1 | /*! |
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2 | \file |
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3 | \brief Bayesian Filtering for generalized autoregressive (ARX) model |
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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 AR_H |
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14 | #define AR_H |
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15 | |
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16 | #include "../math/functions.h" |
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17 | #include "../stat/exp_family.h" |
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18 | #include "../base/user_info.h" |
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19 | //#include "../estim/kalman.h" |
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20 | #include "arx_straux.h" |
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21 | |
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22 | namespace bdm { |
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23 | |
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24 | /*! |
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25 | * \brief Linear Autoregressive model with Gaussian noise |
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26 | |
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27 | Regression of the following kind: |
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28 | \f[ |
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29 | y_t = \theta_1 \psi_1 + \theta_2 + \psi_2 +\ldots + \theta_n \psi_n + r e_t |
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30 | \f] |
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31 | where unknown parameters \c rv are \f$[\theta r]\f$, regression vector \f$\psi=\psi(y_{1:t},u_{1:t})\f$ is a known function of past outputs and exogeneous variables \f$u_t\f$. Distrubances \f$e_t\f$ are supposed to be normally distributed: |
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32 | \f[ |
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33 | e_t \sim \mathcal{N}(0,1). |
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34 | \f] |
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35 | |
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36 | See \ref tut_arx for mathematical treatment. |
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37 | |
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38 | The easiest way how to use the class is: |
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39 | \include arx_simple.cpp |
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40 | |
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41 | \todo sort out constant terms - bayes should accept vec without additional 1s |
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42 | */ |
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43 | class ARX: public BMEF { |
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44 | protected: |
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45 | //! switch if constant is modelled or not |
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46 | bool have_constant; |
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47 | //! vector of dyadic update |
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48 | vec dyad; |
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49 | //! posterior density |
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50 | egiw est; |
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51 | //! Alternative estimate of parameters, used in stabilized forgetting, see [Kulhavy] |
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52 | egiw alter_est; |
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53 | public: |
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54 | //! \name Constructors |
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55 | //!@{ |
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56 | ARX ( const double frg0 = 1.0 ) : BMEF ( frg0 ), have_constant(true), dyad(), est() {}; |
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57 | ARX ( const ARX &A0 ) : BMEF (A0.frg), have_constant(A0.have_constant), dyad(A0.dyad),est(est) { }; |
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58 | ARX* _copy_() const; |
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59 | void set_parameters ( double frg0 ) { |
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60 | frg = frg0; |
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61 | } |
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62 | void set_constant ( bool const0 ) { |
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63 | have_constant=const0; |
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64 | } |
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65 | void set_statistics ( int dimy0, const ldmat V0, double nu0 = -1.0 ) { |
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66 | est.set_parameters ( dimy0, V0, nu0 ); |
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67 | last_lognc = est.lognc(); |
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68 | dimy = dimy0; |
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69 | } |
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70 | //!@} |
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71 | |
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72 | //! Set sufficient statistics |
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73 | void set_statistics ( const BMEF* BM0 ); |
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74 | |
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75 | //!\name Mathematical operations |
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76 | //!@{ |
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77 | |
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78 | //! Weighted Bayes \f$ dt = [y_t psi_t] \f$. |
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79 | void bayes_weighted ( const vec &yt, const vec &cond=empty_vec, const double w=1.0 ); |
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80 | void bayes( const vec &yt, const vec &cond=empty_vec ) { |
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81 | bayes_weighted ( yt,cond, 1.0 ); |
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82 | }; |
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83 | double logpred ( const vec &yt ) const; |
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84 | void flatten ( const BMEF* B ) { |
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85 | const ARX* A = dynamic_cast<const ARX*> ( B ); |
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86 | // nu should be equal to B.nu |
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87 | est.pow ( A->posterior()._nu() / posterior()._nu() ); |
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88 | if ( evalll ) { |
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89 | last_lognc = est.lognc(); |
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90 | } |
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91 | } |
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92 | //! Conditioned version of the predictor |
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93 | enorm<ldmat>* epredictor ( const vec &rgr ) const; |
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94 | //! Predictor for empty regressor |
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95 | enorm<ldmat>* epredictor() const { |
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96 | bdm_assert_debug ( dimy == posterior()._V().rows() - 1, "Regressor is not only 1" ); |
