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@m-alcu
Last active October 4, 2019 10:13
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{
"cells": [
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from IPython.display import clear_output\n",
"from random import randint, random\n",
"from time import sleep\n",
"import math\n",
"from scipy.stats import poisson\n",
"import seaborn as sns; sns.set()"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [],
"source": [
"# parameters of the demand model\n",
"true_slop = 30\n",
"true_intercept = -0.5\n",
"\n",
"#simulation data\n",
"num_episodes = 1000\n",
"\n",
"#parameters: 40 items, 5 different prices, and 20 days to the final day\n",
"stock = 40\n",
"prices = [19, 25, 30, 35, 40, 45]\n",
"horizon_steps = 20"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1>Agent</h1>\n",
"\n",
"This agent applies a policy that could be a random policy or a Designed optimal policy (our target)"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [],
"source": [
"def agent(policy, starting_position=None, verbose=False):\n",
"\n",
" agent_position = starting_position\n",
" \n",
" revenue = 0\n",
" action_taken = None\n",
" \n",
" #while not (agent_position == 0):\n",
" for step in range(horizon_steps):\n",
" current_policy = policy[agent_position,step,:]\n",
" next_move = random()\n",
" lower_bound = 0\n",
" demand = 0\n",
" for action in range(len(prices)):\n",
" chance = current_policy[action]\n",
" if chance == 0:\n",
" continue\n",
" if lower_bound <= next_move < lower_bound + chance:\n",
" demand = retrieve_linear_demand(action, step)\n",
" #print(\"action: {} demand: {}\".format(action, demand))\n",
" if (agent_position >= demand ):\n",
" agent_position = agent_position - demand\n",
" else:\n",
" demand = agent_position\n",
" agent_position = 0\n",
" action_taken = action\n",
" break \n",
" lower_bound = lower_bound + chance\n",
" \n",
" revenue = revenue + demand * prices[action] \n",
" \n",
" if verbose:\n",
" clear_output(wait=True)\n",
" print(\"New Demand: {} Revenue acum: {} Remain Stock: {} Price: {}\".format(demand, revenue, agent_position, prices[action_taken]))\n",
" print(\"\\n\")\n",
" sleep(1)\n",
" \n",
" return revenue"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\\lambda = 30 - 0.5p + 0.1e^{t/4}$$"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [],
"source": [
"#this gives us the average demand from a (price) and h (time)\n",
"def retrieve_deterministic_demand(a, h):\n",
" return true_slop + true_intercept * prices[a] +0.1*math.exp(h/4)"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [],
"source": [
"#this gives us an stochastic demand\n",
"def retrieve_linear_demand(a, h): \n",
" demand = retrieve_deterministic_demand(a, h)\n",
" return np.random.poisson(demand, 1)[0]"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 0, 'demand')"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 720x720 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#we plot the demand in 3D\n",
"\n",
"from mpl_toolkits import mplot3d\n",
"\n",
"h = np.linspace(0, horizon_steps-1, horizon_steps)\n",
"p = np.asarray(prices)\n",
"X, Y = np.meshgrid(h, p)\n",
"\n",
"def f(x, y):\n",
" return true_slop + true_intercept * y +0.1*np.exp(x/4)\n",
"\n",
"Z = f(X, Y)\n",
"fig = plt.figure(figsize=(10,10))\n",
"ax = plt.axes(projection='3d')\n",
"ax.contour3D(X, Y, Z, 50, cmap='viridis')\n",
"ax.set_xlabel('horizon')\n",
"ax.set_ylabel('price')\n",
"ax.set_zlabel('demand')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1>Probability distribution</h1>\n",
"\n",
"We calculate de probability from states derived from poisson formula"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [],
"source": [
"def probability_demand(x1, x2, a, h):\n",
" demand = retrieve_deterministic_demand(a, h)\n",
" k = x1 - x2\n",
" rv = poisson(demand)\n",
" return rv.pmf(k)"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [],
"source": [
"def create_probability_map():\n",
" probability_map = np.zeros((stock+1, horizon_steps, stock+1, horizon_steps, len(prices)),dtype=float)\n",
" states = list(range(stock+1))\n",
" steps = list(range(horizon_steps))\n",
"\n",
" for horizon_from in steps:\n",
" for state_from in states:\n",
" for price in range(len(prices)):\n",
" for horizon_to in steps:\n",
" prob_tot = 0\n",
" for state_to in reversed(states):\n",
