1 | |
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2 | #include "kalman.h" |
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3 | |
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4 | namespace bdm { |
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5 | |
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6 | using std::endl; |
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7 | |
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8 | |
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9 | |
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10 | void KalmanFull::bayes ( const vec &yt, const vec &cond ) { |
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11 | bdm_assert_debug ( yt.length() == ( dimy ), "KalmanFull::bayes wrong size of dt" ); |
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12 | |
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13 | const vec &u = cond; // in this case cond=ut |
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14 | const vec &y = yt; |
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15 | |
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16 | vec& mu = est._mu(); |
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17 | mat &P = est._R(); |
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18 | mat& _Ry = fy._R(); |
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19 | vec& yp = fy._mu(); |
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20 | //Time update |
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21 | mu = A * mu + B * u; |
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22 | P = A * P * A.transpose() + ( mat ) Q; |
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23 | |
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24 | //Data update |
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25 | _Ry = C * P * C.transpose() + ( mat ) R; |
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26 | _K = P * C.transpose() * inv ( _Ry ); |
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27 | P -= _K * C * P; // P = P -KCP; |
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28 | yp = C * mu + D * u; |
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29 | mu += _K * ( y - yp ); |
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30 | |
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31 | if ( evalll ) { |
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32 | ll = fy.evallog ( y ); |
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33 | } |
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34 | }; |
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35 | |
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36 | |
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37 | |
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38 | /////////////////////////////// EKFS |
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39 | EKFfull::EKFfull ( ) : KalmanFull () {}; |
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40 | |
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41 | void EKFfull::set_parameters ( const shared_ptr<diffbifn> &pfxu0, const shared_ptr<diffbifn> &phxu0, const mat Q0, const mat R0 ) { |
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42 | pfxu = pfxu0; |
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43 | phxu = phxu0; |
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44 | |
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45 | set_dim ( pfxu0->_dimx() ); |
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46 | dimy = phxu0->dimension(); |
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47 | dimc = pfxu0->_dimu(); |
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48 | est.set_parameters ( zeros ( dimension() ), eye ( dimension() ) ); |
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49 | |
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50 | A.set_size ( dimension(), dimension() ); |
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51 | C.set_size ( dimy, dimension() ); |
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52 | //initialize matrices A C, later, these will be only updated! |
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53 | pfxu->dfdx_cond ( est._mu(), zeros ( dimc ), A, true ); |
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54 | B.clear(); |
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55 | phxu->dfdx_cond ( est._mu(), zeros ( dimc ), C, true ); |
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56 | D.clear(); |
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57 | |
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58 | R = R0; |
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59 | Q = Q0; |
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60 | } |
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61 | |
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62 | void EKFfull::bayes ( const vec &yt, const vec &cond ) { |
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63 | bdm_assert_debug ( yt.length() == ( dimy ), "EKFull::bayes wrong size of dt" ); |
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64 | bdm_assert_debug ( cond.length() == ( dimc ), "EKFull::bayes wrong size of dt" ); |
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65 | |
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66 | const vec &u = cond; |
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67 | const vec &y = yt; //lazy to change it |
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68 | vec &mu = est._mu(); |
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69 | mat &P = est._R(); |
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70 | mat& _Ry = fy._R(); |
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71 | vec& yp = fy._mu(); |
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72 | |
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73 | pfxu->dfdx_cond ( mu, zeros ( dimc ), A, true ); |
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74 | phxu->dfdx_cond ( mu, zeros ( dimc ), C, true ); |
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75 | |
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76 | //Time update |
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77 | mu = pfxu->eval ( mu, u );// A*mu + B*u; |
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78 | P = A * P * A.transpose() + ( mat ) Q; |
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79 | |
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80 | //Data update |
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81 | _Ry = C * P * C.transpose() + ( mat ) R; |
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82 | _K = P * C.transpose() * inv ( _Ry ); |
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83 | P -= _K * C * P; // P = P -KCP; |
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84 | yp = phxu->eval ( mu, u ); |
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85 | mu += _K * ( y - yp ); |
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86 | |
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87 | if ( BM::evalll ) { |
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88 | ll = fy.evallog ( y ); |
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89 | } |
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90 | }; |
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91 | |
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92 | |
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93 | |
