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annotate jmedcouple.c++ @ 29:cf8c8c825c6d

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jmedcouple: change all ints to long, to avoid overflow
author Jordi Gutiérrez Hermoso <jordigh@octave.org>
date Sun, 18 Jan 2015 20:42:02 -0500
parents 65f6fad65f49
children 2e277129e81b
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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<long>& W)
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28 {
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29 typedef pair<double, long> aw_t;
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30
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31 long n = A.size();
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32 vector<aw_t> AW(n);
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33 for (long 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 long beg = 0;
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39 long end = n - 1;
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40
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41 while (true) {
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42 long 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 long wleft = 0, wright = 0;
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47
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48 for (aw_t& aw: AW ) {
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49 if (aw.first > trial)
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50 wleft += aw.second;
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51 else
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52 // This also includes a == trial, i.e. the "middle" weight.
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53 wright += aw.second;
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54 }
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55
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56 if (2*wleft > wtot)
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57 end = mid;
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58 else if (2*wright < wtot)
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59 beg = mid;
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60 else
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61 return trial;
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62 }
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63
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64 return 0;
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65 }
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66
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67 double medcouple(const std::vector<double>& X,
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68 double eps1 = numeric_limits<double>::epsilon(),
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69 double eps2 = numeric_limits<double>::min())
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70 {
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71 long n = X.size(), n2 = (n - 1)/2;
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72
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73 if (n < 3)
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74 return 0;
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75
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76 vector<double> Z = X;
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77 sort(Z.begin(), Z.end(), std::greater<double>());
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78
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79 double Zmed;
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80 if (n % 2 == 1)
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81 Zmed = Z[n2];
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82 else
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83 Zmed = (Z[n2] + Z[n2 + 1])/2;
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84
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85 // Check if the median is at the edges up to relative epsilon
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86 if (abs(Z[0] - Zmed) < eps1*(eps1 + abs(Zmed)))
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87 return -1.0;
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88 if (abs(Z[n - 1] - Zmed) < eps1*(eps1 + abs(Zmed)))
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89 return 1.0;
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90
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91 // Centre Z wrt median, so that median(Z) = 0.
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92 for_each(Z.begin(), Z.end(), [&](double& z){ z -= Zmed;});
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93
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94 // Scale inside [-0.5, 0.5], for greater numerical stability.
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95 double Zden = 2*max(Z[0], -Z[n - 1]);
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96 for_each(Z.begin(), Z.end(), [&](double& z){z /= Zden;});
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97 Zmed /= Zden;
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98
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99 double Zeps = eps1*(eps1 + abs(Zmed));
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100
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101 // These overlap on the entries that are tied with the median
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102 vector<double> Zplus, Zminus;
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103 copy_if(Z.begin(), Z.end(), back_inserter(Zplus),
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104 [=](double z){return z >= -Zeps;});
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105 copy_if(Z.begin(), Z.end(), back_inserter(Zminus),
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106 [=](double z){return Zeps >= z;});
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107
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108 long
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109 n_plus = Zplus.size(),
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110 n_minus = Zminus.size();
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111
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112 /*
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113 Kernel function h for the medcouple, closing over the values of
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114 Zplus and Zminus just defined above.
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115
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116 In case a and be are within epsilon of the median, the kernel
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117 is the signum of their position.
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118 */
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119 auto h_kern = [&](long i, long j) {
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120 double a = Zplus[i];
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121 double b = Zminus[j];
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122
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123 double h;
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124 if (abs(a - b) <= 2*eps2)
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125 h = signum(n_plus - 1 - i - j);
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126 else
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127 h = (a + b)/(a - b);
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128
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129 return h;
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130 };
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131
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132 // Init left and right borders
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133 vector<long> L(n_plus, 0);
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134 vector<long> R(n_plus, n_minus - 1);
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135
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136 long Ltot = 0;
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137 long Rtot = n_minus*n_plus;
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138 long medc_idx = Rtot/2;
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139
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140 // kth pair algorithm (Johnson & Mizoguchi)
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141 while (Rtot - Ltot > n_plus) {
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142
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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<long> W;
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146 for (long 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<long> P(n_plus), Q(n_plus);
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159
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160 {
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161 long j = 0;
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162 for (long 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 long j = n_minus - 1;
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171 for (long 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 (long i = 0; i < n_plus; i++) {
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201 for (long 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)
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240 << medcouple(data, eps1, eps2) << endl;
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241
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242 return 0;
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243 }
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244