lec06.ipynb

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     "text": [
      "\u001b[32m\u001b[1m    Updating\u001b[22m\u001b[39m registry at `~/.julia/registries/General.toml`\n",
      "\u001b[32m\u001b[1m   Resolving\u001b[22m\u001b[39m package versions...\n",
      "\u001b[32m\u001b[1m  No Changes\u001b[22m\u001b[39m to `~/srv/rep/22-course-cse6643/mybinder/Project.toml`\n",
      "\u001b[32m\u001b[1m  No Changes\u001b[22m\u001b[39m to `~/srv/rep/22-course-cse6643/mybinder/Manifest.toml`\n"
     ]
    }
   ],
   "source": [
    "import Pkg; Pkg.add([\"Plots\", \"Interact\"]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7c763c58",
   "metadata": {},
   "outputs": [],
   "source": [
    "const STATIC_LECTURE = false;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3d34d2fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "draw (generic function with 1 method)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function draw(plt)\n",
    "    if STATIC_LECTURE\n",
    "        filename = Base.Filesystem.tempname() * \".png\"\n",
    "        savefig(filename)\n",
    "        return display(\"image/png\", read(filename))\n",
    "    else\n",
    "        return plt\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8b5acc71",
   "metadata": {},
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       "<div style=\"padding: 1em; background-color: #f8d6da; border: 1px solid #f5c6cb; font-weight: bold;\">\n",
       "<p>The WebIO Jupyter extension was not detected. See the\n",
       "<a href=\"https://juliagizmos.github.io/WebIO.jl/latest/providers/ijulia/\" target=\"_blank\">\n",
       "    WebIO Jupyter integration documentation\n",
       "</a>\n",
       "for more information.\n",
       "</div>\n"
      ],
      "text/plain": [
       "WebIO._IJuliaInit()"
      ]
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     "output_type": "display_data"
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    {
     "data": {
      "text/plain": [
       "imshow (generic function with 2 methods)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using LinearAlgebra;\n",
    "using Plots; default(l=2, size=(900,550), label=false);\n",
    "using Interact;\n",
    "\n",
    "imshow(x,_clim=:nothing) = heatmap(x\n",
    "    , aspect_ratio=:equal\n",
    "    , framestyle=:none\n",
    "    , yflip=true\n",
    "    , c=:diverging_gwv_55_95_c39_n256\n",
    "    , clim=if _clim != :nothing\n",
    "          _clim\n",
    "      elseif maximum(abs.(x)) > 1.e-12\n",
    "          (-maximum(abs.(x)),maximum(abs.(x)))\n",
    "      else \n",
    "          (-1,1)\n",
    "      end\n",
    "    , size=(500,500)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "877bb843",
   "metadata": {
    "cell_style": "split",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**(follow along: <https://tinyurl.com/gtcse6643lec6>)**\n",
    "\n",
    "### Warmup\n",
    "\n",
    "1. Use julia to compute the QR factorizations of\n",
    "\n",
    "$$\n",
    "A = \\begin{bmatrix}\n",
    "1 & 0 \\\\ 0 & 1 \\\\ 1 & 0\n",
    "\\end{bmatrix},\n",
    "\\quad\n",
    "B = \\begin{bmatrix}\n",
    "1 & 2 \\\\ 0 & 1 \\\\ 1 & 0\n",
    "\\end{bmatrix}.\n",
    "$$\n",
    "\n",
    "2. What is the simplest (smallest) way to represent the orthogonal projector onto $\\mathrm{range}(A)$ or $\\mathrm{range}(B)$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "082d78a9",
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Matrix{Float64}:\n",
       " 0.833333   0.333333   0.166667\n",
       " 0.333333   0.333333  -0.333333\n",
       " 0.166667  -0.333333   0.833333"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using LinearAlgebra\n",
    "\n",
    "#A = ...\n",
    "#B = ...\n",
    "B = [[1,0,1] [2,1,0]]\n",
    "Q, R = qr(B)\n",
    "R\n",
    "(I - Q[:,3] * Q[:,3]')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5fbd289",
   "metadata": {
    "cell_style": "split"
   },
   "source": [
    "**vector, matrix, \"column vector\" ($m\\times 1$), \"row vector\" ($1 \\times m$) constructors:**\n",
    "\n",
    "- vector: separate entries with commas: `[1.,2.,3.]`\n",
    "- matrix row-wise: spaces between row entries, semicolons between rows, `[1. 2. 3.; 4. 5. 6.]`\n",
    "- matrix column-wise: spaces between vectors: `[[1.,4.] [2.,5.] [3.,6]]`\n",
    "- $1 \\times m$ matrix; spaces between entries, `[1. 2. 3.]`\n",
    "- $m \\times 1$ matrix; double-semicolon after a vector, `[[1.,2.,3.];;]`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15cf47cd",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Gram-Schmidt QR Factorizations\n",
    "\n",
    "**1. Testing QR Algorithms**\n",
    "\n",
    "**2. Gram-Schmidt Orthogonalization, QR Existence, Uniqueness, and Usage**\n",
    "\n",
    "**3. Classical Gram-Schmidt**\n",
    "\n",
    "**4. Modified Gram-Schmidt**\n",
    "\n",
    "**5. Operations Count**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83189909",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Testing QR Algorithms"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab688898",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Test driven development\n",
    "\n",
    "How should we test an implementation of the QR factorization?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31dfffd6",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "**Recal: reduced QR factorization**\n",
    "\n",
    "$$ A \\underbrace{=}_{\\text{(test 1)}} \\hat{Q} \\hat{R}, \\quad \\hat{Q} \\in \\mathbb{C}^{m\\times n}\\ \\underbrace{\\text{(orthonormal columns)}}_{\\text{(test 2)}}, \\quad \\hat{R} \\in \\mathbb{C}^{n \\times n} \\underbrace{\\text{(upper triangular)}}_{\\text{(test 3)}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58738bd1",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Each test may tolerate some rounding error\n",
    "\n",