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94 | void KalmanCh::set_parameters ( const mat &A0, const mat &B0, const mat &C0, const mat &D0, const chmat &Q0, const chmat &R0 ) { |
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95 | |
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96 | ( ( StateSpace<chmat>* ) this )->set_parameters ( A0, B0, C0, D0, Q0, R0 ); |
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97 | |
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98 | _K = zeros ( dimension(), dimy ); |
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99 | } |
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100 | |
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101 | void KalmanCh::initialize() { |
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102 | preA = zeros ( dimy + dimension() + dimension(), dimy + dimension() ); |
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103 | // preA.clear(); |
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104 | preA.set_submatrix ( 0, 0, R._Ch() ); |
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105 | preA.set_submatrix ( dimy + dimension(), dimy, Q._Ch() ); |
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106 | } |
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107 | |
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108 | void KalmanCh::bayes ( const vec &yt, const vec &cond ) { |
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109 | bdm_assert_debug ( yt.length() == dimy, "yt mismatch" ); |
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110 | bdm_assert_debug ( cond.length() == dimc, "yt mismatch" ); |
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111 | |
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112 | const vec &u = cond; |
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113 | const vec &y = yt; |
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114 | vec pom ( dimy ); |
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115 | |
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116 | chmat &_P = est._R(); |
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117 | vec &_mu = est._mu(); |
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118 | mat _K ( dimension(), dimy ); |
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119 | chmat &_Ry = fy._R(); |
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120 | vec &_yp = fy._mu(); |
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121 | //TODO get rid of Q in qr()! |
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122 | // mat Q; |
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123 | |
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124 | //R and Q are already set in set_parameters() |
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125 | preA.set_submatrix ( dimy, 0, ( _P._Ch() ) *C.T() ); |
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126 | //Fixme can be more efficient if .T() is not used |
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127 | preA.set_submatrix ( dimy, dimy, ( _P._Ch() ) *A.T() ); |
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128 | |
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129 | if ( !qr ( preA, postA ) ) { |
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130 | bdm_warning ( "QR in KalmanCh unstable!" ); |
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131 | } |
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132 | |
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133 | ( _Ry._Ch() ) = postA ( 0, dimy - 1, 0, dimy - 1 ); |
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134 | _K = inv ( A ) * ( postA ( 0, dimy - 1 , dimy, dimy + dimension() - 1 ) ).T(); |
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135 | ( _P._Ch() ) = postA ( dimy, dimy + dimension() - 1, dimy, dimy + dimension() - 1 ); |
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136 | |
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137 | _mu = A * ( _mu ) + B * u; |
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138 | _yp = C * _mu - D * u; |
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139 | |
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140 | backward_substitution ( _Ry._Ch(), ( y - _yp ), pom ); |
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141 | _mu += ( _K ) * pom; |
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142 | |
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143 | /* cout << "P:" <<_P.to_mat() <<endl; |
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144 | cout << "Ry:" <<_Ry.to_mat() <<endl; |
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145 | cout << "_K:" <<_K <<endl;*/ |
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146 | |
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147 | if ( evalll == true ) { //likelihood of observation y |
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148 | ll = fy.evallog ( y ); |
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149 | } |
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150 | } |
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151 | |
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152 | void StateCanonical::connect_mlnorm ( const mlnorm<fsqmat> &ml ) { |
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153 | //get ids of yrv |
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154 | const RV &yrv = ml._rv(); |
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155 | //need to determine u_t - it is all in _rvc that is not in ml._rv() |
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156 | RV rgr0 = ml._rvc().remove_time(); |
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157 | RV urv = rgr0.subt ( yrv ); |
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158 | |
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159 | //We can do only 1d now... :( |
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160 | bdm_assert ( yrv._dsize() == 1, "Only for SISO so far..." ); |
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161 | |
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162 | // create names for |
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163 | RV xrv; //empty |
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164 | RV Crv; //empty |
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165 | int td = ml._rvc().mint(); |
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166 | // assuming strictly proper function!!! |
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167 | for ( int t = -1; t >= td; t-- ) { |
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168 | xrv.add ( yrv.copy_t ( t ) ); |
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169 | Crv.add ( urv.copy_t ( t ) ); |
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170 | } |
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171 | |
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172 | // get mapp |
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173 | th2A.set_connection ( xrv, ml._rvc() ); |
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174 | th2C.set_connection ( Crv, ml._rvc() ); |
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175 | th2D.set_connection ( urv, ml._rvc() ); |
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176 | |
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177 | //set matrix sizes |
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178 | this->A = zeros ( xrv._dsize(), xrv._dsize() ); |
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179 | for ( int j = 1; j < xrv._dsize(); j++ ) { |
