scipy_example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     con: array([], dtype=float64)\n",
      "     fun: -524.9999999951665\n",
      " message: 'Optimization terminated successfully.'\n",
      "     nit: 5\n",
      "   slack: array([3.56550345e-10, 6.10128836e-10, 7.13100690e-10])\n",
      "  status: 0\n",
      " success: True\n",
      "       x: array([15., 10.])\n",
      "Time :\n",
      "0.4876985549926758\n"
     ]
    }
   ],
   "source": [
    "from scipy.optimize import linprog\n",
    "import time\n",
    "start = time.time()\n",
    "c = [-25, -15]\n",
    "A = [[2,1],[3,2],[4,2]]\n",
    "b = [40, 65, 80]\n",
    "x0_bounds = (0, None)\n",
    "x1_bounds = (0, None)\n",
    "res = linprog(c, A_ub = A, b_ub = b, bounds=[x0_bounds, x1_bounds])\n",
    "print(res)\n",
    "stop=time.time()\n",
    "print(\"Time :\")\n",
    "print(stop - start)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: pulp in c:\\users\\dmytro\\anaconda3\\lib\\site-packages (2.4)\n",
      "Requirement already satisfied: amply>=0.1.2 in c:\\users\\dmytro\\anaconda3\\lib\\site-packages (from pulp) (0.1.4)\n",
      "Requirement already satisfied: pyparsing in c:\\users\\dmytro\\anaconda3\\lib\\site-packages (from amply>=0.1.2->pulp) (2.4.7)\n",
      "Requirement already satisfied: docutils>=0.3 in c:\\users\\dmytro\\anaconda3\\lib\\site-packages (from amply>=0.1.2->pulp) (0.16)\n",
      "result: \n"
     ]
    },
    {
     "ename": "NameError",
     "evalue": "name 'problem' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-3-b33cac3191d8>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m     12\u001b[0m \u001b[0mprob\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msolve\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     13\u001b[0m \u001b[0mprint\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;34m\"result: \"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 14\u001b[1;33m \u001b[1;32mfor\u001b[0m \u001b[0mvariable\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mproblem\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvariables\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     15\u001b[0m         \u001b[0mprint\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mvariable\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mname\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m\"=\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvariable\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvarValue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     16\u001b[0m \u001b[0mprint\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;34m\"income :\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'problem' is not defined"
     ]
    }
   ],
   "source": [
    "!pip install pulp\n",
    "from pulp import *\n",
    "import time\n",
    "start = time.time()\n",
    "x1 = pulp.LpVariable(\"x1\", lowBound = 0)\n",
    "x2 = pulp.LpVariable(\"x2\", lowBound = 0)\n",
    "prob = pulp.LpProblem('0', LpMaximize)\n",
    "prob += 25 * x1 + 15 * x2\n",
    "prob += 2 * x1 +  x2 <= 40\n",
    "prob += 3 * x1 + 2 * x2 <= 65\n",
    "prob += 4 * x1 + 2 * x2 <= 80\n",
    "prob.solve()\n",
    "print (\"result: \")\n",
    "for variable in problem.variables():\n",
    "\tprint (variable.name, \"=\", variable.varValue)\n",
    "print (\"income :\")\n",
    "print (value(prob.objective))\n",
    "stop = time.time()\n",
    "print('Time: ')\n",
    "print(stop - start)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'value' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-5-8746d215ab88>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mvalue\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mproblem\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mobjective\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m \u001b[0mprint\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mres\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfun\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0mprint\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mallclose\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mres\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfun\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mproblem\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mobjective\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'value' is not defined"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "def F(a1, a2, b, x):\n",
    "    return (b - a1 * x) / a2;\n",
    "\n",
    "x = np.arange(0, 20, 0.1)\n",
    "y1 = F(b = b[0], a1 = A[0][0], x=x, a2=A[0][1])\n",
    "y2 = F(b = b[1], a1 = A[1][0], x=x, a2=A[1][1])\n",
    "y3 = F(b = b[2], a1 = A[2][0], x=x, a2=A[2][1])\n",
    "\n",
    "\n",
    "plt.plot(x,y1)\n",
    "plt.fill_between(x, y1, alpha = 0.2)\n",
    "plt.text(2, 21, '2x1+x2<=40', rotation = 40)\n",
    "plt.plot(x, y2)\n",
    "plt.fill_between(x, y2, alpha = 0.2)\n",
    "plt.text(3, 10, '3x1+2x2<=65', rotation = 60)\n",
    "plt.plot(x, y3)\n",
    "plt.fill_between(x, y3, alpha = 0.2)\n",
    "plt.text(10, 3, '4x1+2x2<=80', rotation = 80)\n",
    "\n",
    "plt.plot(x,(c[0]*c[1]-np.abs(c[0])*x)/np.abs(c[1]),'--', color = 'purple')\n",
    "plt.plot(res.x[0], res.x[1], \"ro\")\n",
    "\n",
    "plt.title('qweasdzxc', fontsize = 25)\n",
    "plt.xlabel('x1', fontsize = 25)\n",
    "plt.ylabel('x2', fontsize = 25)\n",
    "plt.savefig(\"paint.png\", dpi = 600)\n",
    "plt.show;\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[33. 57.  0.  0.  0.]\n",
      " [30.  0.  0. 40.  0.]\n",
      " [ 7.  0. 50.  0.  8.]\n",
      " [ 0. 33.  0. 20. 22.]]\n",
      "Time: \n",
      "0.013958930969238281\n"
     ]
    }
   ],
   "source": [
    "from scipy.optimize import linprog\n",
    "import time\n",
    "start = time.time()\n",
    "c = [9,5,7,10,9,8,15,11,3,12,10,14,6,11,9,16,5,7,4,8,]\n",
    "A_ub = [[1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],\n",
    "\t [0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0],\n",
    "\t [0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0],\n",
    "\t [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1]]\n",
    "b_ub = [90,70,65,75]\n",
    "A_eq = [[1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0],\n",
    "\t [0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0],\n",
    "\t [0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0],\n",
    "\t [0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0],\n",
    "\t [0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1]]\n",
    "b_eq =[70,90,50,60,30]\n",
    "a = linprog(c, A_ub, b_ub, A_eq, b_eq)\n",
    "x=a.x.reshape((4,5))\n",
    "print(x.round())\n",
    "stop = time.time()\n",
    "print(\"Time: \")\n",
    "print(stop - start)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}