1 | /* |
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2 | * Cma.cpp |
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3 | * |
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4 | * Created on: Dec 16, 2009 |
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5 | * Author: Breno Faria |
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6 | * |
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7 | * Institute of Microbiology (Technical University Munich) |
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8 | * http://www.arb-home.de/ |
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9 | */ |
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10 | |
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11 | #include <iostream> |
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12 | #include <iomanip> |
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13 | #include <time.h> |
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14 | |
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15 | #include "Cma.h" |
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16 | |
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17 | //>--------------------------Global definitions-------------------------------- |
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18 | |
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19 | // Some local function prototypes. |
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20 | void unifyCluster(int cluster1, int cluster2, VectorXi & result); |
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21 | |
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22 | //>-----------------------local helper functions------------------------------- |
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23 | |
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24 | /** |
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25 | * Helper function for Cma::computeClusters. Compares MITuples by |
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26 | * mutual information value. |
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27 | * |
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28 | * @param first: the first MITuple |
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29 | * |
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30 | * @param second: the second MITuple |
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31 | * |
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32 | * @returns whether the first element should be placed before the second. |
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33 | */ |
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34 | static bool compareMITuples(MITuple first, MITuple second) { |
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35 | return first.MI > second.MI; |
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36 | } |
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37 | |
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38 | /** |
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39 | * Helper function for Cma::computeClusters. Unites two clusters. |
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40 | * |
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41 | * @param cluster1: the index of the first cluster. |
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42 | * |
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43 | * @param cluster2: the index of the second cluster. |
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44 | */ |
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45 | void unifyCluster(int cluster1, int cluster2, VectorXi & result) { |
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46 | size_t size = result.size(); |
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47 | for (size_t i = 0; i < size; ++i) { |
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48 | if (result[i] == cluster2) { |
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49 | result[i] = cluster1; |
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50 | } |
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51 | } |
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52 | } |
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53 | |
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54 | //>---------------------------Public methods----------------------------------- |
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55 | |
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56 | /** |
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57 | * Constructor. |
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58 | * |
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59 | * @param seq_num: the number of sequences. |
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60 | * |
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61 | * @param alph: the vector containing the alphabet. Notice that letters of the |
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62 | * alphabet might be longer than one character. This is not used |
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63 | * so far, but limiting the length to 1 seems wrong... |
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64 | */ |
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65 | Cma::Cma(vector<string> & alph, int seq_num) { |
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66 | |
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67 | initAlphabet(alph); |
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68 | num_of_seqs = seq_num; |
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69 | |
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70 | } |
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71 | |
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72 | /** |
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73 | * Destructor. |
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74 | */ |
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75 | Cma::~Cma() { |
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76 | } |
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77 | |
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78 | /** |
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79 | * Computes the mutual information of position pairs in a set of |
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80 | * sequences. |
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81 | * Mutual information can be defined as: |
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82 | * |
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83 | * MI(pos1, pos2) = H(pos1) + H(pos2) - H(pos1, pos2), |
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84 | * |
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85 | * i.e. the sum of entropies at two positions minus the joint entropy |
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86 | * of these positions. |
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87 | * |
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88 | * @param seq: the multiple sequence alignment. |
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89 | * |
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90 | * @returns a matrix with the MI values. |
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91 | */ |
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92 | MatrixXd Cma::computeMutualInformation(VecVecType & seq) { |
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93 | |
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94 | JointEntropy = computeJointEntropy(seq); |
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95 | |
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96 | JointEntropy = JointEntropy + JointEntropy.adjoint() - JointEntropy.diagonal().asDiagonal(); |
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97 | |
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98 | entropy = JointEntropy.diagonal(); |
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99 | |
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100 | cout << "computing Mutual Information... "; |
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101 | flush(cout); |
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102 | clock_t start = clock(); |
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103 | |
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104 | VectorXd Ones = VectorXd::Ones(entropy.size()); |
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105 | MatrixXd Hx = (entropy * Ones.transpose()).transpose(); |
