{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example code for delete-one-factor projections"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Any orthogonal array can be reduced to delete-one-factor projection form using `reduceDOPform`. The method is described in the article [A canonical form for non-regular arrays based on\n",
    "generalized wordlength pattern values of\n",
    "delete-one-factor projections](http://pietereendebak.nl/files/Eendebak2014-delete-one-factor.pdf) by Eendebak, P. T.\n",
    "In this notebook, we reduce an example array to its delete-one-factor projection form."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load required libraries and select an example orthogonal array with 16 runs and 7 factors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "array:\n",
      "  0   0   0   0   0   0   0\n",
      "  0   0   0   0   0   0   1\n",
      "  0   0   0   1   1   1   0\n",
      "  0   0   0   1   1   1   1\n",
      "  0   1   1   0   0   1   0\n",
      "  0   1   1   0   0   1   1\n",
      "  0   1   1   1   1   0   0\n",
      "  0   1   1   1   1   0   1\n",
      "  1   0   1   0   1   0   0\n",
      "  1   0   1   0   1   1   1\n",
      "  1   0   1   1   0   0   0\n",
      "  1   0   1   1   0   1   1\n",
      "  1   1   0   0   1   0   1\n",
      "  1   1   0   0   1   1   0\n",
      "  1   1   0   1   0   0   1\n",
      "  1   1   0   1   0   1   0\n"
     ]
    }
   ],
   "source": [
    "import oapackage\n",
    "\n",
    "al = oapackage.exampleArray(4)\n",
    "al = oapackage.reduceDOPform(al)\n",
    "al.showarray()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A key property of the delete-of-factor projection form is that the generalized word length patterns (GWLPs) of the projections are ordered. For details on the GWLP, see [Statistical properties of orthogonal arrays](https://oapackage.readthedocs.io/en/latest/properties.html#statistical-properties-of-orthogonal-arrays)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GWLP (1.0, 0.0, 0.0, 3.5, 2.5, 0.5, 0.5, 0.0)\n",
      "Delete column 0: GWLP (1.0, 0.0, 0.0, 1.5, 1.0, 0.5, 0.0)\n",
      "Delete column 1: GWLP (1.0, 0.0, 0.0, 1.75, 0.75, 0.25, 0.25)\n",
      "Delete column 2: GWLP (1.0, 0.0, 0.0, 1.75, 0.75, 0.25, 0.25)\n",
      "Delete column 3: GWLP (1.0, 0.0, 0.0, 2.0, 1.0, 0.0, 0.0)\n",
      "Delete column 4: GWLP (1.0, 0.0, 0.0, 2.0, 1.0, 0.0, 0.0)\n",
      "Delete column 5: GWLP (1.0, 0.0, 0.0, 2.0, 1.0, 0.0, 0.0)\n",
      "Delete column 6: GWLP (1.0, 0.0, 0.0, 3.0, 2.0, 0.0, 0.0)\n"
     ]
    }
   ],
   "source": [
    "print(f\"GWLP {al.GWLP()}\")\n",
    "for ii in range(0, al.n_columns):\n",
    "    bl = al.deleteColumn(ii)\n",
    "    print(\"Delete column %d: GWLP %s\" % (ii, str(bl.GWLP())))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The symmetry group of the projection GWLPs can be calculated. This symmetry group determines how fast an array can be reduced to normal form."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "symmetry group: 7 elements, 4 subgroups: 1 2 3 1 \n"
     ]
    }
   ],
   "source": [
    "dof_values = oapackage.projectionDOFvalues(al)\n",
    "sg = oapackage.symmetry_group(dof_values, False)\n",
    "sg.show(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is also possible to reduce mixed-level arrays to their delete-of-factor projection forms. We now show an example involving an orthogonal array with 24 runs, one four-level factor, one three-level factor and three two-level factors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "array:\n",
      "  0   0   0   0   0\n",