    "We want to measure the magnitude of the difference between the computed result and the mathematical truth."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "48c62237",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "reconstruction_error (generic function with 1 method)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reconstruction_error(A, Q, R) = norm(A - Q * R, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98bcdd8c",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "(Note that this is $\\|A - Q R \\|_F$: the Frobenius norm can be directly calculated, so it is most common to use for numerical tests.)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9706b206",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Numerical test for orthonormal columns"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09a61dd1",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$\\hat{Q}^* \\hat{Q} = I \\in \\mathbb{C}^{n \\times n}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0dc6003c",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "orthonormality_error (generic function with 1 method)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "orthonormality_error(Q) = norm(I - Q[:,:]' * Q[:,:], 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c302450e",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Test for upper triangularity\n",
    "\n",
    "$$\\hat{R} = \\mathrm{triu}(\\hat{R})$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "1f77d6e4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "upper_triangularity_error (generic function with 1 method)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "upper_triangularity_error(R) = norm(R - UpperTriangular(R), 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2828b1d4",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### All together"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "dd8c0c02",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "qr_test (generic function with 4 methods)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function qr_test(A, Q, R, recon_tol=1.e-12, ortho_tol=1.e-12, triu_tol=0.0)\n",
    "    recon_err = reconstruction_error(A, Q, R)\n",
    "    ortho_err = orthonormality_error(Q)\n",
    "    triu_err = upper_triangularity_error(R)\n",
    "    println(\"Reconstruction error || A - Q R ||_F = $recon_err\")\n",
    "    println(\"Orthonormality error || I - Q'Q ||_F = $ortho_err\")\n",
    "    println(\"Upper-triangularity error || R - triu(R) ||_F = $triu_err\")\n",
    "    return (recon_err <= recon_tol) && (ortho_err <= ortho_tol) && (triu_err <= triu_tol) \n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e45b743f",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Test it out on julia's `qr`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "36c52e98",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reconstruction error || A - Q R ||_F = 3.62544291390759e-14\n",
      "Orthonormality error || I - Q'Q ||_F = 6.191684281259161e-15\n",
      "Upper-triangularity error || R - triu(R) ||_F = 0.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = 100; n = 50;\n",
    "A = randn(m, n);\n",
    "Q, R = qr(A);\n",
    "qr_test(A, Q, R)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0df80c60",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Gram-Schmidt Orthogonalization"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12252539",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Recall the QR factorization written in terms of projectors: the Gram-Schmidt Process"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eae172bf",
   "metadata": {},
   "source": [
    "- At step $j$:\n",
    "\n",
    "$$\\tilde{q}_j = (I - P_{1:j-1}) a_j$$\n",
    "$$q_j = \\frac{\\tilde{q}_j}{\\|\\tilde q_j\\|}$$\n",
    "$$r_{1:j,j} = \\hat{Q}_{1:j}^* a_j$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b79cd2af",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "qr_projectors (generic function with 1 method)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function qr_projectors(A)\n",
    "    m, n = size(A)\n",
    "    Q̂ = zeros(eltype(A), m, n) # <--- use the same datatype (Float32 vs Float64, ℝ vs ℂ)\n",
    "    R̂ = zeros(eltype(A), n, n)\n",
    "    for j in 1:n\n",
    "        Q̂ⱼ₋₁ = Q̂[:,1:j-1]\n",
    "        Pⱼ₋₁ = Q̂ⱼ₋₁ * Q̂ⱼ₋₁'\n",
    "        q̃ⱼ = (I - Pⱼ₋₁) * A[:,j]\n",
    "        Q̂[:,j] = q̃ⱼ / norm(q̃ⱼ)\n",
    "        R̂[1:j,j] = Q̂[:,1:j]' * A[:,j]\n",
    "    end\n",
    "    return Q̂, R̂\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "c4335826",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reconstruction error || A - Q R ||_F = 2.0402726873612872e-14\n",
      "Orthonormality error || I - Q'Q ||_F = 2.6409559838499707e-15\n",
      "Upper-triangularity error || R - triu(R) ||_F = 0.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = 100; n = 50;\n",
    "A = randn(m, n);\n",
    "Q̂, R̂ = qr_projectors(A);\n",
    "qr_test(A, Q̂, R̂)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f1b2b76",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Existence and uniqueness\n",
    "\n",
    "**T&B Theorem 7.1.** Every $A \\in \\mathbb{C}^{m \\times n}$ ($m \\geq n$) has a full $QR$ factorization, hence also a reduced QR factorization.\n",
    "\n",
    "_Proof._ The steps of the algorithm.  There is a need to handle the case when the columns are not linearly independent, but we can just an arbitrary vector $q_j \\perp \\hat{Q}_{1:j-1}$ at that step and the algorithm continues.\n",
    "\n",
    "**T&B Theorem 7.2.** Each $A \\in \\mathbb{C}^{m \\times n}$ ($m \\geq n$) of full rank has a unique reduced QR factorization $A = \\hat{Q} \\hat{R}$ with $r_{jj}$ real and $r_{jj} > 0$.\n",
    "\n",
    "_Proof_.  We will see why when we implement the classical Gram-Schmidt algorithm."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4154128",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Usage: solving $Ax = b$\n",
    "\n",
    "$$A x = b \\Leftrightarrow Q R x = b \\quad \\text{(step 1: QR factorization)}$$\n",
    "\n",
    "$$Q R x = b \\Leftrightarrow R x = Q^* b \\quad \\text{(step 2: compute } y = Q^*b\\text{)}$$\n",
    "\n",
    "$$R x = Q^*b \\Leftrightarrow x = R^{-1} Q^*b \\quad \\text{(step 3:  invert triangular matrix, }x = R^{-1}y\\text{)}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "0417e1a7",
