{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic Order\n",
    "This notebook contains a basic ordering example for vector optimization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from vopy.order import ConeTheta2DOrder"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's define two different cones to see their difference. The former will be an acute cone and the latter will be an obtuse cone."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "order_acute = ConeTheta2DOrder(cone_degree=45)\n",
    "_ = order_acute.ordering_cone.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "order_obtuse = ConeTheta2DOrder(cone_degree=135)\n",
    "_ = order_obtuse.ordering_cone.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "pt1, pt2 = np.array([[0,    0],\n",
    "                     [0.05, 1]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define $\\text{pt1} = (0, 0)$ and $\\text{pt2} = (0.05, 1)$. Surely $\\text{pt2}$ is better than $\\text{pt1}$... right? Actually, it depends on the partial ordering."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Does pt2 dominate pt1 in acute cone ordering?:  [False]\n",
      "Does pt2 dominate pt1 in obtuse cone ordering?: [ True]\n"
     ]
    }
   ],
   "source": [
    "print(\"Does pt2 dominate pt1 in acute cone ordering?: \", order_acute.dominates(pt2, pt1))\n",
    "print(\"Does pt2 dominate pt1 in obtuse cone ordering?:\", order_obtuse.dominates(pt2, pt1))"
   ]
  }
 ],
 "metadata": {
  "language_info": {
   "name": "python"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}