      "  0   0   0   0   0\n",
      "  0   1   0   0   0\n",
      "  0   1   1   1   1\n",
      "  0   2   1   1   1\n",
      "  0   2   1   1   1\n",
      "  1   0   0   1   1\n",
      "  1   0   0   1   1\n",
      "  1   1   0   0   1\n",
      "  1   1   1   1   0\n",
      "  1   2   1   0   0\n",
      "  1   2   1   0   0\n",
      "  2   0   1   0   1\n",
      "  2   0   1   0   1\n",
      "  2   1   0   1   0\n",
      "  2   1   1   0   1\n",
      "  2   2   0   1   0\n",
      "  2   2   0   1   0\n",
      "  3   0   1   1   0\n",
      "  3   0   1   1   0\n",
      "  3   1   0   1   1\n",
      "  3   1   1   0   0\n",
      "  3   2   0   0   1\n",
      "  3   2   0   0   1\n",
      "delete-one-factor GWLP values [(1.0, 0.0, 0.0, 0.0, 0.6666666666666666), (1.0, 0.0, 0.0, 2.111111111111111, 0.0), (1.0, 0.0, 0.0, 1.8888888888888888, 0.4444444444444444), (1.0, 0.0, 0.0, 2.3333333333333335, 0.0), (1.0, 0.0, 0.0, 1.8888888888888888, 0.4444444444444444)]\n"
     ]
    }
   ],
   "source": [
    "al = oapackage.exampleArray(5)\n",
    "al.showarray()\n",
    "dopgwlp = oapackage.projectionGWLPs(al)\n",
    "print(f\"delete-one-factor GWLP values {[x.raw_values() for x in dopgwlp]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The delete-of-factor values for mixel-level arrays consists of the factor level of the deleted column and the GWLP of the projection."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "column 0: factor level 4\n",
      "   delete-of-factor value: [-4.0, 1.0, 0.0, 0.0, 0.0, 0.6666666666666666]\n",
      "column 1: factor level 3\n",
      "   delete-of-factor value: [-3.0, 1.0, 0.0, 0.0, 2.111111111111111, 0.0]\n",
      "column 2: factor level 2\n",
      "   delete-of-factor value: [-2.0, 1.0, 0.0, 0.0, 1.8888888888888888, 0.4444444444444444]\n",
      "column 3: factor level 2\n",
      "   delete-of-factor value: [-2.0, 1.0, 0.0, 0.0, 2.3333333333333335, 0.0]\n",
      "column 4: factor level 2\n",
      "   delete-of-factor value: [-2.0, 1.0, 0.0, 0.0, 1.8888888888888888, 0.4444444444444444]\n"
     ]
    }
   ],
   "source": [
    "oapackage.projectionGWLPs\n",
    "dopgwp = oapackage.projectionGWLPs(al)\n",
    "arrayclass = oapackage.arraylink2arraydata(al)\n",
    "dofvalues = oapackage.projectionDOFvalues(al)\n",
    "factor_levels = arrayclass.factor_levels()\n",
    "\n",
    "for column, dof_value in enumerate(dofvalues):\n",
    "    print(\"column %d: factor level %s\" % (column, factor_levels[column]))\n",
    "    print(f\"   delete-of-factor value: {list(dof_value.raw_values())}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Show the reduced array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "array:\n",
      "  0   0   0   0   0\n",
      "  0   0   0   0   0\n",
      "  0   1   0   0   0\n",
      "  0   1   1   1   1\n",
      "  0   2   1   1   1\n",
      "  0   2   1   1   1\n",
      "  1   0   0   1   1\n",
      "  1   0   0   1   1\n",
      "  1   1   0   0   1\n",
      "  1   1   1   1   0\n",
      "  1   2   1   0   0\n",
      "  1   2   1   0   0\n",
      "  2   0   1   0   1\n",
      "  2   0   1   0   1\n",
      "  2   1   0   1   0\n",
      "  2   1   1   0   1\n",
      "  2   2   0   1   0\n",
      "  2   2   0   1   0\n",
      "  3   0   1   1   0\n",
      "  3   0   1   1   0\n",
      "  3   1   0   1   1\n",
      "  3   1   1   0   0\n",
      "  3   2   0   0   1\n",
      "  3   2   0   0   1\n"
     ]
    }
   ],
   "source": [
    "reduced_array = al.reduceDOP()\n",
    "al.showarray()"
   ]
  }
 ],
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