gistfile1.txt

{
 "metadata": {
  "name": "Lecture21_AnnotatedExamples"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Annotated notes from Lecture 21\n",
      "\n",
      "__GOALS:__\n",
      "\n",
      " *   Learn the tools needed for the data fitting homework assignment\n",
      " *   Learn some generally useful data fitting techniques\n",
      "\n",
      "__TUTORIAL TODAY:__  \n",
      "Load up this ipython notebook and change the values of `m` and `b` in the \"Fitting Lines to Data\" section, `A` and `B` in \"Curve Fitting\", and then again `a` and `b` in \"Fitting a Power Law\"\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# You can ignore this, it's just for aesthetic purposes\n",
      "matplotlib.rcParams['figure.figsize'] = (8,5)\n",
      "rcParams['savefig.dpi'] = 100"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Fitting Lines to Data\n",
      "=====================\n",
      "We'll cover very basic line fitting, largely ignoring the subtleties of the statistics in favor of showing you *how* to perform simple fits of models to data."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# These import commands set up the environment so we have access to numpy and pylab functions\n",
      "import numpy as np\n",
      "import pylab as pl\n",
      "\n",
      "# Data Fitting\n",
      "# First, we'll generate some fake data to use\n",
      "x = np.linspace(0,10,50) # 50 x points from 0 to 10\n",
      "\n",
      "# Remember, you can look at the help for linspace too:\n",
      "# help(np.linspace)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# y = m x + b\n",
      "y = 2.5 * x + 1.2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# let's plot that\n",
      "pl.clf()\n",
      "pl.plot(x,y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "[<matplotlib.lines.Line2D at 0x105959150>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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06AE7dsDMmZZNSQILpySds+JieP55SEkJdp936ADbtsGCBcFISklSwMIpSWcp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\njRg4cCC7d++O9kcoSo4ehd/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OSZIkxZSFU5IkSTFl4ZQkSVJMWTglSZIUUxZOSZIkxZSF\nU5IkSTFl4ZQkSVJMWTglSZIUU/8f66d8WoDkhg4AAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# looks like a simple line.  But we want to see the individual data points\n",
      "pl.plot(x,y,marker='s')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "[<matplotlib.lines.Line2D at 0x1031a3290>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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BAPABFE4AHvXe9iJ1v/s3uubNC3TKUmV2HACAD+AcTgANVt+ao5qTp3W4olqV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\nrkJggg==\n"
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# We need to add noise first\n",
      "noise = pl.randn(y.size)\n",
      "# Like IDL, python has a 'randn' function that is centered at 0 with a standard deviation of 1.  \n",
      "# IDL's 'randomu' is 'pl.rand' instead\n",
      "# What's y.size?\n",
      "print y.size\n",
      "print len(y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "50\n",
        "50\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "`y.size` is the number of elements in y, just like `len(y)` or, in IDL, `n_elements(y)`"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# We can add arrays in python just like in IDL\n",
      "noisy_flux = y + noise\n",
      "# We'll plot it too, but this time without any lines\n",
      "# between the points, and we'll use black dots\n",
      "# ('k' is a shortcut for 'black', '.' means 'point')\n",
      "pl.clf() # clear the figure\n",
      "pl.plot(x,noisy_flux,'k.')\n",
      "# We need labels, of course\n",
      "pl.xlabel(\"Time\")\n",
      "pl.ylabel(\"Flux\")\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "<matplotlib.text.Text at 0x1059705d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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E2DTQ18USAAAATEaANdzZxRLa2toUCoUIsQAAIO0RYA2X6YslAACAzEOANRyL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\nrkJggg==\n"
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we're onto the fitting stage.\n",
      "We're going to fit a function of the form\n",
      "$$y = m*x + b$$\n",
      "which is the same as\n",
      "$$f(x) = p[1]*x + p[0]$$\n",
      "to the data.\n",
      "This is called \"linear regression\", but it is also a special case of a more\n",
      "general concept: this is a first-order polynomial.\n",
      "\"First Order\" means that the highest exponent of x in the equation is 1\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# We'll use polyfit to find the values of the coefficients.  The third\n",
      "# parameter is the \"order\"\n",
      "p = np.polyfit(x,noisy_flux,1)\n",
      "# help(polyfit) if you want to find out more"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# print our fit parameters.  They are not exact because there's noise in the data!\n",
      "# note that this is an array!\n",
      "print p\n",
      "print type(p) # you can ask python to tell you what type a variable is"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 2.59289715  0.71443764]\n",
        "<type 'numpy.ndarray'>\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Great!  We've got our fit.  Let's overplot the data and the fit now\n",
      "pl.clf() # clear the figure\n",
      "pl.plot(x,noisy_flux,'k.') # repeated from above\n",
      "pl.plot(x,p[0]*x+p[1],'r-') # A red solid line\n",
      "pl.xlabel(\"Time\") # labels again\n",
      "pl.ylabel(\"Flux\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "<matplotlib.text.Text at 0x107b2ca50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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HXJGUmQoLC3/S/rl69eqUnDttA+yZZ565+efDDz+cM844g1atWjFv3jw6d+68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\nTkSuQmCC\n"
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Cool, but there's another (better) way to do this.  We'll use the polyval\n",
      "# function instead of writing out the m x + b equation ourselves\n",
      "pl.clf() # clear the figure\n",
      "pl.plot(x,noisy_flux,'k.') # repeated from above\n",
      "pl.plot(x,np.polyval(p,x),'r-') # A red solid line\n",
      "pl.xlabel(\"Time\") # labels again\n",
