lp02_simplex.ipynb

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    "# <center>The simplex algorithm</center>\n",
    "### <center>Alfred Galichon (NYU & Sciences Po)</center>\n",
    "## <center>'math+econ+code' masterclass series</center>\n",
    "#### <center>With python code examples</center>\n",
    "© 2018–2023 by Alfred Galichon with contributions by Antoine Jacquet. Past and present support from NSF grant DMS-1716489, ERC grant CoG-866274 are acknowledged, as well as inputs from contributors listed [here](http://www.math-econ-code.org/team).\n",
    "\n",
    "**If you reuse material from this masterclass, please cite as:**<br>\n",
    "Alfred Galichon, 'math+econ+code' masterclass series. https://www.math-econ-code.org/"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "### Learning objectives\n",
    "\n",
    "* Standard form of a LP and slack variables\n",
    "* The simplex algorithm\n",
    "\n",
    "### References\n",
    "\n",
    "* Vanderbei (1996). *Linear programming.* Springer"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "# 1. Primal simplex via dictionary\n",
    "\n",
    "The simplex algorithm was developed by G. B. Dantzig in 1947 as a way to solve linear programming problems of the canonical form\n",
    "\n",
    "\\begin{align}\n",
    "\\max_{x\\in\\mathbf R_+^J} & ~ c^\\top x \\\\\n",
    "\\text{s.t.} & ~ Ax \\leq d\n",
    "\\end{align}\n",
    "\n",
    "where $c \\in \\mathbf R^J$, $d \\in \\mathbf R^I$, and $A$ is a $I\\times J$ matrix. We assume that $I<J$, and that $A$ is of full rank, hence $rk(A) = I$.\n",
    "\n",
    "The idea of the algorithm is to start from a simple feasible point called a *basic feasible solution*, and then to iteratively identify directions along which the objective function increases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "XTwuussNv7T4"
   },
   "source": [
    "Let's begin by loading the usual packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
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   "source": [
    "#!pip install gurobipy\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import scipy.sparse as spr\n",
    "import gurobipy as grb\n",
    "import sympy\n",
    "from sympy.solvers import solve\n",
    "from sympy import *\n",
    "import matplotlib.pyplot as plt\n",
    "from mec.lp import LP,round_expr, limited_tabulate\n",
    "from mec.data import load_stigler_data\n"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {
    "id": "tdbclc58UxRW"
   },
   "source": [
    "## 1.1 An example\n",
    "\n",
    "Consider the linear programming problem:\n",
    "\n",
    "\\begin{align*}\n",
    "\\max_{x_1, x_2 \\geq 0}  & ~ x_1 + x_2 \\\\\n",
    "\\text{s.t.} & ~ 2 x_1 + x_2 \\leq 2 \\\\\n",
    "            & ~ x_1 + 2 x_2 \\leq 2.\n",
    "\\end{align*}\n"
   ]
  },
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   "source": [
    "Before even starting the algorithm, we first need to transform this linear program into one in *standard form*, that is, to replace inequality constraints with equality ones. To achieve this, we introduce slack variables $s_i$ to rewrite the problem as\n",
    "\n",
    "\\begin{align*}\n",
    "\\max_{x_1, x_2, s_1, s_2 \\geq 0}  & ~ x_1 + x_2 \\\\\n",
    "\\text{s.t.} & ~ s_1 = 2 - 2 x_1 - x_2 \\\\\n",
    "            & ~ s_2 = 2 - x_1 - 2 x_2 .\n",
    "\\end{align*}\n",
    "\n",
    "The variables $s_i$ are called *slack variables*, and the variables $x_j$ are called *decision variables*."
   ]
  },
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   "metadata": {},
   "source": [
    "Linear programming problems in this standard form can be summarized by a structure called a *dictionary*, which restates the constraints and the objective by expressing $I$ variables called *basic variables* as a function of the others called *nonbasic variables*. \n",
    "\n",
    "Given that in our example<br>\n",
    "$s_1 = 2 - 2 x_1 - x_2$ and<br>\n",
    "$s_2 = 2 - x_1 - 2 x_2 $,<br>\n",
    "we see that initially, the slack basic variables are the basic ones, and the decision variables are the nonbasic ones, but this will change over time.\n",
    "\n",
    "\n",
    "We shall call $K=I+J$ the total number of variables (slack or decision variables all together), and denote $z_k$ a generic variable (which concatenates slack and decision variable), so that $z^\\top = (s^\\top,x^\\top)$. We denote $\\{ z_b \\}$ the set of basic variables, and $\\{z_n\\}$ the set of nonbasic variables.\n",
    "\n",
    "We let $B$ be the matrix formed by the set of columns of $(\\mathbf{I}_I~A)$ corresponding to basic variables and $N$ the matrix formed by set of the columns of the same matrix corresponding to the nonbasic variables, so that we have $B (x_b) + N (x_n) = d$, and thus the dictionary is given by<br>\n",
    "$ (z_b) = (t_b) - T (z_n)$<br>\n",
    "where $t=B^{-1} d$ and $T=B^{-1} N$,<br> \n",
    "and the objective is<br>\n",
    "$Obj = (c_b)^\\top B^{-1} d + ((c_n)^\\top - (c_b)^\\top B^{-1} N )z_n$.  \n"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "We begin by defining a `Dictionary` class in Python to handle this type of data.  The expressions of the objective and of the basic variables as a function of the nonbasic ones are encoded into a *dictionary*:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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   "source": [
    "class Dictionary(LP):\n",
    "    def __init__(self, A_i_j, d_i, c_j , slack_var_names_i=None,decision_var_names_j=None): # s_i = d_i - A_i_j @ x_j\n",
    "        LP.__init__(self,A_i_j, d_i, c_j,decision_var_names_j,slack_var_names_i)\n",
    "        self.nonbasic = symbols(self.decision_var_names_j)\n",
    "        self.base = { Symbol('obj') : c_j @ self.nonbasic }\n",
    "        slack_exprs_i = d_i  - A_i_j @ self.nonbasic\n",
    "        self.base.update({Symbol(name): slack_exprs_i[i] for (i,name) in enumerate(self.slack_var_names_i) })\n",
    "\n",
    "    def variables(self):\n",
    "        return( list(self.base.keys())[1:] + self.nonbasic)\n",
    "\n",
    "    def display(self):\n",
    "        print('-------------------------- \\nObjective and constraints:')\n",
    "        for var in self.base:\n",
    "            print(var, '=', round_expr(self.base[var],2))"
   ]
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   "source": [
    "We then define the dictionary corresponding to our example."
