Eigen_stuff.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python and Linear Algebra\n",
    "\n",
    "Insofar as data science is grounded mathematics, we have seen probability at work.  Next we should talk about linear algebra.\n",
    "\n",
    "Think of the primary colors used in most computer graphics. If you have Red, Green and Blue as primary \"directions\" (we could call them vectors) then you're able to describe any color by means of a recipe: this much red, blue and green.\n",
    "\n",
    "Yet other coordinate systems exist for storing pixel data.  Python's ```colorsys``` module relates a few of them.  We also have Python Imaging Lab or pillow.\n",
    "\n",
    "We should get into image processing right away, because this domain is replete with dimensionality reduction, from JPEG to MPEG to what convolutional networks do for a living."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=363x363 at 0x112D68A50>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from PIL import Image\n",
    "\n",
    "%matplotlib inline\n",
    "pil_im = Image.open('./images/eigen_spaces.jpg', 'r')\n",
    "pil_im"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(363, 363, 3)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "matrix = np.asarray(pil_im)\n",
    "matrix.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets look at a patch right in the center of the cartoon. By changing the last column number, you'll get R, G and B layers, of a 10x10 patch of pixels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[200, 202, 201, 191, 187, 186, 185, 185, 186, 187],\n",
       "       [196, 199, 197, 187, 188, 186, 185, 185, 185, 186],\n",
       "       [196, 199, 200, 191, 190, 188, 187, 186, 187, 188],\n",
       "       [202, 206, 208, 200, 191, 189, 188, 189, 190, 192],\n",
       "       [206, 212, 213, 209, 198, 199, 198, 194, 194, 197],\n",
       "       [210, 216, 215, 211, 208, 212, 212, 205, 199, 197],\n",
       "       [217, 220, 217, 210, 212, 218, 219, 212, 201, 196],\n",
       "       [225, 224, 218, 211, 210, 215, 217, 212, 204, 201],\n",
       "       [231, 229, 223, 217, 216, 216, 215, 212, 208, 207],\n",
       "       [234, 232, 229, 227, 225, 220, 216, 214, 211, 208]], dtype=uint8)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix[100:110,100:110,0] # R, G, B planes form 3rd dimension"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[211, 213, 212, 202, 198, 197, 196, 196, 197, 198],\n",
       "       [207, 210, 208, 198, 199, 197, 196, 196, 196, 197],\n",
       "       [207, 210, 211, 202, 201, 199, 198, 197, 198, 199],\n",
       "       [213, 217, 219, 211, 202, 200, 199, 200, 201, 203],\n",
       "       [217, 223, 224, 220, 209, 210, 209, 205, 205, 208],\n",
       "       [221, 227, 226, 222, 219, 223, 223, 216, 210, 208],\n",
       "       [228, 231, 228, 221, 223, 229, 230, 223, 212, 207],\n",
       "       [236, 235, 229, 222, 221, 226, 228, 223, 215, 212],\n",
       "       [242, 240, 234, 228, 227, 227, 226, 223, 219, 218],\n",
       "       [245, 243, 240, 238, 236, 231, 227, 225, 222, 219]], dtype=uint8)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix[100:110,100:110,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Image processing ahead!\n",
    "\n",
    "Lets average the R, G, B values to get just one numeric value for each pixel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=L size=363x363 at 0x113934ED0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "av_matrix = matrix.mean(axis=2)\n",
    "new_image = Image.fromarray(av_matrix)\n",
    "new_image = new_image.convert(\"L\")\n",
    "new_image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=L size=363x363 at 0x113934E10>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "std_matrix = matrix.std(axis=2)\n",
    "new_image = Image.fromarray(std_matrix)\n",
    "new_image.convert(\"L\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When you're confronted with a dataset and hope to study it for predictive power, you're looking for a minimal set of primary features, a basis, that will prove maximally determinative and let you address every data point in the corpus, without overfitting.  \n",
    "\n",
    "What features matter most?  Linear algebra has some techniques for discovering some answers.\n",
    "\n",
    "Imagine a postal service where you had no idea in what order the addressing elements were scrambled. The differences of greatest geographical distance, such as continent or nation, might come at the top, or somewhere in the middle. \n",
    "\n",
    "With linear algebra, we discover what features that we have (are able to measure), vary the most, span the greatest distance.  Then we find the next most varying coordinate (address component), such as city or zip, then the street, and so on.\n",
