{ "cells": [ { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "# Histogramming and Binning Data with Python" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## 1. Histogramming" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "When a measurement is made numerous times, it is often useful to bin (or group) the data\n", "and make a histogram. For example, if the time that it takes a sphere to roll down a ramp\n", "was measured one hundred times, then a histogram of the times would show how they are\n", "distributed. The **`hist`** function from the pylab library is useful for making histograms. The example below makes a histogram from a list of 24 numbers. \n", "You can add labels to the histogram like othe graphs." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 1, "metadata": { "image/png": { "height": 250, "width": 364 } }, "output_type": "execute_result" } ], "source": [ "from pylab import *\n", "t = array([4.94,5.98,5.00,6.06,5.94,5.17,5.12,5.06,\n", " 2.74,2.91,4.24,6.68,4.89,5.88,5.41,5.53,\n", " 3.73,5.80,4.26,5.50,5.73,5.29,7.40,3.55])\n", "figure()\n", "hist(t)\n", "show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "The first line imports the pylab library, which makes the **`hist`** function available.\n", "\n", "As for other plotting commands, the **`figure`** and **`show`** functions are also needed.\n", "\n", "By default, the histogram will have 10 bins. If no additional arguments are sent, the **`hist`** function decides where to put the boundaries of the bins." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "The **`color`** argument can be used to set the color of the bars in the histogram.\n", "Alternatively, the **`edgecolor`** and **`facecolor`** arguments separately set the colors of\n", "the edges and middle of the bars in the histogram, respectively. Some of other color\n", "options are:\n", "
    \n", "r = red
    \n", "g = green
    \n", "b = blue
    \n", "k = black
    \n", "c = cyan
    \n", "m = magenta
    \n", "y = yellow
    \n", "w = white\n", "
\n", "\n", "The default is for the **`edgecolor`** to be the same as the **`facecolor`**. The bins stand out better if the **`edgecolor`** is black. \n", "\n", "The **`facecolor`** argument can also be set to \"None\" so that the bars only have outlines. Alternatively, you can set **`fill`** to False. This is useful if you want to plot data on top of the histograms as shown further below." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 2, "metadata": { "image/png": { "height": 250, "width": 364 } }, "output_type": "execute_result" } ], "source": [ "from pylab import *\n", "t = array([4.94,5.98,5.00,6.06,5.94,5.17,5.12,5.06,\n", " 2.74,2.91,4.24,6.68,4.89,5.88,5.41,5.53,\n", " 3.73,5.80,4.26,5.50,5.73,5.29,7.40,3.55])\n", "figure()\n", "hist(t, facecolor='b', edgecolor='k')\n", "show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "The **`hist`** function returns the number of events in each bin, the edges of the bins, and\n", "things called patches (which will not be discussed further). These values can be captured\n", "by providing three variable names for them as follows." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 2. 1. 1. 2. 4. 6. 5. 1. 1. 1.]\n", "[ 2.74 3.206 3.672 4.138 4.604 5.07 5.536 6.002 6.468 6.934 7.4 ]\n" ] }, { "data": { "image/png": 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" }, "execution_count": 3, "metadata": { "image/png": { "height": 250, "width": 364 } }, "output_type": "execute_result" } ], "source": [ "from pylab import *\n", "t = array([4.94,5.98,5.00,6.06,5.94,5.17,5.12,5.06,\n", " 2.74,2.91,4.24,6.68,4.89,5.88,5.41,5.53,\n", " 3.73,5.80,4.26,5.50,5.73,5.29,7.40,3.55])\n", "figure()\n", "events, edges, patches = hist(t, edgecolor='k')\n", "print(events)\n", "print(edges)\n", "show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "The array `events` contains the numbers of occurences in the 10 bins. The array `edges`\n", "contain 11 elements. (The first 10 elements are the lower edges of the bins and the final element is the upper edge of the final bin.) The bins are the same width, but the edges may end up in unusual places. A number is included in a bin if it is greater than or equal to its lower edge and less than its upper edge." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "If you set the **`density`** argument to “True”, the function will make an area-normalized\n", "histogram. For each bin, the height on the histogram is the probability density, which is\n", "the number of events in the bin divided by the total number of events and the width of the\n", "bin. The area of each bin in the histogram is the probability of an event being in that bin,\n", "so the total area is one. With this option, the probability density is returned instead of the\n", "number of events. Compare the example below with the previous example." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0.1788269 0.08941345 0.08941345 0.1788269 0.35765379 0.53648069\n", " 0.44706724 0.08941345 0.08941345 0.08941345]\n", "[ 2.74 3.206 3.672 4.138 4.604 5.07 5.536 6.002 6.468 6.934 7.4 ]\n" ] }, { "data": { "image/png": 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o2WK9qo6tqquq6s6qur+q9lbVFVV19AZfv6uqfrSq/ltV3VxV91XVvVX1R1X10qr6mrlmBQCA7eCwOTapqhOTXJ/kmCTvTnJzkjOSvDjJ+VV1dnffdYBtvjfJ25PcneS6JL+R5DFJnp7k55M8q6rO7e7PzzEzAACMbpZYT/LGLEL9ou5+/cqDVfXaJC9JclmSFxxgj08l+bEk7+ruL6za44gkv5/ku5O8KMlrZpoZAACGtunLYKrqhCTnJdmb5A1rDl+S5L4kF1TVrgfbp7s/2t3/dXWoT4/fm78P9Cdtdl4AANgu5rhm/Zxpvba7H1h9YArtDyV5ZJKzNvEefzetX9zEHgAAsK3McRnMKdN66zrHP57FmfeTk7z/IN/jJ6b1fRt5clXduM6h3Qf5/gAAsOXmOLN+1LTes87xlccffTCbV9VPJTk/yUeTXHUwewAAwHY01wdMH0xNaz/kF1Y9K8kVWXz49J92998d4CWLN+o+fZ39bkxy2kOdAwAAlmGOM+srZ86PWuf4kWuetyFV9cwk70jymSRP6u5PHNx4AACwPc0R67dM68nrHD9pWte7pv0rVNWzk7wryaeTfF9333KAlwAAwCFnjli/blrPq6ov22+6R/rZSfYluWEjm1XVjyT570