2. Power Method ( 1.0 ).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ranking via Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Creating Team List"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Enter Number of Teams: 5\n",
      "1.  Team: SL\n",
      "2.  Team: SA\n",
      "3.  Team: NZ\n",
      "4.  Team: E\n",
      "5.  Team: NE\n",
      "\n",
      " ['SL', 'SA', 'NZ', 'E', 'NE']\n"
     ]
    }
   ],
   "source": [
    "n = int(input(\"Enter Number of Teams: \"))\n",
    "teams = []\n",
    "for i in range(n):\n",
    "    print(str(i+1)+ \". \", end = \" \")\n",
    "    team = input(\"Team: \")\n",
    "    teams.append(team)\n",
    "print(\"\\n\", teams)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Creating Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Enter '1' if first team wins, else '0'.\n",
      "SL  Vs  SA  : 1\n",
      "SL  Vs  NZ  : 1\n",
      "SL  Vs  E  : 0\n",
      "SL  Vs  NE  : 1\n",
      "SA  Vs  NZ  : 1\n",
      "SA  Vs  E  : 1\n",
      "SA  Vs  NE  : 1\n",
      "NZ  Vs  E  : 1\n",
      "NZ  Vs  NE  : 1\n",
      "E  Vs  NE  : "
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "l = []\n",
    "\n",
    "print(\"Enter '1' if first team wins, else '0'.\")\n",
    "for i in range(len(teams)):\n",
    "    l.append([])\n",
    "    for j in range(len(teams)):\n",
    "        if i==j:\n",
    "            l[i].append(0)\n",
    "        else:\n",
    "            if j>i:\n",
    "                print(teams[i], \" Vs \", teams[j], \" :\", end = \" \")\n",
    "                wol = int(input())\n",
    "                l[i].append(wol)\n",
    "            else:\n",
    "                if l[j][i]== 1:\n",
    "                    l[i].append(0)\n",
    "                else:\n",
    "                    l[i].append(1)\n",
    "                    \n",
    "mat = np.matrix(l)\n",
    "print(\"\\n\", mat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Finding Dominant Eigen Value and Eigen Vector via Power Method1  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"import numpy as np\n",
    "row = int(input(\"Enter number of Rows: \"))\n",
    "col = int(input(\"Enter number of Columns: \"))\n",
    "def create_matrix():\n",
    "    mat = []\n",
    "    \n",
    "    for x in range(row):\n",
    "        mat.append([])\n",
    "        for y in range(col):\n",
    "            a = int(input(\"Enter Number: \"))\n",
    "            mat[x].append(a)\n",
    "\n",
    "    mat = np.matrix(mat)\n",
    "    print(mat)\n",
    "    return mat\n",
    "mat = create_matrix()\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      " Iteration Number:  1 \n",
      "\n",
      "Eigen Value:  6.0\n",
      "Eigen Vector: \n",
      " [[0.66666667]\n",
      " [0.33333333]\n",
      " [0.5       ]\n",
      " [1.        ]\n",
      " [1.        ]\n",
      " [0.5       ]\n",
      " [0.16666667]\n",
      " [0.5       ]]\n",
      "\n",
      "\n",
      " Iteration Number:  2 \n",
      "\n",
      "Eigen Value:  3.1666666666666665\n",
      "Eigen Vector: \n",
      " [[0.47368421]\n",
      " [0.21052632]\n",
      " [0.63157895]\n",
      " [1.        ]\n",
      " [0.84210526]\n",
