1 | /*! |
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2 | \file |
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3 | \brief Probability distributions for Exponential Family models. |
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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 EF_H |
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14 | #define EF_H |
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15 | |
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16 | |
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17 | #include "libBM.h" |
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18 | #include "../math/chmat.h" |
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19 | //#include <std> |
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20 | |
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21 | namespace bdm { |
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22 | |
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23 | |
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24 | //! Global Uniform_RNG |
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25 | extern Uniform_RNG UniRNG; |
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26 | //! Global Normal_RNG |
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27 | extern Normal_RNG NorRNG; |
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28 | //! Global Gamma_RNG |
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29 | extern Gamma_RNG GamRNG; |
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30 | |
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31 | /*! |
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32 | * \brief General conjugate exponential family posterior density. |
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33 | |
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34 | * More?... |
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35 | */ |
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36 | |
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37 | class eEF : public epdf { |
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38 | public: |
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39 | // eEF() :epdf() {}; |
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40 | //! default constructor |
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41 | eEF ( ) :epdf ( ) {}; |
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42 | //! logarithm of the normalizing constant, \f$\mathcal{I}\f$ |
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43 | virtual double lognc() const =0; |
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44 | //!TODO decide if it is really needed |
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45 | virtual void dupdate ( mat &v ) {it_error ( "Not implemented" );}; |
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46 | //!Evaluate normalized log-probability |
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47 | virtual double evallog_nn ( const vec &val ) const{it_error ( "Not implemented" );return 0.0;}; |
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48 | //!Evaluate normalized log-probability |
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49 | virtual double evallog ( const vec &val ) const {double tmp;tmp= evallog_nn ( val )-lognc();it_assert_debug ( std::isfinite ( tmp ),"Infinite value" ); return tmp;} |
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50 | //!Evaluate normalized log-probability for many samples |
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51 | virtual vec evallog ( const mat &Val ) const { |
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52 | vec x ( Val.cols() ); |
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53 | for ( int i=0;i<Val.cols();i++ ) {x ( i ) =evallog_nn ( Val.get_col ( i ) ) ;} |
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54 | return x-lognc(); |
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55 | } |
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56 | //!Power of the density, used e.g. to flatten the density |
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57 | virtual void pow ( double p ) {it_error ( "Not implemented" );}; |
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58 | }; |
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59 | |
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60 | /*! |
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61 | * \brief Exponential family model. |
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62 | |
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63 | * More?... |
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64 | */ |
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65 | |
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66 | class mEF : public mpdf { |
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67 | |
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68 | public: |
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69 | //! Default constructor |
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70 | mEF ( ) :mpdf ( ) {}; |
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71 | }; |
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72 | |
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73 | //! Estimator for Exponential family |
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74 | class BMEF : public BM { |
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75 | protected: |
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76 | //! forgetting factor |
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77 | double frg; |
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78 | //! cached value of lognc() in the previous step (used in evaluation of \c ll ) |
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79 | double last_lognc; |
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80 | public: |
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81 | //! Default constructor (=empty constructor) |
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82 | BMEF ( double frg0=1.0 ) :BM ( ), frg ( frg0 ) {} |
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83 | //! Copy constructor |
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84 | BMEF ( const BMEF &B ) :BM ( B ), frg ( B.frg ), last_lognc ( B.last_lognc ) {} |
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85 | //!get statistics from another model |
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86 | virtual void set_statistics ( const BMEF* BM0 ) {it_error ( "Not implemented" );}; |
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87 | //! Weighted update of sufficient statistics (Bayes rule) |
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88 | virtual void bayes ( const vec &data, const double w ) {}; |
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89 | //original Bayes |
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90 | void bayes ( const vec &dt ); |
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91 | //!Flatten the posterior according to the given BMEF (of the same type!) |
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92 | virtual void flatten ( const BMEF * B ) {it_error ( "Not implemented" );} |
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93 | //!Flatten the posterior as if to keep nu0 data |
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94 | // virtual void flatten ( double nu0 ) {it_error ( "Not implemented" );} |
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95 | |