   ]
  },
  {
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   "execution_count": 3,
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     "base_uri": "https://localhost:8080/"
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    "outputId": "0705f22d-ac67-449e-df30-daffdd2edc1b"
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     "output_type": "stream",
     "text": [
      "-------------------------- \n",
      "Objective and constraints:\n",
      "obj = x_1 + x_2\n",
      "s_1 = -2*x_1 - x_2 + 2\n",
      "s_2 = -x_1 - 2*x_2 + 2\n"
     ]
    }
   ],
   "source": [
    "def build_simple_example():\n",
    "    return ({'A_i_j': np.array([[2, 1], [1, 2]]),\n",
    "            'd_i': np.array([2,2]),\n",
    "            'c_j': np.array([1,1])\n",
    "           })\n",
    "\n",
    "dictionary_example = Dictionary(**build_simple_example(),\n",
    "                                slack_var_names_i = ['s_1', 's_2'],\n",
    "                                decision_var_names_j = ['x_1', 'x_2']\n",
    "                                )\n",
    "\n",
    "dictionary_example.display()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "18VVg1KnOgp5"
   },
   "source": [
    "## 1.2 Description of the algorithm\n",
    "\n",
    "Let's take a step-by-step approach to understand the simplex algorithm.\n",
    "Along the way, we will also code these steps.\n",
    "\n",
    "#### **Step 1: Initialize.**\n",
    "Our first step is to establish a (feasible) starting point. There is an obvious one which consists in setting $x_1 = x_2 = 0$ and $s_1 = 2$, $s_2 = 2$. This starting point is called a *basic feasible solution* because it is zero outside of the basic variables. The value of the objective at this solution is $0$.\n",
    "\n",
    "We create a method which computes the basic feasible solution associated with a dictionary, as well as the value of the objective at this solution."
   ]
  },
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   "source": [
    "def Dictionary_primal_solution(self, verbose=0):\n",
    "    x_j = np.zeros(self.nbj)\n",
    "    for j,var in enumerate(symbols(self.decision_var_names_j)):\n",
    "        x_j[j]=float( self.base.get(var,sympy.Integer(0)).subs([(variable,0) for variable in self.nonbasic]) )\n",
    "        if verbose > 0:\n",
    "            print(var, '=', x_j[j])\n",
    "    return x_j\n",
    "\n",
    "Dictionary.primal_solution = Dictionary_primal_solution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "A9AV61IMOgp6"
   },
   "source": [
    "We plot the feasible region and our initial solution using:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
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     "height": 435
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_1 = 0.0\n",
      "x_2 = 0.0\n"
     ]
    },
    {
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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "path_example = [dictionary_example.primal_solution(verbose=1)]\n",
    "dictionary_example.plot2d(path_example)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "in7Rbjge88k7"
   },
   "source": [
    "#### **Step 2: Entering variable.**\n",
    "We want to grow a nonbasic variable in order to increase our objective. This variable is called *entering variable*. This growth will be offset by an adjustment in the basic variables. Any nonbasic variable whose coefficient in the objective is positive is therefore a potential entering variable.\n",
    "\n",
    "There are several ways to choose the entering variable. One possibility is to choose the variable that has the highest coefficient in the objective.\n",
    "\n",
    "Another method is to follow *Bland's rule*, i.e. to select the first variable (in the alphabetical order) which has a positive coefficient in the objective. This method is the safest as it prevents the algorithm from cycling in some pathological cases, and therefore we will implement it here.\n",
    "\n",
    "Recall that the objective in our example is $x_1 + x_2$, and therefore Bland's rule selects $x_1$ as the entering variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 36
    },
    "id": "0r30XChw1OaL",
    "outputId": "2dfcdf53-69bc-4459-cc11-7df6124d8f2b"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x_{1}$"
      ],
      "text/plain": [
       "x_1"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def Dictionary_determine_entering(self):\n",
    "    self.nonbasic.sort(key=str) # Bland's rule\n",
    "    for entering_var in self.nonbasic:\n",
    "        if diff(self.base[Symbol('obj')],entering_var) > 0 :\n",
    "            return entering_var\n",
    "    return None # If no entering variable found, None returned\n",
    "\n",
    "Dictionary.determine_entering = Dictionary_determine_entering\n",
    "\n",
    "entering_var = dictionary_example.determine_entering()\n",
    "entering_var"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "INYg4--r1I3j"
   },
   "source": [
    "#### **Step 3: Departing variable.**\n",
    "Recall, the increase in the nonbasic variable $x_1$ needs to be offset by an adjustment in the basic variables. Here, the basic variables are the slack variables $s_i$. More precisely, if we set $x_1>0$, we need to adjust $s_i$ by $- A_{i1} x_1$. If $A_{i1}\\leq 0$, this does not threaten the feasibility constraint $s_i \\geq 0$, but if $A_{i1}>0$, it does. Hence we shall increase the value of $x_1$ until we hit any of the constraints $s_i \\geq 0$. Recall:\n",
    "\n",
    "\\begin{align*}\n",
    "s_1 &= 2 - 2 x_1 - x_2 \\\\\n",
    "s_2 &= 2 - x_1 - 2 x_2.\n",
    "\\end{align*}\n",
    "\n",
    "Note that we keep $x_2=0$ along the way. Here it is the constraint $s_1 \\geq 0$ which will hit first (for $x_1 = 1$). Therefore we choose $s_1$ as our *departing variable*.\n",
    "\n",
    "In general, if $n^\\star$ is the entering variable, the formula for determining the departing variable is\n",
    "\n",
    "$b^\\star = \\arg\\min_{b} \\left\\{ \\frac {t_b} {T_{b \\, n^\\star}} : T_{b \\, n^\\star} > 0  \\right\\}$.\n",
    "\n",
