{ "metadata": { "name": "", "signature": "sha256:7d3d5b572e957b3871f1009aa0bac0692e201bb02ef5d6e49f7bcc8ffc6c2a17" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Smoothing and Binning Data\n", "\n", "By James Keaveney (<james.keaveney@durham.ac.uk>)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "_In this tutorial, we show two commonly used data processing techniques. The first is a moving-average smoothing routine, and the second is a data-binning routine. We then give an example script to show the differences between the two._" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's set up the python environments and import everything we'll need later on:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "from IPython.display import display\n", "\n", "from numpy import array,append,arange,zeros,exp,sin,random,std\n", "from pylab import plot,show,figure,clf" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Moving-average smoothing" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We first define our moving average smoothing. It is based on a triangular weighting function of a specified width. For convenience, the output array is the same length as the input, but the smoothing is only applied over *N - 2n* data points (removing *n* from each end of the array), where *N* is the length of the data array and *n* is the width of the smoothing window." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def smooth_triangle(data,npts):\n", " \"\"\" performs moving average smoothing with a triangular weighting. \n", " Effective length of smoothed array is shorter by 'npts' points. \n", " Inputs data: 1D array or list\n", " Outputs: smoothed: 1D array\n", " \"\"\"\n", " \n", " # if not an array already, make it an array\n", " data = array(data)\n", " \n", " # define triangular weighting - twice the length of npts\n", " # [::-1] means reverse order\n", " triangle = array(range(npts) + [npts] + range(npts)[::-1]) + 1\n", "\n", " smoothed=[]\n", " for i in range(0,len(data)-len(triangle)):\n", " point=data[i:i+len(triangle)]*triangle\n", " smoothed.append(sum(point)/sum(triangle))\n", "\n", " j = len(data)-len(smoothed)\n", " # add half of j (rounded) data points back on to the smoothed array at either end\n", " # slightly different for odd and even array length\n", " if j%2==1:\n", " for i in range(0,(j-1)/2):\n", " smoothed.append(data[-1-(j-1)/2+i])\n", " smoothed.insert(0,data[(j-1)/2-i])\n", " smoothed.append(data[-1])\n", " else:\n", " for i in range(0,j/2):\n", " smoothed.append(data[-1-i])\n", " smoothed.insert(0,data[i])\n", "\n", " return array(smoothed)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Data binning" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Binning data is useful where the initial data size is very large. The output from this function is smaller by a specified factor *n*, which also removes some noise since every *n* data points are averaged into one." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def bin_data(x,y,blength):\n", " \"\"\" Takes 2 arrays x and y and bins them into groups of blength.\n", " blength must be odd, if not it's made odd. \n", " Inputs: x, y: 1D lists or numpy arrays\n", " Outputs:\txout, yout, yerrout: 1D numpy arrays\n", " \"\"\"\n", "\n", " # convert to arrays if necessary\n", " x = array(x)\n", " y = array(y)\n", "\n", " # check oddness\n", " if blength % 2 == 0: \n", " blength += 1\n", "\n", " nobins = len(x)/blength\n", " xmid = (blength-1)/2\n", " xbinmax = nobins*blength - xmid\n", " xout,yout,yerrout = [],[],[]\n", " for i in range(int(xmid),int(xbinmax),int(blength)):\n", " xmin = i-int(xmid)\n", " xmax = i+int(xmid)\n", " xout.append(sum(x[xmin:xmax+1])/blength)\n", " yout.append(sum(y[xmin:xmax+1])/blength)\n", " yerrout.append(std(y[xmin:xmax+1]))\n", " \n", " return array(xout),array(yout),array(yerrout)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Comparing the two:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, here's an example where both functions do just about the same thing. The data length is reasonable at 10k points (typical of an oscilloscope output file, for example), and the data is fairly noisy." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Start with a 10k array\n", "x = arange(0,300,0.03)\n", "print 'Initial array length:',len(x)\n", "\n", "# random data\n", "A = 200; B = 0.3; C = 4\n", "y = exp(-x/A) * sin(B*x) * C\n", "\n", "# Add Gaussian noise\n", "y_noise = random.randn(len(x))*0.4\n", "y += y_noise\n", "\n", "# Plot raw data - two separate figures for saving, one for viewing\n", "fig1 = figure(1)\n", "clf()\n", "ax1 = fig1.add_subplot(111)\n", "ax1.plot(x,y,'k',lw=2)\n", "\n", "#display(fig1)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Initial array length: 10000\n" ] }, { "metadata": {}, "output_type": "pyout", "prompt_number": 4, "text": [ "[<matplotlib.lines.Line2D at 0x107013250>]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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k21izZk0oW7asYddhRj3nm4WJgsrNzYUBAwbAv//9bzh27BgsWrQIzp49a6pM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\nUZsUvdAiatSrV0/VWEtOenq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BQRAE4YxbKqgOHToU+M3TxHzevHkQEhLCrXwEQRBEGbdU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\nEMSWoIJCEARBbAkqKARBEMSW/D+pF2b0DHReWQAAAABJRU5ErkJggg==\n", "text": [ "<matplotlib.figure.Figure at 0x1045c2710>" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's smooth this data - we start with the moving average, taking 100 points as our smoothing window (play around with this number to see it's effect)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig2 = figure(2)\n", "clf()\n", "ax2 = fig2.add_subplot(111)\n", "\n", "# smooth with moving average\n", "window = 100\n", "y_smoothed = smooth_triangle(y,window)\n", "\n", "ax2.plot(x,y,'k',lw=2)\n", "ax2.plot(x,y_smoothed,'r.',ms=3)\n", "\n", "#display(fig2)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 5, "text": [ "[<matplotlib.lines.Line2D at 0x107180850>]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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0tKCIFc8884zwsXYWZtpVOlZGNjzPJr0QOdqRh5MYg1oeeeQRLFiwAN26dQNw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\nCIKISP4fHoIfFI8DI0wAAAAASUVORK5CYII=\n", "text": [ "<matplotlib.figure.Figure at 0x1045c25d0>" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This looks pretty good, the data is much smoother without losing much information. Note the ends of the data where the smoothing isn't applied (only really visible on the right side in this example) - it's easy to crop this off if desired, just do\n", "\n", " x_smoothed = x[window:-window]\n", " y_smoothed = y_smoothed[window:-window]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, let's bin the data instead." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig3 = figure(3)\n", "clf()\n", "ax3 = fig3.add_subplot(111)\n", "\n", "# bin and plot\n", "window = 25\n", "x_binned,y_binned,y_error = bin_data(x,y,window)\n", "ax3.plot(x,y,'k',lw=2)\n", "ax3.plot(x_binned,y_binned,'r.',ms=9)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 6, "text": [ "[<matplotlib.lines.Line2D at 0x10766b110>]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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2MnPnzjUd/FktN5gSOTRVBIDhS5YA8JrAm30m3mCCANRC4PmIXO9yGtdHUPEF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\ndexY2AkJyabyjgBQC/6x5DwCUkZ//vnnQI8eftv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"text": [ "<matplotlib.figure.Figure at 0x1071aee10>" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "In both these examples, we've only plotted the data points in red - with no line between them. The length of the binned data arrays is much smaller than the smoothed data. There are a couple of reasons to choose one over the other:\n", "\n", "* If fitting the data, the binned data will process faster since there are fewer points\n", "* If the data array is large, the plot may be slow and resulting figure file size may be large\n", "* However, if the data array is already short, binning the data may introduce aliasing\n", "\n", "We'll look at the last case in more detail now." ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Bad binning - aliasing" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's take the same data we had in the previous example and plot it as a line, instead of just the points." ] }, { "cell_type": "code", "collapsed": false, "input": [ "#clear the axes...\n", "ax3.cla()\n", "\n", "#...and redraw\n", "ax3.plot(x,y,'k',lw=1.5)\n", "ax3.plot(x_binned,y_binned,'r-',lw=1.5)\n", "\n", "display(fig3)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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xBiDzTCELdCwi/tfibSkS1HokiHfeyb2KZoi19krBo5NRKwLVvHnz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\n4YYbmDpV0kq1eZ0pUElRgTJLPeqekW2BglwUmkknpBTVWov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V6cGDBzh27FjMWXwyChxK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\nrkJggg==\n", "text": [ "<matplotlib.figure.Figure at 0x1071aee10>" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's bin the data with a very large window and add it to the plot:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#select large binning window, relative to the data size\n", "window = 400\n", "x_binned, y_binned, y_error = bin_data(x,y,window)\n", "\n", "ax3.plot(x_binned,y_binned,'g-',lw=3)\n", "\n", "display(fig3)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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AuVwu7v7hbp7e+DTcA/s98cx1EBd6uAQKMnG5XI6EmkuBikJMrv4kYTuRRwzK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TAAAA\nZElEQVT7devWWWVlZVZxcbF19tlnW/PmzQs8Z/K8i5OEIAiCkJaIk4QgCIKQlohACYIgCGmJCJQg\nCIKQlohACYIgCGmJCJQgCIKQlohACYIgCGmJCJQgCIKQlohACYIgCGnJ/wBewZukh35WkQAAAABJ\nRU5ErkJggg==\n", "text": [ "<matplotlib.figure.Figure at 0x1071aee10>" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can see that bad things are happening... The data has been binned far too much and aliasing has resulted.\n", "\n", "As a rule of thumb, the binning window should never be bigger than **some fraction** of the data array length, otherwise aliasing could occur. Of course, there's nothing to stop running both smoothing and binning - just run the moving average smoothing first, for the best results." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* * *" ] } ], "metadata": {} } ] }