[97] | 1 | #include "arx.h" |
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[270] | 2 | namespace bdm { |
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[13] | 3 | |
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[700] | 4 | void ARX::bayes_weighted ( const vec &yt, const vec &cond, const double w ) { |
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[1064] | 5 | bdm_assert_debug ( yt.length() == dimy, "BM::bayes yt is of size "+num2str(yt.length())+" expected dimension is "+num2str(dimy) ); |
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| 6 | bdm_assert_debug ( cond.length() == rgrlen , "BM::bayes cond is of size "+num2str(cond.length())+" expected dimension is "+num2str(rgrlen) ); |
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[679] | 7 | |
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[1064] | 8 | BMEF::bayes_weighted(yt,cond,w); //potential discount scheduling |
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| 9 | double lnc; |
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| 10 | //cache |
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| 11 | ldmat &V = est._V(); |
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| 12 | double &nu = est._nu(); |
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[679] | 13 | |
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[1064] | 14 | dyad.set_subvector ( 0, yt ); |
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| 15 | if (cond.length()>0) |
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| 16 | dyad.set_subvector ( dimy, cond ); |
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| 17 | // possible "1" is there from the beginning |
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[737] | 18 | |
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[1064] | 19 | if ( frg < 1.0 ) { |
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| 20 | est.pow ( frg ); // multiply V and nu |
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[737] | 21 | |
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| 22 | |
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[1064] | 23 | //stabilize |
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| 24 | ldmat V0 = alter_est._V(); //$ copy |
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| 25 | double &nu0 = alter_est._nu(); |
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[97] | 26 | |
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[1064] | 27 | V0 *= ( 1 - frg ); |
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| 28 | V += V0; //stabilization |
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| 29 | nu += ( 1 - frg ) * nu0; |
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| 30 | |
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| 31 | // recompute loglikelihood of new "prior" |
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| 32 | if ( evalll ) { |
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| 33 | last_lognc = est.lognc(); |
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| 34 | } |
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| 35 | } |
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| 36 | V.opupdt ( dyad, w ); |
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| 37 | nu += w; |
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| 38 | |
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| 39 | // log(sqrt(2*pi)) = 0.91893853320467 |
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| 40 | if ( evalll ) { |
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| 41 | lnc = est.lognc(); |
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| 42 | ll = lnc - last_lognc - 0.91893853320467; |
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| 43 | last_lognc = lnc; |
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| 44 | } |
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[97] | 45 | } |
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| 46 | |
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[1009] | 47 | double ARX::logpred ( const vec &yt, const vec &cond ) const { |
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[1064] | 48 | egiw pred ( est ); |
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| 49 | ldmat &V = pred._V(); |
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| 50 | double &nu = pred._nu(); |
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[170] | 51 | |
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[1064] | 52 | double lll; |
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| 53 | vec dyad_p = dyad; |
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| 54 | dyad_p.set_subvector ( 0, yt ); |
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| 55 | dyad_p.set_subvector(dimy,cond); |
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[170] | 56 | |
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[1064] | 57 | if ( frg < 1.0 ) { |
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| 58 | pred.pow ( frg ); |
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| 59 | lll = pred.lognc(); |
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| 60 | } else//should be save: last_lognc is changed only by bayes; |
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| 61 | if ( evalll ) { |
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| 62 | lll = last_lognc; |
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| 63 | } else { |
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| 64 | lll = pred.lognc(); |
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| 65 | } |
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| 66 | |
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| 67 | V.opupdt ( dyad_p, 1.0 ); |
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| 68 | nu += 1.0; |
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| 69 | // log(sqrt(2*pi)) = 0.91893853320467 |
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| 70 | return pred.lognc() - lll - 0.91893853320467; |
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[170] | 71 | } |
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| 72 | |
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[1166] | 73 | vec ARX::samplepred(const vec &cond) const{ |
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| 74 | mat M; |
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| 75 | chmat R; |
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| 76 | est.sample_mat(M,R); |
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| 77 | |
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| 78 | vec tmp; |
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| 79 | if (dimc>0){ |
