1 | /*! |
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2 | \file |
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3 | \brief Bayesian Filtering using stochastic sampling (Particle Filters) |
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4 | \author Vaclav Smidl. |
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5 | |
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6 | ----------------------------------- |
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7 | BDM++ - C++ library for Bayesian Decision Making under Uncertainty |
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8 | |
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9 | Using IT++ for numerical operations |
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10 | ----------------------------------- |
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11 | */ |
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12 | |
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13 | #ifndef PARTICLES_H |
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14 | #define PARTICLES_H |
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15 | |
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16 | |
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17 | #include "../estim/arx_ext.h" |
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18 | #include "../stat/emix.h" |
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19 | |
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20 | namespace bdm { |
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21 | |
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22 | //! class used in PF |
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23 | class MarginalizedParticleBase : public BM{ |
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24 | protected: |
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25 | //! discrte particle |
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26 | dirac est_emp; |
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27 | //! internal Bayes Model |
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28 | shared_ptr<BM> bm; |
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29 | |
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30 | //! custom posterior - product of empirical and exact part |
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31 | class eprod_2:public eprod_base { |
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32 | protected: |
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33 | MarginalizedParticleBase ∓ |
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34 | public: |
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35 | eprod_2(MarginalizedParticleBase &m):mp(m){} |
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36 | const epdf* factor(int i) const {return (i==0) ? &mp.bm->posterior() : &mp.est_emp;} |
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37 | const int no_factors() const {return 2;} |
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38 | } est; |
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39 | |
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40 | public: |
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41 | MarginalizedParticleBase():est(*this){}; |
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42 | MarginalizedParticleBase(const MarginalizedParticleBase &m2):est(*this){ |
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43 | bm = m2.bm->_copy(); |
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44 | est_emp = m2.est_emp; |
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45 | validate(); |
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46 | }; |
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47 | void bayes(const vec &dt, const vec &cond) NOT_IMPLEMENTED_VOID; |
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48 | |
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49 | const eprod_2& posterior() const {return est;} |
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50 | |
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51 | void set_prior(const epdf *pdf0){ |
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52 | const eprod *ep=dynamic_cast<const eprod*>(pdf0); |
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53 | if (ep){ // full prior |
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54 | bdm_assert(ep->no_factors()==2,"Incompatible prod"); |
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55 | bm->set_prior(ep->factor(0)); |
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56 | est_emp.set_point(ep->factor(1)->sample()); |
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57 | } else { |
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58 | // assume prior is only for emp; |
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59 | est_emp.set_point(pdf0->sample()); |
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60 | } |
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61 | } |
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62 | void from_setting(const Setting &set){ |
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63 | BM::from_setting ( set ); |
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64 | bm = UI::build<BM> ( set, "bm", UI::compulsory ); |
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65 | } |
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66 | void validate() { |
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67 | BM::validate(); |
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68 | bdm_assert(bm,"Internal BM is not given"); |
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69 | } |
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70 | }; |
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71 | |
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72 | class MarginalizedParticle : public MarginalizedParticleBase{ |
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73 | protected: |
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74 | //! pdf with for transitional par |
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75 | shared_ptr<pdf> par; // pdf for non-linear part |
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76 | //! link from this to bm |
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77 | shared_ptr<datalink_part> cond2bm; |
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78 | //! link from cond to par |
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79 | shared_ptr<datalink_part> cond2par; |
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80 | //! link from emp 2 par |
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81 | shared_ptr<datalink_part> emp2bm; |
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82 | //! link from emp 2 par |
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83 | shared_ptr<datalink_part> emp2par; |
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84 | |
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85 | public: |
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86 | BM* _copy() const{return new MarginalizedParticle(*this);}; |
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87 | void bayes(const vec &dt, const vec &cond){ |
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88 | vec par_cond(par->dimensionc()); |
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89 | cond2par->filldown(cond,par_cond); // copy ut |
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90 | emp2par->filldown(est_emp._point(),par_cond); // copy xt-1 |
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91 | |
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92 | //sample new particle |
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93 | est_emp.set_point(par->samplecond(par_cond)); |