      "pl.ylabel(\"Flux\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "<matplotlib.text.Text at 0x105978dd0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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HXJGUmQoLC3/S/rl69eqUnDttA+yZZ565+efDDz+cM844g1atWjFv3jw6d+68\nzdeNHTuWtm3bVkWJkrTdfrx7VTQarfoQm0zCggXBRIHHHgtWXUeOhPPOC0JsDROJRCgpKSGRSJR5\ni1tJP7W1BcRFixbRrl277T532rYQ/FiLFi1o0qQJy5YtC7sUSUqZUFf7SkuDHbKOPhqOPTbY7nXq\nVHjvvWDltQaGVwh2B8vPzyc3N5f8/PzwV8Ul/UTarsD+2Mcff8yqVato7o4ukqqRUFb7NmyAadOC\nVdYlS4LwWlQE3brBjybC1FSGVim9hRZg16xZwzvvvLP5/tKlS3n55Zdp3Lgxu+++O9deey29evWi\ncePGPPnkk4wfP54jjjiCX//612GVLEkpF4vFqq4H9ssv4fbbYexYWLECevaEyZOhY8fKe09JqgSh\nBdgXX3xxcy9rVlYWQ4YMAYINDMaPH89rr73G1KlTWb16NXvvvTcnnXQS1113HbVr1w6rZEmqFJW+\n2vfpp0FonTgR1q+Hvn1h2LBgpqskZaDQAuxxxx1HaWnpNp9//PHHq7AaSaqGliwJ2gTuuQfq1YOL\nLoJBg2DvvcOuTJK2S8b0wEqSyuj554OJAjNnwp57BnNcL7gg2D1LkqoBA6wkVQelpTBrFowYAf/+\nd9AecOed0Ls37Lhj2NVJUkplzBgtSdJWfPstTJkChx4K3bvD998Ho7HefBOiUcOrpGrJACtJmejr\nr2H0aGjVCvr1gxYtYP58iMfhd7+Dn9mxUJIynS0EkpRJVq6EceNYM3Ikdb/9lhf2359Or70GBx8c\ndmWSVGX8T3RJygTvvhtMEWjWjHXDhzO1dm1aAqd++SXR0aMr5S2j0Sh5eXlEo9FKOb8kVZQBVpLS\n2X/+A6efDrm58PDDcPXVHNusGZesW8fHVN72s9FolKKiIoqLiykqKjLESkorBlhJ+hmhrEImkzBn\nDhx/PLRvD4sXw4QJsGwZ/PnPHHLssWRnZwNU2vaz8XicRCIBVF5IlqSKMsBK0jZU+Srk99/DvffC\nEUdA167B1q8PPBBsSHDhhbDTTkCwc1d+fj65ubnk5+dXyk5ekUik0kOyJFVUuQPs+vXrt/ncp59+\nul3FSFI6qbJVyLVr4dZb4YADgrmte+4JTz0FL74YtA9sZQvtWCzGkiVLyhxey7uSXBUhWZIqqtwB\n9ogjjmDx4sU/efwf//gHhx56aEqKkqR0UOmrkJ9/Dn/9K+y3HwweDEcfHbQLPP44dO4MWVkpeZuK\nriSXNySg7lzgAAAgAElEQVRLUlUpd4D9zW9+Q8eOHfn73/8OwDfffEO/fv3o06cPf/7zn1NeoCSF\npdJWIZctg4EDoVmzYMvXggJ45x2YPh0OPzw17/ED9rNKqm7KPQd2/Pjx/Pa3v+W8887jscce45NP\nPqF+/fq8+OKLHOwcQknVTEpXH195Jdjq9f77oVEjuOIKGDAAmjRJ3XtsRSQSoaSkhEQiYT+rpGqh\nQhsZdO3alVNOOYWJEydSu3ZtioqKDK+StDXJJDzzTBBc58wJVl3HjAm2ed1llyopIRaLEY1Gicfj\nRCIRWwIkZbxyB9h3332X3r178+mnnzJnzhz+9a9/0b17dwYNGsQNN9xAnTp1KqNOScosGzfCQw8F\nwfU//4HDDgtaBE4/HUL4e9LQKqk6qdBFXM2bN+fVV1/lhBNO4Prrr2fevHk89NBDtG/fvjJqlKTM\nsX493H47tG4NZ5wBu+4aXJS1eDGcfXYo4VWSqptyB9jbbruN+++/n0aNGm1+7Oijj+bll1+mbdu2\nKS1OkjJGSQnccEPQInDxxcHFWAsXwtNPw0knpWyigCSpAi0Effv23erju+66q19RSap5PvoIxo6F\nSZPgu++gXz8YOjSY6SpJqhTlDrBTp0792ee3FXAlqVp54w0YOTLoa61fPxiLNXAg5OSEXZkkVXvl\nDrADBw4k6wdfhW3YsIH169dTp04ddt55ZwOspCoRylX1ySTE48Hs1qIi2Hff4Ofzzw96XSVJVaLc\nPbCrV6+mpKRk8+3LL79k9uzZtG/fnqKiosqoUZK2UNGdpSqstBRmzoRIBI45BpYuhcmT4b33YMgQ\nw6skVbEKzYH9oTp16nDSSSfx9ddfc/nll7Nw4cJU1CVJ21RlO0tt2BC0CIwcCW+/HYTXRx+Fbt2g\nVrn/+1+SlCIp+xt4l112YcmSJak6nSRtUyQSITs7G6Bydpb68ssgtLZsCeeeG4zEevZZmD8f8vN/\nNrxGo1Hy8vIqf1VYkmqwcq/APvLII1vcLy0tZfHixUyfPp2jjjoqZYVJ0rZU2s5Sn34KN98MEybA\nunXQty8MGxYE2DLY1NqQSCQoKSkhGo06nUWSKkG5A2zPnj23uJ+VlUV2djadO3dm1KhRKStMkn5O\nSoPhkiVw000wdSrUqwcXXQSDBsHee5frNFXW2iBJNVy5A2xpaWll1CFJVe+FF4IpAv/8J+y5J1x3\nHVx4ITRsWKHTRSIRSkpKSCQSldPaIEkCUtgDK0kZIZmEWbPg17+Gjh3hzTfhjjvg/ffhyisrHF4h\nWBXOz88nNzeX/Px82wckqZKUaQX28ssv32L269Ykk0mysrIYPXp0SgqTpJT67ju47z4YMQJefz0I\nrw8/DD16pHSigKFVkipfmQLs4sWLfxJgNwXWbd2XpLTwzTdw550wenSw7Wu3bnDbbcFILP/OkqSM\nVKYAO2/ePN577z1atGhBLWcfSsoEn30G48YFYfXrr+Hss4OJAoccEnZlkqTtVOY0mpuby+eff775\n/plnnsnKlSsrpShJqrD33oNLLoFmzWDMGOjXL3hsyhTDqyRVE2UOsMlkcov7s2bNYs2aNSkvSJIq\n5KWX4MwzITcXHnwQ/ud/4MMPg9aB/fYLuzpJUgrZDyDpZ6X1zlLJJDzxBBx/PBx5ZBBib7sNPvgA\n/vIX2H33sCuUJFUCA6ykbdq0s1RxcTFFRUXpE2K//x4KC6FtWzjppGDr1wceCDYkuOgi2GmnsCuU\nJFWicm1k0L9/f3bccUeSySTr16/n4osvZuedd978fFZWFg899FDKi5QUjrTbWWrtWojFYNQoWLYM\nTjgB5s6Fzp2dKCBJNUiZA2zfvn3Jysra3Avbu3fvnxzjGC2pekmbnaVWrYJbbw2mCpSUBL2uDz8M\nhx9ertNEo1Hi8TiRSMR5rZKUwcocYCdPnlyJZUhKR7FYLNzQt2xZcBHWXXcF/a7nngtDhkCLFuU+\n1aZ2iEQiQUlJCdFo1BArSRmqXC0EkmqeUELeK68EO2bdf3+wtesVV8Cll0J2doVPmXbtEJKkCjPA\nSkoPySTMmwfDh8OcOf8/xzUahV122e7Tp007hCRpuzmFQFK4Nm4M5rZ26BBcjPXppzB9OrzzDlx2\nWUrCKwQryfn5+eTm5pKfn2/7gCRlMFdgJYVj/fpgd6ybboJ334XjjoPZs4OxWJV0QaihVZKqBwOs\npKpVUgITJsAtt8Bnn8Fpp8G990L79mFXJknKELYQSDVMaDtrffwxDB0abOv6v/8LPXsGGw/MmGF4\nlSSViwFWqkGqametLULym29Cv37B6Ku77gr6Wpctg4kT4YADKuX9JUnVW2gBdv78+XTv3p199tmH\nWrVqMXPmzJ8cM2rUKA488ECaNGlCz549WbFiRQiVStVHVYyS2hSSs4uLOWP6dDjooGC3rL//HT76\nCG64AfbcM+XvK0mqOUILsGvXruWII47gtttuA366i9e4ceO4/vrrGT58OM888wwAxx13HKWlpVVe\nq1RdRCIRsv87S7VSRkmVlrLjnDk8nEiwAGj67bf8MScHli4N2gd23TW17ydJqpFCu4ira9eudO3a\ndavPJZNJxowZw1VXXUX37t0BmDp1Kjk5ORQVFdGjR4+qLFWqNiptZ60NG4LRVyNHMuGTT3i+Th26\nf/cdC5s04bfdukHduql5H0mSSNMpBCtXrmTZsmV06dJl82MNGjSgQ4cOPP/88wZYaTukdJTUV1/B\npEnBhgOffAK/+x3cdReT7ryT4nic34ax/awkqdpLywC7fPlyAHJycrZ4PCcnZ/Nz2zJ48GAaNWq0\nxWMFBQUUFBSktkipJvv002AM1oQJsHYt/P73MGwYtGkDQOzoo0MuUJIUtsLCQgoLC7d4bPXq1Sk5\nd1oG2G1JJpM/6ZX9sbFjx9K2bdsqqkiqYYqLg40HpkyBHXeEiy6CQYNgn33CrkySlGa2toC4aNEi\n2rVrt93nTssxWvv891+GK1eu3OLxlStXbn5OUhV64YVgw4HWreHRR4M5rh9+CCNGGF4lSVUuLQNs\nTk4OLVq0YO7cuZsf++qrr1i4cCEdO3YMsTKpBkkmYdasYIvXjh3h9deDftf334c//AF+1KojSVJV\nCa2FYM2aNbzzzjub7y9dupSXX36Zxo0b07RpUy6//HKuvvpqDjjgAJo3b85VV11F8+bNyc/PD6tk\nqWb47ju4775gdfX116FDB3jooeACrVpp+d+8kqQaJrQA++KLL9K5c2cgmAE7ZMgQAPr160csFmPA\ngAFs2LCBK6+8kkQiQadOnZg3b94v9sBKqqBvvoE774TRo4MNB7p1g9tug2OOAf9/J0lKI6EF2LJs\nSjB06FCGDh1aRRVJ4aqU+axl8dlnMG5cEFa//hoKCuCKK+CQQ6quBkmSyiGjphBI1dWm7VcTiQQl\nJSVEo9HKD7FLl8KoURCLQe3acP75cPnlsN9+lfu+kiRtJxvapDQQj8dJJBIAJBIJ4vF4mV4XjUbJ\ny8sjGo2W/c0WLYKzzoIDDoAZM+AvfwkmCowZE2p4rdDvIkmqkQywUhqIRCJkZ2cDkJ2dTSQS+cXX\nbFq1LS4upqio6OeDXzIJTz4JJ5wA7drBiy/CrbfCBx/A//wP7L57qn6VCinX7yJJqvEMsFIaiMVi\n5Ofnk5ubS35+fpnaB8q0avv998FEgXbt4MQT4YsvgvtLlsDFF8NOO6X6V6mQiq5AS5JqJntgpTRR\n3p7XSCRCSUkJiUTip6u2a9fC3XcHPa7vvx+svM6dC507p+VEgZ/9XSRJ+hFXYKUMtdVV21Wrgl2y\nmjWDgQODGa6LFsETT8Dxx6dleIWKrUBLkmouV2ClDLY56H3wAQwaFMxxTSYhGoWhQ6FFi3ALLAdD\nqySprAywUiZ79dVgx6z77oOGDWHYMBgwAP57QZgkSdWRAVbKNMkkzJsXBNfHHw9GX40eDeeeC7vs\nEnZ1kiRVOntgpUyxcSP84x9BX2vnzvDJJzBtGrz7btDvaniVJNUQBlgp3a1fD5MmQZs20KsX1K8P\ns2fDyy9D795Qp07YFUqSVKVsIZDS1erVMGEC3HwzfPYZnHpqsOL6q1+FXZkkSaEywErp5uOPYexY\nuP12+O47OOec4OKsAw4IuzJJktKCAVZKF2++CSNHwvTpsPPOcNllQW/rnnuGXZkkSWnFACuFLR6H\n4cPh0Udhn33gxhvh/POhQYOwK5MkKS0ZYKUwlJZCUVEQXJ99NrhA6+674eyzoW7dsKuTJCmtOYVA\nqkrffhsE1YMPht/9Ltja9ZFH4PXXoV8/w6skSWVggJUqSTQaJS8vj2g0Cl99BTfdFGztGo0GF2Qt\nWBDcuneHWv5fUZKksrKFQKoE0WiUoqIiaiUSHPbRR6ydPp2dk0no0yeYKHDggWGXKElSxjLASpVg\n+TPPcH0iwTnAhnXruHe33Tjv1Vdh333DLk2SpIzn95aqcbb4aj/VFi6E005j9rJl9MzK4lqgbePG\nPNuzp+FVkqQUMcCqRtn01X5xcTFFRUWpCbHJZLC1629+Ax06wGuvUWvSJP6nTx8eys3l2B49iMVi\n2/8+kiQJsIVANUw8HieRSACQSCSIx+MVP9l338H998OIEfDaa8EWr//4RzBdoHZtJp1/foqqliRJ\nP+QKrGqUSCRCdnY2ANnZ2UQikfKfZM0auPlm2H9/+P3vg9aAefPg+efh1FOhdu3UFi1JkrZggFWN\nEovFyM/PJzc3l/z8/PJ9tZ9IwDXXwH77wdChcOyx8MorMGsW/PrXwUxXSZJU6WwhUI1T7n7UpUth\n9GiIxYJ5reefD4MHQ7NmlVOgJEn6WQZYaVsWLQr6W2fMgN13hz/9CS69NPhZkiSFxgAr/VAyCU89\nBcOHw9y5wc5Z48YF27zuvHPY1UmSJOyBlQLffw/33Qft2sEJJ8CqVcH94mK45BLDqyRJacQVWNVs\na9fC3XfDqFHw/vvQpQs8+SQcf7wXZUmSlKYMsKqZVq2C8ePhllvgiy/g9NPhwQehbduwK5MkSb/A\nAKua5YMPYMwYuOMOKC2FaDQYidWyZdiVSZKkMrIHVjXDq68Gmw60agVTpwah9cMP4bbbyhReo9Eo\neXl5qdl6VpIkbRcDrKqvZDLYIatbNzjsMPjXv4Je1w8/hP/9X/jvjly/JBqNUlRURHFxMUVFRYZY\nSZJCZguBqp+NG+Gf/wxmuC5cCIccAvfcA2eeCXXqlPt08XicRCIBQCKRIB6Pp7piSZJUDq7AKq1s\n11f169fDpEnQpg306gX16sFjjwXbvfbpU6HwChCJRMj+72ptdnY2kUikQueRJEmpYYBV2qjwV/Wr\nV8ONN0Lz5nDRRcGK6/PPBy0D3bpt9zisWCxGfn4+ubm55Ofnl38rWkmSlFK2EChtlPur+uXLYexY\nuP122LABzjkHhg2D3NyU12ZolSQpfRhglTYikQglJSUkEomf/6r+rbeC/tbp04Mdsi69FAYOhL32\nqtqCJUlSKGwhUNr4xa/q43H43e/gwAPhiSfghhuCiQI33mh4lSSpBnEFVmnlJ6G1tBSKioIV13gc\nWreGWAx694a6dcMpUpIkhcoVWJVZlQ7z//ZbuPtuOPjgYNU1mYSZM+GNN6B/f8OrJEk1mAFWZVJl\nw/y//jrYbKBly2Cb1/33hwULgtXXHj2glv/ISpJU09lCoDKp9GH+K1bALbfA+PGwdm3QInDFFUG/\nqyRJ0g+k9XLWtddeS61atba4HWigCUWlDfN/5x248MJghuu4cXDeebB0adA+4GctSZK2Iu1XYA8+\n+GDmzp27+f4OO6R9ydVSLBYjGo0Sj8eJRCLbPxd14cLgwqyHHoI99oBrroGLL4ZGjVJTsCRJqrbS\nPg3Wrl2bPfbYI+wyRAqG+SeTMGcODB8O8+YF/a0TJ0LfvsG2r5IkSWWQ1i0EAO+88w777LMPrVq1\nok+fPnz00Udhl6Ty+u67YNOBww+Hk0+GNWvgwQfh7bfhggsMr5IkqVzSOsB27NiRKVOmMHv2bIYM\nGcLrr7/OMcccwzfffBN2aSqLNWuCC7P23x/69IG994ZnnoEXXoDTToPatcOuUJIkZaC0biHo2rXr\n5p8PPfRQ+vTpQ7NmzXjggQe2OcZp8ODBNPpRH2VBQQEFBQWVWqt+IJGAW28Nbl9+CWedBVdeCYce\nWilvl9LeXEmSlBKFhYUUFhZu8djq1atTcu60DrA/1rBhQ3Jzc1m2bNk2jxk7dixt27atuqL0/95/\nP5jhGotBVlYwUWDIEGjWrNLectN82kQiQUlJCdFo1BArSVIa2NoC4qJFi2jXrt12nzujAuw333zD\nu+++S/PmzcMuRT+0eHEwUeCBB2D