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| 80 | if (have_constant){ |
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| 81 | tmp = M*concat(cond,1.0); |
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| 82 | } else { |
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| 83 | tmp = M*cond; |
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| 84 | } |
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| 85 | } else { |
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| 86 | tmp = zeros(dimy); |
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| 87 | } |
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| 88 | tmp += R._Ch().T()*randn(dimy); |
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| 89 | return tmp; |
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| 90 | } |
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| 91 | |
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[1013] | 92 | void ARX::flatten ( const BMEF* B , double weight =1.0) { |
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[1064] | 93 | const ARX* A = dynamic_cast<const ARX*> ( B ); |
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| 94 | // nu should be equal to B.nu |
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| 95 | est.pow ( A->posterior()._nu() / posterior()._nu() *weight); |
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| 96 | if ( evalll ) { |
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| 97 | last_lognc = est.lognc(); |
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| 98 | } |
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[738] | 99 | } |
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| 100 | |
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[766] | 101 | ARX* ARX::_copy ( ) const { |
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[1064] | 102 | ARX* Tmp = new ARX ( *this ); |
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| 103 | return Tmp; |
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[170] | 104 | } |
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| 105 | |
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| 106 | void ARX::set_statistics ( const BMEF* B0 ) { |
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[1064] | 107 | const ARX* A0 = dynamic_cast<const ARX*> ( B0 ); |
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[170] | 108 | |
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[1064] | 109 | bdm_assert_debug ( dimension() == A0->dimension(), "Statistics of different dimensions" ); |
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| 110 | set_statistics ( A0->dimensiony(), A0->posterior()._V(), A0->posterior()._nu() ); |
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[170] | 111 | } |
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[180] | 112 | |
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[1003] | 113 | enorm<ldmat>* ARX::epredictor ( const vec &cond ) const { |
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[1064] | 114 | bdm_assert_debug ( cond.length() == rgrlen , "ARX::epredictor cond is of size "+num2str(cond.length())+" expected dimension is "+num2str(rgrlen) ); |
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[270] | 115 | |
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[1064] | 116 | mat mu ( dimy, posterior()._V().rows() - dimy ); |
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| 117 | mat R ( dimy, dimy ); |
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[198] | 118 | |
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[1064] | 119 | vec ext_rgr; |
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| 120 | if (have_constant) { |
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| 121 | ext_rgr = concat(cond,vec_1(1.0)); |
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| 122 | } else { |
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| 123 | ext_rgr = cond; |
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| 124 | } |
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| 125 | |
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| 126 | enorm<ldmat>* tmp; |
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| 127 | tmp = new enorm<ldmat> ( ); |
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| 128 | //TODO: too hackish |
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| 129 | if ( yrv._dsize() > 0 ) { |
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| 130 | } |
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| 131 | |
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| 132 | est.mean_mat ( mu, R ); //mu = |
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| 133 | //correction for student-t -- TODO check if correct!! |
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[1166] | 134 | R*=posterior()._nu()/(posterior()._nu()-2); |
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[1064] | 135 | if (mu.cols()>0) {// nonempty egiw |
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| 136 | mat p_mu = mu.T() * ext_rgr; //the result is one column |
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| 137 | tmp->set_parameters ( p_mu.get_col ( 0 ), ldmat ( R ) ); |
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| 138 | } else { |
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| 139 | tmp->set_parameters ( zeros( R.rows() ), ldmat ( R ) ); |
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| 140 | } |
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| 141 | if (dimy==yrv._dsize()) |
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| 142 | tmp->set_rv(yrv); |
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| 143 | return tmp; |
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[198] | 144 | } |
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| 145 | |
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[270] | 146 | mlstudent* ARX::predictor_student ( ) const { |
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[1064] | 147 | const ldmat &V = posterior()._V(); |
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[737] | 148 | |
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[1064] | 149 | mat mu ( dimy, V.rows() - dimy ); |
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| 150 | mat R ( dimy, dimy ); |
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| 151 | mlstudent* tmp; |
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| 152 | tmp = new mlstudent ( ); |
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[198] | 153 | |
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[1064] | 154 | est.mean_mat ( mu, R ); // |
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| 155 | mu = mu.T(); |
