{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1e392f52",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def power_iteration(A, num_simulations: int):\n",
    "    # Ideally choose a random vector\n",
    "    # To decrease the chance that our vector\n",
    "    # Is orthogonal to the eigenvector\n",
    "    b_k = np.random.rand(A.shape[1])\n",
    "\n",
    "    for _ in range(num_simulations):\n",
    "        # calculate the matrix-by-vector product Ab\n",
    "        b_k1 = np.dot(A, b_k)\n",
    "    \n",
    "        rayleigh = (b_k.T @ b_k1)/(b_k.T @ b_k)\n",
    "    \n",
    "        # calculate the norm\n",
    "        b_k1_norm = np.linalg.norm(b_k1)\n",
    "\n",
    "        # re normalize the vector\n",
    "        b_k = b_k1 / b_k1_norm\n",
    "        \n",
    "        \n",
    "\n",
    "    return b_k, rayleigh\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4315f9cd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 0.09834601,  0.99128595, -0.08763689]), 8.187637295029564)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "power_iteration(np.asarray([[-1, 1 ,1], [1, 8, -1], [1, -1, -2]]), 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c99ef5a1",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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