    "We code this into:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 36
    },
    "id": "g2oygb0o6JEd",
    "outputId": "4c880339-441e-42e4-d9e2-c4f1a5d29398"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle s_{1}$"
      ],
      "text/plain": [
       "s_1"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def Dictionary_determine_departing(self,entering_var):\n",
    "    runmin = float('inf')\n",
    "    departing_var = None\n",
    "    for var in self.base.keys() - {Symbol('obj')}:\n",
    "        the_expr_list = solve(self.base[var] - var,entering_var)\n",
    "        if the_expr_list: # if one can invert the previous expression\n",
    "            the_expr = the_expr_list[0] # express entering variable as a function of the other ones:\n",
    "            val_entering_var = the_expr.subs([ (variable,0) for variable in [var]+self.nonbasic])\n",
    "            if (val_entering_var >= 0) & (val_entering_var < runmin) :\n",
    "                runmin,departing_var = val_entering_var, var\n",
    "    return departing_var # if no variable is found, None returned\n",
    "\n",
    "Dictionary.determine_departing = Dictionary_determine_departing\n",
    "\n",
    "departing_var = dictionary_example.determine_departing(entering_var)\n",
    "departing_var"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3ZmiyS9e6KgT"
   },
   "source": [
    "#### **Step 4: Updating.**\n",
    "We reformulate our problem with our new basis $(x_1, s_2)$. We use the constraint associated with our departing variable $s_1$ as a pivot to eliminate the entering variable $x_1$ from the other equalities:\n",
    "\n",
    "\\begin{matrix}\n",
    "&\\tfrac{1}{2}s_1  &       &~+ x_1 &+~ \\tfrac{1}{2} x_2 &= 1 \\\\\n",
    "&-\\tfrac{1}{2}s_1 &+~ s_2 &       &+~ \\tfrac{3}{2} x_2 &= 1\n",
    "\\end{matrix}\n",
    "\n",
    "and we rewrite the objective as a function of the new nonbasic variables:\n",
    "\n",
    "\\begin{align*}\n",
    "x_1 + x_2\n",
    "&= \\left(1 - \\tfrac{1}{2}s_1 - \\tfrac{1}{2}x_2\\right) + x_2 \\\\\n",
    "&= 1 + \\tfrac{1}{2}x_2 - \\tfrac{1}{2}s_1.\n",
    "\\end{align*}\n",
    "\n",
    "In general, once the entering variable $n^\\star$ and the departing variable $b^\\star$ have been determined, we need to update our set of nonbasic variables by removing $b^\\star$ from it and adding $n^\\star$. We also need to update our dictionary with the expression of our entering variable,\n",
    "\n",
    "$z_{n^\\star}\n",
    "= \\frac {t_{b^\\star}} {T_{b^\\star n^\\star}}\n",
    "- \\sum_{n \\neq n^\\star} \\frac {T_{b^\\star n}} {T_{b^\\star n^\\star}} z_n\n",
    "- \\frac {z_{b^\\star}} {T_{b^\\star n^\\star}}$\n",
    "\n",
    "and substituting out this expression in\n",
    "\n",
    "$z_b = t_b - \\sum_n T_{bn} z_n, \\quad b \\neq b^\\star$\n",
    "\n",
    "yields the expression of the new basic variables as a function of the new nonbasic variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "S6p_H4Vg8j8c",
    "outputId": "94c712ac-f571-4309-bd0c-d64d7b273ac4"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Entering = x_1; departing = s_1\n",
      "x_1 = -0.5*s_1 - 0.5*x_2 + 1\n",
      "-------------------------- \n",
      "Objective and constraints:\n",
      "obj = -0.5*s_1 + 0.5*x_2 + 1\n",
      "s_2 = 0.5*s_1 - 1.5*x_2 + 1\n",
      "x_1 = -0.5*s_1 - 0.5*x_2 + 1\n"
     ]
    }
   ],
   "source": [
    "def Dictionary_pivot(self,entering_var,departing_var, verbose = 0):\n",
    "    expr_entering = solve(self.base[departing_var] - departing_var,entering_var)[0]\n",
    "    for var in self.base:\n",
    "        self.base[var] = self.base[var].subs([(entering_var, expr_entering)])\n",
    "    self.base[entering_var] = expr_entering\n",
    "    del self.base[departing_var]\n",
    "    self.nonbasic.remove(entering_var)\n",
    "    self.nonbasic.append(departing_var)\n",
    "    if verbose > 0:\n",
    "        print('Entering = ' + str( entering_var)+'; departing = '+ str( departing_var))\n",
    "    if verbose > 1:\n",
    "        print(str( entering_var)+' = '+str(round_expr(expr_entering,2)))\n",
    "    return expr_entering\n",
    "\n",
    "Dictionary.pivot = Dictionary_pivot\n",
    "\n",
    "expr_entering_var = dictionary_example.pivot(entering_var,departing_var,verbose = 2)\n",
    "\n",
    "dictionary_example.display()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-iyU4tinYg75"
   },
   "source": [
    "This completes one iteration of the algorithm."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "XjDwx93pq43z"
   },
   "source": [
    "### Iterating\n",
    "\n",
    "The transformed program is now:\n",
    "\n",
    "\\begin{align*}\n",
    "\\max_{x_1, x_2, s_1, s_2 \\geq 0}  & ~ 1 + \\tfrac{1}{2}x_2 - \\tfrac{1}{2}s_1 \\\\\n",
    "\\text{s.t.} & ~ x_1 = 1 - \\tfrac{1}{2} x_2 - \\tfrac{1}{2} s_1 \\\\\n",
    "            & ~ s_2 = 1 - \\tfrac{3}{2} x_2 + \\tfrac{1}{2}s_1 .\n",
    "\\end{align*}\n",
    "\n",
    "Our new basic feasible solution is $x_2 = s_1 = 0$ (nonbasic variables) and $x_1 = 1$, $s_2 = 1$ (basic variables). The value of the objective is $1$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "AqFmiHtWDxBW"
   },
   "source": [
    "\n",
    "Let's look at the path that the algorithm took using the graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 517
    },
    "id": "DbPvkDxRYq8G",
    "outputId": "6bbde542-b9da-4d4d-e3e8-1193f125c986"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_1 = 1.0\n",
      "x_2 = 0.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "currentx_j = dictionary_example.primal_solution(verbose=2)\n",
    "path_example.append(currentx_j)\n",
    "dictionary_example.plot2d(path_example)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "IYLPRwSB9dx0"
   },
   "source": [
    "We can now repeat the process on the new program. Since the coefficient of $x_2$ in our new objective is positive, we now choose $x_2$ as an entering variable. In that case, the constraint associated with the basic variable $s_2$ will hit first, so $s_2$ will be our departing variable.\n",
    "\n",
    "The pivot operation yields\n",
    "\n",
    "\\begin{matrix}\n",