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[270] | 156 | |
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[1064] | 157 | int end = V._L().rows() - 1; |
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| 158 | ldmat Lam ( V._L() ( dimy, end, dimy, end ), V._D() ( dimy, end ) ); //exp val of R |
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[198] | 159 | |
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| 160 | |
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[1064] | 161 | if ( have_constant ) { // no constant term |
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| 162 | //Assume the constant term is the last one: |
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| 163 | if ( mu.cols() > 1 ) { |
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| 164 | tmp->set_parameters ( mu.get_cols ( 0, mu.cols() - 2 ), mu.get_col ( mu.cols() - 1 ), ldmat ( R ), Lam ); |
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| 165 | } else { |
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| 166 | tmp->set_parameters ( mat ( dimy, dimc ), mu.get_col ( mu.cols() - 1 ), ldmat ( R ), Lam ); |
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| 167 | } |
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| 168 | } else { |
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| 169 | // no constant term |
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| 170 | tmp->set_parameters ( mu, zeros ( dimy ), ldmat ( R ), Lam ); |
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| 171 | } |
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| 172 | return tmp; |
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[180] | 173 | } |
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| 174 | |
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[585] | 175 | |
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| 176 | |
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[97] | 177 | /*! \brief Return the best structure |
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| 178 | @param Eg a copy of GiW density that is being examined |
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| 179 | @param Eg0 a copy of prior GiW density before estimation |
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| 180 | @param Egll likelihood of the current Eg |
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[896] | 181 | @param indices current indices |
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[97] | 182 | \return best likelihood in the structure below the given one |
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| 183 | */ |
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[896] | 184 | double egiw_bestbelow ( egiw Eg, egiw Eg0, double Egll, ivec &indices ) { //parameter Eg is a copy! |
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[1064] | 185 | ldmat Vo = Eg._V(); //copy |
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| 186 | ldmat Vo0 = Eg._V(); //copy |
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| 187 | ldmat& Vp = Eg._V(); // pointer into Eg |
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| 188 | ldmat& Vp0 = Eg._V(); // pointer into Eg |
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| 189 | int end = Vp.rows() - 1; |
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| 190 | int i; |
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| 191 | mat Li; |
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| 192 | mat Li0; |
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| 193 | double maxll = Egll; |
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| 194 | double tmpll = Egll; |
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| 195 | double belll = Egll; |
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[97] | 196 | |
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[1064] | 197 | ivec tmpindices; |
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| 198 | ivec maxindices = indices; |
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[97] | 199 | |
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[115] | 200 | |
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[1064] | 201 | cout << "bb:(" << indices << ") ll=" << Egll << endl; |
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[115] | 202 | |
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[1064] | 203 | //try to remove only one rv |
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| 204 | for ( i = 0; i < end; i++ ) { |
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| 205 | //copy original |
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| 206 | Li = Vo._L(); |
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| 207 | Li0 = Vo0._L(); |
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| 208 | //remove stuff |
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| 209 | Li.del_col ( i + 1 ); |
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| 210 | Li0.del_col ( i + 1 ); |
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| 211 | Vp.ldform ( Li, Vo._D() ); |
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| 212 | Vp0.ldform ( Li0, Vo0._D() ); |
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| 213 | tmpll = Eg.lognc() - Eg0.lognc(); // likelihood is difference of norm. coefs. |
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[115] | 214 | |
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[1064] | 215 | cout << "i=(" << i << ") ll=" << tmpll << endl; |
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[170] | 216 | |
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[1064] | 217 | // |
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| 218 | if ( tmpll > Egll ) { //increase of the likelihood |
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| 219 | tmpindices = indices; |
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| 220 | tmpindices.del ( i ); |
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| 221 | //search for a better match in this substructure |
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| 222 | belll = egiw_bestbelow ( Eg, Eg0, tmpll, tmpindices ); |
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| 223 | if ( belll > maxll ) { //better match found |
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| 224 | maxll = belll; |
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| 225 | maxindices = tmpindices; |
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| 226 | } |
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| 227 | } |
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| 228 | } |
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| 229 | indices = maxindices; |