    "\n",
    "Perhaps we only needed to be in the ballpark.  Actual street address or room number, or table leg is overkill, in terms of zooming in on some location.  The extra precision is of no consequence, given our marketing strategy.  So linear algebra has helped us dismiss the irrelevant.\n",
    "\n",
    "Once we know how to order the dimensions, we know which ones we might safely dispense with. Such is one purpose of singular value decomposition (SVD), such as when used in principal components analysis, to project from higher to lower dimensional spaces.  That's what homeomorphism is all about (versus isomorphism, which doesn't allow for lossy compression).\n",
    "\n",
    "If you didn't already know about R, G, B you might have a hard time working backwards (reverse engineering) starting from the millions of colors, to get just those three, or four in the case of C, Y, M, K.  \n",
    "\n",
    "Given any data set, you'll be looking for the principal components, or factors, that seem to explain (predict) most of the data (future outcomes).\n",
    "\n",
    "This idea relates to eigenvectors and eigenvalues, which stem from methods for finding the axes of rotation in a dataset, such that instead of rotating ourselves (and getting dizzy) we see more of the simpler linear relationships. \n",
    "\n",
    "![Eigen Spaces](./images/eigen_spaces.jpg)\n",
    "\n",
    "We've like discovered a control panel or \"more with less\" API.\n",
    "\n",
    "If by turning this dial, I make the lights dim, and by flipping this switch, I make something else happen, then I feel I've got my mind wrapped around a working model at last.  \n",
    "\n",
    "I'm in the driver's seat, at least in terms of understanding the most with the least.  If I'm able to generate what appear to be believable vistas from my model (using a model to simulate new data), such as we find in the real world -- like with fractals -- then maybe I'm onto something, in terms of finally having a handle on what we're dealing with here.\n",
    "\n",
    "Eigenvectors are the directions in which a transformation may be regarded as purely linear, and the corresponding eigenvalues have to do with by how much (designated with $\\lambda$), by what scale or weight."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we dive in too deeply, lets add T for Transpose to our vocabulary. Given a rectangle of numbers (matrix), turning rows into columns and columns into rows, is known as transposing the matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "rng = np.random.default_rng(42) # one ring to rule them all..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2, 3, 4],\n",
       "       [5, 6, 7, 8, 9]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array(range(10)).reshape(2,5) # two rows, five columns\n",
    "A  # show me!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A lot of the time, you'll have a lying down vector you'll want to stand up and \"stand tall\" (turn a row vector into a column vector).  Note that when numpy arrays are born, of lower life forms, such as Python lists and ranges, they have only one dimension, not even rows and columns yet.  They're not really in condition to play matrix multiplication games at all, until \"hardened\" with at least one row and one column."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![transpose](https://i.imgur.com/16Afrj1.gif)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 5],\n",
       "       [1, 6],\n",
       "       [2, 7],\n",
       "       [3, 8],\n",
       "       [4, 9]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = A.T\n",
    "B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limp_spaghetti = np.array(range(10))\n",
    "limp_spaghetti.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limp_spaghetti"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matrix multiplication is working just fine, so I must have exaggerated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "285"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limp_spaghetti @ limp_spaghetti"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# means one row, take as many columns as you need\n",
    "hard_spaghetti = limp_spaghetti.reshape(1, -1) \n",
    "hard_spaghetti.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hard_spaghetti"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 10)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hard_spaghetti.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  4,  9, 16, 25, 36, 49, 64, 81]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hard_spaghetti * hard_spaghetti # elementwise multiplication is different"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No the dimensions don't work here\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    hard_spaghetti @ hard_spaghetti\n",