" if (horizon_to != (horizon_from+1)) or (state_to > state_from):\n",
" prob = 0\n",
" else:\n",
" prob = probability_demand(state_from, state_to, price, horizon_from)\n",
" prob_tot = prob_tot + prob\n",
" if (state_to == 0):\n",
" prob = prob + ( 1 - prob_tot )\n",
" probability_map[state_from][horizon_from][state_to][horizon_to][price] = prob\n",
" #print(\"prob {} {} {}: {}\".format(state_from, state_to, price, prob))\n",
" return probability_map"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"result = create_probability_map()"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x234eeb34e10>"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1440x360 with 4 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Soms subplots to inspect how the probability behaves\n",
"fig = plt.figure(figsize=(20,5))\n",
"ax1 = plt.subplot2grid((1,2), (0,0))\n",
"ax2 = plt.subplot2grid((1,2), (0,1))\n",
"\n",
"sns.heatmap(result[stock,0,:,:,5], ax=ax1)\n",
"sns.heatmap(result[10,2,:,:,5], ax=ax2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1>Create greedy policy based on poisson probs V(s)</h1>\n",
"\n",
"We test 1000 dandom episodes with the agent aplying a random policy"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1>Random Policy test</h1>"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [],
"source": [
"def create_random_policy():\n",
" policy = np.zeros((stock+1, horizon_steps, len(prices)),dtype=float)\n",
"\n",
" for horizon in range(horizon_steps-1):\n",
" for state in range(stock+1): \n",
" for p in range(len(prices)):\n",
" policy[state][horizon][p] = 1 / len(prices)\n",
" return policy"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"100.0%\n",
"\n",
"Average revenue (average total income): 1182.516\n"
]
}
],
"source": [
"data = []\n",
"\n",
"for i in range(num_episodes):\n",
" clear_output(wait=True)\n",
" print(\"{}%\\n\".format((i + 1) * 100 / num_episodes))\n",
" data.append(agent(create_random_policy(), starting_position=stock, verbose=False))\n",
" \n",
"print(\"Average revenue (average total income): {}\".format(sum(data)/len(data)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1>Value iteration</h1>\n",
"\n",
"We calculate optimal policy from Value Iteration Bellman Equation"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [],
"source": [
"def create_greedy_policy(A_s):\n",
"\n",
" policy = np.zeros((stock+1, horizon_steps, len(prices)),dtype=float)\n",
" for horizon in range(horizon_steps):\n",
" for state in range(stock+1):\n",
" for a in range(len(prices)):\n",
" if a == A_s[state][horizon]:\n",
" policy[state][horizon][a] = 1\n",
" return policy"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [],
"source": [
"def value_iteration(V_s, theta=0.01, discount_rate=0.5):\n",
" probabilitiy_map = create_probability_map()\n",
" \n",
" A_s = np.zeros((stock+1, horizon_steps),dtype=int)\n",
" \n",
" states = list(range(stock+1))\n",
" horizons = list(range(horizon_steps))\n",
" \n",
" delta = 100\n",
" while not delta < theta:\n",
" delta = 0\n",
" for horizon in reversed(horizons):\n",
" for state in states:\n",
" v = V_s[state][horizon]\n",
" totals = {}\n",
" for action in range(len(prices)):\n",
" total = 0\n",
" if horizon + 1 < horizon_steps:\n",
" for state_prime in states:\n",
" reward = ( state - state_prime ) * prices[action]\n",
" total += probabilitiy_map[state][horizon][state_prime][horizon+1][action] * (reward + discount_rate * V_s[state_prime][horizon+1])\n",
" totals[action] = total\n",
" V_s[state][horizon] = round(max(totals.values()), 4)\n",
" f = lambda i: totals[i]\n",
" A_s[state][horizon] = max(range(len(totals)), key=f)\n",
" delta = max(delta, abs(v - V_s[state][horizon]))\n",
" return V_s, A_s"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [],
"source": [
"V_s = np.zeros((stock+1, horizon_steps),dtype=float)\n",
"V_s, A_s = value_iteration(V_s)\n",
