projectile- GitHub-V2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyomo.environ import *\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import random \n",
    "import operator\n",
    "import pandas as pd\n",
    "from skimage.transform import rescale, resize, downscale_local_mean\n",
    "\n",
    "from matplotlib.image import imread"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "image = imread('Pyomo.png')\n",
    "scale = 2\n",
    "image_resized = resize(image, (image.shape[0] // scale, image.shape[1] //scale),\n",
    "                       anti_aliasing=True)\n",
    "imageToMatrice=image_resized"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>index</th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>s</th>\n",
       "      <th>Dark</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>3377.000000</td>\n",
       "      <td>3377.000000</td>\n",
       "      <td>3377.000000</td>\n",
       "      <td>3377.000000</td>\n",
       "      <td>3377.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3687.061889</td>\n",
       "      <td>45.668345</td>\n",
       "      <td>55.261771</td>\n",
       "      <td>0.883324</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2068.114757</td>\n",
       "      <td>19.536245</td>\n",
       "      <td>21.909907</td>\n",
       "      <td>0.125102</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>98.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>0.501343</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>2007.000000</td>\n",
       "      <td>32.000000</td>\n",
       "      <td>38.000000</td>\n",
       "      <td>0.806151</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>3508.000000</td>\n",
       "      <td>44.000000</td>\n",
       "      <td>57.000000</td>\n",
       "      <td>0.892696</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>5299.000000</td>\n",
       "      <td>59.000000</td>\n",
       "      <td>73.000000</td>\n",
       "      <td>0.999861</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>8177.000000</td>\n",
       "      <td>93.000000</td>\n",
       "      <td>93.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             index            x            y            s    Dark\n",
       "count  3377.000000  3377.000000  3377.000000  3377.000000  3377.0\n",
       "mean   3687.061889    45.668345    55.261771     0.883324     0.0\n",
       "std    2068.114757    19.536245    21.909907     0.125102     0.0\n",
       "min      98.000000     1.000000     8.000000     0.501343     0.0\n",
       "25%    2007.000000    32.000000    38.000000     0.806151     0.0\n",
       "50%    3508.000000    44.000000    57.000000     0.892696     0.0\n",
       "75%    5299.000000    59.000000    73.000000     0.999861     0.0\n",
       "max    8177.000000    93.000000    93.000000     1.000000     0.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dic={}\n",
    "c=0\n",
    "for i in range(imageToMatrice.shape[0]):\n",
    "    for j in range(imageToMatrice.shape[1]):\n",
    "        dic[c,'x']=j\n",
    "        dic[c,'y']=imageToMatrice.shape[1]-i\n",
    "        dic[c,'s']=20*sum(imageToMatrice[i,j])/len(imageToMatrice[i,j])\n",
    "        c+=1   \n",
    "dic[c-1,'s']\n",
    "dfN=pd.DataFrame()\n",
    "dfN['x']=[dic[i,'x'] for i in range(c)]\n",
    "dfN['y']=[dic[i,'y'] for i in range(c)]\n",
    "dfN['s']=[80*(dic[i,'s']) for i in range(c)]\n",
    "\n",
    "dfN['s']=(1*dfN['s']/dfN['s'].max() )\n",
    "dfN['Dark']=1-round(dfN['s'],0)\n",
    "dfN['marker']=['o' for i in range(c)]\n",
    "\n",
    "fig= plt.figure(figsize=(8, 8))\n",
    "R=20\n",
    "x0=0.5*(dfN['x'].max()-dfN['x'].min())\n",
    "y0=-1+0.5*(dfN['y'].max()-dfN['y'].min())\n",
    "M = 300\n",
    "theta =np.linspace(0,2*np.pi,M)\n",
    "\n",
    "df=pd.DataFrame()\n",
    "df['X']=x0+R*np.cos(theta)\n",
    "df['Y']=3+y0+R*np.sin(theta)\n",
    "\n",
    "\n",
    "plt.scatter(dfN['x'],dfN['y'],s=8*(1-dfN['Dark']), marker='o',c='k')\n",
    "#plt.scatter(dfN['x'],dfN['y'],s=8*(1-dfN['Dark']), marker='.',c='b')\n",
    "\n",
    "#plt.scatter(df['X'],df['Y'],s=8, marker='o',c='r')\n",
    "\n",
    "dfN=dfN[dfN['Dark']==0 ]\n",
    "dfN=dfN.reset_index()\n",
