{
 "cells": [
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   "cell_type": "markdown",
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   "source": [
    "# Prey-Predator\n",
    "\n",
    "Hare: \n",
    "* inflow: natural birth\n",
    "* outflow: death due to predation\n",
    "\n",
    "Lynx:\n",
    "* inflow: growth and give birth thanks to preying on hare\n",
    "* outflow: natural death\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Test_Initialization(init_func, hare_number, lynx_number) :\n",
    "    global hare_total, lynx_total\n",
    "    init_func(hare_number, lynx_number)\n",
    "    assert (hare_total == hare_number and lynx_total == lynx_number) , \"Mismatch initial population size\"\n",
    "    print(\"Pass initalization test:\", init_func.__name__, hare_number, lynx_number)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Global variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import random\n",
    "\n",
    "hare_id = 1\n",
    "hare_total = 0\n",
    "hare = []\n",
    "\n",
    "lynx_id = -1\n",
    "lynx_total = 0\n",
    "lynx = []\n",
    "\n",
    "random_generator = random.RandomState(1111)\n",
    "\n",
    "param = {\n",
    "    \"hare_birth\": 0.8,\n",
    "    \"hare_death\" : 0.3, # come into contact with lynx AND die\n",
    "    \"lynx_birth\": 0.1,\n",
    "    \"lynx_death\": 0.2\n",
    "}\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initialization function \n",
    "\n",
    "This sets up the simulation with initial numbers of hares and lynxes.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Initialize(hare_number=0, lynx_number=0):\n",
    "    global hare_total, lynx_total, hare_id, lynx_id, hare, lynx\n",
    "    hare_id = 0\n",
    "    hare = []\n",
    "    lynx_id = 0\n",
    "    lynx = []\n",
    "    \n",
    "    # ask for inputs if not given\n",
    "    if hare_number >= 0:\n",
    "        hare_total = hare_number\n",
    "    else :\n",
    "        hare_total = int(input(\"Initial number of hares: \"))\n",
    "    if lynx_number > 0:\n",
    "        lynx_total = lynx_number\n",
    "    else:\n",
    "        lynx_total = int(input(\"Initial number of lynxes: \"))\n",
    "    \n",
    "    # add individuals to approriate lists\n",
    "    for i in range(hare_total) :\n",
    "        hare_id += 1\n",
    "        hare.append( hare_id )\n",
    "        \n",
    "    for i in range(lynx_total) :\n",
    "        lynx_id -= 1\n",
    "        lynx.append( lynx_id )\n",
    "        \n",
    "# Test_Initialization(Initialize, 10, 9)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulate each time step (daily)\n",
    "\n",
    "This will do the following:\n",
    "* Calculate the total births of hare: $ \\text{hare_birth} \\times \\text{hare_total} $\n",
    "* Calculate the total deaths of hare due to predation: $ \\text{hare_predation} \\times \\text{hare_total} \\times \\text{lynx_total} $ \n",
    "* Calculate the total births of lynx: $ \\text{lynx_birth} \\times \\text{hare_total} \\times \\text{lynx_total} $\n",
    "* Calculate the total deaths of hare due to predation: $ \\text{lynx_death} \\times \\text{lynx_total} $ \n",
    "* Calculate the amount of changes to hare population (birth - death):\n",
    "    + if change is 0: do nothing to hare population\n",
    "    + if change > 0: add new individuals to hare list\n",
    "    + if change < 0: choose random individuals from hare list and remove them\n",
    "* Calculate the amount of changes to lynx population (birth - death):\n",
    "    + if change is 0: do nothing to lynx population\n",
    "    + if change > 0: add new individuals to lynx list\n",
    "    + if change < 0: choose random individuals from lynx list and remove them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Modify_Hare(amount_change):\n",
    "    global hare_total, hare_id, hare, random_generator\n",
    "    \n",
    "#     if amount_change > 0 :\n",
    "#         for i in range(amount_change) :\n",
    "#             hare_id += 1\n",
    "#             hare.append( hare_id )\n",
    "            \n",
    "#     elif amount_change + hare_total <= 0 :\n",
    "#         hare = []\n",
    "        \n",
    "#     else :\n",
    "#         new_hare = []\n",
    "        \n",
    "#         indices = sorted(random_generator.choice(hare_total, abs(amount_change), replace=False))\n",
    "        \n",
    "#         i, j = 0, 0\n",
    "#         while j < hare_total :\n",
