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 "../stat/exp_family.h" |
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18 | |
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19 | namespace bdm { |
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20 | |
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21 | /*! |
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22 | * \brief Trivial particle filter with proposal density equal to parameter evolution model. |
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23 | |
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24 | Posterior density is represented by a weighted empirical density (\c eEmp ). |
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25 | */ |
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26 | |
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27 | class PF : public BM { |
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28 | protected: |
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29 | //!number of particles; |
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30 | int n; |
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31 | //!posterior density |
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32 | eEmp est; |
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33 | //! pointer into \c eEmp |
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34 | vec &_w; |
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35 | //! pointer into \c eEmp |
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36 | Array<vec> &_samples; |
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37 | //! Parameter evolution model |
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38 | shared_ptr<mpdf> par; |
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39 | //! Observation model |
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40 | shared_ptr<mpdf> obs; |
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41 | //! internal structure storing loglikelihood of predictions |
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42 | vec lls; |
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43 | |
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44 | //! which resampling method will be used |
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45 | RESAMPLING_METHOD resmethod; |
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46 | //! resampling threshold; in this case its meaning is minimum ratio of active particles |
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47 | //! For example, for 0.5 resampling is performed when the numebr of active aprticles drops belo 50%. |
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48 | double res_threshold; |
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49 | |
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50 | //! \name Options |
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51 | //!@{ |
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52 | |
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53 | //! Log all samples |
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54 | bool opt_L_smp; |
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55 | //! Log all samples |
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56 | bool opt_L_wei; |
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57 | //!@} |
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58 | |
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59 | public: |
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60 | //! \name Constructors |
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61 | //!@{ |
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62 | PF ( ) : est(), _w ( est._w() ), _samples ( est._samples() ), opt_L_smp ( false ), opt_L_wei ( false ) { |
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63 | LIDs.set_size ( 5 ); |
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64 | }; |
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65 | |
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66 | void set_parameters (int n0, double res_th0=0.5, RESAMPLING_METHOD rm = SYSTEMATIC ) { |
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67 | n = n0; |
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68 | res_threshold = res_th0; |
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69 | resmethod = rm; |
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70 | }; |
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71 | void set_model ( shared_ptr<mpdf> par0, shared_ptr<mpdf> obs0) { |
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72 | par = par0; |
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73 | obs = obs0; |
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74 | // set values for posterior |
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75 | est.set_rv(par->_rv()); |
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76 | }; |
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77 | void set_statistics ( const vec w0, const epdf &epdf0 ) { |
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78 | est.set_statistics ( w0, epdf0 ); |
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79 | }; |
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80 | void set_statistics ( const eEmp &epdf0 ) { |
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81 | bdm_assert_debug(epdf0._rv().equal(par->_rv()),"Incompatibel input"); |
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82 | est=epdf0; |
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83 | }; |
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84 | //!@} |
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85 | //! Set posterior density by sampling from epdf0 |
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86 | //! Extends original BM::set_options by two more options: |
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87 | //! \li logweights - meaning that all weightes will be logged |
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88 | //! \li logsamples - all samples will be also logged |
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89 | void set_options ( const string &opt ) { |
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90 | BM::set_options ( opt ); |
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91 | opt_L_wei = ( opt.find ( "logweights" ) != string::npos ); |
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92 | opt_L_smp = ( opt.find ( "logsamples" ) != string::npos ); |
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93 | } |
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94 | //! bayes I - generate samples and add their weights to lls |
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95 | virtual void bayes_gensmp(); |
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96 | //! bayes II - compute weights of the |
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97 | virtual void bayes_weights(); |
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98 | //! important part of particle filtering - decide if it is time to perform resampling |
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99 | virtual bool do_resampling(){ |
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100 | double eff = 1.0 / ( _w * _w ); |
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101 | return eff < ( res_threshold*n ); |
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102 | } |
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103 | void bayes ( const vec &dt ); |
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104 | //!access function |
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105 | vec& __w() { return _w; } |
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106 | //!access function |
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107 | vec& _lls() { return lls; } |
