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   "cell_type": "markdown",
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   "source": [
    "# Minimal number of runs for an orthognal array"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example we calculate the minimum number of runs required for an orthogonal array. For more details, see [Schoen et al.](https://onlinelibrary.wiley.com/doi/abs/10.1002/jcd.20236)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import itertools\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "def minimum_number_of_runs(factor_levels, strength):\n",
    "    \"\"\"Calculate the minimum number of runs for an orthogonal array\n",
    "\n",
    "    The minimum number of runs is based on the strength conditions. IWhether a design actually exists\n",
    "    Args:\n",
    "        factor_levels: Factor levels of the design\n",
    "        strength: Strength of the array\n",
    "    Returns:\n",
    "        Minimum number of runs\n",
    "\n",
    "    \"\"\"\n",
    "    runs = [np.prod(tt) for tt in itertools.combinations(factor_levels, strength)]\n",
    "    N = np.lcm.reduce(runs)\n",
    "    return N"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We run the method on several examples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "for a design of strength 3 and factor levels [2, 3, 3, 4, 5] we require (a multiple of) 360 runs\n"
     ]
    }
   ],
   "source": [
    "strength = 3\n",
    "factor_levels = [2, 3, 3, 4, 5]\n",
    "N = minimum_number_of_runs(factor_levels, strength)\n",
    "\n",
    "print(f\"for a design of strength {strength} and factor levels {factor_levels} we require (a multiple of) {N} runs\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "for a design of strength 2 and factor levels [3, 2, 2, 2, 2] we require (a multiple of) 12 runs\n"
     ]
    }
   ],
   "source": [
    "strength = 2\n",
    "factor_levels = [3, 2, 2, 2, 2]\n",
    "N = minimum_number_of_runs(factor_levels, strength)\n",
    "\n",
    "print(f\"for a design of strength {strength} and factor levels {factor_levels} we require (a multiple of) {N} runs\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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