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 | //!size of output variable (needed in regressors) |
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46 | int dimx; |
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47 | //!description of modelled data \f$ y_t \f$ in the likelihood function |
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48 | //! Do NOT access directly, only via \c get_yrv(). |
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49 | RV _yrv; |
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50 | //! rv of regressor |
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51 | RV rgrrv; |
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52 | //! Posterior estimate of \f$\theta,r\f$ in the form of Normal-inverse Wishart density |
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53 | egiw est; |
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54 | //! cached value of est.V |
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55 | ldmat &V; |
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56 | //! cached value of est.nu |
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57 | double ν |
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58 | //! switch if constant is modelled or not |
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59 | bool have_constant; |
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60 | //! cached value of data vector for have_constant =true |
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61 | vec _dt; |
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62 | //! Alternative estimate of parameters, used in stabilized forgetting, see [Kulhavy] |
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63 | egiw alter_est; |
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64 | public: |
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65 | //! \name Constructors |
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66 | //!@{ |
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67 | ARX ( const double frg0 = 1.0 ) : BMEF ( frg0 ), est (), V ( est._V() ), nu ( est._nu() ), have_constant(true), _dt() {}; |
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68 | ARX ( const ARX &A0 ) : BMEF (A0.frg), est (A0.est), V ( est._V() ), nu ( est._nu() ), have_constant(A0.have_constant), _dt(A0._dt) { |
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69 | dimx = A0.dimx; |
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70 | _yrv = A0._yrv; |
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71 | rgrrv = A0.rgrrv; |
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72 | set_drv(A0._drv()); |
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73 | }; |
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74 | ARX* _copy_() const; |
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75 | void set_parameters ( double frg0 ) { |
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76 | frg = frg0; |
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77 | } |
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78 | void set_constant ( bool const0 ) { |
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79 | have_constant=const0; |
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80 | } |
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81 | void set_statistics ( int dimx0, const ldmat V0, double nu0 = -1.0 ) { |
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82 | est.set_parameters ( dimx0, V0, nu0 ); |
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83 | last_lognc = est.lognc(); |
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84 | dimx = dimx0; |
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85 | } |
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86 | //!@} |
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87 | |
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88 | //! Set sufficient statistics |
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89 | void set_statistics ( const BMEF* BM0 ); |
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90 | |
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91 | //!\name Mathematical operations |
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92 | //!@{ |
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93 | |
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94 | //! Weighted Bayes \f$ dt = [y_t psi_t] \f$. |
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95 | void bayes ( const vec &dt, const double w ); |
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96 | void bayes ( const vec &dt ) { |
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97 | bayes ( dt, 1.0 ); |
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98 | }; |
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99 | double logpred ( const vec &dt ) const; |
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100 | void flatten ( const BMEF* B ) { |
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101 | const ARX* A = dynamic_cast<const ARX*> ( B ); |
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102 | // nu should be equal to B.nu |
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103 | est.pow ( A->nu / nu ); |
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104 | if ( evalll ) { |
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105 | last_lognc = est.lognc(); |
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106 | } |
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107 | } |
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108 | //! Conditioned version of the predictor |
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109 | enorm<ldmat>* epredictor ( const vec &rgr ) const; |
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110 | //! Predictor for empty regressor |
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111 | enorm<ldmat>* epredictor() const { |
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112 | bdm_assert_debug ( dimx == V.rows() - 1, "Regressor is not only 1" ); |
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113 | return epredictor ( vec_1 ( 1.0 ) ); |
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114 | } |
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115 | //! conditional version of the predictor |
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116 | mlnorm<ldmat>* predictor() const; |
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117 | mlstudent* predictor_student() const; |
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118 | //! Brute force structure estimation.\return indeces of accepted regressors. |
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119 | ivec structure_est ( egiw Eg0 ); |
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120 | //! Smarter structure estimation by Ludvik Tesar.\return indeces of accepted regressors. |
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121 | ivec structure_est_LT ( egiw Eg0 ); |
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122 | //!@} |
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123 | |
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124 | //!\name Access attributes |
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125 | //!@{ |
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126 | const egiw& posterior() const { |
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127 | return est; |
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128 | } |
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129 | //!@} |
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130 | |
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131 | //!\name Connection |
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132 | //!@{ |
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133 | void set_rv ( const RV &yrv0 , const RV &rgrrv0 ) { |
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134 | _yrv = yrv0; |
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135 | rgrrv=rgrrv0; |
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136 | set_drv(concat(yrv0, rgrrv)); |
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137 | } |
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138 | |
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139 | RV& get_yrv() { |
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140 | //if yrv is not ready create it |
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141 | if ( _yrv._dsize() != dimx ) { |
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142 | int i = 0; |
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143 | while ( _yrv._dsize() < dimx ) { |
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144 | _yrv.add ( drv ( vec_1 ( i ) ) ); |
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145 | i++; |
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146 | } |
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147 | } |
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148 | //yrv should be ready by now |
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149 | bdm_assert_debug ( _yrv._dsize() == dimx, "incompatible drv" ); |
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150 | return _yrv; |
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151 | } |
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152 | //!@} |
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153 | |
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154 | /*! UI for ARX estimator |
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155 | |
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156 | \code |
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157 | class = 'ARX'; |
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158 | rv = RV({names_of_dt} ) // description of output variables |
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159 | rgr = RV({names_of_regressors}, [-1,-2]} // description of regressor variables |
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160 | constant = 1; // 0/1 switch if the constant term is modelled or not |
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161 | |
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162 | --- optional --- |
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163 | V0 = [1 0;0 1]; // Initial value of information matrix V |
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164 | --- OR --- |
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165 | dV0 = [1e-3, 1e-5, 1e-5, 1e-5]; // Initial value of diagonal of information matrix V |
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166 | // default: 1e-3 for rv, 1e-5 for rgr |
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167 | nu0 = 6; // initial value of nu, default: rgrlen + 2 |
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168 | frg = 1.0; // forgetting, default frg=1.0 |
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169 | |
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170 | rv_param = RV({names_of_parameters}} // description of parametetr names |
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171 | // default: ["theta_i" and "r_i"] |
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172 | \endcode |
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173 | */ |
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174 | void from_setting ( const Setting &set ); |
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175 | |
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176 | void validate() { |
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177 | bdm_assert(dimx == _yrv._dsize(), "RVs of parameters and regressor do not match"); |
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178 | |
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179 | } |
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180 | }; |
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181 | |
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182 | UIREGISTER ( ARX ); |
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183 | SHAREDPTR ( ARX ); |
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184 | |
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185 | /*! ARX model conditined by knowledge of the forgetting factor |
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186 | \f[ f(\theta| d_1 \ldots d_t , \phi_t) \f] |
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187 | */ |
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188 | class ARXfrg : public ARX{ |
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189 | public: |
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190 | ARXfrg():ARX(){}; |
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191 | ARXfrg(const ARXfrg &A0):ARX(A0){}; |
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192 | ARXfrg* _copy_() const {ARXfrg *A = new ARXfrg(*this); return A;} |
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193 | void condition(const vec &val){ |
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194 | frg = val(0); |
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195 | } |
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196 | }; |
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197 | UIREGISTER(ARXfrg); |
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198 | }; |
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199 | #endif // AR_H |
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200 | |
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