33eGPf4RLL4XGjSv9rSt9Pq0kSUo7ad0DO2zYMObPn8/SpUuZ\nOnUqJ510Ervuuiu9evUKuzQlk/DUU3DiidC2bdDXesst8MEHcPXVVRJeoRLn00qSpLSV1iuwy5cv\np6CggFWrVpGdnc0xxxzDtGnTaNCgQdil1Vzffx/Mbh0xAl56CY44AgoLoVcvCGFGb8rn00qSpLSX\n1gH2x42/CtG6dTB5Mtx0U7BTVpcu8MQTwZ9ZWaGWZmiVJKlmSesAqzTwxRcwfnzQHrBqVbDS+sAD\nkIIGbEmSpIowwGrrPvwQxoyBO+6AjRshGoWhQ6Fly7ArkyRJNVxaX8SlyhONRsnLy/vpPN3XXw+2\ndm3VCqZMCcZgffAB3Hab4VWSJKUFV2BroJ/MTu3fn1j//jB8OMyaBU2bBr2u554L9euHXa4kSdIW\nDLA10KbZqVlAJJFg4H33BRdoHXII3HMPnHkm1KkTdpmSJElbZYCtgX7dsSPdPvmEi775hjzg7UaN\ngt2zunYNfaKAJEnSLzHA1iRffgkTJzLpiSco/eYbnqxfnweOO46rHn007MokSZLKzIu40tA2L7Cq\nqOXL4corg97Wq6+G7t2ptWQJJ339teFVkiRlHANsmtl0gVVxcTFFRUXbF2Lfeiu4EKtFC5g0CS69\nFJYtC37OzU1ZzduS8iAuSZKEATbtbLrACiCRSBCPx8t/kmefhZ494cAD4fHH4YYbgrmuN94Ie+2V\n4oq3LqVBXJIk6QcMsGkmEomQnZ0NQHZ2NpFIpGwvLC2FRx+FTp0gEoElS4ILs95/H4YNgwYNKrHq\nn0pJEJckSdoKA2wlK+/X6LFYjPz8fHJzc8nPzycWi/38C7799v9HYPXoAckkzJwJb7wB/ftD3brb\n/0tUQIWDuCRJ0i9wCkEl+smGAdHoLwdSKNMxfP110Ms6ZkxwkVb37sH9NAmKsViMaDRKPB4nEomU\n7XeSJEkqAwNsJaqUr9FXroSbb4bx42HtWujdG664Iuh3TTOGVkmSVBkMsJUoEolQUlJCIpHY/q/R\n33kn2N51ypRgl6wLL4TBg2HffVNXsCRJUgawB7YSlbufdWtefBF69YK8vKC39ZprgokCN91keJUk\nSTWSK7CVrEKhNZmEOXNg+HCYNw/23x8mToS+faFevZTXKEmSlElcgU0n338P06fD4YfDySfDmjXw\n4IPw9ttwwQWGV0mSJAyw6WHNGrjllmCltU8f2HtvePppeOEFOO00qF077AolSZLShi0EYfr8cxg3\nDm69Fb78Es46Cx55BA49NOzKJEmS0pYrsGF4/30YMAD22y+4GKtPH3jvPZg2rULhtbybJUiSJGUy\nV2Cr0uLFMHIkPPAANGoEf/wjXHopNG5c4VNWdLMESZKkTGWArWzJZNDPOmIEPPEENG8OY8dCNAo7\n77zdp6+UzRIkSZLSmC0ElWXjRpgxA9q3hy5d4LPP4N57gw0JBgxISXiFYLOE7OxsgO3fLEGSJCkD\nGGBTbd26YGZrXh6ccUbQKjBnDixaBAUFsENqF71TslmCJElSBrGFIFW++AImTAjGYX3+ebB71n33\nwZFHVvpbG1olSVJNYoDdXh99BGPGwKRJQdtA//4wZEgw01WSJEkpZ4CtqNdfDyYK3Hsv7LorXH45\nXHYZ7LFH2JVJkiRVawbY8kgmYcECGD4cHnsMmjYNQux550H9+mFXJ0mSVCN4EVdZlJbCP/8JRx8N\nxx4LH3wAU6cGmw8MHmx4lSRJqkIG2J+zYQPcdRcceCCccgrUrQtFRfDqq/D730OdOmFXKEmSVOPY\nQrA1X34Jt98ebDiwYgX07AmTJ0PHjmFXJkmSVOMZYH/ok0/g5puDOa7r10PfvjBsWDDTVZIkSWnB\nAAvw9ttw001wzz1Qrx5cfDEMGgR77RV2ZZIkSfqRmh1gn3sORoyAmTNhzz3h+uvhwguhQYOwK5Mk\nSdI21LwAW1oKs2YFwfXf/w7aA+68E3r3hh13DLs6SZIk/YKaM4Xg229hyhQ49FDo3h2+/55bjj+e\n1qWlRBcsMLxKkiRliOofYL/+GkaPhlatoF8/aNEC/v1vonl5XP/qqyx55x2KioqIRqNhVypJkqQy\nqL4tBCtXwrhxcNtt8M03QYvAFVfAQQcBED/3XBKJBACJRIJ4PB5mtZIkSSqj6hdgP/oI7rgD7r47\n2GjggguC3bKaNt3isEgkQklJCYlEguzsbCKRSEgFS5IkqTyqX4A95RTIzoarrw7GYe2221YPi8Vi\nRKNR4vE4kUiEWCxWxYVKkiSpIqpfgP3Tn+Cqq4J5rr/A0CpJkpR5qt9FXKedVqbwWlHRaJS8vDwv\n+pIkSQpJ9QuwlSgajVJUVERxcbGTCyRJkkJigC2HeDzu5AJJkqSQpX2AnTZtGocddhi77bYbXbp0\nYcmSJaHVEolEyM7OBnBygSRJUkjSOsA++uijnHfeeQwZMoTnnnuOVq1a0alTJ7766qtQ6onFYuTn\n55Obm0t+fr4XgUmSJIUgrQPsqFGjuOCCCzjnnHNo3bo1EydOZMcdd2Ty5Mmh1RSLxViyZInhVZIk\nKSRpHWAXLlxIly5dNt/PysqiS5cuPP/88yFWJUmSpDCl7RzYVatWsX79enJycrZ4fI899uCFF17Y\n5usGDx5Mo0aNtnisoKCAgoKCSqlTkiRJP1VYWEhhYeEWj61evTol507bAFtRu+22GzNnzgy7DEmS\npBptawuIixYtol27dtt97rRtIWjcuDH16tVj5cqVWzy+cuVK9t13322+bv78+c5nlSRJqsbSNsAC\ndOjQgblz526+X1paylNPPUXHjh23+ZrVq1c7n1WSJKkaS+sWgqFDh3L66adz5JFH0r59e8aOHcuG\nDRvo16/fNl/TqFEj57NKkiRVY2kdYPPz87njjjsYOXIkH3zwAUceeSQLFixg11133eZrjj32WEdc\nSZIkVWNpHWAB+vTpQ58+fcp8/DXXXFOJ1UiSJClsad0DK0mSJP2YAVaSJEkZxQArSZKkjGKAlSRJ\nUkYxwEqSJCmjGGAlSZKUUQywkiRJyigGWEmSJGUUA6wkSZIyigFWkiRJGcUAK0mSpIxigJUkSVJG\nMcBKkiQpoxhgJUmSlFEMsJIkScooBlhJkiRlFAOsJEmSMooBVpIkSRnFACtJkqSMYoCVJElSRjHA\nSpIkKaMYYCVJkpRRDLCSJEnKKAZYSZIkZRQDrCRJkjKKAVaSJEkZxQArSZKkjGKAlSRJUkYxwEqS\nJCmjGGAlSZKUUQywkiRJyigGWEmSJGUUA6wkSZIyigFWkiRJGcUAK0mSpIxigJUkSVJGMcBKkiQp\noxhgJUmSlFEMsJIkScooBlhJkiRlFAOsJEmSMooBVpIkSRnFACtJkqSMYoBVxiosLAy7BFUhP++a\nxc+7ZvHzVnmlbYBt3rw5tWrV2uI2YsSIsMtSGvEvvJrFz7tm8fOuWfy8VV47hF3AtmRlZXHddddx\n/vnnb36sfv36IVYkSZKkdJC2ARaCwLrHHnuEXYYkSZLSSNq2EAD8/e9/p0mTJrRt25abbrqJjRs3\nhl2SJEmSQpa2K7ADBw6kXbt21K1blxkzZnD99dfz6aefMmrUqK0ev379egDeeuutqixTIVq9ejWL\nFi0KuwxVET/vmsXPu2bx8645NuW0devWbd+JklXoD3/4QzIrK+tnb0uWLNnqa+++++5knTp1kt9+\n++1Wn582bVoS8ObNmzdv3rx585bmt2nTpm1XpsxKJpNJqsjnn3/OF1988bPHtGjRgjp16vzk8Tfe\neINDDjmEd999l5YtW2713HPmzKF58+bstNP/tXevIVG8CxjAn93SLE3zQmu45ZYaIbKhZZYX2sq2\nD128pEVQskV+yDZtFSroQlBWQolkpUV/Qu1iJKIEpWGKVmRWpBRdFDWKQAsppExJds6HaM/fY+ef\nnuPs6+jzgwXn3WXm2S+7z868vjN5xDITERER0cjo7e1Fe3s7Vq1aBS8vr/95P3YtsP+PK1euwGQy\noaen57cFl4iIiIjGh1E5B7a+vh719fVYtmwZ1Go1SktLcfbsWezYsYPllYiIiGicG5VnYJ89e4aU\nlBS8fv0afX19mDNnDrZs2YL09HQWWCIiIqJxblQWWCIiIiKi/2ZUrwM7VJcvX8b8+fPh7u6O6Oho\nvHnzRnQkksnx48cRGhoKV1dXaDQaxMXFobm5WXQssoMTJ05ArVbDYrGIjkIy+fLlC5KTk+Hv748p\nU6ZAr9fj6dOnomORDPr7+5GdnQ2j0QgvLy+sXr0a586dEx2LRkhdXR3Wrl0LHx8fqNVqlJeXD3rN\nqVOnEBgYCC8vL8TGxqKjo2NYx1B8gb158ya2b9+O9PR0PHz4EH5+foiMjER3d7foaCSDuro67Nq1\nC48ePUJhYSE+f/4Mo9GInp4e0dFIRo8fP8aFCxeg1+uhUqlExyEZfPv2DaGhobBarSguLsarV6+Q\nnZ0Nd3d30dFIBseOHcOBAweQlJSE+/fvIyYmBqmpqcjNzRUdjUZAT08PgoODcfbsWQAY9Lmdm5uL\no0ePIisrCzU1NQAAg8EAq9U65GMofgqBwWCAXq/H6dOnAQCSJGHmzJnYs2cPUlNTBacjub18+RJB\nQVjnOTEAAAbQSURBVEGoq6tDZGSk6Dgkg69fv2LBggXIy8vDkSNHEBwcjOzsbNGxaIRlZmbizp07\nqK2tFR2F7CAxMRGSJKGkpMQ2tmzZMsydOxfnz58XmIxGmlqtRllZGdatWwfgZ0/z8/OD2WxGeno6\nAKC7uxsajQbXr1+3ve6P+5UtsZ00NDQgOjratq1SqRAdHY36+nqBqchefv1a8/DwEJyE5LJz506s\nWbMGy5cvh8J/b9M/KCsrQ2RkJEwmE2bNmoWQkBBcvHhRdCySSUJCAqqrq1FfX4++vj5UV1ejoaEB\n69evFx2NZNbZ2Ym3b98O6G6urq4ICwsbVncblctoDVVXVxd6e3uh0WgGjE+fPh2PHj0SlIrsxWq1\nIi0tDUajEYGBgaLjkAyKi4vR2NiIx48fAxh8GYrGjtbWVuTk5CAhIQFFRUWoqKiA2WyGo6MjkpKS\nRMejEbZx40b09fUhPDwcavXPc2mlpaUwGo2Ck5HcPnz4AACDuptGo7E9NxSKLrA0vu3cuRPt7e14\n8OCB6Cgkg/fv3yMtLQ1VVVVwdHQE8PPSE8/Cjk39/f3w9PREQUEBAGDp0qV4+fIl8vPzWWDHoMLC\nQuzbtw+nTp1CREQEampqkJycDKvVitjYWNHxSABJkoZ1kkLRUwg8PT3h5OSEzs7OAeOdnZ3QarWC\nUpE9mM1m3Lp1CzU1NZgxY4boOCSDp0+f4tOnTwgJCYGDgwMcHBxQV1eH06dPw9HRkUV2jNFqtYiK\nihowFhUVhXfv3glKRHI6efIkTCYTLBYLFi1ahL179yI+Ph45OTmio5HMfHx8AOC33e3Xc0Oh6AIL\nAGFhYaiqqrJtW61W3L17F4sXLxaYiuRkNptRXl6O6upq+Pr6io5DMomOjsaLFy/Q1NSEpqYmNDY2\nYuHChdi8eTMaGxs5nWCMiYiIGHQ15cGDB9DpdGICkaw6OjoG3Zho4sSJw15KiZRHo9Fg9uzZA7pb\nd3c3GhoahtXdFD+FICMjA4mJiVi4cCFCQ0ORk5ODvr4+mEwm0dFIBikpKbh27RrKy8vh7Oxs+7Cb\nNm0anJycBKejkeTi4jJobvOUKVPg4eHBOc9j0O7du1FUVISUlBRs27YNlZWVqKysxF9//SU6Gskg\nNjYWeXl50Gq1WLJkCWpra1FYWIiUlBTR0WgEfPv2DS0tLbbttrY2NDY2wtPTEzNnzoTFYsGhQ4cQ\nEBAAnU6HgwcPQqfTYc2aNUM/iDQGFBUVSXq9XnJzc5NWrFghvX79WnQkkolKpZLUarWkUqkGPAoK\nCkRHIzswGAySxWIRHYNkcu/ePSkiIkKaOnWqFBgYKF28eFF0JJLJ169fpYyMDEmn00mTJ0+W/P39\npYMHD0o/fvwQHY1GQE1Nje37+e/f2Vu3brW95uTJk9K8efMkT09PKSYmRuro6BjWMRS/DiwRERER\njS+KnwNLREREROMLCywRERERKQoLLBEREREpCgssERERESkKCywRERERKQoLLBGRQCaTCXFxcaJj\nEBEpiuJvZEBENFqp1f98juDw4cPIzc3lbXGJiIaJ68ASEcnk48ePtr+Li4tx6NAhNDc328acnZ3h\n7OwsIhoRkaJxCgERkUymT59ue7i6ukKlUg0Yc3Z2HjSFwGAw2G6zqNPpEBQUhJKSEvT398NsNkOr\n1SIgIAAVFRUDjtXe3o64uDh4e3vD29sbSUlJ6OrqsvdbJiKyCxZYIiKBVCoVVCrVgLHCwkJMmjQJ\nt2/fhsFgwNatW7Fp0ya4ubmhvLwcwcHB2LJlC75//w4A+PLlC8LCwqDRaFBaWopLly6htbUVGzZs\nEPGWiIhkxzmwREQCSZI0aA6sq6sr9u/fDwDIzMxEXl4ePn36hBs3bgAADhw4gJKSEjx//hyLFi3C\nmTNnoNFokJ+fb9uHu7s7wsPD0dLSgoCAAPu9ISIiO2CBJSIaRVQqFVauXGnbdnNzg1arhdFotI0F\nBQUB+Pcc26amJjQ3N2Pq1KmD9tXW1sYCS0RjDgssEdEo4+LiMmBbrVYPGPu1uoHVagXw8yzuunXr\nkJWVNWhf3t7eMiYlIhKDBZaISOHmz5+Pq1evwtfXFxMmTBAdh4hIdvwnLiKiUeR3c2L/JDU1Fd3d\n3di0aROePHmC1tZWVFZWYtu2bbaztEREYwkLLBGRnfznagO/xv4+/rtVCf7Ezc0NDQ0NcHBwQHx8\nPPR6PSwWC9zd3f94MwUiIiXijQyIiIiISFH405yIiIiIFIUFloiIiIgUhQWWiIiIiBSFBZaIiIiI\nFIUFloiIiIgUhQWWiIiIiBSFBZaIiIiIFIUFloiIiIgUhQWWiIiIiBTlX6uudds8uZsoAAAAAElF\nTkSuQmCC\n"
