N3Presults.ipynb

{
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   "cell_type": "markdown",
   "id": "c1fecce6",
   "metadata": {},
   "source": [
    "$\\newcommand{\\calf}{{\\cal F}}\n",
    "\\newcommand{\\dnu}{d \\nu}\n",
    "\\newcommand{\\mf}{{\\bf F}}\n",
    "\\newcommand{\\md}{{\\bf D}}\n",
    "\\newcommand{\\mP}{{\\bf P}}\n",
    "\\newcommand{\\mU}{{\\bf U}}\n",
    "\\newcommand{\\vu}{{\\bf u}}\n",
    "\\newcommand{\\vx}{{\\bf x}}\n",
    "\\newcommand{\\vw}{{\\bf w}}\n",
    "\\newcommand{\\vy}{{\\bf y}}\n",
    "\\newcommand{\\vf}{{\\bf f}}\n",
    "\\newcommand{\\vs}{{\\bf s}}\n",
    "\\newcommand{\\ve}{{\\bf e}}\n",
    "\\newcommand{\\vd}{{\\bf d}}\n",
    "\\newcommand{\\vb}{{\\bf b}}\n",
    "\\newcommand{\\vz}{{\\bf z}}\n",
    "\\newcommand{\\mg}{{\\bf G}}\n",
    "\\newcommand{\\ml}{{\\bf L}}\n",
    "\\newcommand{\\mg}{{\\bf G}}\n",
    "\\newcommand{\\mv}{{\\bf V}}\n",
    "\\newcommand{\\ma}{{\\bf A}}\n",
    "\\newcommand{\\mi}{{\\bf I}}\n",
    "\\newcommand{\\mm}{{\\bf M}}\n",
    "\\newcommand{\\mb}{{\\bf B}}\n",
    "\\newcommand{\\ball}{{\\cal B}}\n",
    "\\newcommand{\\ptc}{{\\Psi TC}}\n",
    "\\newcommand{\\diag}{\\mbox{diag}}\n",
    "\\newcommand{\\begeq}{{\\begin{equation}}}\n",
    "\\newcommand{\\endeq}{{\\end{equation}}}\n",
    "$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "aade7b0c",
   "metadata": {},
   "outputs": [],
   "source": [
    "include(\"n3pnote.jl\"); "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ecf8540",
   "metadata": {},
   "source": [
    "Here is an example from <cite data-cite=\"ctk:roots\"><a href=\"n3pbib.html#ctk:roots\">(Kel95)</cite> and \n",
    "    <cite data-cite=\"ctk:sirev20\"><a href=\"n3pbib.html#ctk:sirev20\">(Kel22a)</cite>,\n",
    "<cite data-cite=\"ctk:fajulia\"><a href=\"n3pbib.html#ctk:fajulia\">(Kel22d)</cite>,\n",
    "<cite data-cite=\"ctk:notebooknl\"><a href=\"n3pbib.html#ctk:notebooknl\">(Kel22b)</cite>, and\n",
    "<cite data-cite=\"ctk:n3pbibnl\"><a href=\"n3pbib.html#ctk:Newton3p\">(Kel22c)</cite>.\n",
    "    \n",
    "This notebook reproduces the results from the paper\n",
    "    \n",
    "C. T. Kelley, _Newton's Method in Three Precisions_, 2023, <cite data-cite=\"ctk:n3pbibnl\"><a href=\"n3pbib.html#ctk:Newrton3p\">(Kel23)</cite>\n",
    "    \n",
    "The example is the Chandrasekhar H-equation <cite data-cite=\"ctk:n3pbibnl\"><a href=\"n3pbib.html#chand\">(Cha60)</cite>.\n",
    "    \n",
    "The computations were done in Julia <cite data-cite=\"Juliasirev\"><a href=\"n3pbib.html#Juliasirev\">(BEKS17)</cite>\n",
    "    \n",
    "We use the software from <cite data-cite=\"ctk:fajulia\"><a href=\"n3pbib.html#ctk:fajulia\">(Kel22d)</cite>,\n",
    "<cite data-cite=\"ctk:notebooknl\"><a href=\"n3pbib.html#ctk:notebooknl\">(Kel22b)</cite>, and\n",
    "<cite data-cite=\"ctk:n3pbibnl\"><a href=\"n3pbib.html#ctk:siamfanl\">(Kel22c)</cite>. Our nonlinear solvers from <cite data-cite=\"ctk:n3pbibnl\"><a href=\"n3pbib.html#ctk:siamfanl\">(Kel22c)</cite> work well with our data structures for iterative refinement. The Julia module with the data structures we use for IR is ```src/N3Presults.jl```\n",
    "    \n",
    "The results are in Table 2 and Table 3.\n",
    "    \n",
    "The first computation generates Table 2. This is the ill-conditioned example from <cite data-cite=\"ctk:sirev20\"><a href=\"n3pbib.html#ctk:sirev20\">(Kel22a)</cite> and is the well conditioned example from the paper. The function that creates the examples is the Julia function ```htest1``` from the file ```H_equation_examples.jl```. We also put a plot in this notebook.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0717d534",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximum iterations (maxit) of 10 exceeded\n",
      "Convergence failure: residual norm too large  4.05010e-01\n",
