1 | #ifndef _theplu_yat_normalizer_qquantile_normalizer_ |
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2 | #define _theplu_yat_normalizer_qquantile_normalizer_ |
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3 | |
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4 | /* |
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5 | Copyright (C) 2009 Jari Häkkinen, Peter Johansson |
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6 | |
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7 | This file is part of the yat library, http://dev.thep.lu.se/yat |
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8 | |
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9 | The yat library is free software; you can redistribute it and/or |
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10 | modify it under the terms of the GNU General Public License as |
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11 | published by the Free Software Foundation; either version 3 of the |
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12 | License, or (at your option) any later version. |
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13 | |
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14 | The yat library is distributed in the hope that it will be useful, |
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15 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
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16 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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17 | General Public License for more details. |
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18 | |
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19 | You should have received a copy of the GNU General Public License |
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20 | along with yat. If not, see <http://www.gnu.org/licenses/>. |
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21 | */ |
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22 | |
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23 | #include "yat/regression/CSplineInterpolation.h" |
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24 | #include "yat/utility/DataWeight.h" |
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25 | #include "yat/utility/iterator_traits.h" |
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26 | #include "yat/utility/Vector.h" |
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27 | #include "yat/utility/yat_assert.h" |
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28 | |
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29 | #include <algorithm> |
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30 | #include <iterator> |
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31 | #include <stdexcept> |
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32 | #include <vector> |
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33 | |
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34 | namespace theplu { |
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35 | namespace yat { |
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36 | namespace utility { |
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37 | class VectorBase; |
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38 | } |
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39 | namespace normalizer { |
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40 | |
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41 | /** |
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42 | \brief Perform Q-quantile normalization |
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43 | |
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44 | After a Q-quantile normalization each column has approximately |
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45 | the same distribution of data (the Q-quantiles are the |
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46 | same). Also, within each column the rank of an element is not |
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47 | changed. |
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48 | |
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49 | There is currently no weighted version of qQuantileNormalizer |
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50 | |
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51 | The normalization goes like this |
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52 | - Data is not assumed to be sorted. |
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53 | - Partition sorted target data in N parts. N must be 3 larger |
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54 | because of requirements from the underlying cspline fit |
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55 | - Calculate the arithmetic mean for each part, the mean is |
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56 | assigned to the mid point of each part. |
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57 | - Do the above for the data to be tranformed (called source |
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58 | here). |
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59 | - For each part, calculate the difference between the target and |
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60 | the source. Now we have N differences d_i with associated rank |
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61 | (midpoint of each part). |
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62 | - Create a cubic spline fit to this difference vector d. The |
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63 | resulting curve is used to recalculate all column values. |
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64 | - Use the cubic spline fit for values within the cubic spline |
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65 | fit range [midpoint 1st part, midpoint last part]. |
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66 | - For data outside the cubic spline fit use linear |
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67 | extrapolation, i.e., a constant shift. d_first for points |
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68 | below fit range, and d_last for points above fit range. |
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69 | |
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70 | \since New in yat 0.5 |
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71 | */ |
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72 | class qQuantileNormalizer |
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73 | { |
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74 | public: |
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75 | /** |
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76 | \brief Documentation please. |
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77 | |
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78 | \a Q is the number of parts and must be within \f$ [3,N] \f$ |
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79 | where \f$ N \f$ is the total number of data points in the |
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80 | target. However, if \f$ N \f$ is larger than the number of points |
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81 | in the data to be normalized the behaviour of the code is |
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82 | undefined. Keep \f$ N \f$ equal to or less than the smallest |
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83 | number of data points in the target or each data set to be |
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84 | normalized against a given target. The lower bound of three is |
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85 | due to restrictions in the cspline fit utilized in the |
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86 | normalization. |
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87 | */ |
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88 | template<typename BidirectionalIterator> |
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89 | qQuantileNormalizer(BidirectionalIterator first, BidirectionalIterator last, |
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90 | unsigned int Q); |
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91 | |
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92 | /** |
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93 | \brief perform the Q-quantile normalization. |
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94 | |
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95 | It is possible to normalize "in place"; it is permissible for |
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96 | \a matrix and \a result to reference the same Matrix. |
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97 | |
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98 | \note dimensions of \a matrix and \a result must match. |
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99 | */ |
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100 | template<typename RandomAccessIterator1, typename RandomAccessIterator2> |
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101 | RandomAccessIterator2 operator()(RandomAccessIterator1 first, |
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102 | RandomAccessIterator1 last, |
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103 | RandomAccessIterator2 result) const; |
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104 | |
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105 | private: |
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106 | |
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107 | /** |
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108 | \brief Partition a vector of data into equal sizes. |
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109 | |
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110 | The class also calculates the average of each part and assigns |
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111 | the average to the mid point of each part. The midpoint is a |
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112 | double, i.e., it is not forced to be an integer index. |
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113 | */ |
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114 | class Partitioner |
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115 | { |
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116 | public: |
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117 | /** |
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118 | \brief Create the partition and perform required calculations. |
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119 | */ |
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120 | template<typename BidirectionalIterator> |
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121 | Partitioner(BidirectionalIterator first, BidirectionalIterator last, |
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122 | unsigned int N); |
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123 | |
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124 | /** |
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125 | \brief Return the averages for each part. |
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126 | |
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127 | \return The average vector. |
