1 | #include "emix.h" |
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2 | |
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3 | namespace bdm { |
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4 | |
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5 | void emix::set_parameters ( const vec &w0, const Array<shared_ptr<epdf> > &Coms0 ) { |
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6 | w = w0 / sum ( w0 ); |
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7 | |
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8 | bool isnamed = Coms0 ( 0 )->isnamed(); |
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9 | RV tmp_rv; |
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10 | if ( isnamed ) tmp_rv = Coms0 ( 0 )->_rv(); |
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11 | Coms = Coms0; |
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12 | |
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13 | if ( isnamed ) epdf::set_rv ( tmp_rv ); //coms aer already OK, no need for set_rv |
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14 | } |
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15 | |
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16 | void emix::validate (){ |
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17 | dim = Coms ( 0 )->dimension(); |
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18 | bool isnamed = Coms ( 0 )->isnamed(); |
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19 | int i; |
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20 | RV tmp_rv; |
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21 | if ( isnamed ) tmp_rv = Coms ( 0 )->_rv(); |
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22 | for ( i = 0; i < w.length(); i++ ) { |
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23 | bdm_assert ( dim == ( Coms ( i )->dimension() ), "Component sizes do not match!" ); |
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24 | bdm_assert ( !isnamed || tmp_rv.equal ( Coms ( i )->_rv() ), "Component RVs do not match!" ); |
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25 | } |
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26 | |
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27 | } |
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28 | |
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29 | |
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30 | |
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31 | |
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32 | vec emix::sample() const { |
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33 | //Sample which component |
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34 | vec cumDist = cumsum ( w ); |
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35 | double u0; |
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36 | #pragma omp critical |
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37 | u0 = UniRNG.sample(); |
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38 | |
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39 | int i = 0; |
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40 | while ( ( cumDist ( i ) < u0 ) && ( i < ( w.length() - 1 ) ) ) { |
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41 | i++; |
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42 | } |
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43 | |
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44 | return Coms ( i )->sample(); |
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45 | } |
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46 | |
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47 | vec emix::mean() const { |
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48 | int i; |
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49 | vec mu = zeros ( dim ); |
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50 | for ( i = 0; i < w.length(); i++ ) { |
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51 | mu += w ( i ) * Coms ( i )->mean(); |
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52 | } |
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53 | return mu; |
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54 | } |
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55 | |
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56 | vec emix::variance() const { |
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57 | //non-central moment |
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58 | vec mom2 = zeros ( dim ); |
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59 | for ( int i = 0; i < w.length(); i++ ) { |
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60 | mom2 += w ( i ) * ( Coms ( i )->variance() + pow ( Coms ( i )->mean(), 2 ) ); |
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61 | } |
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62 | //central moment |
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63 | return mom2 - pow ( mean(), 2 ); |
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64 | } |
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65 | |
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66 | double emix::evallog ( const vec &val ) const { |
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67 | int i; |
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68 | double sum = 0.0; |
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69 | for ( i = 0; i < w.length(); i++ ) { |
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70 | sum += w ( i ) * exp ( Coms ( i )->evallog ( val ) ); |
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71 | } |
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72 | if ( sum == 0.0 ) { |
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73 | sum = std::numeric_limits<double>::epsilon(); |
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74 | } |
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75 | double tmp = log ( sum ); |
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76 | bdm_assert_debug ( std::isfinite ( tmp ), "Infinite" ); |
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77 | return tmp; |
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78 | } |
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79 | |
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80 | vec emix::evallog_mat ( const mat &Val ) const { |
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81 | vec x = zeros ( Val.cols() ); |
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82 | for ( int i = 0; i < w.length(); i++ ) { |
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83 | x += w ( i ) * exp ( Coms ( i )->evallog_mat ( Val ) ); |
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84 | } |
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85 | return log ( x ); |
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86 | }; |
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87 | |
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88 | mat emix::evallog_coms ( const mat &Val ) const { |
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89 | mat X ( w.length(), Val.cols() ); |
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90 | for ( int i = 0; i < w.length(); i++ ) { |
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91 | X.set_row ( i, w ( i ) *exp ( Coms ( i )->evallog_mat ( Val ) ) ); |
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92 | } |
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93 | return X; |
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94 | } |
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95 | |
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96 | shared_ptr<epdf> emix::marginal ( const RV &rv ) const { |
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97 | emix *tmp = new emix(); |
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98 | shared_ptr<epdf> narrow ( tmp ); |
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99 | marginal ( rv, *tmp ); |
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100 | return narrow; |
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101 | } |
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102 | |
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103 | void emix::marginal ( const RV &rv, emix &target ) const { |
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104 | bdm_assert ( isnamed(), "rvs are not assigned" ); |
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105 | |
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106 | Array<shared_ptr<epdf> > Cn ( Coms.length() ); |
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107 | for ( int i = 0; i < Coms.length(); i++ ) { |
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108 | Cn ( i ) = Coms ( i )->marginal ( rv ); |
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109 | } |
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110 | |
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111 | target.set_parameters ( w, Cn ); |
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112 | target.validate(); |
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113 | } |
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114 | |
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115 | shared_ptr<pdf> emix::condition ( const RV &rv ) const { |
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116 | bdm_assert ( isnamed(), "rvs are not assigned" ); |
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117 | mratio *tmp = new mratio ( this, rv ); |
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118 | return shared_ptr<pdf> ( tmp ); |
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119 | } |
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120 | |
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121 | void egiwmix::set_parameters ( const vec &w0, const Array<egiw*> &Coms0, bool copy ) { |
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122 | w = w0 / sum ( w0 ); |
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123 | dim = Coms0 ( 0 )->dimension(); |
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124 | int i; |
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125 | for ( i = 0; i < w.length(); i++ ) { |
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126 | bdm_assert_debug ( dim == ( Coms0 ( i )->dimension() ), "Component sizes do not match!" ); |
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127 | } |
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128 | if ( copy ) { |
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129 | Coms.set_length ( Coms0.length() ); |
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130 | for ( i = 0; i < w.length(); i++ ) { |
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131 | bdm_error ( "Not implemented" ); |
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132 | // *Coms ( i ) = *Coms0 ( i ); |
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133 | } |
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134 | destroyComs = true; |
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135 | } else { |
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136 | Coms = Coms0; |
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137 | destroyComs = false; |
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138 | } |
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139 | } |
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140 | |
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141 | vec egiwmix::sample() const { |
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142 | //Sample which component |
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143 | vec cumDist = cumsum ( w ); |
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144 | double u0; |
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145 | #pragma omp critical |
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146 | u0 = UniRNG.sample(); |
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147 | |
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148 | int i = 0; |
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149 | while ( ( cumDist ( i ) < u0 ) && ( i < ( w.length() - 1 ) ) ) { |
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150 | i++; |
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151 | } |
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152 | |
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153 | return Coms ( i )->sample(); |
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154 | } |
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155 | |
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156 | vec egiwmix::mean() const { |
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157 | int i; |
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158 | vec mu = zeros ( dim ); |
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159 | for ( i = 0; i < w.length(); i++ ) { |
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160 | mu += w ( i ) * Coms ( i )->mean(); |
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161 | } |
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162 | return mu; |
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163 | } |
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164 | |
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165 | vec egiwmix::variance() const { |
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166 | // non-central moment |
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167 | vec mom2 = zeros ( dim ); |
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168 | for ( int i = 0; i < w.length(); i++ ) { |
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169 | // pow is overloaded, we have to use another approach |
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170 | mom2 += w ( i ) * ( Coms ( i )->variance() + elem_mult ( Coms ( i )->mean(), Coms ( i )->mean() ) ); |
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171 | } |
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172 | // central moment |
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173 | // pow is overloaded, we have to use another approach |
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174 | return mom2 - elem_mult ( mean(), mean() ); |
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175 | } |
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176 | |
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177 | shared_ptr<epdf> egiwmix::marginal ( const RV &rv ) const { |
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178 | emix *tmp = new emix(); |
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179 | shared_ptr<epdf> narrow ( tmp ); |
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180 | marginal ( rv, *tmp ); |
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181 | return narrow; |
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182 | } |
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183 | |
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184 | void egiwmix::marginal ( const RV &rv, emix &target ) const { |
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185 | bdm_assert_debug ( isnamed(), "rvs are not assigned" ); |
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186 | |
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187 | Array<shared_ptr<epdf> > Cn ( Coms.length() ); |
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188 | for ( int i = 0; i < Coms.length(); i++ ) { |
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189 | Cn ( i ) = Coms ( i )->marginal ( rv ); |
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190 | } |
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191 | |
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192 | target.set_parameters ( w, Cn ); |
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193 | target.validate(); |
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194 | } |
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195 | |
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196 | egiw* egiwmix::approx() { |
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197 | // NB: dimx == 1 !!! |
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198 | // The following code might look a bit spaghetti-like, |
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199 | // consult Dedecius, K. et al.: Partial forgetting in AR models. |
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200 | |
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201 | double sumVecCommon; // common part for many terms in eq. |
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202 | int len = w.length(); // no. of mix components |
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203 | int dimLS = Coms ( 1 )->_V()._D().length() - 1; // dim of LS |