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106 | MatrixXd Hy = Hx.transpose(); |
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107 | |
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108 | MutualInformation = Hx + Hy - JointEntropy; |
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109 | |
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110 | cout << "completed in " << ((double) clock() - start) / CLOCKS_PER_SEC |
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111 | << "s." << endl; |
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112 | |
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113 | return MutualInformation; |
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114 | |
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115 | } |
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116 | |
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117 | /** |
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118 | * Computes the noiseless mutual information, or MIp (see classdoc), which is |
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119 | * defined as: |
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120 | * |
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121 | * MIp(pos1, pos2) = MI(pos1, pos2) - (mMI(pos1) * mMI(pos2)) / mMI, |
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122 | * |
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123 | * where MIp is the noiseless mutual information between positions 1 and 2 and |
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124 | * MI similarly. mMI(x) is the mean mutual information of position x, which is |
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125 | * defined as: |
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126 | * |
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127 | * mMI(pos1) = 1 / m * \sum_{i \in positions} MI(pos1, i), where m is the |
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128 | * length of the sequences. |
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129 | * |
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130 | * mMI is the overall mean mutual information, defined as: |
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131 | * |
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132 | * mMI = 2 / m * \sum_{i \in positions} \sum_{j in positions} MI(i, j), where |
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133 | * again m is the length of the sequences. |
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134 | * |
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135 | * @param seq: the multiple sequence alignment. |
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136 | * |
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137 | * @returns the noiseless mutual information. |
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138 | */ |
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139 | MatrixXd Cma::computeMutualInformationP(VecVecType & seq) { |
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140 | |
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141 | if (MutualInformation.size() == 0) { |
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142 | computeMutualInformation(seq); |
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143 | } |
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144 | |
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145 | cout << "computing noiseless Mutual Information (MIp)... "; |
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146 | flush(cout); |
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147 | clock_t start = clock(); |
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148 | /* |
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149 | * We must remove negative MI values (the negative values are artificially |
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150 | * generated, see comments in computeJointEntropy). |
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151 | */ |
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152 | for (int i = 0; i < MutualInformation.rows(); ++i) { |
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153 | for (int j = 0; j < MutualInformation.cols(); ++j) { |
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154 | if (MutualInformation(i, j) < 0.) { |
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155 | MutualInformation(i, j) = 0.; |
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156 | } |
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157 | } |
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158 | } |
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159 | |
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160 | VectorXd mMIs = computeMeanMutualInformationVector(); |
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161 | double mMI = computeOveralMeanMutualInformation(); |
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162 | |
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163 | MutualInformationP = MutualInformation - ((mMIs * mMIs.transpose()) / mMI); |
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164 | |
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165 | cout << "completed in " << ((double) clock() - start) / CLOCKS_PER_SEC |
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166 | << "s." << endl; |
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167 | |
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168 | return MutualInformationP; |
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169 | |
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170 | } |
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171 | |
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172 | /** |
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173 | * Given a MI-matrix, computes the sorted list of the highest MI values. |
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174 | * |
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175 | * @param mutualInformation: a matrix with MI (or MIp) measures. |
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176 | * |
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177 | * @returns the list of tuples of positions sorted by their MI value. |
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178 | */ |
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179 | list<MITuple> Cma::compute_mituples(MatrixXd mutualInformation) { |
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180 | size_t size = mutualInformation.cols(); |
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181 | |
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182 | list<MITuple> mituples; |
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183 | |
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184 | // populate the mituples list with all entries in the upper triangular matrix |
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185 | // of mutualInformation. |
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186 | for (size_t i = 0; i < size; ++i) { |
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187 | for (size_t j = i + 1; j < size; ++j) { |
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188 | MITuple curr; |
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189 | curr.MI = mutualInformation(i, j); |
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190 | curr.pos1 = i; |
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191 | curr.pos2 = j; |
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192 | mituples.push_back(curr); |
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193 | } |
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194 | } |
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195 | |
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196 | // sort mituples by MI-value |
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197 | mituples.sort(compareMITuples); |
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198 | |
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199 | return mituples; |
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200 | } |
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201 | |
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202 | /** |
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203 | * Computes the clusters of positions that are most correlated, up to |
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204 | * threshold. |
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205 | * |