    "&\\tfrac{2}{3}s_1  &-~ \\tfrac{1}{3} s_2       &~+ x_1 & &= \\tfrac{2}{3} \\\\\n",
    "&-\\tfrac{1}{3}s_1 &+~ \\tfrac{2}{3} s_2 &       &+~ x_2 &= \\tfrac{2}{3}\n",
    "\\end{matrix}\n",
    "\n",
    "and the new objective is\n",
    "\n",
    "\\begin{align*}\n",
    "1 + \\tfrac{1}{2}x_2 - \\tfrac{1}{2}s_1\n",
    "&= 1 + \\tfrac{1}{2}\\left(\\tfrac{2}{3} + \\tfrac{1}{3}s_1 - \\tfrac{2}{3}s_2\\right) - \\tfrac{1}{2}s_1 \\\\\n",
    "&= \\tfrac{4}{3} - \\tfrac{1}{3}s_1 - \\tfrac{1}{3}s_2.\n",
    "\\end{align*}\n",
    "\n",
    "We encode this second iteration as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Dictionary_step(self,verbose=0):\n",
    "    entering_var = self.determine_entering()\n",
    "    if entering_var is None:\n",
    "        print('Optimal solution found.\\n=======================')\n",
    "        self.primal_solution(verbose)\n",
    "    else:\n",
    "        departing_var = self.determine_departing(entering_var)\n",
    "        if departing_var is None:\n",
    "            print('Unbounded solution.')\n",
    "        else:\n",
    "            expr_entering_var = self.pivot(entering_var,departing_var, verbose)\n",
    "            return False # not finished\n",
    "    return True # finished\n",
    "\n",
    "Dictionary.step = Dictionary_step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 550
    },
    "id": "-RwTfmmlhcFh",
    "outputId": "3c60656c-e6e2-4887-b240-b821f3df1115"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Entering = x_2; departing = s_2\n",
      "x_2 = 0.33*s_1 - 0.67*s_2 + 0.67\n",
      "x_1 = 0.6666666666666666\n",
      "x_2 = 0.6666666666666666\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dictionary_example.step( verbose=2)\n",
    "\n",
    "path_example.append( dictionary_example.primal_solution(verbose=1) )\n",
    "dictionary_example.plot2d(path_example)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "q_5eppZSiMXF"
   },
   "source": [
    "Our new basic feasible solution is $s_1 = s_2 = 0$ (nonbasic variables) and $x_1 = \\tfrac{2}{3}$, $x_2 = \\tfrac{2}{3}$ (basic variables). But because the coefficients of the nonbasic variables in the objective are negative, we cannot increase it anymore: the algorithm stops."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "od8jJs_t9-Pl"
   },
   "source": [
    "### Geometric interpretation\n",
    "\n",
    "The simplex algorithm has a simple geometric interpretation.\n",
    "\n",
    "The feasible set of the linear programming problem, delimited by its constraints, forms a polygon in $\\mathbb R^2$ (a polyhedron in $\\mathbb R^3$, etc.).\n",
    "\n",
    "We start from one of the corners of this polygon. At each iteration of the algorithm, we move along the edge of the polygon to a neighboring corner, always moving in the direction that most increases the value of the objective function. When it reaches the corner with the highest possible value of the objective function, the algorithm stops, and we have our solution.\n",
    "\n",
    "The simplex algorithm must stop eventually since there is a finite limited number of corners. Furthermore, it can be shown that if a corner isn't a maximum, then there must be an adjoining edge leading to a higher value of the objective function. This guarantees that the end point of the algorithm is indeed an optimal solution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We verify this with our code that there is no entering variable anymore."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "yNS_h09LiFj5",
    "outputId": "d2dcf2b5-315b-4bc9-c83c-c3c03412309d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Entering = None\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([0.66666667, 0.66666667])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Entering =',dictionary_example.determine_entering())\n",
    "dictionary_example.primal_solution()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ON3ZsdVrlASD"
   },
   "source": [
    "The value of the initial problem is thus $\\tfrac{4}{3}$, and the optimal solution is\n",
    "\n",
    "\\begin{equation}\n",
    "  x_1^* = x_2^* = \\tfrac{2}{3}.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Dual simplex\n",
    "\n",
    "The dual program is\n",
    "\n",
    "\n",
    "\\begin{align}\n",
    "\\min_{(y_j) \\geq 0} & d^\\top y  \\\\\n",
    "\\text{s.t.} & ~ A ^\\top y \\geq c\n",
    "\\end{align}\n",
    "\n",
    "and we introduce dual slack variables\n",
    "\n",
    "$t_j = (A^\\top y)_j - c_j$\n",
    "\n",
    "After adding the slack variables, the constraint matrix becomes $[A^\\top ~ I]$. This is a $J \\times (I+J)$ matrix, which has $J$ free columns, and thus it is of rank $J$. Therefore a dual basis will be of cardinality $J$ -- in contrast with the primal basis, which is of cardinality $I$.\n",
    "\n",
    "\n",
    "## 2.1 Dual dictionary\n",
    "An initial dual basis is provided by the dual slack variables $t_j$. We note that at step zero, the dual basis $(t_j)$ is in an a one-to-one correspondence with the complement of the primal basis, which is $(s_i)$. Indeed, we associate an nonbasic primal variable $x_j$ to each basic dual variable $t_j$, and a basic primal variable $t_i$ to each nonbasic dual variable $y_i$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{s_1: y_1, s_2: y_2, x_1: t_1, x_2: t_2}\n"
     ]
    }
   ],
   "source": [
    "A_i_j,d_i,c_j = build_simple_example().values()\n",
    "\n",
    "primal_dictionary = Dictionary(A_i_j,d_i,c_j ,\n",
    "                                slack_var_names_i = ['s_1', 's_2'],\n",
    "                                decision_var_names_j = ['x_1', 'x_2']\n",
    "                                )\n",
    "\n",
    "dual_dictionary = Dictionary(A_i_j.T,c_j ,d_i,\n",
    "                                slack_var_names_i = ['t_1', 't_2'],\n",
    "                                decision_var_names_j = ['y_1', 'y_2']\n",
    "                                )\n",
    "corresp = {Symbol(primalvar):Symbol(dualvar) \n",
    "           for (primalvar,dualvar) in zip(primal_dictionary.slack_var_names_i+primal_dictionary.decision_var_names_j,\n",
