josePhoenix/downsampling.ipynb

## downsampling.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1],\n",
       "       [2, 3],\n",
       "       [4, 5],\n",
       "       [6, 7],\n",
       "       [8, 9]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(10).reshape((5, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  5,  9, 13, 17])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(10).reshape((5, 2)).sum(-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Define a rebin function\n",
    "\n",
    "Uses NumPy reshaping tricks to sum `factor` adjacent elements, as above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def rebin(a, factor):\n",
    "    sh = a.shape[0] // factor, factor\n",
    "    return a.reshape(sh).sum(-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  5,  9, 13, 17])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rebin(np.arange(10), 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Good, that looks the same."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Define the bin centers\n",
    "\n",
    "When you have $\\left(y_n, x_n\\right)$ and $\\left(y_{n+1}, x_{n+1}\\right)$, and sum adjacent entries (i.e. bin by 2), you get $y'_{n'} = y_n + y_{n+1}$. This is the sum of the values between $x_n$ and $x_{n+1}$, or in other words the value of the histogram for a bin centered at $\\frac{x_n + x_{n+1}}{2}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def bin_centers(x, factor):\n",
    "    sh = x.shape[0] // factor, factor\n",
    "    return x.reshape(sh).mean(-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Evaluate $y = x^2$ at 30 discrete points (samples)\n",
    "\n",
    "The blue line is connected by matplotlib; the blue dots are the actual samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.linspace(-5, 5, 30)\n",
    "y = x ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x11412e978>"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Lf1i2B1nZB+DLgQG1VXnuPO58Zyu+2FOGp6YNwX/fOJRhHoS4sIg6JTLUhPl3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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11412e278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y)\n",
    "plt.scatter(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Downsample naively by dropping every other point (sample)\n",
    "\n",
    "The red points are the odd points (1st, 3rd, etc.) of the `x` and `y` arrays. They still describe the same function ( $y = x^2$ )."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x11373fa20>"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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aHUm4sdUZhxn/zRau7BTBXwd1MDqOqKWGGKFfobXuWZsrsMJYzZr489ZdfTh8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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113ecdb38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y)\n",
    "plt.scatter(x, y)\n",
