{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Data Driven Modeling\n", "
\n", "### PhD seminar series at Chair for Computer Aided Architectural Design (CAAD), ETH Zurich\n", "\n", "\n", "[Vahid Moosavi](https://vahidmoosavi.com/)\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "# Second Session: Introduction to Probability \n", "
\n", " 27th Semptember 2016\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![](Images/DataDrivenModelingKW.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Topics to be discussed \n", "\n", "\n", "**Probability Theory**\n", "* Certainty and Determinism\n", "* Laplace’s demon\n", "* Poncare and the end of determinism\n", "* Deterministic Unpredictability (Chaos Theory and Bifurcation)\n", "* Uncertainty and Randomness\n", "* Fuzziness, vagueness and ambiguity\n", "* Variable and Parameter\n", "* Random Variable\n", "* Probability (Kolmogrov) axioms\n", "* Independent Random Variables \n", "* Joint Probability \n", "* Baysian Rules and Conditional Probability\n", "* Probability distributions\n", "* Expected Value\n", "* Variance\n", "* Covariance\n", "* Law of Large Numbers\n", "* Central Limit Theorem\n", "\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "import pandas as pd\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "pd.__version__\n", "import sys\n", "import sompylib.sompy as SOM\n", "import sompylib1.sompy as SOM1\n", "\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "### Determinism\n", "* **Starting gradually from 16th century** \n", "* **Newotonian Mechanics and rapid growth of science**\n", "* **To beiliev in Objective Truth** \n", "* **Determinism turns to beileve in the truth of equations in describing the underlying mechansim of natural phenomena.**\n", "* **Laplace's Deamon**\n", "\n", "# but it really works in many systems!" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/jpeg": 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"text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import YouTubeVideo\n", "YouTubeVideo('EZNpnCd4ZBo',width=700, height=600)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Now simply a Double Pendulum!\n", "\n", "![](https://upload.wikimedia.org/wikipedia/commons/thumb/7/78/Double-Pendulum.svg/294px-Double-Pendulum.svg.png)\n", "\n", "### still one can write the underlying equations \n", "\n", "\n", "![](Images/Double_P.svg)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Double pendulum formula translated from the C code at\n", "# http://www.physics.usyd.edu.au/~wheat/dpend_html/solve_dpend.c\n", "\n", "from numpy import sin, cos\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.integrate as integrate\n", "import matplotlib.animation as animation\n", "\n", "G = 9.8 # acceleration due to gravity, in m/s^2\n", "L1 = 1.0 # length of pendulum 1 in m\n", "L2 = 0.7 # length of pendulum 2 in m\n", "M1 = 1.0 # mass of pendulum 1 in kg\n", "M2 = 1.0 # mass of pendulum 2 in kg\n", "\n", "\n", "def derivs(state, t):\n", "\n", " dydx = np.zeros_like(state)\n", " dydx[0] = state[1]\n", "\n", " del_ = state[2] - state[0]\n", " den1 = (M1 + M2)*L1 - M2*L1*cos(del_)*cos(del_)\n", " dydx[1] = (M2*L1*state[1]*state[1]*sin(del_)*cos(del_) +\n", " M2*G*sin(state[2])*cos(del_) +\n", " M2*L2*state[3]*state[3]*sin(del_) -\n", " (M1 + M2)*G*sin(state[0]))/den1\n", "\n", " dydx[2] = state[3]\n", "\n", " den2 = (L2/L1)*den1\n", " dydx[3] = (-M2*L2*state[3]*state[3]*sin(del_)*cos(del_) +\n", " (M1 + M2)*G*sin(state[0])*cos(del_) -\n", " (M1 + M2)*L1*state[1]*state[1]*sin(del_) -\n", " (M1 + M2)*G*sin(state[2]))/den2\n", "\n", " return dydx\n", "\n", "# create a time array from 0..100 sampled at 0.05 second steps\n", "dt = 0.05\n", "t = np.arange(0.0, 30, dt)\n", "\n", "# th1 and th2 are the initial angles (degrees)\n", "# w10 and w20 are the initial angular velocities (degrees per second)\n", "th1 = 120.0\n", "w1 = 0.0\n", "th2 = -10.0\n", "w2 = 0.0\n", "\n", "# initial state\n", "state = np.radians([th1, w1, th2, w2])\n", "\n", "# integrate your ODE using scipy.integrate.\n", "y = integrate.odeint(derivs, state, t)\n", "\n", "x1 = L1*sin(y[:, 0])\n", "y1 = -L1*cos(y[:, 0])\n", "\n", "x2 = L2*sin(y[:, 2]) + x1\n", "y2 = -L2*cos(y[:, 2]) + y1\n", "\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111, autoscale_on=False, xlim=(-2, 2), ylim=(-2, 2))\n", "ax.grid()\n", "\n", "line, = ax.plot([], [], 'o-r',markersize=3, lw=2)\n", "trace1, = ax.plot([], [], '-', c='r',lw=.4)\n", "trace2, = ax.plot([], [], '-', c='g',lw=.4)\n", "time_template = 'time = %.1fs'\n", "time_text = ax.text(0.05, 0.9, '', transform=ax.transAxes)\n", "\n", "\n", "def init():\n", " line.set_data([], [])\n", " trace1.set_data([], [])\n", " trace2.set_data([], [])\n", " time_text.set_text('')\n", " return line, time_text\n", "\n", "\n", "def animate(i):\n", " thisx = [0, x1[i], x2[i]]\n", " thisy = [0, y1[i], y2[i]]\n", "\n", " line.set_data(thisx, thisy)\n", " trace1.set_data(x1[:i], y1[:i])\n", " trace2.set_data(x2[:i], y2[:i])\n", " time_text.set_text(time_template % (i*dt))\n", " return line, time_text\n", "\n", "ani = animation.FuncAnimation(fig, animate, np.arange(1, len(y)),\n", " interval=25, blit=True, init_func=init)\n", "\n", "# ani.save('./Images/double_pendulum.mp4', fps=15)\n", "ani.save('./Images/double_pendulum.mp4', fps=15, extra_args=['-vcodec', 'libx264'],dpi=200)\n", "plt.close()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import HTML\n", "HTML(\"\"\"\n", "\n", "\"\"\")\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/jpeg": 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kjDDj0LmLDPM4PfJC0DmgQUPacVMUNnYC6UjWXnEBuFMTkAuodaHBt2Vl1wq1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\nB6ar7LrTHcdtOZhmWHD3hcn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"text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import YouTubeVideo\n", "YouTubeVideo('04mbMblhXog',width=600, height=400)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### In many real world problems, we just observe this kind of behaviours\n", "* Stock market\n", "* buidling energy\n", "* weather\n", "* People's movement patterns\n", "\n", "# \n", "## What can we say if we don't know the underlying mechanisms or equations?" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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qgzDpZ9omAspeZnA0k8cmClMGWSqfjo5yR3O5UgCkqQn4xCeAL34R+NGPgLe+\nNfx/ayGArG6XqBxEjrKJ5MSkNHnycRVLAXNkMDLCv8PUF8BkcPQo2wJveEPlZ3ltojhlAABvfjPw\nnvdwQkFDoBfIGzOICiDbihkAnHK8dWulRQS4sYmAfGSdhgxOnABuuKGshJP21QQKQwZ5baLZs/lm\nHBnhztV2ABkok4EJm0jtYBsbuUPJsjzeqVN8owUf1L/+a+CRR/i8RJFB2gdWTt6yMc8gSIjLl/MI\nemiIbYgwpH1Ak1JLTdlESR1zczNw/fX84F9/feVneckgrHNWcffdfP4+/vHxn5myieKUQVYyiLpW\n8+fz/aDOPgbcBJCBfEHktMrgiit4oaykwV/e+khBFIYMdJXBqVPcSQdHQTaUgcwoMmETBb3FrFZR\nlLfe2so33MaN48+JRNrO8Ny5conuIHTnGQTjJldfDfz7v3MGTNR+p31AXdlESWQAAN/6Fqf/BgnV\nRswA4Aym48eB1avHf2YqgDxlCj8XL73E6bMqWlr4vpGqKQlxyuC//mt8arQJZSCt5jjkIYO0MQO5\n8mDStZhwZJClIw3GDCQZhI0kXSqDrB1jmPWSdX+j8vEBHvlE+cpA+s4wyiIC9Co7AuPjJtdfD/zq\nV8DKldH/k3Zk64oM4iaASSxaVJlSKqETM0hqMwqmUksB4Npr+f3gsRFlex6iLL358/lZuzSwgopu\nAFntQ+JgShnIQZ7MTDpxgl2Njo7KZXTDMOHIYPJk9r/TLHKtKgM5oefkSU4zDcJmzEDXJgqTxqaU\nQRqk7RSiLCJgfHmOrAiOom64gdXBLbdE/0/aBzQptVReL901nOMmgCVBJ2YQR/Sm24win9e9jgk8\nrOBb1nksYcS9di3/DqZG6waQ05JBnvs7jAwaGyv3WfZXHR0cT4rC2Ji5JAdXJay1oY4kki5SMGZw\n5gxLcJdkcPo0E1dHR/n9rGQQdkNmJYM4ZZCELMogaoQ9fTofR9YqmOq2g2W8f/e7+P8xpQzUBzTu\ne0nQGaXbsonikFcZhA0IPvzh6M7SBBmsXAk89BAPElToPtdpyUCdx5QWYTYRUD4fbW3pyUAOxEwQ\nQmGUAZD+oFW/j4gl6nPPxZNBlgydIKJsIin1JLLc/KOjfNPopsK6UAZxNlFzM//kHaUFbaI0MBUz\nAMxYRTods07JA5dkEKVE5s0bP3dCIus8lqhrddtt44sNuiKD2bMrV1NMg7ByFED5Xhsd5Wve3l6Z\nDRmGNPMmbuADAAAgAElEQVQh0qJQZJDGYxwbG58JsHgxr58bFjPIk6ETRJRNFCSDLMqgr4+PNxgk\nzaoMomIlaZC2I4yziYDxxfuyIKgM0iCLMoiziQAzZJAmZhAFW6mlSW2aSC1NQpa5BmmIW4UOGQwP\n8/+maS8vGYQRp+zfTp/ma9DUVFlbLQxps57SoHBkkHTzDAyMX0jjVa/ioGNwco2E7igi+ODJbCId\nMojKZshKBjo3S9qHNc4mAvTiBjaVQVJqKWAmvVQnZtDayvfm6Gj2NvPGDPIsfRnVwcUhC9EmxXeC\n0KnwG7W+dhhmz85uE8WRwcBAZXwz6dmZsGSQxiYaGBh/ct74Rn5fLu0XhC4ZRCmDkycryWDqVH5I\n0wQk1TLcOvsaVoIjLdLK+DibCNAnA5vKoNZtooaGfJ2za2WQpz0TMYMo6DzTaS0iIJ8ySIoZqP2G\nVwYRSGMThVkWa9ZwIObVrw7/H93Mg7B5BidPjlcGRPzApLlJo+qpZx3xZB1RqUirDNLYRHnJII9N\nVGsxAx2bCMg/CawWUkvjYJsMzp7NFwu0TQZR50oOdlVl4JIMCpNNBKRXBsGbZt48Ti+NmqSkqwyC\nI+OlS3n1MGB8hy478yTrI+qGzGMT5SWDLMqglmyiLDOQk86NKZvINRnotCnTuM+fj14FzkR7ac9t\n3Az3KDQ08CTIPERcLTKQ9y1RJRnEPTtpy2akQV0qg7COKYoIADNkoI5e5c3X0hIeANZRBi5tImlr\nJfnVNm2ivMqg1myivDEDIN/EJp2YAVF2q8imMjh7tlxzKgvyPtdRFm0YLriACSfLmtFhK50B5Qlm\nhw4BCxbwe0nJFxPaJsqjDJKgSwZRo9ewLJ60I/sTJ8JTYV0qg4YGbi+PNaeiFpWBHG3WeswAcK8M\ngOyKKA/5ZMlWyzPPI28QOYsyIMoeRI5SpB0dvLbI/v3l1e7S2EQ1lVpKRGuI6CUi2k5En4z4zleI\naAcRbSaiVXnayWsTJUF36nrYyPg73wG++93wttLcoAcPcomCILLGN3SUAZAubmDbJrIRM0g72jRh\nExUtZiDbzKJG8rSXlgzyDmjyDvLS1iWSyGoVRaU0ywlm+/eX18FOsolqShkQUQOAewDcAmAlgHcT\n0aWB76wFsFwIcTGAuwB8PU9bOjZRHEzbRAAvLfnGN4a3pUMGWYgr7eg3DmniBrVmE8lFVeKQJq0U\nMKMMdDvmrDbRyAhf+6y2ioqs1yyPTZSWaHt6Khe7TwsdmygLGcyalY0M4pTB0aPAvn1lZSDvv6hA\neE2RAYDrAOwQQuwTQgwDeBDArYHv3ArgPwBACLERwHQiChSdTYYtZWDLJgqDrjLIIn0HB7kT0ukU\n0iiDpHPu2iaSdfTjMknS3iemyCCvfw9kVwbSsslT/kNi5kw+h1natKUMsnbOEq7IwKRNtH9/pTKY\nNImvY9Sk2Fojg4UADih/Hyy9F/edQyHfSUSRlEEU4jrze+7h9NehITM2kU5aqUSaB7bWlIEM3Med\np7T3SdYVucJQDTLQUSJAslcdhM0AchHIIK0yOHeOBylhWVpLlrAqaG9PX+Cy7lNL161b98rrzs5O\ndJbWZazVAHJSZ6gijgy+/GX+/ZGPsC0QrAEv/z/tvubpSINII+WTAshJvmcUhMgXMwDKVlHUfmWx\niXRjBibIYPfubO3pkkE9KAOdAHKWoKxcQCsNZLwgTLVNncorz0mLSEIOgtWElK6uLnR1deH554Hv\nfS/9vsbBBBkcArBE+XtR6b3gdxYnfOcVqGSgIq1NpFYKTQMdMhgby5ZJEdWZDw5yStkLLwDLlvE6\nxWGLxWS5wXU7ISC9MrBhE50/zxZXHptLWkVh6gpI3meJWrCJslYuda0MhLAbQK51ZbBgAbBpU7rv\nJqn1xx4b/16YMpCD5IceAj72MeD++9en3+EImLCJngVwEREtJaJmAO8CsCHwnQ0A3gMARHQDgB4h\nRMKSDeORxiZK+5Cr0CED+RDEzWNQEdWZb9vGqzVdeCGnl33ta9H7Gvb/Bw6wBA3umwtlYMsm0lE2\nSSPbtGquFsggb8xAB1nIYHi4XPAxC2R58yS4JoMTJ7KVfV+8mJ+/NEgiA6LxqiFuEJwnphYFbTIQ\nQowCuBvAEwBeAPCgEGIbEd1FRB8sfeenAPYQ0U4A9wH4mzxt1aJNlMUiAqLJYNcu4OKL+XVHR3Sl\n0Shl8Zd/Cfznf1a+50oZJNlEMhsma2kAnRs9KaMo7XUzkVoaNckoLbJWfTWhDLLYRHnvs7RrAbgm\ng6xl35csyUYGWfunuJhBXhs1DEZiBkKIxwCsCLx3X+Dvu3XbSVP1M+u0dYBvmqxTyiWyXoyokX2w\njlEUwshkbIwXBb/22sr3TZBBWmUQd4NPmsQzcLOqNq8MGFnz2E3EDLIog7zttbZyGmzS+dEhg6wx\ng5ERHrhkKfueRRmkKZseRJwjYpIM/Axk1IYyCFY4jULYDb5jBx/3li2V77uMGSSdgzxWkc6NLmMG\nUSgSGSQtcBKEa2WQV8HJGjxJ6uDkyXzzDPJMJj1+nI9dLYGfhBkzeEBmqh5WEEk20YQkg1qcZxBV\nQygKUWQQVX4i7P+D+7p7N1tM27dXvu9CGYyOpvOo85JBPdhEJpTByZPp12J2HUDOOiBSkYYMjh/P\nt1pfnuc6z8qARJz0sWtX8nfzkkGYMhgZ4Z+wRJM8KBQZ1OI8gzxkENaWjk104gQvLRgcyZlSBnGd\noRyZJAXQ85BBLdhEshRy1sVlVOheh+Zm3te0589UADmtMtAhgzQTtvKu4+2KDADgoovKlYrjYDJm\nIBNEdCYXqigUGUyeXGbDKBSBDKJsojTKIMwmOnGCs5DOnKk8N6aUQZwaS9sRFNUmamjItkJdGExc\nhyxWkQllMGMGZzClUSN54nQSaZVBrZPBxRezXZuEPMogahBs0iICCkYGRMkPpmsyyDpBJc4mSqMM\nJk/mVD51pHriBN/AwVQ9EzdLkk2StiPIqwyqbRMB+laRKTJIG0Q2EUBuauLzk8YHz5POLZEUHB8c\n5Cy0PPdBngDysWO8/klWpFUGeQLIUfb4hCYDID6gl2cRDEBvvdSsFQ6jbtC0C9cTjScvSSRBn9eF\nTZS2I3CtDEzZRIB+ENnEdZg3j4uYpYEJZQCkK/gH6JH2/PnA4cPRn0tVkMcKyRNA1lEGaW0iUzED\nTwYxD2beRTB0bABTNlEWRRPchgw+2yCDpFFxFpsoS648oBdANmUTAbVBBgsW8GTENDARMwDSxw10\nbKKFC7kOVxSOHctnEQHuYwZpbSJTMYMJTwZxHXfecs06D7spMsha+dSVMqi2TVQLykCnWN3YGJfV\n0B2pL1gQP4JWYUoZpCUDHZto4UIuwxKFAwc4jz8PXJLB/Pn8nCTZiXljBt4mCkFcx52XDHSUQdYJ\nMVGTxrKUjghaTdJiqpYyMGETHT8O3Htv5Xs6N7vswKNmPWdVBnljBrJj1s34yEIGJmIGAA8w0pKB\njjKIIwO1tn9WuCSDhgZg+fJkqyhvzMArgxDUgzII3qBDQxwYzlvfSI42bMUMTHSqSZVLP/EJ4O67\nKzNLdDqZpqbyrOcwuCIDE9cAqI4ySDvzWec6LVrENlHU/aVDBnligTq2VJogso8ZGIQNZSBvmrST\nelQcP54uCyjYloqs3niQUOQNFqxuaaIjkp1q1EOV9pwnKYMtW7hjeOKJ8nu6N3vcou5ZfO6si8Or\nqAYZ6HTOKtKSgU7MoL2d77Fjx8I/d60MTp3K9jyrSBNE9mRgEElkkOembGzkkVTcjXP+PHDXXZWd\nFcASN2zdgSiEkUHWh7elpfLmUMlATQU0UbUUiLeKTMwzEALYs4fLdm/eXH5ftyKjif0Gsq8HrEK3\nSJ1ELZOBTsyACLj8cuDFF8M/376d7Zc8yKrohof5WPIuCJUmiJwngOxjBhGIs4l0bsqkuMGDDwIb\nN/LaxtLKGB3lEc38+enbmTKFS02rKiRroFSdhCJXTpo8eXypY1Oj0jgCNkEG0tp63euAl16q3LbO\nzW6KDLKuJ6DC1DWYOZMf/jQj3WqQgU57K1fyOh5h2927F7jssnzbzbqokoz/pbVrg1i2LHkRIh8z\nMAgbNlHSdgHgqadYGdxxB/D3f8/vdXfzQ5qlNgjReBWSdQSsdvpSFRCNJwNTo9K4TtWETbRnD8+g\nvuwyXtdBIms8JoiodQBGR5lE056brAvSqzBFBkQ86EiTXuqaDHSXXrz6auA3vxn//nPPMVGELRGZ\nBtLeS1tK5PTpbNVKg+jo4D4hDt4mMoi4+kS6ZBCnDJ5+GnjjG4HPfx74zndYDma1iCSCVlHWh1ft\nnNWbK2hnmOqITIyw49Y0OHyYz+Py5ewRDw/z+6dP56tWmbTfkiTTjgBrgQyA9FaRazLQXWt7zRrg\n8cfHl5l59FF+5vKisZH3K62qO3VK736bNy869gGw1Tw6yio+C/wM5AjEVS7VIYO47Q4PA/v3c4Bo\n7lzgk58EPvQhYOtW9gmzIhgAzmqHhCkDwE4AGUhWBmk6nqYmVkRh51jWZZo8mR8oWRs+bx37pP3O\n2llmXWlMxUQgA11lsHgxK4BvfrP8Xn8/8MADbMvqIEv11bRVAKIwcyafCzmYCSJu/eM4tLZyxx8c\nSHkysJBaCsTbRPv28YMo5erHP8778P73A29/e/a2gsogq02kdnKqB2krZpCkDNKe8yj1pRbpu/BC\nto0AfTKI6sSzdpYTVRnMmsVkkLRCnS4ZAMA99wBf+AJw5ZXATTcBV13Fz9bq1XrbzTLZUVeJNjTw\nOYsqKJi3f2ps5IFSMF5kmgyMrHTmEklk0NFhfru7dlVmNDQ1Ad/7HnDffcCtt2Zvy4RNJKfwF8Um\nAqLPsUoGy5YxGYyNcSejEzOIUwZZHsqJSgZTp3JHlHS+TJDBlVfydX/++XLhxVe/Wm+bgFtlALCy\n7e7maxWEjp0mnx2185/wZDB1qntlsHv3+PS2RYvKgeSsCM4gznpRo2yiMGVgO7U0Szpv1Dk+ebJc\ncuDCC/l89/fzvmetM6WiHm2irVuTv2eKDICyVRT1XAmhHzOQaG7WVwJBZCED3QAywCQWFTfQtbEH\nBysnxJl6viW0bCIiaieiJ4joZSJ6nIhCx3FEtJeIniOiTUT0W502bdlEcds9dIg7f1OwFUBWYwZC\nmCtYFpevnWWUHXWO1RGZVAa6FhEQPVks6/nOU2RPwrUyEEJ/foaKpLjB2bOsHvJm/NhGFptIN4AM\nxFd61SHNqMmqNUMGAD4F4GdCiBUAfgHg0xHfGwPQKYR4jRDiOp0GqxEzOHw4XPblRRgZmFAGkyez\nvXLuHGcuNDXlz5lWYdImigsgA+WYgQkyiMokyUoGs2bFBwbj4JoMzp7lVOcsa/jGIYkMTFhENuHa\nJoojH9ODVVOp4xK6XcWtAB4ovX4AwG0R3yMDbQEoR9bDYEsZ2CYDnQCySgbqXAOTnZBJmyhJGUgy\nSLsmdBxM2USNjSzP064noMI1GehO1Aui6GSQNYBskwzqXRnMFUJ0A4AQ4iiAqHp/AsCTRPQsEX1A\np8F6UQbB1FKdSWfqMcvPTI4a4ko4Z7WJwrajTi7r6OD937KFiUEHpmwiIFs5CBUmyWDaNM5TN7G+\nRFokLUtpKl5gC1mVga5NlEQGppWB0wAyET0JQF0IjsCd++dCvh6VhHajEOIIEc0Bk8I2IcTTUW2u\nW7fuldednZ3o7Ox85e8kMsj7ILS1cQppGA4fzlZyIgm6NlFQGagT39TMF9vKQIjs1T/Drl1/f3l0\n2dDAM5E3bADe+tb8+wyYs4mA9LN/gzhzxtxAgqi8yE1UB2yaDJI601pXBtWwiaL6kTylKCSCiTNd\nXV04dKgL3/ymPoFJJJKBEOKmqM+IqJuI5gkhuomoA0BoHF0IcaT0+zgRPQTgOgCpyCAI1wHk4WHu\nXPNWMgyDrk0UFTNQP2tutk8G58/z77TBw6hzHDyGq68GvvUt4IMfzL6vKkzZREDy8oxRMBnMBcoK\n5ZJLwj83TQZxnRtQ+2RQazaRTv+k9hmdnZ2YPLkTn/40q+n169fn27ACXZtoA4D3ll7/FYAfBb9A\nRFOJqK30uhXAzQCez9ugZMiwiTA2bKITJ/gGMRGIlQimlmZ9gFtb2X6QlkEYGZhMO4vqxLPm64fZ\nRLJonzpF/7pSisFVV2XfVxUmbaLLLgN+//vs+2BayifZVa6VgarqahFplYEQ9m0iHWXgwibS7eK+\nCOAmInoZwFsA/CMAENF8Ivpx6TvzADxNRJsAPAPgESHEE6FbS4FJk7hjlqNSFTaqlsoFuU1C1yZq\naCh3rGFk0NtrNpAYRwZZOp4wm0h2JuoU/fe+lzu8lStz7e4rMKkM3vEO4JFH0hc902krDrVGBn19\ntR8zSKMMBge5b8laNygIVwFkmUJsMptIa9KZEOIUgHHObskWenvp9R4Aq3TaCUJ2TuqFGxnRW2s2\nShm4IIM8VoLs6II3mJxrYHLEFhX4zarEWlu5JLGKsAdk0iQzMRoZMxCikmzydJjLlvE+/frXwBve\nkP7/bCiDuGUifcygEmnniOiWolDbc5FaOjzMg8IsFZOTULjaREB4eqlUBXnXmnWtDHSyiYCyBRJl\nE5kcsUUFfk0oA5sjy+ZmTgs9d67y/bwd5u23Aw8/nO1/iq4Mkjz3WicDSWZJ9ZVMBI8Bd8rA9CAD\nKDAZBDsVHdYFqqsM8lg6ctQbZROZVgYmyCBMYdj2nMNmT+ftMNeuHb/SXRImQsyglm2iyZN5UJC0\nxrmJ4DHgThl4MijBBhlUM2aQxyaKUgZykpDJEXdLC4+ug355HpsoLGZgszMJazNvh3nNNWzRZEkx\nLboyKLpNBHAnf+pU/HdMBI8BtqllKZggTBSqk/BkUELRlYFuNhHAN1WYApg7l/fZZCdLZGbtZtc2\nUVSbeTvMxkbgj/4I+NnP0v+P6YdWprhG2R6mU1lbWzkWF5awARSDDJImzgHmbCIijtuFqQOdPsrb\nRBEIq1xqShkEH7ITJ+wqg7GxfLNUp03j8ghTplRW9pRVE03bL2EWT9ZJftWwiUwqA4Br7Wexikx3\nzm1tfL2jSmqbVgZE8dZHEcggjTIwZRMBfL7Cro9XBhZgQxk0NXFkPijvbNtEZ8+yr5m1sFh7O2fm\nBOv9SzIwPeKOGmFnOedRqaW2lUGQgHQ6zJtvZmWQFJBU2zL90Er1F9WeSTIA4q2iWo8ZAOmVgamZ\nvFHk6ZWBBdggAyC847BNBnkf3rlzeR3m4KhMVQYmH1ITI+wwZWDbJjKtDJYt4+v3fIppk8PDTBom\n0/8Avh9rhQzqRRmYsomAcDIYG9O7Nl4ZRCAstVSnLpG63WDHYTu1NO/Ice5cYOfO8crgggvY3+3u\nNm8ThRFwVjKImnRmC2EEpNth3nQT8OSTyd+T7eRNd47C7NmeDLIgjTIwbRMFyUBOEMtbWtyTQQRc\nKYOxMbMjBglVGeT1lKOUAREvxPPCC26UQZ5yFKrF4sImUvdbztzUeZDSkoGNBxbgwUlUWWmd+jdR\nmAgxA9M2UZA8de9zbxNFwBYZBLd76hTf6KZlftAmyqsMzp8PXyP46qv5ZtQt56DChN0yaRLHZtRJ\nYLY7k+B+Dw3li9GoePObgaefDk8fVGFjlA7E20Q69W+iEKUMxsb4PjZNPqbhMpsIqFxxUEKXpL0y\niIArZWAjkwjgDCBZoE0nZgCEd6TXXAO85jX6K4WpMJFNBIwfqbuYZ6Dut4kOur0duPxyLk0RB1vK\nIM4msnE+o8hgYICPz2QRRxuYOTOdTWRKGYStma1L0mHKwGRdIqCgZGAjtRQYTzInT5otXS1BxIQw\nNJTfJppXWmEi7CG9807gn/5Jbx+DMJFNBIzvnF3bRKZG62vWAI89Fv8dm8ogyiYy8RwEEUUGRbCI\nAFYGLgPIYWSgqwwkGUiL1SuDElwqA92lF6MgL25em6i1Ffj614EPhKwbt2gRWxkmYSorJ9g5u7aJ\nTHXQa9cCjz4a/x2bMQOXykBdMElFUcggSRmMjPB9YepYws6XrjJoauIfaU3auLe0qpZWCyaCmVHb\nDZKBDWUAlDOKdCYl3XWX2X2Kg4lsIrkd18rAtE0EANdey2Up9u8HliwJ/44tZRBnE9lQBjYmUblE\nkjLo6eEO3JTdFaUMdM+VzKKUFQxMrr4IFFgZhKWWmlAGaodnmwykMrDRYZiGKQIObsd1bSJT57ux\nka2iOHXgOptoeJhHuXnLuEchKpuoKMpA2lxjY+Gfm84YjIoZmLSxvU1Ugiub6OTJ2rWJXMOkTaSe\nYxc2kQ1lAABvexvw059Gf+46m0g+A6bnNUTV2ikKGUyaxNchbD1swOwcA8CeMgimpHsygLvUUtvK\nYGDAfO0aWwibnZ3nnKvneGSER7OmsyJU2AogA8AttwBPPTV+vQQJW8qgrY3Pm7omBmBPZRXdJgLi\n4wYm5xgA4amlXhlYgssAsi0ykCuVFd0m0lEGMsPC9EhWhS2bCGDVeMUVwC9/Gf65rWtLFG4V2Zhj\nABTfJgLi4wY2bKIgeXplYAmuUktdkUERbSJZbTXrvqvbcdGZ2AogS8RZRbaUARBuFdmYfQwU3yYC\n4pWBC5vIdP+U59lLghYZENE7ieh5IholotUx31tDRC8R0XYi+qROm4C5zJYgXMYM5OI0RbGJwmZA\ntrRkz8BQt+PCZrCpDAAmg6ggsk3VF5ZRZOt8TpnCaiQ447pIZJCkDEzaRFOncnWA4eHye6ayiWrZ\nJtoK4HYA/xX1BSJqAHAPgFsArATwbiK6VKfR4AMuhJkHr1rKoIhkkHe/gzaRCzIIKgOTo+dVq9gS\n2LVr/Ge2lUGYTWSrNESYOqinmIFJZUBUHuxJmLg2NW0TCSFeFkLsABDn+l4HYIcQYp8QYhjAgwBu\n1Wm3pYVHKTJVbGiI1zlt0pw1oXZUo6P8kJscMaiQaxgXxSYyFYithk2k7rfpDrOhIXoCmk2ij7KJ\nbHXOYXGDelEGpm0iYHzcYCIogzRYCOCA8vfB0nu50dDAhCCzKUw94Ooo8vRpHg3pFDSLg1QGRbKJ\n1BF23nPuWhlMnsxZSyMj/LeN0XNU3MCmMgiziWwqg7CMoiKRgctsImB83MBEPMe2MkgcSxPRkwDm\nqW8BEAA+K4R4xOzuMNatW/fK687OTnR2do77jmRJ2UmZeAjUUaRNiwjgTnDHjuIoA1M2UTBmYLsz\nkes3Dw4yudsYrb/1rcD73jf+AbVJdnPmAJs2Vb5ns70wm6hIZDBrFvDss+Gf2VIGKhmYyPSqfHa6\n8C//0oXmZr1tqkgkAyHETZptHAKgTthfVHovEioZREE9MSbJQI5abZOB9BSLGjMwoQxsr3KmtinJ\nwFa5htWrga4uVgkSNjvLMJvIVmopEG4TFS1mELVAjw1lEJxrYEIZtLayOhMCOH++E1/4QucrCRzr\n16/X2zjM2kRRcYNnAVxEREuJqBnAuwBs0G1MTS81aRO5VAZFsommTOHsiNFR/jtvR+A6m0i2KQnI\nlpUSllXU1xe+3oQJRGUTeZsoHHEL3NhYwCoYMzBB1NImkuummy4drptaehsRHQBwA4AfE9Gjpffn\nE9GPAUAIMQrgbgBPAHgBwINCiG16u21HGagrcdlMKwWKF0AmMnPOgzEDF52Jav/ZJIOf/rRyFbfe\nXrvKwNWkM6D4NlEUGQhhdi0DCdUmEsKcMhgctBeL0sq/EUI8DODhkPePAHi78vdjAFbotBWE2jGZ\nShdsbma2PX/evjKQxbOKYhMBZbKcNs2cTbR0qdl9DEPwXrFxvq+4gu+b7duBFaU73bVNZFsZ1CMZ\nnDnDSSKmi/upZHD+PA+mJk/W26ZUBrbIoJAzkAE7ygAod1a2yUDKfBszCW3BhMWjjtLrySYiqswq\nGh21uyTkzJncOUvbDrCvDFTb4/x5OxVSbUGSWbByqQ2LCKiMGZi6z20rg0KTgUyz6u83N9qTJ9zm\nwjYAk0F3N1dUtJW+ahomCFjtmOvJJgIqyUCO0m0tCdnYyB2cOtp1qQzktbNZV8okJk3iDjRYJsJG\nJhFQGTMwHdO0seQlUHAysJGiKJWBrSUvJaRklPnvRYDpmIGrbKLgftuy5d7yFuCZZ7gNm8FjiaBV\n5HLSWZEsIomwjCIbmURApU1k6rqoJWy8MlBgayarHLnatokkiqIKADM2UXOzTI1zbxPJbChd7zYK\nbW3ADTcAP/+53eCxRDCjyKVNVKS0UomwuIEtm0glA1PKQG7Tk0EAamqpaWUgbSIXZBC1ZGItwoTd\nQlRWB65tIploYNPakCmmLsggmFHk0iYqqjIIkoEtm8hGzMCTQQSCysDUKEVVBjZjBhKXapXsc4ug\n35/3nMvO2aVNNDBg1yKSWLuW4wb79wOLF9ttK2gTuZx0Vi9kYNMmMh0zsE0GmqXdqofWVuBQaR6z\nyRuzrY0vYl+fvSJ1Es8+6ya10hRMZXDJztmlMjh61G7wWGLFCi6Y+NBD5RRTW1BtorExuxMYgzZR\nvZCBzQCyjWyioSHenlcGCmzFDNragAMHeCRk28+/5hoe3RUFpshAEu7QkJs5FnK/TZevDoNMMf3+\n94FLLrHblmoT5V1fIi3a2rgNmfBQTzED2wFkU4MQIj7nR496MqhAMLXUZAB53z438YKiwVQpCTlS\nb211k5ro0iYCuGgdAKxcabcd1SayGS8AmGRUdVAvyqBI8wwAPueeDAKwFTNoa2MycBEvKBpM5etP\nm1ZWXy4g99uFTQQAV1/NHcDVV9ttR7WJbMYLJOqRDGzZRC0t5dXOTBK1J4MQqNlEplNL9+71ZBAG\nUzbRjBl8jl2RgaoMXJAB4KYd1SZyYduoQeR6IYOTJ+3YRHK1s74+s0TtySAEtmIGs2bxOgO2M0GK\nCLWQn47/7poMgqml9QLVJnJBdGqxuiLGDGQ9MBU2J5dKMjCpDKZPB44c8TOQKyDJQGZRmDrZF13E\nE4SDJX4AAAq9SURBVJMuvNDM9uoJ6nT4yZPzB9iroQykTVSUooBpIG0iWRXThTKoN5vIZnViGTcw\nqQzmzWMb20biSeHJQD7gprIoLrqIf3syGA95znVHOu3tTAa2yzVIVMMmcoGWFq65I9N0bR9bvdlE\nZ8+yp2/rvEllYPJcLVjA5L9Qa+HgcBSeDExPXFq8mEsmeDIYDzUQq3POZYG1eg0gu4S0inp77ZOr\nahMVmQzkmhNSFdjKaJMTz0xemwUL+LcnAwUytdT0TdnYCHzpS8Dll5vbZr1AVWM6naokAdcB5CKt\nHZEW0irq7bV/PlWbqIgxg5YW7viHhvhv2yVnpE1kgwzmzzezPRWFJgNpWZgeoXzsY8Wp0+4S6jnX\nVQbqb9uQAwcX9YJcQ2YU9fS4IYMiKwOg0iqyvZqhtIlM3nfz5/Mx+ACygkmTOHh88mQxb8oiwpT3\nLlP5XFlxjY1s/R0+bCenvJqQNpELMii6TQRUkoFtZaCSgSllsHIl8IlPmNlWELprIL+TiJ4nolEi\nWh3zvb1E9BwRbSKi3+q0Wd4md05HjhRPrhYVpgLIV10F/OY3wJ/+qbl9S0JrKxePqzcykDaRK2XQ\n2+sue8kGXCuDU6fYljI56ewznzGzrSB0C9VtBXA7gPsSvjcGoFMIcTrhe5nQ2soTMIo4QikiZOlp\n3Y6noYHr/ruErDllu/iga6g2ke0A8owZ5XW7m5tZnRcNLpXB9OnAtm1MmrZqRpmE1i4KIV4WQuwA\nkBSPJ922wiCVgScDN5BzCw4fLl6nKuMG9aYMXNpEsiO1Vc/HBVwrg/373aVQ68IVXwkATxLRs0T0\nAVMb9WTgHu3twK5dxesMZBZR0fY7CS5tolmzuAM9fbp4gwEJdelL28pgzhxg587i9E+JZEBETxLR\nFuVna+n3n2Ro50YhxGoAbwPwYSJ6fe49VtDayqPUojBvPaC9Hdi9u3idqpTpNrIwqgmXNpFKBkW7\n/hLt7e6UwcKFbGMX5VwlxgyEEDfpNiKEOFL6fZyIHgJwHYCno76/bt26V153dnais7Mz9HutrcDm\nzUBHh+4eeqRFezuPdoo2Mpw7t9p7YAdz5vCA6ORJ+8/B1KlMqkWOvcycyeUcAPvKQE4Mk1UNTKKr\nqwtdXV1Gt2lypbPQuAERTQXQIIQYIKJWADcDWB+3IZUM4jB1KktkGxMwPMLR3g50dxdntCPx9a8D\nN2kPa2oPs2ezL710Ka+wZhuzZhVzMCDhMmYgt21jnfPgIHn9+tguNRV0U0tvI6IDAG4A8GMierT0\n/nwi+nHpa/MAPE1EmwA8A+ARIcQTOu1KSFaXs/I87EN2AkXrDBYsAD7ykWrvhXm4mrgnIav6Fm0w\nIKGWpOjutqsYZZmLopRA0RpLCCEeBvBwyPtHALy99HoPgFU67UThNa/h314ZuIMkgaJ2BvUG2eFI\n68M2Zs9mMihquRZJBv395WUkbeLv/x648067bZiCA2FpD5ddxr9dj44mMrq7+feiRdXdD48yNmwA\nzp1z09aCBcCvfgV88INu2jMNmX115IibQeTnPme/DVMoNBnceCPw1a+6WUfXg/EP/8A3eBEnHNUr\n/iRLXp8mLr2USz9feqm7Nk1i/nzg2DEOgntHoRKFJoPJk4EPfajaezGx4Et7T2xIEpCqvGiYNInV\nwaZNPtYYRAEmSXt4eNQKVq7kFFabKZm2sWgRsHGjVwZBeDLw8PBIjRUrgOeeq/Ze6GHhQuDxx4ur\nbmzBk4GHh0cmFH0C38UXc8HFVVZyHIsLEnINuBoBEYla2ycPD4/6wYsvst01OMgTV+sBRAQhhFYq\njScDDw+PCQcXhf1cwpOBh4eHh4cRMvAxAw8PDw8PTwYeHh4eHp4MPDw8PDzgycDDw8PDA54MPDw8\nPDzgycDDw8PDA54MPDw8PDzgycDDw8PDA54MPDw8PDzgycDDw8PDA5pkQERfIqJtRLSZiH5ARNMi\nvreGiF4iou1E9EmdNj08PDw8zENXGTwBYKUQYhWAHQA+HfwCETUAuAfALQBWAng3ERV00Tw9dHV1\nVXsXrMIfX7Hhj29iQ4sMhBA/E0KMlf58BkDYMunXAdghhNgnhBgG8CCAW3XaLSrq/Wb0x1ds+OOb\n2DAZM/hrAI+GvL8QwAHl74Ol9zw8PDw8agRNSV8goicBzFPfAiAAfFYI8UjpO58FMCyE+K6VvfTw\n8PDwsArt9QyI6L0APgDgzUKIcyGf3wBgnRBiTenvTwEQQogvRmzPL2bg4eHhkRG66xkkKoM4ENEa\nAP8bwBvDiKCEZwFcRERLARwB8C4A747apu4BeXh4eHhkh27M4P8CaAPwJBH9gYi+CgBENJ+IfgwA\nQohRAHeDM49eAPCgEGKbZrseHh4eHgZRc8teenh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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(range(len(x2)),x2);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Limits to Determinism\n", "### Dependency to initial conditions and parameters\n", "#### Bifurcation process" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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pQQPe6NGjqVu3LgB169ZlypQpJBIJpkyZ4q04AO8GLrvUhw4dSo8ePRg6dKh3\njT179mTcuHH07NkT8FdacgtOzgCR80jAHyglV1cvv/wygFMlWmgAUSKNzHucKrLZTnaLy1UKwPbt\n25127twZKKlykrkKmU8ZPHgwxhjnxiuruGQV1Lx585g7dy7z5s3zris8A132bkijR9l9LhsZAS9o\nyNWJrBxToocGECXSnEze40TO9cEHHwDwwQcfeElv8N14ZSOi3JqSflnGGPcAv6lvxowZZGZmMmPG\nDBo2bEhaWprLxaRCuvsGncijRo3yelfCY3hloJJzQ+RzJXpoAFEizcnkPVIhv43LFcgTTzxBbm4u\nTzzxBOCvAF599VUAXn31VW8FIhv8xo4dSzKZdFP/ZFPf+PHjKSoqYvz48WzdupXi4uIyOZTs7GxW\nrFjhzBRl74dcNckO97AXlnQHliN5r7zyStLS0twMeCVaaABRlNOEXHXIVca8efMoKChwW0tLlixx\nKoOJzEEsXLiQnJwcFi5c6J0rjFypSMNDiTGG7Oxst4KRDsByq2zTpk0UFxezadMmb8sK8NyBX3qp\nxG3opZde8n5HiR4aQBTlNCFXEDK5LW/S4G8hyZu5bB7cuHEja9asYePGjWW6veXNXa4U5KrneMgh\nVHJyoqzCCvtvSf8r+XdKO3klemgAUZTThNxaevTRRwF49NFHvVJZ8Kf7ybzHxIkTycnJYeLEiSST\nSRKJBMlkkq5duwI4laNvZUVXuGM9YP/+/cTjcdezIhsZr732WgCuvfZab457OBjJ2enyeqZPn05m\nZqazXlGihQYQJVKEE9Knys6dOzHGsHPnTi8YyOR0OIBIO3dppjh+/HhWrlzJ+PHj2bx5M8XFxWze\nvLnMCkQm0R9//HEAHn/8ca/BT1KrVi2SyaS7PulzlZeXhzGGvLw8FixYAMCCBQu8IAV4Kw3Z7/LY\nY49RVFTEY489dqofpVIJ0QCinPOc7qAhkbM5ZOJbbvN0794dwGmjRo2cyq0hGRhk3iM8aVCqHEMr\nO9yPh+wjKSgowFpLQUGB19QYnkg4ePBgYrEYgwcP9gwgw9tzSrTQAKKck5zJoCGR20HS1kTmGcI3\nfpm3kH0YcttIboeFK6Jk0JFVXNdccw2A01TI1ZHsXt+9ezcAu3fvLtMgGIvFMMY4hZLPWAZQJXpo\nAFHOGU4kaFhr3eN0IBPirVq1AqBVq1bce++95OTkcO+993q5DfDNEGfOnElmZiYzZ870LNxlT4Zc\nGYDf/JjzQgS8AAAgAElEQVTKvkQiO9wBb/BVy5YtAWjZsqUXwOR2HEBBQQGJRIKCggJvSy09PZ20\ntDTnr6VECw0gyjnP6Q4aEjkfXPpfDRw40CW5H3vsMVauXOnyBH369HEq+zgkGRkZVK1alYyMjDK+\nVHJ10L9/f9LS0ujfv38Z08SAL774wtOgn2Ts2LHeueW2mwyGAB06dCAej9OhQwdvqyxV74kSDTSA\nKJWaVKuOMxk0wu8fqMwbBE172dnZtG/fHmMM7du3B/CS3bLcV65msrOzmTp1KtnZ2V7SGvyKqGbN\nmtG+fXuaNWvmlQRLwhVVciiWLB2W/R2ypBdKbFcSiQTbt29n2rRpAG5+COhEwqiiAUSpVBxvm6q8\ngoZEzu3405/+BMCf/vQnN3BqxIgRTJ8+HWut26KSW0pyq+itt94C4K233mLt2rX069ePtWvXltlO\nkmXAvXv3pqCggN69e5fxzApo0KCBp7LcV1qWyBzOJZdcAuBUJvhl0Aj3iyjRQgOIctZzJhPip+rG\n27p1a6eyq1ze9OWKAfxViwwm8sZsrXU3a3ljB2jevLnT/Px8GjRoQH5+Ptu3b8da68waA8I28XLA\nVdBBvmnTJi85H54HIrvcZRnwiTYvKucmFR5AjDEdjTFbjDHbjDHDUhzze2PMdmPMWmNMVnlfo3L2\ncqqrjlN145V5h8zMTKBkZrmcDhje5pHjYmUneLjaKgg0Xbp08VSeb8CAAezYsYMBAwawYsUKAKcB\n559/vqeBK++6deuYNWsWubm5zJo1i5tuugmAm266iT179gA4lWjprhJQoQHEGBMDngTygCuBnsaY\nxqFjOgFXWGsbAncCT5X7hSrlTnnlNk7VjVdaq//zn/8E4J///CdHjhwB4MiRI/zlL38BcDplyhSS\nySRTpkzxphjKlYpcgcycORPAaapGRPn78vOrXr06gNPA+PDKK6+kqKiI1157rcx0w3r16gE4lfYp\nctWSKmgp0SBlADHGvGKM+f4Zfv+WwHZr7fvW2mPAHKBb6JhuwHQAa+2bQA1jTJ0zfF1KBVARCXHp\nxnsi21ljxozBGMOYMWMA6NevH2lpafTr189ztpWE8wSyckv2e8jjZCd627ZtAZzKCilpK5Kenk4s\nFitTUnvw4EFPFy5c6HTTpk0cO3aMTZs2ec2L4SmGsjM9IyMDKKkUC1drKdHieCuQfKDAGHO/MebU\nhyV8NZcBu8S/d5e+drxj9nzFMYpyypzIdtaDDz7oafPmzXnooYdo3rw5kydPBnAa8OWXX3oqt6Q6\ndepEPB6nU6dOXgCSN3NZKQV+PkJue02bNo1kMumqpAIuvvhiT3Nzc53KoCUHXf385z8nJyeHn//8\n54DfuyKnGMp8ihI9UgYQa+08oDlQHVhljBlsjBkYPMrtCr8ho0aNco/CwsKKvhzlOJxtFVUnsp0l\nS2ChZK758OHDmThxImlpacTjcdLS0rxeieAmHGiqiiY5nEkmqmV5L+B1nMsbuCwjlp/foUOHAJzK\npLzcmpJd5b1792blypXummQpsdzekrNFlMpBYWGhd588FdK+5udHgcPAecBFQPKU3q0sewBZvlGv\n9LXwMZd/zTGOU/1AlIqjonsJ5FCpqlWrcuzYMapUqeK9PmLECFeiCzBkyBCnv/zlL0kkEkyePJle\nvXrx6quvevMzgtxBsP01ZswY8vLySCQS5Ofnu6CxePFibwtJlgQvWbLEW6kEK5CPPvrIdYjv2iUX\n7JTJgUgvLJn3+OyzzwD47LPPGDhwIM8++yx333034Cfu5bhbOQdeqRy0a9fOWe0AjB49+qTPdbwc\nSEdgLXAB0NxaO9JaOzp4nPQ7+rwNNDDG1DfGVAVuBl4KHfMS0Lv0mnKAz6y1+07T+yvlTHl5VJ0q\nJ1qdJSucli5dCsDSpUs9u49wH0ezZs2cyiS8rI6SSMt1wOsXkTd2aX8iCVdNdezYkXg8TseOHb3S\n40GDBgEwaNCgMs6+sntelvvKbS8lehwvB3I/8HNr7b3W2i/PxJtbaxPAXUABsBGYY63dbIy50xjz\ny9JjXgF2GmN2AE8Dvz4T16KUPxWxTXWiyO2s4yXXW7Ro4VSuRlJ1qAPce++9GGO49957ycoqqUrP\nysryGgHlNtfQoUPJzMxk6NChgL8FJSuvbrnlFmbPns0tt9ziXaMsKYaSfpBEIsHWrVu9jvNUdvCA\n59Mle19+8YtfADhVosXxciDXWGs3nukLsNYutNamW2sbWmt/V/ra09baSeKYu6y1