nuzCLUPz7DjAAAsO1sOta7+7Yk1yY5PosvLVrt0iS7klzT3fetPFhVu6vqK+7MUlU/nuRtSf48yRNd+gIAwE421wdMX5jk+iRXVtW5SfYkOTPJk7O4/OXiNc/fM60rHz5NVT05i7u9PCKLs/UXVtWal+Wz3X3FTDMDAMDQZon17r6tqh6f5GeyuM3iU5J8MsmVSS7t7rs3sM1x+fsz/T+xznNuz+LuMAAAcMib7daN3X1Hkgs3+NyvOGXe3VcnuXqueQAAYLub4wOmAADAw0CsAwDAoMQ6AAAMSqwDAMCgxDoAAAxKrAMAwKDEOgAADGq2+6zz4Pbzbaw7RncvewQeJjv55xoAtoIz6wAAMChn1rfYcS9/z7JH2DK3X/60ZY/AFvFzDQAPD2fWAQBgUGIdAAAGJdYBAGBQYh0AAAYl1gEAYFBiHQAABiXWAQBgUGIdAAAGJdYBAGBQYh0AAAYl1gEAYFBiHQAABiXWAQBgUGIdAAAGJdYBAGBQYh0AAAYl1gEAYFBiHQAABiXWAQBgUGIdAAAGJdYBAGBQYh0AAAYl1gEAYFBiHQAABiXWAQBgUGIdAAAGJdYBAGBQYh0AAAYl1gEAYFBiHQAABiXWAQBgUGIdAAAGJdYBAGBQYh0AAAYl1gEAYFBiHQAABiXWAQBgUGIdAAAGJdYBAGBQYh0AAAYl1gEAYFBiHQAABiXWAQBgUGIdAAAGJdYBAGBQYh0AAAYl1gEAYFBiHQAABiXWAQBgUGIdAAAGJdYBAGBQYh0AAAY1W6xX1bFVdVVV3VlV91fV3qq6oqqOfgh7/EBVvaaq3l9Vd1dVV9UfzDUjAABsJ4fNsUlVnZjk+iTHJHl3kpuTnJHkxUnOr6qzu/uuDWz1oiTPSPL5JH+aZMOhDwAAh5q5zqy/MYtQv6i7n9ndr+juc5K8LskpSS7b4D6XJ3lckkclefpMswEAwLa06VivqhOSnJdkb5I3rDl8SZL7klxQVbsOtFd3f7i7/6S7v7TZuQAAYLub48z6OdN6bXc/sPpAd9+b5ENJHpnkrBneCwAAdow5rlk/ZVpvXef4x7M4835ykvfP8H4HVFU3rnNo91a8PwAAzGGOM+tHTes96xxfefzRM7wXAADsGLPcDeYAalp7C95r8Ubdp+93kMUZ99O2ag4AANiMOc6sr5w5P2qd40eueR4AALABc8T6LdN68jrHT5rW9a5pBwAA9mOOWL9uWs+rqi/br6qOSHJ2kn1JbpjhvQAAYMfYdKx3921Jrk1yfBbfQLrapUl2Jbmmu+9bebCqdleVO7MAAMCDmOsDpi9Mcn2SK6vq3CR7kpyZ5MlZXP5y8Zrn75nWWv1gVX1PkudOv3zUtJ5UVVevPKe7nzPTzAAAMLRZYr27b6uqxyf5mSTnJ3lKkk8muTLJpd199wa3+uYkP77msWPWPPaczU0LAADbw2y3buzuO5JcuMHn1jqPX53k6rlmYgxV+/2fG4AB+T2bQ1X3lt1FfFZzfMAUAAB4GGzFlyKxwx338vcse4Qtc/vlT0uyc/6eV/5+gUPHTvn9K9l5v2cnO/vvebtyZh0AAAYl1gEAYFBiHQAABiXWAQBgUGIdAAAGJdYBAGBQYh0AAAYl1gEAYFBiHQAABiXWAQBgUGIdAAAGJdYBAGBQYh0AAAYl1gEAYFBiHQAABiXWAQBgUGIdAAAGJdYBAGBQYh0AAAYl1gEAYFBiHQAABiXWAQBgUGIdAAAGJdYBAGBQYh0AAAYl1gEAYFBiHQAABiXWAQBgUGIdAAAGJdYBAGBQYh0AAAYl1gEAYFBiHQAABiXWAQBgUGIdAAAGJdYBAGBQYh0AAAYl1gEAYFBiHQAABiXWAQBgUGIdAAAGJdYBAGBQYh0AAAYl1gEAYFBiHQAABiXWAQBgUGIdAAAGJdYBAGBQYh0AAAYl1gEAYFBiHQAABiXWAQBgUGIdAAAGJdYBAGBQYh0AAAYl1gEAYFBiHQAABiXWAQBgUGIdAAAGJdYBAGBQs8V6VR1bVVdV1Z1VdX9V7a2qK6rq6Ie4z2Om1+2d9rlz2vfYuWYFAIDt4LA5NqmqE5Ncn+SYJO9OcnOSM5K8OMn5VXV2d9+1gX0eO+1zcpLfS/KOJLuTXJjkqVX1hO7+xBwzAwDA6OY6s/7GLEL9ou5+Zne/orvPSfK6JKckuWyD+/ynLEL9dd197rTPM7OI/mOm9wEAgB1h07FeVSckOS/J3iRvWHP4kiT3JbmgqnYdYJ9dSS6Ynn/JmsO/OO3/g9P7AQDAIW+OM+vnTOu13f3A6gPdfW+SDyV5ZJKzDrDPE5IcnuRD0+tW7/NAkmunXz550xMDAMA2MEesnzKtt65z/OPTevIW7QMAAIeE6u7NbVD15iTPS/K87n7Lfo5fluSVSV7Z3T/7IPu8Motr2y/r7lft5/jzkrw5yZu7+/kHmOnGdQ59++GHH/5Vp5566oO9/GFx0003bfl7AgCwcNppp23p++3Zsyf79u27u7sfu5l9ZrkbzAHUtG7u3wrm2edL+/btu+emm27au8lZtrPd03rzUqdg2fwcsMLPAiv8LJAcwj8HSzhxenySv9nsJnPE+j3TetQ6x49c87yHe5909+kHes5OtfKnDv472tn8HLDCzwIr/CyQ+DkY0RzXrN8yretdS37StK53Lfrc+wAAwCFhjli/blrPq6ov26+qjkhydpJ9SW44wD43TM87e3rd6n0ekcXtIVe/HwAAHNI2HevdfVsWt1U8PsmL1hy+NMmuJNd0930rD1bV7qravfqJ3f25JG+bnv/qNfv81LT/b/sGUwAAdoq5PmD6wiTXJ7myqs5NsifJmVncE/3WJBevef6eaa01j78yyZOS/HRVfUeSP0xyapJnJPlMvvJfBgAA4JA1x2UwK2fXH5/k6iwi/aVJTkxyZZIndPddG9znriy+HOnKJN887XNmkrcmOX16HwAA2BE2fZ91AADg4THLmXUAAGB+Yh0AAAYl1gEAYFBiHQAABiXWAQBgUGIdAAAGJdYBAGBQYn0HqKrLq+r9VXVHVe2rqrur6iNVdUlVPXbZ87E8VXVBVfX013OXPQ9bo6r2rvrffe1fn1r2fGy9qvreqvofVfXJqrp/Wq+tqqcsezYeflX1nAf5PWHlry8te86d6rBlD8CWeEmSm5L8TpLPJNmV5Kwkr07yk1V1VnffsbzxWIaq+idJXp/kc0keteRx2Hr3JLliP49/bqsHYbmq6lVJ/kOSv0ryniSfTPJ1Sb4zyZOS/NbShmOrfDTJpesc+94k5yR579aNw2pifWc4srs/v/bBqrosySuT/NskL9zyqViaqqokb01yV5JfT/Ky5U7EEny2u1+97CFYrqp6dhah/rtJntXd9645/tVLGYwt1d0fzSLYv0JVfXj6j2/euolYzWUwO8D+Qn3yzmk9aatmYRgXZXGm5MIk9y15FmAJquoRSS5P8rdJfmRtqCdJd//dlg/GMKrqcVn8Sfz/S/KbSx5nx3JmfWd7+rT+8VKnYEtV1alJfi7JL3T3B6vqnGXPxFL8g6r6sSTfmMW/sP1xkg92t+tSd47vTvJNSX4tyV9X1VOTPC7J55P8YXd/+MFezI7w/Gn9Zb83LI9Y30Gq6mVZXJt8VJLHJ/meLP4B/XPLnIutU1WHJXlbkj/P4hIodq6vz+JnYbU/q6oLu/sDyxiILfdd0/rpLD7X9G2rD1bVB5P8s+7+y60ejOWrqsOT/FiSB5K8Zcnj7Ggug9lZXpbkkiT/KotQf1+S8/xGvKP8+yw+NPac7t637GFYmrcmOTeLYN+VRaS9KcnxSd5bVd++vNHYQsdM6wuSHJ7k+5MckcXZ9d9O8sQk71rOaAzgnyd5dJL3ugnFcon1HaS7v767K4t/QD8ryQlJPlJVpy13MrZCVZ2Rxdn01/jj7Z2tuy/t7t/r7k9399929//p7hckeW0W0fbq5U7IFvmqaa0szqC/v7s/191/kuSHkvxFku+rqicsbUKW6Sen9U1LnQKxvhNN/4D+n0nOS/LYJNcseSQeZqsuf7k1yb9b8jiM679M6xOXOgVb5a+n9RPd/b9XH5j+5O23p1+esaVTsXRV9S1ZfKbhL+LWnUsn1new7r49yf9N8q1V9XXLnoeH1aOSnJzk1CSfX/1FF1lcGpUkvzQ9tr97b7MzfGZady11CrbKLdP62XWOr8T84VswC2PxwdKB+IAp/3ha/Z/x0HZ/kl9e59hpWVzH/gdZ/MPbJTI718rlDp9Y6hRslQ8m+WKSk6rqa7r7C2uOP25a927pVCxVVX1tkguy+GDpev/cYAuJ9UNcVe3O4stPPrXm8Udk8UUYxyS5vrv/en+v59Aw/ZH2c/d3rKpenUWs/0p3+8T/Ia6qvjXJJ7v77jWPH5fkF6dfvn3LB2PLdfdfVdWvJvnRLD58/qqVY1X1A0l+MItvun3fciZkSZ6d5Ogk7/HB0jGI9UPf+Un+83QLrtuy+MbKf5Tk+7L4gOmnkjxveeMBW+zZSV5RVdcl+bMk9yY5MclTk3xtFten/vzyxmOL/XSSM5NcXFVPTPKHSY7L4gOmX0ryvO5e7zIZDk0rHyz1jaWDEOuHvt/N4v9wZyf59ixuw3RfFh80fFuSK9eeYQMOadclOSWLP015QhbXp382i8ug3pbkbd3dyxuPrdTdn6mqM7M4q/5DWXxb5b1ZfFvlz3b3Dcucj601fWne98QHS4dSfk8GAIAxuRsMAAAMSqwDAMCgxDoAAAxKrAMAwKDEOgAADEqsAwDAoMQ6AAAMSqwDAMCgxDoAAAxKrAMAwKDEOgAADEqsAwDAoMQ6AAAMSqwDAMCgxDoAAAxKrAMAwKDEOgAADOr/A7yTkKyJd9w5AAAAAElFTkSuQmCC" }, "execution_count": 4, "metadata": { "image/png": { "height": 250, "width": 373 } }, "output_type": "execute_result" } ], "source": [ "from pylab import *\n", "t = array([4.94,5.98,5.00,6.06,5.94,5.17,5.12,5.06,\n", " 2.74,2.91,4.24,6.68,4.89,5.88,5.41,5.53,\n", " 3.73,5.80,4.26,5.50,5.73,5.29,7.40,3.55])\n", "figure()\n", "events, edges, patches = hist(t, density=True, edgecolor='k')\n", "print(events)\n", "print(edges)\n", "show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "You can control the number of bins by setting the **`bins`** argument to an integer, but this doesn’t control the locations of the edges. Choosing an appropriate number of bins is important. If there are too few or too many bins, the histogram won’t show how the events are distributed very well. For example, the same example data is histogrammed below with 3 and 30 bins." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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A0G1d43OfluQxSZ44xth2Vx6gqjYtcejguzwVAABMrOVMeVUdltnZ8beOMS7umAEAAFaKyc+UL9i2cmmSN9ydxxpjbFjiOTYlOfTuPDYAAEyl40z5/ZIclGR9klsWvGHQSPLG+X3ePb/t7Q3zAQDApDr2lN+a5L1LHDs0s33mn0vy9SS2tgAAsOpNHuXzizpP2tGxqtqYWZT/6RjjPVPOBQAAXVbCmwcBAMCaJsoBAKDZioryMcbGMUbZugIAwFqyoqIcAADWIlEOAADNRDkAADQT5QAA0EyUAwBAM1EOAADNRDkAADQT5QAA0EyUAwBAM1EOAADNRDkAADQT5QAA0EyUAwBAM1EOAADNRDkAADQT5QAA0EyUAwBAM1EOAADNRDkAADQT5QAA0EyUAwBAM1EOAADNRDkAADQT5QAA0EyUAwBAM1EOAADNRDkAADQT5QAA0EyUAwBAM1EOAADNRDkAADQT5QAA0EyUAwBAM1EOAADNRDkAADQT5QAA0EyUAwBAM1EOAADNRDkAADQT5QAA0EyUAwBAM1EOAADNRDkAADQT5QAA0EyUAwBAM1EOAADNRDkAADQT5QAA0EyUAwBAM1EOAADNRDkAADQT5QAA0EyUAwBAM1EOAADNWqK8qh5UVSdV1Ueq6ptVta2qrq+qz1XVi6vKfywAALBmrGt63hOS/FGSK5NcmOTbSX42yXOTvCfJL1fVCWOM0TQfAABMpivKL01yXJKPjjF+vP3GqnpdkkuS/Gpmgf7hnvEAAGA6LdtExhgXjDH+18Ign9/+vSTvmn969OSDAQBAg5W4d/u2+Xp76xQAADCRFRXlVbUuyb+df3pe5ywAADCVrj3lS3lLkkOSnDvG+Pid3bmqNi1x6OBlnQoAAO5BK+ZMeVWdnOTVSb6W5MTmcQAAYDIr4kx5Vb08yTuSfDXJU8YY1+7K140xNizxeJuSHLp8EwIAwD2n/Ux5Vb0iyR8m+dskT56/AgsAAKwZrVFeVa9J8rYkX84syK/qnAcAADq0RXlVvSGzCzs3ZbZl5equWQAAoFPLnvKqemGS305yR5LPJjm5qhbfbesY48yJRwMAgMl1Xei5/3zdI8krlrjPZ5KcOck0AADQqGX7yhhj4xij7uTj6I7ZAABgau2vvgIAAGudKAcAgGaiHAAAmolyAABoJsoBAKCZKAcAgGaiHAAAmolyAABoJsoBAKCZKAcAgGaiHAAAmolyAABoJsoBAKCZKAcAgGaiHAAAmolyAABoJsoBAKCZKAcAgGaiHAAAmolyAABoJsoBAKCZKAcAgGaiHAAAmolyAABoJsoBAKCZKAcAgGaiHAAAmolyAABoJsoBAKCZKAcAgGaiHAAAmolyAABoJsoBAKCZKAcAgGaiHAAAmolyAABoJsoBAKCZKAcAgGaiHAAAmolyAABoJsoBAKCZKAcAgGaiHAAAmolyAABoJsoBAKCZKAcAgGaiHAAAmolyAABoJsoBAKCZKAcAgGaiHAAAmolyAABoJsoBAKCZKAcAgGatUV5V/6yq/qSq/k9V3VpVW6vq7VX1051zAQDAlNZ1PXFVPTzJF5I8JMlfJflaksOS/GaSp1fVEWOMa7rmAwCAqXSeKf8vmQX5yWOMZ48xXjvGOCbJ25I8IsnvNM4GAACTaYnyqjogydOSbE3ynxcdfmOSHyY5sar2nng0AACYXNeZ8mPm6/ljjB8vPDDGuDHJ55PcN8njpx4MAACm1hXlj5ivly5x/Bvz9aAJZgEAgFZdF3ruO1+vX+L49tsfsLMHqapNSxx61JYtW7Jhw4a7Mtvddvnpz2x5Xtjd+LsCu8bfFdg1He23ZcuWJHnY3X2ctldfuRM1X8dd/Po7tm3bdv3mzZu3LtM8u5uD5+vXWqdgJfC9wHa+F0h8H/CPVuX3wubNmzue9mFJbri7D9IV5dvPhO+7xPF9Ft1vh8YYPafCV7jtv0Hwvw++F9jO9wKJ7wP+ke+FladrT/nX5+tSe8YPnK9L7TkHAIBVoyvKL5yvT6uq/2eGqrp/kiOSbEvyxakHAwCAqbVE+Rjj75Ocn9kenJcvOvymJHsnef8Y44cTjwYAAJPrvNDzN5J8IckZVfWUJFuSPC7JkzPbtvL6xtkAAGAyXdtXtp8tf2ySMzOL8VcneXiSM5IcPsa4pms2AACYUo1xV191EAAAWA5tZ8oBAIAZUQ4AAM1EOQAANBPlAADQTJQDAEAzUQ4AAM1EOQAANBPlq0hVnV5Vn6qq71TVtqq6tqq+VFVvrKoHdc9Hn6o6sarG/OOk7nmYRlVtXfD/++KP73XPx7Sq6klV9eGqurKqbp2v51fVsd2zcc+rql/byb8H2z/u6J5zLVvXPQDL6pVJNif5RJKrkuyd5PFJNiZ5aVU9fozxnb7x6FBVP5fknUluSnK/5nGY3vVJ3r6D22+aehD6VNWpSd6c5Ook5yS5MsmDkzwmydFJzm0bjql8Ocmbljj2pCTHJPnYdOOwmChfXfYZY9yy+Maq+p0kr0vyH5L8xuRT0aaqKsn7klyT5H8kOaV3Ihr8YIyxsXsI+lTVCZkF+SeTPHeMceOi4z/VMhiTGmN8ObMw//9U1cXzP/7X6SZiMdtXVpEdBfncX8zXA6eahRXj5MzOfrwoyQ+bZwEmVlX3SnJ6kpuTPH9xkCfJGOO2yQdjxaiqQzL7rfp3k3y0eZw1zZnyteFX5utXWqdgUlW1PslbkrxjjHFRVR3TPRMt9qyqFyT555n9h9lXklw0xrB3dG14QpL9k5yd5LqqekaSQ5LckuSSMcbFO/ti1oRfn6/v9e9CL1G+ClXVKZntHd43yWOTPDGzH8Rv6ZyL6VTVuiRnJfl2ZluXWLsemtn3wkLfqqoXjTE+0zEQk/qF+fr9zK45+vmFB6vqoiTHjzH+YerB6FdVeyV5QZIfJ3lP8zhrnu0rq9MpSd6Y5BWZBfl5SZ7mH9015bTMLuD6tTHGtu5haPO+JE/JLMz3zizI/jjJw5J8rKoe1TcaE3nIfH1Zkr2SPDXJ/TM7W/7xJEcm+VDPaKwA/yrJA5J8zAtB9BPlq9AY46FjjMrsB/FzkxyQ5EtVdWjvZEyhqg7L7Oz4W/1qem0bY7xpjHHBGOP7Y4ybxxh/O8Z4WZI/yCzQNvZOyAT2mK+V2RnxT40xbhpj/F2S5yS5IslRVXV424R0eul8/ePWKUgiyle1+Q/ijyR5WpIHJXl/80jcwxZsW7k0yRuax2Hletd8PbJ1CqZw3Xy9bIzxNwsPzH+L9vH5p4dNOhXtqupfZHbNwRXxkpgrgihfA8YYlyf5apJHVtWDu+fhHnW/JAclWZ/kloVvCpHZlqYkeff8th29djVrw1Xzde/WKZjC1+frD5Y4vj3a95pgFlYWF3iuMC70XDv+yXz1F291uzXJe5c4dmhm+8w/l9kPaltb1q7tWxUua52CKVyU5PYkB1bVvccYP1p0/JD5unXSqWhVVfdJcmJmF3gu9TODiYnyVaKqDs7sTUK+t+j2e2X2phEPSfKFMcZ1O/p6Vof5r6NP2tGxqtqYWZT/6RjDVfarXFU9MsmVY4xrF92+X5I/nH/6gckHY1JjjKur6oNJ/k1mF4Cfuv1YVf1ikl/K7F1fz+uZkCYnJPnpJOe4wHPlEOWrx9OT/N785a3+PrN3cPzZJEdldqHn95K8pG88YGInJHltVV2Y5FtJbkzy8CTPSHKfzPaQ/n7feEzoVUkel+T1VXVkkkuS7JfZhZ53JHnJGGOp7S2sTtsv8PQOniuIKF89PpnZX64jkjwqs5c4+mFmF/ydleSMxWfMgFXtwiSPyOy3I4dntn/8B5ltXzoryVljjNE3HlMZY1xVVY/L7Cz5czJ798YbM3v3xt8dY3yxcz6mNX9juSfGBZ4rTvk3GQAAenn1FQAAaCbKAQCgmSgHAIBmohwAAJqJcgAAaCbKAQCgmSgHAIBmohwAAJqJcgAAaCbKAQCgmSgHAIBmohwAAJqJcgAAaCbKAQCgmSgHAIBmohwAAJqJcgAAaPZ/ATJKr5rGZYEWAAAAAElFTkSuQmCC" }, "execution_count": 5, "metadata": { "image/png": { "height": 250, "width": 370 } }, "output_type": "execute_result" }, { "data": { "image/png": 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" }, "execution_count": 5, "metadata": { "image/png": { "height": 250, "width": 373 } }, "output_type": "execute_result" } ], "source": [ "from pylab import *\n", "t = array([4.94,5.98,5.00,6.06,5.94,5.17,5.12,5.06,\n", " 2.74,2.91,4.24,6.68,4.89,5.88,5.41,5.53,\n", " 3.73,5.80,4.26,5.50,5.73,5.29,7.40,3.55])\n", "figure()\n", "hist(t, bins=3, edgecolor='k')\n", "\n", "figure()\n", "hist(t, bins=30, edgecolor='k')\n", "\n", "show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "If you want to have control over the number and location of the bins, you can make the\n", "**`bins`** argument an array. If you want *N* bins, the array will have (*N* + 1) elements. The\n", "first *N* elements are the lower edges of the bins and the final element is the upper edge of\n", "the final bin. Usually the bins have equal widths, but they can be made unequal. The array can be made with the **`linspace`** function from the scipy library, which will need to be imported.\n", "You must specify the first element of the array (the lower edge of the first bin), the last\n", "element of the array (the upper edge of the final bin), and the number of elements in the\n", "array (one more than the number of bins). The example below would produce2 10 bins\n", "(not 11) starting at 0 and ending at 10. For the example data, some of the bins are\n", "empty and aren't displayed." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 6, "metadata": { "image/png": { "height": 250, "width": 370 } }, "output_type": "execute_result" } ], "source": [ "from pylab import *\n", "from scipy import *\n", "t = array([4.94,5.98,5.00,6.06,5.94,5.17,5.12,5.06,\n", " 2.74,2.91,4.24,6.68,4.89,5.88,5.41,5.53,\n", " 3.73,5.80,4.26,5.50,5.73,5.29,7.40,3.55])\n", "bins = linspace(0, 10, 11)\n", "figure()\n", "hist(t, bins, edgecolor='k')\n", "show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "It is also possible to set the upper and lower limits of the bins using the **`range`** argument.\n", "Values outside of the specified range are ignored. The following example does the same\n", "as the previous example because the default number of bins is 10." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.]\n" ] }, { "data": { "image/png": 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" }, "execution_count": 7, "metadata": { "image/png": { "height": 250, "width": 370 } }, "output_type": "execute_result" } ], "source": [ "from pylab import *\n", "t = array([4.94,5.98,5.00,6.06,5.94,5.17,5.12,5.06,\n", " 2.74,2.91,4.24,6.68,4.89,5.88,5.41,5.53,\n", " 3.73,5.80,4.26,5.50,5.73,5.29,7.40,3.55])\n", "figure()\n", "events, edges, patches = hist(t, range=(0.0,10.0), edgecolor='k')\n", "print(edges)\n", "show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Note that in all of the examples above the center of each bin is placed midway between the edges, which define what values are counted in that bin. If the values being histogrammed are all integers, it makes more sense for the to shift the bins to the left so that they are centered over integers. Setting **`align`** to \"left\" will put the center of the bin over the left edge, which will center them over integers." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 8, "metadata": { "image/png": { "height": 250, "width": 375 } }, "output_type": "execute_result" } ], "source": [ "from pylab import *\n", "N = array([4,5,5,6,5,5,5,5,2,2,4,6,4,5,5,5,3,5,4,5,5,5,7,3])\n", "\n", "figure()\n", "hist(t, range=(0.0,10.0), edgecolor='b',align='left')\n", "show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "If the bins aren't filled, you can graph points (using **`scatter`**) or curves (using **`plot`**) on the same figure. If the bins are filled, they can hide the points or curves." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 9, "metadata": { "image/png": { "height": 250, "width": 375 } }, "output_type": "execute_result" } ], "source": [ "from pylab import *\n", "N = array([4,5,5,6,5,5,5,5,2,2,4,6,4,5,5,5,3,5,4,5,5,5,7,3])\n", "bins = linspace(0, 10, 11)\n", "\n", "x = array([2,3,4,5,6,7])\n", "y = array([1,2,3,12,3,2])\n", "\n", "figure()\n", "hist(t, bins, edgecolor='b', fill=False,align='left')\n", "scatter(x,y,c='g')\n", "show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## 2. Binning Data" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Sometimes data is binned before it is analyzed. For example, a set of decay times could\n", "be binned before fitting the data to an exponential function. The **`histogram`** function\n", "from the numpy library can be used to bin data without making a plot. The **`histogram`** function is similar to the **`hist`** function described in the previous section. The **`range`** and **`bins`** arguments can be used, but it doesn’t return patches. Associating the locations of the bins and the numbers of events in them is a little tricky\n", "because the `edges` array is one element longer than the `events` array. \n", "\n", "If your counting the occurences of integers, the lower edges are the appropriate thing to use. In the example below, the **`resize`** function makes an array called\n", "`lower` which has a length one less than the length of the `edges` array, so it just contains the lower edges." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9.]\n", "[ 0 0 2 2 4 13 2 1 0 0]\n" ] } ], "source": [ "from numpy import *\n", "N = array([4,5,5,6,5,5,5,5,2,2,4,6,4,5,5,5,3,5,4,5,5,5,7,3])\n", "\n", "events, edges = histogram(t,range=(0.0,10.0))\n", "lower = resize(edges, len(edges)-1)\n", "\n", "print(lower)\n", "print(events)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "For non-integer data, it makes more sense to associate the number of events with the center of bin. For example, the number\n", "of event wiht values of `t` between 0 and 1 should be associated with 0.5. The example\n", "below will make an array called `tmid` which is the same length as `events` and contains\n", "the values of `t` in the middle of the bins. Again, the **`resize`** function makes an array called\n", "`lower` which contains the locations of the lower edges of the bins because the final element is dropped.\n", "An array containing the difference between consecutive elements of the `edges` array is returned by the function **`diff`**. \n", "Adding half of the difference between the edges to the\n", "lower edge gives the value in the middle of a bin. Note that \"`diff(edges)`\" is the same\n", "length as `lower`. " ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5]\n", "[ 0 0 2 2 4 13 2 1 0 0]\n" ] } ], "source": [ "from numpy import *\n", "t = array([4.94,5.98,5.00,6.06,5.94,5.17,5.12,5.06,\n", " 2.74,2.91,4.24,6.68,4.89,5.88,5.41,5.53,\n", " 3.73,5.80,4.26,5.50,5.73,5.29,7.40,3.55])\n", "\n", "events, edges = histogram(t,range=(0.0,10.0))\n", "lower = resize(edges, len(edges)-1)\n", "tmid = lower + 0.5*diff(edges)\n", "\n", "print(tmid)\n", "print(events)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## Additional Documentation" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Further information is available at: \n", "http://matplotlib.sourceforge.net/api/pyplot_api.html#matplotlib.pyplot.hist \n", "http://docs.scipy.org/doc/numpy/reference/generated/numpy.histogram.html" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2 (SageMath)", "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": "2.7.15" } }, "nbformat": 4, "nbformat_minor": 0 }