1 | // ----------------------------------------------------------------------- |
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2 | // linear_regression.cc: Performs linear regression on a set of (x,y) |
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3 | // values. |
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4 | // ----------------------------------------------------------------------- |
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5 | // Copyright (C) 2006, Matthew Whiting, ATNF |
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6 | // |
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7 | // This program is free software; you can redistribute it and/or modify it |
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8 | // under the terms of the GNU General Public License as published by the |
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9 | // Free Software Foundation; either version 2 of the License, or (at your |
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10 | // option) any later version. |
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11 | // |
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12 | // Duchamp is distributed in the hope that it will be useful, but WITHOUT |
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13 | // ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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14 | // FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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15 | // for more details. |
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16 | // |
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17 | // You should have received a copy of the GNU General Public License |
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18 | // along with Duchamp; if not, write to the Free Software Foundation, |
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19 | // Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA |
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20 | // |
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21 | // Correspondence concerning Duchamp may be directed to: |
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22 | // Internet email: Matthew.Whiting [at] atnf.csiro.au |
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23 | // Postal address: Dr. Matthew Whiting |
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24 | // Australia Telescope National Facility, CSIRO |
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25 | // PO Box 76 |
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26 | // Epping NSW 1710 |
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27 | // AUSTRALIA |
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28 | // ----------------------------------------------------------------------- |
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29 | #include <iostream> |
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30 | #include <math.h> |
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31 | int linear_regression(int num, float *x, float *y, int ilow, int ihigh, float &slope, float &errSlope, float &intercept, float &errIntercept, float &r) |
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32 | { |
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33 | /** |
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34 | * Computes the linear best fit to data: $y=a x + b$, where $x$ and |
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35 | * $y$ are arrays of size num, $a$ is the slope and $b$ the |
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36 | * y-intercept. The values used in the arrays are those from ilow |
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37 | * to ihigh. (ie. if the full arrays are being used, then ilow=0 |
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38 | * and ihigh=num-1. Returns the values of slope & intercept (with |
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39 | * errors) as well as r, the regression coefficient. |
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40 | * |
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41 | * \param num Size of the x & y arrays. |
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42 | * \param x Array of abscissae. |
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43 | * \param y Array of ordinates. |
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44 | * \param ilow Minimum index of the arrays to be used (ilow=0 means |
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45 | * start at the beginning). |
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46 | * \param ihigh Maximum index of the arrays to be used (ihigh=num-1 |
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47 | * means finish at the end). |
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48 | * \param slope Returns value of the slope of the best fit line. |
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49 | * \param errSlope Returns value of the estimated error in the slope |
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50 | * value. |
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51 | * \param intercept Returns value of the y-intercept of the best fit |
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52 | * line. |
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53 | * \param errIntercept Returns value of the estimated error in the |
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54 | * value of the y-intercept. |
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55 | * \param r Returns the value of the regression coefficient. |
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56 | * \return If everything works, returns 0. If slope is infinite (eg, |
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57 | * all points have same x value), returns 1. |
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58 | */ |
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59 | |
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60 | if (ilow>ihigh) { |
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61 | std::cerr << "Error! linear_regression.cc :: ilow (" << ilow |
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62 | << ") > ihigh (" << ihigh << ")!!\n"; |
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63 | return 1; |
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64 | } |
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65 | if (ihigh>num-1) { |
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66 | std::cerr << "Error! linear_regression.cc :: ihigh (" <<ihigh |
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67 | << ") out of bounds of array (>" << num-1 << ")!!\n"; |
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68 | return 1; |
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69 | } |
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70 | if(ilow<0){ |
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71 | std::cerr << "Error! linear_regression.cc :: ilow (" << ilow |
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72 | << ") < 0. !!\n"; |
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73 | return 1; |
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74 | } |
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75 | |
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76 | double sumx,sumy,sumxx,sumxy,sumyy; |
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77 | sumx=0.; |
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78 | sumy=0.; |
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79 | sumxx=0.; |
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80 | sumxy=0.; |
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81 | sumyy=0.; |
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82 | int count=0; |
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83 | for (int i=ilow;i<=ihigh;i++){ |
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84 | count++; |
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85 | sumx = sumx + x[i]; |
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86 | sumy = sumy + y[i]; |
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87 | sumxx = sumxx + x[i]*x[i]; |
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88 | sumxy = sumxy + x[i]*y[i]; |
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89 | sumyy = sumyy + y[i]*y[i]; |
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90 | } |
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91 | |
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92 | const float SMALLTHING=1.e-6; |
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93 | if(fabs(count*sumxx-sumx*sumx)<SMALLTHING) return 1; |
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94 | else{ |
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95 | |
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96 | slope = (count*sumxy - sumx*sumy)/(count*sumxx - sumx*sumx); |
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97 | errSlope = count / (count*sumxx - sumx*sumx); |
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98 | |
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99 | intercept = (sumy*sumxx - sumxy*sumx)/(count*sumxx - sumx*sumx); |
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100 | errIntercept = sumxx / (count*sumxx - sumx*sumx); |
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101 | |
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102 | r = (count*sumxy - sumx*sumy) / |
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103 | (sqrt(count*sumxx-sumx*sumx) * sqrt(count*sumyy-sumy*sumy) ); |
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104 | |
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105 | return 0; |
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106 | |
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107 | } |
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108 | } |
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