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180 | A ( j, j - 1 ) = 1.0; // off diagonal |
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181 | } |
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182 | this->B = zeros ( xrv._dsize(), 1 ); |
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183 | this->B ( 0 ) = 1.0; |
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184 | this->C = zeros ( 1, xrv._dsize() ); |
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185 | this->D = zeros ( 1, urv._dsize() ); |
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186 | this->Q = zeros ( xrv._dsize(), xrv._dsize() ); |
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187 | // R is set by update |
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188 | |
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189 | //set cache |
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190 | this->A1row = zeros ( xrv._dsize() ); |
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191 | this->C1row = zeros ( xrv._dsize() ); |
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192 | this->D1row = zeros ( urv._dsize() ); |
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193 | |
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194 | update_from ( ml ); |
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195 | validate(); |
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196 | }; |
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197 | |
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198 | void StateCanonical::update_from ( const mlnorm<fsqmat> &ml ) { |
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199 | |
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200 | vec theta = ml._A().get_row ( 0 ); // this |
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201 | |
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202 | th2A.filldown ( theta, A1row ); |
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203 | th2C.filldown ( theta, C1row ); |
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204 | th2D.filldown ( theta, D1row ); |
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205 | |
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206 | R = ml._R(); |
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207 | |
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208 | A.set_row ( 0, A1row ); |
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209 | C.set_row ( 0, C1row + D1row ( 0 ) *A1row ); |
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210 | D.set_row ( 0, D1row ); |
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211 | } |
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212 | |
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213 | void StateFromARX::connect_mlnorm ( const mlnorm<chmat> &ml, RV &xrv, RV &urv ) { |
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214 | //get ids of yrv |
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215 | const RV &yrv = ml._rv(); |
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216 | //need to determine u_t - it is all in _rvc that is not in ml._rv() |
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217 | const RV &rgr = ml._rvc(); |
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218 | RV rgr0 = rgr.remove_time(); |
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219 | urv = rgr0.subt ( yrv ); |
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220 | |
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221 | // create names for state variables |
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222 | xrv = yrv; |
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223 | |
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224 | int y_multiplicity = -rgr.mint ( yrv ); |
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225 | int y_block_size = yrv.length() * ( y_multiplicity ); // current yt + all delayed yts |
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226 | for ( int m = 0; m < y_multiplicity - 1; m++ ) { // ========= -1 is important see arx2statespace_notes |
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227 | xrv.add ( yrv.copy_t ( -m - 1 ) ); //add delayed yt |
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228 | } |
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229 | //! temporary RV for connection to ml.rvc, since notation of xrv and ml.rvc does not match |
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230 | RV xrv_ml = xrv.copy_t ( -1 ); |
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231 | |
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232 | // add regressors |
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233 | ivec u_block_sizes ( urv.length() ); // no_blocks = yt + unique rgr |
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234 | for ( int r = 0; r < urv.length(); r++ ) { |
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235 | RV R = urv.subselect ( vec_1 ( r ) ); //non-delayed element of rgr |
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236 | int r_size = urv.size ( r ); |
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237 | int r_multiplicity = -rgr.mint ( R ); |
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238 | u_block_sizes ( r ) = r_size * r_multiplicity ; |
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239 | for ( int m = 0; m < r_multiplicity; m++ ) { |
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240 | xrv.add ( R.copy_t ( -m - 1 ) ); //add delayed yt |
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241 | xrv_ml.add ( R.copy_t ( -m - 1 ) ); //add delayed yt |
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242 | } |
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243 | } |
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244 | // add constant |
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245 | if ( any ( ml._mu_const() != 0.0 ) ) { |
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246 | have_constant = true; |
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247 | xrv.add ( RV ( "bdm_reserved_constant_one", 1 ) ); |
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248 | } else { |
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249 | have_constant = false; |
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250 | } |
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251 | |
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252 | |
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253 | // get mapp |
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254 | th2A.set_connection ( xrv_ml, ml._rvc() ); |
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255 | th2B.set_connection ( urv, ml._rvc() ); |
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256 | |
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257 | //set matrix sizes |
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258 | this->A = zeros ( xrv._dsize(), xrv._dsize() ); |
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259 | //create y block |
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260 | diagonal_part ( this->A, yrv._dsize(), 0, y_block_size - yrv._dsize() ); |
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261 | |
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262 | this->B = zeros ( xrv._dsize(), urv._dsize() ); |
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263 | //add diagonals for rgr |
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264 | int active_x = y_block_size; |
