{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example: Water Management"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Miranda and Fackler, <i>Applied Computational Economics and Finance</i>, 2002,\n",
    "Section 7.6.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from __future__ import division\n",
    "import numpy as np\n",
    "import itertools\n",
    "import matplotlib.pyplot as plt\n",
    "from quantecon.markov import DiscreteDP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "M = 30\n",
    "n = M + 1  # Number of states\n",
    "m = n  # Number of actions\n",
    "\n",
    "a1, b1 = 14, 0.8\n",
    "a2, b2 = 10, 0.4\n",
    "F = lambda s, x: a1 * x**b1\n",
    "G = lambda s, x: a2 * (s - x)**b2\n",
    "\n",
    "beta = 0.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Reward array\n",
    "R = np.empty((n, m))\n",
    "for s, x in itertools.product(range(n), range(m)):\n",
    "    R[s, x] = F(s, x) + G(s, x) if x <= s else -np.inf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Probability transition array\n",
    "probs = np.array([0.1, 0.2, 0.4, 0.2, 0.1])\n",
    "size_supp = len(probs)\n",
    "Q = np.zeros((n, m, n))\n",
    "for s, x in itertools.product(range(n), range(m)):\n",
    "    if x <= s:\n",
    "        for j in range(size_supp):\n",
    "            Q[s, x, np.minimum(s-x+j, n-1)] += probs[j]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Create a DiscreteDP\n",
    "ddp = DiscreteDP(R, Q, beta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solve the dynamic optimization problem (by policy iteration)\n",
    "res = ddp.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Number of iterations\n",
    "res.num_iter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4,\n",
       "       4, 4, 4, 5, 5, 5, 5, 5])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Optimal policy\n",
    "res.sigma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 338.41645251,  361.98791375,  377.4257383 ,  391.4257383 ,\n",
       "        405.2360958 ,  417.9622843 ,  429.86115765,  441.17106277,\n",
       "        452.06672421,  462.66012607,  473.03554185,  483.40234488,\n",
       "        493.51237732,  503.35334776,  512.93797732,  522.31628408,\n",
       "        531.65601391,  540.88902181,  549.98545145,  558.93954761,\n",
       "        567.74582688,  576.47074514,  585.14046164,  593.69786291,\n",
       "        602.15675175,  610.510884  ,  618.80539659,  627.0562497 ,\n",
       "        635.2098027 ,  643.28164235,  651.27787278])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Optimal value function\n",
    "res.v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Simulate the controlled Markov chain for num_rep times\n",
    "# and compute the average\n",
    "init = 0\n",
    "ts_length = 50+1\n",
    "num_rep = 10**4\n",
    "ave_path = np.zeros(ts_length)\n",
    "for i in range(num_rep):\n",
    "    path = res.mc.simulate(ts_length=ts_length, init=init)\n",
    "    ave_path = (i/(i+1)) * ave_path + (1/(i+1)) * path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0.    ,   2.0186,   3.7242,   4.8964,   5.9481,   6.931 ,\n",
       "         7.827 ,   8.6082,   9.2431,   9.7545,  10.1598,  10.5033,\n",
       "        10.7833,  11.0077,  11.1962,  11.3612,  11.5109,  11.6388,\n",
       "        11.7362,  11.8301,  11.8986,  11.9682,  12.0206,  12.0719,\n",
       "        12.1497,  12.2144,  12.2503,  12.2689,  12.2866,  12.3155,\n",
       "        12.3397,  12.3851,  12.4065,  12.4222,  12.4389,  12.4539,\n",
       "        12.4536,  12.4624,  12.4744,  12.4728,  12.4814,  12.477 ,\n",
       "        12.4861,  12.4904,  12.4886,  12.4784,  12.4898,  12.4767,\n",
       "        12.4718,  12.4864,  12.4848])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ave_path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Stationary distribution of the Markov chain\n",
    "stationary_dist = res.mc.stationary_distributions[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0.00000000e+00,   0.00000000e+00,   1.15115026e-07,\n",
       "         1.03603524e-06,   8.05805183e-06,   5.98598136e-05,\n",
       "         4.44344001e-04,   3.29804550e-03,   2.44792103e-02,\n",
       "         6.08112470e-02,   1.20881706e-01,   1.39769288e-01,\n",
       "         1.50250205e-01,   1.50250201e-01,   1.39769301e-01,\n",
       "         1.20881695e-01,   6.08112091e-02,   2.44793930e-02,\n",
       "         3.29774206e-03,   4.43926815e-04,   5.70763048e-05,\n",
       "         6.34181165e-06,   0.00000000e+00,   0.00000000e+00,\n",
       "         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
       "         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
       "         0.00000000e+00])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stationary_dist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtIAAAIJCAYAAACIk9pGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110ddf630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot sigma, v, ave_path, stationary_dist\n",
    "hspace = 0.3\n",
    "fig, ax = plt.subplots(2, 2, figsize=(12, 8+hspace))\n",
    "fig.subplots_adjust(hspace=hspace)\n",
    "\n",
    "ax[0, 0].plot(res.sigma, '*')\n",
    "ax[0, 0].set_xlim(-1, 31)\n",
    "ax[0, 0].set_ylim(-0.5, 5.5)\n",
    "ax[0, 0].set_xlabel('Water Level')\n",
    "ax[0, 0].set_ylabel('Irrigation')\n",
    "ax[0, 0].set_title('Optimal Irrigation Policy')\n",
    "\n",
    "ax[0, 1].plot(res.v)\n",
    "ax[0, 1].set_xlabel('Water Level')\n",
    "ax[0, 1].set_ylabel('Value')\n",
    "ax[0, 1].set_title('Optimal Value Function')\n",
    "\n",
    "ax[1, 0].plot(ave_path)\n",
    "ax[1, 0].set_xlabel('Year')\n",
    "ax[1, 0].set_ylabel('Water Level')\n",
    "ax[1, 0].set_title('Average Optimal State Path')\n",
    "\n",
    "ax[1, 1].bar(range(n), stationary_dist, align='center')\n",
    "ax[1, 1].set_xlim(-1, n)\n",
    "ax[1, 1].set_xlabel('Water Level')\n",
    "ax[1, 1].set_ylabel('Probability')\n",
    "ax[1, 1].set_title('Stationary Distribution')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}