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96 | BMEF* _copy_ ( bool changerv=false ) {it_error ( "function _copy_ not implemented for this BM" ); return NULL;}; |
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97 | }; |
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98 | |
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99 | template<class sq_T> |
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100 | class mlnorm; |
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101 | |
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102 | /*! |
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103 | * \brief Gaussian density with positive definite (decomposed) covariance matrix. |
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104 | |
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105 | * More?... |
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106 | */ |
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107 | template<class sq_T> |
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108 | class enorm : public eEF { |
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109 | protected: |
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110 | //! mean value |
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111 | vec mu; |
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112 | //! Covariance matrix in decomposed form |
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113 | sq_T R; |
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114 | public: |
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115 | //!\name Constructors |
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116 | //!@{ |
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117 | |
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118 | enorm ( ) :eEF ( ), mu ( ),R ( ) {}; |
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119 | enorm ( const vec &mu,const sq_T &R ) {set_parameters ( mu,R );} |
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120 | void set_parameters ( const vec &mu,const sq_T &R ); |
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121 | //!@} |
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122 | |
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123 | //! \name Mathematical operations |
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124 | //!@{ |
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125 | |
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126 | //! dupdate in exponential form (not really handy) |
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127 | void dupdate ( mat &v,double nu=1.0 ); |
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128 | |
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129 | vec sample() const; |
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130 | mat sample ( int N ) const; |
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131 | double evallog_nn ( const vec &val ) const; |
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132 | double lognc () const; |
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133 | vec mean() const {return mu;} |
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134 | vec variance() const {return diag ( R.to_mat() );} |
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135 | // mlnorm<sq_T>* condition ( const RV &rvn ) const ; |
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136 | mpdf* condition ( const RV &rvn ) const ; |
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137 | // enorm<sq_T>* marginal ( const RV &rv ) const; |
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138 | epdf* marginal ( const RV &rv ) const; |
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139 | //!@} |
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140 | |
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141 | //! \name Access to attributes |
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142 | //!@{ |
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143 | |
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144 | vec& _mu() {return mu;} |
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145 | void set_mu ( const vec mu0 ) { mu=mu0;} |
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146 | sq_T& _R() {return R;} |
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147 | const sq_T& _R() const {return R;} |
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148 | //!@} |
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149 | |
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150 | }; |
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151 | |
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152 | /*! |
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153 | * \brief Gauss-inverse-Wishart density stored in LD form |
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154 | |
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155 | * For \f$p\f$-variate densities, given rv.count() should be \f$p\times\f$ V.rows(). |
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156 | * |
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157 | */ |
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158 | class egiw : public eEF { |
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159 | protected: |
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160 | //! Extended information matrix of sufficient statistics |
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161 | ldmat V; |
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162 | //! Number of data records (degrees of freedom) of sufficient statistics |
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163 | double nu; |
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164 | //! Dimension of the output |
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165 | int dimx; |
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166 | //! Dimension of the regressor |
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167 | int nPsi; |
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168 | public: |
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169 | //!\name Constructors |
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170 | //!@{ |
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171 | egiw() :eEF() {}; |
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172 | egiw ( int dimx0, ldmat V0, double nu0=-1.0 ) :eEF() {set_parameters ( dimx0,V0, nu0 );}; |
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173 | |
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174 | void set_parameters ( int dimx0, ldmat V0, double nu0=-1.0 ) { |
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175 | dimx=dimx0; |
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176 | nPsi = V0.rows()-dimx; |
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177 | dim = dimx* ( dimx+nPsi ); // size(R) + size(Theta) |
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178 | |
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179 | V=V0; |
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180 | if ( nu0<0 ) { |
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181 | nu = 0.1 +nPsi +2*dimx +2; // +2 assures finite expected value of R |
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182 | // terms before that are sufficient for finite normalization |
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183 | } |
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184 | else { |
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185 | nu=nu0; |
