[301] | 1 | // ----------------------------------------------------------------------- |
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| 2 | // getStats.cc: Basic functions to calculate statistical parameters |
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| 3 | // such as mean, median, rms, madfm, min, max. |
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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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[3] | 29 | #include <iostream> |
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[204] | 30 | #include <algorithm> |
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[3] | 31 | #include <math.h> |
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[393] | 32 | #include <duchamp/Utils/utils.hh> |
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[3] | 33 | |
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[190] | 34 | template <class T> T absval(T value) |
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[70] | 35 | { |
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[528] | 36 | /// Type-independent way of getting the absolute value. |
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[190] | 37 | if( value > 0) return value; |
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| 38 | else return 0-value; |
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| 39 | } |
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[222] | 40 | template int absval<int>(int value); |
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| 41 | template long absval<long>(long value); |
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| 42 | template float absval<float>(float value); |
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| 43 | template double absval<double>(double value); |
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[190] | 44 | //-------------------------------------------------------------------- |
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| 45 | |
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| 46 | template <class T> void findMinMax(const T *array, const int size, |
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| 47 | T &min, T &max) |
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| 48 | { |
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[528] | 49 | /// @details |
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| 50 | /// A function to find the minimum and maximum values of a set of numbers. |
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| 51 | /// \param array The array of data values. Type independent. |
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| 52 | /// \param size The length of the array |
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| 53 | /// \param min The returned value of the minimum value in the array. |
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| 54 | /// \param max The returned value of the maximum value in the array. |
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[70] | 55 | min = max = array[0]; |
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| 56 | for(int i=1;i<size;i++) { |
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| 57 | if(array[i]<min) min=array[i]; |
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| 58 | if(array[i]>max) max=array[i]; |
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| 59 | } |
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| 60 | } |
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[190] | 61 | template void findMinMax<int>(const int *array, const int size, |
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[222] | 62 | int &min, int &max); |
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| 63 | template void findMinMax<long>(const long *array, const int size, |
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| 64 | long &min, long &max); |
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[190] | 65 | template void findMinMax<float>(const float *array, const int size, |
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[222] | 66 | float &min, float &max); |
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| 67 | template void findMinMax<double>(const double *array, const int size, |
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| 68 | double &min, double &max); |
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[190] | 69 | //-------------------------------------------------------------------- |
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[70] | 70 | |
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[190] | 71 | template <class T> float findMean(T *array, int size) |
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[53] | 72 | { |
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[528] | 73 | /// @details |
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| 74 | /// Find the mean of an array of numbers. Type independent. |
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| 75 | /// \param array The array of numbers. |
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| 76 | /// \param size The length of the array. |
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| 77 | /// \return The mean value of the array, returned as a float |
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[653] | 78 | double mean = double(array[0]); |
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| 79 | for(int i=1;i<size;i++) mean += double(array[i]); |
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| 80 | mean /= double(size); |
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| 81 | return float(mean); |
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[53] | 82 | } |
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[190] | 83 | template float findMean<int>(int *array, int size); |
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[222] | 84 | template float findMean<long>(long *array, int size); |
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[190] | 85 | template float findMean<float>(float *array, int size); |
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[222] | 86 | template float findMean<double>(double *array, int size); |
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[190] | 87 | //-------------------------------------------------------------------- |
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[53] | 88 | |
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[190] | 89 | template <class T> float findStddev(T *array, int size) |
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[53] | 90 | { |
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[528] | 91 | /// @details |
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| 92 | /// Find the rms or standard deviation of an array of numbers. Type independent. |
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| 93 | /// \param array The array of numbers. |
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| 94 | /// \param size The length of the array. |
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| 95 | /// \return The rms value of the array, returned as a float |
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[653] | 96 | double mean = double(findMean(array,size)); |
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| 97 | double stddev = (double(array[0])-mean) * (double(array[0])-mean); |
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| 98 | for(int i=1;i<size;i++) stddev += (double(array[i])-mean)*(double(array[i])-mean); |
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| 99 | stddev = sqrt(stddev/double(size-1)); |
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| 100 | return float(stddev); |
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[53] | 101 | } |