      " [0.31578947]\n",
      " [0.15789474]\n",
      " [0.36842105]]\n",
      "\n",
      "\n",
      " Iteration Number:  3 \n",
      "\n",
      "Eigen Value:  2.368421052631579\n",
      "Eigen Vector: \n",
      " [[0.44444444]\n",
      " [0.22222222]\n",
      " [0.71111111]\n",
      " [1.        ]\n",
      " [0.91111111]\n",
      " [0.42222222]\n",
      " [0.26666667]\n",
      " [0.46666667]]\n",
      "\n",
      "\n",
      " Iteration Number:  4 \n",
      "\n",
      "Eigen Value:  2.7333333333333334\n",
      "Eigen Vector: \n",
      " [[0.50406504]\n",
      " [0.26829268]\n",
      " [0.6097561 ]\n",
      " [1.        ]\n",
      " [0.92682927]\n",
      " [0.43902439]\n",
      " [0.2601626 ]\n",
      " [0.51219512]]\n",
      "\n",
      "\n",
      " Iteration Number:  5 \n",
      "\n",
      "Eigen Value:  2.9105691056910565\n",
      "Eigen Vector: \n",
      " [[0.50837989]\n",
      " [0.26536313]\n",
      " [0.60893855]\n",
      " [1.        ]\n",
      " [0.89106145]\n",
      " [0.39106145]\n",
      " [0.20949721]\n",
      " [0.44972067]]\n",
      "\n",
      "\n",
      " Iteration Number:  6 \n",
      "\n",
      "Eigen Value:  2.7150837988826817\n",
      "Eigen Vector: \n",
      " [[0.4845679 ]\n",
      " [0.24279835]\n",
      " [0.65329218]\n",
      " [1.        ]\n",
      " [0.89609053]\n",
      " [0.39917695]\n",
      " [0.22427984]\n",
      " [0.44547325]]\n",
      "\n",
      "\n",
      " Iteration Number:  7 \n",
      "\n",
      "Eigen Value:  2.6923868312757206\n",
      "Eigen Vector: \n",
      " [[0.48719908]\n",
      " [0.24875812]\n",
      " [0.64157432]\n",
      " [1.        ]\n",
      " [0.90982041]\n",
      " [0.41612533]\n",
      " [0.24264425]\n",
      " [0.47420711]]\n",
      "\n",
      "\n",
      " Iteration Number:  8 \n",
      "\n",
      "Eigen Value:  2.778754298815437\n",
      "Eigen Vector: \n",
      " [[0.49724972]\n",
      " [0.2579758 ]\n",
      " [0.62472497]\n",
      " [1.        ]\n",
      " [0.90346535]\n",
      " [0.40772827]\n",
      " [0.23088559]\n",
      " [0.4679593 ]]\n",
      "\n",
      "\n",
      " Iteration Number:  9 \n",
      "\n",
      "Eigen Value:  2.7652640264026402\n",
      "Eigen Vector: \n",
      " [[0.49346064]\n",
      " [0.25272266]\n",
      " [0.63474066]\n",
      " [1.        ]\n",
      " [0.89919936]\n",
      " [0.40270526]\n",
      " [0.22591874]\n",
      " [0.45686011]]\n",
      "\n",
      "\n",
      " Iteration Number:  10 \n",
      "\n",
      "Eigen Value:  2.7308667760704166\n",
      "Eigen Vector: \n",
      " [[0.49003005]\n",
      " [0.25002276]\n",
      " [0.63942457]\n",
      " [1.        ]\n",
      " [0.90315943]\n",
      " [0.40770281]\n",
      " [0.23243194]\n",
      " [0.46262406]]\n",
      "\n",
      "\n",
      " Iteration Number:  11 \n",
      "\n",
      "Eigen Value:  2.7459710461622504\n",
      "Eigen Vector: \n",
      " [[0.49264233]\n",
      " [0.25311847]\n",
      " [0.63367486]\n",
      " [1.        ]\n",
      " [0.9039557 ]\n",
      " [0.40855466]\n",
      " [0.23285918]\n",
      " [0.46597699]]\n",
      "\n",
      "\n",
      " Iteration Number:  12 \n",