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204 | vec vecNu ( len ); // vector of dfms of components |
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205 | vec vecD ( len ); // vector of LS reminders of comps. |
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206 | vec vecCommon ( len ); // vector of common parts |
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207 | mat matVecsTheta; // matrix which rows are theta vects. |
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208 | |
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209 | // fill in the vectors vecNu, vecD and matVecsTheta |
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210 | for ( int i = 0; i < len; i++ ) { |
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211 | vecNu.shift_left ( Coms ( i )->_nu() ); |
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212 | vecD.shift_left ( Coms ( i )->_V()._D() ( 0 ) ); |
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213 | matVecsTheta.append_row ( Coms ( i )->est_theta() ); |
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214 | } |
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215 | |
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216 | // calculate the common parts and their sum |
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217 | vecCommon = elem_mult ( w, elem_div ( vecNu, vecD ) ); |
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218 | sumVecCommon = sum ( vecCommon ); |
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219 | |
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220 | // LS estimator of theta |
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221 | vec aprEstTheta ( dimLS ); |
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222 | aprEstTheta.zeros(); |
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223 | for ( int i = 0; i < len; i++ ) { |
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224 | aprEstTheta += matVecsTheta.get_row ( i ) * vecCommon ( i ); |
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225 | } |
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226 | aprEstTheta /= sumVecCommon; |
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227 | |
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228 | |
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229 | // LS estimator of dfm |
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230 | double aprNu; |
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231 | double A = log ( sumVecCommon ); // Term 'A' in equation |
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232 | |
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233 | for ( int i = 0; i < len; i++ ) { |
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234 | A += w ( i ) * ( log ( vecD ( i ) ) - psi ( 0.5 * vecNu ( i ) ) ); |
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235 | } |
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236 | |
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237 | aprNu = ( 1 + sqrt ( 1 + 2 * ( A - LOG2 ) / 3 ) ) / ( 2 * ( A - LOG2 ) ); |
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238 | |
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239 | |
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240 | // LS reminder (term D(0,0) in C-syntax) |
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241 | double aprD = aprNu / sumVecCommon; |
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242 | |
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243 | // Aproximation of cov |
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244 | // the following code is very numerically sensitive, thus |
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245 | // we have to eliminate decompositions etc. as much as possible |
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246 | mat aprC = zeros ( dimLS, dimLS ); |
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247 | for ( int i = 0; i < len; i++ ) { |
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248 | aprC += Coms ( i )->est_theta_cov().to_mat() * w ( i ); |
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249 | vec tmp = ( matVecsTheta.get_row ( i ) - aprEstTheta ); |
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250 | aprC += vecCommon ( i ) * outer_product ( tmp, tmp ); |
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251 | } |
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252 | |
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253 | // Construct GiW pdf :: BEGIN |
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254 | ldmat aprCinv ( inv ( aprC ) ); |
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255 | vec D = concat ( aprD, aprCinv._D() ); |
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256 | mat L = eye ( dimLS + 1 ); |
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257 | L.set_submatrix ( 1, 0, aprCinv._L() * aprEstTheta ); |
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258 | L.set_submatrix ( 1, 1, aprCinv._L() ); |
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259 | ldmat aprLD ( L, D ); |
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260 | |
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261 | egiw* aprgiw = new egiw ( 1, aprLD, aprNu ); |
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262 | return aprgiw; |
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263 | }; |
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264 | |
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265 | double mprod::evallogcond ( const vec &val, const vec &cond ) { |
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266 | int i; |
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267 | double res = 0.0; |
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268 | for ( i = pdfs.length() - 1; i >= 0; i-- ) { |
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269 | /* if ( pdfs(i)->_rvc().count() >0) { |
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270 | pdfs ( i )->condition ( dls ( i )->get_cond ( val,cond ) ); |
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271 | } |
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272 | // add logarithms |
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273 | res += epdfs ( i )->evallog ( dls ( i )->pushdown ( val ) );*/ |
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274 | res += pdfs ( i )->evallogcond ( |
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275 | dls ( i )->pushdown ( val ), |
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276 | dls ( i )->get_cond ( val, cond ) |
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277 | ); |
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278 | } |
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279 | return res; |
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280 | } |
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281 | |
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282 | vec mprod::evallogcond_mat ( const mat &Dt, const vec &cond ) { |
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283 | vec tmp ( Dt.cols() ); |
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284 | for ( int i = 0; i < Dt.cols(); i++ ) { |
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285 | tmp ( i ) = evallogcond ( Dt.get_col ( i ), cond ); |
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286 | } |
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287 | return tmp; |
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288 | } |
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289 | |
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290 | vec mprod::evallogcond_mat ( const Array<vec> &Dt, const vec &cond ) { |
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291 | vec tmp ( Dt.length() ); |
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292 | for ( int i = 0; i < Dt.length(); i++ ) { |
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293 | tmp ( i ) = evallogcond ( Dt ( i ), cond ); |
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294 | } |
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295 | return tmp; |
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296 | } |
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297 | |
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298 | void mprod::set_elements ( const Array<shared_ptr<pdf> > &mFacs ) { |
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299 | pdfs = mFacs; |