    "#             # done removing\n",
    "#             if i == abs(amount_change) :\n",
    "#                 new_hare.append(hare[j:])\n",
    "#                 break\n",
    "#             elif j != indices[i] :\n",
    "#                 new_hare.append(hare[j])\n",
    "#             else :\n",
    "#                 i += 1\n",
    "#             j += 1\n",
    "        \n",
    "#         hare = new_hare[:]\n",
    "        \n",
    "    hare_total = hare_total + amount_change if hare_total + amount_change > 0 else 0\n",
    "    \n",
    "    return hare_total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Modify_Lynx(amount_change):\n",
    "    global lynx_total, lynx_id, lynx, random_generator\n",
    "    \n",
    "#     if amount_change > 0 :\n",
    "#         for i in range(amount_change) :\n",
    "#             lynx_id += 1\n",
    "# #             lynx.append( lynx_id )\n",
    "            \n",
    "#     elif amount_change + lynx_total <= 0 :\n",
    "#         lynx = []\n",
    "        \n",
    "#     else :\n",
    "#         new_lynx = []\n",
    "        \n",
    "#         indices = sorted(random_generator.choice(lynx_total, abs(amount_change), replace=False))\n",
    "        \n",
    "#         i, j = 0, 0\n",
    "#         while j < lynx_total :\n",
    "#             # done removing\n",
    "#             if i == abs(amount_change) :\n",
    "#                 new_lynx.append(lynx[j:])\n",
    "#                 break\n",
    "#             elif j != indices[i] :\n",
    "#                 new_lynx.append(lynx[j])\n",
    "#             else :\n",
    "#                 i += 1\n",
    "#             j += 1\n",
    "        \n",
    "#         lynx = new_lynx[:]\n",
    "        \n",
    "    lynx_total = lynx_total + amount_change if lynx_total + amount_change > 0 else 0\n",
    "    \n",
    "    return lynx_total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Simulate_One_Step():\n",
    "    global param\n",
    "    # calculate births, deaths, changes\n",
    "    hare_in = param[\"hare_birth\"] * hare_total\n",
    "    hare_out = param[\"hare_death\"] * hare_total * lynx_total\n",
    "    lynx_in = param[\"lynx_birth\"] * hare_total * lynx_total\n",
    "    lynx_out = param[\"lynx_death\"] * lynx_total\n",
    "    hare_change = int(hare_in - hare_out)\n",
    "    lynx_change = int(lynx_in - lynx_out)\n",
    "    # note: one can condensed all calculations above to just 2 lines\n",
    "    \n",
    "    # make change to hare population\n",
    "    if hare_change != 0 :\n",
    "        Modify_Hare(hare_change)\n",
    "    # make change to lynx population\n",
    "    if lynx_change != 0 :\n",
    "        Modify_Lynx(lynx_change)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Run the simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---day 0 ---\n",
      "Hare total: 5999  Lynx total: 300\n",
      "---day 4 ---\n",
      "Oops! One of the population has died out....\n",
      "Hare total: 0  Lynx total: 60633847\n"
     ]
    }
   ],
   "source": [
    "# param = {\n",
    "#     \"hare_birth\": 0.6,\n",
    "#     \"hare_death\" : 0.001,\n",
    "#     \"lynx_birth\": 0.00001,\n",
    "#     \"lynx_death\": 0.5\n",
    "# }\n",
    "# Initialize(50000, 600) # equilibrium\n",
    "\n",
    "\n",
    "def Print_Day(day) :\n",
    "    global hare, lynx, hare_total, lynx_total\n",
    "    print(\"---day\", str(day), \"---\")\n",
    "#     print(hare)\n",
    "#     print(lynx)\n",
    "    print(\"Hare total:\", hare_total, \" Lynx total:\", lynx_total)\n",
    "\n",
    "\n",
    "param = { \n",
    "    \"hare_birth\": 0.2,\n",
    "    \"hare_death\" : 0.00003, \n",
    "    \"lynx_birth\": 0.1,\n",
    "    \"lynx_death\": 1\n",
    "}    \n",
    "    \n",
    "Initialize(5000, 6)\n",
    "# print(hare)\n",
    "# print(lynx)\n",
    "    \n",
    "for day in range(0,101):\n",
    "    if hare_total == 0 or lynx_total == 0:\n",
    "        print(\"---day\", str(day), \"---\")\n",
    "        print(\"Oops! One of the population has died out....\")\n",
    "        print(\"Hare total:\", hare_total, \" Lynx total:\", lynx_total)\n",
    "        break\n",
    "    Simulate_One_Step()\n",
    "    if day % 10 == 0 :\n",
    "        Print_Day(day)\n",
    "\n",
    "# print(hare)\n",
    "# print(lynx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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