    "except:\n",
    "    print(\"No the dimensions don't work here\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[285]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hard_spaghetti @ hard_spaghetti.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0],\n",
       "       [ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9],\n",
       "       [ 0,  2,  4,  6,  8, 10, 12, 14, 16, 18],\n",
       "       [ 0,  3,  6,  9, 12, 15, 18, 21, 24, 27],\n",
       "       [ 0,  4,  8, 12, 16, 20, 24, 28, 32, 36],\n",
       "       [ 0,  5, 10, 15, 20, 25, 30, 35, 40, 45],\n",
       "       [ 0,  6, 12, 18, 24, 30, 36, 42, 48, 54],\n",
       "       [ 0,  7, 14, 21, 28, 35, 42, 49, 56, 63],\n",
       "       [ 0,  8, 16, 24, 32, 40, 48, 56, 64, 72],\n",
       "       [ 0,  9, 18, 27, 36, 45, 54, 63, 72, 81]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hard_spaghetti.T @ hard_spaghetti"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That there (what you just witnessed) is ```@``` and/or ```__matmul__``` in action, newly an overloadable operator [in standard Python as well](https://www.python.org/dev/peps/pep-0465/). \n",
    "\n",
    "The all-important algorithm (credited to whom again?) is also triggered by ```np.dot(A, B)``` in the 3rd party [numpy library](https://numpy.org/doc/stable/reference/generated/numpy.dot.html), already imported up top if you were paying attention.\n",
    "\n",
    "In theory, the 2nd dimension of the left argument has to match the first dimension of the 2nd argument.  \n",
    "\n",
    "With an N x 1 column vector, and a 1 x M row vector (or even N, as above), that can work.  Or maybe it's an M x N matrix times an N x P matrix.  In both cases, the column dimension of the first matches the row dimension of the 2nd."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-193,  -49,   75],\n",
       "       [ -81,  -52,  -31],\n",
       "       [  92,  157,  -16],\n",
       "       [  52,  308,   36],\n",
       "       [  91,  -74, -141],\n",
       "       [  66,  -20,   -5],\n",
       "       [  24,  158,   33]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_backup = A\n",
    "\n",
    "M = 7\n",
    "N = 10\n",
    "P = 3\n",
    "\n",
    "A = np.array(rng.integers(-10, 11, size = M*N)).reshape(M,N)\n",
    "B = np.array(rng.integers(-10, 11, size = N*P)).reshape(N,P)\n",
    "A @ B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  7],\n",
       "       [ -6],\n",
       "       [  6],\n",
       "       [-10],\n",
       "       [  6],\n",
       "       [  6],\n",
       "       [  6],\n",
       "       [  3],\n",
       "       [ -1],\n",
       "       [  4]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array(rng.integers(-10, 11, size = N)).reshape(N,1)\n",
    "B = np.array(rng.integers(-10, 11, size = M)).reshape(1,M)\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ -5,   6,   1,  -1,   0,   1, -10]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-35,  42,   7,  -7,   0,   7, -70],\n",
       "       [ 30, -36,  -6,   6,   0,  -6,  60],\n",
       "       [-30,  36,   6,  -6,   0,   6, -60],\n",
       "       [ 50, -60, -10,  10,   0, -10, 100],\n",
       "       [-30,  36,   6,  -6,   0,   6, -60],\n",
       "       [-30,  36,   6,  -6,   0,   6, -60],\n",
       "       [-30,  36,   6,  -6,   0,   6, -60],\n",
       "       [-15,  18,   3,  -3,   0,   3, -30],\n",
       "       [  5,  -6,  -1,   1,   0,  -1,  10],\n",
       "       [-20,  24,   4,  -4,   0,   4, -40]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = A @ B\n",
    "C"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just for fun lets review what it means to normalize our data columns, as before feeding to some Machine Learning algorithms, as well as to PCA itself, this step is a part of routine data cleaning."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import zscore"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "mask = (C == 0).all(0)\n",
    "column_indices = np.where(mask)[0]\n",
    "# Update C to only include the columns where non-zero values occur.\n",
    "C = C[:,~mask] # all rows, not these columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.88,  0.88,  0.88, -0.88,  0.88, -0.88],\n",
       "       [ 1.45, -1.45, -1.45,  1.45, -1.45,  1.45],\n",
       "       [-0.7 ,  0.7 ,  0.7 , -0.7 ,  0.7 , -0.7 ],\n",
       "       [ 2.17, -2.17, -2.17,  2.17, -2.17,  2.17],\n",
       "       [-0.7 ,  0.7 ,  0.7 , -0.7 ,  0.7 , -0.7 ],\n",
