| 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 "../shared_ptr.h" |
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| 18 | #include "../base/bdmbase.h" |
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| 19 | #include "../math/chmat.h" |
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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 | |
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| 25 | //! Global Uniform_RNG |
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| 26 | extern Uniform_RNG UniRNG; |
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| 27 | //! Global Normal_RNG |
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| 28 | extern Normal_RNG NorRNG; |
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| 29 | //! Global Gamma_RNG |
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| 30 | extern Gamma_RNG GamRNG; |
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| 31 | |
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| 32 | /*! |
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| 33 | * \brief General conjugate exponential family posterior density. |
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| 34 | |
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| 35 | * More?... |
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| 36 | */ |
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| 37 | |
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| 38 | class eEF : public epdf |
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| 39 | { |
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| 40 | public: |
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| 41 | // eEF() :epdf() {}; |
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| 42 | //! default constructor |
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| 43 | eEF ( ) :epdf ( ) {}; |
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| 44 | //! logarithm of the normalizing constant, \f$\mathcal{I}\f$ |
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| 45 | virtual double lognc() const =0; |
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| 46 | //!TODO decide if it is really needed |
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| 47 | virtual void dupdate ( mat &v ) {it_error ( "Not implemented" );}; |
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| 48 | //!Evaluate normalized log-probability |
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| 49 | virtual double evallog_nn ( const vec &val ) const{it_error ( "Not implemented" );return 0.0;}; |
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| 50 | //!Evaluate normalized log-probability |
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| 51 | virtual double evallog ( const vec &val ) const { |
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| 52 | double tmp; |
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| 53 | tmp= evallog_nn ( val )-lognc(); |
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| 54 | // it_assert_debug ( std::isfinite ( tmp ),"Infinite value" ); |
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| 55 | return tmp;} |
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| 56 | //!Evaluate normalized log-probability for many samples |
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| 57 | virtual vec evallog ( const mat &Val ) const |
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| 58 | { |
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| 59 | vec x ( Val.cols() ); |
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| 60 | for ( int i=0;i<Val.cols();i++ ) {x ( i ) =evallog_nn ( Val.get_col ( i ) ) ;} |
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| 61 | return x-lognc(); |
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| 62 | } |
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| 63 | //!Power of the density, used e.g. to flatten the density |
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| 64 | virtual void pow ( double p ) {it_error ( "Not implemented" );}; |
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| 65 | }; |
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| 66 | |
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| 67 | /*! |
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| 68 | * \brief Exponential family model. |
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| 69 | |
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| 70 | * More?... |
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| 71 | */ |
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| 72 | |
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| 73 | class mEF : public mpdf |
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| 74 | { |
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| 75 | |
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| 76 | public: |
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| 77 | //! Default constructor |
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| 78 | mEF ( ) :mpdf ( ) {}; |
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| 79 | }; |
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| 80 | |
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| 81 | //! Estimator for Exponential family |
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| 82 | class BMEF : public BM |
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| 83 | { |
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| 84 | protected: |
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| 85 | //! forgetting factor |
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| 86 | double frg; |
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| 87 | //! cached value of lognc() in the previous step (used in evaluation of \c ll ) |
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| 88 | double last_lognc; |
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| 89 | public: |
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| 90 | //! Default constructor (=empty constructor) |
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| 91 | BMEF ( double frg0=1.0 ) :BM ( ), frg ( frg0 ) {} |
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| 92 | //! Copy constructor |
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| 93 | BMEF ( const BMEF &B ) :BM ( B ), frg ( B.frg ), last_lognc ( B.last_lognc ) {} |
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| 94 | //!get statistics from another model |
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| 95 | virtual void set_statistics ( const BMEF* BM0 ) {it_error ( "Not implemented" );}; |
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| 96 | //! Weighted update of sufficient statistics (Bayes rule) |
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| 97 | virtual void bayes ( const vec &data, const double w ) {}; |
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| 98 | //original Bayes |
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| 99 | void bayes ( const vec &dt ); |
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| 100 | //!Flatten the posterior according to the given BMEF (of the same type!) |
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| 101 | virtual void flatten ( const BMEF * B ) {it_error ( "Not implemented" );} |
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| 102 | //!Flatten the posterior as if to keep nu0 data |
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| 103 | // virtual void flatten ( double nu0 ) {it_error ( "Not implemented" );} |
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| 104 | |
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| 105 | BMEF* _copy_ () const {it_error ( "function _copy_ not implemented for this BM" ); return NULL;}; |
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| 106 | }; |
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| 107 | |
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| 108 | template<class sq_T> |
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| 109 | class mlnorm; |
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| 110 | |
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| 111 | /*! |
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| 112 | * \brief Gaussian density with positive definite (decomposed) covariance matrix. |
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| 113 | |
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| 114 | * More?... |
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| 115 | */ |
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| 116 | template<class sq_T> |
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| 117 | class enorm : public eEF |
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| 118 | { |
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| 119 | protected: |
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| 120 | //! mean value |
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| 121 | vec mu; |
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| 122 | //! Covariance matrix in decomposed form |
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| 123 | sq_T R; |
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| 124 | public: |
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| 125 | //!\name Constructors |
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| 126 | //!@{ |
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| 127 | |
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| 128 | enorm ( ) :eEF ( ), mu ( ),R ( ) {}; |
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| 129 | enorm ( const vec &mu,const sq_T &R ) {set_parameters ( mu,R );} |
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| 130 | void set_parameters ( const vec &mu,const sq_T &R ); |
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| 131 | void from_setting(const Setting &root); |
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| 132 | void validate() { |
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| 133 | it_assert(mu.length()==R.rows(),"parameters mismatch"); |
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| 134 | dim = mu.length(); |
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| 135 | } |
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| 136 | //!@} |