      "\n",
      "Eigen Value:  2.7571073311449315\n",
      "Eigen Vector: \n",
      " [[0.49345533]\n",
      " [0.25346716]\n",
      " [0.63318565]\n",
      " [1.        ]\n",
      " [0.90196941]\n",
      " [0.40609682]\n",
      " [0.22983322]\n",
      " [0.46247336]]\n",
      "\n",
      "\n",
      " Iteration Number:  13 \n",
      "\n",
      "Eigen Value:  2.747295301593716\n",
      "Eigen Vector: \n",
      " [[0.49207326]\n",
      " [0.25199569]\n",
      " [0.63586994]\n",
      " [1.        ]\n",
      " [0.90216423]\n",
      " [0.40639462]\n",
      " [0.23047601]\n",
      " [0.46195095]]\n",
      "\n",
      "\n",
      " Iteration Number:  14 \n",
      "\n",
      "Eigen Value:  2.7450547622591293\n",
      "Eigen Vector: \n",
      " [[0.49209119]\n",
      " [0.25224523]\n",
      " [0.63534942]\n",
      " [1.        ]\n",
      " [0.90299127]\n",
      " [0.4074023 ]\n",
      " [0.23164199]\n",
      " [0.46364852]]\n",
      "\n",
      "\n",
      " Iteration Number:  15 \n",
      "\n",
      "Eigen Value:  2.750020491613747\n",
      "Eigen Vector: \n",
      " [[0.49270107]\n",
      " [0.25283103]\n",
      " [0.63429943]\n",
      " [1.        ]\n",
      " [0.90267642]\n",
      " [0.40699211]\n",
      " [0.23103443]\n",
      " [0.46341244]]\n",
      "\n",
      "\n",
      " Iteration Number:  16 \n",
      "\n",
      "Eigen Value:  2.74964749178138\n",
      "Eigen Vector: \n",
      " [[0.49252495]\n",
      " [0.25255851]\n",
      " [0.63482032]\n",
      " [1.        ]\n",
      " [0.90239586]\n",
      " [0.40665754]\n",
      " [0.23068391]\n",
      " [0.4627233 ]]\n",
      "\n",
      "\n",
      " Iteration Number:  17 \n",
      "\n",
      "Eigen Value:  2.747544067884613\n",
      "Eigen Vector: \n",
      " [[0.49230266]\n",
      " [0.25237346]\n",
      " [0.63514303]\n",
      " [1.        ]\n",
      " [0.90261283]\n",
      " [0.40693168]\n",
      " [0.23105009]\n",
      " [0.46301778]]\n",
      "\n",
      "\n",
      " Iteration Number:  18 \n",
      "\n",
      "Eigen Value:  2.7482885171057716\n",
      "Eigen Vector: \n",
      " [[0.49244212]\n",
      " [0.25254549]\n",
      " [0.63482277]\n",
      " [1.        ]\n",
      " [0.90267768]\n",
      " [0.40700479]\n",
      " [0.23110493]\n",
      " [0.46324278]]\n",
      "\n",
      "\n",
      " Iteration Number:  19 \n",
      "\n",
      "Eigen Value:  2.749017796717289\n",
      "Eigen Vector: \n",
      " [[0.49250245]\n",
      " [0.25258029]\n",
      " [0.63476767]\n",
      " [1.        ]\n",
      " [0.90256341]\n",
      " [0.40686284]\n",
      " [0.23092712]\n",
      " [0.46304993]]\n",
      "\n",
      "\n",
      " Iteration Number:  20 \n",
      "\n",
      "Eigen Value:  2.7484860374014186\n",
      "Eigen Vector: \n",
      " [[0.49242389]\n",
      " [0.2524943 ]\n",
      " [0.63492509]\n",
      " [1.        ]\n",
      " [0.90256609]\n",
      " [0.40686948]\n",
      " [0.23095175]\n",
      " [0.46300313]]\n",
      "\n",
      "\n",
      " Iteration Number:  21 \n",
      "\n",
      "Eigen Value:  2.7483086300893556\n",
      "Eigen Vector: \n",
      " [[0.49241873]\n",
      " [0.25250253]\n",