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[190] | 102 | template float findStddev<int>(int *array, int size); |
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[222] | 103 | template float findStddev<long>(long *array, int size); |
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[190] | 104 | template float findStddev<float>(float *array, int size); |
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[222] | 105 | template float findStddev<double>(double *array, int size); |
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[190] | 106 | //-------------------------------------------------------------------- |
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[53] | 107 | |
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[646] | 108 | template <class T> T findMedian(T *array, int size, bool changeArray) |
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[53] | 109 | { |
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[528] | 110 | /// @details |
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| 111 | /// Find the median value of an array of numbers. Type independent. |
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| 112 | /// \param array The array of numbers. |
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| 113 | /// \param size The length of the array. |
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[646] | 114 | /// \param changeArray [false] Whether to use the provided array in calculations. If true, the input array will be altered (ie. the order of elements will be changed). |
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[528] | 115 | /// \return The median value of the array, returned as the same type as the array. |
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[646] | 116 | T *newarray; |
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| 117 | if(changeArray) newarray = array; |
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| 118 | else{ |
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| 119 | newarray = new T[size]; |
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| 120 | for(int i=0;i<size;i++) newarray[i] = array[i]; |
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| 121 | } |
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[190] | 122 | T median; |
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[657] | 123 | bool isEven = ((size/2)==0); |
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[646] | 124 | std::nth_element(newarray,newarray+size/2,newarray+size); |
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| 125 | median = newarray[size/2]; |
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[657] | 126 | if(isEven){ |
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[646] | 127 | std::nth_element(newarray,newarray+size/2-1,newarray+size); |
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| 128 | median += newarray[size/2-1]; |
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[699] | 129 | median /= T(2); |
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[646] | 130 | } |
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| 131 | if(!changeArray) delete [] newarray; |
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[53] | 132 | return median; |
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| 133 | } |
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[646] | 134 | template int findMedian<int>(int *array, int size, bool changeArray); |
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| 135 | template long findMedian<long>(long *array, int size, bool changeArray); |
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| 136 | template float findMedian<float>(float *array, int size, bool changeArray); |
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| 137 | template double findMedian<double>(double *array, int size, bool changeArray); |
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[190] | 138 | //-------------------------------------------------------------------- |
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[53] | 139 | |
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[646] | 140 | template <class T> T findMADFM(T *array, int size, bool changeArray) |
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[53] | 141 | { |
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[528] | 142 | /// @details |
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| 143 | /// Find the median absolute deviation from the median value of an |
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| 144 | /// array of numbers. Type independent. |
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| 145 | /// |
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| 146 | /// \param array The array of numbers. |
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| 147 | /// \param size The length of the array. |
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[646] | 148 | /// \param changeArray [false] Whether to use the provided array in calculations. If true, the input array will be altered - both the order and values of the elements will be changed. |
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[528] | 149 | /// \return The median absolute deviation from the median value of |
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| 150 | /// the array, returned as the same type as the array. |
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[646] | 151 | T *newarray; |
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| 152 | if(changeArray) newarray = array; |
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| 153 | else newarray = new T[size]; |
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| 154 | |
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| 155 | T median = findMedian<T>(array,size,changeArray); |
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[190] | 156 | T madfm; |
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[657] | 157 | bool isEven = ((size/2)==0); |
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[190] | 158 | for(int i=0;i<size;i++) newarray[i] = absval(array[i]-median); |
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[646] | 159 | std::nth_element(newarray,newarray+size/2,newarray+size); |
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| 160 | madfm = newarray[size/2]; |
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[657] | 161 | if(isEven){ |
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[646] | 162 | std::nth_element(newarray,newarray+size/2-1,newarray+size); |
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| 163 | madfm += newarray[size/2-1]; |
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[699] | 164 | madfm /= T(2); |
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[646] | 165 | } |
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| 166 | if(!changeArray) delete [] newarray; |
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[53] | 167 | return madfm; |
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| 168 | } |
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[646] | 169 | template int findMADFM<int>(int *array, int size, bool changeArray); |
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| 170 | template long findMADFM<long>(long *array, int size, bool changeArray); |
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| 171 | template float findMADFM<float>(float *array, int size, bool changeArray); |
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| 172 | template double findMADFM<double>(double *array, int size, bool changeArray); |
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[190] | 173 | //-------------------------------------------------------------------- |