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186 | } |
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187 | } |
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188 | //!@} |
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189 | |
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190 | vec sample() const; |
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191 | vec mean() const; |
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192 | vec variance() const; |
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193 | void mean_mat ( mat &M, mat&R ) const; |
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194 | //! In this instance, val= [theta, r]. For multivariate instances, it is stored columnwise val = [theta_1 theta_2 ... r_1 r_2 ] |
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195 | double evallog_nn ( const vec &val ) const; |
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196 | double lognc () const; |
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197 | void pow ( double p ) {V*=p;nu*=p;}; |
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198 | |
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199 | //! \name Access attributes |
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200 | //!@{ |
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201 | |
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202 | ldmat& _V() {return V;} |
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203 | const ldmat& _V() const {return V;} |
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204 | double& _nu() {return nu;} |
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205 | const double& _nu() const {return nu;} |
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206 | //!@} |
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207 | }; |
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208 | |
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209 | /*! \brief Dirichlet posterior density |
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210 | |
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211 | Continuous Dirichlet density of \f$n\f$-dimensional variable \f$x\f$ |
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212 | \f[ |
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213 | f(x|\beta) = \frac{\Gamma[\gamma]}{\prod_{i=1}^{n}\Gamma(\beta_i)} \prod_{i=1}^{n}x_i^{\beta_i-1} |
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214 | \f] |
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215 | where \f$\gamma=\sum_i \beta_i\f$. |
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216 | */ |
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217 | class eDirich: public eEF { |
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218 | protected: |
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219 | //!sufficient statistics |
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220 | vec beta; |
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221 | //!speedup variable |
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222 | double gamma; |
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223 | public: |
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224 | //!\name Constructors |
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225 | //!@{ |
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226 | |
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227 | eDirich () : eEF ( ) {}; |
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228 | eDirich ( const eDirich &D0 ) : eEF () {set_parameters ( D0.beta );}; |
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229 | eDirich ( const vec &beta0 ) {set_parameters ( beta0 );}; |
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230 | void set_parameters ( const vec &beta0 ) { |
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231 | beta= beta0; |
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232 | dim = beta.length(); |
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233 | gamma = sum ( beta ); |
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234 | } |
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235 | //!@} |
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236 | |
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237 | vec sample() const {it_error ( "Not implemented" );return vec_1 ( 0.0 );}; |
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238 | vec mean() const {return beta/gamma;}; |
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239 | vec variance() const {return elem_mult ( beta, ( beta+1 ) ) / ( gamma* ( gamma+1 ) );} |
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240 | //! In this instance, val is ... |
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241 | double evallog_nn ( const vec &val ) const { |
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242 | double tmp; tmp= ( beta-1 ) *log ( val ); it_assert_debug ( std::isfinite ( tmp ),"Infinite value" ); |
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243 | return tmp; |
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244 | }; |
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245 | double lognc () const { |
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246 | double tmp; |
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247 | double gam=sum ( beta ); |
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248 | double lgb=0.0; |
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249 | for ( int i=0;i<beta.length();i++ ) {lgb+=lgamma ( beta ( i ) );} |
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250 | tmp= lgb-lgamma ( gam ); |
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251 | it_assert_debug ( std::isfinite ( tmp ),"Infinite value" ); |
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252 | return tmp; |
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253 | }; |
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254 | //!access function |
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255 | vec& _beta() {return beta;} |
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256 | //!Set internal parameters |
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257 | }; |
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258 | |
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259 | //! \brief Estimator for Multinomial density |
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260 | class multiBM : public BMEF { |
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261 | protected: |
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262 | //! Conjugate prior and posterior |
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263 | eDirich est; |
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264 | //! Pointer inside est to sufficient statistics |
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265 | vec β |
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266 | public: |
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267 | //!Default constructor |
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268 | multiBM ( ) : BMEF ( ),est ( ),beta ( est._beta() ) {if ( beta.length() >0 ) {last_lognc=est.lognc();}else{last_lognc=0.0;}} |
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269 | //!Copy constructor |
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270 | multiBM ( const multiBM &B ) : BMEF ( B ),est ( B.est ),beta ( est._beta() ) {} |
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271 | //! Sets sufficient statistics to match that of givefrom mB0 |
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272 | void set_statistics ( const BM* mB0 ) {const multiBM* mB=dynamic_cast<const multiBM*> ( mB0 ); beta=mB->beta;} |
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273 | void bayes ( const vec &dt ) { |
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274 | if ( frg<1.0 ) {beta*=frg;last_lognc=est.lognc();} |
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275 | beta+=dt; |
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276 | if ( evalll ) {ll=est.lognc()-last_lognc;} |
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277 | } |
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278 | double logpred ( const vec &dt ) const { |
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279 | eDirich pred ( est ); |
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280 | vec &beta = pred._beta(); |
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281 | |
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282 | double lll; |
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283 | if ( frg<1.0 ) |
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284 | {beta*=frg;lll=pred.lognc();} |
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285 | else |
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286 | if ( evalll ) {lll=last_lognc;} |
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287 | else{lll=pred.lognc();} |
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288 | |
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289 | beta+=dt; |
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290 | return pred.lognc()-lll; |
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291 | } |
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292 | void flatten ( const BMEF* B ) { |
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293 | const multiBM* E=dynamic_cast<const multiBM*> ( B ); |
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294 | // sum(beta) should be equal to sum(B.beta) |
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295 | const vec &Eb=E->beta;//const_cast<multiBM*> ( E )->_beta(); |
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296 | beta*= ( sum ( Eb ) /sum ( beta ) ); |
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297 | if ( evalll ) {last_lognc=est.lognc();} |
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298 | } |
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299 | const epdf& posterior() const {return est;}; |
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300 | const eDirich* _e() const {return &est;}; |
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301 | void set_parameters ( const vec &beta0 ) { |
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302 | est.set_parameters ( beta0 ); |
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303 | if ( evalll ) {last_lognc=est.lognc();} |
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304 | } |
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305 | }; |
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306 | |
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307 | /*! |
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308 | \brief Gamma posterior density |
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309 | |
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310 | Multivariate Gamma density as product of independent univariate densities. |
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311 | \f[ |
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312 | f(x|\alpha,\beta) = \prod f(x_i|\alpha_i,\beta_i) |
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313 | \f] |
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314 | */ |
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315 | |
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316 | class egamma : public eEF { |
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317 | protected: |
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318 | //! Vector \f$\alpha\f$ |
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319 | vec alpha; |
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320 | //! Vector \f$\beta\f$ |
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321 | vec beta; |
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322 | public : |
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323 | //! \name Constructors |
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324 | //!@{ |
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325 | egamma ( ) :eEF ( ), alpha(), beta() {}; |
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326 | egamma ( const vec &a, const vec &b ) {set_parameters ( a, b );}; |
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327 | void set_parameters ( const vec &a, const vec &b ) {alpha=a,beta=b;dim = alpha.length();}; |
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328 | //!@} |
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329 | |
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330 | vec sample() const; |
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331 | //! TODO: is it used anywhere? |
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332 | // mat sample ( int N ) const; |
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333 | double evallog ( const vec &val ) const; |
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334 | double lognc () const; |
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335 | //! Returns poiter to alpha and beta. Potentially dengerous: use with care! |
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336 | vec& _alpha() {return alpha;} |
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337 | vec& _beta() {return beta;} |
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338 | vec mean() const {return elem_div ( alpha,beta );} |
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339 | vec variance() const {return elem_div ( alpha,elem_mult ( beta,beta ) ); } |
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340 | }; |
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341 | |
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342 | /*! |
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343 | \brief Inverse-Gamma posterior density |
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344 | |
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345 | Multivariate inverse-Gamma density as product of independent univariate densities. |
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346 | \f[ |
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347 | f(x|\alpha,\beta) = \prod f(x_i|\alpha_i,\beta_i) |
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348 | \f] |
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349 | |
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350 | Inverse Gamma can be converted to Gamma using \f[ |
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351 | x\sim iG(a,b) => 1/x\sim G(a,1/b) |
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352 | \f] |
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353 | This relation is used in sampling. |
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354 | */ |
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355 | |
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356 | class eigamma : public eEF { |
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357 | protected: |
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358 | //!internal egamma |
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359 | egamma eg; |
