t20_eigenvalues.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Table of Contents](table_of_contents.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Topic 20.  Eigenvalues and Eigenvectors\n",
    "Author: Mat Haskell - mhaskell9@gmail.com"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Introduction\n",
    "Eigen values and eigen vectors are very cool and show up all over the place. Eigenvalues and eigenvectors exist generally for linear operators, but this notebook will just look at matrices. The basic idea is that certain vectors exist where, after the matrix operates on them, the direction of the vector has not changed. The magnitude can be changed, but not the direction. These special vectors are eigenvectors of the operator. This makes sense when thinking about a rotation matrix. If you try to rotate a vector purely in the x-direction about the x-axis, it does not rotate. This means that the axis of rotation must be an eigenvector of the rotation matrix since it cannot change the direction of the vector it is operating on.\n",
    "\n",
    "Another way to think about eigenvalues is that there are special cases where matrix multiplication is turned into scalar multiplication. This seems strange since the output of matrix multiplication is not really intuitive by just looking at the equation. Matrices are linear operators that can be used to accomplish various tasks. However, when multiplying a matrix by one of its eigenvectors, that vector will just be scaled by the value of the corresponding eigenvalue. The eigenvector can grow, shrink, and flip directions (i.e. eigenvalues can be negative). Eigenvalues can even be zero, in which case the eigenvector multiplied by the matrix will be scaled down to zero.\n",
    "\n",
    "The physical meaning of eigenvalues and eigenvectors is also cool. For special symmetric matrices, like inertia tensors, stress tensors, and strain tensors, the eigenvectors are the principal axes of the matrix. So if you were to rotate the original matrix axes to line up with the eigenvectors (or principal axes), all of the cross terms would go away leaving only numbers along the main diagonal. Also, the eigenvalues are the principal stresses/strains of a stress/strain tensor. Another physical meaning comes with differential and difference equations. Eigenvalues are the poles of the system and show stability based off if the eigenvalues are positive or negative. The last example I will include here is with Google. I don't know their algorithm, but I do know that Google's search engine optimization algorithm forms a giant matrix of info regarding links between websites and they use eigenvalues and eigenvectors to determine which websites are most closely related to your search. So eigenvalues are the magic that Google uses to make sure you don't have to look past the first few links to find what you are looking for! "
   ]
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   "cell_type": "markdown",
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   "source": [
    "$\\newcommand{\\real}{\\mathbb{R}}$\n",
    "$\\newcommand{\\complex}{\\mathbb{C}}$\n",
    "$\\newcommand{\\script}[1]{\\mathcal{#1}}$\n",
    "$\\newcommand{\\chi}{\\script{X}}$\n",
    "## Explanation of the theory\n",
    "Eigenvalues only exist for square matrices.\n",
    "$$A\\in \\complex^{n\\times n}$$\n",
    "\n",
    "Let $x\\in\\complex^{n\\times1}$ be an eigenvector of A and $\\lambda\\in\\complex$ be the corresponding eigenvalue of A, then the idea that matrix multiplication is turned into scalar multiplication yields the equation:\n",
    "$$Ax=\\lambda x$$\n",
    "\n",
    "Here are the formal definitions for eigen pairs:\n",
    "\n",
    "__Def:__ $(\\lambda,x)$ is a __right eigen pair__ if $Ax=\\lambda x$.\n",
    "\n",
    "__Def:__ $(\\lambda,x)$ is a __left eigen pair__ if $x^HA^H=\\lambda x^H$."
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Most of the time we deal with right eigen pairs. So here is how to actually solve for the eigenvalues. Before any computational work, we need to rearrange the equation $Ax=\\lambda x$ into a useful form.\n",
    "\n",
    "- Get everything onto 1 side of the equation (it doesn't matter which side):\n",
    "\n",
    "$$Ax-\\lambda x=0$$\n",
    "\n",
    "- Multiply x by identity (which doesn't change it):\n",
    "\n",
    "$$Ax-\\lambda Ix=0$$\n",
    "\n",
    "- Factor out the x:\n",
    "\n",
    "$$(A-\\lambda I)x=0$$\n",
    "\n",
    "__Note:__ some textbooks write it as $(\\lambda I-A)x=0$, but they are equivalent.\n",
    "\n",
    "We can see that $x\\in\\mathcal{N}(A-\\lambda I)$. Since there is a non-trivial null space we know that $(A-\\lambda I)$ is not full rank, which implies that $det(A-\\lambda I)=0$. We will use this fact to solve for the eigenvalues of A."
   ]
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   "cell_type": "markdown",
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   "source": [
    "### Finding the eigenvalues of a matrix\n",
    "Here are the computational steps for finding the eigenvalues of A:\n",
    "\n",
    "1. Start with the equation we just derived:\n",
    "\n",
    "$$det(A-\\lambda I)=0$$\n",
    "\n",
    "$$\n",
    "\\Rightarrow\n",
    "\\left|\n",
    "\\begin{pmatrix}\n",
    "a_{11} & a_{12} & \\cdots & a_{1n}\\\\\n",
    "a_{21} & a_{22} & \\cdots & a_{2n}\\\\\n",
    "\\vdots & \\vdots & \\ddots & \\vdots\\\\\n",
    "a_{n1} & a_{n2} & \\cdots & a_{nn}\n",
    "\\end{pmatrix}\n",
    "-\n",
    "\\begin{pmatrix}\n",
    "\\lambda & 0 & \\cdots & 0\\\\\n",
    "0 & \\lambda & \\cdots & 0\\\\\n",
    "\\vdots & \\vdots & \\ddots & \\vdots\\\\\n",
    "0 & 0 & \\cdots & \\lambda\n",
    "\\end{pmatrix}\n",
    "\\right|\n",
    "=0\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\Rightarrow\n",
    "\\begin{vmatrix}\n",
    "a_{11}-\\lambda & a_{12} & \\cdots & a_{1n}\\\\\n",
    "a_{21} & a_{22}-\\lambda & \\cdots & a_{2n}\\\\\n",
    "\\vdots & \\vdots & \\ddots & \\vdots\\\\\n",
    "a_{n1} & a_{n2} & \\cdots & a_{nn}-\\lambda\n",
    "\\end{vmatrix}\n",
    "=0\n",
    "$$\n",
    "\n",
    "2. Take the determinant. This will give the characteristic polynomial of A, $\\chi_A(\\lambda)$, and characteristic equation of A, $\\chi_A(\\lambda)=0$. Let $\\alpha_i$ be a scalar, then the charateristic polynomial can be written as:\n",
    "\n",
    "$$\\chi_A(\\lambda)\\triangleq\\lambda^n+\\alpha_{n-1}\\lambda^{n-1}+\\cdots+\\alpha_1\\lambda+\\alpha_0=0$$\n",
    "\n",
    "3. Find the roots of the characteristic polynomial, which are the eigenvalues. By the fundamental theorem of algebra, we know that the characteristic polynomial will have n roots. This means that there are going to be n eigenvalues, although some of them may be repeated. When eigenvalues are repeated, there are p distict eigenvalues, where p counts repeated eigenvalues only once.\n",
    "\n",
    "__Note:__ In practice, you will most likely never write an algorithm that finds eigenvalues. There are existing software tools to find eigenvalues (e.g. the eig() function in Matlab and Python). I would strongly recommend using those tools and not going through any of this process by hand! If you really wanted to find eigenvalues on paper, you could try polynomial division to get the roots. This can get tricky pretty fast as the number of roots increases (there is a lot of guessing and checking). Also, writing your own algorithm to find eigenvalues is more difficult than it might appear and you would need to do more research on your own to learn how. This is because numerical root finding algorithms typically only find real roots. Writing an algorithm to find complex roots is tricky and will not be discussed here. In fact, I believe that complex root finding tools actually use eigenvalue solvers to get the roots. Anyways, the Gershgorin Circle Theorem and Cauchy-Riemann Equations would be a good place to start your research.\n",
    "\n",
    "__Note:__ we can write $\\chi_A$ with all of the eigenvalues factored out (which would be the result of polynomial division):\n",
    "\n",
    "$$\\chi_A(\\lambda)=(\\lambda-\\lambda_{1})(\\lambda-\\lambda_{2})\\cdots(\\lambda-\\lambda_{n})=\\Pi_{i=0}^n(\\lambda-\\lambda_i)$$\n",
    "\n",
    "__Def:__ Algebraic multiplicity, $m_i$, of $\\lambda_i$ is the number of times it is repeated. So $\\chi_A$ can be written like this:\n",
    "$$\\chi_A(\\lambda)=(\\lambda-\\lambda_{1})^{m_1}(\\lambda-\\lambda_{2})^{m_2}\\cdots(\\lambda-\\lambda_{p})^{m_p},\\ \\ \\ \\ \\ p\\leq n$$"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Finding the eigenvectors of a matrix\n",
    "After finding the roots/eigenvalues, we can solve for the eigenvectors by plugging in each eigenvalue into the equation $(A-\\lambda_iI)x=0$. You are just solving for the null space of $(A-\\lambda I)$. \n",
    "\n",
    "__Note:__ any linear combination of vectors from $\\mathcal{N}(A-\\lambda I)$ are also eigenvectors. Because any scalar multiple of an eigenvector is also an eigenvector, most software libraries will return the eigenvectors with a norm of 1."