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| 230 | return maxll; |
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[97] | 231 | } |
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| 232 | |
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[1003] | 233 | ivec ARX::structure_est ( const egiw &est0 ) { |
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[1064] | 234 | ivec ind = linspace ( 1, est.dimension() - 1 ); |
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| 235 | egiw_bestbelow ( est, est0, est.lognc() - est0.lognc(), ind ); |
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| 236 | return ind; |
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[97] | 237 | } |
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[254] | 238 | |
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[577] | 239 | |
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| 240 | |
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[1003] | 241 | ivec ARX::structure_est_LT ( const egiw &est0 ) { |
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[1064] | 242 | //some stuff with beliefs etc. |
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| 243 | ivec belief = vec_1 ( 2 ); // default belief |
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| 244 | int nbest = 1; // nbest: how many regressors are returned |
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| 245 | int nrep = 5; // nrep: number of random repetions of structure estimation |
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| 246 | double lambda = 0.9; |
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| 247 | int k = 2; |
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| 248 | |
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| 249 | Array<str_aux> o2; |
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| 250 | |
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| 251 | ivec ind = bdm::straux1(est._V(),est._nu(), est0._V(), est0._nu(), belief, nbest, nrep, lambda, k, o2); |
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| 252 | |
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| 253 | return ind; |
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[577] | 254 | } |
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| 255 | |
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[477] | 256 | void ARX::from_setting ( const Setting &set ) { |
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[1064] | 257 | BMEF::from_setting(set); |
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[737] | 258 | |
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[1064] | 259 | UI::get (rgr, set, "rgr", UI::compulsory ); |
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[585] | 260 | |
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[1064] | 261 | dimy = yrv._dsize(); |
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| 262 | bdm_assert(dimy>0,"ARX::yrv should not be empty"); |
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| 263 | rgrlen = rgr._dsize(); |
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[357] | 264 | |
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[1064] | 265 | int constant; |
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| 266 | if ( !UI::get ( constant, set, "constant", UI::optional ) ) { |
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| 267 | have_constant = true; |
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| 268 | } else { |
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| 269 | have_constant = constant > 0; |
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| 270 | } |
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| 271 | dimc = rgrlen; |
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| 272 | rvc = rgr; |
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| 273 | |
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| 274 | //init |
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| 275 | shared_ptr<egiw> pri = UI::build<egiw> ( set, "prior", UI::optional ); |
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| 276 | if (pri) { |
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| 277 | set_prior(pri.get()); |
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| 278 | } else { |
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| 279 | shared_ptr<egiw> post = UI::build<egiw> ( set, "posterior", UI::optional ); |
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| 280 | set_prior(post.get()); |
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| 281 | } |
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| 282 | |
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| 283 | |
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| 284 | shared_ptr<egiw> alt = UI::build<egiw> ( set, "alternative", UI::optional ); |
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| 285 | if ( alt ) { |
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| 286 | bdm_assert ( alt->_dimx() == dimy, "alternative is not compatible" ); |
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| 287 | bdm_assert ( alt->_V().rows() == dimy + rgrlen + int(have_constant==true), "alternative is not compatible" ); |
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| 288 | alter_est.set_parameters ( alt->_dimx(), alt->_V(), alt->_nu() ); |
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| 289 | alter_est.validate(); |
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| 290 | } |
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| 291 | // frg handled by BMEF |
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| 292 | |
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[270] | 293 | } |
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[850] | 294 | |
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[1064] | 295 | void ARX::set_prior(const epdf *pri) { |
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| 296 | const egiw * eg=dynamic_cast<const egiw*>(pri); |
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| 297 | if ( eg ) { |
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| 298 | bdm_assert ( eg->_dimx() == dimy, "prior is not compatible" ); |
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| 299 | bdm_assert ( eg->_V().rows() == dimy + rgrlen + int(have_constant==true), "prior is not compatible" ); |
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| 300 | est.set_parameters ( eg->_dimx(), eg->_V(), eg->_nu() ); |
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| 301 | est.validate(); |
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| 302 | } else { |