Day1zay1q8/0\nNSmnl8qy6pDI6qzjrUZkGa50s+3ZsyezZ8+mZ8+e3nApwHO1lSuIYC76q6++ygsvvADACy+8wC9+\n8QuKiorcTfpHP/qRUzlGN5FI8OKLL5bpzwg75sokvKwIk4Eu3PwoczLymsOWJ0q0qPBGQiVanM2r\njlQcL7kuk9ipfKHk/A8o8ZBKJBJMmzaNoqIiAIqKiryu7m3btgGwbdu2MnmGYcOGYYxh2LBh3u/f\ncsstzJ07t8wKRAYZwAt0MkEvS3XD89Vl86M0YAw7/SrRQgOIckaojKuOVMjVSJg2bdo4lTmMYCtp\n9uzZ3gAmgFtvvdXpkCFDiMViDBkyxNu2kiubcId6PB53DznSNux5FSC3ycDfAlu1ahUAq1at8no6\nwrPOFy5cSDKZZOHChZ7/l/xblOihAaSUc+mGd7ZRGVcdJ8qcOXOcSisT+Q1eVj0BPPLII06rVKni\nHrLjXAYdWd4LeBbqcqDUE088AeA0IFxqKwNVeKsqoHPnzp6uWbPGqexRGTlyJIBTJVpoAEmBBpRv\nThQ/M5mg3rixJGW4ceNGryJKWrYDns9Us2bNGDlyJM2aNfNyFbJ5cOrUqQBOZVWVXJ0EW1fhLSw5\nHRH8FUmjRo0wxtCoUaPjOutKQ0a57ZXqPZVooAHkBIjijfFUOVdXHWErE7nqkBbox7M8l414s2fP\nZvjw4cyePduzNZEmjWE3Xuk/NWjQIDIzMxk0aFCZrbKAsF+VDDoPPPAA1loeeOABr3JMBkPwg548\nTm6BKdFDA0gpJ3rD02Dyb6L4WYStTGSCXd6YZaL58OHDAE5lX4istpINgnI1EnbjlRVRffr0oaio\niD59+pCfnw/gNCDciZ6qy112z8teD/BnmMg+FFnSq0QPDSApOJGAEsUb6PE4V1cdkrCViayckrmO\nCRMmkJOTw4QJE8rkQGTllrwxyyR2x44dgZKmv6CzPNB7772XHj16cO+99zJw4EBisRgDBw70elIk\nQfI/0GC07mOPPeYFPdkHIoMM+M2Mffv2JR6P07dvX3r27Mm4cePo2bPnyX6kSiVGA8gJoMFECRgx\nYgTWWmcvcuONNzoNvNcKCwuZMGECK1euZMKECZ5FCPheVo8++iiXX345jz76qLftNXHiRKDEaytc\nHvzss88yd+5cnn32We9/d+GbfkD4/eWqQZbu9unTh1gs5hT+vd21evVqpz/60Y94++23+dGPfsSa\nNWt48MEHXZJdiRYaQL4hUfiWfTzkDSvqnwX823tt1KhRXr/HoEGDyM3NZdCgQd4IWfAnEnbt2pVd\nu3bRtWtXb2voiiuuAOCKK64oY1Ei7UemTp1KIpFg6tSp/PSnPwVwGhAOBnLbTZbkbt68mWQyyebN\nm8tMGgxvowUsXLiQ4uJiZxGvRAsNIKfA8W6guiKJBjK5LG/U48ePp6CggPHjx5dptpPf5mWgkNte\nr7/+OgCvv/56mSS87NFo2rQpAE2bNqVTp04ATgPCjZD9+/cnLS2N/v37e8OhAtPHl156yVuZAJ63\n16pVq2jRogWrVq1K6b+lRAMNIKcJDSaKtDyRM8WlFTr4pb+yXPeRRx5h5cqVPPLII57houzbAJg1\naxY9evRg1qxZ/OY3vwHgN7/5TRnTxYDBgwd7mpWVxc9+9jOysrK8fg/5nuGKLrmNNmXKFBKJBFOm\nTOFnP/sZDRo04Gc/+9kpf35K5UMDSDlT2YOJblul5n//93+dytXI559/DuB0+fLlVK1aleXLl3vf\n7D/88EMAPvzwQ/r16weUTDyUjr1QMshp2LBhpKWlccEFFwBwwQUXsH79egCnAZ07dyYWi7lgcddd\ndzF37lzuuusur1pMIi1SwG8+lEGvXbt27Nixw7MHV6KDBpAzxLmUeK8s11kRfPzxxxhj+Pjjj72Z\n6PIbu7QlgRLbk6NHj9KmTRumTp1KzZo1mTp1qleFJWdu9O7dG2OM60RfvXo1V199NatXr/Z6SmRC\nX1JQUEAymaSgoADAa2yUqyNZOiwnEAIsWLDAqbR9l/PVleihAaQcOJeCieJTq1YtkskktWrV8hoB\n5Qpk9erV1KxZ0+U+pJtu+/btOXDgAO3btycjI4MqVaqQkZHh9WHMnDkTa62zOpFzzD/99FMAPv30\n05SriTAFBQVUq1aNgoKCMl3p8XicRo0alZl1LsuKlyxZAsCSJUvKrFSUaKEBpJw5mYZFDS6VA5ms\nljfjYcOGceDAAYYNGwbgKpYWLlxIdnY2ANnZ2SQSCYqLi0kkEt6W0cSJE+nRo4cr7ZXuuh06dACg\nQ4cOXkJeIqu2oKR898iRI7Ru3dqbfPjKK6+QSCR45ZVXvEqx4OeBSisVuQJSoocGkArkZPIJFRFM\nNO9xYki/KDm0Sa44AL788kunTzzxBJmZmTzxxBOuF+TRRx/17EvWr1/PCy+84HIbw4YN46677mLY\nsGFeMJHvL1m2bJmnQcL7Zz/7mRcoZHWXtFIBPKNH2TEf3upSooUGkLOEyhJMlNTIhj056lXefME3\nNxw8eDBFRUUMHjw4ZQ5j06ZNHD161JXcLl++nCeffJLly5fzxRdfAPDFF1+QlpYG4DRg3LhxGGMY\nN26c9/O0tDQaN27s9MILLwTgwgsvLNO8ePHFFzuVFVpqZRJtNICcpciAoj5dlYP77rvP6bx58wCY\nN2+e13kO8H/+z/9xevPNNwNw8803exbwGRkZAGRkZJQZ7tS+fXund955JwB33nlnmWR9QDCWN9hi\nk8EhmUw6DdvGS4YNG0YsFmPYsGFe5Vh4paJECw0glYzyCiYajL45Y8aMYdy4cYwZM8Yb7tSpUydi\nsZhr8Nu7d6/TO+64A4A77riDuXPnAjB37lxmzZoFlPR8yGZF8Etq5XHNmzcHcBrQtGlT7rjjDtd0\nKMuFJ02aRCKRYNKkSd542nAOJDs7m5///OdkZ2d7+RC5naVEjwoLIMaYS4wxBcaYrcaYRcaYGimO\ne88Ys84Ys8YY81Z5X+fZjK5Mzi7i8Tj33XdfmZ6O/Px8ksmkc8mV1Vqyikq69l533XUAXHfddWUa\nEeUK4ODBgwAcPHjQ616XPPLIIzz55JNukJXMr8i8h+zvkCNsAe655x7mzp3LPffcQ3p6OmlpaaSn\np6cc46tEg4pcgdwLvGqtTQf+F7gvxXFJoJ21Ntta27Lcrq4SouXCZw+yETB8k5VVUf379wdK7EWO\nHDkCwJEjR7ytIRkkwLdWlzd9OY9E0qFDB+LxuKvYkrmWli1L/i/VsmVLb3JhuHdE5j22bdtGcXEx\n27Zto3///sRiMfd3KNGiIgNIN2Ba6fNpwE9SHGfQrbZvzMkEEzVKPH1Ii5HwQChpmy5Leps0aQJA\nkyZNvEl/cu46wOzZs53KfEqqpr5YLEY8Hne9KW+//bZTWUUlVzbSrwsgLy+PWCxGXl6em9PesGFD\ntm3bRjKZZNu2baf8mSmVj4q8Mde21u4DsNZ+BKSqA7TAYmPM28aYO8rt6s4hNBiUP3LVMWTIEIwx\nDBkyBIAHHnjAqSzplTfwSZMmATBp0qQyEwUnTJjgtHHjxgA0btyYN954A8BpQDKZ9HpLrr76aqey\nckyugMLIbbhFixaRTCZZtGhRmR4TJVqkff0hJ48xZjEg52saSgLCA19xeKq7Wxtr7V5jzHcoCSSb\nrbXLUr1nYK8NJWWS6tHjI4OIbmOVD8YYYrGY+7xlfqRt27Zs3bqVtm3bYoyhsLCQBg0a0L9/f1q3\nbs0TTzzhZo8ESCuS5cuXAzB58mRnvR54bgUsWrSIRCLBokWLaNGihReounTpwp///Ge6dOnCRRdd\nRH5+Pv/5n//pphcGx4ZXUVCS1F+3bh1Qknjv27fv6fnAlDNKYWGhm11zqpzRAGKt7ZDqZ8aYfcaY\nOtbafcaYusA/Upxjb6l+bIx5AWgJnFAAUY5PeEWiK5TTx/Lly2nTpg3Lly8nPz+fRCJBfn4+LVu2\n9Dq5Zb9I0J/x7rvvejNEpHUIQM2aNXn//fepWbMm9evXZ+nSpWRkZLgAddFFF3nXEnbzle+fkZFB\nPB4nIyPDNSX+4Ac/oF69ejz33HMuXzJw4ED+/Oc/M3DgQF599VWgpAjg0ksv5bnnnnMVXsrZT/iL\n9ejRo0/6XBW5hfUS0Lf0eR/gxfABxpgLjDHfKn1+IZALbCivC1SUk6V169ZYa2ndunWZbm25ApH2\nJ3K2hkyiyyY+wPOvko18wQogvBKQ1vKAV667adMmEokEmzZt8o6Tw60AL4jJYVMdO3YkFos5rywl\nWlRkAHkY6GCM2QpcD/wOwBjzXWPM/NJj6gDLjDFrgJXAy9baggq52oih1Vqnj40bN3oqt6BefPFF\n6tSpw4svvuhVW8kyWmnZDvC3v/3N6fTp0wGYPn2613sikb0igDcDRP6+NGMM93fI4CaHTW3dupVk\nMlnGPkWJBhUWQKy1B6y1N1hr0621udbaz0pf32ut7VL6fKe1Nqu0hDfTWvu7irpeRTlZwolmaYDY\nu3dv9u3bR+/evb0y3AULFpBMJlmwYIGXswC8+SLSZ6tr164ATgN+8YtfeCqT7W3btgWgbdu2ngOv\nNHmEku52YwwNGzb0SnplMFOih5bHKsoZ5t133/U0yCG8+uqr3khZGSiC5PS6des8vyvA2xKbPXs2\nderUYfbs2Zx33nkATgOuuuoqqlatylVXXQX4W1iy90OOzg2Pqs3Pz8daS35+vvc7so9EiR4aQJSv\nREt/Tx8y5wFw++23O33mmWcAeOaZZ6hVqxZQMmPk6NGjABw9epTvfOc7AE5l6W+3bt3Yt28f3bp1\n835fkpWVxahRo1zuRM5OD4LKVVdd5fUDheewb9myxamcVSI72ZXooQFEUc4w4RJYmZMI7E3y8/N5\n+umnAXj66ae9BsNwDuTHP/6x05ycHABycnK8G7tk7ty5DB8+3HltyRWRzM8MHTqU3Nxchg4dWqZy\nSw7IklYsN910E4BTJVpoAFGUM0x4BbFjxw6nsrpJBgN5A5d+WYA3xEmOmg17ZgU0aNCAWCzmkuty\nq+uee+4BSryuxo8fT0FBAePHj/cCBuCNu61fvz4A9evXp3HjxsRiMdfQqEQLDSDK16IVWafGe++9\nx+WXX+5Kc6W7riyJ7d69OwDdu3f3tpPCXlrhLbGAAQMGeBqwePFikskkixcvBqBnz55OR44cCcDI\nkSO9ZH940qBUWa21cOFCksmkWzEp0UIDiKKcYS644AI++OCDr9yCkj5X4W/9AWGTxH379jmVN/Zn\nn30WwGlAXl4eaWlp5OXlAfDOO+84lVVYEunXBX4psrRC0Zno0UYDiKKUM3Lw01NPPQXAU0895VVe\nyUqrcACREwUDy5FDhw55qwlJdnY2Dz30kCvJlUaNst8jGJm7fv36MsOp5OpGrkBmzZpFbm6uy+so\n0UIDiPK1aEXW6UUGgGrVqgFQrVo1HnvsMQAee+wxr6RXfuMHaNasmVOZj5D5DMmcOXMYPnw4c+bM\nAfAmD1566aUAXHrppV6uRb4O/oqkV69eAPTq1YsNGzbw+uuvu9JeJVpoAFG+EZoPOXVkw55sCpTJ\nbVnGO2XKFACnQ4YMITMzkyFDhrBo0SKgxDBRnut4fPe733UqVx2y4VBWWgHeSuXxxx8H4PHHH9cv\nFxFHA4iilDPBkKaCggKvYe/YsWMAHDt2jPT0dADS09PLDJTq1asXRUVF9OrVy5sHIlc2kp49ezJ7\n9myXPJf+W3K41O7duwHYvXs3Y8eOBXD6ySefOB04cCBQYrAYtopXooUGEEUpZ/70pz85TdUwKCcN\nhs0UpZuutBL56U9/CuA0wBhD48aN3apR9ousWrUKgFWrVnnVXTVr1gRwKivHpFPwggULSCQSrpxY\niRYaQJRvhNyy0O2sk0O66UqbEpkQlzf5wJ49UJlgl5VbBw4cAHAasGrVKlq0aOGChZxc2KJFCwBa\ntGjh5UbC/l0y8S7Zu3evp0q00ACiKOXMihUryMnJYcWKFd63/vPPPx+A888/3yublVtO4M/3kGW8\nqW7ykydPJpFIMHnyZACv4fCll14C4KWXXuKRRx4B4JFHHvGCGfjNh927dycnJ4fu3buXSbYr0UID\niHLa0BXJiXHeeeexYsWKMqaHsgpKNhKGq7DkGFrJoEGDPA2QQ6vA97WSiXe5TSVXSeCP6O3Vqxcr\nV66kV69eXiOkEj00gCgnjVbgnF7q1q3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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "xa=.15\n", "xb=3.