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108 | RESAMPLING_METHOD _resmethod() const { return resmethod; } |
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109 | //!access function |
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110 | const eEmp& posterior() const {return est;} |
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111 | |
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112 | /*! configuration structure for basic PF |
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113 | \code |
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114 | parameter_pdf = mpdf_class; // parameter evolution pdf |
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115 | observation_pdf = mpdf_class; // observation pdf |
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116 | prior = epdf_class; // prior probability density |
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117 | --- optional --- |
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118 | n = 10; // number of particles |
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119 | resmethod = 'systematic', or 'multinomial', or 'stratified' |
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120 | // resampling method |
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121 | res_threshold = 0.5; // resample when active particles drop below 50% |
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122 | \endcode |
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123 | */ |
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124 | void from_setting(const Setting &set){ |
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125 | par = UI::build<mpdf>(set,"parameter_pdf",UI::compulsory); |
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126 | obs = UI::build<mpdf>(set,"observation_pdf",UI::compulsory); |
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127 | |
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128 | prior_from_set(set); |
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129 | resmethod_from_set(set); |
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130 | // set resampling method |
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131 | //set drv |
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132 | //find potential input - what remains in rvc when we subtract rv |
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133 | RV u = par->_rvc().remove_time().subt( par->_rv() ); |
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134 | //find potential input - what remains in rvc when we subtract x_t |
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135 | RV obs_u = obs->_rvc().remove_time().subt( par->_rv() ); |
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136 | |
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137 | u.add(obs_u); // join both u, and check if they do not overlap |
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138 | |
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139 | set_drv(concat(obs->_rv(),u) ); |
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140 | } |
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141 | //! auxiliary function reading parameter 'resmethod' from configuration file |
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142 | void resmethod_from_set(const Setting &set){ |
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143 | string resmeth; |
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144 | if (UI::get(resmeth,set,"resmethod",UI::optional)){ |
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145 | if (resmeth=="systematic") { |
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146 | resmethod= SYSTEMATIC; |
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147 | } else { |
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148 | if (resmeth=="multinomial"){ |
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149 | resmethod=MULTINOMIAL; |
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150 | } else { |
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151 | if (resmeth=="stratified"){ |
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152 | resmethod= STRATIFIED; |
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153 | } else { |
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154 | bdm_error("Unknown resampling method"); |
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155 | } |
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156 | } |
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157 | } |
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158 | } else { |
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159 | resmethod=SYSTEMATIC; |
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160 | }; |
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161 | if(!UI::get(res_threshold, set, "res_threshold", UI::optional)){ |
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162 | res_threshold=0.5; |
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163 | } |
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164 | } |
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165 | //! load prior information from set and set internal structures accordingly |
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166 | void prior_from_set(const Setting & set){ |
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167 | shared_ptr<epdf> pri = UI::build<epdf>(set,"prior",UI::compulsory); |
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168 | |
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169 | eEmp *test_emp=dynamic_cast<eEmp*>(&(*pri)); |
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170 | if (test_emp) { // given pdf is sampled |
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171 | est=*test_emp; |
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172 | } else { |
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173 | int n; |
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174 | if (!UI::get(n,set,"n",UI::optional)){n=10;} |
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175 | // sample from prior |
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176 | set_statistics(ones(n)/n, *pri); |
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177 | } |
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178 | //validate(); |
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179 | } |
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180 | |
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181 | void validate(){ |
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182 | n=_w.length(); |
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183 | lls=zeros(n); |
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184 | if (par->_rv()._dsize()>0) { |
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185 | bdm_assert(par->_rv()._dsize()==est.dimension(),"Mismatch of RV and dimension of posterior" ); |
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186 | } |
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187 | } |
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188 | //! resample posterior density (from outside - see MPF) |
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189 | void resample(ivec &ind){ |
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190 | est.resample(ind,resmethod); |
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191 | } |
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192 | Array<vec>& __samples(){return _samples;} |
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193 | }; |
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194 | UIREGISTER(PF); |
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195 | |
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196 | /*! |
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197 | \brief Marginalized Particle filter |
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198 | |
