cpp/scaled-norm.ipynb

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     "execution_count": 1,
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   "source": [
    "#include <cmath>\n",
    "#include <iostream>\n",
    "#include <limits>\n",
    "\n",
    "using namespace std;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
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     "data": {
      "text/plain": [
       "(double) 0.000000\n"
      ]
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     "execution_count": 2,
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   "source": [
    "double epsilon = numeric_limits<double>::epsilon();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(double [2]) { 1.000000, 1.000000 }\n"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "double x[2] = {1, 1};"
   ]
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   ],
   "source": [
    "double normNaive(double* x) {\n",
    "    double normSquared = 0;\n",
    "    for (int i = 0; i < 2; i++)\n",
    "        normSquared += x[i] * x[i];\n",
    "    return sqrt(normSquared);\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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     "text": [
      "1.41421\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(std::__1::basic_ostream &) @0x7fffcfcfa660\n"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "cout << normNaive(x) << endl;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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     "execution_count": 7,
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   ],
   "source": [
    "double normBetter(double* x, int n) {\n",
    "    double maxElement = epsilon;\n",
    "    double normSquared = 0;\n",
    "    \n",
    "    for (int i=0; i < n; i++) {\n",
    "        maxElement = max(maxElement, fabs(x[i]));\n",
    "    }\n",
    "    \n",
    "    for (int i=0; i < n; i++) {\n",
    "        double scaled = x[i] / maxElement;\n",
    "        normSquared += scaled * scaled;\n",
    "    }\n",
    "    \n",
    "    return sqrt(normSquared) * maxElement;\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.41421\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(std::__1::basic_ostream &) @0x7fffcfcfa660\n"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cout << normBetter(x, 2) << endl;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(double) 1.414214\n"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "normBetter(x, 2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(double) 3.741657\n"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "normBetter((double[3]){1,2,3}, 3);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(double) 5.477226\n"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "normBetter((double[4]){1,2,3,4}, 4);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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