\n", "\n", "C=np.linspace(xa,xb,num=100)\n", "# print C\n", "iter=range(1000)\n", "Y = C*0+1\n", "YS = []\n", "for x in iter:\n", " Y=Y**2-C\n", "# plt.plot(C,Y, '.k', markersize = 2)\n", "for x in iter:\n", " \n", " Y = Y**2 - C\n", " YS.append(Y)\n", " plt.plot(C,Y, '.k', markersize = 2);\n", "\n", "plt.xlabel('C')\n", "plt.ylabel('Y')\n", "plt.show();" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "C : 1.58939393939\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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PlJ4kaGsYCrjTocMi//t/dxfb6HY4r2RMWnViFYgu9vpROF5LzpCk4LlVoK26dqJKOKjT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\nGYBteZ7fk+f5UQCfA3B1qG2XEuMyUaksWFjKVm0B/QwsIxI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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "YS = np.asarray(YS)\n", "#Change this parameter and see how the range of possible values is changing\n", "which_c = 50\n", "plt.plot(YS[:,which_c][:200],'.-');\n", "print 'C : {}'.format(C[which_c])\n", "plt.xlabel('Iterations')\n", "plt.ylabel('Y')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulation of Lorenz Attractors " ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#Code from: https://jakevdp.github.io/blog/2013/02/16/animating-the-lorentz-system-in-3d/\n", "\n", "\n", "# import numpy as np\n", "# from scipy import integrate\n", "\n", "# # Note: t0 is required for the odeint function, though it's not used here.\n", "# def lorentz_deriv((x, y, z), t0, sigma=10., beta=8./3, rho=28.0):\n", "# \"\"\"Compute the time-derivative of a Lorenz system.\"\"\"\n", "# return [sigma * (y - x), x * (rho - z) - y, x * y - beta * z]\n", "\n", "# x0 = [1, 1, 1] # starting vector\n", "# t = np.linspace(0, 3, 1000) # one thousand time steps\n", "# x_t = integrate.odeint(lorentz_deriv, x0, t)\n", "\n", "\n", "\n", "\n", "\n", "import numpy as np\n", "from scipy import integrate\n", "\n", "from matplotlib import pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from matplotlib.colors import cnames\n", "from matplotlib import animation\n", "%matplotlib inline\n", "N_trajectories = 30\n", "\n", "\n", "#dx/dt = sigma(y-x)\n", "#dy/dt = x(rho-z)-y\n", "#dz/dt = xy-beta*z\n", "\n", "\n", "def lorentz_deriv((x, y, z), t0, sigma=10., beta=8./3, rho=28.0):\n", " \"\"\"Compute the time-derivative of a Lorentz system.\"\"\"\n", " return [sigma * (y - x), x * (rho - z) - y, x * y - beta * z]\n", "\n", "\n", "# Choose random starting points, uniformly distributed from -15 to 15\n", "np.random.seed(1)\n", "x0 = -15 + 30 * np.random.random((N_trajectories, 3))\n", "\n", "# Solve for the trajectories\n", "t = np.linspace(0, 10, 1000)\n", "x_t = np.asarray([integrate.odeint(lorentz_deriv, x0i, t)\n", " for x0i in x0])\n", "\n", "# Set up figure & 3D axis for animation\n", "fig = plt.figure()\n", "ax = fig.add_axes([0, 0, 1, 1], projection='3d')\n", "ax.axis('off')\n", "plt.set_cmap(plt.cm.YlOrRd_r)\n", "# choose a different color for each trajectory\n", "colors = plt.cm.jet(np.linspace(0, 1, N_trajectories))\n", "\n", "# set up lines and points\n", "lines = sum([ax.plot([], [], [], '-', c=c)\n", " for c in colors], [])\n", "pts = sum([ax.plot([], [], [], 'o', c=c)\n", " for c in colors], [])\n", "\n", "# prepare the axes limits\n", "ax.set_xlim((-25, 25))\n", "ax.set_ylim((-35, 35))\n", "ax.set_zlim((5, 55))\n", "\n", "# set point-of-view: specified by (altitude degrees, azimuth degrees)\n", "ax.view_init(30, 0)\n", "\n", "# initialization function: plot the background of each frame\n", "def init():\n", " for line, pt in zip(lines, pts):\n", " line.set_data([], [])\n", " line.set_3d_properties([])\n", "\n", " pt.set_data([], [])\n", " pt.set_3d_properties([])\n", " return lines + pts\n", "\n", "# animation function. This will be called sequentially with the frame number\n", "def animate(i):\n", " # we'll step two time-steps per frame. This leads to nice results.\n", " i = (2 * i) % x_t.shape[1]\n", "\n", " for line, pt, xi in zip(lines, pts, x_t):\n", " x, y, z = xi[:i].T\n", " line.set_data(x, y)\n", " line.set_3d_properties(z)\n", "\n", " pt.set_data(x[-1:], y[-1:])\n", " pt.set_3d_properties(z[-1:])\n", "\n", " ax.view_init(30, 0.3 * i)\n", " fig.canvas.draw()\n", " return lines + pts\n", "\n", "# instantiate the animator.\n", "anim = animation.FuncAnimation(fig, animate, init_func=init,\n", " frames=500, interval=10, blit=True)\n", "\n", "# Save as mp4. This requires mplayer or ffmpeg to be installed\n", "anim.save('./Images/lorentz_attractor.mp4', fps=15, extra_args=['-vcodec', 'libx264'],dpi=200)\n", "\n", "plt.close()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import HTML\n", "HTML(\"\"\"\n", "\n", "\"\"\")" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/jpeg": 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T1jNIkUekGCCuaLtcDk7nBUpmex4jqniOoj+yqNhG4rhVPC0zfBJy1zf4E7hm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\n3WoDNWU32sYmZ6bMj2I4qWhHauH1rIrxRvp3YaC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"text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import YouTubeVideo\n", "YouTubeVideo('JZoGO0MrZPA',width=400, height=400)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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DjopkInqKiCqJaJ5tW3si+oiIFhHRh0TULtr77eEWQciTvHy5TNn07u2el3Db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\ntW3sWCsv+ZVXgEmTrG2jR1sl2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17kC+rahJdIzs+XCzLTZjoZkdyjh1NY1qSTbCASh3bm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TJrAMlpf27Z0TdiS2bePqMdGulgYMoOi58EJm2777zn/fyrsWumHRImYhBwwIzfq5Wb2anysa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\nVRJJDvtNxPGNb8All8DnPw9PPtl+7IUXrCHK3LnJ1mrPvJP81lv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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# No regularity in the behavior \n", "# The effect of initial value\n", "figure =plt.figure(figsize=(10,10))\n", "for i in range(20):\n", " plt.subplot(5,4,i+1);\n", " plt.plot(x_t[i,:,1]);\n", " plt.xlabel('time')\n", " plt.ylabel('x')\n", "plt.tight_layout();" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Non-Predictable Determinism --- > End of Determinism?!