      "Try increasing maxit and checking your function and\n",
      "                 Jacobian for bugs.\n",
      "Give the history array a look to see what's happening.\n",
      "  \n",
      "\\begin{tabular}{llllll} \n",
      " n&        F64&        F32&        F16&   IR 32-16&      IR-GM \\\\ \\hline \n",
      " 0 &  1.000e+00 &  1.000e+00 &  1.000e+00 &  1.000e+00 &  1.000e+00  \\\\ \n",
      " 1 &  2.289e-01 &  2.289e-01 &  5.065e-01 &  2.289e-01 &  2.289e-01  \\\\ \n",
      " 2 &  3.934e-02 &  3.934e-02 &  2.958e-01 &  3.934e-02 &  3.934e-02  \\\\ \n",
      " 3 &  2.737e-03 &  2.737e-03 &  1.890e-01 &  2.737e-03 &  2.737e-03  \\\\ \n",
      " 4 &  1.767e-05 &  1.767e-05 &  1.255e-01 &  1.767e-05 &  1.767e-05  \\\\ \n",
      " 5 &  7.486e-10 &  7.536e-10 &  8.518e-02 &  7.538e-10 &  7.506e-10  \\\\ \n",
      " 6 &            &            &  6.068e-02 &            &             \\\\ \n",
      " 7 &            &            &  4.240e-02 &            &             \\\\ \n",
      " 8 &            &            &  3.195e-02 &            &             \\\\ \n",
      " 9 &            &            &  2.280e-02 &            &             \\\\ \n",
      "10 &            &            &  1.713e-02 &            &             \\\\ \n",
      "\\hline \n",
      "\\end{tabular} \n",
      "[1.62595e-10 1.50632e-10 5.97601e-02]\n",
      "[6 6 11 6 6]\n",
      "1.75821e-06\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "PyPlot.Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "htest1(4096,.99);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d82774e3",
   "metadata": {},
   "source": [
    "Table 3 is a very ill-conditioned example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "81cddf26",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximum iterations (maxit) of 10 exceeded\n",
      "Convergence failure: residual norm too large  7.07016e-01\n",
      "Try increasing maxit and checking your function and\n",
      "                 Jacobian for bugs.\n",
      "Give the history array a look to see what's happening.\n",
      "  \n",
      "Maximum iterations (maxit) of 10 exceeded\n",
      "Convergence failure: residual norm too large  1.06833e-02\n",
      "Try increasing maxit and checking your function and\n",
      "                 Jacobian for bugs.\n",
      "Give the history array a look to see what's happening.\n",
      "  \n",
      "\\begin{tabular}{llllll} \n",
      " n&        F64&        F32&        F16&   IR 32-16&      IR-GM \\\\ \\hline \n",
      " 0 &  1.000e+00 &  1.000e+00 &  1.000e+00 &  1.000e+00 &  1.000e+00  \\\\ \n",
      " 1 &  2.494e-01 &  2.494e-01 &  5.182e-01 &  2.494e-01 &  2.494e-01  \\\\ \n",
      " 2 &  6.093e-02 &  6.093e-02 &  3.123e-01 &  6.093e-02 &  6.093e-02  \\\\ \n",
      " 3 &  1.480e-02 &  1.480e-02 &  2.067e-01 &  1.480e-02 &  1.480e-02  \\\\ \n",
      " 4 &  3.454e-03 &  3.454e-03 &  1.421e-01 &  3.455e-03 &  3.454e-03  \\\\ \n",
      " 5 &  6.762e-04 &  6.762e-04 &  1.012e-01 &  6.766e-04 &  6.762e-04  \\\\ \n",
      " 6 &  7.049e-05 &  7.049e-05 &  7.552e-02 &  6.360e-04 &  7.049e-05  \\\\ \n",
      " 7 &  1.223e-06 &  1.223e-06 &  5.773e-02 &  5.811e-04 &  1.223e-06  \\\\ \n",
      " 8 &  3.947e-10 &  3.957e-10 &  4.543e-02 &  5.312e-04 &  3.952e-10  \\\\ \n",
      " 9 &            &            &  3.639e-02 &  4.862e-04 &             \\\\ \n",
      "10 &            &            &  2.949e-02 &  4.456e-04 &             \\\\ \n",
      "\\hline \n",
      "\\end{tabular} \n",
      "[1.07201e-02 1.58618e-10 2.82749e-01]\n",
      "[9 9 11 11 9]\n",
      "1.02072e-06\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "htest1(4096,.9999);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.9.1",
   "language": "julia",
   "name": "julia-1.9"
  },
  "language_info": {
   "file_extension": ".jl",
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