Mercurial > hg > medcouple

annotate jmedcouple.c++ @ 28:65f6fad65f49

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jmedcouple: get rid of unused trace_lev parameter
author Jordi Gutiérrez Hermoso <jordigh@octave.org>
date Sun, 18 Jan 2015 20:41:04 -0500
parents 40cbfb64e952
children cf8c8c825c6d
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1 #include <vector>
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2 #include <limits>
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3 #include <iostream>
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4 #include <string>
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5 #include <fstream>
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6 #include <iomanip>
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7 #include <algorithm>
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8 #include <utility>
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9
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10 using namespace std;
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11
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12 template <typename T>
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13 int signum(T val) {
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14 return (T(0) < val) - (val < T(0));
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15 }
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16
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17 template <typename Container, typename Out = typename Container::value_type>
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18 Out sum(const Container& C) {
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19 return accumulate(C.begin(), C.end(), Out());
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20 }
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21
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22 /*
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23 This computes the weighted median of array A with corresponding
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24 weights W.
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25 */
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26 double wmedian(const vector<double>& A,
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27 const vector<int>& W)
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28 {
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29 typedef pair<double,int> aw_t;
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30
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31 int n = A.size();
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32 vector<aw_t> AW(n);
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33 for (int i = 0; i < n; i ++)
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34 AW[i] = make_pair(A[i], W[i]);
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35
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36 long wtot = sum(W);
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37
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38 int beg = 0;
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39 int end = n - 1;
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40
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41 while (true) {
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42 int mid = (beg + end)/2;
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43 nth_element(AW.begin(), AW.begin() + mid, AW.end(),
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44 [](const aw_t& l, const aw_t& r){return l.first > r.first;});
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45 double trial = AW[mid].first;
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46
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47 long wleft = 0, wright = 0;
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48
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49 for (aw_t& aw: AW ) {
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50 if (aw.first > trial)
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51 wleft += aw.second;
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52 else
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53 // This also includes a == trial, i.e. the "middle" weight.
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54 wright += aw.second;
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55 }
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56
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57 if (2*wleft > wtot)
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58 end = mid;
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59 else if (2*wright < wtot)
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60 beg = mid;
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61 else
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62 return trial;
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63 }
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64
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65 return 0;
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66 }
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67
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68 double medcouple(const std::vector<double>& X,
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69 double eps1 = numeric_limits<double>::epsilon(),
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70 double eps2 = numeric_limits<double>::min())
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71 {
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72 size_t n = X.size(), n2 = (n - 1)/2;
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73
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74 if (n < 3)
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75 return 0;
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76
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77 vector<double> Z = X;
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78 sort(Z.begin(), Z.end(), std::greater<double>());
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79
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80 double Zmed;
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81 if (n % 2 == 1)
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82 Zmed = Z[n2];
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83 else
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84 Zmed = (Z[n2] + Z[n2 + 1])/2;
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85
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86 // Check if the median is at the edges up to relative epsilon
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87 if (abs(Z[0] - Zmed) < eps1*(eps1 + abs(Zmed)))
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88 return -1.0;
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89 if (abs(Z[n - 1] - Zmed) < eps1*(eps1 + abs(Zmed)))
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90 return 1.0;
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91
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92 // Centre Z wrt median, so that median(Z) = 0.
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93 for_each(Z.begin(), Z.end(), [&](double& z){ z -= Zmed;});
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94
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95 // Scale inside [-0.5, 0.5], for greater numerical stability.
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96 double Zden = 2*max(Z[0], -Z[n - 1]);
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97 for_each(Z.begin(), Z.end(), [&](double& z){z /= Zden;});
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98 Zmed /= Zden;
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99
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100 double Zeps = eps1*(eps1 + abs(Zmed));
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101
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102 // These overlap on the entries that are tied with the median
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103 vector<double> Zplus, Zminus;
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104 copy_if(Z.begin(), Z.end(), back_inserter(Zplus),
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105 [=](double z){return z >= -Zeps;});
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106 copy_if(Z.begin(), Z.end(), back_inserter(Zminus),
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107 [=](double z){return Zeps >= z;});
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108
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109 size_t
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110 n_plus = Zplus.size(),
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111 n_minus = Zminus.size();
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112
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113 /*
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114 Kernel function h for the medcouple, closing over the values of
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115 Zplus and Zminus just defined above.