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example:\n",
    "Find the eigenvalues and eigenvectors of A by following the steps above.\n",
    "$$A=\\begin{pmatrix}4 & -2\\\\5 & -7\\end{pmatrix}$$\n",
    "\n",
    "1. First set $det(A-\\lambda I)=0$:\n",
    "\n",
    "$$\n",
    "\\begin{vmatrix}\n",
    "4-\\lambda & -2\\\\\n",
    "5 & -7-\\lambda\n",
    "\\end{vmatrix}\n",
    "=0\n",
    "$$\n",
    "\n",
    "2. Take the determinant to find the characteristic equation:\n",
    "\n",
    "\\begin{eqnarray}\n",
    "\\chi_A(\\lambda)&=&(4-\\lambda)(-7-\\lambda)+10=0\\\\\n",
    "&=&\\lambda^2+3\\lambda-18=0\n",
    "\\end{eqnarray}\n",
    "\n",
    "3. Find the roots/eigenvalues.\n",
    "\n",
    "$$\\chi_A(\\lambda)=(\\lambda+6)(\\lambda-3)$$\n",
    "\n",
    "The order of assigning $\\lambda_1$ and $\\lambda_2$ doesn't really matter. I will use these:\n",
    "$$\\lambda_1=3$$ \n",
    "$$\\lambda_2=-6$$\n",
    "\n",
    "Neither of these are repeated, so the algebraic multiplicity of both are just 1.\n",
    "$$m_1=1$$ \n",
    "$$m_2=1$$"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's continue with the example and find the eigenvectors of A.\n",
    "- For $\\lambda_1=3$:\n",
    "\n",
    "\\begin{eqnarray}\n",
    "\\begin{pmatrix}\n",
    "4-\\lambda & -2\\\\\n",
    "5 & -7-\\lambda\n",
    "\\end{pmatrix}\n",
    "\\begin{pmatrix}x_1\\\\x_2\\end{pmatrix}&=&\\begin{pmatrix}0\\\\0\\end{pmatrix} \\\\\n",
    "\\begin{pmatrix}\n",
    "4-3 & -2\\\\\n",
    "5 & -7-3\n",
    "\\end{pmatrix}\n",
    "\\begin{pmatrix}x_1\\\\x_2\\end{pmatrix}&=&\\begin{pmatrix}0\\\\0\\end{pmatrix} \\\\\n",
    "\\begin{pmatrix}\n",
    "1 & -2\\\\\n",
    "5 & -10\n",
    "\\end{pmatrix}\n",
    "\\begin{pmatrix}x_1\\\\x_2\\end{pmatrix}&=&\\begin{pmatrix}0\\\\0\\end{pmatrix}\n",
    "\\end{eqnarray}\n",
    "\n",
    "Notice that both rows of A when multiplied by x give the same equation:\n",
    "\\begin{eqnarray}\n",
    "&x_1&-2x_2=0 \\\\\n",
    "\\Rightarrow &x_1&=2x_2\n",
    "\\end{eqnarray}\n",
    "Now we can solve for x:\n",
    "$$\n",
    "x=\n",
    "\\begin{pmatrix}2x_2 \\\\ x_2\\end{pmatrix}=\n",
    "\\begin{pmatrix}2 \\\\ 1\\end{pmatrix}x_2\n",
    "$$\n",
    "An eigenvector associated with $\\lambda_1$, $\\mathbf{v_1}$, is any scalar multiple of $\\begin{pmatrix}2 \\\\ 1\\end{pmatrix}$.\n",
    "\n",
    "- For $\\lambda_2=-6$:\n",
    "\n",
    "\\begin{eqnarray}\n",
    "\\begin{pmatrix}\n",
    "4-\\lambda & -2\\\\\n",
    "5 & -7-\\lambda\n",
    "\\end{pmatrix}\n",
    "\\begin{pmatrix}x_1\\\\x_2\\end{pmatrix}&=&\\begin{pmatrix}0\\\\0\\end{pmatrix} \\\\\n",
    "\\begin{pmatrix}\n",
    "4+6 & -2\\\\\n",
    "5 & -7+6\n",
    "\\end{pmatrix}\n",
    "\\begin{pmatrix}x_1\\\\x_2\\end{pmatrix}&=&\\begin{pmatrix}0\\\\0\\end{pmatrix} \\\\\n",
    "\\begin{pmatrix}\n",
    "10 & -2\\\\\n",
    "5 & -1\n",
    "\\end{pmatrix}\n",
    "\\begin{pmatrix}x_1\\\\x_2\\end{pmatrix}&=&\\begin{pmatrix}0\\\\0\\end{pmatrix}\n",
    "\\end{eqnarray}\n",
    "\n",
    "Notice that both rows of A when multiplied by x give the same equation:\n",
    "\\begin{eqnarray}\n",
    "&5x_1&-x_2=0 \\\\\n",
    "\\Rightarrow &x_2&=5x_1\n",
    "\\end{eqnarray}\n",
    "Now we can solve for x:\n",
    "$$\n",
    "x=\n",
    "\\begin{pmatrix}x_1 \\\\ 5x_1\\end{pmatrix}=\n",
    "\\begin{pmatrix}1 \\\\ 5\\end{pmatrix}x_1\n",
    "$$\n",
    "An eigenvector associated with $\\lambda_2$, $\\mathbf{v_2}$, is any scalar multiple of $\\begin{pmatrix}1 \\\\ 5\\end{pmatrix}$."
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Eigenvalue decomposition\n",
    "The eigenvalue decomposition of A is as such:\n",
    "$$A=S\\Lambda S^{-1}$$\n",
    "\n",
    "Where,\n",
    "$$\n",
    "\\Lambda=diag([\\lambda_1, \\lambda_2, \\cdots, \\lambda_n])\n",
    "=\n",
    "\\begin{pmatrix}\n",
    "\\lambda_1 & 0 & \\cdots & 0 \\\\\n",
    "0 & \\lambda_2 & \\cdots & 0 \\\\\n",
    "\\vdots & \\vdots & \\ddots & 0 \\\\\n",
    "0 & 0 & \\cdots & \\lambda_n\n",
    "\\end{pmatrix}\n",
    "$$\n",
    "\n",
    "$$\n",
    "S=\\begin{pmatrix}\n",
    "\\mathbf{v_1} & \\mathbf{v_2} & \\cdots & \\mathbf{v_n}\n",
    "\\end{pmatrix}\n",
    "$$\n",
    "\n",
    "__Note:__ it does not matter in which order the eigenvalues are placed to form $\\Lambda$. However, for $A=S\\Lambda S^{-1}$ to be true, the position of the column of $\\lambda_i$ must match the position of the column of $\\mathbf{v_i}$ (where $\\mathbf{v_i}$ is an eigenvector corresponding to $\\lambda_i$).\n",
    "\n",
    "__Def:__ Geometric multiplicity, $q_i$, of $\\lambda_i$ is the number of linearly independent eigenvectors that can be formed from $\\lambda_i$. Also, $1\\leq q_i\\leq m_i$.\n",
    "This means at least 1 eigenvector can be formed from every eigenvalue, but at most $m_i$. For example: if an eigenvalue is repeated 3 times, there will be at most 3 corresponding linearly independent eigenvectors but at least 1 eigenvector.\n",
    "\n",
    "The geometric multiplicity of an eigenvalue is a very important concept for eigenvalue decomposition. In order to perform the eigenvalue decomposition, as described above where $A=S\\Lambda S^{-1}$, the geomectric multiplicity must be equal to the algebraic multiplicity for each eigenvalue. i.e.\n",
    "\n",
    "$$m_i=q_i\\ \\ \\ \\forall\\lambda_i$$\n",
    "\n",
    "This means that however many times an eigenvalue is repeated, there must be that same number of linearly independent eigenvectors derived from that eigenvalue. Otherwise, there isn't enough eigenvectors to fill the columns of S.\n",
    "\n",
    "When $m_i\\neq q_i$, there is a process to find what are called generalized eigenvectors to fill up the missing columns of S. When this happens, $\\Lambda$ is replaced with $J$ and is not strictly diagonal. This is called the Jordan form and is a topic for another day."