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265 | for ( int r = 0; r < urv.length(); r++ ) { |
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266 | if (u_block_sizes(r)>0){ |
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267 | diagonal_part ( this->A, active_x + urv.size ( r ), active_x, u_block_sizes ( r ) - urv.size ( r ) ); |
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268 | this->B.set_submatrix ( active_x, 0, eye ( urv.size ( r ) ) ); |
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269 | } |
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270 | active_x += u_block_sizes ( r ); |
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271 | } |
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272 | this->C = zeros ( yrv._dsize(), xrv._dsize() ); |
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273 | this->C.set_submatrix ( 0, 0, eye ( yrv._dsize() ) ); |
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274 | this->D = zeros ( yrv._dsize(), urv._dsize() ); |
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275 | this->R.setCh ( zeros ( yrv._dsize(), yrv._dsize() ) ); |
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276 | this->Q.setCh ( zeros ( xrv._dsize(), xrv._dsize() ) ); |
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277 | // Q is set by update |
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278 | |
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279 | update_from ( ml ); |
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280 | validate(); |
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281 | } |
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282 | |
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283 | void StateFromARX::update_from ( const mlnorm<chmat> &ml ) { |
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284 | vec Arow = zeros ( A.cols() ); |
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285 | vec Brow = zeros ( B.cols() ); |
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286 | // ROW- WISE EVALUATION ===== |
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287 | for ( int i = 0; i < ml._rv()._dsize(); i++ ) { |
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288 | |
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289 | vec theta = ml._A().get_row ( i ); |
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290 | |
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291 | th2A.filldown ( theta, Arow ); |
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292 | if ( have_constant ) { |
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293 | // constant is always at the end no need for datalink |
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294 | Arow ( A.cols() - 1 ) = ml._mu_const() ( i ); |
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295 | } |
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296 | this->A.set_row ( i, Arow ); |
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297 | |
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298 | th2B.filldown ( theta, Brow ); |
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299 | this->B.set_row ( i, Brow ); |
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300 | } |
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301 | this->Q._Ch().set_submatrix ( 0, 0, ml.__R()._Ch() ); |
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302 | |
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303 | } |
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304 | |
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305 | |
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306 | void EKFCh::set_parameters ( const shared_ptr<diffbifn> &pfxu0, const shared_ptr<diffbifn> &phxu0, const chmat Q0, const chmat R0 ) { |
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307 | pfxu = pfxu0; |
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308 | phxu = phxu0; |
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309 | |
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310 | set_dim ( pfxu0->_dimx() ); |
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311 | dimy = phxu0->dimension(); |
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312 | dimc = pfxu0->_dimu(); |
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313 | |
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314 | vec &_mu = est._mu(); |
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315 | // if mu is not set, set it to zeros, just for constant terms of A and C |
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316 | if ( _mu.length() != dimension() ) _mu = zeros ( dimension() ); |
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317 | A = zeros ( dimension(), dimension() ); |
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318 | C = zeros ( dimy, dimension() ); |
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319 | preA = zeros ( dimy + dimension() + dimension(), dimy + dimension() ); |
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320 | |
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321 | //initialize matrices A C, later, these will be only updated! |
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322 | pfxu->dfdx_cond ( _mu, zeros ( dimc ), A, true ); |
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323 | // pfxu->dfdu_cond ( *_mu,zeros ( dimu ),B,true ); |
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324 | B.clear(); |
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325 | phxu->dfdx_cond ( _mu, zeros ( dimc ), C, true ); |
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326 | // phxu->dfdu_cond ( *_mu,zeros ( dimu ),D,true ); |
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327 | D.clear(); |
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328 | |
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329 | R = R0; |
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330 | Q = Q0; |
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331 | |
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332 | // Cholesky special! |
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333 | preA.clear(); |
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334 | preA.set_submatrix ( 0, 0, R._Ch() ); |
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335 | preA.set_submatrix ( dimy + dimension(), dimy, Q._Ch() ); |
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336 | } |
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337 | |
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338 | |
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339 | void EKFCh::bayes ( const vec &yt, const vec &cond ) { |
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340 | |
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341 | vec pom ( dimy ); |
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342 | const vec &u = cond; |
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343 | const vec &y = yt; |
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344 | vec &_mu = est._mu(); |
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345 | chmat &_P = est._R(); |
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346 | chmat &_Ry = fy._R(); |
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347 | vec &_yp = fy._mu(); |
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348 | |
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349 | pfxu->dfdx_cond ( _mu, u, A, false ); //update A by a derivative of fx |
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350 | phxu->dfdx_cond ( _mu, u, C, false ); //update A by a derivative of fx |