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94 | //if (evalll) |
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95 | vec bm_cond(bm->dimensionc()); |
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96 | cond2bm->filldown(cond, bm_cond);// set e.g. ut |
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97 | emp2bm->filldown(est_emp._point(), bm_cond);// set e.g. ut |
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98 | bm->bayes(dt, bm_cond); |
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99 | ll=bm->_ll(); |
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100 | } |
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101 | |
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102 | /*! parse structure |
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103 | \code |
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104 | class = "MarginalizedParticle"; |
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105 | parameter_pdf = {class = 'epdf_offspring', ...}; |
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106 | bm = {class = 'bm_offspring',...}; |
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107 | \endcode |
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108 | If rvs are set, then it checks for compatibility. |
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109 | */ |
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110 | void from_setting(const Setting &set){ |
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111 | MarginalizedParticleBase::from_setting ( set ); |
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112 | par = UI::build<pdf> ( set, "parameter_pdf", UI::compulsory ); |
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113 | } |
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114 | |
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115 | void to_setting(Setting &set){ |
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116 | MarginalizedParticleBase::to_setting(set); |
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117 | UI::save(par,set,"parameter_pdf"); |
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118 | } |
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119 | void validate(){ |
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120 | if (est_emp.point.length()!=par->dimension()) |
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121 | est_emp.set_point(zeros(par->dimension())); |
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122 | est.validate(); |
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123 | |
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124 | yrv = bm->_yrv(); |
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125 | dimy = bm->dimensiony(); |
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126 | set_rv( concat(bm->_rv(), par->_rv())); |
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127 | set_dim( par->dimension()+bm->dimension()); |
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128 | |
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129 | rvc = par->_rvc(); |
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130 | rvc.add(bm->_rvc()); |
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131 | rvc=rvc.subt(par->_rv()); |
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132 | rvc=rvc.subt(par->_rv().copy_t(-1)); |
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133 | rvc=rvc.subt(bm->_rv().copy_t(-1)); // |
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134 | |
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135 | cond2bm=new datalink_part; |
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136 | cond2par=new datalink_part; |
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137 | emp2bm =new datalink_part; |
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138 | emp2par =new datalink_part; |
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139 | cond2bm->set_connection(bm->_rvc(), rvc); |
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140 | cond2par->set_connection(par->_rvc(), rvc); |
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141 | emp2bm->set_connection(bm->_rvc(), par->_rv()); |
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142 | emp2par->set_connection(par->_rvc(), par->_rv().copy_t(-1)); |
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143 | |
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144 | dimc = rvc._dsize(); |
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145 | }; |
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146 | }; |
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147 | UIREGISTER(MarginalizedParticle); |
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148 | |
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149 | //! class used in PF |
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150 | class BootstrapParticle : public BM{ |
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151 | dirac est; |
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152 | shared_ptr<pdf> par; |
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153 | shared_ptr<pdf> obs; |
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154 | shared_ptr<datalink_part> cond2par; |
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155 | shared_ptr<datalink_part> cond2obs; |
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156 | shared_ptr<datalink_part> xt2obs; |
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157 | shared_ptr<datalink_part> xtm2par; |
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158 | public: |
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159 | BM* _copy() const{return new BootstrapParticle(*this);}; |
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160 | void bayes(const vec &dt, const vec &cond){ |
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161 | vec par_cond(par->dimensionc()); |
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162 | cond2par->filldown(cond,par_cond); // copy ut |
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163 | xtm2par->filldown(est._point(),par_cond); // copy xt-1 |
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164 | |
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165 | //sample new particle |
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166 | est.set_point(par->samplecond(par_cond)); |
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167 | //if (evalll) |
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168 | vec obs_cond(obs->dimensionc()); |
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169 | cond2obs->filldown(cond, obs_cond);// set e.g. ut |
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170 | xt2obs->filldown(est._point(), obs_cond);// set e.g. ut |
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171 | ll=obs->evallogcond(dt,obs_cond); |
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172 | } |
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173 | const dirac& posterior() const {return est;} |
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174 | |
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175 | void set_prior(const epdf *pdf0){est.set_point(pdf0->sample());} |
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176 | |
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177 | /*! parse structure |
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178 | \code |
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179 | class = "BootstrapParticle"; |
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180 | parameter_pdf = {class = 'epdf_offspring', ...}; |
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181 | observation_pdf = {class = 'epdf_offspring',...}; |
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182 | \endcode |
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183 | If rvs are set, then it checks for compatibility. |