       "       [-0.7 ,  0.7 ,  0.7 , -0.7 ,  0.7 , -0.7 ],\n",
       "       [-0.7 ,  0.7 ,  0.7 , -0.7 ,  0.7 , -0.7 ],\n",
       "       [-0.16,  0.16,  0.16, -0.16,  0.16, -0.16],\n",
       "       [ 0.56, -0.56, -0.56,  0.56, -0.56,  0.56],\n",
       "       [-0.34,  0.34,  0.34, -0.34,  0.34, -0.34]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.round(zscore(C), 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### In sum...\n",
    "\n",
    "A rectangular matrix multiplied by its own transpose gives a square matix.  \n",
    "\n",
    "However we've seen  \"multiplication\" in the sense of ```@``` or ```__matmul__``` is not elementwise. Additing and subtraction would elementwise also, unless we're talking about broadcasting, a way in which numpy is smart enough to find the applicable axis.  \n",
    "\n",
    "In the case of \"matrix multiply\" we really mean to take the dot product.\n",
    "\n",
    "In other words, numpy gives us two convenient ways to take the dot product of two matrices.  \n",
    "\n",
    "Either matrix may be only a single row or column, in which case we may refer to it as a row or column vector, or just a vector for short."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-35,  42,   7,  -7,   0,   7, -70],\n",
       "       [ 30, -36,  -6,   6,   0,  -6,  60],\n",
       "       [-30,  36,   6,  -6,   0,   6, -60],\n",
       "       [ 50, -60, -10,  10,   0, -10, 100],\n",
       "       [-30,  36,   6,  -6,   0,   6, -60],\n",
       "       [-30,  36,   6,  -6,   0,   6, -60],\n",
       "       [-30,  36,   6,  -6,   0,   6, -60],\n",
       "       [-15,  18,   3,  -3,   0,   3, -30],\n",
       "       [  5,  -6,  -1,   1,   0,  -1,  10],\n",
       "       [-20,  24,   4,  -4,   0,   4, -40]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(A,B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-35,  42,   7,  -7,   0,   7, -70],\n",
       "       [ 30, -36,  -6,   6,   0,  -6,  60],\n",
       "       [-30,  36,   6,  -6,   0,   6, -60],\n",
       "       [ 50, -60, -10,  10,   0, -10, 100],\n",
       "       [-30,  36,   6,  -6,   0,   6, -60],\n",
       "       [-30,  36,   6,  -6,   0,   6, -60],\n",
       "       [-30,  36,   6,  -6,   0,   6, -60],\n",
       "       [-15,  18,   3,  -3,   0,   3, -30],\n",
       "       [  5,  -6,  -1,   1,   0,  -1,  10],\n",
       "       [-20,  24,   4,  -4,   0,   4, -40]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A @ B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below is a way to make Jupyter Notebook code cells output all their representations instead of the last expression only."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.core.interactiveshell import InteractiveShell\n",
    "InteractiveShell.ast_node_interactivity = \"all\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2, 3, 4],\n",
       "       [5, 6, 7, 8, 9]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = A_backup\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "B = A.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[0]             # all columns, row 0\n",
    "B[:,0].flatten() # all rows, column 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[What trick was that again?](https://www.dataquest.io/blog/jupyter-notebook-tips-tricks-shortcuts/)  How did we get to see both outputs?\n",
    "\n",
    "For reference, the options for that are 'all', 'none', 'last' and 'last_expr'."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remember, the plain old multiplication operator, the asterisk, is an element-wise operator. \n",
    "\n",
    "Since the two vectors are the same, the resulting elementwise multiplication raises each element to a 2nd power."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  4,  9, 16])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[0] * B[:,0].flatten()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this second case, the B column is different.  The dot product would sum these terms as a final operation, distilling the result to a single number."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([ 0,  6, 14, 24, 36])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "80"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B[:,1]         # all rows, column 1 (start from 0)\n",
    "A[0]           # row 0 of A\n",
    "A[0] * B[:,1]  # elementwise multiply\n",
