Marsyas
0.6.0-alpha
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00001 /* 00002 ** Copyright (C) 2011 Eric Nichols <epnichols@gmail.com> 00003 ** 00004 ** This program is free software; you can redistribute it and/or modify 00005 ** it under the terms of the GNU General Public License as published by 00006 ** the Free Software Foundation; either version 2 of the License, or 00007 ** (at your option) any later version. 00008 ** 00009 ** This program is distributed in the hope that it will be useful, 00010 ** but WITHOUT ANY WARRANTY; without even the implied warranty of 00011 ** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 00012 ** GNU General Public License for more details. 00013 ** 00014 ** You should have received a copy of the GNU General Public License 00015 ** along with this program; if not, write to the Free Software 00016 ** Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. 00017 */ 00018 00019 00020 #include "statistics.h" 00021 #include <algorithm> 00022 00023 using std::ostringstream; 00024 using std::numeric_limits; 00025 using std::endl; 00026 using std::cout; 00027 using std::cerr; 00028 using std::min; 00029 using std::max; 00030 00031 00032 using namespace Marsyas; 00033 00034 statistics::statistics() 00035 { 00036 } 00037 00038 statistics::~statistics() 00039 { 00040 } 00041 00042 // PRIVATE 00043 00044 // Returns the nth moment about the mean for data that's already been converted to z-scores. 00045 mrs_real 00046 statistics::momentN(const realvec& zData, const realvec& weights, int n) 00047 { 00048 if (zData.getSize() != weights.getSize()) 00049 { 00050 MRSERR("statistics::momentN - wrong size for weights vector!"); 00051 return -1.0; 00052 } 00053 00054 mrs_real sum = 0.0; 00055 00056 for (mrs_natural i=0; i < zData.getSize(); i++) 00057 { 00058 sum += weights(i) * pow(zData(i), n); 00059 } 00060 00061 return sum; 00062 } 00063 00064 00065 // Computes z scores for a set of data, given a mean. 00066 // The mean is needed so that this fxn can be used to compute moments about 0 00067 // (instead of about the actual mean). 00068 realvec 00069 statistics::zDataWeighted(const realvec& data, const realvec& weights, mrs_real mean) 00070 { 00071 realvec zData; 00072 zData.create(data.getSize()); 00073 00074 if (data.getSize() != weights.getSize()) 00075 { 00076 MRSERR("statistics::zDataWeighted - wrong size for weights vector!"); 00077 return zData; 00078 } 00079 00080 mrs_real sd = statistics::stddevWeighted(data, weights, mean); 00081 00082 if (sd == 0) 00083 { 00084 MRSWARN("statistics::zDataWeighted - standard deviation is 0."); 00085 return zData; 00086 } 00087 00088 for (mrs_natural i=0; i < zData.getSize(); i++) 00089 zData(i) = (data(i) - mean) / sd; 00090 00091 return zData; 00092 } 00093 00094 00095 00096 // PUBLIC 00097 00098 00099 // Computes the mean for a vector where each element has an 00100 // associated weight (i.e. computes the weighted mean). 00101 mrs_real 00102 statistics::meanWeighted(const realvec& data, const realvec& weights) 00103 { 00104 if (data.getSize() != weights.getSize()) 00105 { 00106 MRSERR("statistics::meanWeighted - wrong size for weights vector!"); 00107 return -1.0; 00108 } 00109 00110 mrs_real sum = 0.0; 00111 mrs_real weightsSum = 0.0; 00112 00113 for (mrs_natural i=0; i < data.getSize(); i++) 00114 { 00115 mrs_real w = weights(i); 00116 00117 sum += w * data(i); 00118 weightsSum += w; 00119 } 00120 00121 if (weightsSum != 0.0) sum /= weightsSum; 00122 return sum; 00123 } 00124 00125 00126 // Computes the standard deviation for a vector where each element has an 00127 // associated weight. 00128 // Assumes weights sum to 1. 00129 mrs_real 00130 statistics::stddevWeighted(const realvec& data, const realvec& weights, mrs_real mean) 00131 { 00132 mrs_real variance = varWeighted(data, weights, mean); 00133 return sqrt(variance); 00134 } 00135 00136 // Computes the variance for a vector where each element has an 00137 // associated weight. 00138 // Assumes weights sum to 1. 00139 mrs_real 00140 statistics::varWeighted(const realvec& data, const realvec& weights, mrs_real mean) 00141 { 00142 if (data.getSize() != weights.getSize()) 00143 { 00144 MRSERR("statistics::varWeighted - wrong size for weights vector!"); 00145 return -1.0; 00146 } 00147 00148 mrs_real sum = 0.0; 00149 00150 for (mrs_natural i=0; i < data.getSize(); i++) 00151 { 00152 mrs_real w = weights(i); 00153 mrs_real diff = data(i) - mean; 00154 00155 sum += w * diff * diff; 00156 } 00157 00158 return sum; 00159 } 00160 00161 // Computes the weighted skewness (3rd moment) about the given mean value. 00162 // Assumes weights sum to 1 00163 mrs_real 00164 statistics::skewnessWeighted(const realvec& data, const realvec& weights, mrs_real mean) 00165 { 00166 realvec zData = zDataWeighted(data, weights, mean); 00167 return statistics::momentN(zData, weights, 3); 00168 } 00169 00170 00171 // Computes the weighted kurtosis (4rd moment) about the given mean value. 00172 // Assumes weights sum to 1 00173 mrs_real 00174 statistics::kurtosisWeighted(const realvec& data, const realvec& weights, mrs_real mean) 00175 { 00176 realvec zData = zDataWeighted(data, weights, mean); 00177 return statistics::momentN(zData, weights, 4) - 3.0; 00178 } 00179