ofp2map.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\n",
    "import numpy as np\n",
    "# import matplotlib.pyplot as plt\n",
    "# import plotly.express as px\n",
    "import plotly.graph_objects as go"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "outputs": [],
   "source": [
    "N = 100000\n",
    "n_stations = 150"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "outputs": [],
   "source": [
    "np.random.seed(34)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "outputs": [],
   "source": [
    "stations = np.random.uniform(low= 0, high=N, size=(n_stations, 2))\n"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "outputs": [],
   "source": [
    "plane_route = np.array([[x,int(0.3 * x)] for x in range(0,int(N/2),1000 )] + [[x, x - int(0.7 * N/2)] for x in range(int(N/2),N+1,1000 )])"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "outputs": [],
   "source": [
    "def find_closest_point(point, stations):\n",
    "    d = np.linalg.norm(stations - point, axis=1)\n",
    "    return np.argmin(d)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "outputs": [],
   "source": [
    "def closest_path(route, stations):\n",
    "    res = [stations[find_closest_point(p, stations), :] for p in route]\n",
    "    return res"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "outputs": [],
   "source": [
    "path_long = np.array(closest_path(plane_route, stations))\n",
    "path = np.unique(path_long, axis=0)\n"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "outputs": [],
   "source": [
    "from scipy.spatial.distance import cosine\n"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "outputs": [],
   "source": [
    "def compute_penalty(path):\n",
    "    return sum([cosine(path[i+1]-path[i], path[i]- path[i-1]) for i in range(1,len(path)-1)])\n",
    "\n"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "outputs": [],
   "source": [
    "def compute_distances(path, route):\n",
    "    return np.array([np.linalg.norm(path-r,axis=1)**2 for r in route])\n",
    "distances = compute_distances(path, plane_route)\n",
    "distance_dict = {i:min(distances[:, i]) for i in range(len(path))}"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "outputs": [],
   "source": [
    "filter_indices = [np.argmin(distances[:, i]) for i in range(len(path))]\n",
    "plane_route_meteo = np.take(plane_route, filter_indices, axis=0)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8\n"
     ]
    }
   ],
   "source": [
    "from collections import namedtuple\n",
    "import math\n",
    "Result = namedtuple('Result', ['fpl', 'ogimet'])\n",
    "\n",
    "class Point(object):\n",
    "    def __init__(self, value, name=None):\n",
    "        self.value = value\n",
    "        if name is None:\n",
    "            self.name = '{0}_{1}'.format(*value)\n",
    "        else:\n",
    "            self.name = name\n",
    "        self.x = value[0]\n",
    "        self.y = value[1]\n",
    "    def xtd_to(self, segment):\n",
    "        \"\"\"\n",
    "        Given the segment AB, computes cross track error\n",
    "        :param segment: (Point, Point) the segment AB\n",
    "        :return: float the cross track error\n",
    "        \"\"\"\n",
    "        p1 = segment[0]\n",
    "        p2 = segment[1]\n",
    "        x_diff = p2.x - p1.x\n",
    "        y_diff = p2.y - p1.y\n",
    "        num = abs(y_diff*self.x - x_diff*self.y + p2.x*p1.y - p2.y*p1.x)\n",
    "        den = math.sqrt(y_diff**2 + x_diff**2)\n",
    "        return num / den\n",
    "    def distance_to(self, other):\n",
    "        x_diff = other.x - self.x\n",
    "        y_diff = other.y - self.y\n",
    "        return  math.sqrt(y_diff**2 + x_diff**2)\n",
    "\n",
    "def find_strategic(start, end, results):\n",
    "    \"\"\"\n",
    "    Find point you can not suppress without increasing xtd\n",
    "    :param start: int\n",
    "    :param end: int\n",
    "    :param results: [Result]\n",
    "    :return:\n",
    "    \"\"\"\n",
    "    # search in reverse order to stop at the latest point in the route direction\n",