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300 | dls.set_size ( mFacs.length() ); |
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301 | |
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302 | rv = get_composite_rv ( pdfs, true ); |
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303 | dim = rv._dsize(); |
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304 | |
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305 | for ( int i = 0; i < pdfs.length(); i++ ) { |
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306 | RV rvx = pdfs ( i )->_rvc().subt ( rv ); |
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307 | rvc.add ( rvx ); // add rv to common rvc |
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308 | } |
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309 | dimc = rvc._dsize(); |
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310 | |
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311 | // rv and rvc established = > we can link them with pdfs |
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312 | for ( int i = 0; i < pdfs.length(); i++ ) { |
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313 | dls ( i ) = new datalink_m2m; |
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314 | dls ( i )->set_connection ( pdfs ( i )->_rv(), pdfs ( i )->_rvc(), _rv(), _rvc() ); |
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315 | } |
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316 | } |
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317 | |
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318 | vec mmix::samplecond ( const vec &cond ) { |
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319 | //Sample which component |
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320 | vec cumDist = cumsum ( w ); |
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321 | double u0; |
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322 | #pragma omp critical |
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323 | u0 = UniRNG.sample(); |
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324 | |
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325 | int i = 0; |
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326 | while ( ( cumDist ( i ) < u0 ) && ( i < ( w.length() - 1 ) ) ) { |
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327 | i++; |
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328 | } |
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329 | |
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330 | return Coms ( i )->samplecond ( cond ); |
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331 | } |
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332 | |
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333 | vec eprod::mean() const { |
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334 | vec tmp ( dim ); |
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335 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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336 | vec pom = epdfs ( i )->mean(); |
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337 | dls ( i )->pushup ( tmp, pom ); |
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338 | } |
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339 | return tmp; |
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340 | } |
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341 | |
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342 | vec eprod::variance() const { |
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343 | vec tmp ( dim ); //second moment |
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344 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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345 | vec pom = epdfs ( i )->mean(); |
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346 | dls ( i )->pushup ( tmp, pow ( pom, 2 ) ); |
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347 | } |
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348 | return tmp - pow ( mean(), 2 ); |
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349 | } |
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350 | vec eprod::sample() const { |
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351 | vec tmp ( dim ); |
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352 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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353 | vec pom = epdfs ( i )->sample(); |
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354 | dls ( i )->pushup ( tmp, pom ); |
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355 | } |
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356 | return tmp; |
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357 | } |
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358 | double eprod::evallog ( const vec &val ) const { |
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359 | double tmp = 0; |
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360 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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361 | tmp += epdfs ( i )->evallog ( dls ( i )->pushdown ( val ) ); |
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362 | } |
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363 | bdm_assert_debug ( std::isfinite ( tmp ), "Infinite" ); |
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364 | return tmp; |
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365 | } |
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366 | |
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367 | } |
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368 | // mprod::mprod ( Array<pdf*> mFacs, bool overlap) : pdf ( RV(), RV() ), n ( mFacs.length() ), epdfs ( n ), pdfs ( mFacs ), rvinds ( n ), rvcinrv ( n ), irvcs_rvc ( n ) { |
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369 | // int i; |
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370 | // bool rvaddok; |
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371 | // // Create rv |
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372 | // for ( i = 0;i < n;i++ ) { |
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373 | // rvaddok=rv.add ( pdfs ( i )->_rv() ); //add rv to common rvs. |
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374 | // // If rvaddok==false, pdfs overlap => assert error. |
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375 | // epdfs ( i ) = & ( pdfs ( i )->posterior() ); // add pointer to epdf |
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376 | // }; |
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377 | // // Create rvc |
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378 | // for ( i = 0;i < n;i++ ) { |
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379 | // rvc.add ( pdfs ( i )->_rvc().subt ( rv ) ); //add rv to common rvs. |
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380 | // }; |
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381 | // |
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382 | // // independent = true; |
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383 | // //test rvc of pdfs and fill rvinds |
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384 | // for ( i = 0;i < n;i++ ) { |
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385 | // // find ith rv in common rv |
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386 | // rvsinrv ( i ) = pdfs ( i )->_rv().dataind ( rv ); |
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387 | // // find ith rvc in common rv |
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388 | // rvcinrv ( i ) = pdfs ( i )->_rvc().dataind ( rv ); |
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389 | // // find ith rvc in common rv |
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390 | // irvcs_rvc ( i ) = pdfs ( i )->_rvc().dataind ( rvc ); |
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391 | // // |
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392 | // /* if ( rvcinrv ( i ).length() >0 ) {independent = false;} |
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393 | // if ( irvcs_rvc ( i ).length() >0 ) {independent = false;}*/ |
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394 | // } |
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395 | // }; |
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