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.388788336792875e-13"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = 100\n",
    "A = randn(m, m)\n",
    "b = randn(m)\n",
    "Q, R = qr(A)\n",
    "x = R \\ (Q' * b)\n",
    "norm(b - A * x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d32b171",
   "metadata": {
    "cell_style": "split"
   },
   "source": [
    "This method is more stable but more expensive than the more conventional Gaussian elimination."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42dbfdf5",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Note on HW2, problem 3\n",
    "\n",
    "($A \\in \\mathbb{C}^{m \\times n}$ ($m \\geq n$) is full rank if and only if $\\hat{R}$ from the reduced QR factoriation has all nonzeros on the diagonal.)\n",
    "\n",
    "What is the determinant of a triangular matrix?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53d35357",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Classical Gram-Schmidt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8f1baf2",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Slim down the work in the projection\n",
    "\n",
    "$$\\tilde q_j = (I - P_{1:j-1}) a_j = (I - \\hat{Q}_{1:j-1} \\hat{Q}_{1:j-1}^*) a_j = a_j - \\hat{Q}_{1:j-1}(\\hat{Q}_{1:j-1}^* a_j)$$\n",
    "\n",
    "$O((j-1)m)$ work to compute the projection this ways, as opposed to $O(m^2)$ if using the constructed matrix\n",
    "$(I - P_{1:j-1})$\n",
    "\n",
    "So we will initialize $\\tilde{q}_j^{(0)} = a_j$ and then do\n",
    "\n",
    "$$\\tilde{q}_j = \\tilde{q}_j^{(0)} - \\hat{Q}_{1:j-1}(\\hat{Q}_{1:j-1} \\tilde{q}_j^{(0)}).$$\n",
    "\n",
    "(Only use $A$ to make a copy, try to do most operations _in place_ on $\\hat{Q}$.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c0d46ccc",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "qr_projectors_slim (generic function with 1 method)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function qr_projectors_slim(A)\n",
    "    m, n = size(A)\n",
    "    Q̂ = copy(A)\n",
    "    R̂ = zeros(eltype(A), n, n)\n",
    "    for j in 1:n\n",
    "        # Project Q̂[:,1:j-1] component out of Q̂[:,j]\n",
    "        Q̂[:,j] -= Q̂[:,1:j-1] * (Q̂[:,1:j-1]' * Q̂[:,j]) # parentheses to do this matvec first\n",
    "        # Normalize  \n",
    "        Q̂[:,j] /= norm(Q̂[:,j])\n",
    "        R̂[1:j,j] = Q̂[:,1:j]' * A[:,j]\n",
    "    end\n",
    "    return Q̂, R̂\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "4292aa47",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reconstruction error || A - Q R ||_F = 1.4103008033299413e-14\n",
      "Orthonormality error || I - Q'Q ||_F = 2.8165584740012686e-15\n",
      "Upper-triangularity error || R - triu(R) ||_F = 0.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = 100; n = 50;\n",
    "A = randn(m, n);\n",
    "Q̂, R̂ = qr_projectors_slim(A);\n",
    "qr_test(A, Q̂, R̂)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc496a8f",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Slim down the work in the calculation of $\\hat{R}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2df0765e",
   "metadata": {
    "cell_style": "split"
   },
   "source": [
    "$$ r_{1:j,j} = \\hat{Q}_{1:j}^* a_j = \n",
    "\\begin{bmatrix}\n",
    " \\\\\n",
    "\\hat{Q}_{i:j-1}^* a_j \\\\\n",
    " \\\\ \\hline\n",
    "q_j^* a_j \\\\\n",
    "\\end{bmatrix}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "702fceeb",
   "metadata": {
    "cell_style": "split"
   },
   "source": [
    "- The top of the vector $\\hat{Q}_{i:j-1}^* a_j = \\hat{Q}_{i:j-1}^* \\tilde{q}_j^{(0)}$ was already computed as part of the projector to compute $\\tilde{q}_j$: save and reuse the computation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bde446ce",
   "metadata": {
    "cell_style": "split"
   },
   "source": [
    "- The final value is\n",
    "\n",
    "$$\n",
    "q_j^* a_j = \\frac{1}{\\|\\tilde{q}_j\\|} \\tilde{q}_j^* \\tilde{q}_j^{(0)}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1ab52cc",
   "metadata": {
    "cell_style": "center"
   },
   "source": [
    "- We can use the fact that $\\tilde{q}_j^{(0)} = \\tilde{q}_j + P_{1:j-1} \\tilde{q}_j^{(0)}$ to see that we don't need to recompute this quantity:\n",
    "\n",
    "$$\n",
    "\\frac{1}{\\|\\tilde{q}_j\\|} \\tilde{q}_j^* \\tilde{q}_j^{(0)} = \\frac{1}{\\|\\tilde{q}_j\\|}\\tilde{q}_j^*(\\tilde{q}_j + P_{1:j-1} \\tilde{q}_j^{(0)}) = \\frac{1}{\\|\\tilde{q}_j\\|}\\tilde{q}_j^* \\tilde{q}_j = \\|\\tilde{q}_j\\|.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c328ef68",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Result: the (unstable) Classical Gram-Schmidt algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "936f168a",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "qr_classical_gram_schmidt (generic function with 1 method)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function qr_classical_gram_schmidt(A)\n",
    "    m, n = size(A)\n",
    "    Q̂ = copy(A)\n",
    "    R̂ = zeros(eltype(A), n, n)\n",
    "    for j in 1:n\n",
    "        # Compute coefficients of aⱼ in Q̂[:,1:j-1] basis\n",
    "        R̂[1:j-1,j] = Q̂[:,1:j-1]' * Q̂[:,j]\n",
    "        # Project Q̂[:,1:j-1] components out of Q̂[:,j]\n",
    "        Q̂[:,j] -= Q̂[:,1:j-1] * R̂[1:j-1,j]\n",
    "        # Normalize\n",
    "        R̂[j,j] = norm(Q̂[:,j])\n",
    "        Q̂[:,j] /= R̂[j,j]\n",
    "    end\n",
    "    return Q̂, R̂\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "ee7324a5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reconstruction error || A - Q R ||_F = 9.50100877647782e-15\n",
      "Orthonormality error || I - Q'Q ||_F = 2.9489178298166906e-15\n",
      "Upper-triangularity error || R - triu(R) ||_F = 0.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = 100; n = 50;\n",
    "A = randn(m, n);\n",
    "Q̂, R̂ = qr_classical_gram_schmidt(A);\n",
    "qr_test(A, Q̂, R̂)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ffe5d8fa",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Classical Gram-Schmidt in action"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "27c9b2dc",
   "metadata": {
    "hideCode": true,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Saved animation to \n",