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206 | * @param mituples: the mutualInformation matrix, as generated by |
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207 | * Cma::computeMutualInformation. |
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208 | * |
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209 | * @param size: the original size of the alignment. |
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210 | * |
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211 | * @param threshold: the mutual information threshold. If two positions have |
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212 | * mi < threshold, they won't be united in one cluster. |
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213 | * |
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214 | * @returns a vector with the cluster indices for each position. |
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215 | */ |
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216 | VectorXi Cma::computeClusters(list<MITuple> mituples, size_t size, |
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217 | double threshold) { |
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218 | |
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219 | cout << "computing clusters of correlated positions... "; |
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220 | flush(cout); |
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221 | |
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222 | VectorXi result = VectorXi::Zero(size); |
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223 | |
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224 | //compute the clusters. |
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225 | int cluster = 1; |
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226 | int rest = int(size); |
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227 | for (list<MITuple>::iterator it = mituples.begin(); it != mituples.end(); ++it) { |
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228 | double result1 = abs(result[it->pos1]); |
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229 | double result2 = abs(result[it->pos2]); |
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230 | if (it->MI <= threshold || rest == 0) { |
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231 | break; |
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232 | } |
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233 | if (result1 < epsilon and result2 < epsilon) { |
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234 | result[it->pos1] = cluster; |
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235 | result[it->pos2] = cluster++; |
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236 | rest -= 2; |
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237 | } |
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238 | else if (result1 > epsilon and result2 < epsilon) { |
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239 | result[it->pos2] = result[it->pos1]; |
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240 | rest -= 1; |
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241 | } |
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242 | else if (result1 < epsilon and result2 > epsilon) { |
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243 | result[it->pos1] = result[it->pos2]; |
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244 | rest -= 1; |
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245 | } |
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246 | else if (result1 > epsilon and result2 > epsilon && result1 - result2 > epsilon) { |
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247 | unifyCluster(result[it->pos1], result[it->pos2], result); |
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248 | } |
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249 | } |
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250 | |
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251 | clusters = result; |
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252 | |
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253 | cout << "done." << endl; |
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254 | |
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255 | return result; |
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256 | } |
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257 | |
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258 | //>-------------------------getters and setters-------------------------------- |
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259 | |
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260 | MatrixXd Cma::getEntropy() { |
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261 | |
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262 | return entropy; |
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263 | |
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264 | } |
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265 | |
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266 | MatrixXd Cma::getJointEntropy() { |
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267 | |
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268 | return JointEntropy; |
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269 | |
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270 | } |
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271 | |
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272 | MatrixXd Cma::getMI() { |
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273 | |
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274 | return MutualInformation; |
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275 | |
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276 | } |
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277 | |
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278 | MatrixXd Cma::getMIp() { |
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279 | |
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280 | return MutualInformationP; |
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281 | |
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282 | } |
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283 | |
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284 | VectorXi Cma::getClusters() { |
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285 | |
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286 | return clusters; |
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287 | |
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288 | } |
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289 | |
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290 | //>----------------------------private methods--------------------------------- |
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291 | |
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292 | /** |
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293 | * Here we define the alphabet. |
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294 | */ |
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295 | void Cma::initAlphabet(vector<string> alph) { |
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296 | |
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297 | alphabet = vector<string> (alph); |
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298 | |
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299 | int i = 0; |
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300 | for (vector<string>::iterator it = alph.begin(); it != alph.end(); ++it) { |
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301 | alphabet_map[*it] = i; |
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302 | i++; |
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303 | } |
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304 | for (vector<string>::iterator it = alph.begin(); it != alph.end(); ++it) { |
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305 | for (vector<string>::iterator it2 = alph.begin(); it2 != alph.end(); ++it2) { |
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306 | alphabet_map[*it + *it2] = i; |
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307 | i++; |
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308 | } |
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309 | } |
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310 | alphabet_map["total"] = i; |
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311 | } |