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184 | */ |
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185 | void from_setting(const Setting &set){ |
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186 | BM::from_setting ( set ); |
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187 | par = UI::build<pdf> ( set, "parameter_pdf", UI::compulsory ); |
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188 | obs = UI::build<pdf> ( set, "observation_pdf", UI::compulsory ); |
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189 | } |
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190 | void validate(){ |
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191 | yrv = obs->_rv(); |
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192 | dimy = obs->dimension(); |
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193 | set_rv( par->_rv()); |
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194 | set_dim( par->dimension()); |
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195 | |
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196 | rvc = par->_rvc().subt(par->_rv().copy_t(-1)); |
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197 | rvc.add(obs->_rvc()); // |
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198 | |
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199 | cond2obs=new datalink_part; |
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200 | cond2par=new datalink_part; |
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201 | xt2obs =new datalink_part; |
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202 | xtm2par =new datalink_part; |
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203 | cond2obs->set_connection(obs->_rvc(), rvc); |
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204 | cond2par->set_connection(par->_rvc(), rvc); |
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205 | xt2obs->set_connection(obs->_rvc(), _rv()); |
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206 | xtm2par->set_connection(par->_rvc(), _rv().copy_t(-1)); |
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207 | |
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208 | dimc = rvc._dsize(); |
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209 | }; |
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210 | }; |
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211 | UIREGISTER(BootstrapParticle); |
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212 | |
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213 | |
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214 | /*! |
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215 | * \brief Trivial particle filter with proposal density equal to parameter evolution model. |
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216 | |
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217 | Posterior density is represented by a weighted empirical density (\c eEmp ). |
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218 | */ |
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219 | |
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220 | class PF : public BM { |
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221 | //! \var log_level_enums weights |
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222 | //! all weightes will be logged |
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223 | |
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224 | //! \var log_level_enums menas |
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225 | //! means of particles will be logged |
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226 | LOG_LEVEL(PF,logweights,logmeans,logvars); |
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227 | |
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228 | class pf_mix: public emix_base{ |
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229 | Array<BM*> &bms; |
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230 | public: |
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231 | pf_mix(vec &w0, Array<BM*> &bms0):emix_base(w0),bms(bms0){} |
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232 | const epdf* component(const int &i)const{return &(bms(i)->posterior());} |
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233 | int no_coms() const {return bms.length();} |
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234 | }; |
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235 | protected: |
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236 | //!number of particles; |
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237 | int n; |
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238 | //!posterior density |
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239 | pf_mix est; |
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240 | //! weights; |
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241 | vec w; |
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242 | //! particles |
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243 | Array<BM*> particles; |
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244 | //! internal structure storing loglikelihood of predictions |
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245 | vec lls; |
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246 | |
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247 | //! which resampling method will be used |
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248 | RESAMPLING_METHOD resmethod; |
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249 | //! resampling threshold; in this case its meaning is minimum ratio of active particles |
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250 | //! For example, for 0.5 resampling is performed when the numebr of active aprticles drops belo 50%. |
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251 | double res_threshold; |
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252 | |
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253 | //! \name Options |
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254 | //!@{ |
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255 | //!@} |
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256 | |
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257 | public: |
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258 | //! \name Constructors |
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259 | //!@{ |
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260 | PF ( ) : est(w,particles) { }; |
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261 | |
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262 | void set_parameters ( int n0, double res_th0 = 0.5, RESAMPLING_METHOD rm = SYSTEMATIC ) { |
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263 | n = n0; |
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264 | res_threshold = res_th0; |
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265 | resmethod = rm; |
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266 | }; |
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267 | void set_model ( const BM *particle0, const epdf *prior) { |
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268 | if (n>0){ |
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269 | particles.set_length(n); |
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270 | for (int i=0; i<n;i++){ |
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271 | particles(i) = particle0->_copy(); |
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272 | particles(i)->set_prior(prior); |
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273 | } |
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274 | } |
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275 | // set values for posterior |
