docs/examples/example_optimal_orthogonal_arrays.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generate orthogonal arrays with high D-efficiency"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook contains example code from the article [Two-level designs to estimate all main effects and two-factor interactions](https://doi.org/10.1080/00401706.2016.1142903) by Eendebak, P. T. and Schoen, E. D.\n",
    "This example shows how to generate orthogonal arrays with a high $D$-efficiency in a reasonable amount of time (< 1 minute). For more results and details, see the paper.\n",
    "\n",
    "Generate a D-optimal orthogonal array of strength 2 with 32 runs and 7 factors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "import oapackage\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "In this example we generate orthogonal arrays in the class: arrayclass: N 32, k 7, strength 2, s {2,2,2,2,2,2,2}, order 0\n"
     ]
    }
   ],
   "source": [
    "run_size = 32\n",
    "number_of_factors = 7\n",
    "factor_levels = 2\n",
    "strength = 2\n",
    "nkeep = 24  # Number of designs to keep at each stage\n",
    "\n",
    "arrayclass = oapackage.arraydata_t(factor_levels, run_size, strength, number_of_factors)\n",
    "print(\"In this example we generate orthogonal arrays in the class: %s\" % arrayclass)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, generate orthogonal arrays with the function `extend_arraylist`. Next, keep the arrays with the best $D$-efficiency."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "extend 1 arrays with 2 columns with a single column\n",
      "  generated 5 arrays, selected 5 arrays with D-efficiency 0.0000 to 1.0000\n",
      "extend 5 arrays with 3 columns with a single column\n",
      "  generated 19 arrays, selected 19 arrays with D-efficiency 0.0000 to 1.0000\n",
      "extend 19 arrays with 4 columns with a single column\n",
      "  generated 491 arrays, selected 24 arrays with D-efficiency 0.9183 to 1.0000\n",
      "extend 24 arrays with 5 columns with a single column\n",
      "  generated 2475 arrays, selected 24 arrays with D-efficiency 0.9196 to 1.0000\n",
      "extend 24 arrays with 6 columns with a single column\n",
      "  generated 94 arrays, selected 24 arrays with D-efficiency 0.7844 to 0.8360\n"
     ]
    }
   ],
   "source": [
    "arraylist = [arrayclass.create_root()]\n",
    "\n",
    "# %% Extend arrays and filter based on D-efficiency\n",
    "options = oapackage.OAextend()\n",
    "options.setAlgorithmAuto(arrayclass)\n",
    "\n",
    "for extension_column in range(strength + 1, number_of_factors + 1):\n",
    "    print(\"extend %d arrays with %d columns with a single column\" % (len(arraylist), arraylist[0].n_columns))\n",
    "    arraylist_extensions = oapackage.extend_arraylist(arraylist, arrayclass, options)\n",
    "\n",
    "    # Select the best arrays based on the D-efficiency\n",
    "    dd = np.array([a.Defficiency() for a in arraylist_extensions])\n",
    "    ind = np.argsort(dd)[::-1][0:nkeep]\n",
    "    selection = [arraylist_extensions[ii] for ii in ind]\n",
    "    dd = dd[ind]\n",
    "    print(\n",
    "        \"  generated %d arrays, selected %d arrays with D-efficiency %.4f to %.4f\"\n",
    "        % (len(arraylist_extensions), len(ind), dd.min(), dd.max())\n",
    "    )\n",
    "\n",
    "    arraylist = selection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Show the best array from the list of D-optimal orthogonal arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Generated a design in OA(32, 2, 2^7) with D-efficiency 0.8360\n",
      "The array is (in transposed form):\n",
      "\n",
      "00000000000000001111111111111111\n",
      "00000000111111110000000011111111\n",
      "00000111000111110001111100000111\n",
      "00011001011001110110011100011001\n",
      "00101010101010111010101100101010\n",
      "01001011010110011101000101101001\n",
      "01110010001101010111001010100011\n"
     ]
    }
   ],
   "source": [
    "selected_array = selection[0]\n",
    "print(\n",
    "    \"Generated a design in OA(%d, %d, 2^%d) with D-efficiency %.4f\"\n",
    "    % (selected_array.n_rows, arrayclass.strength, selected_array.n_columns, dd[0])\n",
    ")\n",
    "print(\"The array is (in transposed form):\\n\")\n",
    "selected_array.transposed().showarraycompact()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We calculate the $D$-, $D_s$- and $D_1$-efficiencies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.8360354  0.72763273 1.        ]\n",
      " [0.83481532 0.78995185 1.        ]\n",
      " [0.82829522 0.70849985 1.        ]\n",
      " [0.82829522 0.65037401 1.        ]\n",
      " [0.82545286 0.75411444 1.        ]\n",
      " [0.8185915  0.65157148 1.        ]\n",
      " [0.81676643 0.68965719 1.        ]\n",
      " [0.81559279 0.72218391 1.        ]\n",
      " [0.81557799 0.66966068 1.        ]\n",
      " [0.81302642 0.74299714 1.        ]\n",
      " [0.80973102 0.73354611 1.        ]\n",
      " [0.80286424 0.67455544 1.        ]\n",
      " [0.79907785 0.72697978 1.        ]\n",
      " [0.79762174 0.58515515 1.        ]\n",
      " [0.79514152 0.65199837 1.        ]\n",
      " [0.79348419 0.74167976 1.        ]\n",
      " [0.7928208  0.70038649 1.        ]\n",
      " [0.79225237 0.71961467 1.        ]\n",
      " [0.79171981 0.62994172 1.        ]\n",
      " [0.79160277 0.66978711 1.        ]\n",
      " [0.7883109  0.62733236 1.        ]\n",
      " [0.78683679 0.60799604 1.        ]\n",
      " [0.78477264 0.69310129 1.        ]\n",
      " [0.7843891  0.7533355  1.        ]]\n"
     ]
    }
   ],
   "source": [
    "efficiencies = np.array([array.Defficiencies() for array in arraylist])\n",
    "print(efficiencies)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualize the $D$-efficiencies using a scatter plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(efficiencies[:, 0], efficiencies[:, 1], \".b\")\n",
    "plt.title(\"Scatterplot of effiencies of designs with %d columns\" % arraylist[0].n_columns)\n",
    "plt.xlabel(\"D-efficiency\")\n",
    "_ = plt.ylabel(\"Ds-efficiency\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}