      "│   fn = /home/tisaac/srv/rep/22-course-cse6643/mybinder/tmp.gif\n",
      "└ @ Plots /home/tisaac/.julia/packages/Plots/Xv2qA/src/animation.jl:114\n"
     ]
    },
    {
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\" />"
      ],
      "text/plain": [
       "Plots.AnimatedGif(\"/home/tisaac/srv/rep/22-course-cse6643/mybinder/tmp.gif\")"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = 10; n = 5;\n",
    "A = randn(m, n)\n",
    "A /= maximum(abs.(A))\n",
    "Q̂ = copy(A)\n",
    "R̂ = zeros(n, n)\n",
    "r_scale = maximum(abs.(qr(A).R))\n",
    "anim = Animation()\n",
    "function step_plot(A,Q̂,R̂,j)\n",
    "    Q_plot = imshow(Q̂,(-1,1))\n",
    "    plot!(Q_plot,title=\"Q\")\n",
    "    ortho_plot = imshow(Q̂' * Q̂,(-1,1))\n",
    "    plot!(ortho_plot,title=\"Q'Q\")\n",
    "    recon_plot = imshow(A - Q̂ * R̂,(-1,1))\n",
    "    plot!(recon_plot,title=\"A - QR\")\n",
    "    R_plot = imshow(R̂,(-r_scale,r_scale))\n",
    "    plot!(R_plot,title=\"R\")\n",
    "    return plot(Q_plot, R_plot, ortho_plot, recon_plot, layout=(1,4), size=(1300,800), plot_title=\"Step $j\")\n",
    "end\n",
    "frame(anim,step_plot(A,Q̂,R̂,0))\n",
    "for j in 1:n\n",
    "    # Compute coefficients of aⱼ in Q̂[:,1:j-1] basis\n",
    "    R̂[1:j-1,j] = Q̂[:,1:j-1]' * Q̂[:,j]\n",
    "    # Project Q̂[:,1:j-1] components out of Q̂[:,j]\n",
    "    Q̂[:,j] -= Q̂[:,1:j-1] * R̂[1:j-1,j]\n",
    "    # Normalize\n",
    "    R̂[j,j] = norm(Q̂[:,j])\n",
    "    Q̂[:,j] /= R̂[j,j]\n",
    "    frame(anim,step_plot(A,Q̂,R̂,j))\n",
    "end\n",
    "frame(anim,step_plot(A,Q̂,R̂,n))\n",
    "gif(anim,fps=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e0b1a58",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Each step of CGS is a matrix transformation applied to $\\hat{Q}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5accaab3",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "```julia\n",
    "        # Project Q̂[:,1:j-1] components out of Q̂[:,j]\n",
    "        Q̂[:,j] -= Q̂[:,1:j-1] * R̂[1:j-1,j]\n",
    "```\n",
    "\n",
    "\"Subtract from column $j$: $r_{1,j} \\cdot$ column 1 and $r_{2,j} \\cdot$ column 2 and ...\"\n",
    "\n",
    "```julia\n",
    "        # Normalize\n",
    "        Q̂[:,j] /= R̂[j,j]\n",
    "```\n",
    "\n",
    "\"Scale column $j$ by $\\|r_{j,j}\\|^{-1}$\"\n",
    "\n",
    "(Remember warmup for lecture 2: each of these transformations is a matrix applied on the _right_)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae8cc31b",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Step $j$: multiply $\\hat{Q}$ by an upper-triangular matrix\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "    & & & & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "    & & & \\hat{Q} & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "\\end{bmatrix}\n",
    "\\gets\n",
    "\\begin{bmatrix}\n",
    "    & & & & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "    & & & \\hat{Q} & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "\\end{bmatrix}\n",
    "\\underbrace{\n",
    "\\begin{bmatrix}\n",
    "   1 & & & -r_{1,j} / r_{jj} & & & \\\\\n",
    "    & \\ddots & & \\vdots & & & \\\\\n",
    "    & & 1 & -r_{j-1,j} / r_{jj} & & & \\\\\n",
    "    & & & 1 / r_{jj} & & & \\\\\n",
    "    & & & & 1 & & \\\\\n",
    "    & & & & & \\ddots & \\\\\n",
    "    & & & & & & 1\n",
    "\\end{bmatrix}\n",
    "}_{Z_j}\n",
    "$$\n",
    "\n",
    "$Z_j$ is an upper-triangular matrix one nonzero column in column $j$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b4820e2",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### CGS Constructs $\\hat{Q}$ from $A$ by Triangular Orthogonalization\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    " & & \\\\\n",
    " & & \\\\\n",
    " & A & \\\\\n",
    " & & \\\\\n",
    " & & \\\\\n",
    "\\end{bmatrix}\n",
    "\\underbrace{\n",
    "\\begin{bmatrix}\n",
    "& & \\\\\n",
    "& Z_1 & \\\\\n",
    "& & \\\\\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "& & \\\\\n",
    "& Z_2 & \\\\\n",
    "& & \\\\\n",
    "\\end{bmatrix}\n",
    "\\dots\n",
    "\\begin{bmatrix}\n",
    "& & \\\\\n",
    "& Z_n & \\\\\n",
    "& & \\\\\n",
    "\\end{bmatrix}\n",
    "}_{\\hat{R}^{-1}}\n",
    "=\n",
    "\\begin{bmatrix}\n",
    " & & \\\\\n",
    " & & \\\\\n",
    " & \\hat{Q} & \\\\\n",
    " & & \\\\\n",
    " & & \\\\\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "The product of the $Z_j$'s is $\\hat{R}^{-1}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09e0b9e4",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Classical Gram-Schmidt meets its adversary: the Kahan matrix\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "& & & & \\\\\n",
    "& & & & \\\\\n",
    "& & M_\\theta & & \\\\\n",
    "& & & & \\\\\n",
    "& & & & \\\\\n",
    "\\end{bmatrix}\n",
    "=\n",
    "\\begin{bmatrix}\n",
    "1 & & & & \\\\\n",
    "& s & & & \\\\\n",
    "& & \\ddots & & \\\\\n",
    "& & & s^{n-2} & \\\\\n",
    "& & & & s^{n-1} \\\\\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "1 & -c & -c & \\dots & -c \\\\\n",
    "& 1 & -c & & -c \\\\\n",
    "& & \\ddots & \\ddots & \\vdots \\\\\n",
    "& & & 1 & -c\\\\\n",
    "& & & & 1 \\\\\n",
    "\\end{bmatrix}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "17d6fc54",
   "metadata": {
    "cell_style": "center"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "kahan (generic function with 1 method)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function kahan(m, θ)\n",
    "    s = sin(θ)\n",
    "    c = cos(θ)\n",
    "    S = Diagonal(s .^ collect(0:m-1))\n",
    "    K = UnitUpperTriangular(-c * ones(m,m))\n",
    "    return S * K\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "cc66b47b",
   "metadata": {
    "hideCode": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
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     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p0 = imshow(kahan(10,eps())); plot!(p0, title=\"θ = 0\")\n",
    "p4 = imshow(kahan(10,π/4)); plot!(p4, title=\"θ = π/4\")\n",
