Minor update

doc/pub/How2ReadData/ipynb/How2ReadData.ipynb

@@ -10,7 +10,7 @@
     "<!-- Author: -->  \n",
     "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
     "\n",
-    "Date: **May 9, 2018**\n",
+    "Date: **May 11, 2018**\n",
     "\n",
     "Copyright 1999-2018, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
     "\n",
@@ -1216,7 +1216,7 @@
     "\n",
     "## Simulating financial transcations\n",
     "\n",
-    "The aim of this project is to simulate financial transactions among financial agents\n",
+    "The aim here is to simulate financial transactions among financial agents\n",
     "using Monte Carlo methods. The final goal is to extract a distribution of income  as function\n",
     "of the income $m$.   From Pareto's work ([V. Pareto, 1897](http://www.institutcoppet.org/2012/05/08/cours-deconomie-politique-1896-de-vilfredo-pareto)) it is known from empirical studies\n",
     "that the higher end of the distribution of money follows a distribution"
@@ -1344,9 +1344,9 @@
     "\n",
     "\n",
     "\n",
-    "### Project 4a): Simulation of Transactions\n",
+    "### Simulation of Transactions\n",
     "\n",
-    "Your task is to first set up an algorithm which simulates the above transactions with an initial\n",
+    "Our task is to first set up an algorithm which simulates the above transactions with an initial\n",
     "  amount $m_0$.\n",
     "  The challenge here is to figure out a Monte Carlo  simulation  based on the\n",
     "  above equations.\n",
@@ -1355,14 +1355,58 @@
     "  $w_m\\Delta m$. You will need to set up a value for the interval $\\Delta m$  (typically $0.01-0.05$).\n",
     "  That means you need to account for the number of times you register an income in the interval\n",
     "  $m,m+\\Delta m$. The number of times you register this income, represents the value that enters the histogram.\n",
-    "  You will also need to find a criterion for when the equilibrium situation has been reached.\n",
+    "  You will also need to find a criterion for when the equilibrium situation has been reached."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "#!/usr/bin/env python\n",
+    "import numpy as np\n",
+    "import matplotlib.mlab as mlab\n",
+    "import matplotlib.pyplot as plt\n",
+    "import random\n",
     "\n",
-    "### Project 4b): Recognizing the distribution\n",
+    "# initialize the rng with a seed\n",
+    "random.seed()\n",
+    "# Hard coding of input parameters\n",
+    "Agents  = 500\n",
+    "MCcounts = 1000\n",
+    "Transactions = 100000\n",
+    "startMoney = 1.0\n",
+    "Lambda = 0.0\n",
+    "FinancialAgents = startMoney*np.ones(Agents)\n",
+    "for i in range (1, MCcounts, 1):\n",
+    "    for j in range (1, Transactions, 1):\n",
+    "        agent_i = int(Agents*random.random())\n",
+    "        agent_j = int(Agents*random.random())\n",
+    "        epsilon = random.random()\n",
+    "        if agent_i != agent_j:\n",
+    "           m1 = Lambda*FinancialAgents[agent_i] + (1-Lambda)*epsilon*(FinancialAgents[agent_i] + FinancialAgents[agent_j])\n",
+    "           m2 = Lambda*FinancialAgents[agent_j] + (1-Lambda)*(1-epsilon)*(FinancialAgents[agent_i] + FinancialAgents[agent_j])\n",
+    "           FinancialAgents[agent_i] = m1\n",
+    "           FinancialAgents[agent_j] = m2\n",
     "\n",
-    "Make thereafter a plot of  $\\log{(w_m)}$ as function of $m$\n",
-    "  and see if you get a straight line.\n",
-    "  Comment the result.\n",
+    "# the histogram of the data\n",
+    "n, bins, patches = plt.hist(FinancialAgents, 50, facecolor='green')\n",
     "\n",
+    "plt.xlabel('$x$')\n",
+    "plt.ylabel('Distribution of wealth')\n",
+    "plt.title(r'Money')\n",
+    "plt.axis([0, 10, 0, 500])\n",
+    "plt.grid(True)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
     "We can then change our model to allow for a saving criterion, meaning that the agents save\n",
     "  a fraction $\\lambda$ of the money they have before the transaction is made. The final distribution will then no longer be given by Gibbs distribution. It could also include a taxation on financial transactions.\n",
     "\n",
@@ -1452,7 +1496,6 @@
     "  equilibrium distributions and compare these with the Gibbs distribution. Comment your results.\n",
     "Extract a parametrization of the above curves, see for example [Patriarca and collaborators](http://www.sciencedirect.com/science/article/pii/S0378437104004327) and see if you can parametrize the high-end tails of the distributions in terms of power laws. Comment your results.\n",
     "\n",
-    "In the rest of this project we will follow the work of [Goswami and Sen](http://www.sciencedirect.com/science/article/pii/S0378437114006967). \n",
     "In the studies above the agents were selected randomly, irrespective of whether we allowed for\n",
     "saving or not during a transaction. What is often observed is that various agents tend to make preferences for for whom to interact with. We will now study the evolution of the distribution of wealth $w_m$ by assuming that there is a likelihood"
    ]