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# help(polyval) if you want to find out more"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's do the same thing with a noisier data set.  I'm going to leave out most of the comments this time."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "noisy_flux = y+noise*10\n",
      "p = polyfit(x,noisy_flux,1)\n",
      "print p"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 3.4289715  -3.65562359]\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# plot it\n",
      "pl.clf() # clear the figure\n",
      "pl.plot(x,noisy_flux,'k.') # repeated from above\n",
      "pl.plot(x,np.polyval(p,x),'r-',label=\"Best fit\") # A red solid line\n",
      "pl.plot(x,2.5*x+1.2,'b--',label=\"Input\") # a blue dashed line showing the REAL line\n",
      "pl.legend(loc='best') # make a legend in the best location\n",
      "pl.xlabel(\"Time\") # labels again\n",
      "pl.ylabel(\"Flux\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "<matplotlib.text.Text at 0x107617750>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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aBuEyCrkiUiOZmZkB3ZMa6K9f5IIVF8PKlc7+2u++g/r1oW9fyMw0477Cw62u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\nAQAAYDqUXAAAAJjO/wGfSXwd4XE+VAAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Despite the noisy data, our fit is still pretty good!  One last plotting trick, then we'll move on."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pl.clf() # clear the figure\n",
      "pl.errorbar(x,noisy_flux,yerr=10,marker='.',color='k',linestyle='none') # errorbar requires some extras to look nice\n",
      "pl.plot(x,np.polyval(p,x),'r-',label=\"Best fit\") # A red solid line\n",
      "pl.plot(x,2.5*x+1.2,'b--',label=\"Input\") # a blue dashed line showing the REAL line\n",
      "pl.legend(loc='best') # make a legend in the best location\n",
      "pl.xlabel(\"Time\") # labels again\n",
      "pl.ylabel(\"Flux\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "<matplotlib.text.Text at 0x1036977d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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7G+dPn3Zt4dfIrUPuJ598ctVzxowZw5gxY0qgGhHXy8rK4vz581SuXJmyZd36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\nFQAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Curve Fitting\n",
      "=============\n",
      "\n",
      "We'll now move on to more complicated curves.  What if the data looks more like a sine curve?  We'll create \"fake data\" in basically the same way as above."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# this time we want our \"independent variable\" to be in radians\n",
      "x = np.linspace(0,2*np.pi,50)\n",
      "y = np.sin(x)\n",
      "pl.clf()\n",
      "pl.plot(x,y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "[<matplotlib.lines.Line2D at 0x105f919d0>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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pGDu3cWPsNJKknUnLgjp8OJQtC61axU4iKZl07x7Gzj3ySOwkkqSdSbuCunIl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\nECoMqAAAAAgVBlQAAACEyg9XFo6m/7eJowAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# We'll make it noisy again\n",
      "noise = pl.randn(y.size)\n",
      "noisy_flux = y + noise\n",
      "pl.plot(x,noisy_flux,'k.') # no clear this time"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "[<matplotlib.lines.Line2D at 0x107b1cbd0>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That looks like kind of a mess.  Let's see how well we can fit it.\n",
      "The function we're trying to fit has the form:\n",
      "$$f(x) = A * sin(x - B)$$\n",
      "where $A$ is a \"scale\" parameter and $B$ is the side-to-side offset (or the \"delay\" if the x-axis is time).  For our data, they are $A=1$ and $B=0$ respectively, because we made $y=sin(x)$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# curve_fit is the function we need for this, but it's in another package called scipy\n",
      "from scipy.optimize import curve_fit\n",
      "# we need to know what it does:\n",
      "help(curve_fit)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Help on function curve_fit in module scipy.optimize.minpack:\n",
        "\n",
        "curve_fit(f, xdata, ydata, p0=None, sigma=None, **kw)\n",
        "    Use non-linear least squares to fit a function, f, to data.\n",
        "    \n",
        "    Assumes ``ydata = f(xdata, *params) + eps``\n",
        "    \n",
        "    Parameters\n",
        "    ----------\n",
        "    f : callable\n",
        "        The model function, f(x, ...).  It must take the independent\n",
        "        variable as the first argument and the parameters to fit as\n",
        "        separate remaining arguments.\n",
        "    xdata : An N-length sequence or an (k,N)-shaped array\n",
        "        for functions with k predictors.\n",
        "        The independent variable where the data is measured.\n",
        "    ydata : N-length sequence\n",
        "        The dependent data --- nominally f(xdata, ...)\n",
        "    p0 : None, scalar, or M-length sequence\n",
        "        Initial guess for the parameters.  If None, then the initial\n",
        "        values will all be 1 (if the number of parameters for the function\n",
        "        can be determined using introspection, otherwise a ValueError\n",
        "        is raised).\n",
        "    sigma : None or N-length sequence\n",
        "        If not None, it represents the standard-deviation of ydata.\n",
        "        This vector, if given, will be used as weights in the\n",
        "        least-squares problem.\n",
        "    \n",
        "    Returns\n",
        "    -------\n",
        "    popt : array\n",
        "        Optimal values for the parameters so that the sum of the squared error\n",
        "        of ``f(xdata, *popt) - ydata`` is minimized\n",
        "    pcov : 2d array\n",
        "        The estimated covariance of popt.  The diagonals provide the variance\n",
        "        of the parameter estimate.\n",
        "    \n",
        "    See Also\n",
        "    --------\n",
        "    leastsq\n",
        "    \n",
        "    Notes\n",
        "    -----\n",
        "    The algorithm uses the Levenburg-Marquardt algorithm through `leastsq`.\n",
        "    Additional keyword arguments are passed directly to that algorithm.\n",
        "    \n",
        "    Examples\n",
        "    --------\n",
        "    >>> import numpy as np\n",
        "    >>> from scipy.optimize import curve_fit\n",
        "    >>> def func(x, a, b, c):\n",
        "    ...     return a*np.exp(-b*x) + c\n",
        "    \n",
        "    >>> x = np.linspace(0,4,50)\n",
        "    >>> y = func(x, 2.5, 1.3, 0.5)\n",
        "    >>> yn = y + 0.2*np.random.normal(size=len(x))\n",
        "    \n",
        "    >>> popt, pcov = curve_fit(func, x, yn)\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Look at the returns:\n",
      "\n",
      "\n",
      "    Returns\n",
      "    -------\n",
      "    popt : array\n",
      "        Optimal values for the parameters so that the sum of the squared error\n",