    "                                         dual_dictionary.decision_var_names_j+dual_dictionary.slack_var_names_i)}\n",
    "\n",
    "print(corresp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "We will therefore re-run the simplex algorithm, but we will update the dual dictionary in addition to the primal dictionary. If a primal variable enters the primal basis, the corresponding dual variable will exit the dual basis, and conversely. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Entering = x_1; departing = s_1\n",
      "Entering = y_1; departing = t_1\n",
      "Entering = x_2; departing = s_2\n",
      "Entering = y_2; departing = t_2\n",
      "Optimal solution found.\n",
      "=======================\n",
      "x_1 = 0.6666666666666666\n",
      "x_2 = 0.6666666666666666\n",
      "y_1 = 0.3333333333333333\n",
      "y_2 = 0.3333333333333333\n",
      "-------------------------- \n",
      "Objective and constraints:\n",
      "obj = -0.33*s_1 - 0.33*s_2 + 1.33\n",
      "x_1 = -0.67*s_1 + 0.33*s_2 + 0.67\n",
      "x_2 = 0.33*s_1 - 0.67*s_2 + 0.67\n",
      "-------------------------- \n",
      "Objective and constraints:\n",
      "obj = -0.67*t_1 - 0.67*t_2 + 1.33\n",
      "y_1 = -0.67*t_1 + 0.33*t_2 + 0.33\n",
      "y_2 = 0.33*t_1 - 0.67*t_2 + 0.33\n"
     ]
    }
   ],
   "source": [
    "finished = False\n",
    "while not finished:    \n",
    "    entering_var = primal_dictionary.determine_entering()\n",
    "    if entering_var is None:\n",
    "        print('Optimal solution found.\\n=======================')\n",
    "        primal_dictionary.primal_solution(verbose=1)\n",
    "        dual_dictionary.primal_solution(verbose=1)\n",
    "        finished = True\n",
    "    else:\n",
    "        departing_var = primal_dictionary.determine_departing(entering_var)\n",
    "        primal_dictionary.pivot(entering_var,departing_var, verbose=1)\n",
    "        dual_dictionary.pivot(corresp[departing_var],corresp[entering_var], verbose=1)\n",
    "\n",
    "primal_dictionary.display()\n",
    "dual_dictionary.display()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2 Recovering the dual solution from the primal dictionary\n",
    "\n",
    "In fact, we can recover the dual solution directly from the primal dictionary. Recall that the objective is<br>\n",
    "$Obj = (c_b)^\\top B^{-1} d + ((c_n)^\\top - y^\\top N )z_n$<br>\n",
    "where $y^\\top = (c_b)^\\top B^{-1}$.\n",
    "\n",
    "Therefore, we have:<br>\n",
    "$\\frac {\\partial Obj} {\\partial z_n} = c_n - (N^\\top y)_n$<br>\n",
    "but if $z_n$ is the slack variable $s_i$, we have $c_n=0$, and $N_{i^\\prime n} = 1\\{i = i^\\prime \\} $, and thus<br>\n",
    "$\\frac {\\partial Obj} {\\partial z_n} = -y_i$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pi_0= 0.3333333333333333\n",
      "pi_1= 0.3333333333333333\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([0.33333333, 0.33333333])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def Dictionary_dual_solution(self,verbose = 0):\n",
    "    y_i = np.zeros(self.nbi)\n",
    "    for i,slackvar in enumerate(self.slack_var_names_i):\n",
    "        y_i[i] = - diff(self.base[Symbol('obj')],slackvar)\n",
    "        if verbose > 0 and y_i[i] != 0:\n",
    "            print('pi_'+str(i)+'=', y_i[i])\n",
    "    return y_i\n",
    "\n",
    "Dictionary.dual_solution = Dictionary_dual_solution\n",
    "\n",
    "dictionary_example.dual_solution(verbose=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "RQiP_qF-Btrb"
   },
   "source": [
    "# 3. Complements\n",
    "\n",
    "## 3.1 A more complex example\n",
    "\n",
    "Consider a slightly more complex example:\n",
    "\n",
    "\\begin{align*}\n",
    "\\max_{x_1, x_2 \\geq 0}  & ~ 3 x_1 + 2 x_2 \\\\\n",
    "\\text{s.t.} & ~ \\cos\\left(\\tfrac{k}{K}\\tfrac{\\pi}{2}\\right) x_1 + \\sin\\left(\\tfrac{k}{K}\\tfrac{\\pi}{2}\\right) x_2 \\leq 1, \\quad k = 0, \\dots, K.\n",
    "\\end{align*}\n",
    "\n",
    "The constraints actually correspond to $K+1$ tangents to the circle of equation $x_1^2 + x_2^2 = 1$. Therefore, it is as if we were approximating the nonlinear constraint $x_1^2 + x_2^2 \\leq 1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1qLZKqLlfxCy"
   },
   "source": [
    "We code a complete iteration of the simplex algorithm with `Dictionary_loop`, and finally we code the complete simplex algorithm by repeating this loop until there is no entering variable anymore."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Dictionary_simplex_loop(self,verbose = 0):\n",
    "    if verbose >2:\n",
    "        [x1,x2] = symbols(self.decision_var_names_j)\n",
    "        the_path = [self.primal_solution()]\n",
    "    finished = False\n",
    "    while not finished:\n",
    "        finished = self.step()\n",
    "        if verbose>2:\n",
    "            the_path.append(self.primal_solution())\n",
    "    objVal = self.base[Symbol('obj')].subs([ (variable,0) for variable in self.nonbasic])\n",
    "    if verbose>0:\n",
    "        print('\\nValue = ' + str(objVal))\n",
    "    if verbose >2:\n",
    "        self.plot2d(the_path, legend=False)\n",
    "    return (self.primal_solution(),self.dual_solution(),objVal)\n",
    "    \n",
    "\n",
    "Dictionary.simplex_loop = Dictionary_simplex_loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 814
    },
    "id": "KgQK6cAhBver",
    "outputId": "98eea75e-f2b3-4dfc-a563-0b00ea070157"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal solution found.\n",
      "=======================\n",
      "\n",
      "Value = 3.61405855890019\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(array([0.8552767 , 0.52411423]),\n",
       " array([0.        , 0.        , 0.        , 0.9289626 , 2.68509595,\n",
       "        0.        , 0.        , 0.        , 0.        , 0.        ,\n",
       "        0.        ]),\n",
       " 3.61405855890019)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T = 10\n",
    "\n",
    "dictionary_example2 = Dictionary(A_i_j = np.array([(float(cos(t/T*pi/2)), float(sin(t/T*pi/2))) for t in range(0, T+1)]),\n",