    "A[0] @ B[:,1]  # single number (sum of the above)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Multiplying each row of A, by each column of B, is what the plain old multiplication operator does.  The dot product would be summing the elements of each result vector and storing it in the resulting matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  6, 14, 24, 36])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[1] * B[:,0].flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([25, 36, 49, 64, 81])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[1] * B[:,1].flatten()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even though numpy provides a dot product, one could write it from scratch, making use of elementwise multiplication and np.sum internally.  The key line below is:\n",
    "\n",
    "```python\n",
    "output[i,j] = np.sum(A[i,:] * B[:,j].flatten())\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dot_product(A, B, dt=int):\n",
    "    \"\"\"\n",
    "    multiply and sum A[i] * B[j] to get O[i,j]\n",
    "    for i ranging through m rows of A, j through\n",
    "    n columns of B. O will by m x n\n",
    "    dt = int, float\n",
    "    \"\"\"\n",
    "    m = A_rows = A.shape[0]\n",
    "    if B.ndim==1: # lying sideways\n",
    "        B = B.reshape(-1,1) # stand it up as col vector\n",
    "    n = B_cols = B.shape[1]\n",
    "    # if you don't want or expect integer output\n",
    "    # change dtype to float\n",
    "    output = np.zeros(shape=(m,n), dtype=dt)\n",
    "    for i in range(A_rows):\n",
    "        for j in range(B_cols):\n",
    "            output[i,j] = np.sum(A[i,:] * B[:,j].flatten())\n",
    "    return output"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Same answer as above, using the built-in numpy function or operator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 30,  80],\n",
       "       [ 80, 255]])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dot_product(A, B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [2],\n",
       "       [3],\n",
       "       [4],\n",
       "       [5]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3, 4, 5]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U1 = np.array([1,2,3,4,5]).reshape(-1,1)\n",
    "V1 = np.array([1,2,3,4,5]).reshape(1,5)\n",
    "U1\n",
    "V1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3,  4,  5],\n",
       "       [ 2,  4,  6,  8, 10],\n",
       "       [ 3,  6,  9, 12, 15],\n",
       "       [ 4,  8, 12, 16, 20],\n",
       "       [ 5, 10, 15, 20, 25]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3,  4,  5],\n",
       "       [ 2,  4,  6,  8, 10],\n",
       "       [ 3,  6,  9, 12, 15],\n",
       "       [ 4,  8, 12, 16, 20],\n",
       "       [ 5, 10, 15, 20, 25]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U1 @ V1\n",
    "dot_product(U1, V1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* [Academo.org](https://academo.org/)\n",
    "* [Matrix Multiply (MM) GIF](https://pages.hep.wisc.edu/~jnb/poster_group/matrix_multiply.html)\n",
    "* [MM Exhibit](http://matrixmultiplication.xyz/)\n",
    "![MM](https://pages.hep.wisc.edu/~jnb/poster_group/examples/matrix_times_vector_large.gif)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 30,  80],\n",
       "       [ 80, 255]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(A,B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 30,  80],\n",
       "       [ 80, 255]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A @ B  # preferred"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Singular Value Decomposition\n",
    "\n",
    "According to SVD, any matrix (non-square OK) may be decomposed into a dot product of three matrices:\n",
    "\n",
    "* left hand singular vectors in an orthogonal matrix\n",
    "* a diagonal matrix of singular values\n",
    "* right hand singular vectors in an orthogonal matrix\n",
    "\n",
    "These operations correspond to a rotation, a stretching in several directions, and another rotation.  \n",
    "\n",
    "The stretching will be biggest in one direction, with other such linear transformations then ranked in order of equal or lesser magnitude.\n",
    "\n",
    "This ranking of stretch factors, or singular values, may serve as a basis for eliminating those of lesser importance, thereby reducing the overall number of columns required of the original matrix, to get a best approximation using some number of principal components.\n",
    "\n",
    "Some linear combination of a subset of the original columns, will make the greatest contribution to landing us in the target neighborhood of predicted clusters.  \n",
    "\n",