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199 | A composition of particle filter with exact (or almost exact) bayesian models (BMs). |
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200 | The Bayesian models provide marginalized predictive density. Internaly this is achieved by virtual class MPFmpdf. |
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201 | */ |
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202 | |
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203 | class MPF : public BM { |
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204 | protected: |
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205 | shared_ptr<PF> pf; |
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206 | Array<BM*> BMs; |
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207 | |
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208 | //! internal class for MPDF providing composition of eEmp with external components |
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209 | |
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210 | class mpfepdf : public epdf { |
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211 | shared_ptr<PF> &pf; |
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212 | Array<BM*> &BMs; |
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213 | public: |
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214 | mpfepdf (shared_ptr<PF> &pf0, Array<BM*> &BMs0): epdf(), pf(pf0), BMs(BMs0) { }; |
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215 | //! a variant of set parameters - this time, parameters are read from BMs and pf |
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216 | void read_parameters(){ |
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217 | rv = concat(pf->posterior()._rv(), BMs(0)->posterior()._rv()); |
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218 | dim = pf->posterior().dimension() + BMs(0)->posterior().dimension(); |
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219 | bdm_assert_debug(dim == rv._dsize(), "Wrong name "); |
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220 | } |
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221 | vec mean() const { |
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222 | const vec &w = pf->posterior()._w(); |
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223 | vec pom = zeros ( BMs(0)->posterior ().dimension() ); |
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224 | //compute mean of BMs |
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225 | for ( int i = 0; i < w.length(); i++ ) { |
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226 | pom += BMs ( i )->posterior().mean() * w ( i ); |
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227 | } |
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228 | return concat ( pf->posterior().mean(), pom ); |
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229 | } |
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230 | vec variance() const { |
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231 | const vec &w = pf->posterior()._w(); |
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232 | |
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233 | vec pom = zeros ( BMs(0)->posterior ().dimension() ); |
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234 | vec pom2 = zeros ( BMs(0)->posterior ().dimension() ); |
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235 | vec mea; |
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236 | |
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237 | for ( int i = 0; i < w.length(); i++ ) { |
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238 | // save current mean |
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239 | mea = BMs ( i )->posterior().mean(); |
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240 | pom += mea * w ( i ); |
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241 | //compute variance |
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242 | pom2 += ( BMs ( i )->posterior().variance() + pow ( mea, 2 ) ) * w ( i ); |
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243 | } |
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244 | return concat ( pf->posterior().variance(), pom2 - pow ( pom, 2 ) ); |
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245 | } |
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246 | |
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247 | void qbounds ( vec &lb, vec &ub, double perc = 0.95 ) const { |
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248 | //bounds on particles |
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249 | vec lbp; |
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250 | vec ubp; |
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251 | pf->posterior().qbounds ( lbp, ubp ); |
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252 | |
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253 | //bounds on Components |
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254 | int dimC = BMs ( 0 )->posterior().dimension(); |
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255 | int j; |
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256 | // temporary |
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257 | vec lbc ( dimC ); |
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258 | vec ubc ( dimC ); |
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259 | // minima and maxima |
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260 | vec Lbc ( dimC ); |
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261 | vec Ubc ( dimC ); |
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262 | Lbc = std::numeric_limits<double>::infinity(); |
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263 | Ubc = -std::numeric_limits<double>::infinity(); |
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264 | |
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265 | for ( int i = 0; i < BMs.length(); i++ ) { |
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266 | // check Coms |
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267 | BMs ( i )->posterior().qbounds ( lbc, ubc ); |
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268 | //save either minima or maxima |
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269 | for ( j = 0; j < dimC; j++ ) { |
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270 | if ( lbc ( j ) < Lbc ( j ) ) { |
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271 | Lbc ( j ) = lbc ( j ); |
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272 | } |
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273 | if ( ubc ( j ) > Ubc ( j ) ) { |
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274 | Ubc ( j ) = ubc ( j ); |
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275 | } |
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276 | } |
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277 | } |
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278 | lb = concat ( lbp, Lbc ); |
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279 | ub = concat ( ubp, Ubc ); |
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280 | } |
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281 | |
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282 | vec sample() const { |
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283 | bdm_error ( "Not implemented" ); |
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284 | return vec(); |
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285 | } |
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286 | |
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287 | double evallog ( const vec &val ) const { |
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288 | bdm_error ( "not implemented" ); |
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289 | return 0.0; |