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| 174 | |
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[756] | 175 | template <class T> T findMADFM(T *array, int size, T median, bool changeArray) |
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| 176 | { |
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| 177 | /// @details |
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| 178 | /// Find the median absolute deviation from the median value of an |
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| 179 | /// array of numbers. Type independent. This version accepts a previously- |
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| 180 | /// calculated median value. |
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| 181 | /// |
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| 182 | /// \param array The array of numbers. |
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| 183 | /// \param size The length of the array. |
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| 184 | /// \param median The median of the array. |
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| 185 | /// \param changeArray [false] Whether to use the provided array in calculations. If true, the input array will be altered - both the order and values of the elements will be changed. |
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| 186 | /// \return The median absolute deviation from the median value of |
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| 187 | /// the array, returned as the same type as the array. |
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| 188 | T *newarray; |
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| 189 | if(changeArray) newarray = array; |
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| 190 | else newarray = new T[size]; |
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| 191 | |
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| 192 | T madfm; |
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| 193 | bool isEven = ((size/2)==0); |
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| 194 | for(int i=0;i<size;i++) newarray[i] = absval(array[i]-median); |
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| 195 | std::nth_element(newarray,newarray+size/2,newarray+size); |
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| 196 | madfm = newarray[size/2]; |
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| 197 | if(isEven){ |
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| 198 | std::nth_element(newarray,newarray+size/2-1,newarray+size); |
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| 199 | madfm += newarray[size/2-1]; |
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| 200 | madfm /= T(2); |
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| 201 | } |
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| 202 | if(!changeArray) delete [] newarray; |
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| 203 | return madfm; |
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| 204 | } |
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| 205 | template int findMADFM<int>(int *array, int size, int median, bool changeArray); |
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| 206 | template long findMADFM<long>(long *array, int size, long median, bool changeArray); |
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| 207 | template float findMADFM<float>(float *array, int size, float median, bool changeArray); |
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| 208 | template double findMADFM<double>(double *array, int size, double median, bool changeArray); |
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| 209 | //-------------------------------------------------------------------- |
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| 210 | |
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[190] | 211 | template <class T> void findMedianStats(T *array, int size, |
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| 212 | T &median, T &madfm) |
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[3] | 213 | { |
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[528] | 214 | /// @details |
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| 215 | /// Find the median and the median absolute deviation from the median |
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| 216 | /// value of an array of numbers. Type independent. |
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| 217 | /// |
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| 218 | /// \param array The array of numbers. |
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| 219 | /// \param size The length of the array. |
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| 220 | /// \param median The median value of the array, returned as the same |
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| 221 | /// type as the array. |
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| 222 | /// \param madfm The median absolute deviation from the median value |
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| 223 | /// of the array, returned as the same type as the array. |
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[190] | 224 | if(size==0){ |
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| 225 | std::cerr << "Error in findMedianStats: zero sized array!\n"; |
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| 226 | return; |
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| 227 | } |
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| 228 | T *newarray = new T[size]; |
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[646] | 229 | for(int i=0;i<size;i++) newarray[i] = array[i]; |
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[3] | 230 | |
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[646] | 231 | median = findMedian(newarray,size,true); |
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[756] | 232 | // madfm = findMADFM(newarray,size,true); |
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| 233 | madfm = findMADFM(newarray,size,median,true); |
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[3] | 234 | |
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| 235 | delete [] newarray; |
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| 236 | } |
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[190] | 237 | template void findMedianStats<int>(int *array, int size, |
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[222] | 238 | int &median, int &madfm); |
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[190] | 239 | template void findMedianStats<long>(long *array, int size, |
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[222] | 240 | long &median, long &madfm); |
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[190] | 241 | template void findMedianStats<float>(float *array, int size, |
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[222] | 242 | float &median, float &madfm); |
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[190] | 243 | template void findMedianStats<double>(double *array, int size, |
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[222] | 244 | double &median, double &madfm); |
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[190] | 245 | //-------------------------------------------------------------------- |
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| 246 | |
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[275] | 247 | template <class T> void findMedianStats(T *array, int size, bool *mask, |
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[190] | 248 | T &median, T &madfm) |
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[3] | 249 | { |