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276 | est.set_rv ( particle0->posterior()._rv() ); |
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277 | }; |
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278 | void set_statistics ( const vec w0, const epdf &epdf0 ) { |
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279 | //est.set_statistics ( w0, epdf0 ); |
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280 | }; |
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281 | /* void set_statistics ( const eEmp &epdf0 ) { |
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282 | bdm_assert_debug ( epdf0._rv().equal ( par->_rv() ), "Incompatible input" ); |
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283 | est = epdf0; |
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284 | };*/ |
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285 | //!@} |
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286 | |
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287 | //! bayes compute weights of the |
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288 | virtual void bayes_weights(); |
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289 | //! important part of particle filtering - decide if it is time to perform resampling |
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290 | virtual bool do_resampling() { |
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291 | double eff = 1.0 / ( w * w ); |
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292 | return eff < ( res_threshold*n ); |
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293 | } |
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294 | void bayes ( const vec &yt, const vec &cond ); |
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295 | //!access function |
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296 | vec& _lls() { |
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297 | return lls; |
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298 | } |
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299 | //!access function |
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300 | RESAMPLING_METHOD _resmethod() const { |
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301 | return resmethod; |
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302 | } |
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303 | //! return correctly typed posterior (covariant return) |
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304 | const pf_mix& posterior() const { |
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305 | return est; |
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306 | } |
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307 | |
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308 | /*! configuration structure for basic PF |
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309 | \code |
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310 | parameter_pdf = pdf_class; // parameter evolution pdf |
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311 | observation_pdf = pdf_class; // observation pdf |
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312 | prior = epdf_class; // prior probability density |
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313 | --- optional --- |
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314 | n = 10; // number of particles |
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315 | resmethod = 'systematic', or 'multinomial', or 'stratified' |
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316 | // resampling method |
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317 | res_threshold = 0.5; // resample when active particles drop below 50% |
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318 | \endcode |
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319 | */ |
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320 | void from_setting ( const Setting &set ) { |
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321 | BM::from_setting ( set ); |
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322 | UI::get ( log_level, set, "log_level", UI::optional ); |
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323 | |
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324 | shared_ptr<BM> bm0 = UI::build<BM>(set, "particle",UI::compulsory); |
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325 | |
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326 | shared_ptr<epdf> pri = UI::build<epdf> ( set, "prior", UI::compulsory ); |
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327 | n =0; |
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328 | UI::get(n,set,"n",UI::optional);; |
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329 | if (n>0){ |
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330 | particles.set_length(n); |
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331 | for(int i=0;i<n;i++){particles(i)=bm0->_copy();} |
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332 | w = ones(n)/n; |
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333 | } |
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334 | set_prior(pri.get()); |
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335 | // set resampling method |
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336 | resmethod_from_set ( set ); |
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337 | //set drv |
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338 | |
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339 | rvc = bm0->_rvc(); |
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340 | dimc = bm0->dimensionc(); |
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341 | BM::set_rv(bm0->_rv()); |
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342 | yrv=bm0->_yrv(); |
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343 | dimy = bm0->dimensiony(); |
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344 | } |
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345 | |
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346 | void log_register ( bdm::logger& L, const string& prefix ){ |
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347 | BM::log_register(L,prefix); |
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348 | if (log_level[logweights]){ |
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349 | L.add_vector( log_level, logweights, RV ( particles.length()), prefix); |
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350 | } |
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351 | if (log_level[logmeans]){ |
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352 | for (int i=0; i<particles.length(); i++){ |
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353 | L.add_vector( log_level, logmeans, RV ( particles(i)->dimension() ), prefix , i); |
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354 | } |
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355 | } |
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356 | if (log_level[logvars]){ |
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357 | for (int i=0; i<particles.length(); i++){ |
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358 | L.add_vector( log_level, logvars, RV ( particles(i)->dimension() ), prefix , i); |
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359 | } |
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360 | } |
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361 | }; |
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362 | void log_write ( ) const { |
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363 | BM::log_write(); |
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364 | if (log_level[logweights]){ |
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365 | log_level.store( logweights, w); |