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| 303 | est.set_parameters ( dimy, zeros ( dimy + rgrlen +int(have_constant==true)) ); |
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| 304 | set_prior_default ( est ); |
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| 305 | } |
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| 306 | //check alternative |
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| 307 | if (alter_est.dimension()!=dimension()) { |
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| 308 | alter_est = est; |
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| 309 | } |
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[679] | 310 | } |
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[1025] | 311 | |
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| 312 | void ARXpartialforg::bayes ( const vec &val, const vec &cond ) { |
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[1064] | 313 | #define LOG2 0.69314718055995 |
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[1025] | 314 | vec frg = cond.right(cond.length() - rgrlen); |
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| 315 | vec cond_rgr = cond.left(rgrlen); // regression vector |
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| 316 | |
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| 317 | int dimV = est._V().cols(); |
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| 318 | int nparams = dimV - 1; // number of parameters |
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[1030] | 319 | int nalternatives = 1 << nparams; // number of alternatives |
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| 320 | |
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[1025] | 321 | // Permutation matrix |
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| 322 | mat perm_matrix = ones(nalternatives, nparams); |
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| 323 | int i, j, period, idx_from, idx_to, start, end; |
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| 324 | for(i = 0; i < nparams; i++) { |
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[1064] | 325 | idx_from = 1 << i; |
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| 326 | period = ( idx_from << 1 ); |
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[1030] | 327 | idx_to = period - 1; |
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[1064] | 328 | j = 0; |
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[1025] | 329 | start = idx_from; |
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| 330 | end = idx_to; |
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[1064] | 331 | while ( start < nalternatives ) { |
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[1025] | 332 | perm_matrix.set_submatrix(start, end, i, i, 0); |
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| 333 | j++; |
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| 334 | start = idx_from + period * j; |
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| 335 | end = idx_to + period * j; |
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| 336 | } |
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| 337 | } |
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| 338 | |
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| 339 | // Array of egiws for approximation |
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| 340 | Array<egiw*> egiw_array(nalternatives + 1); |
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| 341 | // No. of conditioning rows in LD |
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| 342 | int nalternatives_cond, position; |
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| 343 | |
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| 344 | for(int i = 0; i < nalternatives; i++) { |
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| 345 | // vector defining alternatives |
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| 346 | vec vec_alt = perm_matrix.get_row(i); |
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| 347 | |
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| 348 | // full alternative or filtered |
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| 349 | if( sum(vec_alt) == vec_alt.length() ) { |
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| 350 | egiw_array(i) = &alter_est; |
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| 351 | continue; |
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| 352 | } else if( sum(vec_alt) == 0 ) { |
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| 353 | egiw_array(i) = &est; |
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| 354 | continue; |
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| 355 | } |
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| 356 | |
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[1030] | 357 | nalternatives_cond = (int) sum(vec_alt) + 1; |
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[1025] | 358 | ivec vec_perm(0); // permutation vector |
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| 359 | |
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| 360 | for(int j = 0; j < nparams; j++) { |
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| 361 | position = dimV - j - 2; |
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| 362 | if ( vec_alt(position) == 0 ) { |
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| 363 | vec_perm.ins(j, position + 1); |
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| 364 | } |
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| 365 | else { |
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| 366 | vec_perm.ins(0, position + 1); |
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| 367 | } |
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| 368 | } |
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| 369 | vec_perm.ins(0, 0); |
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| 370 | |
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| 371 | ldmat filt (est._V(), vec_perm); |
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| 372 | ldmat alt (alter_est._V(), vec_perm); |
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| 373 | |
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| 374 | mat tmpL(dimV, dimV); |
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| 375 | tmpL.set_rows( 0, alt._L().get_rows(0, nalternatives_cond - 1) ); |
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| 376 | tmpL.set_rows( nalternatives_cond, filt._L().get_rows(nalternatives_cond, nparams) ); |
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| 377 | |
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| 378 | vec tmpD(dimV); |