    "                                 d_i = np.ones(T+1),\n",
    "                                 c_j = np.array([3,2]),\n",
    "                                 slack_var_names_i = ['s_'+str(t) for t in range(0,T+1)],\n",
    "                                 decision_var_names_j = ['x_1', 'x_2'])\n",
    "\n",
    "dictionary_example2.simplex_loop(verbose=3)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.8552767 , 0.52411423])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dictionary_example2.primal_solution()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "F82rdD4vCgU9"
   },
   "source": [
    "Our algorithm still works -- however we see that it becomes quite slow for higher values of $K$ -- not surprising, given that it had to visit a large number of intermediate vertices before reaching the solution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dEg6YXOkNb7N"
   },
   "source": [
    "\n",
    "## 3.2 Application to the diet problem\n",
    "\n",
    "Recall the diet problem:\n",
    "\n",
    "* Assume there are nutrients $i \\in \\{1,\\dots,I\\}$ (calories, protein, calcium, iron, etc.) that matter for a person's health, in such way that the minimum daily intake of nutrient $i$ should be $d_{i}$.\n",
    "\n",
    "* Nutrients do not come as standalone elements, but are combined into various foods. One dollar worth of food $j \\in \\{1,\\dots,J\\}$ yields a quantity $N_{ij}$ of nutrient $i \\in \\{1,\\dots,I\\}$.\n",
    "\n",
    "The problem is to find the diet that achieves the minimal intake of each nutrient for the cheapest price. If $q\\in\\mathbb{R}^{J}$ is a vector such that $q_{j}\\geq0$ is the quantity of food $j$ purchased, the quantity of nutrient $i$ ingested is $\\sum_{j=1}^{J}N_{ij}q_{j}$, and the cost of the diet is $\\sum_{j=1}^{J}q_{j}$. Letting $c_j = 1$ for all $j \\in \\{1,\\dots,n\\}$, the optimal diet is therefore given by\n",
    "\n",
    "\\begin{align*}\n",
    "\\min_{q\\geq 0} & ~ c^{\\top}q \\\\\n",
    "\\text{s.t.} & ~ Nq \\geq d\n",
    "\\end{align*}\n",
    "\n",
    "which has dual\n",
    "\n",
    "\\begin{align*}\n",
    "\\max_{\\pi\\geq0} & ~ d^{\\top}\\pi \\\\\n",
    "\\text{s.t.} & ~ N^{\\top}\\pi \\leq c.\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "hyCMGHTnNb7O"
   },
   "source": [
    "We load the data using:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "id": "CDcxAkpDNb7O"
   },
   "outputs": [],
   "source": [
    "[N_i_j,minallowance_i,unitcost_j,_,_] = load_stigler_data(7,5).values()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5zpveeeyNb7S"
   },
   "source": [
    "We code this up as a `Dictionary`object. First, we define the basic dual variables (the $s_j$), and the nonbasic dual variables (the $\\pi_i$) ."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "XZbRB6MUNb7S",
    "outputId": "82e0948b-1325-4224-b7b3-b813169109de"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal solution found.\n",
      "=======================\n",
      "\n",
      "Value = 0.227818067377138\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([0.03431968, 0.        , 0.03168609, 0.        , 0.1618123 ])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stigler_dictionary = Dictionary(N_i_j.T, unitcost_j , minallowance_i,\n",
    "                             ['s_' + str(j) for j in range(N_i_j.shape[1])],\n",
    "                             ['π_' + str(i) for i in range(N_i_j.shape[0])])\n",
    "stigler_dictionary.simplex_loop(verbose=2)[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Benchmark with Gurobi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "4_sTHq4ONb7Z"
   },
   "source": [
    "We benchmark our solution with the one obtained by `Gurobi`, and verify that it is the same:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2023-12-23\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([0.03431968, 0.        , 0.03168609, 0.        , 0.1618123 ])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stigler_dictionary.gurobi_solve()[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dUbcFd4uq6Zo"
   },
   "source": [
    "Gurobi finds the same solution as our simplex algorithm coding — although significantly faster."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4. Alternative implementation via tableaux\n",
    "\n",
    "\n",
    "Our implementation so far of the simplex algorithm provides a quick and intuitive version of the simplex, but the fact that it relies on `sympy` makes it extremely slow. In the sequel, we shall see a different implementation of the same algorithm using *tableaux*. \n",
    "\n",
    "\n",
    "The program in standard form is thus\n",
    "\n",
    "\\begin{align*}\n",
    "\\max_{z \\geq 0}  & ~ (0^\\top_I, c^\\top) z \\\\\n",
    "\\text{s.t.}~& ~ (\\mathbf{I_I}~A )~z = d.\n",
    "\\end{align*}\n",
    "\n",
    "At each point in the algorithm, we denote $\\{z_b\\}$ the set of basic variables, and $\\{z_n \\}$ the set of nonbasic variables, and we have<br>\n",
    "$B (z_b) + N (z_n) = d$\n",
    "\n",
    "\n",
    "A tableau is a representation of the dictionary<br>\n",
    "$ (z_b) = B^{-1} d - B^{-1} N (z_n)$<br>\n",
    "under the form<br>\n",
    "$T z  = B^{-1} d$.\n",
    "Therefore, each row of the tableau will be associated with one basic variable $b\\in B$; each column before the last of the tableau will be associated with a variable (basic or nonbasic).\n",
    "\n",
    "Each row is associated with a basic variable $b$, the entry in the column associated with that basic variable is one; the column entries associated with the other basic variables are zero; and the column entries assocaited with nonbasic variables $n$ are equal with $(B^{-1} N)_{bn}$. \n",
    "\n",
    "The tableau also stores the objective in a similar fashion<br>\n",
    "$Obj = (c_b)^\\top( B^{-1} d )+ (c_n^\\top -  B^{-1} N) (z_n)  $\n",
    "\n",
    "For practical purposes, we will append a first row of the tableau where we store the expression of the objective, and add a last column where we store the right hand side $ B^{-1} d$.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "#from tabulate import tabulate\n",
    "\n",