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360 | //! Vector \f$\alpha\f$ |
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361 | vec α |
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362 | //! Vector \f$\beta\f$ (in fact it is 1/beta as used in definition of iG) |
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363 | vec β |
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364 | public : |
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365 | //! \name Constructors |
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366 | //!@{ |
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367 | eigamma ( ) :eEF ( ), eg(),alpha ( eg._alpha() ), beta ( eg._beta() ) {}; |
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368 | eigamma ( const vec &a, const vec &b ) :eEF ( ), eg(),alpha ( eg._alpha() ), beta ( eg._beta() ) {eg.set_parameters ( a,b );}; |
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369 | void set_parameters ( const vec &a, const vec &b ) {eg.set_parameters ( a,b );}; |
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370 | //!@} |
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371 | |
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372 | vec sample() const {return 1.0/eg.sample();}; |
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373 | //! TODO: is it used anywhere? |
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374 | // mat sample ( int N ) const; |
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375 | double evallog ( const vec &val ) const {return eg.evallog ( val );}; |
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376 | double lognc () const {return eg.lognc();}; |
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377 | //! Returns poiter to alpha and beta. Potentially dangerous: use with care! |
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378 | vec mean() const {return elem_div ( beta,alpha-1 );} |
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379 | vec variance() const {vec mea=mean(); return elem_div ( elem_mult ( mea,mea ),alpha-2 );} |
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380 | vec& _alpha() {return alpha;} |
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381 | vec& _beta() {return beta;} |
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382 | }; |
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383 | /* |
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384 | //! Weighted mixture of epdfs with external owned components. |
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385 | class emix : public epdf { |
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386 | protected: |
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387 | int n; |
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388 | vec &w; |
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389 | Array<epdf*> Coms; |
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390 | public: |
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391 | //! Default constructor |
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392 | emix ( const RV &rv, vec &w0): epdf(rv), n(w0.length()), w(w0), Coms(n) {}; |
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393 | void set_parameters( int &i, double wi, epdf* ep){w(i)=wi;Coms(i)=ep;} |
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394 | vec mean(){vec pom; for(int i=0;i<n;i++){pom+=Coms(i)->mean()*w(i);} return pom;}; |
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395 | vec sample() {it_error ( "Not implemented" );return 0;} |
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396 | }; |
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397 | */ |
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398 | |
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399 | //! Uniform distributed density on a rectangular support |
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400 | |
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401 | class euni: public epdf { |
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402 | protected: |
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403 | //! lower bound on support |
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404 | vec low; |
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405 | //! upper bound on support |
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406 | vec high; |
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407 | //! internal |
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408 | vec distance; |
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409 | //! normalizing coefficients |
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410 | double nk; |
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411 | //! cache of log( \c nk ) |
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412 | double lnk; |
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413 | public: |
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414 | //! \name Constructors |
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415 | //!@{ |
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416 | euni ( ) :epdf ( ) {} |
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417 | euni ( const vec &low0, const vec &high0 ) {set_parameters ( low0,high0 );} |
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418 | void set_parameters ( const vec &low0, const vec &high0 ) { |
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419 | distance = high0-low0; |
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420 | it_assert_debug ( min ( distance ) >0.0,"bad support" ); |
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421 | low = low0; |
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422 | high = high0; |
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423 | nk = prod ( 1.0/distance ); |
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424 | lnk = log ( nk ); |
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425 | dim = low.length(); |
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426 | } |
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427 | //!@} |
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428 | |
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429 | double eval ( const vec &val ) const {return nk;} |
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430 | double evallog ( const vec &val ) const {return lnk;} |
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431 | vec sample() const { |
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432 | vec smp ( dim ); |
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433 | #pragma omp critical |
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434 | UniRNG.sample_vector ( dim ,smp ); |
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435 | return low+elem_mult ( distance,smp ); |
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436 | } |
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437 | //! set values of \c low and \c high |
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438 | vec mean() const {return ( high-low ) /2.0;} |
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439 | vec variance() const {return ( pow ( high,2 ) +pow ( low,2 ) +elem_mult ( high,low ) ) /3.0;} |
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440 | }; |
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441 | |
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442 | |
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443 | /*! |