    "p2 = imshow(kahan(10,π/2)); plot!(p2, title=\"θ = π/2\")\n",
    "draw(plot(p0, p4, p2, layout=(1,3), size=(1300,800)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5bc36718",
   "metadata": {},
   "source": [
    "If $0 < \\theta < \\pi/2$, each column has its largest component in its first entry; the entries get smaller geometrically."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba79680f",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### CGS on a Kahan matrix vs. CGS on a perturbed Kahan matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "e42ec83a",
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reconstruction error || A - Q R ||_F = 0.0\n",
      "Orthonormality error || I - Q'Q ||_F = 0.0\n",
      "Upper-triangularity error || R - triu(R) ||_F = 0.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = 10; θ = π/20\n",
    "M = kahan(m, θ)\n",
    "Q, R = qr_classical_gram_schmidt(M)\n",
    "qr_test(M, Q, R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "12c35b45",
   "metadata": {
    "cell_style": "split",
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reconstruction error || A - Q R ||_F = 0.0\n",
      "Orthonormality error || I - Q'Q ||_F = 1.084717103369114\n",
      "Upper-triangularity error || R - triu(R) ||_F = 0.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "false"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ϕ = eps(Float64)\n",
    "M_p = copy(M[:,:])\n",
    "rot = [cos(ϕ) sin(ϕ); -sin(ϕ) cos(ϕ)]\n",
    "M_p[1:2,:] = rot * M[1:2,:]\n",
    "Q_p, R_p = qr_classical_gram_schmidt(M_p)\n",
    "qr_test(M_p, Q_p, R_p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "65da65df",
   "metadata": {},
   "outputs": [
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       "  \"/>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D = M - M_p; dscale = maximum(abs.(D)); p = imshow(D, (-dscale, dscale)); draw(plot!(p, size=(1300, 500)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "78e0dd13",
   "metadata": {
    "hideCode": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Saved animation to \n",
      "│   fn = /home/tisaac/srv/rep/22-course-cse6643/mybinder/tmp.gif\n",
      "└ @ Plots /home/tisaac/.julia/packages/Plots/Xv2qA/src/animation.jl:114\n"
     ]
    },
    {
     "data": {
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/>"
      ],
      "text/plain": [
       "Plots.AnimatedGif(\"/home/tisaac/srv/rep/22-course-cse6643/mybinder/tmp.gif\")"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = 10; n = 10;\n",
    "M = kahan(m, θ)\n",
    "M_p = copy(M[:,:])\n",
    "rot = [cos(ϕ) sin(ϕ); -sin(ϕ) cos(ϕ)]\n",
    "M_p[1:2,:] = rot * M[1:2,:]\n",
    "Q̂ = copy(M_p)\n",
    "R̂ = zeros(n, n)\n",
    "r_scale = maximum(abs.(qr(M_p).R))\n",
    "anim = Animation()\n",
    "function step_plot(A,Q̂,R̂,j)\n",
    "    Q_plot = imshow(Q̂,(-1,1))\n",
    "    plot!(Q_plot,title=\"Q\")\n",
    "    ortho_plot = imshow(Q̂' * Q̂)\n",
    "    plot!(ortho_plot,title=\"Q'Q\")\n",
    "    recon_plot = imshow(M_p - Q̂ * R̂,(-1,1))\n",
    "    plot!(recon_plot,title=\"M_p - QR\")\n",
    "    R_plot = imshow(R̂,(-r_scale,r_scale))\n",
    "    plot!(R_plot,title=\"R\")\n",
    "    return plot(Q_plot, R_plot, ortho_plot, recon_plot, layout=(1,4), size=(1300,800), plot_title=\"Step $j\")\n",
    "end\n",
    "frame(anim,step_plot(M_p,Q̂,R̂,0))\n",
    "for j in 1:n\n",
    "    # Compute coefficients of aⱼ in Q̂[:,1:j-1] basis\n",
    "    R̂[1:j-1,j] = Q̂[:,1:j-1]' * Q̂[:,j]\n",
    "    # Project Q̂[:,1:j-1] components out of Q̂[:,j]\n",
    "    Q̂[:,j] -= Q̂[:,1:j-1] * R̂[1:j-1,j]\n",
    "    # Normalize\n",
    "    R̂[j,j] = norm(Q̂[:,j])\n",
    "    Q̂[:,j] /= R̂[j,j]\n",
    "    frame(anim,step_plot(M_p,Q̂,R̂,j))\n",
    "end\n",
    "frame(anim,step_plot(M_p,Q̂,R̂,n))\n",
    "gif(anim,fps=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa9d4544",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### What happens in the last column of the perturbed Kahan matrix?\n",
    "\n",
    "$$ \\tilde{q}_m \\gets (I - P_{1:m-1}) a_m = a_m - q_1 q_1^* a_m - q_2 q_2^* a_m - \\dots $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78568248",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- In exact arithmetic, $\\|\\tilde{q}_m\\|_2$ is very small: $\\sin(\\theta)^{m-1} \\approx 6 \\cdot 10^{-8}$ "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8304b0ea",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Consider just the first projection:\n",
    "\n",
    "$$s_1 = a_m - q_1 (q_1^* a_m)$$\n",
    "  \n",
    "- In the presence of rounding error, a perturbed vector $\\hat s_1 = s_1 + \\delta_1$ is computed with error $\\delta_1$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40b0524e",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Later on in the class we will see that $\\|\\delta_1\\|$ is proportional to $\\epsilon\\|a_m\\|$, where $\\epsilon \\approx 10^{-16}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59ed3ebc",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### The accumulation of roundoff errors has swamped the result\n",
    "\n",
    "- There were similar small but growing errors in the previous $q_j$s.  Instead of calculating $\\tilde{q}_m$, we have calculated\n",
    "\n",
    "$$\\tilde{q}_m + \\delta_1 + \\delta_2 + \\dots + \\delta_{m-1}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0647c9e2",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- The errors are as big as the desired quantity, \n",
    "\n",
    "$$\\|\\tilde{q}_m\\| \\approx \\|\\delta_1 + \\delta_2 + \\dots + \\delta_{m-1}\\|.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a77012a2",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- When we then normalize, $q_m \\gets \\tilde{q}_m / \\|\\tilde{q}_m\\|$, the errors are magnified from $\\sim 10^{-8}$ to $\\sim 10^{0}$: catastrophe!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "1b5e70a3",
   "metadata": {
    "hideCode": true,
    "scrolled": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
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     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ortho_errs_cgs = Float64[]\n",