"policy = create_greedy_policy(A_s)"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x234effc5f98>"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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QKKSCggKNGTPGTNUAACQwN5rglxhD0iF/AQBgXwbzbK64rqvTp0/r7NmzOnfunM6cOaO//du/1fnz53Xp0qVY1QgAAJAyyF8AACSOkpISlZSUtHs/z+bKvffeq+HDh8t1Xc2cOVNTp05Vfn6+du/erW984xvGigUAIGGxoS1ijPwFAICsy2CezZUxY8aosLBQzc3NysrK0q233qpXX31Vjz76qL785S/HqkYAAOKHDW0RY+QvAABkXQZr92pBGRkZLf//uc99Tp/73Oeu+sG6uoGr/tpYSOzq7BCwYFmcE+8C2mH6+9CP72vT/86m/018OWfD4zmGn0N+fwHJxWT+AgAA/mu3uQIAQEqzbDM1AACApGBZBuPNTgAAAAAAgE5g5goAAF4s20wNAAAgKViWwWiuAADgxbIXdgAAgKRgWQZjWRAAAAAAAEAn0FwBAMCL6/pz64DNmzdr5MiRGjlypJ544glJ0sGDB1VSUqLCwkLNmzdPTU1NkqT6+nrdfffdKioq0gMPPKAPP/zQ+FMCAADguzjnr46iuQIAQAI7d+6cHn/8ca1bt06bN2/W3r17tWvXLs2cOVMLFizQyy+/LNd1tWHDBknSokWLVFpaqtraWg0YMECrVq2K8xkAAAAkP5orAAB4iUZ9uTU2NurIkSNtbo2Nja0evrm5WdFoVOfOnVNTU5OampoUDAZ1/vx5DR48WJJUUlKi2tpaXbp0SXv27FFhYWGr4wAAANbxI4P5iA1tAQCIg8rKSq1cubLN8fLyclVUVLR83LVrVz388MMaMWKEMjMzdeuttyoUCik3N7flPrm5uTp+/LhOnTqlrl27KhgMtjoOAAAAf9FcAQDAS9Sf9bmTJ09WcXFxm+PZ2dmtPn7rrbf04osv6he/+IWuueYaPfroo/r1r38tx3Fa7uO6rhzHafnvx33yYwAAACv4lMH8EtPmSle7rqSUcFJxDZcf5+wk+M+o6XMO+nC+pv9UM12jH39KBg1vgGX639n0OQd83vDLKq4/L17Z2dltGimf5tVXX1V+fr7+7u/+TtJHS32effZZNTQ0tNzn5MmTikQiysnJ0enTp9Xc3Ky0tDQ1NDQoEon4Uj8AAICvfMpgfknFv9cBALDGTTfdpF27duns2bNyXVfbt2/X0KFDlZ6ern379kn66GpCBQUFCoVCGjJkiGpqaiRJ1dXVKigoiGf5AAAAKYFlQQAAeInzlNSvfOUr+u1vf6uSkhKFQiF9/vOf13333afbb79d8+fP15kzZ3TzzTdr0qRJkqSFCxdqzpw5evrpp9W9e3c9+eSTca0fAADgqrAsCAAAmHTffffpvvvua3Xspptu0saNG9vct2fPnlq3bl2sSgMAAIBorgAA4Mn1+bJ9AAAAaMu2DEZzBQAAL5ZNSQUAAEgKlmWwdpsrO3fuVG1trY4dO6ZAIKBIJKKCggIVFhbGoj4AAICURAYDAMAens2VFStWqK6uTnfeeacikYhc11VDQ4M2btyo3/zmN5o9e3as6gQAID4suwwgkgMZDACQ8izLYJ7NlZqaGm3btk2BQOsrNo8aNUqjRo3ihR0AAMAHZDAAAOwS8Ppkenq6jh071uZ4fX29wuGwb0UBAJAwoq4/N8ADGQwAkPIsy1+eM1fmzJmju+++W71791Zubq4cx9GJEyd0+PBhLVmyxNfCAABICJbtVI/kQAYDAKQ8yzKYZ3PlS1/6kmpra1VXV6cTJ04oGo2qW7duGjRo0FW9a5Jl13PTaU68C4gDz6lQCSJguGFp+t85ILMFBn1o0Jo+56Brtsg0w8+hJIUSvEbTP3uOD88hgCtnOoMBAAB/eTZX6uvrJUk9e/ZUz549W46fPHlSktSjRw8fSwMAIAGwhAdxQAYDAKQ8yzKYZ3Nl2rRpOnz4cMsu9R/nOI5eeeUVX4sDAABIRWQwAADs4tlcWb9+vUpLS7Vw4ULl5eXFqiYAABKHZZcBRHIggwEAUp5lGcxzmX7Xrl21ePFiVVdXx6oeAACAlEcGAwDALp4zVyRp4MCBGjhwYCxqAQAg8Vi23hfJgwwGAEhplmWwdpsrAACkMteyywACAAAkA9symA1XzgUAAAAAAEhYzFwBAMCLZVNSAQAAkoJlGYyZKwAAAAAAAJ0Q05krXSzrPKWCRO+uOT6MGXDNfh+afg7TZLg+H37sTNdoeryQzK/PDDlmawwGzNaYZni8gOHztRqvXbBc0+ZV8S4h5oJjHox3CQCAzrIsg7EsCAAAL65dm6kBAAAkBcsyWKJPXAAAAAAAAEhozFwBAMCLZVNSAQAAkoJlGYyZKwAAAAAAAJ3AzBUAADy4lr1rAgAAkAxsy2CeM1eamppUWVmppUuXau/eva0+96Mf/cjXwgAASAhR158b4IEMBgBIeZblL8/myoIFC3Tw4EFFIhHNmjVLzzzzTMvntm/f7mthAAAAqYoMBgCAXTyXBe3fv19btmyRJI0dO1b33HOPMjIydM8998h1edcNAJAConZdBhDJgQwGAEh5lmUwz+aK67o6e/asunTpopycHK1Zs0YTJkxQTk6OHMeJVY0AAAAphQwGAIBdPJcFTZw4UcXFxdq9e7ck6frrr9eaNWu0fPlyvfPOOzEpEACAuGLPFcQBGQwAkPIsy1+eM1fGjx+vL37xiwqHwy3H+vbtq5deekkbN27s8IN1ce2a1pMKAgme7x2ZL9D09cdNj2f6nNN8eA6Djtkxg47Z3w2hgPnfNaFgs9HxgmlmawwGzY7nJPovByDJmc5gqaZp86p4l4BPCI55MN4lAICvPJsr9fX1LS/q9fX1rT43fPhw/6oCACBRMMsEcUAGAwCkPMsymGdzZdq0aTp8+LAikUibzdMcx9Err7zia3EAAMQbm4ciHshgAIBUZ1sG82yurF+/XqWlpVq4cKHy8vJiVRMAAEBKI4MBAGAXz+0iunbtqsWLF6u6ujpW9QAAkFjY0BZxQAYDAKQ8y/KX58wVSRo4cKAGDhzoaxEAAABojQwGAIA92m2uAACQ0phlAgAAEHuWZTCaKwAAeHAte2EHAABIBrZlMM89VwAAAAAAAOCNmSsAAHix7F0TAACApGBZBotpcyXDjRodj2k3necosb9hAwlenyQFHLPjpRk+57SA2Z87SUpzzNYYTDNbYyjYbHQ8SQqFzY4ZCpkdL5hu/pwBADClafOqeJfQruCYB+NdAgCLWTtzhcYKACAmzPcnAQAA0B7LMpi1zRUAAGLBts3UAAAAkoFtGYwJIAAAAAAAAJ3AzBUAALxY9q4JAABAUrAsgzFzBQAAAAAAoBM63Fz5zne+40cdAAAkpqhPN6CDyGAAgJRiWf7yXBZUVlYmx2l9ndn9+/dr0qRJkqTnn3/ev8oAAABSFBkMAAC7eDZXCgsLtWbNGj388MPq1auXXNfVY489pvLy8ljVBwBAXNm2Uz2SAxkMAJDqbMtgnsuCJk6cqGeffVYvvvii6uvr9cUvflFZWVkaOnSohg4dGqsaAQCIH5YFIQ7IYACAlGdZ/mp3z5V+/frpueee01tvvaXp06fr4sWL/lYEAAAAMhgAABa5oksxh8NhzZkzR7/+9a/1X//1X1f9YF2c5qv+WkiOY9e0KBMCPpyz0/5dOsR0jab/ndMC5p/DYJrZtm8waPZ3Qyhk/ndNMGz2nEOZZmsMZvD71S+2TUlFcjGVwQC0r2nzKqPjBcc8aHQ8INXYlsE8myv19fWtPr7xxhtVXl7ecrxHjx7+VQYAAJCiyGAAANjFs7kybdo0HT58WJFIRK77UdfIcRy5rivHcfTKK6/EpEgAAOKG/VEQB2QwAEDKsyyDeTZX1q9fr9LSUi1cuFB5eXmxqgkAgIThWvbCjuRABgMApDrbMpjnhrZdu3bV4sWLVV1dHat6AAAAUh4ZDAAAu7S7oe3AgQM1cODAWNQCAEDisexdEyQPMhgAIKVZlsHavRQzAAAAAAAALu+KLsUMAECqsm29LwAAQDKwLYPRXAEAwItlL+wAAABJwbIMxrIgAAAAAACATmDmCgAAHmybkgoAAJAMbMtgMW2upAebYvlwSSfguPEuoV2OE+8K2ucYfh5N/7uYfg7TAuZ/K6WFzI4ZDJodL5Rh/ndNMGy4xiyz46V1NTqcXH5dAwDQKU2bVxkdLzjmQaPjATCLmSsAAHiw7V0TAACAZBDvDLZixQq9/PLLchxH48aN05QpUzzvT3MFAAAP8X5hBwAASEXxzGCvv/66XnvtNW3ZskVNTU264447NGzYMPXp0+eyX0NzBQAAAAAAJL3GxkY1Nja2OZ6dna3s7OyWj4cOHarnn39ewWBQx48fV3Nzs7p06eI5Ns0VAAC8uBZsJgUAAJBsfMhglZWVWrlyZZvj5eXlqqioaHUsFArpqaee0tq1a1VUVKTrr7/ec2zP5kpTU5M2btyo22+/Xddcc43+7d/+TW+++aZuvvlmTZs2Tenp6VdxOgAAAPBCBgMAwLzJkyeruLi4zfGPz1r5uOnTp+vee+/V/fffrw0bNmj8+PGXHTvg9cCzZ8/Wnj17FAgE9MQTT+j9999XaWmpTp06pblz53bwNAAAsI8b9ecGeCGDAQBSnR/5Kzs7W7169Wpz+2Rz5Z133tHBgwclSZmZmRo+fLh+97vfedbrOXPl97//vV566SVJ0r59+1RVVSXHcTRs2DDdcccdnXmeAAAAcBlkMAAA4ufIkSN66qmntH79eknSK6+8om984xueX+PZXOnSpYvefvtt9e/fX3369NHRo0fVo0cPHT9+XOFw2FzlAAAkKDfKniuIPTIYACDVxTODDRs2THV1dRo7dqzS0tI0fPhwjRw50vNrPJsrc+bM0ZQpU/SFL3xBmZmZ+uY3v6lBgwbpwIEDWrRokdHiAQBIRCzhQTyQwQAAqS7eGayioqLNJrdePJsrt9xyi2pra7Vr1y69++67uvHGG3XdddfpscceU7du3TpcXDjY3OGvsZljwZudjuPGuwRPAR/qcwJmxzT97xxIM/tbxI/nMC1ktsZg2PB46eZ/EwczzY6Z1tXocErLNnvxN/c8HQUgnkxnMAAA4C/PNF5fXy9JGjBggAYMGNByPBqNqr6+Xj169PC3OgAA4szlUsyIAzIYACDV2ZbBPJsr06ZN0+HDhxWJROS6H7377TiOXNeV4zh65ZVXYlIkAABAKiGDAQBgF8/myvr161VaWqqFCxcqLy8vVjUBAJAw4r3eF6mJDAYASHW2ZbCA1ye7du2qxYsXq7q6Olb1AACQUNyo48utI7Zv366SkhKNGDFCixcvliTt2rVLo0eP1vDhw7V8+fKW+x48eFAlJSUqLCzUvHnz1NTUZPT5QGyQwQAAqS7e+aujPJsrkjRw4ED9y7/8i69FAACAT/fHP/5RCxcu1KpVq7Rlyxb99re/1Y4dOzR37lytWrVKNTU12r9/v3bs2CFJmjlzphYsWKCXX35Zrutqw4YNcT4DXC0yGAAA9mi3uQIAQCpzXX9ujY2NOnLkSJtbY2Njq8f/2c9+pjvuuEPdunVTKBTS8uXLlZmZqc985jO64YYbFAwGNXr0aNXW1ur999/X+fPnNXjwYElSSUmJamtr4/G0AQAAdIof+ctPZq/dCQAArkhlZaVWrlzZ5nh5ebkqKipaPn733XcVCoV0//336+jRo/ra176m/v37Kzc3t+U+kUhEx48f14kTJ1odz83N1fHjx/09EQAAANBcAQDAi1/rcydPnqzi4uI2x7Ozs1t93NzcrL1792rdunXq0qWLHnjgAWVkZMhx/q+uv15BJhqNfupxAAAA2/i9R4ppNFcAAPDg1wt7dnZ2m0bKp7nuuuuUn5+vnJwcSdI///M/q7a2VmlpaS33aWhoUCQSUbdu3dTQ0NBy/OTJk4pEIuaLBwAA8JltzRX2XAEAIIF9/etf16uvvqrGxkY1Nzdr586dKioq0qFDh/Tuu++qublZW7duVUFBgXr27Kn09HTt27dPkrR582YVFBTE+QwAAACSX0xnroRCzbF8uA5LxZnTTsDsrj6OY3a8gOHxJMkx3FI0fs5phscLmr9AvOkag+lma0xLN/99k9bV9Hhmf/0Grkk3Ol40cNHoeDbze/Oz9gwaNEjf/va3VXP0fw0AACAASURBVFpaqkuXLunLX/6yJkyYoD59+qiiokIXLlzQsGHDVFRUJElatmyZ5s+frzNnzujmm2/WpEmT4nsCAAAjmjavMj5mcMyDxscETIl3BusolgUBAJDgxo0bp3HjxrU6lp+fry1btrS570033aSNGzfGqjQAAACI5goAAJ5sW+8LAACQDGzLYOy5AgAAAAAA0AnMXAEAwIPr2vWuCQAAQDKwLYPRXAEAwINrfk9oAAAAtMO2DOa5LKipqUkbN27U1q1bdenSJX3ve9/T6NGj9d3vflcffPBBrGoEAABIKWQwAADs4tlcmT9/vn71q19p69atKisrUzAY1PLly9W7d28tWLAgVjUCABA3Udfx5QZ4IYMBAFKdbfnLc1nQgQMH9NJLL6m5uVnDhg3TCy+8IEnq16+fxowZ42thAAAAqYoMBgCAXTybK4FAQIcOHdLp06d1+vRpHTlyRL169dKf//xnNTU1xapGAADixrbN1JAcyGAAgFRnWwbzbK7MnDlTU6ZMUTQa1Q9/+EPde++9+uxnP6s333xT06dP7/CDhULNV11oLDgpeGFqx3HNjhcwPJ4PP0/GazQ8XiAtsceTpLSw4RpDZsdL62J0OElSoEua2fGyQkbHc7IyjI6XlpWh6AcfGh3TVm7Urhd2JAfTGQwAkJrO1e9UZo+vxruMq2JbBvNsrnzlK1/RL3/5y5aPBw8erL1792r69Onq27ev37UBAOKExgoQX2QwAIAJtjZWbOTZXKmvr29zbODAgS2f69Gjhz9VAQCQIFzzk7+AdpHBAACpzrYM5tlcmTZtmg4fPqxIJCL3E2fmOI5eeeUVX4sDAABIRWQwAADs4tlcWb9+vUpLS7Vw4ULl5eXFqiYAABKGbet9kRzIYACAVGdbBvPcwrVr165avHixqqurY1UPAAAJJeo6vtwAL2QwAECqsy1/ec5ckT5a3/vXNb4AAACIDTIYAAD2aLe5AgBAKnOZZQIAABBztmUwz2VBAAAAAAAA8MbMFQAAPNh2GUAAAIBkYFsGY+YKAAAAAABAJ8R05kowHI3lw8WdE0j8VpvpGh3Dy+L8eA4dwy1FxzFbYyBoeLyQ+ecwEE7w8bqY7xsHupj9del0TTc7Xlam2fFOnzM6ns24sg8AIFk1bV5ldLzgmAeNjofUZlsGY1kQAAAebNtMDQAAIBnYlsFYFgQAAAAAANAJzFwBAMCDbZupAQAAJAPbMhgzVwAAAAAAADqh3ZkrO3fuVG1trY4dO6ZAIKBIJKKCggIVFhbGoj4AAOLKts3UkBzIXwCAVGdbBvNsrqxYsUJ1dXW68847FYlE5LquGhoatHHjRv3mN7/R7NmzY1UnAABxYdtmarAf+QsAAPsymGdzpaamRtu2bVMg0Hr10KhRozRq1Che3AEAAAwjfwEAYB/P5kp6erqOHTumHj16tDpeX1+vcDjsa2EAACQC26akwn7kLwAA7Mtgns2VOXPm6O6771bv3r2Vm5srx3F04sQJHT58WEuWLIlVjQAAACmD/AUAgH08mytf+tKX9Oijj+rQoUNKS0tTr1691K1bNw0aNEhVVVW67bbbYlUnAABxYdlVAJEEyF8AANiXwTybK8uWLdOBAwfUp08fbdu2TbNnz9att94qSXrhhRc0fvz4Dj1YWih69ZXGgBNI7H8+x4ILZzuO2efQj3MOBA3/Oxs+50C71/Dq4Hg+zCB3DI8ZyDD7Dx3oYvhJlORkmj1pJzM9ocdTMM3seBazbUoq7Gc6fwEAYCPbMpjnXyA7duxQVVWVgsGgysrKNHXqVIXDYY0YMUKum9iNCAAAABuRvwAAsI9nc8V1XTnOR92i3r17a/Xq1ZoyZYpycnJajgMAkMxsuwwg7Ef+AgDAvgzmORe/qKhIZWVlqqurkyT1799fK1as0IwZM/Tee+/FpEAAAIBUQv4CAMA+njNXysvLlZeXp6ysrJZjeXl52rRpk9auXet7cQAAxFti7xaGZET+AgDAvgzW7q6P+fn5bY51795d8+bN86UgAACAVEf+AgDALuYvqQEAQBJxZdd6XwAAgGRgWwajuQIAgIcoF2cBAACIOdsymOeGtgAAAAAAAPDGzBUAADxELZuSCgAAkAxsy2Axba4E023b7zexOIHEnxflGJ4L5aSZP2fjNRr+KTI9XiBs/peSY3hMJyPN7Hjp5n+1OZlhswNmZJgdr0sXs+MF7HoxA3B5jev2xrsE62WXDYl3CQCABMfMFQAAPNi2mRoAAEAysC2D0VwBAMADcy4BAABiz7YMxoa2AAAAAAAAncDMFQAAPNg2JRUAACAZ2JbBPGeuNDU1qbKyUkuXLtXeva03Q/vRj37ka2EAAACpiPwFAIB9PJsrCxYs0MGDBxWJRDRr1iw988wzLZ/bvn2778UBABBvUZ9uwOWQvwAAsC9/eS4L2r9/v7Zs2SJJGjt2rO655x5lZGTonnvukesm/mWBAQDoLBohiDXyFwAA9mUwz+aK67o6e/asunTpopycHK1Zs0YTJkxQTk6OHMeu9U8AAAA2IH8BAGAfz2VBEydOVHFxsXbv3i1Juv7667VmzRotX75c77zzTkwKBAAgnlw5vtyAyyF/AQDgTwbzk+fMlfHjx6uxsVH/+7//q549e+rv//7v1bdvX7300kv6z//8T18LAwAASEXkLwAA7OPZXFm2bJn279+vvn37asKECZo1a5bGjBmjrl27atu2bbrvvvs69GCBUGKvmnI85/EkJ9PnbPw59OHfxPg5G76guRM221F1wuafRNNjBjJDRsdzMsyOJ0lOZnpij5eRYXa8YAr+QryMKJNMEGOm8xc6r3Hd3vbvlGSyy4bEuwRYqGnzKqPjBcc8aHQ8G5h+Dm1mWwbz/LNwx44dqq6uVlpamsrKyjR16lSFw2GNGDGCDdUAAAB8QP4CAMA+7W5o+1e9e/fW6tWrNWXKFDZUAwCkjCj7oyDGyF8AANiXwTznfRcVFamsrEx1dXWSpP79+2vFihWaMWOG3nvvvZgUCABAPLk+3YDLIX8BAGBf/vKcuVJeXq68vDxlZWW1HMvLy9OmTZu0du1an0sDAABIPeQvAADs0+5WnPn5+W2Ode/eXfPmzfOlIAAAEklib8WOZEX+AgCkOtsyGJeDAAAAAAAA6ATDF5EFACC5RNlAFAAAIOZsy2A0VwAA8MDmswAAALFnWwZjWRAAAAAAAEAnxHTmSlrY8IAp2BpyEv2cDdfny/marjFodrqaEzZ/0qbHDKSb/dXhZISMjidJTma62QHTDf8Cy8wwO15GptHh0m4ZqOa6A0bHtJVtm6kBgAmN6/YaHzO7bIjxMZHcmjavUnDMg/Euw2qnn56gax5YH+8yroptGSzR/1S/PHsrv2oJ31hBQvKjWZPojDdWUhCNFQCASTRWcDVorHSerY0VG7HnCgAAHqJ27aUGAACQFGzLYDRXAADwEJVlr+wAAABJwLYMRnMFAAAAAADgY1auXKlt27ZJkoYNG6ZZs2Z53r/DmzF85zvfubrKAACwkOvTDegI8hcAINXEM3/t2rVLr776qqqqqlRdXa0DBw7oZz/7mefXeM5cKSsrk+O0noqzf/9+TZo0SZL0/PPPd6A8AAAAtIf8BQCAPxobG9XY2NjmeHZ2trKzs1s+zs3N1Zw5cxQOf3TF0L59+6q+vt5zbM/mSmFhodasWaOHH35YvXr1kuu6euyxx1ReXn415wEAgHVs20wN9iN/AQDgTwarrKzUypUr2xwvLy9XRUVFy8f9+/dv+f/Dhw9r27ZtWr/e+8pLns2ViRMn6rbbbtPChQt11113aezYscrKytLQoUM7eg4AAAC4AuQvAAD8MXnyZBUXF7c5/vFZKx/39ttva9q0aZo1a5Z69+7tOXa7G9r269dPzz33nJ588klNnz5dFy9evLKqAQBIAtF4F4CURP4CAKQ6PzLYJ5f/eNm3b5+mT5+uuXPnauTIke3ev93mys9//nMdPXpUpaWlOnLkiLZu3SpJ+slPfqLx48dfUVEAANiKzWcRD+QvAECqi2cGO3r0qB566CEtX75c+fn5V/Q1ns2VZcuWaf/+/erbt6+eeeYZzZo1S9///vclSS+88EKHX9ydcIfu3v54Hb7WkeV8OF8nkOCbCfhxzkHD52z4OXTCZk/aCacZHU+SFDZ8FfeQ4fHSDf+ykeQYHtPJyDQ6njINj5fovxuAJGY6fwGJoHHdXuNjZpcNMT4mAEjSs88+qwsXLmjp0qUtx771rW9pwoQJl/0az79oduzYoaqqKgWDQZWVlWnq1KkKh8MaMWKEXDe+7+WlXGMFABAXibKh7RNPPKFTp05p6dKlOnjwoObNm6cPP/xQQ4YM0aJFixQMBlVfX6+ZM2fqT3/6k2688UYtW7ZMWVlZ8S4dHZTI+QsAgFiJZwabP3++5s+f36Gv8WxRuK7bcinA3r17a/Xq1Xr88cf1P//zP20uEQgAAPyxe/duVVVVtXw8c+ZMLViwQC+//LJc19WGDRskSYsWLVJpaalqa2s1YMAArVq1Kl4loxPIXwAA2MezuVJUVKSysjLV1dVJ+uhyRCtWrNCMGTP03nvvxaRAAADiKerT7Up98MEHWr58ue6//35J0vvvv6/z589r8ODBkqSSkhLV1tbq0qVL2rNnjwoLC1sdh33IXwAAxDd/XQ3PZUHl5eXKy8trNaU4Ly9PmzZt0tq1a30uDQCA+PPrhbixsVGNjY1tjn9yF/sFCxbokUce0dGjRyVJJ06cUG5ubsvnc3Nzdfz4cZ06dUpdu3ZVMBhsdRz2IX8BAGDfFRvb3UXy03bG7d69u+bNm+dLQQAApILKykqtXLmyzfHy8nJVVFRIkn7605+qe/fuys/P16ZNmyRJ0Wi01dKQvy4h+fhSkr9iCYm9yF8AANjF8CU6AABILq5P/YnJkyeruLi4zfGPz1qpqalRQ0ODxowZo7/85S86e/asHMdRQ0NDy31OnjypSCSinJwcnT59Ws3NzUpLS1NDQ4MikYg/xQMAAPjMrwzmF5orAADEwSeX/3ya5557ruX/N23apNdff11LlizRqFGjtG/fPuXl5Wnz5s0qKChQKBTSkCFDVFNTo9GjR6u6uloFBQV+nwYAAABEcwUAAE+JuN532bJlmj9/vs6cOaObb75ZkyZNkiQtXLhQc+bM0dNPP63u3bvrySefjHOlAAAAVycRM5gXmisAAHhIlBf2kpISlZSUSJJuuukmbdy4sc19evbsqXXr1sW6NAAAAOMSJYNdKc9LMQMAAAAAAMBbTGeuBMIGd6RJwbaQE/BhR59Efx59OGcnaHZMJ2j4STQ8nhNKMzqeJDnpIcPjhRN6PElSerrZ8cKGx0vvYnQ4J5Dovxxix413AQCAT9W4bq/R8bLLhhgdD0Dn2JbBSM8AAAAAAACdwJ4rAAB4iFp2GUAAAIBkYFsGY+YKAAAAAABAJzBzBQAAD7btVA8AAJAMbMtgnjNXmpqa9MILL+hPf/qTLl68qJUrV2ratGl66qmndOHChVjVCABA3ER9ugGXQ/4CAMC+/OXZXJk9e7b27NmjQCCgJ554Qu+//75KS0t16tQpzZ071+fSAAAAUg/5CwAA+3guC/r973+vl156SZK0b98+VVVVyXEcDRs2THfccUdMCgQAIJ5suwwg7Ef+AgDAvgzmOXOlS5cuevvttyVJffr00dGjRyVJx48fVzgc9r86AACAFEP+AgDAPp4zV+bMmaMpU6boC1/4gjIzM/XNb35TgwYN0oEDB7Ro0aJY1QgAQNzYdhlA2I/8BQCAfRnMs7lyyy236NFHH9WRI0eUkZGhG2+8Udddd50ee+wx7dixo8MP5oQT/NkJJHZ9ToLXJ8n8xb19OGcnaLZIJ83wSZuuL2z+omDGxzQ9Xrr5d3Yd02NmZpodLz3D7HhoweaziDXT+QvAlWlct9foeNllQ4yOl4qaNq8yPmZwzIPGx4Q/bMtgnn/FLVu2TJs3b9apU6e0du1ade/eXePGjVO3bt30wgsvxKpGAACAlEH+AgDAPp5vF+/YsUNVVVUKBoMqKyvT1KlTFQ6HNWLECLmubdvLAADQcbzaIdbIXwAA2JfBPJsrruvKcT5altG7d2+tXr1aU6ZMUU5OTstxAAAAmEP+AgDAPp7LgoqKilRWVqa6ujpJUv/+/bVixQrNmDFD7733XkwKBAAgnqJyfbkBl0P+AgDAnwzmJ8+ZK+Xl5crLy1NWVlbLsby8PG3atElr1671tTAAABKBbZupwX7kLwAA7Mtg7V6iIz8/v82x7t27a968eb4UBAAAkOrIXwAA2MX8NVoBAEgiLOABAACIPdsymOeeKwAAAAAAAPDGzBUAADzYtt4XAAAgGdiWwZi5AgAAAAAA0AkxnbnihFOslxNw4l1BuxzTNSb6eJKcNMPfh8E0o8M5QcP1hXz4MTc8phMKGR1PpseTpHC64fEyEns8tIgm/q9yAACApGNbBmNZEAAAHqLWbacGAABgP9syWIpNJQEAAAAAADCLmSsAAHiw6z0TAACA5GBbBmPmCgAAAAAAQCd4zlxpampSdXW1MjIyVFhYqCVLlmjPnj0aMGCAZs+erWuvvTZWdQIAEBe2XQYQ9iN/AQBgXwbznLkyf/58/epXv9LWrVtVVlamYDCo5cuXq3fv3lqwYEGsagQAIG6icn25AZdD/gIAwJ8M5ifPmSsHDhzQSy+9pObmZg0bNkwvvPCCJKlfv34aM2aMr4UBAACkIvIXAAD28WyuBAIBHTp0SKdPn9bp06d15MgR9erVS3/+85/V1NQUqxoBAIgb5pgg1shfAADYl8E8myszZ87UlClTFI1G9cMf/lD33nuvPvvZz+rNN9/U9OnTY1UjAABAyiB/AQBgH8/myle+8hXNnz9f9fX1+uxnP6t169Zp7969mj59uvbu3RurGgEAiBvbNlOD/chfAADYl8E8myvLli3TgQMH1KdPH02YMEGzZs1qWev76KOPavz48R16MCeY4Fd+DjjxrsCbD/U5ToKfsx/fMwGzYxr/vg55/lh2mBM2O54kKZhmdjzT55weNjqeJCk9w+x4IbM1OuFMo+Ml/O/DGGLzWcSa6fwFID4a15lthmaXDTE6HpDobMtgnn/R7NixQ1VVVQoGgyorK9PUqVMVDoc1YsQIua5dJwoAAGAD8hcAAPbxbK64rtsys6F3795avXq1pkyZopycnMSf8QAAgAH8KYtYI38BAGBfBvNcz1BUVKSysjLV1dVJkvr3768VK1ZoxowZeu+992JSIAAAQCohfwEAYB/PmSvl5eXKy8tTVlZWy7G8vDxt2rRJa9eu9b04AADizbbN1GA/8hcAAPZlsHZ3kczPz29zrHv37po3b54vBQEAkEhc6yalIhmQvwAAqc62DJbgl+8BAAAAAABIbD5coxUAgORh25RUAACAZGBbBmPmCgAAAAAAQCcwcwUAAA9Ry9b7AgAAJAPbMlhsmytBsxNlHMcxOl7CC/hwvqbHDBieDOXDOTuGvw+VlmZ0OCdodjyFQmbHk+SYHtP4eGGz40nmawxnmB0vlG52PAAAAABXzNqZKynXWAEAxIVd75kAAAAkB9symLXNFQAAYsG2KakAAADJwLYMxoa2AAAAAAAAncDMFQAAPNh2GUAAAIBkYFsGa7e5snPnTtXW1urYsWMKBAKKRCIqKChQYWFhLOoDAABIOeQvAADs4tlcWbFiherq6nTnnXcqEonIdV01NDRo48aN+s1vfqPZs2fHqk4AAOLCtWy9L+xH/gIAwL4M5tlcqamp0bZt2xT4xOV1R40apVGjRvHiDgBIerZNSYX9yF8AANiXwTw3tE1PT9exY8faHK+vr1c4HPatKAAAgFRF/gIAwD6eM1fmzJmju+++W71791Zubq4cx1FDQ4MOHTqkJUuWxKpGAADixrYpqbAf+QsAAPsymGdz5Utf+pKefvppnT59WidOnNChQ4d09OhRzZw5U7fddlusagQAAEgZ5C8AAOzj2Vz58Y9/rHXr1ikajeq2227T0aNHVVhYqBdffFGHDh3SQw891KEHc9I8VyF1TMAxN5ZfAgbP1y+Gn0fH9L9LWprZ8STz5xw0XGPI8BXS/XgOTdcYCpkdL2h4PEkKZxgdzglnGh1PQZYK+MW29b6wn+n8BSA5NK7ba3zM7LIhxscETLEtg3n+hfTiiy+qpqZGJ0+e1KhRo/Taa68pPT1dd911l8aNG8eLOwAg6UVdu6akwn7kLwAA7MtgnlMrotGowuGwevbsqalTpyo9Pb3lc83Nzb4XBwAAkGrIXwAA2MezuTJ8+HBNnDhRzc3NqqiokCS99dZbKi0t1YgRI2JSIAAA8eT6dAMuh/wFAIB9+ctzWdDDDz+sPXv2KO1jezaEw2FVVFRo2LBhPpcGAACQeshfAADYp91dKW+99dZWH/fp00d9+vTxrSAAABJJlHkmiAPyFwAg1dmWwSy4nA0AAAAAAEDiMnw9VQAAkotr2bsmAAAAycC2DEZzBQAAD9F4FwAAAJCCbMtgLAsCAAAAAADohNjOXAmmtX+fjgg4ZsczzEnw+iSZfw4dw/26oPn+nxMwPGbI8I+R4Z8TJ+zDj3ma4RpN/24I+nDOoXBCj+cE042Oh/9j22ZqAAAAycC2DGbvzBUbGhcAAAAAACDpsecKAAAebNtMDQAAIBnYlsForgAA4MG2zdQAAACSgW0ZzN5lQQAAAAAAAAnAs7nS1NSkyspKLV26VHv37m31uR/96Ee+FgYAQCJwXdeXG3A55C8AAPzJYH7ybK4sWLBABw8eVCQS0axZs/TMM8+0fG779u2+FgYAAJCKyF8AACSGM2fOaNSoUTpy5Ei79/Xcc2X//v3asmWLJGns2LG65557lJGRoXvuuYd33QAAKcG2ywDCfuQvAADin8HeeOMNzZ8/X4cPH76i+3s2V1zX1dmzZ9WlSxfl5ORozZo1mjBhgnJycuQ4XAoZAJD8bNtMDfYjfwEA4E8Ga2xsVGNjY5vj2dnZys7ObnVsw4YNWrhwoWbNmnVFY3suC5o4caKKi4u1e/duSdL111+vf//3f9fy5cv1zjvvXGn9AAAAuELkLwAA/FFZWal/+qd/anOrrKxsc9/HH39cQ4YMueKxPWeujB8/XkOHDlVGRoYk6ac//al+97vfacaMGTp16lQHTwMAAPu4cZ6SunLlSm3btk2SNGzYMM2aNUu7du3SkiVLdOHCBY0YMUKPPPKIJOngwYOaN2+ePvzwQw0ZMkSLFi1SMOj5Uo8ERP4CAMCfDDZ58mQVFxe3Of7JWStXwzNx/fjHP9a6desUjUZ122236ejRo7r99tu1ZcsW3XLLLR1+MCdo8MrPAQumxToWXOna9PNoeDwnmGZ0PElSmuExDdfohEJGxzN+vpIUNlxjKGx4PMP1SVLQcI3BdLPjpfEHdDLatWuXXn31VVVVVclxHH3729/W1q1btWzZMq1bt07du3fXtGnTtGPHDg0bNkwzZ87U4sWLNXjwYM2dO1cbNmxQaWlpvE8DHWQ6fwEA/k/T5lXxLgFx9GnLf0zxTOMvvviiampqdPLkSY0aNUqvvfaa0tPTddddd2ncuHEqLy/3pSgAABKFX5upXcma39zcXM2ZM0fh8EfNvb59++rw4cP6zGc+oxtuuEGSNHr0aNXW1qpfv346f/68Bg8eLEkqKSnRU089RXPFQuQvAADiv6FtR3k2V6LRqMLhsHr27KmpU6cqPf3/3mltbm72vTgAAJJVZWWlVq5c2eZ4eXm5KioqJEn9+/dvOX748GFt27ZNEydOVG5ubsvxSCSi48eP68SJE62O5+bm6vjx4z6eAfxC/gIAwD6ezZXhw4dr4sSJev7551uC3ltvvaX58+drxIgRMSkQAIB48uvStx1Z8/v2229r2rRpmjVrltLS0lpdEtB1XTmOo2g02upKMn89DvuQvwAA8C+DddT27duv6H6ezZWHH35Ye/bsUdrH9mwIh8OqqKjQsGHDOlchAAAW8OtSzFe65nffvn2aPn265s6dq5EjR+r1119XQ0NDy+cbGhoUiUTUrVu3VsdPnjypSCTiS+3wF/kLAAD/Mphf2t1x9dZbb231cZ8+fXhhBwAgBo4ePaqHHnpIy5Yt08iRIyVJgwYN0qFDh/Tuu++qublZW7duVUFBgXr27Kn09HTt27dPkrR582YVFBTEs3x0AvkLAAC7cHkJAAA8xPNSzM8++6wuXLigpUuXthz71re+paVLl6qiokIXLlzQsGHDVFRUJElatmyZ5s+frzNnzujmm2/WpEmT4lU6AABAp8Qzg10NmisAACSo+fPna/78+Z/6uS1btrQ5dtNNN2njxo1+lwUAAIBPoLkCAIAH2y4DCAAAkAxsy2A0VwAA8JAoO9UDAACkEtsyWLsb2gIAAAAAAODyYjtz5WOXFOy0gGNuLFv4cM5OwHB/zXSNJr9n/ipoeEzTNZoeLxQyO54kpRn+1WH6nINhs+NJUsjsmE440+h4CqWbHQ8tbJuSCgAAkAxsy2DMXAEAAAAAAOgE9lwBAMCDbZcBBAAASAa2ZTCaKwAAeIhatpkaAABAMrAtg7EsCAAAAAAAoBM63Fz5zne+40cdAAAkJNenG9AR5C8AQKqxLX95LgsqKyuT47S++sv+/fs1adIkSdLzzz/vX2UAAAApiPwFAIB9PJsrhYWFWrNmjR5++GH16tVLruvqscceU3l5eazqAwAgrmy7DCDsR/4CAMC+DOa5LGjixIl69tln9eKLL6q+vl5f/OIXlZWVpaFDh2ro0KGxqhEAACBlkL8AALBPu3uu9OvXT88995zeeustTZ8+XRcvXoxFXQAAJISoXF9ugBfyF/D/2rvz4Krq+//jr5vlpkFkKJWAAykYLcWhEAGRIEsKlYvZCEuAkBKWlAIthjQ4sn0pWKVsybbjZgAAGRJJREFUxUEpnU5tFRSwgCxSKJsFtRAWgbGmRUHKTokhAW0SiVnuPb8//JECkou559zknuT5YJjxZvDF+yQ53Nd88jnnAGjo7Na/7voo5nPnzik8PFwzZszQunXr1LhxY23fvl3x8fE+/G2B/XAiR1Bgz6cgx93/TE05LD5mq2cMCbY2T7L8mB1WzxjoeZIcoaHWBoY6rc0Ltv4p847QMGsDQ6w9ZocfjhlfMWz2GEDUD5b2LwCoRtGqo5bmNUl/1NI8NGx262Be2/jKlSu1atUqeTwexcTE6NNPP9UTTzyhjRs36uzZs5o8eXJtzQkAANAg0L8AALAfr4srGzdu1Pbt21VYWKjExEQdOnRIYWFhGjZsmFJSUnhzBwDUe1zCg9pG/wIAwH4dzOv1ER6PR06nU61atVJGRobCwv63Ld7tdvt9OAAAgIaG/gUAgP14XVxxuVwaNWqU3G63MjMzJUknTpxQWlqa4uLiamVAAADqkuGnX0B16F8AAPing/mT18uCsrKydOTIEQUH/++GmE6nU5mZmYqNjfXrYAAABAK73UwN9kf/AgDAfh3sro+X6Nat2y2vo6KiFBUV5beBAAAAGjr6FwAA9sKzOwEA8MJuN1MDAACoD+zWwbzecwUAAAAAAADesXMFAAAv7Ha9LwAAQH1gtw7G4goAAF7YbUsqAABAfWC3DlariyuOkOC7/6H6xGHxVVdBDmvzJCkowGe0+nMoP3wfBgd6nh9O80A/5lCntXmS9Z/H0DBr84JDrc0DAAAA8I2xcwUAAC8Mm/3UBAAAoD6wWwfjhrYAAAAAAAAmsHMFAAAvPDa7mRoAAEB9YLcOxs4VAAAAAAAAE7wurlRWVmrt2rW6evWqysvLtXz5ck2cOFHLli1TWVlZbc0IAECdMfz0C6gO/QsAAP90MH/yurgyffp0HTlyREFBQVq0aJH+85//KC0tTZ999plmzZrl18EAAAgEHsPwy2+gOvQvAAD808H8yes9Vz755BNt3bpVknTs2DFt3rxZDodDsbGxio+P9+tgAAAADRH9CwAA+/G6c6VRo0Y6deqUJCkqKkp5eXmSpPz8fDmdTv9PBwBAHeOyINQ2+hcAAPa7LMjrzpUZM2Zo3Lhx6tKli8LDwzV8+HBFR0fr+PHj+tWvfuXXwQAAABoi+hcAAPbjdXGlc+fO+tOf/qQTJ06ooKBAkZGR+uMf/6jnn39esbGxNf/bHBY/nCjIYW2e1YJs8DAmqz+HFn+NHSHBluZJkoItzrQ6z+Jjdlg9nyQFW/wU90DPk6SQMEvjHCEW//TZH8cMSfZ7DCDsz/L+BQCADdmtg3lt4ytXrtSqVavk8XgUExOjvLw8TZs2TVu2bNHFixc1efLk2prz6wJ9YQUAUC9wCQ9qW0D3LwAAaondOpjXxZWNGzdq+/btKiwsVGJiog4dOqSwsDANGzZMKSkpvLkDAABYjP4FAID9eF1c8Xg8cjqdatWqlTIyMhQW9r9t8W632+/DAQBQ1+y2JRX2R/8CAMB+HczrDTJcLpdGjRolt9utzMxMSdKJEyeUlpamuLi4WhkQAACgIaF/AQBgP153rmRlZenIkSMKvumGmE6nU5mZmdxQDQDQINjtel/YH/0LAAD7dbC7Pl6iW7dut7yOiopSVFSU3wYCACCQGIanrkdAA0T/AgA0dHbrYDZ4VjAAAAAAAEDguuvOFQAAGjKPzbakAgAA1Ad262DsXAEAAAAAADCBnSsAAHhh2OwxgAAAAPWB3TpY7S6uhATf/c/UJ0EOa/McfthoZPGMjiCLZwz2w/eM1d+Hlh+zxadliB9Oc6szrT5mq/P8kRkcammcwx//PgAAAAD4Rti5AgCAF3a73hcAAKA+sFsHY3EFAAAv7LYlFQAAoD6wWwdjHzkAAAAAAIAJ7FwBAMALj81+agIAAFAf2K2Ded25UllZqQ0bNmjbtm2qqKjQc889p6SkJM2cOVOff/55bc0IAADQYNC/AACwH6+LK7Nnz9bf//53bdu2Tenp6QoJCdHSpUvVtm1bzZkzp7ZmBACgzhh++gVUh/4FAIB/Opg/eb0s6Pjx49q6davcbrdiY2O1du1aSdJDDz2k5ORkvw4GAEAgsNvN1GB/9C8AAOzXwbwurgQFBens2bMqLi5WcXGxLl26pNatW+vq1auqrKysrRkBAAAaDPoXAAD243Vx5ZlnntG4cePk8Xj0wgsv6Kc//anatWunf/7zn5oyZUptzQgAQJ3xcAkPahn9CwAA+3Uwr4srvXr10ooVK9SoUSO1aNFCJ0+e1I4dO5SamqpBgwbV1owAAAANBv0LAAD78bq4snLlSq1atUoej0cxMTHKy8vTyJEjtXfvXlVUVGjy5Mk1+9uCHGZm9T+H1/v71lygH68kR5DFxxwcbG2ePz6HDoszQ6w9ZofVx2z118QfmaFOS+McwaGW5kmSIyTM2jyLjxn+Y7frfWF/lvcvAABsyG4dzOviysaNG7V9+3YVFhYqMTFRhw4dUlhYmIYNG6aUlBTe3AEA9Z7HZm/ssD/6FwAA9utgXrcteDweOZ1OtWrVShkZGQoL+99Pbt1ut9+HAwAAaGjoXwAA2I/XxRWXy6VRo0bJ7XYrMzNTknTixAmlpaUpLi6uVgYEAKAuGYbhl99AdehfAAD4p4P5k9fLgrKysnTkyBEF33R/BafTqczMTMXGxvp1MAAAgIaI/gUAgP14XVyRpG7dut3yOioqSlFRUX4bCACAQGK3xwCifqB/AQAaOrt1MIsfFQMAAAAAANCw3HXnCgAADRn3RwEAAKh9dutgLK4AAOCF3R4DCAAAUB/YrYNxWRAAAAAAAIAJtbtzxWHxWk6Qw9o8izmCbHC8gf41uelJCZYJsfjb3urPYXCAzydZP6PVeVZ/jSU/HHOotXket7V5qGLY7GZqAAAA9YHdOph9d64E+MIKAAAAAABoGLjnCgAAXtjtel8AAID6wG4djMUVAAC8sNud6gEAAOoDu3Uw+14WBAAAAAAAEACq3bni8Xi0fv167dixQ/n5+QoKClJERIT69Omj9PR0hYZafDNGAAACkN1upgb7o4MBAGC/Dlbt4srcuXPl8XiUmZmpiIgIGYahgoIC/eUvf9HMmTO1ZMmS2pwTAACgQaCDAQBgP9Uurhw5ckQ7d+685WNt2rTRo48+qvj4eL8PBgBAILDb9b6wPzoYAAD262DV3nPlnnvuUW5u7tc+/sEHH+iee+7x61AAAAQKwzD88rsmtm7dqvj4eLlcLq1Zs8ZPR4pAQQcDAMA/Hawmatq/qt25Mm/ePE2bNk1lZWVq3ry5HA6HCgoK5HQ69Zvf/KZGQwEAAN/k5+dr6dKl2rRpk5xOp1JTU9W9e3c99NBDdT0a/IQOBgBA3fKlf1W7uPLwww9r69atunz5sq5cuSKPx6MNGzZo/vz5fhkeAIBA5K8NqUVFRSoqKvrax5s0aaImTZpUvT5w4IBiYmLUtGlTSdKAAQO0c+dOPfXUU36aDHWNDgYAgH86mD/7V7WLKzNnzvzax/bu3Vv18QULFnzzI/j/7vm/12v8/wAAal/o8+stz6x83vLIWlFZ/h+/5P72t7/V8uXLv/bxp556SpmZmVWvr1y5oubNm1e9joiIuOMlI6g/rO5gLd5914qxAAA2VPkT+94E3R8dzJ/9q9rFlaZNm+qtt97SpEmTqlZwDh06pMcee6zGBwAAAG41ZswYDR48+Gsfv/mnJtJXj+V1OBxVrw3DuOU16h86GAAA/uHP/lXt4sr06dPVp08fvfjii5o6daq6d++u11577Y6DAACAmrl9+2l1WrZsqaNHj1a9LigoUEREhD9HQx2jgwEA4B/+7F/VPi1Iknr06KE//OEPeuONN7Ro0SK53e5vODIAALDC448/roMHD+ratWsqLS3V7t271adPn7oeC35GBwMAoO740r+8Lq5IX21NfemllxQVFXXLNUcAAMD/WrRooezsbI0ePVqDBg1SYmKiOnXqVNdjoRbQwQAAqBu+9C+HUdOHPQMAAAAAAKDKXXeuAAAAAAAAoHosrgAAAAAAAJjA4goAAAAAAIAJLK4AAAAAAACYwOIKAAAAAACACQG1uLJ161bFx8fL5XJpzZo1lmSWlJQoMTFRly5dsiRv+fLlSkhIUEJCghYvXmw676WXXlJ8fLwSEhK0YsUKCyb8yqJFizRjxgxLstLT05WQkKDk5GQlJyfrww8/NJW3d+9eDRkyRHFxcZo3b56prDfffLNqruTkZHXt2lXPPfecqUxJ2rJlS9XXedGiRabzXn75ZQ0YMEBJSUn6/e9/73PO7d/PBw4cUFJSklwul5YuXWo6T5IqKio0ZswYHT582HTeunXrlJiYqKSkJM2cOVPl5eWmM9944w0lJCQoPj5eixYtUk0feFbdvwmrV69Wenq66flmzpwpl8tV9T359ttvm8784IMPNHz4cCUkJGjq1Kk1/jzenPfee+/dcs7ExMRo4sSJpubbv3+/Bg4cqMTERE2bNs3UfJK0adMmxcfHKykpSfPmzVNlZWWN8gDUXKB3MKv7lxT4Hczq/iUFfgezun9JdDBfO5jV/etOmTcESgezun/dnkkHawCMAPHpp58affv2NT777DPjiy++MJKSkoxTp06ZyvzHP/5hJCYmGh06dDAuXrxoesacnBxjxIgRRllZmVFeXm6MHj3a2L17t895hw8fNlJTU42KigqjtLTU6Nu3r3H69GnTcx44cMDo3r27MX36dNNZHo/H6NWrl1FRUWE6yzAM48KFC0avXr2MvLw8o7y83Bg5cqTx7rvvWpL9ySefGP379zeuXr1qKuf69etGt27djKtXrxoVFRVGSkqKkZOT43NeTk6OkZiYaBQXFxuVlZXGxIkTjV27dtU45/bv59LSUiM2Nta4cOGCUVFRYWRkZNToc3mn8+P06dPGiBEjjI4dOxqHDh0yNd+ZM2eM/v37G8XFxYbH4zGmTZtmrFixwlTmhQsXjP79+xtffPGFUVlZaYwYMcLYt2+fz3k3nDp1yujdu7cxatQoU/MZhmEkJiYa+fn5NcrxlllcXGz07NnT+Pjjjw3DMIzs7GxjzZo1pma84cqVK8aPfvQj4+zZs6by+vTpY/z73/82DMMwMjMzjfXr1/ucd/r0aaN3795Vn8O5c+car