      "        of ``f(xdata, *popt) - ydata`` is minimized\n",
      "    pcov : 2d array\n",
      "        The estimated covariance of popt.  The diagonals provide the variance\n",
      "        of the parameter estimate.\n",
      "    \n",
      "\n",
      "So the first set of returns is the \"best-fit parameters\", while the second set is the \"covariance matrix\""
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def sinfunc(x,a,b):\n",
      "    return a*np.sin(x-b)\n",
      "fitpars, covmat = curve_fit(sinfunc,x,noisy_flux)\n",
      "# The diagonals of the covariance matrix are variances\n",
      "# variance = standard deviation squared, so we'll take the square roots to get the standard devations!\n",
      "# You can get the diagonals of a 2D array easily:\n",
      "variances = covmat.diagonal()\n",
      "std_devs = np.sqrt(variances)\n",
      "print fitpars,std_devs"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 1.24208994  0.15896795] [ 0.2237797   0.17677306]\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Let's plot our best fit, see how well we did\n",
      "# These two lines are equivalent:\n",
      "pl.plot(x, sinfunc(x, fitpars[0], fitpars[1]), 'r-')\n",
      "pl.plot(x, sinfunc(x, *fitpars), 'r-')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "[<matplotlib.lines.Line2D at 0x105978110>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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cEbGFQgCAoiFoHsRxpHfesRYvDz1ka9OWLJEGDJAqbtsktWlji9cKZ2FuvDHc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\nIYQQQkhM0KBJCCGEEEJi4jeV03FEn7cuVAAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Again, this is pretty good despite the noisiness."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Fitting a Power Law\n",
      "===================\n",
      "\n",
      "Power laws occur all the time in physis, so it's a good idea to learn how to use them.\n",
      "\n",
      "What's a power law?  Any function of the form:\n",
      "$$f(t) = a t^b$$\n",
      "where $x$ is your independent variable, $a$ is a scale parameter, and $b$ is the exponent (the power).\n",
      "\n",
      "When fitting power laws, it's very useful to take advantage of the fact that \"a power law is linear in log-space\".\n",
      "That means, if you take the log of both sides of the equation (which is allowed) and change variables, you get a \n",
      "linear equation!\n",
      "$$\\ln(f(t)) = \\ln(a t^b) = \\ln(a) + b \\ln(t)$$\n",
      "We'll use the substitutions $y=\\ln(f(t))$, $A=\\ln(a)$, and $x=\\ln(t)$, so that\n",
      "$$y=a+bx$$\n",
      "which looks just like our linear equation from before (albeit with different letters for the fit parameters).\n",
      "\n",
      "We'll now go through the same fitting exercise as before, but using powerlaws instead of lines."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t = np.linspace(0.1,10)  \n",
      "a = 1.5\n",
      "b = 2.5\n",
      "z = a*t**b "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pl.clf()\n",
      "pl.plot(t,z)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "[<matplotlib.lines.Line2D at 0x1077799d0>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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J5cdjj0GnTtCmTXBNe69jr3hV6HNKX3zxxfz7LVq0oHHjxhx33HEsX76clJQU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\n"
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Change the variables\n",
      "# np.log is the natural log\n",
      "y = np.log(z)\n",
      "x = np.log(t)\n",
      "pl.clf()\n",
      "pl.plot(x,y)\n",
      "pl.ylabel(\"log(z)\")\n",
      "pl.xlabel(\"log(t)\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "<matplotlib.text.Text at 0x10779f190>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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1alXYI0lSlu3fD3/5S9C27tsHs2cHOwsYXCXp6CIVXidPnsztt99O3759+fTT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\nRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It's a straight line.  Now, for our \"fake data\", we'll add the noise *before* transforming from \"linear\" to \"log\" space"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "noisy_z = z + pl.randn(z.size)*10\n",
      "pl.clf()\n",
      "pl.plot(t,z)\n",
      "pl.plot(t,noisy_z,'k.')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "[<matplotlib.lines.Line2D at 0x107785c10>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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9+vSpWFdWkrTN1p7Xjz6Cn/8cHn8cGjWCq66Ca6+Fww9PbX2SVNUy\nEolEItVFVIWtPRXz5s2zB1ZSnbJgAdx9NzzzDLRsCcOHwy9+Ad+4n1WSUq6q8lqNWYVAkrTnysvh\npZfgvvuCtVtzcuCBB4J2gYMOSnV1kpRc1X4TlyRp175tTdf16+Ghh6BTp2C717VroaAAPvwwaBkw\nvEqqC5yBlaQaYndruq5cGSx99dBDweoCAwbAxInQs6cbD0iqewywklRD7GxN13ffhXHj4Kmn4IAD\n4Ior4JproF27FBcrSSlkgJWkGiIUClFSUkI8HiczM4vS0hBdu8IRR8Bdd8Hll0OzZqmuUpJSzwAr\nSTXEuHFR/vGPCGvWxCgtDdGpU5T77w/aBRr4r7UkVfCfRElKsfffD/pbp0yBjRujnHMOjBgR7Jwl\nSdqRAVaSUmDzZnjuuSC4vvlmsNnA9dfDkCHwne+kujpJqtkMsJJUjVasgIcfhkcfhVWr4NRT4emn\ngzaBhg1TXZ0kpQcDrCQlWSIBM2cGs61/+UuwVuvFFwfrth57bKqrk6T0Y4CVpCRZsyboa/3DH+Cf\n/4SOHeH3vw/Ca2ZmqquTpPTlTlyStIe+bZcsCGZbZ82CwYODvtbhw4Nds954AxYtgquvNrxK0v4y\nwEqqs/YkkG4/trCwkKKiIgoLC3d4T3Ex3HMPHH100Nf6t7/BLbfA+edHeP/9PJ58MuKOWZJURQyw\nkuqkbwuk37SzXbLKyuCll+Dcc6FNG7j5ZjjhBJgxA4qKoKgowuuv7/k1JEl7xh5YSXXSzgLp7my/\nS1aLFlk0bhwiJwc+/RQ6d4b77oOLLoIWLfb9GpKkPeMMrKQ6KRQKkZWVBUBWVhahUGi34ydMiHLM\nMWEaN87lyy/DLFkS5ayz4K234L33YNiwyuF1X64hSdozzsBKqpOi0SiRSIRYLEYoFCIaje4wprwc\nYjGYPBmeeQZKS6OcdBJccQVccAE0abL/15Ak7T0DrKQ6a1eB8sMP4ckng8eyZZCTA9dcEyx/lZtb\nNdeQJO07A6ykpEuHWcgvvwx2xJo8GebMCZa6uuCCILTm50M9G64kqcbwn2RJSbW3d/vvz3X2dEms\nrTZvDnbGOuccaNVqWx/rU08F27w++iiccorhVZJqGmdgJSVVddyJvzUkx+NxSkpKiEQiu5zpLSuD\nv/41CKl//nMw83r88cEargMHQnZ2lZcnSapiBlhJSbX98lPJuhP/20JyeXmwscBTT8Gf/hRsOpCT\nA1deCYMGwbHHVnlJkqQkMsBKSqrquBN/ZyE5kYC33w76Wp95JlivtXXrYK3WCy8MNhxwZyxJSk8G\nWElJl+wbt7YPyR07hsjOjtK+PSxdGrQEnH9+EFp79rSfVZJqAwOspLSWSMCCBdC6dZSMDJg6Fd58\nE847Lwitp54K9eunukpJUlUywEraKzVhSayysmCDgeeeCx4ffwzNm8PZZ8P48fCjH0HDhikpTZJU\nDQywkvbY3tztX9U2bYLXXw8C69SpEI/Dd74D/fvDgAHBTKuhVZLqBgOsVMftzYxqdSyJtb21a2Ha\ntCC0TpsWfN+hA1x2WbB26wkn2NMqSXWRAVaqw/Z2RrU6lsT65BN48UUoLITp04OZ1+OPh1GjgpnW\nTp1cPUCS6joDrFSH7e2MajKWxCorC7ZuffHF4LFwIUCEgw6KcdxxIZ5+OkpOzn5fRpJUixhgpTps\nX2ZUqyK0fvklvPxyEFhffjn4vmVLOPNMaNEiwvvvF7J6dZylS0v47W+rr89WkpQeDLBSHVYdmwxA\nsNTV++9vm2X9+9+D3bG+9z34xS8gHA76WevXh7y8GKtXV1+frSQp/RhgpTouWaE1Hg96WF97DV59\nFVasgMaN4bTT4KGH4Kyzgp2xvqk6+mwlSenNACupSmzcGKzN+uqrQWh9993g+DHHwAUXQJ8+wVJX\nBx64+/NU16ywJCl9GWAl7ZOtbQFbZ1hnzQpCbHZ2MMs6fDj07h2s1bq3DK2SpN0xwEraI4kELF0K\nM2fCjBlBcC0uDmZUTzkFbr89CK6dO7vMlSQpuQywUjWpjl+LV+U1Egn46KMgsP71r8Hzp58G4fT4\n4+GSS+D00yEU+va2AEmSqpIBVqoG1bEF6/5eI5GAJUuCoLo1tK5YEex01bUrXHgh9OoF+fnQvHmV\nli5J0l4xwErVoDq2YN3ba5SVwaJF8Le/Bf2rM2fCZ58FgbVbN/jpT4ObrvLzoVmzKi9XkqR9ZoCV\nqkF1LA31bdcoLYW5c4PAGosFu1+tXRusvdqtG1x8cTDDGgpBZmaVlydJUpUxwErVoDqWhvrmNW66\nKcqTTwaB9W9/C1YMSCSgRQvo2RNuvDF4/v734eCDq7wcSZKSxgArVZNkLg21Zg288w506BClpCTY\n7WrSpOC1jh2DoHrttcFzXp6rBEiS0psBVkoz//lPsEnA229veyxZErzWtGnQDnDFFUErQI8ewYyr\nJEm1iQFWqsE2bQp+9b99WP3HP6C8PFi66vjj4cwz4YQTgkdubnATliRJtZkBVqohVq+G996DBQuC\nx3vvBWF1yxZo0CDYIKBnT7jmmiCsHnMMNGyY6qolSap+BlipmpWXBxsEbA2pW58//TR4/aCDgrDa\nowf87GdBS0CXLsFxSZJkgJWSJpEI1lVdtCiYSV20CD74ABYuDPpYAQ4/HL73PRg0KHg+7jjo0CFY\n2kqSJO2cAVY1XnVswbo/EglYuXJbSN0aWP/xj2B1AAj6VY8+Ovi1/znnBEH1uOPgsMNSW7skSemo\n1gfYmh5+tHvVsQXrntq4MfjV/4cfQlFR8NgaVL/6Khhz4IHBslWdOkE4HATWTp2gXbt9m1X1768k\nSTuq1QG2JoUf7Zvq2IJ1e1u2wMcfVw6pW7/++ONgthWC5apyc4Ow2rdvEFSPOQZycqru1//+/ZUk\naedqdYCt7vCjqpeMLVi/+gqWLoV//zt43vr497+DGdavvw7GHXAAHHVUEFQvvDDoTc3NDR6HHZb8\nzQD8+ytJ0s7V6gBbHfvPK7n2ZQvWdevgk09g2bLKAXXro6Rk29jGjYNf77drB6efvi2g5uZCmzap\nvZnKv7+SJO1crQ6w1bH/vJJv+89tw4YgnH76afC89bH991tvnIJg/dQjjwwCarducN552wJru3aQ\nlVVzt1X1768kSTtX4wPslClTuPfee1m+fDndunVjwoQJ5OXl7fH79+X/9A0NybWzP9/162HVqmDZ\nqZ09r1wZhNPVqyufKysrmClt2xZOOWXb123bBv2orVun95JU/v2TJGlHNTrAvvDCC1xxxRU8/PDD\ndO/enXHjxpGfn89HH31EZmZmUq5ZXTfO1PaQXFYGX34J8Th88cW250ceifDPfxayYUOcpUtL+POf\nIyQSUdaurfz+Ro2gVatgndRWrYJF/c8/PwimW0NqmzbBXf+SJKluqdEBduzYsQwZMoRLLrkEgIce\neogXX3yRxx9/nGuuuSYp16yOG2fSKSSXlQU3PZWUBL+aLynZ8fHll5VDajweHNt6x/5W9epBRkaM\nsrLgz/frr+M0aRLjV7/aFlS3Ph9ySM391b4kSUqtGh1g33rrLUaOHFnxfUZGBr1792bOnDlJC7DV\nceNMskNyIgGXXhrhxRcLWb06TjxeQjweYdiwYKZz7VooLWWnX8+dG6GkJEbDhiHq149SWrpjEIUg\nXDZrBlu2RPj66xgtW4b4wQ+inHBC8Gv9li13fD7kELjiihCFhdv+fMPhENdfX6U/viRJquVqbIBd\nvXo1GzduJDs7u9Lxww47jLlz5ybtuvty40wiEexvv2VLsATT1sf232//dW5uiM8/L2HNmjjNmmXR\ntm2Ip5+GTZuCxfI3bdr2+Ob369dve/znP5W/3/5RXh4DgpBcUhKnsDBGYeG2mg88MFjLNDMzeG7a\nFJYujVBSUsimTXHq1y/h6KMjDBkS5ZBD2OGRmQlXXBHMJK9bF2fz5hIaNoxw3327//OqqTcm7UtN\nNfHnkCSpLqixAbaqLFgAAwcGIXPPH1ESCXjpJcjODn6NXl5e+Xn7r3c2Q7l7USACxPjqqxCvvx7l\n9deDVzIygvVHtz4OPLDy940bw8EHB8+HHho8b//Y+tof/xhiwYISSkvjNG+exQ9+EGLcuG1htWHD\nHavKy4uxaVMQetevj1NaGuPKK3f9U+zrTHJNC3v70tLhJgOSJKVOjQ2whx56KAceeCDFxcWVjhcX\nF9OmTZtdvm/48OE0b9684vv16+G73x1Ix44DK3oqMzL27FG/fvCoV2/3X299btgwWLapYcNtj+2/\nr/x1lEaNdgyoDRtWTe/nkCF7P9O5t+0TNXmd0r352fcliLvJgCRJu1dQUEBBQUGlY2u2X+tyP9TY\nAAvQvXt3pk+fTr9+/QAoLy/n9ddf54Ybbtjle8aPH0/Xrl2rq8QabW9nBPf21/s1uR1gb2ZH9yWI\n1+TwLklSTTBw4EAGDhxY6dj8+fPp1q3bfp+7RgfY6667jvPPP5/vf//7nHDCCYwfP55NmzZx6aWX\nprq0HdTEILcv9iX01jR7Ozu6L0G8poZ3SZLqghodYMPhMI8++ij33nsvH3/8Md///veZPXs2TZs2\nTXVpldgPWbPsy+zovnxefsaSJKVGvVQX8G0GDRrEe++9x5o1a5g+ffpe7cJVXaqrHzISiZCXl0ck\nEknK+WuLaDRKOBwmNzeXcDhs0JQkqZap0TOw6aI6+iGd5d07/tlIklR71fgZ2HRQHTN+3vUuSZIU\ncAa2iiR7xs+73iVJkgLOwKYJ+zolSZICzsCmEUOrJEmSM7CSJElKMwZYSZIkpRUDrCRJktKKAVaS\nJElpxQArSZKktGKAlSRJUloxwEqSJCmtGGAlSZKUVgywkiRJSisGWEmSJKUVA6wkSZLSigFWkiRJ\nacUAK0mSpLRigJUkSVJaMcBKkiQprRhgJUmSlFYMsJIkSUorBlhJkiSlFQOsJEmS0ooBVpIkSWnF\nACtJkqS0YoCVJElSWjHASpIkKa0YYCVJkpRWDLCSJElKKwZYSZIkpRUDrCRJktKKAVaSJElpxQAr\nSZKktGKAlSRJUloxwEqSJCmtGGAlSZKUVgywkiRJSisGWEmSJKUVA6wkSZLSigFWkiRJacUAK0mS\npLRigJUkSVJaMcBKkiQprRhgJUmSlFYMsJIkSUorBlhJkiSlFQOsJEmS0ooBVpIkSWnFACtJkqS0\nYoCVJElSWjHASpIkKa0YYCVJkpRWDLBKWwUFBakuQdXIz7tu8fOuW/y8tbeSEmDvuOMOevbsSePG\njTnkkEN2Omb16tWcf/75HHbYYeTm5nLbbbftMGbp0qWcccYZtGjRgs6dO/Pwww8no1ylKf/Bq1v8\nvOsWP++6xc9be6tBMk769ddfc+GFF9KzZ08mTpy40zF9+vTh0EMPZfr06axcuZLBgwdTr149brrp\nJgA2btzIySefzA9/+ENisRgLFy4kEonQpEkTLrroomSULUmSpDSQlAB76623AvD444/v9PWZM2ey\nYMECPvvsM7KysujSpQu33XYbt9xyCzfccAMNGjTgqaeeYsOGDUSjURo0aEDHjh1ZsGABY8eONcBK\nkiTVYSnpgZ0zZw5dunQhKyur4tjpp5/O559/ztKlSyvGnHrqqTRo0KDSmAULFrB58+Zqr1mSJEk1\nQ1JmYL/NihUrOOywwyody87OrnitQ4cOrFixgjZt2ux0zMqVK8nJyan02saNGwH45z//maSqVdOs\nWbOG+fPnp7oMVRM/77rFz7tu8fOuO7bmtA0bNuzXefY4wI4ePZp77rlnt2P+9a9/kZubu18FbZWR\nkbFX47fO3A4aNKhKrq/00K1bt1SXoGrk5123+HnXLX7edcuyZcsIhUL7/P49DrDXX389kUhkt2Pa\ntWu3R+dq06YNs2fPrnSsuLgYgNatW1c8r1q1aqdjvvOd7+xwzj59+jBlyhRycnI46KCD9qgOSZIk\nVZ+NGzeydOlS+vTps1/n2eMA27JlS1q2bLlfF9uqR48e3HTTTcTj8Yo+2Ndee43s7OyKENyjRw9G\njhzJli1bKvpgX3vtNY4//ngaNWq00/q8uUuSJKlm69mz536fIyk3cS1fvpwFCxawfPlyysrKeO+9\n91iwYAH/+c9/ADj11FM5/vjjufjii1m4cCGvvPIKY8aMYdiwYRVh9Sc/+QmNGzfm8ssv5x//+AdP\nP/00999/P9ddd10ySpYkSVKayEgkEomqPumll17K5MmTgwtkZJBIJMjIyGDGjBmccsopAHz55Zf8\n/Oc/Z+bMmTRr1oxLLrmEX//615XOs2zZMn7xi18wd+5cWrduzbBhwxgyZEhVlytJkqQ0kpQAK0mS\nJCVLStaBrWpTpkzhuOOO45BDDqF3794sXrw41SUpSX73u99xwgknkJmZSXZ2NgMGDKCoqCjVZaka\n3HXXXdSrV48RI0akuhQlyZo1a7jyyis56qijaNy4MV26dGHevHmpLktJsGXLFu677z5OP/10WrZs\nyY9//GP+8Ic/pLosVZFZs2bRt29fWrduTb169Zg6deoOY8aOHUunTp1o2bIl/fv33+HG/W+T9gH2\nhRde4IorrmDkyJH8/e9/p3379uTn51NaWprq0pQEs2bNYtiwYcydO5fJkydTUlLC6aefzvr161Nd\nmpLo7bff/r/27i+kqTYAA/iz0cT+l4NGNGvRH0JkoGlqU1g1vJKUUrwJmYE3c2hLsC6ym1QITIYi\natiF7iKDCL2JDNvQEnQRTBAVJBVDUKQbUWkk5+0iPHzix/cp7Phy9PnBLs4fdp6rneecvbwvXr58\nCbvdvuMp9kgfVldXkZ6eDkVR0N3djYmJCTQ2NuLkyZOyo5EG6uvr8eTJE5SUlODLly/Iz89HRUUF\nmpubZUejGFhbW0NKSgpaWloAbJ0atbm5GbW1tXj+/DlCoRAAwOl0QlGUbV9D90MInE4n7HY7mpqa\nAABCCCQmJqK6uhoVFRWS05HWxsfHkZycjMHBQWRnZ8uOQxpYWVnB1atX0draimfPniElJQWNjY2y\nY1GM1dXV4ePHjxgYGJAdhXZBUVERhBB4+/atuu/GjRu4fPky2tvbJSajWDMajejp6cHt27cB/O1p\nFy5cgNfrxcOHDwEAy8vLsFgsePPmjXre/36vZol3STgchsvlUrcNBgNcLheGh4clpqLdsvG0lpCQ\nIDkJaaW8vBx5eXm4efMmdP68Tf+hp6cH2dnZcLvdOHv2LFJTU9HR0SE7FmmksLAQwWAQw8PDiEaj\nCAaDCIfDuHv3ruxopLHFxUXMzs5u6m7Hjh1DRkbGjrqblKVkY+Xnz5/49euXusTshlOnTmFkZERS\nKjynQxsAAANWSURBVNotiqKgsrISubm5SEpKkh2HNNDd3Y1IJIKvX78C2PkKfaQf379/h9/vR2Fh\nIQKBAD58+ACv14u4uDiUlJTIjkcxVlxcjGg0iuvXr8No/Psu7d27d8jNzZWcjLQ2Pz8PAFu6m8Vi\nUY9th64LLO1v5eXlmJmZwdDQkOwopIEfP36gsrIS/f396uIlQgi+hd2j1tfXYTab0dnZCeDvfOHj\n4+Noa2tjgd2Durq68PjxY7x48QIOhwOhUAhlZWVQFAUFBQWy45EEG1OubpeuhxCYzWbEx8erS8xu\nWFxchNVqlZSKdoPX68X79+8RCoVw+vRp2XFIA9++fcPS0hJSU1NhMplgMpkwODiIpqYmxMXFscju\nMVarFTk5OZv25eTkYG5uTlIi0lJDQwPcbjd8Ph+uXbuGR48e4c6dO/D7/bKjkcbOnDkDAP/a3TaO\nbYeuCywAZGRkoL+/X91WFAWfPn1CZmamxFSkJa/Xi97eXgSDQZw7d052HNKIy+XC2NgYRkdH1dX8\n0tLScO/ePUQiEQ4n2GMcDseWf1OGhoZgs9nkBCJNLSwswGQybdp34MCBHU+lRPpjsVhw/vz5Td1t\neXkZ4XB4R91N90MIqqqqUFRUhLS0NKSnp8Pv9yMajcLtdsuORhrweDx4/fo1ent7cfjwYfXH7sSJ\nE4iPj5ecjmLpyJEjW8Y2Hzp0CAkJCRzzvAc9ePAAgUAAHo8H9+/fR19fH/r6+vDq1SvZ0UgDBQUF\naG1thdVqRVZWFgYGBtDV1QWPxyM7GsXA6uoqpqam1O3p6WlEIhGYzWYkJibC5/Ph6dOnuHTpEmw2\nG2pqamCz2ZCXl7f9i4g9IBAICLvdLo4fPy5u3bolJicnZUcijRgMBmE0GoXBYNj06ezslB2NdoHT\n6RQ+n092DNLI58+fhcPhEEePHhVJSUmio6NDdiTSyMrKiqiqqhI2m00cPHhQXLx4UdTU1Ijfv3/L\njkYxEAqF1PvzP+/ZpaWl6jkNDQ3iypUrwmw2i/z8fLGwsLCja+h+HlgiIiIi2l90PwaWiIiIiPYX\nFlgiIiIi0hUWWCIiIiLSFRZYIiIiItIVFlgiIiIi0hUWWCIiIiLSFRZYIiIiItIVFlgiIiIi0hUW\nWCIiIiLSlT8hewy+zrEoegAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "noisy_y = np.log(noisy_z)\n",
      "pl.clf()\n",
      "pl.plot(x,y)\n",
      "pl.plot(x,noisy_y,'k.')\n",
      "pl.ylabel(\"log(z)\")\n",
      "pl.xlabel(\"log(t)\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "<matplotlib.text.Text at 0x105a9aed0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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DadeuHTVq1GDYsGE0b96cAQMG8PDDD5dXvZKkfbBuHQwbBt27Q9OmQbd16FCD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\nMsQrAADJEK8AACRDvAIAkAzxCgBAMj4Bql2w8THMt9wAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note how different this looks from the \"noisy line\" we plotted earlier.  Power laws are much more sensitive to noise!  In fact, there are some data points that don't even show up on this plot because you can't take the log of a negative number.  Any points where the random noise was negative enough that the curve dropped below zero ended up being \"NAN\", or \"Not a Number\".  Luckily, our plotter knows to ignore those numbers, but `polyfit` doesnt."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print noisy_y"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 2.64567168  1.77226366         nan  1.49412348         nan  1.28855427\n",