\n", "* **Dependency to initial conditions and parameters**\n", "* **Butterfly Effect**\n", "* **Henri Poncare's work on N-Body Problem 1880s**\n", "* **Lorenz Attractors 1960s**\n", "* Further readings:\n", " * * Deterministic Nonperiodic Flow: #Paper: http://eaps4.mit.edu/research/Lorenz/Deterministic_63.pdf \n", " * Heisenberg's uncertainty principle\n", " * \"God Doesn't play dice\" \n", " * Is randomness the nature of things or due to lack of understanding?\n", " * Is it appropriate to look at probability and statistics as some sorts of pragmatism?\n", " * Important people from the History of Probability and Statistics: http://www.economics.soton.ac.uk/staff/aldrich/Figures.htm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# \n", "# Now Uncertainty and Randomness\n", "\n", "![](https://upload.wikimedia.org/wikipedia/commons/7/77/Nuvola_apps_atlantik.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Important terms\n", "* ## Variable\n", " * a symbolization of specific number, vector, matrix or even a function, which takes a range of values\n", " * Then, we have **discrete** or **continuous** variables, depending on the range of values\n", " * **Dependent** and **independent** variables\n", " $$y = 2x + sin(x) $$\n", "* ## Parameter or Constant\n", " * A Variable, which we assume is not varying (i.e. is constant) in our experiment\n", "* ## Random Variable (contribution of probability theory)\n", " * To add likelihood or chance (or formally probability) to any values of a variable\n", "* ## Fuzziness, vagueness and ambiguity (possibility theory)\n", "\n", "\n", "# \n", "# " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Some important principles of Probability Theory\n", "* ## Probability (Kolmogrov) axioms\n", "https://en.wikipedia.org/wiki/Probability_axioms\n", " \n", " * **First axiom**\n", "\n", "![](https://wikimedia.org/api/rest_v1/media/math/render/svg/ac12b631af7065f7f811d265b249a030f37484c8)\n", " \n", " * **Second axiom** \n", " * sum of all probabilities\n", "![](https://wikimedia.org/api/rest_v1/media/math/render/svg/1f0f26c0fa97e701b5fd9459d1b7fe3b6f4ea326)\n", " \n", " * Third axiom\n", " * probability of disjoint elements is the sum of their individual probabilities\n", " ![](https://wikimedia.org/api/rest_v1/media/math/render/svg/47f22fe03df467b1d20785e5026bac39fabd9edc)\n", " \n", " * **Consequences**\n", "![](https://wikimedia.org/api/rest_v1/media/math/render/svg/76817e6fd9cc41a3e844f540590132c36cf9bade)\n", " \n", "## \n", "![](https://wikimedia.org/api/rest_v1/media/math/render/svg/efd8ec693a89b5ea1c222660fefe5239565e6551)\n", "\n", "## \n", "\n", " ![](https://wikimedia.org/api/rest_v1/media/math/render/svg/024906557ab6af34620cb2ac901fd61911372944) \n", "## \n", "\n", "\n", "* **Some set theoretical intuitions** \n", " * venn diagrams from set theory\n", " \n", "\n", "## \n", "![](Images/venn.gif)\n", "\n", "* **Conditional Probability**\n", "![](https://wikimedia.org/api/rest_v1/media/math/render/svg/c7f0ff7bcd50dd11514f9f02b1273dab360a4cef)\n", "\n", "## \n", "![](https://upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Probability_tree_diagram.svg/424px-Probability_tree_diagram.svg.png)\n", "\n", "## \n", "\n", "* **Independent variables**\n", " * results of coin toss and rolling a dice\n", "![](https://wikimedia.org/api/rest_v1/media/math/render/svg/fd349a98748a1e64afd94e53e11e5cc1e3996d4e)\n", "## \n", "\n", "![](https://wikimedia.org/api/rest_v1/media/math/render/svg/7676b3c8f234867216f16c94eaa893354b1bca6a)\n", "## \n", "\n", "* **Law of total probability**\n", "![](https://wikimedia.org/api/rest_v1/media/math/render/svg/1f629ea8dda22bcc5fa6afe2d066ad753e215f2b)\n", "![](https://wikimedia.org/api/rest_v1/media/math/render/svg/a3fd649bac7848b022c2d1453bcd77070ab9a788)\n", "# \n", "\n", "\n", "* **Bayes Rule**\n", "![](https://wikimedia.org/api/rest_v1/media/math/render/svg/b1078eae6dea894bd826f0b598ff41130ee09c19)\n", "# \n", "\n", "![](https://upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Bayes_theorem_visualisation.svg/600px-Bayes_theorem_visualisation.svg.png)\n", "\n", "# Further readings\n", "* A First Course on Probability by Sheldon Ross\n", "* Richard Feynman intro to probability theory: http://www.feynmanlectures.caltech.edu/I_06.html" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# \n", "\n", "\n", "## Random Variable\n", "* ### A random variable is always coming with a likelihood function (probability density)\n", "* ### discrete random variable \n", " * examples: Coin:{'head','tail'}, \n", " * Dice:{1,...,6}\n", " * **Probability mass function** indicates the likelihood of each discrete event\n", "\n", " ![](https://wikimedia.org/api/rest_v1/media/math/render/svg/289f3e31c4faf8cbf2c78ebdec04e3994092c6e5)\n", "* ### continuous random variable\n", " * temperature in a building\n", " * Height of a random person\n", " * **Probability Density function** indicates the likelihood of each discrete event\n", " \n", "![](https://wikimedia.org/api/rest_v1/media/math/render/svg/45fd7691b5fbd323f64834d8e5b8d4f54c73a6f8)\n", "\n", "* **Cumulative distribution function**\n", "\n", "![](https://wikimedia.org/api/rest_v1/media/math/render/svg/4080d882376474e2d20b1f5d942f890539308c6f)\n", "\n", "![](https://wikimedia.org/api/rest_v1/media/math/render/svg/237edf4296a8ef4a946134c613b04b250d2de5be)\n", "\n", "* **joint functions**\n", "\n", "![](https://wikimedia.org/api/rest_v1/media/math/render/svg/2925d7334ee04f933179892c7f407efaacd33123)\n", "\n", "\n", "## \n", "\n", "\n", "![](https://wikimedia.org/api/rest_v1/media/math/render/svg/f8d052b8b354ed30ad25da7f4bc8c3e87cdc71ea)\n", "\n", "* **Expected value**\n", "\n", "![](https://wikimedia.org/api/rest_v1/media/math/render/svg/ef6f4efe003752f5353cfb1ed00235f374455805)\n", "## \n", "\n", "\n", "![](https://wikimedia.org/api/rest_v1/media/math/render/svg/caa946e993c976ed0f95e60748fcd7afce6bb2ff)\n", "* **Variance**\n", "\n", "![](https://wikimedia.org/api/rest_v1/media/math/render/svg/55622d2a1cf5e46f2926ab389a8e3438edb53731)\n", "## \n", "\n", "![](https://wikimedia.org/api/rest_v1/media/math/render/svg/c2ace8c9ac8568598540df05d0db70c4e957192b)\n", "\n", "* **CoVariance** \n", "![](https://wikimedia.org/api/rest_v1/media/math/render/svg/7120384a1c843727d9589e2b33dbc33901d14f42)\n", "## \n", "![](https://wikimedia.org/api/rest_v1/media/math/render/svg/7331bb9b6e36128d1d9cb735b11b65427929105d)\n", "### Therefore, two independent (uncorelated) variables have a covariance of zero and not the other way necessarily\n", "### Covariance is the heart of many ML and statistical learning methods such as PCA." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Known probability functions\n", "![](Images/PDFSandPMFS.png)\n", "\n", "* There are many more : https://en.wikipedia.org/wiki/List_of_probability_distributions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Gaussian (Normal) distribution\n", "![](https://upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Boxplot_vs_PDF.svg/598px-Boxplot_vs_PDF.svg.png)\n", "## \n", "###