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| 379 | tmpD.set_subvector( 0, alt._D()(0, nalternatives_cond - 1) ); |
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| 380 | tmpD.set_subvector( nalternatives_cond, filt._D()(nalternatives_cond, nparams) ); |
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| 381 | |
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| 382 | ldmat tmpLD (tmpL, tmpD); |
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| 383 | |
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| 384 | vec_perm = sort_index(vec_perm); |
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| 385 | ldmat newLD (tmpLD, vec_perm); |
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| 386 | |
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| 387 | egiw_array(i) = new egiw(1, newLD, alter_est._nu()); |
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| 388 | } |
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| 389 | |
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| 390 | // Approximation |
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| 391 | double sumVecCommon; // frequently used term |
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| 392 | vec vecNu(nalternatives); // vector of nus of components |
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[1064] | 393 | vec vecD(nalternatives); // vector of LS reminders |
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[1025] | 394 | vec vecCommon(nalternatives); // vector of common parts |
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| 395 | mat matVecsTheta; // matrix whose rows are theta vects. |
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| 396 | |
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| 397 | for (i = 0; i < nalternatives; i++) { |
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| 398 | vecNu.shift_left( egiw_array(i)->_nu() ); |
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| 399 | vecD.shift_left( egiw_array(i)->_V()._D()(0) ); |
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| 400 | matVecsTheta.append_row( egiw_array(i)->est_theta() ); |
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| 401 | } |
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| 402 | |
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| 403 | vecCommon = elem_mult ( frg, elem_div(vecNu, vecD) ); |
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| 404 | sumVecCommon = sum(vecCommon); |
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| 405 | |
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| 406 | // approximation of est. regr. coefficients |
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[1064] | 407 | vec aprEstTheta(nparams); |
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| 408 | aprEstTheta.zeros(); |
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[1025] | 409 | for (i = 0; i < nalternatives; i++) { |
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| 410 | aprEstTheta += matVecsTheta.get_row(i) * vecCommon(i); |
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| 411 | } |
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| 412 | aprEstTheta /= sumVecCommon; |
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[1064] | 413 | |
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[1025] | 414 | // approximation of degr. of freedom |
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| 415 | double aprNu; |
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| 416 | double A = log( sumVecCommon ); // Term 'A' in equation |
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| 417 | for ( int i = 0; i < nalternatives; i++ ) { |
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| 418 | A += frg(i) * ( log( vecD(i) ) - psi( 0.5 * vecNu(i) ) ); |
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| 419 | } |
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| 420 | aprNu = ( 1 + sqrt(1 + 4 * (A - LOG2)/3 ) ) / ( 2 * (A - LOG2) ); |
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| 421 | |
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| 422 | // approximation of LS reminder D(0,0) |
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| 423 | double aprD = aprNu / sumVecCommon; |
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| 424 | |
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| 425 | // Aproximation of covariance of LS est. |
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| 426 | mat aprC = zeros(nparams, nparams); |
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| 427 | for ( int i = 0; i < nalternatives; i++ ) { |
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[1064] | 428 | aprC += egiw_array(i)->est_theta_cov().to_mat() * frg(i); |
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[1025] | 429 | vec tmp = ( matVecsTheta.get_row(i) - aprEstTheta ); |
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| 430 | aprC += vecCommon(i) * outer_product( tmp, tmp); |
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| 431 | } |
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| 432 | |
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| 433 | // Construct GiW pdf |
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| 434 | ldmat aprCinv ( inv(aprC) ); |
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| 435 | vec D = concat( aprD, aprCinv._D() ); |
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| 436 | mat L = eye(dimV); |
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| 437 | L.set_submatrix(1, 0, aprCinv._L() * aprEstTheta); |
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| 438 | L.set_submatrix(1, 1, aprCinv._L()); |
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| 439 | ldmat aprLD (L, D); |
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| 440 | est = egiw(1, aprLD, aprNu); |
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| 441 | |
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[1064] | 442 | if ( evalll ) { |
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| 443 | last_lognc = est.lognc(); |
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| 444 | } |
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| 445 | |
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[1025] | 446 | // update |
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| 447 | ARX::bayes ( val, cond_rgr ); |
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[973] | 448 | } |
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[357] | 449 | |
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[1025] | 450 | } |
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