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97 | return epredictor ( vec_1 ( 1.0 ) ); |
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98 | } |
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99 | //! conditional version of the predictor |
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100 | mlnorm<ldmat>* predictor() const; |
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101 | mlstudent* predictor_student() const; |
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102 | //! Brute force structure estimation.\return indeces of accepted regressors. |
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103 | ivec structure_est ( egiw Eg0 ); |
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104 | //! Smarter structure estimation by Ludvik Tesar.\return indeces of accepted regressors. |
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105 | ivec structure_est_LT ( egiw Eg0 ); |
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106 | //!@} |
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107 | |
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108 | //!\name Access attributes |
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109 | //!@{ |
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110 | //! return correctly typed posterior (covariant return) |
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111 | const egiw& posterior() const { |
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112 | return est; |
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113 | } |
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114 | //!@} |
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115 | |
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116 | /*! UI for ARX estimator |
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117 | |
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118 | \code |
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119 | class = 'ARX'; |
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120 | rv = RV({names_of_dt} ) // description of output variables |
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121 | rgr = RV({names_of_regressors}, [-1,-2]} // description of regressor variables |
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122 | constant = 1; // 0/1 switch if the constant term is modelled or not |
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123 | |
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124 | --- optional --- |
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125 | prior = {class='egiw',...}; // Prior density, when given default is used instead |
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126 | alternative = {class='egiw',...}; // Alternative density in stabilized estimation, when not given prior is used |
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127 | |
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128 | frg = 1.0; // forgetting, default frg=1.0 |
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129 | |
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130 | rv_param = RV({names_of_parameters}} // description of parametetr names |
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131 | // default: ["theta_i" and "r_i"] |
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132 | \endcode |
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133 | */ |
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134 | void from_setting ( const Setting &set ); |
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135 | |
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136 | void validate() { |
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137 | //if dimc not set set it from V |
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138 | if (dimc==0){ |
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139 | dimc = posterior()._V().rows()-dimy-int(have_constant==true); |
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140 | } |
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141 | |
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142 | if (have_constant) { |
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143 | dyad = ones(dimy+dimc+1); |
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144 | } else { |
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145 | dyad = zeros(dimy+dimc); |
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146 | } |
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147 | |
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148 | } |
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149 | //! function sets prior and alternative density |
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150 | void set_prior(const RV &drv, egiw &prior){ |
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151 | //TODO check ranges in RV and build prior |
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152 | }; |
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153 | //! build default prior and alternative when all values are set |
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154 | void set_prior_default(egiw &prior){ |
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155 | //assume |
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156 | vec dV0(prior._V().rows()); |
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157 | dV0.set_subvector(0,prior._dimx()-1, 1.0); |
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158 | dV0.set_subvector(prior._dimx(),dV0.length()-1, 1e-5); |
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159 | |
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160 | prior.set_parameters(prior._dimx(),ldmat(dV0)); |
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161 | } |
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162 | }; |
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163 | |
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164 | UIREGISTER ( ARX ); |
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165 | SHAREDPTR ( ARX ); |
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166 | |
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167 | /*! ARX model conditined by knowledge of the forgetting factor |
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168 | \f[ f(\theta| d_1 \ldots d_t , \phi_t) \f] |
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169 | */ |
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170 | class ARXfrg : public ARX{ |
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171 | public: |
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172 | ARXfrg():ARX(){}; |
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173 | //! copy constructor |
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174 | ARXfrg(const ARXfrg &A0):ARX(A0){}; |
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175 | ARXfrg* _copy_() const {ARXfrg *A = new ARXfrg(*this); return A;} |
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176 | void condition(const vec &val){ |
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177 | frg = val(0); |
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178 | } |
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179 | }; |
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180 | UIREGISTER(ARXfrg); |
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181 | }; |
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182 | #endif // AR_H |
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183 | |
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