        "  0.58257979 -0.50719229  1.84461177  2.72918637         nan -1.02747374\n",
        " -0.65048639  3.4827123   2.60910913  3.48086587  3.84495668  3.90751514\n",
        "  4.10072678  3.76322421  4.06432005  4.23511474  4.26996586  4.25153639\n",
        "  4.4608377   4.5945862   4.66004888  4.8084364   4.81659305  4.97216304\n",
        "  5.05915226  5.02661678  5.05308181  5.26753675  5.23242563  5.36407125\n",
        "  5.41827503  5.486903    5.50263105  5.59005234  5.6588601   5.7546482\n",
        "  5.77382726  5.82299095  5.92653466  5.93264584  5.99879722  6.07711596\n",
        "  6.13466015  6.12248799]\n"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# try to polyfit a line\n",
      "pars = np.polyfit(x,noisy_y,1)\n",
      "print pars"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ nan  nan]\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In order to get around this problem, we need to *mask the data*.  That means we have to tell the code to ignore all the data points where `noisy_y` is `nan`.\n",
      "\n",
      "My favorite way to do this is to take advantage of a curious fact:  $1=1$, but `nan`!=`nan`"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print 1 == 1\n",
      "print np.nan == np.nan"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "True\n",
        "False\n"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So if we find all the places were `noisy_y` != `noisy_y`, we can get rid of them.  Or we can just use the places where `noisy_y` equals itself."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "OK = noisy_y == noisy_y\n",
      "print OK"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ True  True False  True False  True  True  True  True  True False  True\n",
        "  True  True  True  True  True  True  True  True  True  True  True  True\n",
        "  True  True  True  True  True  True  True  True  True  True  True  True\n",
        "  True  True  True  True  True  True  True  True  True  True  True  True\n",
        "  True  True]\n"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This `OK` array is a \"boolean mask\".  We can use it as an \"index array\", which is pretty neat.  "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"There are %i OK values\" % (OK.sum())\n",
      "masked_noisy_y = noisy_y[OK]\n",
      "masked_x = x[OK]\n",
      "print \"masked_noisy_y has length\",len(masked_noisy_y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "There are 47 OK values\n",
        "masked_noisy_y has length 47\n"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# now polyfit again\n",
      "pars = np.polyfit(masked_x,masked_noisy_y,1)\n",
      "print pars"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 1.50239281  1.9907672 ]\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# cool, it worked.  But the fit looks a little weird!\n",
      "fitted_y = polyval(pars,x)\n",
      "pl.plot(x, fitted_y, 'r--')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 32,
       "text": [
        "[<matplotlib.lines.Line2D at 0x10368e1d0>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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lscce47HHHmObbbZh9uzZzJ49m2XLlkVdmhSZDXWrVA7Uq1dhgitAbm4u+fn5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\nIiLV+AsHwBTZNw7+5AAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The noise seems to have affected our fit. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Convert bag to linear-space to see what it \"really\" looks like\n",
      "fitted_z = np.exp(fitted_y)\n",
      "pl.clf()\n",
      "pl.plot(t,z)\n",
      "pl.plot(t,noisy_z,'k.')\n",
      "pl.plot(t,fitted_z,'r--')\n",
      "pl.xlabel('t')\n",
      "pl.ylabel('z')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "<matplotlib.text.Text at 0x10761fb50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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TJc3tdTqd/P67mTb10UeQlma2Kg6A1kwJRN26wfXXww03QM2adldTLgq/IiIi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\nAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That's pretty bad.  A \"least-squares\" approach, as with `curve_fit`, is probably going to be the better choice.  However, in the absence of noise (i.e., on your homework), this approach *should* work"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def powerlaw(x,a,b):\n",
      "    return a*(x**b)\n",
      "pars,covar =  curve_fit(powerlaw,t,noisy_z)\n",
      "pl.clf()\n",
      "pl.plot(t,z)\n",
      "pl.plot(t,noisy_z,'k.')\n",
      "pl.plot(t,powerlaw(t,*pars),'r--')\n",
      "pl.xlabel('t')\n",
      "pl.ylabel('z')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 34,
       "text": [
        "<matplotlib.text.Text at 0x107451e10>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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YfMMNnGnQAAIDOez4luajW+JwwCefmG2/f67oYLPZCA4OBiA4OBibzWZh5VIU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\n"
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Tricks with Arrays\n",
      "==================\n",
      "\n",
      "We need to cover a few syntactic things comparing IDL and python.\n",
      "\n",
      "In IDL, if you wanted the maximum value in an array, you would do:  \n",
      "`maxval = max(array, location_of_max)`\n",
      "\n",
      "\n",
      "In python, it's more straightforward:  \n",
      "`location_of_max = array.argmax()`  \n",
      "or   \n",
      "`location_of_max = np.argmax(array)`  \n",
      "\n",
      "Now, say we want to determine the location of the maximum of a number of different functions.  The functions we'll use are:  \n",
      "`sin(x)`  \n",
      "`sin`$^2$`(x)`  \n",
      "`sin`$^3$`(x)`  \n",
      "`sin(x)cos(x)`  \n",
      "\n",
      "We'll define these functions, then loop over them. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# sin(x) is already defined\n",
      "def sin2x(x):\n",
      "    \"\"\" sin^2 of x \"\"\"\n",
      "    return np.sin(x)**2\n",
      "def sin3x(x):\n",
      "    \"\"\" sin^3 of x \"\"\"\n",
      "    return np.sin(x)**3\n",
      "def sincos(x):\n",
      "    \"\"\" sin(x)*cos(x) \"\"\"\n",
      "    return np.sin(x)*np.cos(x)\n",
      "list_of_functions = [np.sin, sin2x, sin3x, sincos]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# we want 0-2pi for these functions\n",
      "t = np.linspace(0,2*np.pi)\n",
      "# this is the cool part: we can make a variable function\n",
      "for fun in list_of_functions:\n",
      "    # the functions know their own names (in a \"secret hidden variable\" called __name__)\n",
      "    print \"The maximum of \",fun.__name__,\" is \", fun(t).max()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The maximum of  sin  is  0.999486216201\n",
        "The maximum of  sin2x  is  0.998972696375\n",
        "The maximum of  sin3x  is  0.998459440388\n",
        "The maximum of  sincos  is  0.4997431081\n"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# OK, but we wanted the location of the maximum....\n",
