simplex_with_visualization.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_objective_function_value(tableau):\n",
    "    return -tableau[-1][-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simplex_with_visualization(c, A, b, halfspaces, feasible_point):\n",
    "    tableau = to_tableau(c, A, b)\n",
    "\n",
    "    zs = [get_objective_function_value(tableau)]\n",
    "    solutions = [get_solution(tableau)]\n",
    "    while can_be_improved(tableau):\n",
    "        pivot_position = get_pivot_position(tableau)\n",
    "        tableau = pivot_step(tableau, pivot_position)\n",
    "        solutions.append(get_solution(tableau))\n",
    "        zs.append(get_objective_function_value(tableau))\n",
    "    \n",
    "    points = [v[:2] for v in solutions]\n",
    "    xlim = (-1, max([p[0] for p in points]) + 1)\n",
    "    ylim = (-1, max([p[1] for p in points]) + 1)\n",
    "    render_inequalities(halfspaces, feasible_point, xlim, ylim)\n",
    "\n",
    "    for start, end in zip(points[:-1], points[1:]):\n",
    "        dx = end[0] - start[0]\n",
    "        dy = end[1] - start[1]\n",
    "        if dx > 0 and dy > 0:\n",
    "            plt.arrow(\n",
    "                start[0],\n",
    "                start[1],\n",
    "                dx,\n",
    "                dy,\n",
    "                width=0.1,\n",
    "                length_includes_head=True,\n",
    "                color='#1abc9c'\n",
    "            )\n",
    "    plt.show()\n",
    "    \n",
    "    steps = range(len(zs))\n",
    "    plt.plot(steps, zs, color=\"#2c3e50\")\n",
    "    plt.xticks(steps)\n",
    "    plt.xlabel('steps')\n",
    "    plt.ylabel('objective function value')\n",
    "    \n",
    "    return get_solution(tableau)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[4.0, 4.0, 2.0, 0, 0]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "simplex_with_visualization(c, A, b, halfspaces, feasible_point)"
   ]
  }
 ],
 "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}