    "dfN.describe() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame()\n",
    "N=10\n",
    "\n",
    "df['x'] = [10*random.random() for i in range(N)]\n",
    "df['y'] = [10*random.random() for i in range(N)]\n",
    "df['ti'] = [5*random.random() for i in range(N)]\n",
    "\n",
    "df = dfN\n",
    "N= len(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>index</th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>s</th>\n",
       "      <th>Dark</th>\n",
       "      <th>marker</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>98</td>\n",
       "      <td>4</td>\n",
       "      <td>93</td>\n",
       "      <td>0.626367</td>\n",
       "      <td>0.0</td>\n",
       "      <td>o</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>99</td>\n",
       "      <td>5</td>\n",
       "      <td>93</td>\n",
       "      <td>0.834229</td>\n",
       "      <td>0.0</td>\n",
       "      <td>o</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>100</td>\n",
       "      <td>6</td>\n",
       "      <td>93</td>\n",
       "      <td>0.851230</td>\n",
       "      <td>0.0</td>\n",
       "      <td>o</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>101</td>\n",
       "      <td>7</td>\n",
       "      <td>93</td>\n",
       "      <td>0.841159</td>\n",
       "      <td>0.0</td>\n",
       "      <td>o</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>102</td>\n",
       "      <td>8</td>\n",
       "      <td>93</td>\n",
       "      <td>0.830582</td>\n",
       "      <td>0.0</td>\n",
       "      <td>o</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3372</th>\n",
       "      <td>8083</td>\n",
       "      <td>93</td>\n",
       "      <td>9</td>\n",
       "      <td>0.846646</td>\n",
       "      <td>0.0</td>\n",
       "      <td>o</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3373</th>\n",
       "      <td>8092</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>0.628095</td>\n",
       "      <td>0.0</td>\n",
       "      <td>o</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3374</th>\n",
       "      <td>8093</td>\n",
       "      <td>9</td>\n",
       "      <td>8</td>\n",
       "      <td>0.576549</td>\n",
       "      <td>0.0</td>\n",
       "      <td>o</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3375</th>\n",
       "      <td>8113</td>\n",
       "      <td>29</td>\n",
       "      <td>8</td>\n",
       "      <td>0.594815</td>\n",
       "      <td>0.0</td>\n",
       "      <td>o</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3376</th>\n",
       "      <td>8177</td>\n",
       "      <td>93</td>\n",
       "      <td>8</td>\n",
       "      <td>0.584230</td>\n",
       "      <td>0.0</td>\n",
       "      <td>o</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>3377 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      index   x   y         s  Dark marker\n",
       "0        98   4  93  0.626367   0.0      o\n",
       "1        99   5  93  0.834229   0.0      o\n",
       "2       100   6  93  0.851230   0.0      o\n",
       "3       101   7  93  0.841159   0.0      o\n",
       "4       102   8  93  0.830582   0.0      o\n",
       "...     ...  ..  ..       ...   ...    ...\n",
       "3372   8083  93   9  0.846646   0.0      o\n",
       "3373   8092   8   8  0.628095   0.0      o\n",
       "3374   8093   9   8  0.576549   0.0      o\n",
       "3375   8113  29   8  0.594815   0.0      o\n",
       "3376   8177  93   8  0.584230   0.0      o\n",
       "\n",
       "[3377 rows x 6 columns]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>index</th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>s</th>\n",
       "      <th>Dark</th>\n",
       "      <th>marker</th>\n",
       "      <th>ti</th>\n",
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       "      <td>0.626367</td>\n",
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       "      <td>0.841159</td>\n",
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       "      <td>o</td>\n",
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       "      <td>2.111285</td>\n",
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       "      <td>0.628095</td>\n",
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       "      <td>4.135429</td>\n",