    "class Tableau(LP):\n",
    "    def __init__(self, A_i_j, d_i, c_j,slack_var_names_i=None, decision_var_names_j = None): # s_i = d_i - (A_i_j @ x_j\n",
    "        LP.__init__(self,A_i_j, d_i, c_j,decision_var_names_j,slack_var_names_i)\n",
    "        self.nbi,self.nbj = A_i_j.shape\n",
    "        self.nbk = self.nbi+self.nbj\n",
    "        self.names_all_variables =  self.slack_var_names_i + self.decision_var_names_j\n",
    "        self.tableau = np.block([[np.zeros((1,self.nbi)), c_j.reshape((1,-1)), 0],[np.eye(self.nbi),A_i_j,d_i.reshape((-1,1))]])\n",
    "        self.k_b = list(range(self.nbi)) # columns associated with basic variables\n",
    "        self.i_b = list(range(1,1+self.nbi)) # rows associated with basic variables\n",
    "\n",
    "    def display(self):\n",
    "        tableau = []\n",
    "        tableau.append(['Obj'] + list(self.tableau[0,:])  )\n",
    "        for b in range(self.nbi):\n",
    "             tableau.append([self.names_all_variables[self.k_b[b]]]+list(self.tableau[self.i_b[b],:]) )\n",
    "        \n",
    "        print(limited_tabulate(tableau, headers=[''] + self.names_all_variables + ['RHS'], tablefmt=\"grid\"))\n",
    "        \n",
    "\n",
    "    def determine_entering(self):\n",
    "        for k in range(self.nbk):\n",
    "            if self.tableau[0,k] > 0:\n",
    "                return k\n",
    "        return None # If no entering variable found, None returned\n",
    "\n",
    "    def determine_departing(self,kent):\n",
    "        thedic = {b: self.tableau[self.i_b[b],-1] / self.tableau[self.i_b[b],kent] \n",
    "                  for b in range(self.nbi) if self.tableau[self.i_b[b],kent]>0}\n",
    "        bdep = min(thedic, key = thedic.get)\n",
    "        return bdep\n",
    "\n",
    "    def update(self,kent,bdep):\n",
    "        idep = self.i_b[bdep]\n",
    "        self.tableau[idep,:] = self.tableau[idep,:] / self.tableau[idep,kent] \n",
    "        for i in range(1+self.nbi):\n",
    "            if i != idep:\n",
    "                self.tableau[i,:]= self.tableau[i,:] - self.tableau[idep,:] * self.tableau[i,kent] \n",
    "                \n",
    "        self.k_b[bdep] = kent\n",
    "        self.i_b[bdep] = idep\n",
    "        \n",
    "    def simplex_step(self,verbose=0):\n",
    "        if verbose>1:\n",
    "            self.display()\n",
    "        kent = self.determine_entering()\n",
    "        if kent is not None:\n",
    "            bdep= self.determine_departing(kent)\n",
    "            name_entering = self.names_all_variables[kent]\n",
    "            name_departing = self.names_all_variables[self.i_b[bdep]]\n",
    "            if verbose>0:\n",
    "                print('Entering=', name_entering, 'Departing=',name_departing,'Pivot=',(self.i_b[bdep],kent))\n",
    "            self.update(kent,bdep)\n",
    "        else:\n",
    "            if verbose>0:\n",
    "                print ('Optimal solution found.')\n",
    "            if verbose>1:\n",
    "                self.display()\n",
    "        return (kent is not None) # returns false  if optimal solution; true otherwise\n",
    "\n",
    "    def simplex_solve(self,verbose=0):\n",
    "        while self.simplex_step(verbose):\n",
    "            pass\n",
    "        return self.solution()\n",
    "        \n",
    "\n",
    "    def solution(self):\n",
    "        x_j = np.zeros(self.nbj)\n",
    "        s_i = np.zeros(self.nbi)\n",
    "        for b in range(self.nbi):\n",
    "            if self.k_b[b]<self.nbi:\n",
    "                s_i[self.k_b[b]] = self.tableau[self.i_b[b],-1]\n",
    "            else:\n",
    "                x_j[self.k_b[b]-self.nbi] = self.tableau[self.i_b[b],-1]\n",
    "        y_i = - self.tableau[0,:self.nbi] \n",
    "        return(x_j,y_i,x_j@self.c_j)\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-----+-------+-------+-------+-------+-------+-------+\n",
      "|     |   s_0 |   s_1 |   s_2 |   x_0 |   x_1 |   RHS |\n",
      "+=====+=======+=======+=======+=======+=======+=======+\n",
      "| Obj |     0 |     0 |     0 |     1 |     3 |     0 |\n",
      "+-----+-------+-------+-------+-------+-------+-------+\n",
      "| s_0 |     1 |     0 |     0 |     3 |     1 |     2 |\n",
      "+-----+-------+-------+-------+-------+-------+-------+\n",
      "| s_1 |     0 |     1 |     0 |     1 |     3 |     2 |\n",
      "+-----+-------+-------+-------+-------+-------+-------+\n",
      "| s_2 |     0 |     0 |     1 |     5 |     5 |     4 |\n",
      "+-----+-------+-------+-------+-------+-------+-------+\n",
      "Entering= x_0 Departing= s_1 Pivot= (1, 3)\n",
      "+-----+-----------+-------+-------+-------+----------+-----------+\n",
      "|     |       s_0 |   s_1 |   s_2 |   x_0 |      x_1 |       RHS |\n",
      "+=====+===========+=======+=======+=======+==========+===========+\n",
      "| Obj | -0.333333 |     0 |     0 |     0 | 2.66667  | -0.666667 |\n",
      "+-----+-----------+-------+-------+-------+----------+-----------+\n",
      "| x_0 |  0.333333 |     0 |     0 |     1 | 0.333333 |  0.666667 |\n",
      "+-----+-----------+-------+-------+-------+----------+-----------+\n",
      "| s_1 | -0.333333 |     1 |     0 |     0 | 2.66667  |  1.33333  |\n",
      "+-----+-----------+-------+-------+-------+----------+-----------+\n",
      "| s_2 | -1.66667  |     0 |     1 |     0 | 3.33333  |  0.666667 |\n",
      "+-----+-----------+-------+-------+-------+----------+-----------+\n",
      "Entering= x_1 Departing= x_0 Pivot= (3, 4)\n",
      "+-----+-------+-------+-------+-------+-------+-------+\n",
      "|     |   s_0 |   s_1 |   s_2 |   x_0 |   x_1 |   RHS |\n",
      "+=====+=======+=======+=======+=======+=======+=======+\n",
      "| Obj |   1   |     0 |  -0.8 |     0 |     0 |  -1.2 |\n",
      "+-----+-------+-------+-------+-------+-------+-------+\n",
      "| x_0 |   0.5 |     0 |  -0.1 |     1 |     0 |   0.6 |\n",
      "+-----+-------+-------+-------+-------+-------+-------+\n",
      "| s_1 |   1   |     1 |  -0.8 |     0 |     0 |   0.8 |\n",