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fun Facts \n",
    "- If an eigenvalue is complex, its complex conjugate will also be an eigenvalue. \n",
    "- If an eigenvector is complex, its complex conjugate will also be an eigenvector.\n",
    "- Symmetric matrices have real eigenvalues.\n",
    "- For a positive definite matrix $\\Leftrightarrow$ all eigenvalues will be positive ($\\lambda_i>0$).\n",
    "- For a positive semi-definite matrix $\\Leftrightarrow$ all eigenvalues will be non-negative ($\\lambda_i\\geq0$).\n",
    "- For a negative semi-definite matrix $\\Leftrightarrow$ all eigenvalues will be non-positive ($\\lambda_i\\leq0$).\n",
    "- For a negative definite matrix $\\Leftrightarrow$ all eigenvalues will be negative ($\\lambda_i<0$).\n",
    "- The trace of a matrix equals the sum of its eigenvalues ($trace(A)=\\sum\\lambda_i$).\n",
    "- The determinant of a matrix equals the product of its eigenvalues ($det(A)=\\Pi\\lambda_i$).\n",
    "- Eigenvectors of a matrix are all linearly independent.\n",
    "- The eigenvalues of a diagonal matrix are all of the elements along the diagonal.\n",
    "- For every 0 eigenvalue, the rank of a matrix goes down by 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simple Numerical Examples\n",
    "\n",
    "### Setup structure for testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "class Test:\n",
    "    def __init__(self):\n",
    "        self.i = 1\n",
    "    def runTest(self,check,statement):\n",
    "        print('Test %d: ' % self.i)\n",
    "        self.i += 1\n",
    "        if check:\n",
    "            print(statement + ' \\n')\n",
    "        else:\n",
    "            print('error \\n')\n",
    "            \n",
    "def printEigen(vals,vecs):\n",
    "    print('Eigenvalues are {:.2f}, {:.2f}, and {:.2f}. \\n'.format(vals[0],vals[1],vals[2]))\n",
    "    print('The eigenvector corresponding to {:.2f} is:'.format(vals[0]))\n",
    "    print(vecs[:,0][:,None])\n",
    "    print('The eigenvector corresponding to {:.2f} is:'.format(vals[1]))\n",
    "    print(vecs[:,1][:,None])\n",
    "    print('The eigenvector corresponding to {:.2f} is:'.format(vals[2]))\n",
    "    print(vecs[:,2][:,None])\n",
    "    print('') # add a blank line at the end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Verify the example from above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test 1: \n",
      "v1 and l1 are a right eigen pair! \n",
      "\n",
      "Test 2: \n",
      "v2 and l2 are a right eigen pair! \n",
      "\n",
      "Test 3: \n",
      "A = S*L*S_inv! \n",
      "\n",
      "Test 4: \n",
      "It still works when the order is switched! \n",
      "\n",
      "Test 5: \n",
      "The trace equals sum of eigenvalues! \n",
      "\n",
      "Test 6: \n",
      "error \n",
      "\n",
      "Test 7: \n",
      "The determinant equals product of eigenvalues! \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# this is the matrix we used above\n",
    "A = np.array([[4,-2],\n",
    "              [5,-7]])\n",
    "# these are the eigenvalues we found\n",
    "l1 = 3\n",
    "l2 = -6\n",
    "# these are the eigenvectors we found\n",
    "v1 = np.array([[2],\n",
    "               [1]])\n",
    "v2 = np.array([[1],\n",
    "               [5]])\n",
    "\n",
    "# check that Ax-lx=0\n",
    "# note that numerical precision might limit this to being very close to true\n",
    "tests = Test()\n",
    "\n",
    "test1 = np.array_equal(A@v1, l1*v1)\n",
    "tests.runTest(test1,'v1 and l1 are a right eigen pair!')\n",
    "\n",
    "test2 = np.array_equal(A@v2, l2*v2)\n",
    "tests.runTest(test2,'v2 and l2 are a right eigen pair!')\n",
    "    \n",
    "# eigenvalue decomposition\n",
    "L = np.diag([l1, l2])\n",
    "S = np.concatenate((v1,v2), axis=1)\n",
    "S_inv = np.linalg.inv(S)\n",
    "\n",
    "# test that it works\n",
    "test3 = np.array_equal(A, S@L@S_inv)\n",
    "tests.runTest(test3,'A = S*L*S_inv!')\n",
    "\n",
    "# now let's test that the order doesn't matter\n",
    "L = np.diag([l2, l1])\n",
    "S = np.concatenate((v2,v1), axis=1)\n",
    "S_inv = np.linalg.inv(S)\n",
    "\n",
    "test4 = np.array_equal(A, S@L@S_inv)\n",
    "tests.runTest(test4,'It still works when the order is switched!')\n",
    "\n",
    "# test that trace equals sum of eigenvalues\n",
    "test5 = np.trace(A)==l1+l2\n",
    "tests.runTest(test5,'The trace equals sum of eigenvalues!')\n",
    "\n",
    "# test that determinant equals product of eigenvalues\n",
    "test6 = np.linalg.det(A)==l1*l2\n",
    "tests.runTest(test6,'The determinant equals product of eigenvalues!')\n",
    "# this runs into numerical precision errors, try again testing if error is small\n",
    "det_error = np.linalg.det(A)-l1*l2\n",
    "test7 = np.abs(det_error) < 1e-10\n",
    "tests.runTest(test7,'The determinant equals product of eigenvalues!')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Now let's see how to get the eigenvalues through code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalues are 2.00+1.00j, 2.00-1.00j, and 2.00+0.00j. \n",
      "\n",
      "The eigenvector corresponding to 2.00+1.00j is:\n",
      "[[ 0.        +0.j        ]\n",
      " [ 0.81649658+0.j        ]\n",
      " [-0.40824829-0.40824829j]]\n",
      "The eigenvector corresponding to 2.00-1.00j is:\n",
      "[[ 0.        -0.j        ]\n",
      " [ 0.81649658-0.j        ]\n",
      " [-0.40824829+0.40824829j]]\n",
      "The eigenvector corresponding to 2.00+0.00j is:\n",
      "[[1.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]]\n",
      "\n",
      "Test 1: \n",
      "A*x1 = l1*x1! \n",
      "\n",
      "Test 2: \n",
      "A*x2 = l2*x2! \n",
      "\n",
      "Test 3: \n",
      "A*x3 = l3*x3! \n",
      "\n",
      "Test 4: \n",
      "Eigenvalue decomposition worked! \n",
      "\n",
      "Test 5: \n",
      "Eigenvalues came in complex conjugate pairs! \n",