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290 | } |
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291 | }; |
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292 | |
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293 | //! Density joining PF.est with conditional parts |
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294 | mpfepdf jest; |
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295 | |
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296 | //! Log means of BMs |
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297 | bool opt_L_mea; |
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298 | |
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299 | public: |
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300 | //! Default constructor. |
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301 | MPF () : jest (pf,BMs) {}; |
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302 | void set_parameters ( shared_ptr<mpdf> par0, shared_ptr<mpdf> obs0, int n0, RESAMPLING_METHOD rm = SYSTEMATIC ) { |
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303 | pf->set_model ( par0, obs0); |
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304 | pf->set_parameters(n0, rm ); |
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305 | BMs.set_length ( n0 ); |
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306 | } |
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307 | void set_BM ( const BM &BMcond0 ) { |
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308 | |
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309 | int n=pf->__w().length(); |
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310 | BMs.set_length(n); |
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311 | // copy |
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312 | //BMcond0 .condition ( pf->posterior()._sample ( 0 ) ); |
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313 | for ( int i = 0; i < n; i++ ) { |
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314 | BMs ( i ) = BMcond0._copy_(); |
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315 | BMs ( i )->condition ( pf->posterior()._sample ( i ) ); |
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316 | } |
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317 | }; |
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318 | |
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319 | void bayes ( const vec &dt ); |
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320 | const epdf& posterior() const { |
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321 | return jest; |
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322 | } |
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323 | //! Extends options understood by BM::set_options by option |
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324 | //! \li logmeans - meaning |
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325 | void set_options ( const string &opt ) { |
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326 | BM::set_options(opt); |
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327 | opt_L_mea = ( opt.find ( "logmeans" ) != string::npos ); |
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328 | } |
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329 | |
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330 | //!Access function |
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331 | const BM* _BM ( int i ) { |
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332 | return BMs ( i ); |
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333 | } |
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334 | |
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335 | /*! configuration structure for basic PF |
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336 | \code |
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337 | BM = BM_class; // Bayesian filtr for analytical part of the model |
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338 | parameter_pdf = mpdf_class; // transitional pdf for non-parametric part of the model |
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339 | prior = epdf_class; // prior probability density |
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340 | --- optional --- |
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341 | n = 10; // number of particles |
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342 | resmethod = 'systematic', or 'multinomial', or 'stratified' |
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343 | // resampling method |
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344 | \endcode |
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345 | */ |
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346 | void from_setting(const Setting &set){ |
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347 | shared_ptr<mpdf> par = UI::build<mpdf>(set,"parameter_pdf",UI::compulsory); |
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348 | shared_ptr<mpdf> obs= new mpdf(); // not used!! |
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349 | |
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350 | pf = new PF; |
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351 | // rpior must be set before BM |
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352 | pf->prior_from_set(set); |
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353 | pf->resmethod_from_set(set); |
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354 | pf->set_model(par,obs); |
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355 | |
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356 | shared_ptr<BM> BM0 =UI::build<BM>(set,"BM",UI::compulsory); |
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357 | set_BM(*BM0); |
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358 | |
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359 | string opt; |
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360 | if (UI::get(opt,set,"options",UI::optional)){ |
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361 | set_options(opt); |
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362 | } |
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363 | //set drv |
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364 | //find potential input - what remains in rvc when we subtract rv |
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365 | RV u = par->_rvc().remove_time().subt( par->_rv() ); |
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366 | set_drv(concat(BM0->_drv(),u) ); |
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367 | validate(); |
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368 | } |
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369 | void validate(){ |
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370 | try{ |
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371 | pf->validate(); |
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372 | } catch (std::exception &e){ |
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373 | throw UIException("Error in PF part of MPF:"); |
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374 | } |
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375 | jest.read_parameters(); |
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376 | } |
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377 | |
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378 | }; |
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379 | UIREGISTER(MPF); |
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380 | |
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381 | } |
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382 | #endif // KF_H |
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383 | |
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