    "ortho_errs_qr = Float64[]\n",
    "recon_errs_cgs = Float64[]\n",
    "recon_errs_qr = Float64[]\n",
    "range = π ./ (2:.1:20)\n",
    "for θ in range\n",
    "    M = kahan(10, θ)\n",
    "    ϕ = eps(Float64)\n",
    "    M_p = copy(M[:,:])\n",
    "    rot = [cos(ϕ) sin(ϕ); -sin(ϕ) cos(ϕ)]\n",
    "    M_p[1:2,:] = rot * M[1:2,:]\n",
    "    Q_cgs, R_cgs = qr_classical_gram_schmidt(M_p)\n",
    "    Q, R = qr(M_p)\n",
    "    push!(ortho_errs_cgs, orthonormality_error(Q_cgs))\n",
    "    push!(ortho_errs_qr, orthonormality_error(Q[:,:]))\n",
    "    push!(recon_errs_cgs, reconstruction_error(M_p, Q_cgs, R_cgs))\n",
    "    push!(recon_errs_qr, reconstruction_error(M_p, Q, R))\n",
    "end\n",
    "ymin=Inf\n",
    "ymax=0.\n",
    "for series in [ortho_errs_cgs, ortho_errs_qr, recon_errs_cgs, recon_errs_qr]\n",
    "    series[:] = max.(series[:], 0.001*eps())\n",
    "    ymin = min(ymin, minimum(series))\n",
    "    ymax = max(ymax, maximum(series))\n",
    "end\n",
    "ymin *= 0.5\n",
    "ymax *= 2.0\n",
    "p1 = plot( range .^-1, [ortho_errs_cgs recon_errs_cgs]\n",
    "    , yscale=:log10\n",
    "    , label=[\"orthonormality error\" \"reconstruction error\"]\n",
    "    , xlabel=\"Kahan matrix θ⁻¹\"\n",
    "    , title=\"Classical Gram-Schmidt\"\n",
    "    , size=(1300,800)\n",
    "    , ylim=(ymin,ymax)\n",
    ")\n",
    "p2 = plot( range .^-1, [ortho_errs_qr recon_errs_qr]\n",
    "    , yscale=:log10\n",
    "    , label=[\"orthonormality error\" \"reconstruction error\"]\n",
    "    , xlabel=\"Kahan matrix θ⁻¹\"\n",
    "    , title=\"julia QR\"\n",
    "    , size=(1300,800)\n",
    "    , ylim=(ymin,ymax)\n",
    ")\n",
    "draw(plot(p1,p2,layout=(1,2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5167b904",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Modified Gram-Schmidt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b96277f7",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Consider projecting out two components of a vector\n",
    "\n",
    "Let $\\hat{Q} = [q_1 | q_2]$, and project out the $\\hat{Q}$ component of vector $v$,\n",
    "\n",
    "$$w \\gets (I - \\hat{Q} \\hat{Q}^*)v$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed9ee5ac",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "In exact arithmetic, these are equivalent:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80284220",
   "metadata": {
    "cell_style": "split",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "$$w \\gets (I - \\hat{Q}\\hat{Q}^*) v$$\n",
    "\n",
    "AKA:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "w^{(0)} &\\gets v - q_1 (q_1^* v) \\\\\n",
    "w &\\gets w^{(0)} - q_2 (q_2^* v)\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "586bd38b",
   "metadata": {
    "cell_style": "split"
   },
   "source": [
    "$$ w \\gets (I - q_2 q_2^*) ((I - q_1 q_1^*) v) $$\n",
    "\n",
    "AKA:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "w^{(0)} &\\gets v - q_1 (q_1^* v)\n",
    "\\\\\n",
    "w &\\gets w^{(0)} - q_2 (q_2^* w^{(0)})\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e124667a",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Floating point rounding error scales like the inputs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b8eff7f",
   "metadata": {
    "cell_style": "split",
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     "slide_type": "-"
    }
   },
   "source": [
    "$$\n",
    "\\begin{aligned}\n",
    "w^{(0)} &\\gets \\underbrace{v - q_1 (q_1^* v)}_{\\delta_1 \\sim \\epsilon \\|v\\|} \\\\\n",
    "w &\\gets \\underbrace{w^{(0)} - q_2 (q_2^* v)}_{\\delta_2 \\sim \\epsilon \\max\\{\\|w^{(0)}\\|,\\|v\\|\\}}\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2fd61533",
   "metadata": {
    "cell_style": "split",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "$$\n",
    "\\begin{aligned}\n",
    "w^{(0)} &\\gets \\underbrace{v - q_1 (q_1^* v)}_{\\delta_1 \\sim \\epsilon \\|v\\|} \\\\\n",
    "w &\\gets \\underbrace{w^{(0)} - q_2 (q_2^* w^{(0)})}_{\\delta_2 \\sim \\epsilon \\|w^{(0)}\\|}\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e332ed4f",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- The first approach (calculating every projection coefficient $(q_i^*v)$ with the original vector) accumulates a rounding error $\\sim \\epsilon \\|v\\|$ _for each projection_,\n",
    "$\\sim \\epsilon(\\|v\\| + \\|v\\| + \\|v\\| + \\dots)$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "270ab155",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- The second approach (calculating $q_j$'s projection coefficient on the result of the previous projections) accumulates rounding errors $\\sim \\epsilon (\\|v\\| + \\|(I-P_1)v\\| + \\|(I-P_{1:2})v\\| + \\dots)$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44208f92",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Orthogonal projection can only make a vector smaller, $\\|v\\| \\geq \\|(I - P_1) v\\| \\geq \\|(I - P_{1:2})v \\| \\geq \\dots$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf078dd4",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Exercise: Modified Gram-Schmidt (forward looking)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "afe8d4ed",
   "metadata": {
    "cell_style": "split"
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   "source": [
    "At step $i$:\n",
    "\n",
    "1. Normalize:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "r_{i,i} &\\gets \\|\\tilde{q}_i\\| \\\\\n",
    "q_j &\\gets \\tilde{q}_i / r_{ii}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "2. Project $q_i$ out of all subsequent vectors $j > i$\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "r_{i,j} &\\gets q_i^* \\tilde{q}_j \\\\\n",
    "\\tilde{q}_j &\\gets \\tilde{q}_j - r_{i,j} q_i \n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "e1ae8296",
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reconstruction error || A - Q R ||_F = 3.5760557644884744e-16\n",
      "Orthonormality error || I - Q'Q ||_F = 4.1279265136313973e-16\n",
      "Upper-triangularity error || R - triu(R) ||_F = 0.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