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351 | |
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352 | //R and Q are already set in set_parameters() |
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353 | preA.set_submatrix ( dimy, 0, ( _P._Ch() ) *C.T() ); |
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354 | //Fixme can be more efficient if .T() is not used |
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355 | preA.set_submatrix ( dimy, dimy, ( _P._Ch() ) *A.T() ); |
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356 | |
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357 | // mat Sttm = _P->to_mat(); |
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358 | // cout << preA <<endl; |
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359 | // cout << "_mu:" << _mu <<endl; |
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360 | |
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361 | if ( !qr ( preA, postA ) ) { |
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362 | bdm_warning ( "QR in EKFCh unstable!" ); |
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363 | } |
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364 | |
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365 | |
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366 | ( _Ry._Ch() ) = postA ( 0, dimy - 1, 0, dimy - 1 ); |
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367 | _K = inv ( A ) * ( postA ( 0, dimy - 1 , dimy, dimy + dimension() - 1 ) ).T(); |
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368 | ( _P._Ch() ) = postA ( dimy, dimy + dimension() - 1, dimy, dimy + dimension() - 1 ); |
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369 | |
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370 | // mat iRY = inv(_Ry->to_mat()); |
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371 | // mat Stt = Sttm - Sttm * C.T() * iRY * C * Sttm; |
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372 | // mat _K2 = Stt*C.T()*inv(R.to_mat()); |
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373 | |
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374 | // prediction |
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375 | _mu = pfxu->eval ( _mu , u ); |
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376 | _yp = phxu->eval ( _mu, u ); |
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377 | |
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378 | /* vec mu2 = *_mu + ( _K2 ) * ( y-*_yp );*/ |
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379 | |
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380 | //correction //= initial value is already prediction! |
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381 | backward_substitution ( _Ry._Ch(), ( y - _yp ), pom ); |
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382 | _mu += ( _K ) * pom ; |
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383 | |
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384 | /* _K = (_P->to_mat())*C.transpose() * ( _iRy->to_mat() ); |
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385 | *_mu = pfxu->eval ( *_mu ,u ) + ( _K )* ( y-*_yp );*/ |
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386 | |
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387 | // cout << "P:" <<_P.to_mat() <<endl; |
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388 | // cout << "Ry:" <<_Ry.to_mat() <<endl; |
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389 | // cout << "_mu:" <<_mu <<endl; |
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390 | // cout << "dt:" <<dt <<endl; |
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391 | |
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392 | if ( evalll == true ) { //likelihood of observation y |
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393 | ll = fy.evallog ( y ); |
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394 | } |
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395 | } |
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396 | |
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397 | void EKFCh::from_setting ( const Setting &set ) { |
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398 | BM::from_setting ( set ); |
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399 | shared_ptr<diffbifn> IM = UI::build<diffbifn> ( set, "IM", UI::compulsory ); |
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400 | shared_ptr<diffbifn> OM = UI::build<diffbifn> ( set, "OM", UI::compulsory ); |
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401 | |
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402 | //statistics |
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403 | int dim = IM->dimension(); |
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404 | vec mu0; |
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405 | if ( !UI::get ( mu0, set, "mu0" ) ) |
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406 | mu0 = zeros ( dim ); |
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407 | |
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408 | mat P0; |
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409 | vec dP0; |
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410 | if ( UI::get ( dP0, set, "dP0" ) ) |
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411 | P0 = diag ( dP0 ); |
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412 | else if ( !UI::get ( P0, set, "P0" ) ) |
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413 | P0 = eye ( dim ); |
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414 | |
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415 | set_statistics ( mu0, P0 ); |
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416 | |
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417 | //parameters |
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418 | vec dQ, dR; |
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419 | UI::get ( dQ, set, "dQ", UI::compulsory ); |
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420 | UI::get ( dR, set, "dR", UI::compulsory ); |
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421 | set_parameters ( IM, OM, diag ( dQ ), diag ( dR ) ); |
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422 | } |
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423 | |
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424 | void MultiModel::from_setting ( const Setting &set ) { |
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425 | Array<EKFCh*> A; |
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426 | UI::get ( A, set, "models", UI::compulsory ); |
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427 | |
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428 | set_parameters ( A ); |
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429 | set_yrv ( A ( 0 )->_yrv() ); |
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430 | //set_rv(A(0)->_rv()); |
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431 | |
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432 | string options; |
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433 | if ( set.lookupValue ( "options", options ) ) |
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434 | set_options ( options ); |
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435 | } |
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436 | |
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437 | } |
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