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[528] | 250 | /// @details |
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| 251 | /// Find the median and the median absolute deviation from the median |
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| 252 | /// value of a subset of an array of numbers. The subset is defined |
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| 253 | /// by an array of bool variables. Type independent. |
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| 254 | /// |
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| 255 | /// \param array The array of numbers. |
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| 256 | /// \param size The length of the array. |
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| 257 | /// \param mask An array of the same length that says whether to |
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| 258 | /// include each member of the array in the calculations. Only use |
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| 259 | /// values where mask=true. |
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| 260 | /// \param median The median value of the array, returned as the same |
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| 261 | /// type as the array. |
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| 262 | /// \param madfm The median absolute deviation from the median value |
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| 263 | /// of the array, returned as the same type as the array. |
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| 264 | |
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[190] | 265 | int goodSize=0; |
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[275] | 266 | for(int i=0;i<size;i++) if(mask[i]) goodSize++; |
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[190] | 267 | if(goodSize==0){ |
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| 268 | std::cerr << "Error in findMedianStats: no good values!\n"; |
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| 269 | return; |
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| 270 | } |
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| 271 | T *newarray = new T[goodSize]; |
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[646] | 272 | |
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[648] | 273 | goodSize=0; |
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[275] | 274 | for(int i=0;i<size;i++) if(mask[i]) newarray[goodSize++] = array[i]; |
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[646] | 275 | median = findMedian(newarray,goodSize,true); |
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[756] | 276 | // madfm = findMADFM(newarray,goodSize,true); |
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| 277 | madfm = findMADFM(newarray,goodSize,median,true); |
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[3] | 278 | |
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| 279 | delete [] newarray; |
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| 280 | } |
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[275] | 281 | template void findMedianStats<int>(int *array, int size, bool *mask, |
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[222] | 282 | int &median, int &madfm); |
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[275] | 283 | template void findMedianStats<long>(long *array, int size, bool *mask, |
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[222] | 284 | long &median, long &madfm); |
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[275] | 285 | template void findMedianStats<float>(float *array, int size, bool *mask, |
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[222] | 286 | float &median, float &madfm); |
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[275] | 287 | template void findMedianStats<double>(double *array, int size, bool *mask, |
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[222] | 288 | double &median, double &madfm); |
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[190] | 289 | //-------------------------------------------------------------------- |
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[3] | 290 | |
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| 291 | |
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[190] | 292 | template <class T> void findNormalStats(T *array, int size, |
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| 293 | float &mean, float &stddev) |
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[3] | 294 | { |
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[528] | 295 | /// @details |
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| 296 | /// Find the mean and rms or standard deviation of an array of |
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| 297 | /// numbers. Type independent. |
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| 298 | /// |
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| 299 | /// \param array The array of numbers. |
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| 300 | /// \param size The length of the array. |
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| 301 | /// \param mean The mean value of the array, returned as a float. |
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| 302 | /// \param stddev The rms or standard deviation of the array, |
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| 303 | /// returned as a float. |
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| 304 | |
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[190] | 305 | if(size==0){ |
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| 306 | std::cerr << "Error in findNormalStats: zero sized array!\n"; |
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| 307 | return; |
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| 308 | } |
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[3] | 309 | mean = array[0]; |
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| 310 | for(int i=1;i<size;i++){ |
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| 311 | mean += array[i]; |
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| 312 | } |
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| 313 | mean /= float(size); |
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| 314 | |
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[79] | 315 | stddev = (array[0]-mean) * (array[0]-mean); |
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[275] | 316 | for(int i=1;i<size;i++) stddev += (array[i]-mean)*(array[i]-mean); |
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[79] | 317 | stddev = sqrt(stddev/float(size-1)); |
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[3] | 318 | |
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| 319 | } |
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[190] | 320 | template void findNormalStats<int>(int *array, int size, |
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[222] | 321 | float &mean, float &stddev); |
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[190] | 322 | template void findNormalStats<long>(long *array, int size, |
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[222] | 323 | float &mean, float &stddev); |
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[190] | 324 | template void findNormalStats<float>(float *array, int size, |
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[222] | 325 | float &mean, float &stddev); |
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[190] | 326 | template void findNormalStats<double>(double *array, int size, |
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[222] | 327 | float &mean, float &stddev); |