      "+-----+-------+-------+-------+-------+-------+-------+\n",
      "| x_1 |  -0.5 |     0 |   0.3 |     0 |     1 |   0.2 |\n",
      "+-----+-------+-------+-------+-------+-------+-------+\n",
      "Entering= s_0 Departing= s_2 Pivot= (2, 0)\n",
      "+-----+-------+-------+-------+-------+-------+-------+\n",
      "|     |   s_0 |   s_1 |   s_2 |   x_0 |   x_1 |   RHS |\n",
      "+=====+=======+=======+=======+=======+=======+=======+\n",
      "| Obj |     0 |  -1   |   0   |     0 |     0 |  -2   |\n",
      "+-----+-------+-------+-------+-------+-------+-------+\n",
      "| x_0 |     0 |  -0.5 |   0.3 |     1 |     0 |   0.2 |\n",
      "+-----+-------+-------+-------+-------+-------+-------+\n",
      "| s_0 |     1 |   1   |  -0.8 |     0 |     0 |   0.8 |\n",
      "+-----+-------+-------+-------+-------+-------+-------+\n",
      "| x_1 |     0 |   0.5 |  -0.1 |     0 |     1 |   0.6 |\n",
      "+-----+-------+-------+-------+-------+-------+-------+\n",
      "Optimal solution found.\n",
      "+-----+-------+-------+-------+-------+-------+-------+\n",
      "|     |   s_0 |   s_1 |   s_2 |   x_0 |   x_1 |   RHS |\n",
      "+=====+=======+=======+=======+=======+=======+=======+\n",
      "| Obj |     0 |  -1   |   0   |     0 |     0 |  -2   |\n",
      "+-----+-------+-------+-------+-------+-------+-------+\n",
      "| x_0 |     0 |  -0.5 |   0.3 |     1 |     0 |   0.2 |\n",
      "+-----+-------+-------+-------+-------+-------+-------+\n",
      "| s_0 |     1 |   1   |  -0.8 |     0 |     0 |   0.8 |\n",
      "+-----+-------+-------+-------+-------+-------+-------+\n",
      "| x_1 |     0 |   0.5 |  -0.1 |     0 |     1 |   0.6 |\n",
      "+-----+-------+-------+-------+-------+-------+-------+\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(array([0.2, 0.6]), array([-0.,  1., -0.]), 2.0)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tableau_ex = Tableau(np.array([[3, 1], [1, 3], [5,5]]),np.array([2,2,4]),np.array([1,3]))\n",
    "tableau_ex.simplex_solve(verbose = 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare with Gurobi:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.        , 0.66666667]), array([0., 1., 0.]), 2.0)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tableau_ex.gurobi_solve()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Another example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-----+-------+-------+-------+-------+-------+\n",
      "|     |   s_0 |   s_1 |   x_0 |   x_1 |   RHS |\n",
      "+=====+=======+=======+=======+=======+=======+\n",
      "| Obj |     0 |     0 |     3 |     2 |     0 |\n",
      "+-----+-------+-------+-------+-------+-------+\n",
      "| s_0 |     1 |     0 |     1 |     1 |     4 |\n",
      "+-----+-------+-------+-------+-------+-------+\n",
      "| s_1 |     0 |     1 |     2 |     1 |     6 |\n",
      "+-----+-------+-------+-------+-------+-------+\n",
      "Entering= x_0 Departing= x_0 Pivot= (2, 2)\n",
      "+-----+-------+-------+-------+-------+-------+\n",
      "|     |   s_0 |   s_1 |   x_0 |   x_1 |   RHS |\n",
      "+=====+=======+=======+=======+=======+=======+\n",
      "| Obj |     0 |  -1.5 |     0 |   0.5 |    -9 |\n",
      "+-----+-------+-------+-------+-------+-------+\n",
      "| s_0 |     1 |  -0.5 |     0 |   0.5 |     1 |\n",
      "+-----+-------+-------+-------+-------+-------+\n",
      "| x_0 |     0 |   0.5 |     1 |   0.5 |     3 |\n",
      "+-----+-------+-------+-------+-------+-------+\n",
      "Entering= x_1 Departing= s_1 Pivot= (1, 3)\n",
      "+-----+-------+-------+-------+-------+-------+\n",
      "|     |   s_0 |   s_1 |   x_0 |   x_1 |   RHS |\n",
      "+=====+=======+=======+=======+=======+=======+\n",
      "| Obj |    -1 |    -1 |     0 |     0 |   -10 |\n",
      "+-----+-------+-------+-------+-------+-------+\n",
      "| x_1 |     2 |    -1 |     0 |     1 |     2 |\n",
      "+-----+-------+-------+-------+-------+-------+\n",
      "| x_0 |    -1 |     1 |     1 |     0 |     2 |\n",
      "+-----+-------+-------+-------+-------+-------+\n",
      "Optimal solution found.\n",
      "+-----+-------+-------+-------+-------+-------+\n",
      "|     |   s_0 |   s_1 |   x_0 |   x_1 |   RHS |\n",
      "+=====+=======+=======+=======+=======+=======+\n",
      "| Obj |    -1 |    -1 |     0 |     0 |   -10 |\n",
      "+-----+-------+-------+-------+-------+-------+\n",
      "| x_1 |     2 |    -1 |     0 |     1 |     2 |\n",
      "+-----+-------+-------+-------+-------+-------+\n",
      "| x_0 |    -1 |     1 |     1 |     0 |     2 |\n",
      "+-----+-------+-------+-------+-------+-------+\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(array([2., 2.]), array([1., 1.]), 10.0)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "other_ex = Tableau(np.array([[1, 1], [2, 1]]),np.array([4,6]),np.array([3,2]))\n",
    "other_ex.simplex_solve(verbose=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([2., 2.]), array([1., 1.]), 10.0)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "other_ex.gurobi_solve()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Back to the diet problem\n",
    "\n",
    "If we go back to the Stigler diet problem, we can appreciate how much faster we are."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.03431968, -0.        ,  0.03168609, -0.        ,  0.1618123 ])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stigler_tableau = Tableau(N_i_j.T, unitcost_j , minallowance_i,\n",
    "                             ['s_' + str(j) for j in range(N_i_j.shape[1])],\n",
    "                             ['π_' + str(i) for i in range(N_i_j.shape[0])])\n",
    "\n",
    "stigler_tableau.simplex_solve()[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.03431968, 0.        , 0.03168609, 0.        , 0.1618123 ])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stigler_tableau.gurobi_solve()[1]"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "provenance": [],
   "toc_visible": true
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  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
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