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128 | */ |
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129 | const utility::Vector& averages(void) const; |
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130 | |
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131 | /** |
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132 | \brief Return the mid point for each partition. |
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133 | |
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134 | \return The index vector. |
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135 | */ |
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136 | const utility::Vector& index(void) const; |
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137 | |
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138 | /** |
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139 | \return The number of parts. |
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140 | */ |
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141 | size_t size(void) const; |
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142 | |
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143 | private: |
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144 | // unweighted "constructor" |
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145 | template<typename Iterator> |
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146 | void build(Iterator first, Iterator last, unsigned int N, |
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147 | utility::unweighted_iterator_tag); |
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148 | void init(const utility::VectorBase&, unsigned int N); |
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149 | |
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150 | utility::Vector average_; |
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151 | utility::Vector index_; |
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152 | }; |
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153 | |
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154 | |
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155 | Partitioner target_; |
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156 | }; |
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157 | |
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158 | |
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159 | // template implementations |
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160 | |
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161 | template<typename BidirectionalIterator> |
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162 | qQuantileNormalizer::qQuantileNormalizer(BidirectionalIterator first, |
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163 | BidirectionalIterator last, |
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164 | unsigned int Q) |
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165 | : target_(Partitioner(first, last, Q)) |
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166 | { |
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167 | utility::yat_assert<std::runtime_error>(Q>2, |
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168 | "qQuantileNormalizer: Q too small"); |
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169 | } |
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170 | |
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171 | |
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172 | template<typename RandomAccessIterator1, typename RandomAccessIterator2> |
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173 | RandomAccessIterator2 |
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174 | qQuantileNormalizer::operator()(RandomAccessIterator1 first, |
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175 | RandomAccessIterator1 last, |
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176 | RandomAccessIterator2 result) const |
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177 | { |
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178 | size_t N = last-first; |
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179 | utility::yat_assert<std::runtime_error> |
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180 | (N >= target_.size(), "qQuantileNormalizer: Input range too small"); |
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181 | |
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182 | std::vector<size_t> sorted_index(last-first); |
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183 | utility::sort_index(first, last, sorted_index); |
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184 | |
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185 | Partitioner source(first, last, target_.size()); |
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186 | utility::Vector diff(source.averages()); |
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187 | diff-=target_.averages(); |
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188 | const utility::Vector& idx=target_.index(); |
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189 | regression::CSplineInterpolation cspline(idx,diff); |
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190 | |
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191 | // linear interpolation for first part, i.e., use first diff for |
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192 | // all points in the first part. |
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193 | size_t start=0; |
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194 | size_t end=static_cast<unsigned int>(idx(0)); |
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195 | // The first condition below takes care of limiting case number |
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196 | // of parts approximately equal to the number of matrix rows and |
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197 | // the second condition makes sure that index is large enough |
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198 | // when using cspline below ... the static cast above takes the |
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199 | // floor whereas we want to take the "roof" forcing next index |
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200 | // range to be within interpolation range for the cspline. |
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201 | if ((end==0) || (end<idx(0))) |
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202 | ++end; |
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203 | for (size_t row=start; row<end; ++row) { |
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204 | size_t srow=sorted_index[row]; |
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205 | result[srow] = first[srow] - diff(0); |
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206 | } |
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207 | |
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208 | // cspline interpolation for all data between the mid points of |
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209 | // the first and last part |
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210 | start=end; |
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211 | end=static_cast<unsigned int>(idx(target_.size()-1)); |
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212 | // take care of limiting case number of parts approximately |
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213 | // equal to the number of matrix rows |
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214 | if (end==(static_cast<size_t>(N-1)) ) |
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215 | --end; |
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216 | for (size_t row=start; row<=end; ++row) { |
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217 | size_t srow=sorted_index[row]; |
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218 | result[srow] = first[srow] - cspline.evaluate(row) ; |
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219 | } |
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220 | |
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221 | // linear interpolation for last part, i.e., use last diff for |
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222 | // all points in the last part. |
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223 | start=end+1; |
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224 | end=N; |
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225 | for (size_t row=start; row<end; ++row) { |
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226 | size_t srow=sorted_index[row]; |
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227 | result[srow] = first[srow] - diff(diff.size()-1); |
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228 | } |
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229 | return result + N; |
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230 | } |
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231 | |
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232 | |
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233 | template<typename BidirectionalIterator> |
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234 | qQuantileNormalizer::Partitioner::Partitioner(BidirectionalIterator first, |
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235 | BidirectionalIterator last, |
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236 | unsigned int N) |
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237 | : average_(utility::Vector(N)), index_(utility::Vector(N)) |
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238 | { |
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239 | typedef typename |
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240 | utility::weighted_iterator_traits<BidirectionalIterator>::type tag; |
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241 | build(first, last, N, tag()); |
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242 | |
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243 | } |
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244 | |
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245 | |
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246 | template<typename Iterator> |
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247 | void qQuantileNormalizer::Partitioner::build(Iterator first, Iterator last, |
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248 | unsigned int N, |
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249 | utility::unweighted_iterator_tag) |
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250 | { |
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251 | utility::Vector vec(std::distance(first, last)); |
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252 | std::copy(first, last, vec.begin()); |
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253 | std::sort(vec.begin(), vec.end()); |
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254 | init(vec, N); |
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255 | } |
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256 | |
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257 | |
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258 | }}} // end of namespace normalizer, yat and thep |
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259 | |
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260 | #endif |
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