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116
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117 In case a and be are within epsilon of the median, the kernel
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118 is the signum of their position.
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119 */
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120 auto h_kern = [&](int i, int j) {
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121 double a = Zplus[i];
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122 double b = Zminus[j];
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123
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124 double h;
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125 if (abs(a - b) <= 2*eps2)
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126 h = signum(n_plus - 1 - i - j);
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127 else
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128 h = (a + b)/(a - b);
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129
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130 return h;
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131 };
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132
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133 // Init left and right borders
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134 vector<int> L(n_plus, 0);
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135 vector<int> R(n_plus, n_minus - 1);
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136
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137 long Ltot = 0;
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138 long Rtot = n_minus*n_plus;
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139 long medc_idx = Rtot/2;
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140
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141 // kth pair algorithm (Johnson & Mizoguchi)
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142 while (Rtot - Ltot > n_plus) {
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143 // First, compute the median inside the given bounds
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144 vector<double> A;
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145 vector<int> W;
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146 for (int i = 0; i < n_plus; i++) {
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147 if (L[i] <= R[i]) {
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148 A.push_back(h_kern(i, (L[i] + R[i])/2));
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149 W.push_back(R[i] - L[i] + 1);
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150 }
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151 }
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152 double Am = wmedian(A, W);
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153
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154 double Am_eps = eps1*(eps1 + abs(Am));
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155
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156 //Compute new left and right boundaries, based on the weighted
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157 //median
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158 vector<int> P(n_plus), Q(n_plus);
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159
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160 {
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161 int j = 0;
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162 for (int i = n_plus - 1; i >= 0; i--) {
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163 while (j < n_minus and h_kern(i, j) - Am > Am_eps)
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164 j++;
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165 P[i] = j - 1;
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166 }
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167 }
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168
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169 {
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170 int j = n_minus - 1;
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171 for (int i = 0; i < n_plus; i++) {
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172 while (j >= 0 and h_kern(i, j) - Am < -Am_eps)
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173 j--;
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174 Q[i] = j + 1;
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175 }
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176 }
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177
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178 long
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179 sumP = sum(P) + n_plus,
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180 sumQ = sum(Q);
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181
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182 if (medc_idx <= sumP - 1) {
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183 R = P;
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184 Rtot = sumP;
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185 }
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186 else {
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187 if (medc_idx > sumQ - 1) {
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188 L = Q;
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189 Ltot = sumQ;
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190 }
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191 else
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192 return Am;
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193 }
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194 }
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195
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196 // Didn't find the median, but now we have a very small search space
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197 // to find it in, just between the left and right boundaries. This
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198 // space is of size Rtot - Ltot which is <= n_plus
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199 vector<double> A;
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200 for (int i = 0; i < n_plus; i++) {
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201 for (int j = L[i]; j <= R[i]; j++)
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202 A.push_back(h_kern(i, j));
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203 }
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204 nth_element(A.begin(), A.begin() + medc_idx - Ltot, A.end(),
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205 [](double x, double y) {return x > y;});
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206
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207 double Am = A[medc_idx - Ltot];
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208 return Am;
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209 }
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210
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211
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212
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213 int main(int argc, char** argv) {
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214 double
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215 eps1 = numeric_limits<double>::epsilon(),
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216 eps2 = numeric_limits<double>::min();
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217
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218 string fname;
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219 if (argc > 1) {
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220 fname = argv[1];
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221 }
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222 else {
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223 cerr << "Please provide input file." << endl;
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224 return 1;
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225 }
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226
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227 ifstream ifs(fname);
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228 if (not ifs) {
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229 cerr << "File " << fname << " not found." << endl;
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230 return 1;
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231 }
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232
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233 vector<double> data;
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234 double datum;
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235 while (ifs >> datum) {
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236 data.push_back(datum);
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237 }
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238
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239 cout << setprecision(16)
28
65f6fad65f49 jmedcouple: get rid of unused trace_lev parameter
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240 << medcouple(data, eps1, eps2) << endl;
25
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241
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242 return 0;
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243 }
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244