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[190] | 328 | //-------------------------------------------------------------------- |
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[3] | 329 | |
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[275] | 330 | template <class T> void findNormalStats(T *array, int size, bool *mask, |
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[190] | 331 | float &mean, float &stddev) |
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[70] | 332 | { |
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[528] | 333 | /// @details |
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| 334 | /// Find the mean and rms or standard deviation of a subset of an |
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| 335 | /// array of numbers. The subset is defined by an array of bool |
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| 336 | /// variables. Type independent. |
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| 337 | /// |
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| 338 | /// \param array The array of numbers. |
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| 339 | /// \param size The length of the array. |
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| 340 | /// \param mask An array of the same length that says whether to |
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| 341 | /// include each member of the array in the calculations. Only look |
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| 342 | /// at values where mask=true. |
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| 343 | /// \param mean The mean value of the array, returned as a float. |
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| 344 | /// \param stddev The rms or standard deviation of the array, |
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| 345 | /// returned as a float. |
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| 346 | |
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[190] | 347 | int goodSize=0; |
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[275] | 348 | for(int i=0;i<size;i++) if(mask[i]) goodSize++; |
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[190] | 349 | if(goodSize==0){ |
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| 350 | std::cerr << "Error in findNormalStats: no good values!\n"; |
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| 351 | return; |
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| 352 | } |
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| 353 | int start=0; |
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[275] | 354 | while(!mask[start]){start++;} |
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[190] | 355 | mean = array[start]; |
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| 356 | for(int i=start+1;i<size;i++){ |
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[275] | 357 | if(mask[i]) mean += array[i]; |
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[190] | 358 | } |
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| 359 | mean /= float(goodSize); |
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[70] | 360 | |
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[190] | 361 | stddev = (array[start]-mean) * (array[start]-mean); |
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| 362 | for(int i=1;i<size;i++){ |
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[275] | 363 | if(mask[i]) stddev += (array[i]-mean)*(array[i]-mean); |
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[190] | 364 | } |
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| 365 | stddev = sqrt(stddev/float(goodSize-1)); |
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| 366 | |
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| 367 | } |
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[275] | 368 | template void findNormalStats<int>(int *array, int size, bool *mask, |
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[222] | 369 | float &mean, float &stddev); |
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[275] | 370 | template void findNormalStats<long>(long *array, int size, bool *mask, |
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[222] | 371 | float &mean, float &stddev); |
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[275] | 372 | template void findNormalStats<float>(float *array, int size, bool *mask, |
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[222] | 373 | float &mean, float &stddev); |
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[275] | 374 | template void findNormalStats<double>(double *array, int size, bool *mask, |
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[222] | 375 | float &mean, float &stddev); |
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[190] | 376 | //-------------------------------------------------------------------- |
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[275] | 377 | //-------------------------------------------------------------------- |
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| 378 | |
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| 379 | |
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| 380 | template <class T> void findAllStats(T *array, int size, |
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| 381 | float &mean, float &stddev, |
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| 382 | T &median, T &madfm) |
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| 383 | { |
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[528] | 384 | /// @details |
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| 385 | /// Find the mean,rms (or standard deviation), median AND madfm of an |
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| 386 | /// array of numbers. Type independent. |
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| 387 | /// |
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| 388 | /// \param array The array of numbers. |
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| 389 | /// \param size The length of the array. |
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| 390 | /// \param mean The mean value of the array, returned as a float. |
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| 391 | /// \param stddev The rms or standard deviation of the array, |
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| 392 | /// returned as a float. |
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| 393 | /// \param median The median value of the array, returned as the same |
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| 394 | /// type as the array. |
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| 395 | /// \param madfm The median absolute deviation from the median value |
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| 396 | /// of the array, returned as the same type as the array. |
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| 397 | |
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[275] | 398 | if(size==0){ |
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[285] | 399 | std::cerr << "Error in findAllStats: zero sized array!\n"; |
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[275] | 400 | return; |
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| 401 | } |
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| 402 | |
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| 403 | T *newarray = new T[size]; |
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| 404 | |
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| 405 | for(int i=0;i<size;i++) newarray[i] = array[i]; |
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[285] | 406 | |