    "plt.scatter(x[::2], y[::2], c='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compare to the rebinned signal\n",
    "\n",
    "Evidently, the new function differs from the original in more than just sampling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1143f34a8>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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8whLaNIlgZGIcw7rF0qSemrhqAjW5iOOyTxTw0Xd7mJOUzrqMI4QEGS5t15QR\nPeLo36YxYSGVaxoIlJ4z1a3TWsv3B44zb80ePkhOJyM7l3phwVzbJYaRic3pEldf1++sYRTo4lc2\n7zvKnKR05qVkcPB4AWEhteh7biMubhvNgIQmxJfTNzpQxoepap0nCopYtu0gS1KzWJqWxa5DJzAG\n+rduzIgecQw6/5xKfwCKeyjQxS8VFJXwzbYDLE3NYklqJjsOngAgvlGdk+He59xGP+nfHijjw1S0\nTmstWzOPsTQtiyWpWaz8/hAFxSWEhwRxwXmNGJAQzaXtm6rvuAA6KCp+KjS4FpckNCkbDOp8dhw4\nXhZqmcxO2s3MZTsJDa5F71YNubhtNH3ObUTbpvUCZnyYs9WTkZ3LviN5rNmdzdK0LL5KyzoZ/G2a\nRDD2gpZc3LYJPVs1UC8VqbJqBbox5krgWSAIeMVa+6RHqpIaI75xXeIb12XsBfHkFRaz8vtDJwP+\n8U82ARASZAgOMhQW//TbZHX3YD3dLn+2cVdqGejzxJcA1A0Nol/rxky6pDUXtW1MXIM6VV6fyKmq\n3ORijAkC0oDLgXRgFXCTtXbj2f5HTS5SGbsPnWDN7mw27DnKktRMNu/LOe3vBugUV5/L2zelXbNI\nmtUPo0m92jSsG1qhLnzVaZe31nIsv4jMnHyycvLZlnWMjXuO8t8tB9h56MRP6uzVqiFXdTyH82Pr\n0yUuSn30pVK83oZujOkLPGqtHVQ2PQXAWvvE2f5HgS7V8eHqdP76WSr7juYRGRbMudERZJ8oONkO\n/wNjoFHdUKLrhRFdrzbREbWJrlebJvVKf9etHYTB8Ns533HweMFP1tOobih/H9mFohLLwWP5J0M7\nKyefzJw8so6V3s4rLDnt/+qFBdOhWSRhIUF8l55N9olCYuqH8bsr2/nVgVsJPL5oQ48Fdp8ynQ70\nrsb9ifys67rHcV33uJ/MP5ZfRNr+HDKP5p8M26ycvJMhvHV/DlnH8s/YZHMmB48XMP71VafNi6oT\ncvKDoUeLBqUfFD/8RITRslEd4hqEqzuhOMrrB0WNMROBiQAtWrTw9uqkBoqoHUz3Fg1+dhlrLdkn\nCsnMyT/ZxHLbzCSyjuX/ZNnoiNq8PDaRIGNoFBFKo4hQHaiUgFCdQM8Amp8yHVc27zTW2unAdCht\ncqnG+kSqzBhDg7qhNDjlTNWHBrc/Yxv6Q4Pb07V5lBNlilRLdQJ9FdDGGNOK0iD/BTDKI1WJ+MAP\n7dqBcPYvbtTwAAADDElEQVSpSEVUOdCttUXGmLuBBZR2W3zNWrvBY5WJ+MCwbrEKcHGNarWhW2s/\nBT71UC0iIlIN6gwrIuISCnQREZdQoIuIuIQCXUTEJRToIiIuoUAXEXEJn17gwhiTBez02Qo9ozFw\nwOkifEyPuWbQYw4cLa210eUt5NNAD0TGmKSKjHLmJnrMNYMes/uoyUVExCUU6CIiLqFAL990pwtw\ngB5zzaDH7DJqQxcRcQntoYuIuIQCvRKMMb8xxlhjTGOna/E2Y8xUY8xmY8xaY8yHxhjXXvHBGHOl\nMSbVGLPVGPOg0/V4mzGmuTFmsTFmozFmgzHmPqdr8gVjTJAxJsUY87HTtXiLAr2CjDHNgSuAXU7X\n4iMLgY7W2s5AGjDF4Xq8whgTBLwAXAV0AG4yxnRwtiqvKwJ+Y63tAPQBJtWAxwxwH7DJ6SK8SYFe\ncU8DvwNqxEEHa+3n1tqissnllF5i0I16AVuttduttQXAu8BQh2vyKmvtXmvt6rLbOZSGnKuv8mGM\niQMGA684XYs3KdArwBgzFMiw1n7ndC0OuQX4j9NFeEkssPuU6XRcHm6nMsbEA92AFc5W4nXPULpD\nVuJ0Id5UrSsWuYkx5gvgnDP86SHg/yhtbnGVn3vM1tr5Zcs8ROlX9Ld9WZt4nzEmAvgAuN9ae9Tp\nerzFGDMEyLTWJhtjBjhdjzcp0MtYay8703xjTCegFfCdMQZKmx5WG2N6WWv3+bBEjzvbY/6BMWYc\nMAS41Lq3f2sG0PyU6biyea5mjAmhNMzfttbOdboeL+sHXGuMuRoIAyKNMW9Za292uC6PUz/0SjLG\n7AASrbWBOMBPhRljrgT+AVxsrc1yuh5vMcYEU3rQ91JKg3wVMMrNFzw3pXsmM4FD1tr7na7Hl8r2\n0H9rrR3idC3eoDZ0OZvngXrAQmPMGmPMv5wuyBvKDvzeDSyg9ODge24O8zL9gDHAwLLXdk3Z3qsE\nOO2hi4i4hPbQRURcQoEuIuISCnQREZdQoIuIuIQCXUTEJRToIiIuoUAXEXEJBbqIiEv8P44uPZeW\ngol0AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1143f3198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y)\n",
    "plt.scatter(bin_centers(x, 2), rebin(y, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}