      "\n",
      "Test 6: \n",
      "Eigenvectors came in complex conjugate pairs! \n",
      "\n"
     ]
    }
   ],
   "source": [
    "A = np.array([[2,0,0],\n",
    "              [0,1,-2],\n",
    "              [0,1,3]])\n",
    "\n",
    "vals,vecs = np.linalg.eig(A)\n",
    "\n",
    "printEigen(vals,vecs)\n",
    "\n",
    "# check if Ax-lx=0\n",
    "# due to numerical precision error, I will check if norm(Ax-lx) < 1e-10\n",
    "tests = Test()\n",
    "\n",
    "test1 = np.linalg.norm(A@vecs[:,0] - vals[0]*vecs[:,0]) < 1e-10\n",
    "tests.runTest(test1,'A*x1 = l1*x1!')\n",
    "\n",
    "test2 = np.linalg.norm(A@vecs[:,1] - vals[1]*vecs[:,1]) < 1e-10\n",
    "tests.runTest(test2,'A*x2 = l2*x2!')\n",
    "\n",
    "test3 = np.linalg.norm(A@vecs[:,2] - vals[2]*vecs[:,2]) < 1e-10\n",
    "tests.runTest(test3,'A*x3 = l3*x3!')\n",
    "\n",
    "\n",
    "# Eigenvalue decomposition\n",
    "S = vecs\n",
    "Lambda = np.diag([vals[0],vals[1],vals[2]])\n",
    "S_inv = np.linalg.inv(S)\n",
    "\n",
    "# test that A = S*Lambda*S_inv\n",
    "test4 = np.linalg.norm(A - S@Lambda@S_inv) < 1e-10\n",
    "tests.runTest(test4,'Eigenvalue decomposition worked!')\n",
    "\n",
    "# test if eigenvalues came in complex conjugate pairs\n",
    "test5 = vals[0].conj()==vals[1]\n",
    "tests.runTest(test5,'Eigenvalues came in complex conjugate pairs!')\n",
    "\n",
    "# test if eigenvectors came in complex conjugate pairs\n",
    "test6 = np.array_equal(vecs[:,0].conj(), vecs[:,1])\n",
    "tests.runTest(test6,'Eigenvectors came in complex conjugate pairs!')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test 1: \n",
      "The rank went down by 1 for each 0 eigenvalue! \n",
      "\n",
      "Test 2: \n",
      "Repeated eigenvalues did not produce linearly independent eigenvectors \n",
      "\n"
     ]
    }
   ],
   "source": [
    "B = np.array([[1,3,4],\n",
    "              [1,3,4],\n",
    "              [1,3,4]])\n",
    "\n",
    "vals,vecs = np.linalg.eig(B)\n",
    "\n",
    "# test that rank goes down by 1 for each 0 eigenvalue\n",
    "num_0_vals = 0\n",
    "for x in vals:\n",
    "    if x==0:\n",
    "        num_0_vals += 1\n",
    "\n",
    "m,n = B.shape      \n",
    "max_rank = min(m,n)\n",
    "expected_rank = max_rank - num_0_vals\n",
    "\n",
    "tests = Test()\n",
    "\n",
    "test1 = expected_rank==np.linalg.matrix_rank(B)\n",
    "tests.runTest(test1,'The rank went down by 1 for each 0 eigenvalue!')\n",
    "\n",
    "# show that repeated eigenvalues don't always produce lin. ind. eigenvectors\n",
    "test2 = np.array_equal(vecs[:,0], -vecs[:,2]) and vals[0]==vals[2]\n",
    "tests.runTest(test2,'Repeated eigenvalues did not produce linearly independent eigenvectors')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Applications\n",
    "### Find the axis and angle of rotation from a rotation matrix\n",
    "It turns out that the eigenvalues of a 3 dimensional rotation matrix will always be 1, $e^{j\\theta}$, and $e^{-j\\theta}$. Also, the eigenvector associated with $\\lambda=1$ is the axis of rotation. You could also find these values through other means, like quaternions or axis-angle parameterization. But it is cool that the eigenvalues and eigenvectors have real physical meaning for rotation matrices!\n",
    "\n",
    "__Note:__ $e^{j\\theta}=cos(\\theta)+j sin(\\theta)$, so you find the magnitude of theta with $acos(real(\\lambda))$. There are limitations of acos() and asin() that should be considered as well. I will use positve angles below 90 degrees to avoid issues here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'Test' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-3-8173f069d87e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     15\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mR\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     16\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 17\u001b[0;31m \u001b[0mtests\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mTest\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     18\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     19\u001b[0m \u001b[0;31m# test simple rotation about x-axis\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'Test' is not defined"
     ]
    }
   ],
   "source": [
    "def rotx(angle):\n",
    "    R = np.array([[1,0,0],\n",
    "                  [0,np.cos(angle),-np.sin(angle)],\n",
    "                  [0,np.sin(angle),np.cos(angle)]])\n",
    "    return R\n",
    "def roty(angle):\n",
    "    R = np.array([[np.cos(angle),0,np.sin(angle)],\n",
    "                  [0,1,0],\n",
    "                  [-np.sin(angle),0,np.cos(angle)]])\n",
    "    return R\n",
    "def rotz(angle):\n",
    "    R = np.array([[np.cos(angle),-np.sin(angle),0],\n",
    "                  [np.sin(angle),np.cos(angle),0],\n",
    "                  [0,0,1]])\n",
    "    return R\n",
    "\n",
    "tests = Test()\n",
    "\n",
    "# test simple rotation about x-axis\n",
    "theta_x = np.pi/4\n",
    "Rx = rotx(theta_x)\n",
    "x_axis = np.array([[1],[0],[0]])\n",
    "\n",
    "vals,vecs = np.linalg.eig(Rx)\n",
    "\n",
    "# check to see if axis of rotation from eigenvector is the x-axis\n",
    "printEigen(vals,vecs)\n",
    "index = np.where(vals==1)[0]\n",
    "axis_of_rotation = vecs[:,index[0]][:,None]\n",
    "\n",
    "test1 = np.array_equal(x_axis,axis_of_rotation)\n",
    "tests.runTest(test1,'The eigenvector associated with lambda=1 is the axis of rotation!')\n",
    "\n",
    "# check that the amount of rotation from eigenvalue is correct\n",
    "angle = np.arccos(np.real(vals[0]))\n",
    "\n",
    "test2 = angle==theta_x\n",