    "    # in segment [i, j] we try to remove inner elements by checking the xtd\n",
    "    length = len(results)\n",
    "    for k in range(end - 1, start, -1):\n",
    "        # xtd from ogimet point to fpl segment\n",
    "        o_xtd = results[k].ogimet.xtd_to(\n",
    "            (results[k].fpl, results[k + 1].fpl)\n",
    "        )\n",
    "        # xtd from fpl point to ogimet segment\n",
    "        f_xtd = results[k].fpl.xtd_to(\n",
    "            (results[start].ogimet, results[end].ogimet)\n",
    "        )\n",
    "        if abs(f_xtd) > abs(o_xtd):\n",
    "            fpl_d = -1\n",
    "            if k < length - 1:\n",
    "                fpl_d = results[k].fpl.distance_to(results[k+1].fpl)\n",
    "            if  abs(f_xtd) < fpl_d or fpl_d < 0:\n",
    "                return k\n",
    "    return None\n",
    "def filter_by_xtd(results):\n",
    "    \"\"\"\n",
    "    Here we keep significant ogimet points.\n",
    "    By significant, I mean points which increase the xtd if missing.\n",
    "    The algorithm is recursive, if route is A B C D E F\n",
    "    and ogimet route found is A B'C'D'E'F\n",
    "    We try to suppress B', if successful we try to suppress C' and so on\n",
    "    For example if B', C' and E' are not relevant the loop\n",
    "    will try to suppress B' and C', then it will keep D' and\n",
    "    start again from D' to suppress E' and keep F\n",
    "    At the end we try again (recursion) until the route size is constant.\n",
    "    For information a typical NAT route will reduce from 26 to 15 points\n",
    "    and a flight to NRT will end with 26 points (starting from 79)\n",
    "    :param results: [Result]\n",
    "    :return: [Result]\n",
    "    \"\"\"\n",
    "    res = [results[0]]\n",
    "    i = -1\n",
    "    while i < (len(results) - 1):\n",
    "        i += 1\n",
    "        j = i + 2\n",
    "        # we try to remove many consecutive points until it fails\n",
    "        while j <= len(results) - 1:\n",
    "            k = find_strategic(i, j, results)\n",
    "            if k is None:\n",
    "                j += 1  # no significant point yet, try to extend to next\n",
    "            else:\n",
    "                # a significant point was found, store it\n",
    "                if results[k].ogimet.name not in [o.name for _, o in res]:\n",
    "                    res.append(results[k])\n",
    "                i = k - 1  # will start at k on next round\n",
    "                break\n",
    "    res.append(results[-1])\n",
    "    # recursion works, so try it until there is no change\n",
    "    if len(res) < len(results):\n",
    "        return filter_by_xtd(res)\n",
    "    else:\n",
    "        return res\n",
    "\n",
    "\n",
    "ogimet_results = [Result(Point(plane_route_meteo[i]), Point(path[i])) for i in range(len(path))]\n",
    "ogimet_results = filter_by_xtd(ogimet_results)\n",
    "strategics = [[r.ogimet.x, r.ogimet.y] for r in ogimet_results]\n",
    "strategics_np = np.array(strategics)\n",
    "print(len(strategics))"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 98,
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     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "fig = go.Figure()\n",
    "\n",
    "# Add traces\n",
    "fig.add_trace(go.Scatter(x=stations[:,0], y=stations[:,1],\n",
    "                    mode='markers',\n",
    "                    name='stations'))\n",
    "fig.add_trace(go.Scatter(x=plane_route[:,0], y=plane_route[:,1],\n",
    "                    mode='lines',\n",
    "                    name='route'))\n",
    "fig.add_trace(go.Scatter(x=path[:,0], y=path[:,1],\n",
    "                    mode='lines',\n",
    "                    name='meteo'))\n",
    "fig.add_trace(go.Scatter(x=strategics_np[:,0], y=strategics_np[:,1],\n",
    "                    mode='lines',\n",
    "                    name='strategics'))\n"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
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