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     "execution_count": 65,
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   ],
   "source": [
    "function cg_modified_gram_schmidt(A)\n",
    "    n = size(A)[2]\n",
    "    Q = copy(A)\n",
    "    R = zeros(eltype(A), n, n)\n",
    "    for i in 1:n\n",
    "        # precondition: Q[:,i] is orthogonal to prec.\n",
    "        R[i,i] = norm(Q[:,i])\n",
    "        Q[:,i] /= R[i,i]\n",
    "        R[i,i+1:end] = Q[:,i]' * Q[:,i+1:end]\n",
    "        Q[:,i+1:end] -= Q[:,[i]] * R[[i],i+1:end]\n",
    "    end\n",
    "    return Q, R\n",
    "end\n",
    "m = 10; n = 5;\n",
    "A = randn(m,n)\n",
    "Q, R = cg_modified_gram_schmidt(A)\n",
    "qr_test(A, Q, R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "c5fd7db0",
   "metadata": {
    "hideCode": true,
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      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function mgs(A)\n",
    "    m, n = size(A)\n",
    "    Q = copy(A)\n",
    "    R = zeros(eltype(A), n, n)\n",
    "    for i in 1:n\n",
    "        R[i,i] = norm(Q[:,i])\n",
    "        Q[:,i] /= R[i,i]\n",
    "        R[i,i+1:end] = Q[:,i]' * Q[:,i+1:end]\n",
    "        Q[:,i+1:end] -= Q[:,[i]] * R[[i],i+1:end]\n",
    "    end\n",
    "    return Q, R\n",
    "end\n",
    "ortho_errs_mgs = Float64[]\n",
    "recon_errs_mgs = Float64[]\n",
    "for θ in range\n",
    "    M = kahan(10, θ)\n",
    "    ϕ = eps(Float64)\n",
    "    M_p = copy(M[:,:])\n",
    "    rot = [cos(ϕ) sin(ϕ); -sin(ϕ) cos(ϕ)]\n",
    "    M_p[1:2,:] = rot * M[1:2,:]\n",
    "    Q_mgs, R_mgs = mgs(M_p)\n",
    "    push!(ortho_errs_mgs, orthonormality_error(Q_mgs))\n",
    "    push!(recon_errs_mgs, reconstruction_error(M_p, Q_mgs, R_mgs))\n",
    "end\n",
    "ymin=Inf\n",
    "ymax=0.\n",
    "for series in [ortho_errs_cgs, ortho_errs_qr, recon_errs_mgs, recon_errs_mgs]\n",
    "    series[:] = max.(series[:], 0.001*eps())\n",
    "    ymin = min(ymin, minimum(series))\n",
    "    ymax = max(ymax, maximum(series))\n",
    "end\n",
    "ymin *= 0.5\n",
    "ymax *= 2.0\n",
    "p1 = plot( range .^-1, [ortho_errs_cgs recon_errs_cgs]\n",
    "    , yscale=:log10\n",
    "    , label=[\"orthonormality error\" \"reconstruction error\"]\n",
    "    , xlabel=\"Kahan matrix θ⁻¹\"\n",
    "    , title=\"Classical Gram-Schmidt\"\n",
    "    , size=(1300,800)\n",
    "    , ylim=(ymin,ymax)\n",
    ")\n",
    "p2 = plot( range .^-1, [ortho_errs_mgs recon_errs_mgs]\n",
    "    , yscale=:log10\n",
    "    , label=[\"orthonormality error\" \"reconstruction error\"]\n",
    "    , xlabel=\"Kahan matrix θ⁻¹\"\n",
    "    , title=\"Modified Gram-Schmidt\"\n",
    "    , size=(1300,800)\n",
    "    , ylim=(ymin,ymax)\n",
    ")\n",
    "draw(plot(p1,p2,layout=(1,2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a4ffffb",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Modified Gram-Schmidt in Action (go back and compare)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "afe5b4ce",
   "metadata": {
    "hideCode": true,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Saved animation to \n",
      "│   fn = /home/tisaac/srv/rep/22-course-cse6643/mybinder/tmp.gif\n",
      "└ @ Plots /home/tisaac/.julia/packages/Plots/Xv2qA/src/animation.jl:114\n"
     ]
    },
    {
     "data": {
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\" />"
      ],
      "text/plain": [
       "Plots.AnimatedGif(\"/home/tisaac/srv/rep/22-course-cse6643/mybinder/tmp.gif\")"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = 10; n = 5;\n",
    "A = randn(m, n)\n",
    "A /= maximum(abs.(A))\n",
    "Q̂ = copy(A)\n",
    "R̂ = zeros(n, n)\n",
    "r_scale = maximum(abs.(qr(A).R))\n",
    "anim = Animation()\n",
    "function step_plot(A,Q̂,R̂,j)\n",
    "    Q_plot = imshow(Q̂,(-1,1))\n",
    "    plot!(Q_plot,title=\"Q\")\n",
    "    ortho_plot = imshow(Q̂' * Q̂,(-1,1))\n",
    "    plot!(ortho_plot,title=\"Q'Q\")\n",
    "    recon_plot = imshow(A - Q̂ * R̂,(-1,1))\n",
    "    plot!(recon_plot,title=\"A - QR\")\n",
    "    R_plot = imshow(R̂,(-r_scale,r_scale))\n",
    "    plot!(R_plot,title=\"R\")\n",
    "    return plot(Q_plot, R_plot, ortho_plot, recon_plot, layout=(1,4), size=(1300,800), plot_title=\"Step $j\")\n",
    "end\n",
    "frame(anim,step_plot(A,Q̂,R̂,0))\n",
    "for i in 1:n\n",
    "    R̂[i,i] = norm(Q̂[:,i])\n",
    "    Q̂[:,i] /= R̂[i,i]\n",
    "    R̂[i,i+1:end] = Q̂[:,i]' * Q̂[:,i+1:end]\n",
    "    Q̂[:,i+1:end] -= Q̂[:,[i]] * R̂[[i],i+1:end]\n",
    "    frame(anim,step_plot(A,Q̂,R̂,i))\n",
    "end\n",
    "frame(anim,step_plot(A,Q̂,R̂,n))\n",
    "gif(anim,fps=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e11f700",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Modified Gram-Schmidt also constructs $\\hat{Q}$ by Triangular Orthogonalization\n",
    "\n",
    "At step $i$:\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "    & & & & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "    & & & \\hat{Q} & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "\\end{bmatrix}\n",
    "\\gets\n",
    "\\begin{bmatrix}\n",
    "    & & & & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "    & & & \\hat{Q} & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "    & & & & & & \\\\\n",
    "\\end{bmatrix}\n",
    "\\underbrace{\n",
    "\\begin{bmatrix}\n",
    "   1 & & & & & & \\\\\n",
    "    & \\ddots & & & & & \\\\\n",
    "    & & 1 & & & & \\\\\n",
    "    & & & \\frac{1}{r_{ii}} & \\frac{-r_{i,i+1}}{r_{ii}} & \\dots & \\frac{-r_{i,n}}{r_{ii}} \\\\\n",
    "    & & & & 1 & & \\\\\n",
    "    & & & & & \\ddots & \\\\\n",
    "    & & & & & & 1\n",
    "\\end{bmatrix}\n",
    "}_{Z_i}\n",
    "$$\n",
    "\n",
    "$Z_i$ is an upper-triangular matrix with one nonzero row in row $i$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40812f45",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Notes on HW2, problem 4\n",
    "\n",
    "You have seen CGS and MGS in this lecture.  It will probably take you more time to construct the plot.\n",
    "The syntax is intentionally similar to MATLAB / matplotlib, but for reference, go to <https://docs.juliaplots.org>."