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444 | \brief Normal distributed linear function with linear function of mean value; |
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445 | |
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446 | Mean value \f$mu=A*rvc+mu_0\f$. |
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447 | */ |
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448 | template<class sq_T> |
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449 | class mlnorm : public mEF { |
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450 | protected: |
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451 | //! Internal epdf that arise by conditioning on \c rvc |
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452 | enorm<sq_T> epdf; |
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453 | mat A; |
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454 | vec mu_const; |
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455 | vec& _mu; //cached epdf.mu; |
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456 | public: |
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457 | //! \name Constructors |
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458 | //!@{ |
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459 | mlnorm ( ) :mEF (),epdf ( ),A ( ),_mu ( epdf._mu() ) {ep =&epdf; }; |
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460 | mlnorm ( const mat &A, const vec &mu0, const sq_T &R ) :epdf ( ),_mu ( epdf._mu() ) { |
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461 | ep =&epdf; set_parameters ( A,mu0,R ); |
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462 | }; |
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463 | //! Set \c A and \c R |
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464 | void set_parameters ( const mat &A, const vec &mu0, const sq_T &R ); |
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465 | //!@} |
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466 | //! Set value of \c rvc . Result of this operation is stored in \c epdf use function \c _ep to access it. |
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467 | void condition ( const vec &cond ); |
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468 | |
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469 | //!access function |
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470 | vec& _mu_const() {return mu_const;} |
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471 | //!access function |
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472 | mat& _A() {return A;} |
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473 | //!access function |
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474 | mat _R() {return epdf._R().to_mat();} |
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475 | |
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476 | template<class sq_M> |
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477 | friend std::ostream &operator<< ( std::ostream &os, mlnorm<sq_M> &ml ); |
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478 | }; |
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479 | |
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480 | //! Mpdf with general function for mean value |
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481 | template<class sq_T> |
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482 | class mgnorm : public mEF { |
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483 | protected: |
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484 | //! Internal epdf that arise by conditioning on \c rvc |
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485 | enorm<sq_T> epdf; |
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486 | vec μ |
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487 | fnc* g; |
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488 | public: |
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489 | //!default constructor |
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490 | mgnorm() :mu ( epdf._mu() ) {ep=&epdf;} |
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491 | //!set mean function |
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492 | void set_parameters ( fnc* g0, const sq_T &R0 ) {g=g0; epdf.set_parameters ( zeros ( g->_dimy() ), R0 );} |
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493 | void condition ( const vec &cond ) {mu=g->eval ( cond );}; |
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494 | }; |
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495 | |
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496 | /*! (Approximate) Student t density with linear function of mean value |
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497 | |
---|
498 | The internal epdf of this class is of the type of a Gaussian (enorm). |
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499 | However, each conditioning is trying to assure the best possible approximation by taking into account the zeta function. See [] for reference. |
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500 | |
---|
501 | Perhaps a moment-matching technique? |
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502 | */ |
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503 | class mlstudent : public mlnorm<ldmat> { |
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504 | protected: |
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505 | ldmat Lambda; |
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506 | ldmat &_R; |
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507 | ldmat Re; |
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508 | public: |
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509 | mlstudent ( ) :mlnorm<ldmat> (), |
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510 | Lambda (), _R ( epdf._R() ) {} |
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511 | void set_parameters ( const mat &A0, const vec &mu0, const ldmat &R0, const ldmat& Lambda0 ) { |
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512 | it_assert_debug ( A0.rows() ==mu0.length(),"" ); |
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513 | it_assert_debug ( R0.rows() ==A0.rows(),"" ); |
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514 | |
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515 | epdf.set_parameters ( mu0,Lambda ); // |
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516 | A = A0; |
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517 | mu_const = mu0; |
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518 | Re=R0; |
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519 | Lambda = Lambda0; |
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520 | } |
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521 | void condition ( const vec &cond ) { |
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522 | _mu = A*cond + mu_const; |
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523 | double zeta; |
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524 | //ugly hack! |
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525 | if ( ( cond.length() +1 ) ==Lambda.rows() ) { |
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526 | zeta = Lambda.invqform ( concat ( cond, vec_1 ( 1.0 ) ) ); |
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527 | } |
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528 | else { |
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529 | zeta = Lambda.invqform ( cond ); |
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530 | } |
