radiation. We can, however, create for each pixel a modified radiation threshold of:\n",
    "$$\n",
    "b_T - \\Delta b_T\n",
    "$$\n",
    "and aim to minimize the total $\\Delta b_T$ deviations from our recommended dosage $b_T$.\n",
    "\n",
    "To begin, let us create a decision variable of size [number of tumor pixels + number of beams]:"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "outputs": [],
   "source": [
    "tumor_set = tumor_flat[tumor_flat!=0]\n",
    "num_tumor_pixels = len(tumor_set)\n",
    "\n",
    "critical_set = critical_flat[critical_flat!=0]\n",
    "num_critical_pixels = len(critical_set)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "outputs": [
    {
     "data": {
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     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w_hat = np.zeros(num_tumor_pixels+num_beams)\n",
    "w_hat"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "For implementation, we will say that the first length(tumor_set) (our number of tumor pixels, 564) of our $\\hat{w}$ are our decision variables for the tumor constraint boundaries, and the following 126 onward will be the decision variables for the weights of our 126 beams.\n",
    "\n",
    "We must now make modified constraints which incorporate these new decision variables. To do this, we must in essence create"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "outputs": [],
   "source": [
    "tumor_V = tumor_raw.reshape(-1)\n",
    "critical_V = critical_raw.reshape(-1)\n",
    "\n",
    "beam_tumor_V = dosage_matrix[:,tumor_V != 0 ]\n",
    "beam_critical_V = dosage_matrix[:,critical_V != 0]\n",
    "\n",
    "A_critical_1 = np.zeros((num_critical_pixels, num_tumor_pixels))\n",
    "A_critical_2 = beam_critical_V.T\n",
    "A_critical = np.concatenate((A_critical_1,A_critical_2),axis=1)\n",
    "b_critical = np.ones(num_critical_pixels) * max_critical_dose\n",
    "\n",
    "# now the tumor constraints\n",
    "# this allows for each tumor location to have an under-dosage amount\n",
    "# and these under dosage amounts will be minimized in sum\n",
    "\n",
    "A_tumor_1 = - np.eye(num_tumor_pixels)\n",
    "A_tumor_2 = - beam_tumor_V.T\n",
    "A_tumor = np.concatenate((A_tumor_1,A_tumor_2),axis=1)\n",
    "b_tumor = - np.ones(num_tumor_pixels) * min_tumor_dose"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "And now we create an objective function. We know that in practice, if we aim to maximize total radiation provided to all tumor pixels, we will simply select some subset of beams which only radiate the tumor region and assign them weights as high as possible. So, for implementation now, we will simply seek to maximize (or, minimize the negative) of our minimum tumor radiation boundaries."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "outputs": [],
   "source": [
    "# now using optimize.minimize()\n",
    "# using the same matrices as defined above\n",
    "\n",
    "def objective(x):\n",
    "    c_1 = np.ones(num_tumor_pixels)\n",
    "    c_2 = np.zeros(num_beams)\n",
    "    c = np.concatenate((c_1, c_2))\n",
    "    return c @ x\n",
    "\n",
    "def tumor_radiation_constraint(x):\n",
    "    return - (A_tumor @ x) + b_tumor\n",
    "\n",
    "def critical_radiation_constraint(x):\n",
    "    return - (A_critical @ x) + b_critical\n",
    "\n",
    "non_neg_bounds = (0.0, 1e99)\n",
    "non_negativity_constraint = []\n",
    "for i in range(num_tumor_pixels + num_beams ):\n",
    "    non_negativity_constraint.append(non_neg_bounds)\n",
    "\n",
    "cons = [{'type':'ineq','fun':tumor_radiation_constraint},\n",
    "        {'type':'ineq','fun':critical_radiation_constraint}]\n",
    "\n",
    "actual_solution = opt.minimize(objective, x0=w_hat, constraints=cons, bounds=non_negativity_constraint)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "outputs": [
    {
     "data": {
      "text/plain": "<matplotlib.colorbar.Colorbar at 0x7fa5b963ee80>"
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 2 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "radiation_area = np.zeros(beam_set[0].shape)\n",
    "\n",
    "for i in range(0, num_beams):\n",
    "    radiation_area = radiation_area + (actual_solution.x[i+num_tumor_pixels] * beam_set[i])\n",
    "\n",
    "plt.imshow(radiation_area, cmap='cool')\n",
    "plt.colorbar()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Let us get a better visual on how well we radiated our tumor region, and how effectively we avoided radiating our critical region.\n",
    "\n",
    "First, our tumor region:"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": "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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "solution_weights = actual_solution.x[num_tumor_pixels:num_tumor_pixels+num_beams]\n",
    "solution_dosage = dosage_matrix.T @ solution_weights\n",
    "\n",
    "\n",
    "tumor_N = np.where(tumor_V != 0.)[0].reshape(-1)\n",
    "tumor_dosages = solution_dosage[tumor_N]\n",
    "plt.hist(tumor_dosages, bins=1000, cumulative=True, density=True)\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Next, our critical region:"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": "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\n"
     },
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   "source": [
    "critical_N = np.where(critical_V != 0.)[0].reshape(-1)\n",
    "\n",
    "critical_dosages = solution_dosage[critical_N]\n",
    "plt.hist(critical_dosages, bins=1000, cumulative=True, density=True)\n",
    "plt.show()"
   ],
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    "Here, we see that by minimizing the total deviations from the lower limit on tumor radiation per pixel, we achieve a result in which roughly 35% of all tumor pixels receive less than the previously-requested dose of 10, while we were able to achieve a result of 10 or greater in the remaining 65% of all pixels. Furthermore, we are successfully able to avoid radiating any portion of the critical area beyond the required 2 dose limit."
   ],
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    }
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   "source": [],
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