      "for fun in list_of_functions:\n",
      "    print \"The location of the maximum of \",fun.__name__,\" is \", fun(t).argmax()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The location of the maximum of  sin  is  12\n",
        "The location of the maximum of  sin2x  is  12\n",
        "The location of the maximum of  sin3x  is  12\n",
        "The location of the maximum of  sincos  is  6\n"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# well, that's not QUITE what we want, but it's close\n",
      "# We want to know the value of t, not the index!\n",
      "for fun in list_of_functions:\n",
      "    print \"The location of the maximum of \",fun.__name__,\" is \", t[fun(t).argmax()]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The location of the maximum of  sin  is  1.5387392589\n",
        "The location of the maximum of  sin2x  is  1.5387392589\n",
        "The location of the maximum of  sin3x  is  1.5387392589\n",
        "The location of the maximum of  sincos  is  0.769369629451\n"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Finally, what if we want to store all that in an array?\n",
      "# Well, here's a cool trick: you can sort of invert the for loop\n",
      "# This is called a \"list comprehension\":\n",
      "maxlocs = [ t[fun(t).argmax()] for fun in list_of_functions ]\n",
      "print maxlocs"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[1.5387392589011231, 1.5387392589011231, 1.5387392589011231, 0.76936962945056153]\n"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Confused?  OK.  Try this one:\n",
      "print range(6)\n",
      "print [ii**2 for ii in range(6)]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[0, 1, 2, 3, 4, 5]\n",
        "[0, 1, 4, 9, 16, 25]\n"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Recursion\n",
      "=========\n",
      "\n",
      "The next big programming topic is called *recursion*.\n",
      "\n",
      "*Recursion*\n",
      "-----------\n",
      "The next little programming topic is called recursion.\n",
      "\n",
      "<img src=\"http://i.qkme.me/35tnta.jpg\">\n",
      "\n",
      "For better or worse, you must visit <a href=\"http://en.wikipedia.org/wiki/Recursion#Recursive_humor\">the wiki page on recursion</a>\n",
      "\n",
      "Recursion is when a function calls itself.  But, a recursive function *must* have an \"end condition\" to avoid an infinite loop.\n",
      "If you try to make an infinite loop, you will get a \"stack overflow\" (python will give you an error)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def fail(x):\n",
      "    \"\"\" an infinite recursion. Will fail \"\"\"\n",
      "    return fail(x)\n",
      "# WARNING: this will definitely fail, but it may take a long time! \n",
      "# print fail(1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 41
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Recursion is a useful mathematical tool.  There are some problems that are best solved via recursion.  The most commonly used example is the fibonacci sequence:  \n",
      "0 1 1 2 3 5 8 13 21 ....  \n",
      "this sequence is defined by the recursive relation  \n",
      "$$F_n = F_{n-1} + F_{n-2}$$  \n",
      "or $$f(n) = f(n-1) + f(n-2)$$\n",
      "\n",
      "It has the base conditions:\n",
      "$$f(0) = 0$$\n",
      "$$f(1) = 1$$\n",
      "\n",
      "This one is pretty easy to define in code.  But I'll leave it as an exercise.\n",
      "\n",
      "The following code shows a hierarchy of what will happen if you call `fibonacci(5)`.  Don't worry about trying to understand the 'digraph' code, it's just a graph visualization tool."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%install_ext https://raw.github.com/tkf/ipython-hierarchymagic/master/hierarchymagic.py"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Installed hierarchymagic.py. To use it, type:\n",
        "  %load_ext hierarchymagic\n"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%load_ext hierarchymagic"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 43
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%dot --format svg -- \n",
      "digraph G { \n",
      "    f5 [label=\"f(5)\"];\n",
      "    Lf1 [label=\"f(1)\"];\n",
      "LLf0 [label=\"f(0)\"];\n",
      "Lf2 [label=\"f(2)\"];\n",
      "Lf3 [label=\"f(3)\"];\n",
      "RRf1  [label=\"f(1)\"];\n",
      "RRMf1 [label=\"f(1)\"];\n",
      "RRf0 [label=\"f(0)\"];\n",
      "LLf1 [label=\"f(1)\"];\n",
      "RMf0 [label=\"f(0)\"];\n",
      "RMf1 [label=\"f(1)\"];\n",
      "Rf2 [label=\"f(2)\"];\n",
      "RMf2 [label=\"f(2)\"];\n",
      "Rf3 [label=\"f(3)\"];\n",
      "Rf4 [label=\"f(4)\"];\n",
      "    f5->Lf3; f5->Rf4;  \n",
      "    Lf3->Lf2; Lf3->Lf1;\n",
      "    Rf4->Rf3; Rf4->Rf2;\n",
      "    Rf2->RRf1; Rf2->RRf0;\n",
      "    Lf2->LLf1; Lf2->LLf0;\n",
      "    Rf3->RMf2; Rf3->RMf1;\n",
      "    RMf2->RMf0; RMf2->RRMf1;\n",
      "}"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# EXERCISE: Write a recursive Fibonacci function!\n",
      "def fibonacci(n):\n",
      "    return\n",
      "    # put your code here!"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# EXERCISE: Write a recursive factorial function\n",
      "# Recall: factorial(x) = factorial(x-1) * x\n",
      "# factorial(1) = 1\n",
      "def factorial(x):\n",
      "    return"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# This is the test for the fibonacci code.  \n",
      "# Run this after you've written your fibonnacci sequence code\n",
      "# it will fail if your code is wrong!\n",
      "for ii,ff in zip(range(9),[0,1,1,2,3,5,8,13,21]):\n",
      "    assert fibonacci(ii) == ff\n",
      "print \"Success!\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "AssertionError",
       "evalue": "",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
        "\u001b[0;32m<ipython-input-47-02b5a0d0ea36>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;31m# it will fail if your code is wrong!\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mii\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mff\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m9\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m13\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m21\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m     \u001b[0;32massert\u001b[0m \u001b[0mfibonacci\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mii\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mff\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      6\u001b[0m \u001b[0;32mprint\u001b[0m \u001b[0;34m\"Success!\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;31mAssertionError\u001b[0m: "
       ]
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# This is the test for the factorial code.  \n",
      "# Run this after you've written your factorial code\n",
      "# it will fail if your code is wrong!\n",
      "for ii,ff in zip(range(1,9),[1,2,6,24,120,720,5040,40320]):\n",
      "    assert factorial(ii) == ff\n",
      "print \"Success!\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}