{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Enumerate orthogonal arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Orthogonal Array package can completely enumerate all orthogonal arrays of a specified class. In this notebook, we enumerate specific classes of three-level orthogonal arrays and  mixel-level orthogonal arrays."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we specify the class of three-level orthogonal arrays to enumerate. For example, we consider three-level orthogonal arrays of strength 2 with 27 runs and 8 factors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "arrayclass: N 27, k 8, strength 2, s {3,3,3,3,3,3,3,3}, order 0\n"
     ]
    }
   ],
   "source": [
    "import oapackage\n",
    "\n",
    "run_size = 27\n",
    "strength = 2\n",
    "number_of_factors = 8\n",
    "factor_levels = 3\n",
    "arrayclass = oapackage.arraydata_t(factor_levels, run_size, strength, number_of_factors)\n",
    "print(arrayclass)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Second, we create the root array as the starting point of our enumeration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "00\n",
      "00\n",
      "00\n",
      "01\n",
      "01\n",
      "01\n",
      "02\n",
      "02\n",
      "02\n",
      "10\n",
      "10\n",
      "10\n",
      "11\n",
      "11\n",
      "11\n",
      "12\n",
      "12\n",
      "12\n",
      "20\n",
      "20\n",
      "20\n",
      "21\n",
      "21\n",
      "21\n",
      "22\n",
      "22\n",
      "22\n"
     ]
    }
   ],
   "source": [
    "ll2 = [arrayclass.create_root()]\n",
    "ll2[0].showarraycompact()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Third, extend the root array. It is also possible to extend a list of arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "extended to 9 arrays with 3 columns\n",
      "extended to 711 arrays with 4 columns\n"
     ]
    }
   ],
   "source": [
    "list3columns = oapackage.extend_arraylist(ll2, arrayclass)\n",
    "print(\"extended to %d arrays with 3 columns\" % len(list3columns))\n",
    "list4columns = oapackage.extend_arraylist(list3columns, arrayclass)\n",
    "print(\"extended to %d arrays with 4 columns\" % len(list4columns))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is also possible to extend selected arrays from a list."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "extended first 2 arrays to 189 arrays with 5 columns\n"
     ]
    }
   ],
   "source": [
    "ll = oapackage.extend_arraylist(list4columns[0:8], arrayclass)\n",
    "print(\"extended first 2 arrays to %d arrays with 5 columns\" % len(ll))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By adding one column at a time we can enumerate all three-level orthogonal arrays of strength 2 with 27 runs and 8 factors. The total computation time for this would be a couple of hours."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mixed-level orthogonal arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The package can also enumerate mixed-level orthogonal arrays. For instance, consider enumerating all 16-run strength-2 orthogonal arrays with one four-level factor and nine two-level factors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "arrayclass: N 16, k 10, strength 2, s {4,2,2,2,2,2,2,2,2,2}, order 0\n"
     ]
    }
   ],
   "source": [
    "run_size = 16\n",
    "strength = 2\n",
    "number_of_factors = 10\n",
    "factor_levels = [4, 2, 2, 2, 2, 2, 2, 2, 2, 2]\n",
    "arrayclass = oapackage.arraydata_t(factor_levels, run_size, strength, number_of_factors)\n",
    "print(arrayclass)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the root array as the starting point of our enumeration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "00\n",
      "00\n",
      "01\n",
      "01\n",
      "10\n",
      "10\n",
      "11\n",
      "11\n",
      "20\n",
      "20\n",
      "21\n",
      "21\n",
      "30\n",
      "30\n",
      "31\n",
      "31\n"
     ]
    }
   ],
   "source": [
    "al = arrayclass.create_root()\n",
    "al.showarraycompact()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For these arrays, we can extend a single array or lists of arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "extended to 3 arrays with 3 columns\n",
      "extended to 10 arrays with 4 columns\n"
     ]
    }
   ],
   "source": [
    "array_list = [arrayclass.create_root()]\n",
    "array_list_3columns = oapackage.extend_arraylist(array_list, arrayclass)\n",
    "array_list_4columns = oapackage.extend_arraylist(array_list_3columns, arrayclass)\n",
    "print(\"extended to %d arrays with 3 columns\" % len(array_list_3columns))\n",
    "print(\"extended to %d arrays with 4 columns\" % len(array_list_4columns))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, enumerate all 16-run strength-2 orthogonal arrays with one four-level factor and nine two-level factors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "extended to 28 arrays with 5 columns\n",
      "extended to 65 arrays with 6 columns\n",
      "extended to 110 arrays with 7 columns\n",
      "extended to 123 arrays with 8 columns\n",
      "extended to 110 arrays with 9 columns\n",
      "extended to 72 arrays with 10 columns\n"
     ]
    }
   ],
   "source": [
    "arrays = array_list_4columns\n",
    "for extension_column in range(5, number_of_factors + 1):\n",
    "    extensions = oapackage.extend_arraylist(arrays, arrayclass)\n",
    "    print(\"extended to %d arrays with %d columns\" % (len(extensions), extension_column))\n",
    "    arrays = extensions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Notes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The numbers of isomorphism classes for various types of classes can be found at the webpage <a href=\"http://www.pietereendebak.nl/oapackage/series.html\">series of orthogonal arrays</a>.\n",
    "* For larger number of arrays the command line tools are more convenient and more memory efficient."
   ]
  }
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