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531 | _R = Re; |
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532 | _R*= ( 1+zeta );// / ( nu ); << nu is in Re!!!!!! |
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533 | }; |
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534 | |
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535 | }; |
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536 | /*! |
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537 | \brief Gamma random walk |
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538 | |
---|
539 | Mean value, \f$\mu\f$, of this density is given by \c rvc . |
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540 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
---|
541 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
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542 | |
---|
543 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
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544 | */ |
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545 | class mgamma : public mEF { |
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546 | protected: |
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547 | //! Internal epdf that arise by conditioning on \c rvc |
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548 | egamma epdf; |
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549 | //! Constant \f$k\f$ |
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550 | double k; |
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551 | //! cache of epdf.beta |
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552 | vec &_beta; |
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553 | |
---|
554 | public: |
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555 | //! Constructor |
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556 | mgamma ( ) : mEF ( ), epdf (), _beta ( epdf._beta() ) {ep=&epdf;}; |
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557 | //! Set value of \c k |
---|
558 | void set_parameters ( double k, const vec &beta0 ); |
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559 | void condition ( const vec &val ) {_beta=k/val;}; |
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560 | }; |
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561 | |
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562 | /*! |
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563 | \brief Inverse-Gamma random walk |
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564 | |
---|
565 | Mean value, \f$ \mu \f$, of this density is given by \c rvc . |
---|
566 | Standard deviation of the random walk is proportional to one \f$ k \f$-th the mean. |
---|
567 | This is achieved by setting \f$ \alpha=\mu/k^2+2 \f$ and \f$ \beta=\mu(\alpha-1)\f$. |
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568 | |
---|
569 | The standard deviation of the walk is then: \f$ \mu/\sqrt(k)\f$. |
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570 | */ |
---|
571 | class migamma : public mEF { |
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572 | protected: |
---|
573 | //! Internal epdf that arise by conditioning on \c rvc |
---|
574 | eigamma epdf; |
---|
575 | //! Constant \f$k\f$ |
---|
576 | double k; |
---|
577 | //! cache of epdf.alpha |
---|
578 | vec &_alpha; |
---|
579 | //! cache of epdf.beta |
---|
580 | vec &_beta; |
---|
581 | |
---|
582 | public: |
---|
583 | //! \name Constructors |
---|
584 | //!@{ |
---|
585 | migamma ( ) : mEF (), epdf ( ), _alpha ( epdf._alpha() ), _beta ( epdf._beta() ) {ep=&epdf;}; |
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586 | migamma ( const migamma &m ) : mEF (), epdf ( m.epdf ), _alpha ( epdf._alpha() ), _beta ( epdf._beta() ) {ep=&epdf;}; |
---|
587 | //!@} |
---|
588 | |
---|
589 | //! Set value of \c k |
---|
590 | void set_parameters ( int len, double k0 ) { |
---|
591 | k=k0; |
---|
592 | epdf.set_parameters ( ( 1.0/ ( k*k ) +2.0 ) *ones ( len ) /*alpha*/, ones ( len ) /*beta*/ ); |
---|
593 | dimc = dimension(); |
---|
594 | }; |
---|
595 | void condition ( const vec &val ) { |
---|
596 | _beta=elem_mult ( val, ( _alpha-1.0 ) ); |
---|
597 | }; |
---|
598 | }; |
---|
599 | |
---|
600 | /*! |
---|
601 | \brief Gamma random walk around a fixed point |
---|
602 | |
---|
603 | Mean value, \f$\mu\f$, of this density is given by a geometric combination of \c rvc and given fixed point, \f$p\f$. \f$l\f$ is the coefficient of the geometric combimation |
---|
604 | \f[ \mu = \mu_{t-1} ^{l} p^{1-l}\f] |
---|
605 | |
---|
606 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
---|
607 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
---|
608 | |
---|
609 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
---|
610 | */ |
---|
611 | class mgamma_fix : public mgamma { |
---|
612 | protected: |
---|
613 | //! parameter l |
---|
614 | double l; |
---|
615 | //! reference vector |
---|
616 | vec refl; |
---|
617 | public: |
---|
618 | //! Constructor |
---|
619 | mgamma_fix ( ) : mgamma ( ),refl () {}; |
---|
620 | //! Set value of \c k |
---|
621 | void set_parameters ( double k0 , vec ref0, double l0 ) { |
---|
622 | mgamma::set_parameters ( k0, ref0 ); |
---|
623 | refl=pow ( ref0,1.0-l0 );l=l0; |
---|
624 | dimc=dimension(); |
---|
625 | }; |
---|
626 | |
---|
627 | void condition ( const vec &val ) {vec mean=elem_mult ( refl,pow ( val,l ) ); _beta=k/mean;}; |
---|
628 | }; |
---|
629 | |
---|
630 | |
---|
631 | /*! |
---|
632 | \brief Inverse-Gamma random walk around a fixed point |
---|
633 | |
---|
634 | Mean value, \f$\mu\f$, of this density is given by a geometric combination of \c rvc and given fixed point, \f$p\f$. \f$l\f$ is the coefficient of the geometric combimation |
---|
635 | \f[ \mu = \mu_{t-1} ^{l} p^{1-l}\f] |
---|
636 | |
---|
637 | ==== Check == vv = |
---|
638 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
---|
639 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
---|
640 | |
---|
641 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
---|
642 | */ |
---|
643 | class migamma_fix : public migamma { |
---|
644 | protected: |
---|
645 | //! parameter l |
---|
646 | double l; |
---|
647 | //! reference vector |
---|
648 | vec refl; |
---|
649 | public: |
---|
650 | //! Constructor |
---|
651 | migamma_fix ( ) : migamma (),refl ( ) {}; |
---|
652 | //! Set value of \c k |
---|
653 | void set_parameters ( double k0 , vec ref0, double l0 ) { |
---|
654 | migamma::set_parameters ( ref0.length(), k0 ); |
---|
655 | refl=pow ( ref0,1.0-l0 ); |
---|
656 | l=l0; |
---|
657 | dimc = dimension(); |
---|
658 | }; |
---|
659 | |
---|
660 | void condition ( const vec &val ) { |
---|
661 | vec mean=elem_mult ( refl,pow ( val,l ) ); |
---|
662 | migamma::condition ( mean ); |
---|
663 | }; |
---|
664 | }; |
---|
665 | //! Switch between various resampling methods. |
---|
666 | enum RESAMPLING_METHOD { MULTINOMIAL = 0, STRATIFIED = 1, SYSTEMATIC = 3 }; |
---|
667 | /*! |
---|
668 | \brief Weighted empirical density |
---|
669 | |
---|
670 | Used e.g. in particle filters. |
---|
671 | */ |
---|
672 | class eEmp: public epdf { |
---|
673 | protected : |
---|
674 | //! Number of particles |
---|
675 | int n; |
---|
676 | //! Sample weights \f$w\f$ |
---|
677 | vec w; |
---|
678 | //! Samples \f$x^{(i)}, i=1..n\f$ |
---|
679 | Array<vec> samples; |
---|
680 | public: |
---|
681 | //! \name Constructors |
---|
682 | //!@{ |
---|
683 | eEmp ( ) :epdf ( ),w ( ),samples ( ) {}; |
---|
684 | eEmp ( const eEmp &e ) : epdf ( e ), w ( e.w ), samples ( e.samples ) {}; |
---|
685 | //!@} |