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312 | |
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313 | /** |
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314 | * Computes an approximation of the joint entropy for each pair of positions. |
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315 | * |
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316 | * The joint entropy of two positions in a set of aligned sequences |
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317 | * is defined as: |
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318 | * - ( p(A,A) * log2(p(A,A)) + p(A,C) * log2(p(A,C)) + ... + |
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319 | * p(C,A) * log2(p(C,A)) + p(C,C) * log2(p(C,A)) + ... + |
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320 | * ... + |
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321 | * p(T,A) * log2(p(T,A)) + ... + p(T) * log2(p(T,T)) ), |
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322 | * where p(x,y) is the probability of observing base x at position 1 and |
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323 | * base y at position 2. |
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324 | * |
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325 | * @param seqs: the aligned sequences |
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326 | * |
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327 | * @returns a square matrix with the joint entropy values for |
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328 | * each pair of positions. |
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329 | */ |
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330 | MatrixXd Cma::computeJointEntropy(const VecVecType & seqs) { |
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331 | |
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332 | MapMatrixType hist = buildJointHistogram(seqs); |
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333 | return Cma::computeJointEntropy(hist); |
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334 | |
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335 | } |
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336 | |
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337 | /** |
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338 | * Computes an approximation of the joint entropy for each pair of positions. |
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339 | * The measure also includes an heuristic to penalise mismatches in occurrences |
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340 | * (see the documentation of this project for further explanations). |
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341 | * |
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342 | * @param hist: the histogram of labels for each position in the sequence. |
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343 | * |
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344 | * @returns a square matrix with the joint entropy values for |
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345 | * each pair of positions. |
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346 | */ |
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347 | MatrixXd Cma::computeJointEntropy(MapMatrixType & hist) { |
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348 | |
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349 | cout << "computing joint entropy (this may take a while)... "; |
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350 | flush(cout); |
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351 | clock_t start = clock(); |
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352 | |
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353 | int hist_size = int(hist.size()); |
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354 | MatrixXd result(hist_size, hist_size); |
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355 | result.setZero(hist_size, hist_size); |
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356 | for (unsigned int i = 0; i < (unsigned int) hist_size; ++i) { |
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357 | |
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358 | //progress "bar" |
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359 | if (hist_size > 30 and i % (hist_size / 30) == 0) { |
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360 | cout << "(" << setw(6) << setiosflags(ios::fixed) |
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361 | << setprecision(2) << i / float(hist_size) * 100 << "%)"; |
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362 | flush(cout); |
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363 | } |
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364 | |
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365 | for (unsigned int j = i; j < hist[i].size(); ++j) { |
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366 | int total_i_j = hist[i][j][alphabet_map.at("total")]; |
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367 | int total_i_i = hist[i][i][alphabet_map.at("total")]; |
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368 | int total_j_j = hist[j][j][alphabet_map.at("total")]; |
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369 | int mismatches = total_i_i + total_j_j - 2 * total_i_j; |
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370 | if (total_i_j != 0) { |
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371 | double result_i_j = 0.; |
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372 | for (map<int, int>::iterator it = hist[i][j].begin(); it |
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373 | != hist[i][j].end(); ++it) { |
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374 | double pair = double(it->second) + Cma::epsilon; |
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375 | result_i_j += (pair / total_i_j) * log2(pair / total_i_j); |
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376 | } |
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377 | |
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378 | result(i, j) = -result_i_j + double(mismatches) / (total_i_i |
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379 | + total_j_j) * Cma::penalty; |
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380 | |
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381 | } else { |
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382 | /** |
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383 | * We will only fall into this case if we have two positions which |
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384 | * never occur simultaneously. In this case we cannot say anything about |
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385 | * the MI. |
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386 | * To guarantee that this joint entropy value will not come in our way in |
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387 | * the MI calculation we set it artificially to 5.0, which is 1 greater than |
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388 | * max(H(X) + H(Y)). |
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389 | */ |
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390 | result(i, j) = 5.; |
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391 | } |
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392 | |
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393 | } |
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394 | //progress "bar" |
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395 | if (hist_size > 30 and i % (hist_size / 30) == 0) { |
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396 | cout << "\b\b\b\b\b\b\b\b\b"; |
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397 | } |
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398 | } |
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399 | flush(cout); |
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400 | cout << "completed in " << ((double) clock() - start) / CLOCKS_PER_SEC |
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401 | << "s." << endl; |
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402 | return result; |
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403 | |
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404 | } |
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405 | |
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406 | /** |
