steiner_timing.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import itertools \n",
    "\n",
    "import time\n",
    "\n",
    "import networkx as nx\n",
    "from networkx.algorithms import approximation as apx\n",
    "\n",
    "# import landscape as ld\n",
    "import steiner_utils as su"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_pos(g):\n",
    "    '''returns dictionary with nodes physical location'''\n",
    "    return dict( (n, n) for n in g.nodes() )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compute timing\n",
    "Points selected at random. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(1, 81, 144, 9)"
     },
     "metadata": {},
     "execution_count": 4
    }
   ],
   "source": [
    "L0 = 10; Nterm = 10\n",
    "terminals_2 = su.make_random_terminals(box_size = L0, Nterminals = Nterm)\n",
    "G_2 = su.create_graph(box_size = L0, terminals = terminals_2)\n",
    "su.graph_info(G_2, verbosity = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Calculation took 0.02783799171447754 sec\nLength of Steiner tree 22\n"
    }
   ],
   "source": [
    "tic = time.time()\n",
    "steiner_2 = su.naive_steiner(G_2)\n",
    "\n",
    "toc = time.time()\n",
    "print('Calculation took {} sec'.format(toc-tic))\n",
    "print('Length of Steiner tree {}'.format(len(steiner_2)))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def time_steiner(L0, Nterm):\n",
    "    terminals = su.make_random_terminals(box_size = L0, Nterminals = Nterm)\n",
    "    G = su.create_graph(box_size = L0, terminals = terminals)\n",
    "    \n",
    "    info = su.graph_info(G, verbosity = False)\n",
    "    \n",
    "    tic = time.time()\n",
    "    steiner = su.naive_steiner(G)\n",
    "\n",
    "    toc = time.time()\n",
    "    \n",
    "    return (info, (toc-tic))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vary L0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "varyL0 = [time_steiner(L0, 20) for L0 in range(10,41,2)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "[((1, 81, 144, 20), 0.07140612602233887),\n ((1, 121, 220, 19), 0.05689716339111328),\n ((1, 169, 312, 18), 0.11020231246948242),\n ((1, 225, 420, 19), 0.2384488582611084),\n ((1, 289, 544, 19), 0.37606382369995117),\n ((1, 361, 684, 18), 0.6032278537750244),\n ((1, 441, 840, 19), 0.9910483360290527),\n ((1, 529, 1012, 20), 1.5961098670959473),\n ((1, 625, 1200, 20), 2.2409067153930664),\n ((1, 729, 1404, 19), 3.0445804595947266),\n ((1, 841, 1624, 20), 4.241245985031128),\n ((1, 961, 1860, 20), 6.304769039154053),\n ((1, 1089, 2112, 20), 7.103960990905762),\n ((1, 1225, 2380, 20), 10.350186109542847),\n ((1, 1369, 2664, 20), 11.944117069244385),\n ((1, 1521, 2964, 20), 15.962908029556274)]"
     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "source": [
    "varyL0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, Y = [x[-2] for x,y in varyL0], [y for x,y in varyL0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
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     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "line = ax.plot(X, Y, 'o', color='blue')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## vary Nterm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "varyNterm = [(Nterm, time_steiner(30, Nterm)) for Nterm in range(10,61,4)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, Y = [x for x,y in varyNterm], [y[-1] for x,y in varyNterm]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "[<matplotlib.lines.Line2D at 0x7f0d5c710130>]"
     },
     "metadata": {},
     "execution_count": 13
    },
    {
     "output_type": "display_data",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.plot(X,Y,'o')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Shortest path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(1, 1521, 2964, 2)"
     },
     "metadata": {},
     "execution_count": 14
    }
   ],
   "source": [
    "L0 = 40; Nterm = 2\n",
    "terminals_3 = su.make_random_terminals(box_size = L0, Nterminals = Nterm)\n",
    "G_3 = su.create_graph(box_size = L0, terminals = terminals_3)\n",
    "su.graph_info(G_3, verbosity = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def time_shortest_path(L0):\n",
    "    \n",
    "    terminals = su.make_random_terminals(box_size = L0, Nterminals = 2)\n",
    "    G = su.create_graph(box_size = L0, terminals = terminals)\n",
    "    info = su.graph_info(G, verbosity = False)\n",
    "    \n",
    "    s, t = terminals\n",
    "    \n",
    "    tic = time.time()\n",
    "    nx.algorithms.shortest_path(G, source = s, target = t)\n",
    "    toc = time.time()\n",
    "    \n",
    "    return (info, (toc-tic))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "allY = []\n",
    "for i in range(30):\n",
    "    TimingsShortestPath = [time_shortest_path(L0) for L0 in range(10,61,2)]\n",
    "    X = [x[2] for x,y in TimingsShortestPath]\n",
    "    Y = np.array([y for x,y in TimingsShortestPath])\n",
    "    allY.append(Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "meanY = np.mean(allY, axis= 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.plot(X,meanY,'o');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.plot(X,meanY,'o');"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python (landscape_steiner)",
   "language": "python",
   "name": "landscape_steiner"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}