---|
686 | |
---|
687 | //! Set samples and weights |
---|
688 | void set_parameters ( const vec &w0, const epdf* pdf0 ); |
---|
689 | //! Set sample |
---|
690 | void set_samples ( const epdf* pdf0 ); |
---|
691 | //! Set sample |
---|
692 | void set_n ( int n0, bool copy=true ) {w.set_size ( n0,copy );samples.set_size ( n0,copy );}; |
---|
693 | //! Potentially dangerous, use with care. |
---|
694 | vec& _w() {return w;}; |
---|
695 | //! Potentially dangerous, use with care. |
---|
696 | const vec& _w() const {return w;}; |
---|
697 | //! access function |
---|
698 | Array<vec>& _samples() {return samples;}; |
---|
699 | //! access function |
---|
700 | const Array<vec>& _samples() const {return samples;}; |
---|
701 | //! Function performs resampling, i.e. removal of low-weight samples and duplication of high-weight samples such that the new samples represent the same density. |
---|
702 | ivec resample ( RESAMPLING_METHOD method = SYSTEMATIC ); |
---|
703 | //! inherited operation : NOT implemneted |
---|
704 | vec sample() const {it_error ( "Not implemented" );return 0;} |
---|
705 | //! inherited operation : NOT implemneted |
---|
706 | double evallog ( const vec &val ) const {it_error ( "Not implemented" );return 0.0;} |
---|
707 | vec mean() const { |
---|
708 | vec pom=zeros ( dim ); |
---|
709 | for ( int i=0;i<n;i++ ) {pom+=samples ( i ) *w ( i );} |
---|
710 | return pom; |
---|
711 | } |
---|
712 | vec variance() const { |
---|
713 | vec pom=zeros ( dim ); |
---|
714 | for ( int i=0;i<n;i++ ) {pom+=pow ( samples ( i ),2 ) *w ( i );} |
---|
715 | return pom-pow ( mean(),2 ); |
---|
716 | } |
---|
717 | }; |
---|
718 | |
---|
719 | |
---|
720 | //////////////////////// |
---|
721 | |
---|
722 | template<class sq_T> |
---|
723 | void enorm<sq_T>::set_parameters ( const vec &mu0, const sq_T &R0 ) { |
---|
724 | //Fixme test dimensions of mu0 and R0; |
---|
725 | mu = mu0; |
---|
726 | R = R0; |
---|
727 | dim = mu0.length(); |
---|
728 | }; |
---|
729 | |
---|
730 | template<class sq_T> |
---|
731 | void enorm<sq_T>::dupdate ( mat &v, double nu ) { |
---|
732 | // |
---|
733 | }; |
---|
734 | |
---|
735 | // template<class sq_T> |
---|
736 | // void enorm<sq_T>::tupdate ( double phi, mat &vbar, double nubar ) { |
---|
737 | // // |
---|
738 | // }; |
---|
739 | |
---|
740 | template<class sq_T> |
---|
741 | vec enorm<sq_T>::sample() const { |
---|
742 | vec x ( dim ); |
---|
743 | #pragma omp critical |
---|
744 | NorRNG.sample_vector ( dim,x ); |
---|
745 | vec smp = R.sqrt_mult ( x ); |
---|
746 | |
---|
747 | smp += mu; |
---|
748 | return smp; |
---|
749 | }; |
---|
750 | |
---|
751 | template<class sq_T> |
---|
752 | mat enorm<sq_T>::sample ( int N ) const { |
---|
753 | mat X ( dim,N ); |
---|
754 | vec x ( dim ); |
---|
755 | vec pom; |
---|
756 | int i; |
---|
757 | |
---|
758 | for ( i=0;i<N;i++ ) { |
---|
759 | #pragma omp critical |
---|
760 | NorRNG.sample_vector ( dim,x ); |
---|
761 | pom = R.sqrt_mult ( x ); |
---|
762 | pom +=mu; |
---|
763 | X.set_col ( i, pom ); |
---|
764 | } |
---|
765 | |
---|
766 | return X; |
---|
767 | }; |
---|
768 | |
---|
769 | // template<class sq_T> |
---|
770 | // double enorm<sq_T>::eval ( const vec &val ) const { |
---|
771 | // double pdfl,e; |
---|
772 | // pdfl = evallog ( val ); |
---|
773 | // e = exp ( pdfl ); |
---|
774 | // return e; |
---|
775 | // }; |
---|
776 | |
---|
777 | template<class sq_T> |
---|
778 | double enorm<sq_T>::evallog_nn ( const vec &val ) const { |
---|
779 | // 1.83787706640935 = log(2pi) |
---|
780 | double tmp=-0.5* ( R.invqform ( mu-val ) );// - lognc(); |
---|
781 | return tmp; |
---|
782 | }; |
---|
783 | |
---|
784 | template<class sq_T> |
---|
785 | inline double enorm<sq_T>::lognc () const { |
---|
786 | // 1.83787706640935 = log(2pi) |
---|
787 | double tmp=0.5* ( R.cols() * 1.83787706640935 +R.logdet() ); |
---|
788 | return tmp; |
---|
789 | }; |
---|
790 | |
---|
791 | template<class sq_T> |
---|
792 | void mlnorm<sq_T>::set_parameters ( const mat &A0, const vec &mu0, const sq_T &R0 ) { |
---|
793 | it_assert_debug ( A0.rows() ==mu0.length(),"" ); |
---|
794 | it_assert_debug ( A0.rows() ==R0.rows(),"" ); |
---|
795 | |
---|
796 | epdf.set_parameters ( zeros ( A0.rows() ),R0 ); |
---|
797 | A = A0; |
---|
798 | mu_const = mu0; |
---|
799 | dimc=A0.cols(); |
---|
800 | } |
---|
801 | |
---|
802 | // template<class sq_T> |
---|
803 | // vec mlnorm<sq_T>::samplecond (const vec &cond, double &lik ) { |
---|
804 | // this->condition ( cond ); |
---|
805 | // vec smp = epdf.sample(); |
---|
806 | // lik = epdf.eval ( smp ); |
---|
807 | // return smp; |
---|
808 | // } |
---|
809 | |
---|
810 | // template<class sq_T> |
---|
811 | // mat mlnorm<sq_T>::samplecond (const vec &cond, vec &lik, int n ) { |
---|
812 | // int i; |
---|
813 | // int dim = rv.count(); |
---|
814 | // mat Smp ( dim,n ); |
---|
815 | // vec smp ( dim ); |
---|
816 | // this->condition ( cond ); |
---|
817 | // |
---|
818 | // for ( i=0; i<n; i++ ) { |
---|
819 | // smp = epdf.sample(); |
---|
820 | // lik ( i ) = epdf.eval ( smp ); |
---|
821 | // Smp.set_col ( i ,smp ); |
---|
822 | // } |
---|
823 | // |
---|
824 | // return Smp; |
---|
825 | // } |
---|
826 | |
---|
827 | template<class sq_T> |
---|
828 | void mlnorm<sq_T>::condition ( const vec &cond ) { |
---|
829 | _mu = A*cond + mu_const; |
---|
830 | //R is already assigned; |
---|
831 | } |
---|
832 | |
---|
833 | template<class sq_T> |
---|
834 | epdf* enorm<sq_T>::marginal ( const RV &rvn ) const { |
---|
835 | it_assert_debug ( isnamed(), "rv description is not assigned" ); |
---|
836 | ivec irvn = rvn.dataind ( rv ); |
---|
837 | |
---|
838 | sq_T Rn ( R,irvn ); //select rows and columns of R |
---|
839 | |
---|
840 | enorm<sq_T>* tmp = new enorm<sq_T>; |
---|
841 | tmp->set_rv ( rvn ); |
---|
842 | tmp->set_parameters ( mu ( irvn ), Rn ); |
---|
843 | return tmp; |
---|
844 | } |
---|
845 | |
---|
846 | template<class sq_T> |
---|
847 | mpdf* enorm<sq_T>::condition ( const RV &rvn ) const { |
---|
848 | |
---|
849 | it_assert_debug ( isnamed(),"rvs are not assigned" ); |
---|
850 | |
---|
851 | RV rvc = rv.subt ( rvn ); |
---|
852 | it_assert_debug ( ( rvc._dsize() +rvn._dsize() ==rv._dsize() ),"wrong rvn" ); |
---|
853 | //Permutation vector of the new R |
---|
854 | ivec irvn = rvn.dataind ( rv ); |
---|
855 | ivec irvc = rvc.dataind ( rv ); |
---|
856 | ivec perm=concat ( irvn , irvc ); |
---|
857 | sq_T Rn ( R,perm ); |
---|
858 | |
---|
859 | //fixme - could this be done in general for all sq_T? |
---|
860 | mat S=Rn.to_mat(); |
---|
861 | //fixme |
---|
862 | int n=rvn._dsize()-1; |
---|
863 | int end=R.rows()-1; |
---|
864 | mat S11 = S.get ( 0,n, 0, n ); |
---|
865 | mat S12 = S.get ( 0, n , rvn._dsize(), end ); |
---|
866 | mat S22 = S.get ( rvn._dsize(), end, rvn._dsize(), end ); |
---|
867 | |
---|
868 | vec mu1 = mu ( irvn ); |
---|
869 | vec mu2 = mu ( irvc ); |
---|
870 | mat A=S12*inv ( S22 ); |
---|
871 | sq_T R_n ( S11 - A *S12.T() ); |
---|
872 | |
---|
873 | mlnorm<sq_T>* tmp=new mlnorm<sq_T> ( ); |
---|
874 | tmp->set_rv ( rvn ); tmp->set_rvc ( rvc ); |
---|
875 | tmp->set_parameters ( A,mu1-A*mu2,R_n ); |
---|
876 | return tmp; |
---|
877 | } |
---|
878 | |
---|
879 | /////////// |
---|
880 | |
---|
881 | template<class sq_T> |
---|
882 | std::ostream &operator<< ( std::ostream &os, mlnorm<sq_T> &ml ) { |
---|
883 | os << "A:"<< ml.A<<endl; |
---|
884 | os << "mu:"<< ml.mu_const<<endl; |
---|
885 | os << "R:" << ml.epdf._R().to_mat() <<endl; |
---|
886 | return os; |
---|
887 | }; |
---|
888 | |
---|
889 | } |
---|
890 | #endif //EF_H |
---|