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407 | * Checks whether the key is valid (if it pertains to the alphabet). |
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408 | * |
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409 | * @param key: the base to be checked. |
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410 | * |
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411 | * @return whether the key is valid (if it pertains to the alphabet). |
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412 | */ |
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413 | bool Cma::isValid(string & key) { |
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414 | |
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415 | map<string, int>::iterator it = alphabet_map.find(key); |
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416 | return it != alphabet_map.end(); |
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417 | |
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418 | } |
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419 | |
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420 | /** |
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421 | * This method computes a matrix of maps, one for each pair of positions of the |
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422 | * aligned sequences. |
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423 | * Each map has an entry for each pair of occurring letters to count the joint |
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424 | * occurrences of these letters. |
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425 | * |
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426 | * @param alignedSequences: an array of string vectors, containing the sequences. |
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427 | * |
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428 | * @returns a matrix of maps (see method description) |
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429 | */ |
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430 | MapMatrixType Cma::buildJointHistogram(const VecVecType & alignedSequences) { |
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431 | |
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432 | cout << "building histogram (this may take a while)... "; |
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433 | flush(cout); |
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434 | clock_t start = clock(); |
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435 | |
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436 | if (alignedSequences.empty()) { |
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437 | throw "no (marked?) sequences"; |
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438 | } |
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439 | |
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440 | // here we defined one dimension of the matrix as being the same as the |
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441 | // length of the sequences. |
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442 | MapMatrixType result(alignedSequences[0].size(), MapVecType( |
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443 | alignedSequences[0].size())); |
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444 | |
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445 | int ii = 0; |
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446 | // for each sequence: |
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447 | for (VecVecType::const_iterator it = alignedSequences.begin(); it |
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448 | != alignedSequences.end(); ++it) { |
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449 | |
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450 | cout << "(" << setw(6) << setiosflags(ios::fixed) << setprecision(2) |
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451 | << ii / float(num_of_seqs) * 100 << "%)"; |
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452 | flush(cout); |
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453 | |
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454 | // for each first position in the sequence |
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455 | for (size_t i = 0; i < it->size(); ++i) { |
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456 | string key1 = it->at(i); |
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457 | if (isValid(key1)) { |
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458 | |
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459 | //for each second position in the sequence |
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460 | for (size_t j = i; j < it->size(); ++j) { |
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461 | string key2 = it->at(j); |
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462 | if (isValid(key2)) { |
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463 | result[i][j][alphabet_map.at(key1 + key2)] += 1; |
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464 | result[i][j][alphabet_map.at("total")] += 1; |
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465 | } |
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466 | } |
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467 | } |
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468 | } |
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469 | cout << "\b\b\b\b\b\b\b\b\b"; |
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470 | ii++; |
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471 | } |
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472 | flush(cout); |
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473 | cout << "completed in " << ((double) clock() - start) / CLOCKS_PER_SEC |
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474 | << "s." << endl; |
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475 | |
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476 | return result; |
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477 | } |
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478 | |
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479 | /** |
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480 | * Computes the vector of mean mutual information values mMI. |
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481 | * |
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482 | * mMI(pos1) = 1 / m * \sum_{i \in positions} MI(pos1, i), where m is the |
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483 | * length of the sequences. |
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484 | * |
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485 | * @returns the vector of mean mutual information values mMI. |
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486 | */ |
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487 | VectorXd Cma::computeMeanMutualInformationVector() { |
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488 | |
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489 | return MutualInformation.rowwise().sum() / num_of_seqs; |
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490 | |
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491 | } |
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492 | |
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493 | /** |
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494 | * Computes the overall mean mutual information value. |
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495 | * |
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496 | * mMI = 2 / m * \sum_{i \in positions} \sum_{j in positions} MI(i, j), where |
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497 | * again m is the length of the sequences. |
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498 | * |
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499 | * @returns the overall mean mutual information value. |
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500 | */ |
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501 | double Cma::computeOveralMeanMutualInformation() { |
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502 | |
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503 | return 2. * MutualInformation.sum() / num_of_seqs / num_of_seqs; |
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504 | |
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505 | } |
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506 | |
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