    "More columns of data would not provide significantly more accuracy.  That's what we're aiming for in anycase: dimension reduction (fewer columns). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/YPe5OP7Clv4\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x115434f50>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo('YPe5OP7Clv4')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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       "            src=\"https://www.youtube.com/embed/SsNXg6KpLSU\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x1a17452890>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "YouTubeVideo('SsNXg6KpLSU')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/J0arU2PAMls\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x1a1745bb90>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "YouTubeVideo('J0arU2PAMls')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A first rectangular matrix.  Any will do."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2, 3, 4],\n",
       "       [5, 6, 7, 8, 9]])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array(range(10)).reshape(2,5)\n",
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function below uses the native svd algorithm inside numpy, while making the returned matrices suitable for multiplying back together (dot product), thereby giving the original matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "def svd(the_matrix):\n",
    "    # the matrix D needs columns of 0s \n",
    "    # to the right, up to the number of columns \n",
    "    # in the_matrix\n",
    "    U, D, VT = np.linalg.svd(A, full_matrices=True)\n",
    "    # add columns to the right to match number of rows of VT (same as the_matrix)\n",
    "    padding = np.zeros((the_matrix.shape[0], the_matrix.shape[1] - len(D)))\n",
    "    S = np.hstack([np.diag(D), padding])\n",
    "    return U, S, VT"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that rounding only affects the display, not the internals of any of this matrices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "U =\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[-0.304, -0.953],\n",
       "       [-0.953,  0.304]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "S =\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[16.749,  0.   ,  0.   ,  0.   ,  0.   ],\n",
       "       [ 0.   ,  2.111,  0.   ,  0.   ,  0.   ]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "VT =\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[-0.284, -0.359, -0.434, -0.509, -0.585],\n",
       "       [ 0.721,  0.413,  0.106, -0.201, -0.508],\n",
       "       [-0.355, -0.04 ,  0.87 , -0.202, -0.274],\n",
       "       [-0.365,  0.358, -0.141,  0.669, -0.521],\n",
       "       [-0.376,  0.755, -0.152, -0.46 ,  0.232]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U,S,VT = svd(A)\n",
    "print(\"U =\")\n",
    "np.round(U, 3)\n",
    "print(\"S =\")\n",
    "np.round(S, 3)\n",
    "print(\"VT =\")\n",
    "np.round(VT,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 1., 2., 3., 4.],\n",
       "       [5., 6., 7., 8., 9.]])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_reconstructed = U @ S @ VT\n",
    "np.round(A_reconstructed,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[280.5444,   0.    ,   0.    ,   0.    ,   0.    ],\n",
       "       [  0.    ,   4.4556,   0.    ,   0.    ,   0.    ]])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.round(S*S,4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both U and VT are what we call \"orthogonal matrices\" in that each times its own transpose yields the identity matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0.],\n",
       "       [0., 1.]])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.round(U @ U.T, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  0., -0.,  0., -0.],\n",
       "       [ 0.,  1.,  0.,  0.,  0.],\n",
       "       [-0.,  0.,  1.,  0., -0.],\n",
       "       [ 0.,  0.,  0.,  1., -0.],\n",
       "       [-0.,  0., -0., -0.,  1.]])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.round(VT @ VT.T,3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A deeper dive into SVD shows that the matrix U is actually the eigenvectors of A dot A.T.\n",
    "\n",
    "The eigenvectors and U (below) are the same but for column order, with the eigenvalues likewise reversed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.953, -0.304],\n",
       "       [ 0.304, -0.953]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[-0.304, -0.953],\n",
       "       [-0.953,  0.304]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([  4.45562308, 280.54437692])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AAT = dot_product(A, A.T)\n",
    "AAT_evals, AAT_evecs = np.linalg.eig(AAT) # get eigen stuff\n",
    "np.round(AAT_evecs,3)\n",
    "np.round(U,3)\n",
    "AAT_evals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remember these two eigenvalues as you'll be seeing them again. And remember S*S above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[280.5444,   0.    ,   0.    ,   0.    ,   0.    ],\n",