PDF
\n", "![](https://upload.wikimedia.org/wikipedia/commons/thumb/7/74/Normal_Distribution_PDF.svg/720px-Normal_Distribution_PDF.svg.png)\n", "## \n", "###
CDF
\n", "![](https://upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Normal_Distribution_CDF.svg/720px-Normal_Distribution_CDF.svg.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Nevertheless, we use computers! " ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.999999998027\n" ] } ], "source": [ "from scipy.integrate import quad\n", "\n", "#Now CDF\n", "#P(a<=x<=b) for N(m,s)\n", "\n", "# Gaussian Distribution\n", "def Guassianf(m,s,x):\n", " return 1/(s*np.sqrt(2*np.pi)) * np.exp(-np.power((x-m),2)/(2*s*s))\n", "\n", "def integrand(x,m,s,Guassianf):\n", " return Guassianf(m,s,x)\n", "a = -6\n", "b= 6\n", "m = 0\n", "s = 1\n", "P, err = quad(integrand, a, b,args=(m,s,Guassianf))\n", "print P" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2.0 100.0\n" ] } ], "source": [ "#Expected Value and Variance\n", "\n", "from scipy.integrate import quad\n", "\n", "\n", "def integrand(x,m,s,Guassianf):\n", " return x*Guassianf(m,s,x)\n", "\n", "a = -1*np.inf\n", "b= np.inf\n", "m = 2\n", "s = 10\n", "mu, err = quad(integrand, a, b,args=(m,s,Guassianf))\n", "\n", "def integrand(x,m,s,Guassianf):\n", " return x*x*Guassianf(m,s,x)\n", "\n", "mu2, err = quad(integrand, a, b,args=(m,s,Guassianf))\n", "\n", "sigma2 = mu2- mu*mu\n", "\n", "print mu,sigma2\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "5.0 8.33333333333\n" ] } ], "source": [ "from scipy.integrate import quad\n", "\n", "# Uniform Distribution\n", "def f(a,b):\n", " return 1/float(b-a)\n", "\n", "def integrand(x,a,b,f):\n", " return x*f(a,b)\n", "\n", "a = 0\n", "b= 10\n", "\n", "mu, err = quad(integrand, a, b,args=(a,b,f))\n", "\n", "def integrand(x,a,b,f):\n", " return x*x*f(a,b)\n", "\n", "mu2, err = quad(integrand, a, b,args=(a,b,f))\n", "\n", "sigma2 = mu2- mu*mu\n", "\n", "print mu,sigma2\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Excercise\n", "**Calculate the mean and standard deviation of Exponential probability density functions.**\n", "# \n", "# \n", "# \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# But before going further\n", "* we talked about end of determinism, and transition from knowing to learning but \n", "* It seems that there is again some sort of repetition of learning and knowing withing probability and statistics" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import datetime\n", "import pandas as pd\n", "import pandas.io.data\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "import sys\n", "import getngrams as ng# from pandas import Series, DataFrame\n", "# import xkcd as fun\n", "%matplotlib inline\n", "# kw = ['Mainframe Computer','Personal Computer','Sensor','Computer Network','Internet', 'Data Mining','Pervasive Computing',\n", "# 'Smart Phone','Communication Technology','Simulation','Micro Simulation','Web 2.0'\n", "# ]\n", "\n", "kw = ['Probability','Statistics','Machine Learning','stochastics']\n", "A = pd.DataFrame()\n", "for i in range(len(kw)):\n", " try: \n", " tmp = ng.runQuery('-nosave -noprint -startYear=1800 -smoothing=3 -endYear=2008 -caseInsensitive '+kw[i])\n", "# A['year']=tmp.year.values[:]\n", " weights = tmp.values[:,1:]\n", " mx = np.max(weights,axis=0)\n", " mn = np.min(weights,axis=0)\n", " R = mx-mn\n", " weights = (weights-mn)/R\n", " tmp.ix[:,1:]=weights\n", " A[kw[i]]=tmp.values[:,1]\n", "\n", " except:\n", " print kw[i], 'not enough data'\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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hAxs3bsTX1xfTNLl58ybHjh2j4d1zoxKxYcMG1qxZwyeffAJAdHQ0Z86coWjR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\nYsoUeOwxs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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "for i in range(len(kw)):\n", " try: \n", " plt.plot(tmp.year,A[kw[i]],linewidth=1,label=kw[i])\n", " xticks = np.arange(tmp.year[0],2011,10).astype(int)\n", " plt.xticks(xticks)\n", "# plt.yticks([])\n", " except:\n", " print kw[i], 'not enough data'\n", "\n", "# A.plot(A.year,A.columns[1:],label='Date',colormap='jet')\n", "# \n", "plt.legend(loc='best',bbox_to_anchor = (1.0, 1.0),fontsize = 'medium')\n", "fig.set_size_inches(14,7)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Seems now it makes sense to use the term of Learning in Machine Learning!\n", "\n", "### Further readings\n", "* Statistical Modeling: The Two Cultures by Leo Breiman http://www.stat.uchicago.edu/~lekheng/courses/191f09/breiman.pdf\n", "* all the fights between statisticians and ML guys! \n", " * http://statweb.stanford.edu/~jhf/ftp/dm-stat.pdf\n", " * http://statweb.stanford.edu/~tibs/stat315a/glossary.pdf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Next sessions we talk about these estimation methods in details..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The answer to the excersice" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "\n", "from scipy.integrate import quad\n", "\n", "# Exponential \n", "def f(m,x):\n", " return lam*np.exp(-1*lam*x)\n", "\n", "def integrand(x,lam,f):\n", " return x*f(lam,x)\n", "\n", "a = 0\n", "b= np.inf\n", "lam = 2\n", "mu, err = quad(integrand, a, b,args=(lam,f))\n", "\n", "def integrand(x,lam,f):\n", " return x*x*f(lam,x)\n", "\n", "mu2, err = quad(integrand, a, b,args=(lam,f))\n", "\n", "sigma2 = mu2- mu*mu\n", "\n", "print mu,sigma2\n" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [default]", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.13" } }, "nbformat": 4, "nbformat_minor": 0 }