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[646] | 407 | mean = findMean(newarray,size); |
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| 408 | stddev = findStddev(newarray,size); |
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| 409 | median = findMedian(newarray,size,true); |
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[756] | 410 | // madfm = findMADFM(newarray,size,true); |
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| 411 | madfm = findMADFM(newarray,size,median,true); |
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[285] | 412 | |
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[275] | 413 | delete [] newarray; |
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| 414 | |
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| 415 | } |
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| 416 | template void findAllStats<int>(int *array, int size, |
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| 417 | float &mean, float &stddev, |
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| 418 | int &median, int &madfm); |
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| 419 | template void findAllStats<long>(long *array, int size, |
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| 420 | float &mean, float &stddev, |
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| 421 | long &median, long &madfm); |
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| 422 | template void findAllStats<float>(float *array, int size, |
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| 423 | float &mean, float &stddev, |
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| 424 | float &median, float &madfm); |
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| 425 | template void findAllStats<double>(double *array, int size, |
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| 426 | float &mean, float &stddev, |
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| 427 | double &median, double &madfm); |
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| 428 | //-------------------------------------------------------------------- |
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| 429 | |
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| 430 | template <class T> void findAllStats(T *array, int size, bool *mask, |
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| 431 | float &mean, float &stddev, |
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| 432 | T &median, T &madfm) |
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| 433 | { |
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[528] | 434 | /// @details |
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| 435 | /// Find the mean,rms (or standard deviation), median AND madfm of a |
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| 436 | /// subset of an array of numbers. Type independent.The subset is |
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| 437 | /// defined by an array of bool variables. Type independent. |
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| 438 | /// |
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| 439 | /// \param array The array of numbers. |
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| 440 | /// \param size The length of the array. |
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| 441 | /// \param mask An array of the same length that says whether to |
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| 442 | /// include each member of the array in the calculations. Only look |
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| 443 | /// at values where mask=true. |
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| 444 | /// \param mean The mean value of the array, returned as a float. |
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| 445 | /// \param stddev The rms or standard deviation of the array, |
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| 446 | /// returned as a float. |
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| 447 | /// \param median The median value of the array, returned as the same |
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| 448 | /// type as the array. |
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| 449 | /// \param madfm The median absolute deviation from the median value |
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| 450 | /// of the array, returned as the same type as the array. |
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| 451 | |
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[275] | 452 | int goodSize=0; |
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| 453 | for(int i=0;i<size;i++) if(mask[i]) goodSize++; |
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| 454 | if(goodSize==0){ |
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| 455 | std::cerr << "Error in findAllStats: no good values!\n"; |
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| 456 | return; |
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| 457 | } |
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| 458 | |
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| 459 | T *newarray = new T[goodSize]; |
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| 460 | goodSize=0; |
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| 461 | for(int i=0;i<size;i++) if(mask[i]) newarray[goodSize++] = array[i]; |
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| 462 | |
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[646] | 463 | mean = findMean(newarray,goodSize); |
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| 464 | stddev = findStddev(newarray,goodSize); |
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| 465 | median = findMedian(newarray,goodSize,true); |
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[756] | 466 | //madfm = findMADFM(newarray,goodSize,true); |
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| 467 | madfm = findMADFM(newarray,goodSize,median,true); |
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[275] | 468 | |
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[282] | 469 | delete [] newarray; |
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| 470 | |
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[275] | 471 | } |
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| 472 | template void findAllStats<int>(int *array, int size, bool *mask, |
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| 473 | float &mean, float &stddev, |
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| 474 | int &median, int &madfm); |
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| 475 | template void findAllStats<long>(long *array, int size, bool *mask, |
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| 476 | float &mean, float &stddev, |
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| 477 | long &median, long &madfm); |
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| 478 | template void findAllStats<float>(float *array, int size, bool *mask, |
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| 479 | float &mean, float &stddev, |
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| 480 | float &median, float &madfm); |
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| 481 | template void findAllStats<double>(double *array, int size, bool *mask, |
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| 482 | float &mean, float &stddev, |
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| 483 | double &median, double &madfm); |
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| 484 | //-------------------------------------------------------------------- |
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