       "       [  0.    ,   4.4556,   0.    ,   0.    ,   0.    ]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.round(S*S,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -89.57904182, -265.89583537])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[ -5.095,  -2.011,   0.   ,   0.   ,   0.   ],\n",
       "       [-15.956,   0.642,   0.   ,   0.   ,   0.   ]])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AAT_evecs @ AAT_evals\n",
    "np.round(U @ S, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.95261622,  0.30417485])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[-4.24449881],\n",
       "       [ 1.35528847]])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([-4.24449881,  1.35528847])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AAT_evecs[:,0]\n",
    "dot_product(AAT, AAT_evecs[:,0], np.float)\n",
    "AAT_evals[0] * AAT_evecs[:,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([280.544,   4.456,   0.   ,   0.   ,  -0.   ])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ATA = A.T @ A\n",
    "ATA_evals, ATA_evecs = np.linalg.eig(ATA)\n",
    "np.round(ATA_evals, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Aha!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Same matrix computed 3 ways\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[  -4.24449881,  -85.334543  ],\n",
       "       [   1.35528847, -267.25112384]])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[  -4.24449881,  -85.334543  ],\n",
       "       [   1.35528847, -267.25112384]])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[  -4.24449881,  -85.334543  ],\n",
       "       [   1.35528847, -267.25112384]])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------\n",
      "Eigenvalues: [  4.45562308 280.54437692]\n",
      "Eigenvalues times Eigenvectors (same outcome):\n",
      " [[  -4.24449881  -85.334543  ]\n",
      " [   1.35528847 -267.25112384]]\n"
     ]
    }
   ],
   "source": [
    "print(\"Same matrix computed 3 ways\")\n",
    "dot_product(AAT, AAT_evecs, dt=np.float)\n",
    "AAT @ AAT_evecs\n",
    "np.dot(AAT, AAT_evecs)\n",
    "print(\"------------\")\n",
    "print(\"Eigenvalues:\", AAT_evals)\n",
    "print(\"Eigenvalues times Eigenvectors (same outcome):\\n\", AAT_evals * AAT_evecs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Same outcome because the linear transformation of eigenvalues times eigenvectors is a $\\lambda$ kind of solution, i.e. elementwise scalar multiplication is at work.  The matrix multiplies its own eigenvectors, by simply stretching them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0.],\n",
       "       [0., 0.]])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[-0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0., -0.,  0.,  0.],\n",
       "       [-0.,  0.,  0.,  0.,  0.],\n",
       "       [-0.,  0.,  0., -0.,  0.],\n",
       "       [-0.,  0.,  0., -0.,  0.]])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "check1 = AAT @ AAT_evecs - AAT_evals * AAT_evecs\n",
    "check2 = ATA @ ATA_evecs - ATA_evals * ATA_evecs\n",
    "np.round(check1, 5)\n",
    "np.round(check2, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3,  1,  1],\n",
       "       [-1,  3,  1]])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array((3, 1, 1, -1, 3, 1)).reshape(2,3)\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "U =\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[-0.707, -0.707],\n",
       "       [-0.707,  0.707]])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "S =\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[3.464, 0.   , 0.   ],\n",
       "       [0.   , 3.162, 0.   ]])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "VT =\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[-0.408, -0.816, -0.408],\n",
       "       [-0.894,  0.447,  0.   ],\n",
       "       [-0.183, -0.365,  0.913]])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U,S,VT = svd(A)\n",
    "\n",
    "print(\"U =\")\n",
    "np.round(U, 3)\n",
    "print(\"S =\")\n",
    "np.round(S, 3)\n",
    "print(\"VT =\")\n",
    "np.round(VT, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.,  1.,  1.],\n",
       "       [-1.,  3.,  1.]])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_reconstructed = U @ S @ VT\n",
    "A_reconstructed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* [SVD Tutorial](https://datajobs.com/data-science-repo/SVD-Tutorial-%5bKirk-Baker%5d.pdf)\n",
    "* [EigenFaces with Scikit-Learn](http://jaquesgrobler.github.io/Online-Scikit-Learn-stat-tut/auto_examples/decomposition/plot_faces_decomposition.html)"
   ]
  }
 ],
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