      " [0.6349062 ]\n",
      " [1.        ]\n",
      " [0.9026161 ]\n",
      " [0.40693069]\n",
      " [0.23102394]\n",
      " [0.46310167]]\n",
      "\n",
      "\n",
      " Iteration Number:  22 \n",
      "\n",
      "Eigen Value:  2.7485936690279167\n",
      "Eigen Vector: \n",
      " [[0.49245505]\n",
      " [0.25253846]\n",
      " [0.63484148]\n",
      " [1.        ]\n",
      " [0.90260113]\n",
      " [0.40691088]\n",
      " [0.23099311]\n",
      " [0.46309531]]\n",
      "\n",
      "\n",
      " Iteration Number:  23 \n",
      "\n",
      "Eigen Value:  2.7485939396712453\n",
      "Eigen Vector: \n",
      " [[0.49244733]\n",
      " [0.2525249 ]\n",
      " [0.6348677 ]\n",
      " [1.        ]\n",
      " [0.90258304]\n",
      " [0.40688915]\n",
      " [0.23096954]\n",
      " [0.46305329]]\n",
      "\n",
      "\n",
      " Iteration Number:  24 \n",
      "\n",
      "Eigen Value:  2.748467254863014\n",
      "Eigen Vector: \n",
      " [[0.49243333]\n",
      " [0.25251268]\n",
      " [0.63488922]\n",
      " [1.        ]\n",
      " [0.90259468]\n",
      " [0.40690393]\n",
      " [0.23098973]\n",
      " [0.46306769]]\n"
     ]
    }
   ],
   "source": [
    "unit = np.ones((n,1))\n",
    "m = np.matrix(unit)\n",
    "\n",
    "b = True\n",
    "itr = 0\n",
    "while b:\n",
    "    itr += 1\n",
    "    y = 0\n",
    "    p = mat@m\n",
    "    x = p.max()\n",
    "    p = p / x\n",
    "\n",
    "    for i in range(n):\n",
    "        if round(p.item(i), 4) == round(m.item(i), 4):\n",
    "            y += 1\n",
    "\n",
    "    print(\"\\n\\n Iteration Number: \", itr, \"\\n\")\n",
    "\n",
    "    if(y == n):\n",
    "         b=False\n",
    "        \n",
    "    print(\"Eigen Value: \",x)\n",
    "    print(\"Eigen Vector: \\n\",p)        \n",
    "    \n",
    "    m = p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ranking"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.2309897261698752, 0.2525126786629896, 0.4069039347918018, 0.46306769094480976, 0.49243332859688127, 0.6348892215544106, 0.9025946757240018, 1.0]\n",
      "[0.49243332859688127, 0.2525126786629896, 0.6348892215544106, 1.0, 0.9025946757240018, 0.4069039347918018, 0.2309897261698752, 0.46306769094480976]\n",
      "\n",
      "\n",
      " Mumbai Indians\n",
      "\n",
      "\n",
      " Kolkata Knight Riders\n",
      "\n",
      "\n",
      " Rising Pune Supergiants\n",
      "\n",
      "\n",
      " Sunrisers Hyderabad\n",
      "\n",
      "\n",
      " Delhi Daredevils\n",
      "\n",
      "\n",
      " Kings XI Punjab\n",
      "\n",
      "\n",
      " Royal Challengers Bangalore\n",
      "\n",
      "\n",
      " Gujrat Lions\n"
     ]
    }
   ],
   "source": [
    "rank = []\n",
    "rankus = []\n",
    "for i in range(n):\n",
    "    rank.append(p.item(i))\n",
    "    rankus.append(p.item(i))\n",
    "rank.sort()\n",
    "print(rank)\n",
    "print(rankus)\n",
    "\n",
    "for i in range(n):\n",
    "    print(\"\\n\\n\", teams[rankus.index(rank[-(i+1)])])\n",
    "\n",
    "del rank\n",
    "del rankus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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