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       "      <th>3374</th>\n",
       "      <td>8093</td>\n",
       "      <td>10</td>\n",
       "      <td>16</td>\n",
       "      <td>0.576549</td>\n",
       "      <td>0.0</td>\n",
       "      <td>o</td>\n",
       "      <td>1.591232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3375</th>\n",
       "      <td>8113</td>\n",
       "      <td>30</td>\n",
       "      <td>16</td>\n",
       "      <td>0.594815</td>\n",
       "      <td>0.0</td>\n",
       "      <td>o</td>\n",
       "      <td>0.301165</td>\n",
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       "    <tr>\n",
       "      <th>3376</th>\n",
       "      <td>8177</td>\n",
       "      <td>94</td>\n",
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       "      <td>0.584230</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.799038</td>\n",
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       "<p>3377 rows × 7 columns</p>\n",
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      ],
      "text/plain": [
       "      index   x    y         s  Dark marker        ti\n",
       "0        98   5  101  0.626367   0.0      o  4.665668\n",
       "1        99   6  101  0.834229   0.0      o  3.680468\n",
       "2       100   7  101  0.851230   0.0      o  2.816235\n",
       "3       101   8  101  0.841159   0.0      o  1.120722\n",
       "4       102   9  101  0.830582   0.0      o  2.111285\n",
       "...     ...  ..  ...       ...   ...    ...       ...\n",
       "3372   8083  94   17  0.846646   0.0      o  3.064317\n",
       "3373   8092   9   16  0.628095   0.0      o  4.135429\n",
       "3374   8093  10   16  0.576549   0.0      o  1.591232\n",
       "3375   8113  30   16  0.594815   0.0      o  0.301165\n",
       "3376   8177  94   16  0.584230   0.0      o  0.799038\n",
       "\n",
       "[3377 rows x 7 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['x'].min()\n",
    "df['y'].min()\n",
    "\n",
    "df['x'] = [x+abs(df['x'].min()) for x in df['x'] ]\n",
    "df['y'] = [x+abs(df['y'].min()) for x in df['y'] ]\n",
    "df['ti'] = [5*random.random() for i in range(N)]\n",
    "\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0, y0= 0,0 \n",
    "model = AbstractModel()\n",
    "model.i = RangeSet(N)\n",
    "model.V0 = Var(model.i, bounds=(1,100), within=NonNegativeReals)\n",
    "model.alpha = Var(model.i,bounds=(0,np.pi/2), within=Reals)\n",
    "model.t = Var(bounds=(10,30), within=Reals)\n",
    "\n",
    "def rule_x(model,i):\n",
    "    return df.loc[i-1,'x']\n",
    "def rule_y(model,i):\n",
    "    return df.loc[i-1,'y']\n",
    "\n",
    "model.x = Param(model.i, initialize=rule_x)\n",
    "model.y = Param(model.i, initialize=rule_y)\n",
    "def Rule_C1(model,i):\n",
    "    return model.x[i]-x0== model.V0[i]*cos(model.alpha[i])*(model.t-df.loc[i-1,'ti']) \n",
    "model.C1=Constraint(model.i,rule=Rule_C1)\n",
    "\n",
    "def Rule_C2(model,i):\n",
    "    return model.y[i]-y0== -5*((model.t-df.loc[i-1,'ti'])**2) + model.V0[i]*sin(model.alpha[i])*(model.t-df.loc[i-1,'ti']) \n",
    "model.C2=Constraint(model.i,rule=Rule_C2)\n",
    "\n",
    "def rule_OF(model):\n",
    "    return model.t\n",
    "model.obj1 = Objective(rule=rule_OF, sense=minimize)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "opt = SolverFactory('ipopt')\n",
    "instance = model.create_instance()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "this is feasible and optimal\n",
      "9.999999904595846\n"
     ]
    }
   ],
   "source": [
    "results = opt.solve(instance) # solves and updates instance\n",
    "from pyomo.opt import SolverStatus, TerminationCondition\n",
    "if (results.solver.status == SolverStatus.ok) and (results.solver.termination_condition == TerminationCondition.optimal):\n",
    "     print (\"this is feasible and optimal\")\n",
    "elif results.solver.termination_condition == TerminationCondition.infeasible:\n",
    "     print (\"do something about it? or exit?\")\n",
    "else:\n",
    "     print ('ERROR ' + str(results.solver))\n",
    "print(value(instance.obj1) )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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