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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analyse isomorphisms of a set of orthogonal arrays with N=56"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, we show how to identify isomorphic arrays from a list of two-level strength-2 orthogonal arrays with 56 runs and 28 factors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "import oapackage\n",
    "import oapackage.graphtools\n",
    "from oapackage.graphtools import selectIsomorphismClasses"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Read the arrays from a file and determine their class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "arrayclass: N 56, k 28, strength 2, s {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}, order 0\n",
      "loaded 9 arrays\n"
     ]
    }
   ],
   "source": [
    "sols = oapackage.readarrayfile(\"OAN56K28.oa\")\n",
    "arrayclass = oapackage.arraylink2arraydata(sols[0])\n",
    "print(arrayclass)\n",
    "print(\"loaded %d arrays\" % len(sols))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Determine the unique isomorphism classes using <a href=\"http://users.cecs.anu.edu.au/~bdm/nauty/\">Nauty</a>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "from 9 arrays selected 6 unique isomorphism classes\n",
      "indices: [0 4 5 3 1 5 3 2 4]\n"
     ]
    }
   ],
   "source": [
    "b, mm = selectIsomorphismClasses(sols, verbose=0)\n",
    "\n",
    "print(\"from %d arrays selected %d unique isomorphism classes\" % (len(mm), np.unique(b).size))\n",
    "print(f\"indices: {str(b)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Verify that the first two arrays are indeed non-isomorphic:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[    0 18018  2457]\n",
      "[    0 18032  2436]\n"
     ]
    }
   ],
   "source": [
    "jj = np.abs(sols[0].Jcharacteristics(4))\n",
    "n0, _ = np.histogram(jj, [0, 8, 16, 24])\n",
    "print(n0)\n",
    "jj = np.abs(sols[1].Jcharacteristics(4))\n",
    "n1, _ = np.histogram(jj, [0, 8, 16, 24])\n",
    "print(n1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the first two arrays have different $J$-characteristics (see the section [Statistical properties of orthogonal arrays](https://oapackage.readthedocs.io/en/latest/properties.html#statistical-properties-of-orthogonal-arrays) for details), they are non-isomorphic. For the isomorphic arrays, it is possible to obtain the array transformation to make the arrays identical using the function `reduceConferenceTransformation`."
   ]
  }
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