7766jfOA1Bzgd7BrO5fhhH4Hczq/mUYgd/BrO5fhkEH87WDWd2/7pR5Q6B0MKv7V3Uz3kAHq58CZufKgQMHFBMTo6ZNm6pRo0YaMGCAdu7caSpz/fr1mjt3riIiIiyZsXnz5poxY4acTqdCQ0P14IMP6vLlyz7nPfbYY3r99dcVEhKiq1evyu12q1GjRqZm/Pzzz7V06VJNmjTJVM4NZ86ckSRlZGRo4MCBWr16tam8t99+W/Hx8WrZsqVCQ0O1dOlSRUdHWzGqnn32WWVnZ6tZs2amctxutzwej0pLS1VZWanKykqFhYX5nPfRRx+pV69eaty4sYKDg9W7d2/97W9/q3HO7d/Pubm5atOmjSIjIxUSEqKkpKQanTN3Oj82bNig8ePH+/Q1uT3P6XRq7ty5aty4sRwOh9q1a1fj8+X2zMjISP31r39Vo0aNVFRUpJKSEjVp0sTnPEkqLy/XnDlzNGXKlBrNdqe80tJSXb58WbNmzVJSUpKWLVsmj8djKjMnJ0ePPPKI2rdvL0maPXu2+vfv73PezRYvXqzU1FS1bdvWVJ7b7VZJSYncbrfKyspqdL7cnnfy5Ek98sgjVa/79u3r0/kC4JsL9A5mdf+SAr+DWd2/pMDvYFb3L4kO5msHs7p/3SlTCqwOZnX/ulPmzehg9VNIXQ9ww5UrV9S8efOq1xEREcrNzTWV+etf/9rsWLf43ve+V/Xf586d044dO/TnP//ZVGZoaKiWLVumV199VU8++aRatGhhKm/OnDnKzs5WXl6eqZwbioqK1KNHD/3yl79URUWFRo8erQceeEA9e/b0Ke/8+fMKDQ3VpEmTlJeXpx/+8If6xS9+YXrOAwcO6Msvv1RcXJzprMaNGysrK0txcXEKDw9Xt27d1KVLF5/zOnTooPnz52vixIkKDw/X3r17fdpKefv3853Omfz8fJ/zJGnatGmSpNdee830fK1atVKrVq0kSdeuXdOaNWu0YMECU5nSV+fM+vXrtWjRInXq1KnqTc/XvBdeeEFDhw5V69atazTbnfIKCwsVExOjuXPn6t5779XEiRO1YcMGDR8+3OfM8+fPq1GjRsrOztaZM2fUpUuXGm03r+7fwXPnzun999+v8b+Td/rzzz77rNLT09W4cWO1bt1aTz75pM957du318KFC5WXl6eIiAjt3LlThYWFNZoRQM0EegfzR/+SAruDWd2/pMDvYFb3L4kOJvnWwazuX9VlBlIHs7p/3SnzBjpY/RUwO1c8Ho8cDkfVa8MwbnkdSE6dOqWMjAxNmzatRquN1ZkyZYoOHjyovLw8rV+/3uecN998U/fff7969OhheqYbOnfurMWLF+vee+9Vs2bNlJKSovfee8/nPLfbrYMHD2r+/Plat26dcnNztXnzZtNzrl27VuPGjTOdI0knTpzQxo0b9c4772jfvn0KCgrSK6+84nNejx49NGTIEKWnp2v8+PHq2rWrQkNDTc9pl3MmPz9fY8aM0dChQ9W9e3dLMocPH67Dhw/rvvvu0/Lly33OycnJUV5enoYOHWrJXJGRkfrd736niIgIhYeHKz093dT5In11zuzfv19Tp07Vpk2bVFpaqpdfftn0rOvWrVNaWpqcTqepnIKCAi1ZskTbtm3T/v37FR0dXeNFtJs98MADevrpp/Wzn/1MP/7xj/X973/fkvMFQPXs8n5idf+SAreDWd2/pMDvYFb3L4kOZnUHs6p/SYHfwfzVvyQ6WH0WMIsrLVu2VEFBQdXrgoICyy7nsdKxY8c0duxYPf300xo8eLCprNOnT+vjjz+WJIWHh8vlcunkyZM+523fvl05OTlKTk7WsmXLtHfvXs2fP9/UjEePHtXBgwerXhuGoZAQ3zc83XffferRo4eaNWumb33rW3riiSdM/3SsvLxcR44cUb9+/Uzl3LB//3716NFD3/nOd+R0OjVkyBC9//77PueVlJTI5XJp69atWrVqlZxOpyIjI03PaYdz5vTp00pNTdXgwYM1efJk03l5eXk6duyYJCkkJEQJCQmmzplt27bp1KlTSk5O1uzZs/Wvf/3L1E/xTp48qV27dlW9Nnu+SF+dM9HR0YqMjFRwcLDi4uJMnzOStGfPHsXHx5vOOXr0qNq1a6fvfve7CgoK0vDhw02dL2VlZerUqZPeeustrV27Vi1atLDkfAFQPTu8n1jZv6TA72BW9y8p8DuY1f1LooNZ1cGs7l9S4Hcwf/UviQ5WnwXM4srjjz+ugwcP6tq1ayotLdXu3bvVp0+fuh7rFnl5eZo8ebKWLFmihIQE03mXLl3S7NmzVV5ervLycu3Zs0ddu3b1OW/FihXatm2btmzZoilTpqhfv36aNWuWqRmLi4u1ePFilZWVqaSkRJs3b67x9YY369u3r/bv36+ioiK53W7t27dPHTp0MDXjyZMn1bZtW9PXSt/Qvn17HThwQNevX5dhGNq7d686duzoc96lS5f085//XJWVlSouLtaGDRssuXwpOjpaZ8+e1fnz5+V2u7Vt27aAOmdKSkr0k5/8RFlZWcrIyLAks7i4WM8884yKiopkGIZ27dpl6pxZsGCBduzYoS1btmjevHn6wQ9+oBdffNHnPMMwNH/+fP33v/9VRUWF1q1bZ+p8kaRevXrp+PHjVdvM33nnHdPnzLVr1/Tll19a8obZrl075ebmVm0b3bNnj6nz5fr16xo7dqxKSkpUXl6u1atXW1JAAFQv0DuY1f1LCvwOZnX/kgK/g1ndvyQ6mFUdzOr+JQV+B/NH/5LoYPVdwNxzpUWLFsrOztbo0aNVUVGhlJQUderUqa7HusUrr7yisrIyLVy4sOpjqampGjlypE95sbGxys3N1aBBgxQcHCyXy2VZabBK37599eGHH2rQoEHyeDxKS0tT586dfc6Ljo7W+PHjlZaWpoqKCvXs2dP0dsCLFy+qZcuWpjJu1qtXL3300UcaMmSIQkND1bFjR02YMMHnvPbt28vlcmngwIFyu90aO3as6TckSQoLC9PChQuVmZmpsrIyxcbG1ug6S3/bsGGDCgsLtWLFiqpHXPbr109ZWVk+Z7Zr104TJkxQamqqgoOD9eijj1p2OZgV2rdvrwkTJmjkyJGqrKyUy+VSYmKiqcz7779fzz33nCZNmqSysjI9/PDDmj59uqnMS5cuWXbOPPjgg8rKytLo0aMVHBysNm3amHoU57e//W1NnjxZI0aMUGVlZdVjJAH4T6B3MKv7lxT4Hczq/iUFfgezun9JdDCrOlig9y/J+g7mj/4l0cHqO4fhy12dAAAAAAAAICmALgsCAAAAAACwIxZXAAAAAAAATGBxBQAAAAAAwAQWVwAAAAAAAExgcQUAAAAAAMAEFlcAAAAAAABMYHEFAAAAAADAhP8HmTd7k2LtKVQAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 1440x576 with 4 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Soms subplots to inspect how the probability behaves\n",
"fig = plt.figure(figsize=(20,8))\n",
"ax1 = plt.subplot2grid((1,2), (0,0))\n",
"ax2 = plt.subplot2grid((1,2), (0,1))\n",
"\n",
"sns.heatmap(V_s, ax=ax1)\n",
"sns.heatmap(A_s, ax=ax2)"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"100.0%\n",
"\n",
"Average revenue: 1503.59\n"
]
}
],
"source": [
"data = []\n",
"\n",
"for i in range(num_episodes):\n",
" clear_output(wait=True)\n",
" print(\"{}%\\n\".format((i + 1) * 100 / num_episodes))\n",
" data.append(agent(policy, starting_position=stock, verbose=False))\n",
" \n",
"print(\"Average revenue: {}\".format(sum(data)/len(data)))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"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": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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