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366 | } |
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367 | if (log_level[logmeans]){ |
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368 | for (int i=0; i<particles.length(); i++){ |
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369 | log_level.store( logmeans, particles(i)->posterior().mean(), i); |
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370 | } |
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371 | } |
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372 | if (log_level[logvars]){ |
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373 | for (int i=0; i<particles.length(); i++){ |
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374 | log_level.store( logvars, particles(i)->posterior().variance(), i); |
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375 | } |
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376 | } |
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377 | |
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378 | } |
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379 | |
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380 | void set_prior(const epdf *pri){ |
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381 | const emix_base *emi=dynamic_cast<const emix_base*>(pri); |
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382 | if (emi) { |
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383 | bdm_assert(particles.length()>0, "initial particle is not assigned"); |
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384 | n = emi->_w().length(); |
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385 | int old_n = particles.length(); |
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386 | if (n!=old_n){ |
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387 | particles.set_length(n,true); |
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388 | } |
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389 | for(int i=old_n;i<n;i++){particles(i)=particles(0)->_copy();} |
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390 | |
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391 | for (int i =0; i<n; i++){ |
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392 | particles(i)->set_prior(emi->_com(i)); |
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393 | } |
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394 | } else { |
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395 | // try to find "n" |
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396 | bdm_assert(n>0, "Field 'n' must be filled when prior is not of type emix"); |
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397 | for (int i =0; i<n; i++){ |
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398 | particles(i)->set_prior(pri); |
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399 | } |
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400 | |
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401 | } |
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402 | } |
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403 | //! auxiliary function reading parameter 'resmethod' from configuration file |
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404 | void resmethod_from_set ( const Setting &set ) { |
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405 | string resmeth; |
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406 | if ( UI::get ( resmeth, set, "resmethod", UI::optional ) ) { |
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407 | if ( resmeth == "systematic" ) { |
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408 | resmethod = SYSTEMATIC; |
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409 | } else { |
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410 | if ( resmeth == "multinomial" ) { |
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411 | resmethod = MULTINOMIAL; |
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412 | } else { |
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413 | if ( resmeth == "stratified" ) { |
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414 | resmethod = STRATIFIED; |
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415 | } else { |
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416 | bdm_error ( "Unknown resampling method" ); |
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417 | } |
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418 | } |
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419 | } |
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420 | } else { |
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421 | resmethod = SYSTEMATIC; |
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422 | }; |
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423 | if ( !UI::get ( res_threshold, set, "res_threshold", UI::optional ) ) { |
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424 | res_threshold = 0.9; |
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425 | } |
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426 | //validate(); |
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427 | } |
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428 | |
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429 | void validate() { |
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430 | BM::validate(); |
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431 | est.validate(); |
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432 | bdm_assert ( n>0, "empty particle pool" ); |
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433 | n = w.length(); |
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434 | lls = zeros ( n ); |
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435 | |
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436 | if ( particles(0)->_rv()._dsize() > 0 ) { |
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437 | bdm_assert ( particles(0)->_rv()._dsize() == est.dimension(), "Mismatch of RV and dimension of posterior" ); |
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438 | } |
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439 | } |
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440 | //! resample posterior density (from outside - see MPF) |
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441 | void resample ( ) { |
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442 | ivec ind = zeros_i ( n ); |
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443 | bdm::resample(w,ind,resmethod); |
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444 | // copy the internals according to ind |
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445 | for (int i = 0; i < n; i++ ) { |
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446 | if ( ind ( i ) != i ) { |
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447 | particles( i ) = particles( ind ( i ) )->_copy(); |
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448 | } |
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449 | w ( i ) = 1.0 / n; |
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450 | } |
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451 | } |
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452 | //! access function |
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453 | Array<BM*>& _particles() { |
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454 | return particles; |
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455 | } |
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456 | |
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457 | }; |
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458 | UIREGISTER ( PF ); |
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459 | |