   ]
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   "source": [
    "## Gram-Schmidt Complexity"
   ]
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   "source": [
    "### Matrx-Matrix Product Complexity\n",
    "\n",
    "Given matrices $A\\in \\mathbb{C}^{M \\times K}$, $B \\in \\mathbb{C}^{K \\times N}$, and $C \\in \\mathbb{C}^{M \\times N}$, the work $W$ measured in _floating point operations_ (\"flops\") of computing $C \\gets C - AB$ using the standard approach is\n",
    "\n",
    "$$W(C - A \\cdot B) = 2 M N K,$$\n",
    "\n",
    "which is clear from looking at the algorithm written component-wise:\n",
    "\n",
    "```julia\n",
    "for i in 1:M                          # M times ...\n",
    "    for j in 1:N                      # N times ...\n",
    "        for p in 1:K                  # K times ...\n",
    "            C[i,j] -= A[i,p] * B[p,j] # 2 flops per inner loop\n",
    "        end\n",
    "    end\n",
    "end\n",
    "            \n",
    "```"
   ]
  },
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   "source": [
    "if we just compute $C \\gets A B$, there is one subtraction less per entry of $C$, so\n",
    "\n",
    "$$W(A \\cdot B) = 2 M N K - M N.$$"
   ]
  },
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   "source": [
    "### Projection Orthogonalization Complexity\n",
    "\n",
    "If $\\hat{Q} \\in \\mathbb{C}^{m \\times j}$ and $a \\in \\mathbb{C}^m$, what is the complexity of\n",
    "\n",
    "$$\\tilde{q} \\gets a - \\hat{Q}(\\hat{Q}^*a)?$$"
   ]
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   "source": [
    "Rephrase as:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "r &\\gets \\hat{Q}^* a \\\\\n",
    "\\tilde{q} &\\gets a - \\hat{Q}r\n",
    "\\end{aligned}\n",
    "$$"
   ]
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   "source": [
    "- First line is like $C \\gets A B$ with $M = j$, $N = 1$, and $K = m$, so $W = 2 M N K - M N = 2jm - j$."
   ]
  },
  {
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   "id": "973bc374",
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   "source": [
    "- Second line is like $C \\gets C - AB$ with $M = m$, $N = 1$ and $K = j$, so $W = 2 M N K = 2jm$"
   ]
  },
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   "source": [
    "- Total,\n",
    "\n",
    "$$W((I - \\hat{Q}\\hat{Q}^*) a) = 4 jm - j.$$"
   ]
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       "qr_classical_gram_schmidt (generic function with 1 method)"
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   "source": [
    "function qr_classical_gram_schmidt(A)\n",
    "    m, n = size(A)\n",
    "    Q̂ = copy(A)\n",
    "    R̂ = zeros(eltype(A), n, n)\n",
    "    for j in 1:n\n",
    "        # Project\n",
    "        R̂[1:j-1,j] = Q̂[:,1:j-1]' * Q̂[:,j] # 2 m j - j\n",
    "        Q̂[:,j] -= Q̂[:,1:j-1] * R̂[1:j-1,j] # 2 m j\n",
    "        # Normalize\n",
    "        R̂[j,j] = norm(Q̂[:,j])             # 2 m\n",
    "        Q̂[:,j] /= R̂[j,j]                  # m\n",
    "    end\n",
    "    return Q̂, R̂\n",
    "end"
   ]
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   "source": [
    "- Total work in iteration $j$:\n",
    "\n",
    "$$4mj - j + 3 m$$"
   ]
  },
  {
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   "source": [
    "- Total (sum for $j = 1, \\dots, n$):\n",
    "\n",
    "$$\n",
    "W(CGS) = \\sum_{j=1}^n 4mj - j + 3m = \\left\\{(4m - 1) \\sum_{j=1}^n j\\right\\} + \\left\\{3m \\sum_{j=1}^n 1\\right\\}.\n",
    "$$"
   ]
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   "source": [
    "$$W(CGS) = (4m-1)\\frac{1}{2}n(n+1) + 3mn = 2 m n^2 + \\underbrace{\\dots}_{\\text{(lower order terms)}}.$$"
   ]
  },
  {
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   "source": [
    "### Summarize using just the leading term\n",
    "\n",
    "$$W(CGS) \\sim 2 mn^2,$$\n",
    "\n",
    "which means\n",
    "\n",
    "$$ \\lim_{\\min\\{m,n\\} \\to \\infty} \\frac{W(CGS)}{2 m n^2} = 1. $$"
   ]
  },
  {
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   "id": "0f8e8917",
   "metadata": {
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   "source": [
    "### Exercise\n",
    "\n",
    "Convince yourself that $W(MGS) = W(CGS) \\sim 2 m n^2.$"
   ]
  },
  {
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   "source": [
    "### Caveats on the meaning of work $W$\n",
    "\n",
    "- On a serial computer, runtime $T$ should scale like $W$ for large enough inputs.\n",
    "- $W$ does not count moving data to/from the processor, which is more expensive than arithmetic.\n",
    "- Implementation-dependent leading constants are going to be very important, so its possible to have two algorithms with $W_1 < W_2$ but $T_2 < T_1$.\n",
    "- All computers use parallelism for numerical linear algebra now.  $W$ says nothing about how _concurrent_ (parallelizable) CGS and WGS are, so $W$ alone is not enough to understand the performance of an algorithm."
   ]
  }
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