    "tests.runTest(test2,'The eigenvalue gave the correct amount of rotation!')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'np' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-4-a1cdd9c90941>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# Now test a case where there is rotation about all 3 axes\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mtheta_y\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpi\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;36m6\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0mtheta_z\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpi\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mRy\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mroty\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtheta_y\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mRz\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrotz\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtheta_z\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'np' is not defined"
     ]
    }
   ],
   "source": [
    "# Now test a case where there is rotation about all 3 axes\n",
    "theta_y = np.pi/6\n",
    "theta_z = np.pi/5\n",
    "Ry = roty(theta_y)\n",
    "Rz = rotz(theta_z)\n",
    "R = Rx@Ry@Rz\n",
    "\n",
    "vals,vecs = np.linalg.eig(R)\n",
    "\n",
    "# get the axis-angle parameterization\n",
    "expected_angle = np.arccos(0.5*(np.trace(R)-1))\n",
    "expected_axis = np.array([[R[1,2]-R[2,1]],\n",
    "                         [R[2,0]-R[0,2]],\n",
    "                         [R[0,1]-R[1,0]]])/(2*np.sin(expected_angle))\n",
    "\n",
    "# check to see if axis of rotation from eigenvector is correct\n",
    "printEigen(vals,vecs)\n",
    "eigen_axis = vecs[:,0]\n",
    "\n",
    "test3 = np.array_equal(expected_axis, eigen_axis)\n",
    "tests.runTest(test1,'The eigenvector associated with lambda=1 is the axis of rotation!')\n",
    "\n",
    "# check that the amount of rotation from eigenvalue is correct\n",
    "eigen_angle = np.arccos(np.real(vals[2]))\n",
    "\n",
    "test4 = expected_angle==eigen_angle\n",
    "tests.runTest(test2,'The eigenvalue gave the correct amount of rotation!')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Power Iteration\n",
    "by Curtis Johnson\n",
    "\n",
    "Power iteration is a useful algorithm used for optimal control, path planning, and notably early versions of Google's PageRank algorithm.\n",
    "\n",
    "The useful recursive relationship used in this algorithm is given by $b_{k+1} = \\frac{Ab_k}{||Ab_k||}$.\n",
    "\n",
    "#### Lemma:\n",
    "\n",
    "$b_k$ will converge to a multiple of the eigenvector cooresponding to the largest eigenvalue.\n",
    "\n",
    "#### Proof:\n",
    "\n",
    "Let A be diagonalizable nxn matrix with eigenvalues $\\lambda_1, \\lambda_2,\\cdots,\\lambda_m$ such that $\\lambda_1$ is the dominant eigenvalue (i.e. $|\\lambda_1| > |\\lambda_i|, \\forall i > 1$). The cooresponding eigenvectors are $x_1, x_2,\\cdots, x_m$.\n",
    "\n",
    "Also let the initial vector $b_0 \\in span(x_1\\cdots x_p)$ such that $b_0 = c_1x_1 + c_2x_2 +\\cdots+ c_nx_n$ where $c_1 \\neq 0$.\n",
    "\n",
    "$$\\begin{align}\n",
    "\\implies A^kb_0 &= c_1A^kx_1 + c_2A^kx_2 +\\cdots+ c_nA^kx_n \\\\\n",
    "&= c_1\\lambda_1^kx_1 + c_2\\lambda_2^kx_2 +\\cdots+ c_n\\lambda_n^kx_n \\\\\n",
    "&= c_1\\lambda_1^k \\left[x_1 + \\frac{c_2}{c_1}\\left(\\frac{\\lambda_2}{\\lambda_1}\\right)^k x_2 + \\cdots + \\frac{c_n}{c_1}\\left(\\frac{\\lambda_n}{\\lambda_1}\\right)^k x_n\\right] \\\\\n",
    "&= c_1 \\lambda_1^k x_1, k \\rightarrow \\infty \\\\\n",
    "&= \\alpha x_1\n",
    "\\end{align}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalues\n",
      " [-3.10977223  6.10977223]\n",
      "Eigenvectors\n",
      " [[-0.58959436 -0.50629921]\n",
      " [ 0.80769951 -0.86235788]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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nb53qlGXhqDY8M2cnl2//8bS2rSev8PQX25j7bEvKFfN0YoYqr4uMjGTQoEFcuHCBuLi45OnBwTLVeuHChQHYvHkzr732GgANGzbEz88PgO3bt3P48GHatWsHQFxcHG3atKFYsWJ4enrypz/9iccff5wnnngiQ/mMHTs2+RkWqdm8eTNLly4FoGfPnpQsWRKA9evXpzrtOYCHh0fy9ps3b87atWsByyy4CxcupHPnzixYsICXXnqJ27dvs3XrVgYOHJi8zdjYWAB+/vnn5DmyXF1dKV68ONeuXbsvv8DAQFxdXSlXrhwdO3Zk165dFCtWjJYtW9p9vs7miCOOXYCviFQXEQ8sxWFFykYiUhzoCCy3iRUVEe97r4HuwEEH5KSARpWKs+TFdlRPdazHVo7rWA+VBa+88govv/wyBw4c4Msvv7SbKt12uu+05sMzxtCtW7fkaxKHDx9m5syZuLm5sXPnTvr378+yZcvo2bOnQ/JNL48RI0Yk53H06FEmTJgAgLu7e/I05rbTp/fu3ZvVq1dz9epVQkND6dKlC0lJSZQoUcLuOkt4eHiW8wPnTZ+eliwfcRhjEkTkZeAnwBWYZYw5JCKjrcu/sDbtC6wxxtyx6V4OWGr9h3ED5hljfsxqTuoPVUoXYdHoNjw3dzdhv11Pjp+7fpf+07by1YgWtKye+gNkVC6TyWsQ2e3GjRtUrFgRgLlz56bZrn379nz77bd07tyZw4cPc+DAAQBat27NmDFjOHHiBLVq1SI6OprIyEgqVKhAdHQ0vXr1onXr1tSqVQsAb29vbt16+P/s3Mvjr3/9K2vWrEn+H39a056nN3W8l5cXLVu25LXXXuOJJ57A1dWVYsWKUb16db777jsGDhyIMYb9+/fTuHFjAgICmDZtGq+//jqJiYncuXPnvp+nQ4cOfPnll4wYMYKrV6+yadMmJk6cyJEjR9LMw1kcMo7DGLPKGFPbGFPTGPOeNfaFTdHAGDPHGDM4Rb9TxpjG1q8G9/oqxyrtVYj5z7ema72ydvGbMQkMnbmD1Qd0rIdKX3R0NJUqVUr++uSTT5gwYQIDBw7k0UcfTfMJewAvvfQSUVFR+Pn58eGHH+Ln50fx4sUpU6YMc+bMITAwED8/P1q3bs2RI0e4desWTzzxBH5+fnTs2JFPP/0UgMGDBzNx4kSaNm3KyZMn79uO7TWOJk2aEBERYbf8X//6F2vWrKFZs2asXr2a8uXL4+3tbTftuZ+fH926dUu+tpCeQYMGERwczKBBg5JjISEhzJw5k8aNG9OgQQOWL7ecYPnss8/YsGEDjRo1onnz5hw6dIjSpUvTrl07GjZsyBtvvEHfvn3x8/OjcePGdOnShY8++ijNpyQ6m06rXoAkJCbxz+UHmb/zN7u4CEx4sgEj2lZzTmIqXXl9WvXExETi4+Px9PTk5MmTBAQEcOzYMTw8PHI0j9jYWFxdXXFzc2Pbtm28+OKL6T6rPK/LzmnVdXbcAsTN1YX3+zaifPHCfLL2WHLcGPjXikOcv3GXv/aoq8/1UA4VHR1N586diY+PxxjDtGnTcrxoAJw9e5ann36apKQkPDw8mDFjRo7nkF9o4ShgRIRXA3x5pJgnf1uaYqzHL6e4eCOGjwY0xsNNpzFTjuHt7U1uOEPg6+vL3r17nZ1GvqB/HQqop1tU5qsR/hR2tx/rsSzsPM/O2cUtHeuhlEqDFo4CrHOdsiwY1ZrSRe1PG2w+cZmnv9zOxZv6XA+l1P20cBRwjSuXYMlLbalWuohdPPzCTfpN3cqJSzrWQyllTwuHomrpoix+sS2NK9s/18My1mMbuyOuptFTKVUQaeFQwL2xHq3oUtd+rMeNu/EEfbWDHw/+7qTMVG6xdOlSRMSpA9Leeust1q1bl+X1pJyZ9vz58wwYMCDL6y0otHCoZEU83Jg+rDmDW1S2i8cmJPFiSChfb4twSl4qd5g/fz7t27dnwYIFDlnfw0y5/s4779C1a9csbztl4ahQoQKLFi3K8noLCi0cyo6bqwv/6deI17v62sWNgbeWH+LDH4+kO6eOyp9u377Nli1bmDlzZnLh2LhxIx06dKBv377Ur1+f0aNHk5SUBFim5Pi///s/mjVrRkBAAPdmtO7UqRPjx4+nY8eOfPbZZ5w5c4aAgAD8/PwICAhInrG2T58+yZMCfvnllwQFBQEwcuTI5D/w1apVY/z48bRp0wZ/f3/27NlDjx49qFmzJl988UVy3gEBATRr1oxGjRolj+QeN25c8pTmb7zxBhERETRs2BCAmJgYnnnmGRo1akTTpk3ZsGEDAHPmzKFfv3707NkTX19f3nzzzWz/3HMrHceh7iMivN61NuWLezJ+6UG7sR7TNp7k4o0YPujvp2M9nODDnR9y5KpjTxXVLVWXv7b8a7pt7k02WLt2bUqVKsWePXsAy3Tfhw8fpmrVqvTs2ZMlS5YwYMAA7ty5Q7NmzZg0aRLvvPMOb7/9Nv/73/8Ay//2701J/uSTTzJ8+HBGjBjBrFmzePXVV1m2bBnTp0+nXbt2VK9enUmTJrF9+/ZU86pcuTLbtm1j7NixjBw5ki1bthATE0ODBg0YPXo0np6eLF26lGLFinH58mVat25N7969+eCDDzh48GDyyHHb6Uk+//xzAA4cOMCRI0fo3r07x45ZBsyGhYWxd+9eChUqRJ06dXjllVeoXLnyfXnld/qbr9I0qEUVZgxvft9YjyV7z/Hc3F3cjnXc091U7jZ//nwGD7ZMNTd48GDmz7c8HaFly5bUqFEDV1dXAgMD2bx5MwAuLi7JczgNHTo0OQ7Yze20bds2hgwZAsCwYcOS25UrV4533nmHzp07M2nSJEqVSn0izt69ewPQqFEjWrVqhbe3N2XKlMHT05Pr169jjGH8+PH4+fnRtWtXzp07x8WLF9P9WTdv3sywYcMAqFu3LlWrVk0uHAEBARQvXhxPT0/q16/PmTNnMvEp5h96xKHS1aVuOeaPas2zc3Zx9c4fz/X49fhlBn25jdkjW1BWn+uRYx50ZJAdrly5ws8//8zBgwcRERITExERevXqlTzl+D0p36cWT2+KcNt2Bw4coHTp0pw/n9bjfaBQoUKApVDde33vfUJCAiEhIURFRREaGoq7uzvVqlWzm/49NemdirXdhu006wWNHnGoB2pSuQRLXmxL1RRjPQ6dv0m/aVs5GXXbSZmpnLBo0SKGDx/OmTNniIiI4LfffqN69eps3ryZnTt3cvr0aZKSkli4cCHt27cHICkpKflaxLx585LjKbVt2zb5mklISEhyu507d7J69Wr27t3Lxx9/zOnTpx8q9xs3blC2bFnc3d3ZsGFD8hFCelO0d+jQIfkJgMeOHePs2bPUqVPnobafX2nhUBlSzccy1sOvkv1zryOvWZ7rEXrmWho9VV43f/58+vbtaxfr378/8+bNo02bNowbN46GDRtSvXr15HZFixbl0KFDNG/enJ9//pm33nor1XVPnjyZ2bNn4+fnxzfffMNnn31GbGwszz//PLNmzaJChQpMmjSJZ5999qFuyggKCmL37t34+/sTEhJC3bp1Ae6b0tzWSy+9RGJiIo0aNWLQoEHMmTPH7khD6bTqKpPuxCbw8rw9bDhq/9z3Qm4uTA5sSo8GufP5AXlZbp1WfePGjXz88cesXLnyvmVeXl7cvq1Hos6UndOq6xGHypSihdyYMdyfp/0r2cVjE5J4MTiUb7YXzIuFShUkWjhUprm5uvBhfz9eDbAf65Fk4J/LDjLxJx3rURB06tQp1aMNQI828jktHOqhiAh/7lab//RrRMrnPn2+4SR/+W4/8YlJzkkuH9JCrDIju/cXhxQOEekpIkdF5ISIjEtleScRuSEiYdavtzLaV+VugS2rMGO4P57u9rvS4j2RPDd3t471cABPT0+uXLmixUNliDGGK1eu4OmZfbfJZ/niuIi4AseAbkAksAsINMYctmnTCfiLMeaJzPZNTV64OB4VHYVPYZ8072vPb/aevcZzc3fbjfUAaFixGLNGtqCst471eFjx8fFERkY+cPyBUvd4enpSqVIl3N3d7eK56ZnjLYETxphTACKyAOgDpPvH3wF9c634xHieXvk0ZYuUZWi9ofSo1gMP15x/xnJOalqlJItfbMuIWTs5ezU6OX7wnOW5Hl8/25IaZbycmGHe5e7uTvXq1Z2dhlLJHHGqqiLwm837SGsspTYisk9EVotIg0z2RURGichuEdl9b8K03MpgeLHxi8QkxDB+83i6L+rOtLBpXL572dmpZavq1rEejSqmPtZjz1kd66FUfuCIwpHauZiU57/2AFWNMY2BKcCyTPS1BI2ZbozxN8b4lylT5qGTzQkerh48XedplvVZxpddv6R+6fpM3TeV7ou6M/7X8Ry6csjZKWabMt6FWDCqNZ3q2P8bXYuOZ8iM7aw9nP48QUqp3M8RhSMSsJ0eshJgN7mMMeamMea29fUqwF1EfDLSNy8TEdpWbMvUrlP5/qnvGVh7IOvPrmfwysEMXz2cnyJ+IiEp/108vjfWY2Bz+7EeMfFJvPDNbkJ26FgPpfIyR1wcd8NygTsAOIflAvcQY8whmzaPABeNMUZEWgKLgKqA64P6piYvXBxPy624Wyw7sYx54fOIvB1JuSLlGFx3MAN8B1DCs8SDV5CHGGP4dO0xJv984r5lr3apxdhutQvMzQNK5QaOujjukClHRKQX8F8shWCWMeY9ERkNYIz5QkReBl4EEoC7wJ+NMVvT6vug7eXlwnFPYlIimyI3ERIewo7fd+Dp6snjNR4nqF4QviV9H7yCPCRkxxn+uewgSSl2tYHNK/F+v0a4u+pwIqVyQq4qHDktPxQOW8euHWNe+DxWnlpJbGIsrcq3Ymi9oXSo1AEXyR9/VNcevsgr8/cQE28/KLBj7TJMDWpG0UI6w79S2U0LRz4qHPdcj7nOouOLWHBkARejL1LZuzJD6g7hqVpP4eWR929l3XP2Gs/N2cW16Hi7eKOKxZk1sgVlvHUGUqWykxaOfFg47olPimf92fWEHA4hLCqMIm5FeKrWUwypN4Sqxao6O70sORV1mxGzd/Lb1bt28SqlijD32ZZU90n7IT9KqazRwpGPC4etQ5cPERIewuqI1SQmJfJopUcJqhdEm/Jt8uyF5Uu3Ynh2zi4OnrtpFy9V1IOZI/xpWqWkkzJTKn/TwlFACsc9l+9e5tuj37Lw6EKuxlylRvEaBNUL4okaT1DEvciDV5DL3I5N4KWQPWw6Zj+Y09Pdhc+HNCOgXjknZaZU/qWFo4AVjnviEuP4MeJHgg8HE341nGIexejv25/BdQdTwauCs9PLlPjEJMYtPsDiPZF2cReB9/o2IrBlFSdlplT+pIWjgBaOe4wxhEWFEXw4mPVn12MwBFQJIKheEM3KNsszp7GMMUxac4z/bUhlrEeAL2O7+uaZn0Wp3E4LRwEvHLYu3L7AgqMLWHRsETfjblKvVD2G1BvCY9Ufo5Br3rhTKXj7Gd5afv9Yj6f9K/FeXx3roZQjaOHQwnGfuwl3WXlqJfPC53Hi+glKeZZiYO2BDKoziDJFcvf8XgBrDv3OK/P3EptgP9ajc50yfB7UjCIeOtZDqazQwqGFI03GGHb8voOQwyH8EvkLri6u9KjWg6H1htLQp6Gz00tX6JlrPDd3F9dTjPVoXKk4M0e2wMcrbxxBKZUbaeHQwpEhZ2+eZf6R+Sw9sZQ78XdoXKYxQfWC6Fq1K+4u7g9egROcjLrNiFk7ibxmP9ajaukizH2mJdV0rIdSD0ULhxaOTLkdd5vlJ5czL3weZ2+dpWyRsgyuM5gBtQdQ0jP3jZu4dCuGZ2bv4tB5+7EepYt6MHNkC5pUzl8TQiqVE7RwaOF4KEkmic3nNhN8OJhtF7ZRyLUQj9d4nCF1h1CnVB1np2fndmwCLwaH8utx+wdgFXZ35fOgpnSpq2M9lMoMLRxaOLLs5PWThISH8P3J74lJjKHFIy0IqhdEp0qdcHVxdXZ6AMQlJDFu8X6W7D1nF3d1Ed7v25BBLXSsh1IZpYVDC4fD3Ii9wZLjS5h/ZD4X7lygoldFAusG0te3L8U8ijk7PYwxTPzpKFM3nrxv2etdfXktQMd6KEr6VXQAAB10SURBVJURWji0cDhcQlICG37bQPDhYPZc2kNht8L0rtmboHpBVC9e3dnp8c22CN5acYiUu+zgFpV596mGuOlYD6XSpYVDC0e2Cr8STkh4CKtOryI+KZ52FdsxtN5Q2lZo69RnhPx48HdeW3D/WI+AumWZMqSpjvVQKh1aOLRw5Igrd6/w3bHvWHh0IZfvXqZasWoE1Quid83eTptccXfEVZ6bu5sbd1OM9ahcglkj/CmtYz2USpUWDi0cOSo+MZ6fzvxEyOEQDl45iLe7N319+xJYN5BK3pVyPJ8Tl24xYtYuzl23H+tRrbTluR5VS+tYD6VSylWFQ0R6Ap9heW74V8aYD1IsDwL+an17G3jRGLPPuiwCuAUkAgkZ+aG0cDiPMYZ9UfsICQ9h7Zm1GAydKnViaP2h+Jfzz9GL1JduxjBy9i4OX7h/rMfsZ1rgV0nHeihlK9cUDhFxBY4B3YBIYBcQaIw5bNOmLRBujLkmIo8BE4wxrazLIgB/Y8zl+1aeBi0cucPvd37n26Pf8t2x77gee53aJWsztN5QHqv+GJ5unjmSw62YeF4M3sPmE/a7TxEPVz4PakbnOmVzJA+l8oLcVDjaYCkEPazv/wZgjPlPGu1LAgeNMRWt7yPQwpGnxSTEsOr0KoLDgzl+7TglC5VkQO0BDKoziHJFs3+QXlxCEm8u2seysPN2cVcX4T/9GvG0f+Vsz0GpvMBRhcMRt8dUBH6zeR9pjaXlOWC1zXsDrBGRUBEZlVYnERklIrtFZHdUVFRazZQTeLp50s+3H4ufXMysHrNoWrYpXx34ip6Le/LmL2+yL2pftm7fw82FT55uwuiONe3iiUmGNxftZ/L64+TFa3lK5VaOuHcxtZPaqf6WikhnLIWjvU24nTHmvIiUBdaKyBFjzKb7VmjMdGA6WI44sp62cjQRocUjLWjxSAsib0VaJlc8vpTVEatp5NOIIfWG0KNqD9xdHT+5oouLMO6xupQv7smE7+3Henyy9hgXbsTw7z4NdKyHUg7giN+iSMD2XEAl4HzKRiLiB3wF9DHGXLkXN8act36/BCwFWjogJ+Vklbwr8UaLN1g3cB3jW43nVtwt/vbr3+ixuAdf7PuCK3evPHglD2FE22pMC2qGh5v9rj1/51lGB4dyNy4xW7arVEHiiGscblgujgcA57BcHB9ijDlk06YK8DMw3Biz1SZeFHAxxtyyvl4LvGOM+TG9beo1jrwnySSx9fxWgsOD2XJuCx4uHjxW/TGG1h9K3VJ1Hb69XRFX+VMqYz2aVC7BTB3roQqoXHNx3JpML+C/WG7HnWWMeU9ERgMYY74Qka+A/sAZa5cEY4y/iNTAcpQBltNm84wx7z1oe1o48rZTN04xL3weK06u4G7CXZqXa05QvSA6V+6Mm4vjRn6nNdajuk9R5j7TkiqlnTOAUSlnyVWFI6dp4cgfbsbdZOnxpcw/Mp9zt89Rvmh5AusG0s+3H8ULFXfINi7ejGHErJ0c+f2WXdzHy4PZI1vSqJJjtqNUXqCFQwtHvpGYlMjGyI2EhIew6/ddFHYrzJM1niSoXhA1StTI8vpvxsQz+ptQtp60v65SxMOVqUHN6KRjPVQBoYVDC0e+dPTqUULCQ/jh1A/EJcXRtkJbguoF0b5i+yxNrhiXkMQbi/axPMVYDzfrWI+BOtZDFQBaOLRw5GtXY66y6NgiFh5ZyKW7l6harCqBdQN5qtZTFHV/uHmokpIMH/54hC83nbpv2V+612ZM51r6XA+Vr2nh0MJRIMQnxbPuzDqCw4PZH7UfL3cvnqr1FEPqDqFysYc7Spi95TTvrDx833M9glpV4Z0+DXF10eKh8ictHFo4CpwDUQcIDg9mTcQaEk0iHSt1JKh+EK0eaZXpI4VVBy7w+sIw4lI816Nb/XJMHtyUwh6549G5SjmSFg4tHAXWpehLyZMrXo25Sq0StQiqF8TjNR6nsFvhDK9nx6krPP/1bm7GJNjFm1UpwcwRLShZ1MPRqSvlVFo4tHAUeLGJsaw+vZqQ8BCOXD1C8ULFGeA7gMF1B/NI0UcytI5jF28xctZOzt+IsYvXKGMZ61G5lI71UPmHFg4tHMrKGEPoxVDmHZnH+rPrEYSAKgEMrT+UJmWaPPA01u83Yhg5O7WxHoWY80wLGlbUsR4qf9DCoYVDpeL87fMsOLKARccXcSvuFvVL12dovaH0qNYDD9e0Tz3djInnha9D2XbKfqxHUQ9Xpg1tTofaZbI7daWynRYOLRwqHdHx0aw8tZKQ8BBO3ThFac/SDKoziIF1BuJT2CfVPrEJifzlu/18v+/+sR4f9vejf/Ocf0SuUo6khUMLh8oAYwzbzm8jODyYX8/9iruLOz2r9SSofhANSje4r31SkuGDH48wPZWxHm/0qMNLnWrqWA+VZ2nh0MKhMunMzTPMC5/HshPLiE6IpmnZpgTVCyKgSsB9kyvO2nyaf/9w/1iPYa2rMqF3Ax3rofIkLRxaONRDuhV3i2UnljEvfB6RtyMpV6Qcg+sOZoDvAEp4lkhut3L/ef68cB9xifZjPbrXL8fkwKZ4uutYD5W3aOHQwqGyKDEpkV/P/UpweDA7LuzA09WTx2s8TlC9IHxL+gKw3TrW41aKsR7Nq5bkq+H+OtZD5SlaOLRwKAc6fu04IeEhrDy1ktjEWFqVb8XQekPpUKkDxy/eYeTsnVzQsR4qj9PCoYVDZYPrMddZdHwRC44s4GL0RSp7VyawbiBtyvZkzDfhHL1oP9ajjLdlrEeDCjrWQ+V+Wji0cKhslJCUwPqz6wkJD2Hvpb0UcStCr2q9CTvcgL0n3e3aehVy44uhzWnvm/ptvkrlFlo4tHCoHHLoyiFCDoewOmI1iUmJlBQ/Is/4k3inFmC5u8rNRZg40I++TXWsh8q9HFU4Hv7JOPbJ9BSRoyJyQkTGpbJcRGSydfl+EWmW0b5KOVuD0g14/9H3WTtgLaMbj4ZCv1GkykyK1PgU9xLbQeJISDJM+nYdW755G5OU9OCVKpWHZfmIQ0RcgWNANyAS2AUEGmMO27TpBbwC9AJaAZ8ZY1plpG9q9IhDOVNcYhw/RfzEf3fO5FLcSUxiYVyuN+bL27/SJukCO3z64T96Bq5ubg9emVI5KDcdcbQEThhjThlj4oAFQJ8UbfoAXxuL7UAJESmfwb5K5Soerh48WfNJ1g1eygu1PkGiayCltjO6ihtjy/pQ9dpywj7tS2zsXWenqlS2cEThqAj8ZvM+0hrLSJuM9AVAREaJyG4R2R0VFZXlpJXKKhHh5dad2OQRzU+/nWPkjZuEe3hQLCkJcXHF3U3HeKj8yRGFI7W5F1Ke/0qrTUb6WoLGTDfG+Btj/MuU0ZlKVS6QlATLX6bk+V94JDGRsddusCryPKc8GtNwzHxcXHVkucqfHHESNhKwffhzJeB8Btt4ZKCvUrnTun/B/gV2oXOFfKny0lI8PDP+JEKl8hpHHHHsAnxFpLqIeACDgRUp2qwAhlvvrmoN3DDGXMhgX6Vyn63/g62T7WMlq1H55R8oVryUc3JSKodk+YjDGJMgIi8DPwGuwCxjzCERGW1d/gWwCssdVSeAaOCZ9PpmNSelstX+b2HN3+1jRcvA0CXgXc45OSmVg3QAoFKZcWI9zHsakmwmPfTwgpEroUJT5+WlVAbkpttxlSoYzoXCwmH2RcPFHQYFa9FQBYoWDqUy4spJCBkI8Xfs432/gJqdnZOTUk6ihUOpB7n1O3zTF6Kv2Md7fgCNBjgnJ6WcSAuHUumJuQHBA+D6Gft4u9eh9YvOyUkpJ9PCoVRa4mNgQRBcPGAfbzwEuk5wRkZK5QpaOJRKTVIiLB0FEb/ax327Q+/JIKlNeqBUwaCFQ6mUjIHVf4XDy+3jFf1h4BxwdU+1m1IFhRYOpVLa9DHsmmEf86kNQd+BR1Hn5KRULqKFQylboXNhw7v2Me/yllHhRXQqEaVAC4dSfziyCla+bh/zLG4pGiUqp95HqQJIC4dSAGe3w6JnwNg89tW1EAQugHL1nZeXUrmQFg6lLoVb5p9KiPkjJi4wYBZUbeu8vJTKpbRwqILt+m/wTT/LQD9bT3wK9Z5wTk5K5XJaOFTBFX0VgvvDrRTPDus0HpqPdEpKSuUFWjhUwRQXbTk9dfmofdz/Oej4pnNyUiqP0MKhCp7EBMuF8Mhd9vF6vaHXRB0VrtQDaOFQBYsx8P1rcOxH+3jV9tBvBri4OicvpfIQLRyqYFn/DoQF28fKNYTAeeDu6ZyclMpjslQ4RKSUiKwVkePW7yVTaVNZRDaISLiIHBKR12yWTRCRcyISZv3qlZV8lErX9i9g8yf2sRJVIGiRZaCfUipDsnrEMQ5Yb4zxBdZb36eUAPyfMaYe0BoYIyK2I6o+NcY0sX6tymI+SqXu4GL4McXuWaQ0DF0Kxco7Jyel8qisFo4+wFzr67nAUykbGGMuGGP2WF/fAsKBilncrlIZd2ojLHkBMH/E3IvAkO/Ap5azslIqz8pq4ShnjLkAlgIBlE2vsYhUA5oCO2zCL4vIfhGZldqpLpu+o0Rkt4jsjoqKymLaqsA4HwYLhkJS/B8xFzd4+huo1Nx5eSmVhz2wcIjIOhE5mMpXn8xsSES8gMXA68aYm9bwNKAm0AS4AExKq78xZroxxt8Y41+mTJnMbFoVVFdPQcgAiLtlH+8zFXy7OicnpfIBtwc1MMak+RsmIhdFpLwx5oKIlAcupdHOHUvRCDHGLLFZ90WbNjOAlZlJXqk03b5kmUrkToqj0+7vQuNBzslJqXwiq6eqVgAjrK9HAMtTNhARAWYC4caYT1Iss70q2Rc4mMV8lILYW5YjjWun7eNtXoa2rzgnJ6XykawWjg+AbiJyHOhmfY+IVBCRe3dItQOGAV1Sue32IxE5ICL7gc7A2Czmowq6hFhYEAQX9tnH/QZBt387Jyel8pkHnqpKjzHmChCQSvw80Mv6ejOQ6hwOxphhWdm+UnaSkmDpaDj9i328ZgD0+RxcdLyrUo6gv0kqfzAGfhoPh5bYxys0g6e/Bld35+SlVD6khUPlD1v+Czum2cdK1YSg76CQl3NyUiqf0sKh8r69IbBugn3MqxwMWwJFfZySklL5mRYOlbcd+wlWpLhTqlAxGLoYSlZzSkpK5XdaOFTe9dtO+HYEmMQ/Yq4eMHgePNLIeXkplc9p4VB5U9RRyxP8Eu7aBAX6fwXVH3VaWkoVBFo4VN5z45xlVPjda/bxxz+G+pmaCUcp9RC0cKi85e41CO4PNyPt4x3ehBZ/ck5OShUwWjhU3hF/F+YHQlS4fbzZCOg83jk5KVUAaeFQeUNiAix6Ds5us4/XeRwe/wQk1ckJlFLZQAuHyv2MgR/+DEd/sI9XaQMDZoJrlmbOUUplkhYOlftteB/2zLWPla0PgfPBvbBzclKqANPCoXK3nTNg00f2sWKVIGgRFE7zgZFKqWykhUPlXoeWwao37GOFS1qmEimuj61Xylm0cKjc6fSvsOR5wPwRcysMQ76DMnWclpZSSguHyo1+PwALhkBi3B8xcYWn50LlFs7LSykFaOFQuc21CMsAv9ib9vHeU6B2D6ekpJSyp4VD5R53LlumErl90T7edQI0DXJGRkqpVGSpcIhIKRFZKyLHrd9Tvc1FRCKszxYPE5Hdme2vCoDY2xAyEK6etI+3ehHave6cnJRSqcrqEcc4YL0xxhdYb32fls7GmCbGGP+H7K/yq4Q4+HYYnN9jH2/YH3q8r6PClcplslo4+gD3RmbNBZ7K4f4qr0tKguVj4OTP9vEaneCpaeCiZ1OVym2y+ltZzhhzAcD6vWwa7QywRkRCRWTUQ/RHREaJyG4R2R0VFZXFtFWusfafcOBb+1j5xjAoGNwKOScnpVS6HjjJj4isAx5JZdHfM7GddsaY8yJSFlgrIkeMMZsy0R9jzHRgOoC/v795QHOVF2yZDNv+Zx8rWd0yKryQt3NyUko90AMLhzGma1rLROSiiJQ3xlwQkfLApTTWcd76/ZKILAVaApuADPVX+dC+BZajDVtFy1hGhXuleeCplMoFsnqqagUwwvp6BLA8ZQMRKSoi3vdeA92Bgxntr/Kh4+ss1zVseXjD0MVQqoZzclJKZVhWC8cHQDcROQ50s75HRCqIyCprm3LAZhHZB+wEfjDG/Jhef5WPRYZa7qBKSvgj5uIOg0Ms1zaUUrlelh5kYIy5AgSkEj8P9LK+PgWk+hchrf4qn7p8AuYNhPhom6BAvy+hRkenpaWUyhy911HljJsX4Ju+EH3FPv7Yh5bxGkqpPEMLh8p+MTcgZADcOGsfb/9naPWCc3JSSj00LRwqe8XHwPwhcPGgfbzpUAh4yzk5KaWyRAuHyj5JibDkT3Bms328dk944jOdSkSpPEoLh8oexsCqv0D49/bxSi1hwGxwzdJ9GUopJ9LCobLHLx/B7ln2MZ86MGQheBRxTk5KKYfQwqEcb/ds2Pi+fcy7gmVUeJFSzslJKeUwWjiUY4WvhB/+bB/zLG4pGsUrOScnpZRDaeFQjnNmKyx6FkzSHzE3TxjyLZSt57y8lFIOpYVDOcbFQzB/MCTG/hETF8uF8CqtnZeXUsrhtHCorLt+FoL7Wwb62Xriv1C3l3NyUkplGy0cKmvuXIFv+sGtC/bxLv+A5iNS76OUytO0cKiHF3cH5j0NV47bx1s8D4/+xTk5KaWynRYO9XAS4+G7kXBut328fh/LxIU6KlypfEsLh8o8Y2DFq3B8jX282qPQbwa4uDonL6VUjtDCoTJv3QTYN88+Vq6R5WFMboWckpJSKudo4VCZs20qbPmvfaxEVRi6yDLQTymV72nhUBl3YBH89Df7WBEfGLYUvB9xTk5KqRyXpcIhIqVEZK2IHLd+L5lKmzoiEmbzdVNEXrcumyAi52yW6U3/udXJn2HpaPuYe1EI+g5K13ROTkopp8jqEcc4YL0xxhdYb31vxxhz1BjTxBjTBGgORANLbZp8em+5MWZVFvNR2eH8Xlg4DJLi/4i5uMGgb6BiM+flpZRyiqwWjj7AXOvrucBTD2gfAJw0xpzJ4nZVTrlyEoIHQNxt+/hT06BWgHNyUko5VVYLRzljzAUA6/eyD2g/GJifIvayiOwXkVmpnepSTnTrIgT3g+jL9vEe74Pf087JSSnldA8sHCKyTkQOpvLVJzMbEhEPoDfwnU14GlATaAJcACal03+UiOwWkd1RUVGZ2bR6GDE3IaQ/XIuwj7d9FdqMcUpKSqnc4YHP7zTGdE1rmYhcFJHyxpgLIlIeuJTOqh4D9hhjLtqsO/m1iMwAVqaTx3RgOoC/v795UN4qCxJiYWEQ/H7APt44ELq+7ZyclFK5RlZPVa0A7s1kNwJYnk7bQFKcprIWm3v6AgezmI/KqqQkWPoCnN5kH6/VDXpPARe9g1upgi6rfwU+ALqJyHGgm/U9IlJBRJLvkBKRItblS1L0/0hEDojIfqAzMDaL+aisMAZ+/CscWmofr9gcnp4Lru7OyUsplas88FRVeowxV7DcKZUyfh7oZfM+GiidSrthWdm+crBfJ8HO6fax0r4w5DvwKOqcnJRSuY6ed1AWe76Bn/9tH/N6xPKs8KL31XylVAGmhUPB0dXw/Wv2sULFYehiKFHFOTkppXItLRwF3dkdludqmMQ/Yq6FIHA+PNLQaWkppXIvLRwF2aUjlif4JcT8ERMX6P8VVGvnvLyUUrmaFo6C6kakZVR4zHX7+OOToH5v5+SklMoTtHAURNFXIbg/3DxnH+84DvyfdU5OSqk8QwtHQRN/F+YHQtQR+3jzZ6DTfZMbK6XUfbRwFDQublCyqn2s7hOWU1QizslJKZWnaOEoaFzd4akvoO0rlvdV20H/meDi6ty8lFJ5RpZGjqs8ysUFur8LZepajjbcPZ2dkVIqD9HCUZA1HersDJRSeZCeqlJKKZUpWjiUUkplihYOpZRSmaKFQymlVKZo4VBKKZUpWjiUUkplihYOpZRSmaKFQymlVKZkqXCIyEAROSQiSSLin067niJyVEROiMg4m3gpEVkrIset30tmJR+llFLZL6tHHAeBfsCmtBqIiCvwOfAYUB8IFJH61sXjgPXGGF9gvfW9UkqpXCxLhcMYE26MOfqAZi2BE8aYU8aYOGAB0Me6rA8w1/p6LvBUVvJRSimV/XJirqqKwG827yOBVtbX5YwxFwCMMRdEpGxaKxGRUcAo69tYETmYHck6mA9w2dlJZIDm6Th5IUfQPB0tr+RZxxEreWDhEJF1wCOpLPq7MWZ5BraR2kMeTAb62XcwZjow3ZrTbmNMmtdUcgvN07HyQp55IUfQPB0tL+XpiPU8sHAYY7pmcRuRQGWb95WA89bXF0WkvPVoozxwKYvbUkoplc1y4nbcXYCviFQXEQ9gMLDCumwFMML6egSQkSMYpZRSTpTV23H7ikgk0Ab4QUR+ssYriMgqAGNMAvAy8BMQDnxrjDlkXcUHQDcROQ50s77PiOlZyTsHaZ6OlRfyzAs5gubpaAUqTzEm05cblFJKFWA6clwppVSmaOFQSimVKbm2cOSV6Uwysh0RqSMiYTZfN0XkdeuyCSJyzmZZL2fkaG0XISIHrHnszmz/nMhTRCqLyAYRCbfuH6/ZLMvWzzKtfc1muYjIZOvy/SLSLKN9czjPIGt++0Vkq4g0tlmW6j7ghBw7icgNm3/LtzLaN4fzfMMmx4MikigipazLcuSztG5rlohckjTGtzl83zTG5MovoB6WwSobAf802rgCJ4EagAewD6hvXfYRMM76ehzwYTblmantWHP+HahqfT8B+Es2f5YZyhGIAHyy+jNmZ55AeaCZ9bU3cMzm3zzbPsv09jWbNr2A1VjGLrUGdmS0bw7n2RYoaX392L0809sHnJBjJ2Dlw/TNyTxTtH8S+DknP0ubbXUAmgEH01ju0H0z1x5xmLwznUlmtxMAnDTGnMmmfFKT1c8i13yWxpgLxpg91te3sNypVzGb8rGV3r52Tx/ga2OxHSghlvFJGembY3kaY7YaY65Z327HMrYqJ2Xl88hVn2UKgcD8bMolXcaYTcDVdJo4dN/MtYUjg1KbzuTeHxG76UyANKczyaLMbmcw9+9cL1sPH2dl02mgjOZogDUiEiqWKV4y2z+n8gRARKoBTYEdNuHs+izT29ce1CYjfR0ls9t6Dsv/RO9Jax9wpIzm2EZE9onIahFpkMm+jpDhbYlIEaAnsNgmnBOfZUY5dN/Mibmq0iS5ZDqTB24knTwzuR4PoDfwN5vwNODfWPL+NzAJeNZJObYzxpwXy5xha0XkiPV/Mg7jwM/SC8sv6evGmJvWsEM+y7Q2mUos5b6WVpsc2U8fkMP9DUU6Yykc7W3C2b4PZDDHPVhO5962XqtaBvhmsK+jZGZbTwJbjDG2/+vPic8yoxy6bzq1cJg8Mp1JenmKSGa28xiwxxhz0Wbdya9FZAaw0lk5GmPOW79fEpGlWA5jN5HLPksRccdSNEKMMUts1u2QzzIN6e1rD2rjkYG+jpKRPBERP+Ar4DFjzJV78XT2gRzN0eY/AxhjVonIVBHxyUjfnMzTxn1nEnLos8woh+6bef1UVW6YziQz27nvHKj1D+Q9fbE848TRHpijiBQVEe97r4HuNrnkms9SRASYCYQbYz5JsSw7P8v09rV7VgDDrXewtAZuWE+5ZaRvjuUpIlWAJcAwY8wxm3h6+0BO5/iI9d8aEWmJ5W/VlYz0zck8rfkVBzpis7/m4GeZUY7dN3Piiv/DfGH5xY8EYoGLwE/WeAVglU27XljurDmJ5RTXvXhpLA+HOm79Xiqb8kx1O6nkWQTLjl88Rf9vgAPAfus/WHln5Ijlrop91q9DufWzxHJaxVg/rzDrV6+c+CxT29eA0cBo62vB8tCyk9Y8/NPrm42/Ow/K8yvgms3nt/tB+4ATcnzZmsM+LBfw2+bGz9L6fiSwIEW/HPssrdubD1wA4rH83XwuO/dNnXJEKaVUpuT1U1VKKaVymBYOpZRSmaKFQymlVKZo4VBKKZUpWjiUUkplihYOpZRSmaKFQymlVKb8P+IR5gBNtLUyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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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",
    "\n",
    "A = np.array([[1,3],[7,2]])\n",
    "b = np.array([-.75,0.5]) #starting choice of this vector is totally arbitrary\n",
    "\n",
    "eigvals, eigvecs = np.linalg.eig(A)\n",
    "\n",
    "print(\"Eigenvalues\\n\", eigvals)\n",
    "print(\"Eigenvectors\\n\", eigvecs)\n",
    "\n",
    "largest_eigval_ind = np.argmax(np.abs(eigvals))\n",
    "largest_eigvec = eigvecs[:,largest_eigval_ind]\n",
    "\n",
    "smallest_eigval_ind = np.argmin(np.abs(eigvals))\n",
    "smallest_eigvec = eigvecs[:,smallest_eigval_ind]\n",
    "\n",
    "plt.figure()\n",
    "plt.xlim(-1,1)\n",
    "plt.ylim(-1,1)\n",
    "\n",
    "for i in range(0,10):\n",
    "    plt.clf()\n",
    "    plt.plot([0,smallest_eigvec[0]], [0, smallest_eigvec[1]], linewidth=4)\n",
    "    plt.plot([0,largest_eigvec[0]], [0, largest_eigvec[1]], linewidth=4)\n",
    "    plt.plot([0,b[0]], [0, b[1]])\n",
    "    plt.legend(['Smallest Eigenvector','Largest Eigenvector', 'Approximation'])\n",
    "    plt.xlim(-1,1)\n",
    "    plt.ylim(-1,1)\n",
    "\n",
    "    b = A@b\n",
    "    b = b/np.linalg.norm(b)\n",
    "    \n",
    "    plt.pause(1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Homework Problem - The Trillion Dollar Eigenvector\n",
    "by Curtis Johnson"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let the diagram below represent the entire internet where each circle represents a webpage. Outgoing arrows represent links to external websites and incoming arrows represent websites that link to your website (e.g. an example to illustrate).\n",
    "\n",
    "![](4SiteInternet.png)\n",
    "\n",
    "Each website's relative importance can be written as a function of how many websites link to it (e.g. if website 1 is linked to by website 2 and website 3, the relative importance of website 1 ($x_1$) can be written as $x_1 = x_2 + x_3$). \n",
    "\n",
    "You want to rank all of these websites by their relative importance in order to place ads where they are most likely to be seen (i.e. place ads in the most important websites). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a) Find the probability matrix $P$ (also known as a [left stochastic matrix](https://en.wikipedia.org/wiki/Stochastic_matrix)) that describes the probability from moving from each webpage to any other webpage. NOTE: Because this matrix contains probabilities, make sure that each column sum is equal to 1. Row sums do not need to be 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b) Show that $\\lambda=1$ is an eigenvalue of any 4x4 left stochastic matrix $A$ of the same form as $P$ (i.e. column sum is 1)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "c) Find the probability vector $\\boldsymbol{x} = [x_1, x_2, x_3, x_4]^T$ that ranks each of the webpages in the internet by their relative importance. HINT: This is an eigenvector problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cool facts: This algorithm was first applied like this by Larry Page, one of the founders of Google. It formed the foundation for the PageRank system that set Google apart from it's competitors. As of writing, Google's market value is about \\$1,000,000,000,000. \n",
    "\n",
    "This problem can also be solved iteratively using the Power Iteration method explained above. This helps when the P matrix is prohibitively large (as it is for the actual internet). Another helpful fact is that the P matrix is sparse because webpages on the internet are sparsely linked to each other. There are specialized algorithms that deal with sparse matrices very effeiciently, which helps with computation time."
   ]
  }
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