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460 | /*! Marginalized particle for state-space models with unknown parameters of residues distribution |
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461 | |
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462 | \f[ |
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463 | \begin{eqnarray} |
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464 | x_t = g(x_{t-1}) + v_t,\\ |
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465 | z_t = h(x_{t-1}) + w_t,\\ |
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466 | \end{eqnarray} |
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467 | \f] |
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468 | |
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469 | This particle is a only a shell creating the residues calling internal estimator of their parameters. The internal estimator can be of any compatible type, e.g. ARX for Gaussian residues with unknown mean and variance. |
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470 | |
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471 | */ |
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472 | class NoiseParticle : public MarginalizedParticleBase{ |
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473 | protected: |
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474 | //! function transforming xt, ut -> x_t+1 |
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475 | shared_ptr<fnc> g; // pdf for non-linear part |
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476 | //! function transforming xt,ut -> yt |
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477 | shared_ptr<fnc> h; // pdf for non-linear part |
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478 | |
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479 | RV rvv; |
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480 | |
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481 | RV rvx; |
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482 | RV rvxc; |
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483 | RV rvyc; |
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484 | |
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485 | //!link from condition to f |
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486 | datalink_part cond2g; |
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487 | //!link from condition to h |
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488 | datalink_part cond2h; |
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489 | //!link from xt to f |
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490 | datalink_part x2g; |
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491 | //!link from xt to h |
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492 | datalink_part x2h; |
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493 | |
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494 | public: |
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495 | BM* _copy() const{return new NoiseParticle();}; |
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496 | void bayes(const vec &dt, const vec &cond){ |
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497 | epdf* pred_vw=bm->epredictor(); |
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498 | shared_ptr<epdf> pred_v = pred_vw->marginal(rvv); |
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499 | |
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500 | vec vt=pred_v->sample(); |
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501 | |
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502 | //new sample |
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503 | vec &xtm=est_emp.point; |
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504 | vec g_args(g->dimensionc()); |
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505 | x2g.filldown(xtm,g_args); |
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506 | cond2g.filldown(cond,g_args); |
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507 | vec xt = g->eval(g_args) + vt; |
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508 | |
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509 | // residue of observation |
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510 | vec h_args(h->dimensionc()); |
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511 | x2h.filldown(xt,h_args); |
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512 | cond2h.filldown(cond,h_args); |
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513 | vec wt = dt-h->eval(h_args); |
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514 | // the vector [v_t,w_t] is now complete |
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515 | bm->bayes(concat(vt,wt)); |
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516 | ll=bm->_ll(); |
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517 | } |
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518 | void from_setting(const Setting &set){ |
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519 | MarginalizedParticleBase::from_setting(set); //reads bm, yrv,rvc, bm_rv, etc... |
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520 | |
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521 | UI::get(g,set,"g",UI::compulsory); |
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522 | UI::get(h,set,"h",UI::compulsory); |
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523 | RV rvx; |
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524 | UI::get(rvx,set,"rvx",UI::compulsory); |
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525 | est_emp.set_rv(rvx); |
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526 | |
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527 | RV rvxc; |
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528 | UI::get(rvxc,set,"rvxc",UI::compulsory); |
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529 | RV rvyc; |
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530 | UI::get(rvyc,set,"rvyc",UI::compulsory); |
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531 | } |
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532 | void validate(){ |
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533 | MarginalizedParticleBase::validate(); |
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534 | //check dimensions |
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535 | rvc = rvxc; |
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536 | rvc.add( rvyc); |
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537 | rvc.subt(rvx); |
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538 | |
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539 | //establish datalinks |
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540 | x2g.set_connection(rvxc, rvx.copy_t(-1)); |
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541 | cond2g.set_connection(rvxc, rvc); |
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542 | |
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543 | x2h.set_connection(rvyc, rvx); |
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544 | cond2h.set_connection(rvyc, rvc); |
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545 | } |
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546 | }; |
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547 | UIREGISTER(NoiseParticle); |
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548 | |
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549 | |
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550 | |
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551 | } |
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552 | #endif // KF_H |
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553 | |
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