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| 137 | |
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| 138 | //! \name Mathematical operations |
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| 139 | //!@{ |
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| 140 | |
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| 141 | //! dupdate in exponential form (not really handy) |
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| 142 | void dupdate ( mat &v,double nu=1.0 ); |
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| 143 | |
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| 144 | vec sample() const; |
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| 145 | |
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| 146 | double evallog_nn ( const vec &val ) const; |
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| 147 | double lognc () const; |
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| 148 | vec mean() const {return mu;} |
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| 149 | vec variance() const {return diag ( R.to_mat() );} |
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| 150 | // mlnorm<sq_T>* condition ( const RV &rvn ) const ; <=========== fails to cmpile. Why? |
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| 151 | mpdf* condition ( const RV &rvn ) const ; |
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| 152 | enorm<sq_T>* marginal ( const RV &rv ) const; |
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| 153 | // epdf* marginal ( const RV &rv ) const; |
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| 154 | //!@} |
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| 155 | |
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| 156 | //! \name Access to attributes |
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| 157 | //!@{ |
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| 158 | |
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| 159 | vec& _mu() {return mu;} |
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| 160 | void set_mu ( const vec mu0 ) { mu=mu0;} |
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| 161 | sq_T& _R() {return R;} |
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| 162 | const sq_T& _R() const {return R;} |
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| 163 | //!@} |
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| 164 | |
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| 165 | }; |
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| 166 | UIREGISTER(enorm<chmat>); |
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| 167 | UIREGISTER(enorm<ldmat>); |
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| 168 | UIREGISTER(enorm<fsqmat>); |
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| 169 | |
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| 170 | |
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| 171 | /*! |
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| 172 | * \brief Gauss-inverse-Wishart density stored in LD form |
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| 173 | |
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| 174 | * For \f$p\f$-variate densities, given rv.count() should be \f$p\times\f$ V.rows(). |
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| 175 | * |
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| 176 | */ |
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| 177 | class egiw : public eEF |
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| 178 | { |
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| 179 | protected: |
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| 180 | //! Extended information matrix of sufficient statistics |
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| 181 | ldmat V; |
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| 182 | //! Number of data records (degrees of freedom) of sufficient statistics |
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| 183 | double nu; |
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| 184 | //! Dimension of the output |
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| 185 | int dimx; |
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| 186 | //! Dimension of the regressor |
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| 187 | int nPsi; |
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| 188 | public: |
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| 189 | //!\name Constructors |
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| 190 | //!@{ |
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| 191 | egiw() :eEF() {}; |
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| 192 | egiw ( int dimx0, ldmat V0, double nu0=-1.0 ) :eEF() {set_parameters ( dimx0,V0, nu0 );}; |
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| 193 | |
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| 194 | void set_parameters ( int dimx0, ldmat V0, double nu0=-1.0 ) |
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| 195 | { |
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| 196 | dimx=dimx0; |
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| 197 | nPsi = V0.rows()-dimx; |
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| 198 | dim = dimx* ( dimx+nPsi ); // size(R) + size(Theta) |
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| 199 | |
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| 200 | V=V0; |
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| 201 | if ( nu0<0 ) |
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| 202 | { |
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| 203 | nu = 0.1 +nPsi +2*dimx +2; // +2 assures finite expected value of R |
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| 204 | // terms before that are sufficient for finite normalization |
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| 205 | } |
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| 206 | else |
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| 207 | { |
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| 208 | nu=nu0; |
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| 209 | } |
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| 210 | } |
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| 211 | //!@} |
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| 212 | |
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| 213 | vec sample() const; |
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| 214 | vec mean() const; |
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| 215 | vec variance() const; |
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| 216 | |
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| 217 | //! LS estimate of \f$\theta\f$ |
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| 218 | vec est_theta() const; |
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| 219 | |
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| 220 | //! Covariance of the LS estimate |
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| 221 | ldmat est_theta_cov() const; |
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| 222 | |
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| 223 | void mean_mat ( mat &M, mat&R ) const; |
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| 224 | //! 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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| 225 | double evallog_nn ( const vec &val ) const; |
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| 226 | double lognc () const; |
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| 227 | void pow ( double p ) {V*=p;nu*=p;}; |
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| 228 | |
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| 229 | //! \name Access attributes |
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| 230 | //!@{ |
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| 231 | |
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| 232 | ldmat& _V() {return V;} |
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| 233 | const ldmat& _V() const {return V;} |
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| 234 | double& _nu() {return nu;} |
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| 235 | const double& _nu() const {return nu;} |
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| 236 | void from_setting(const Setting &set){ |
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| 237 | UI::get(nu,set,"nu"); |
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| 238 | UI::get(dimx,set,"dimx"); |
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| 239 | set.lookupValue("nu",nu); |
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| 240 | set.lookupValue("dimx",dimx); |
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| 241 | mat V; |
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| 242 | UI::get(V,set,"V", UI::compulsory); |
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| 243 | set_parameters(dimx, V, nu); |
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| 244 | RV* rv=UI::build<RV>(set,"rv", UI::compulsory); |
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| 245 | set_rv(*rv); |
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| 246 | delete rv; |
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| 247 | } |
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| 248 | //!@} |
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| 249 | }; |
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| 250 | UIREGISTER(egiw); |
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| 251 | |
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| 252 | /*! \brief Dirichlet posterior density |
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| 253 | |
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| 254 | Continuous Dirichlet density of \f$n\f$-dimensional variable \f$x\f$ |
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| 255 | \f[ |
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| 256 | 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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| 257 | \f] |
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| 258 | where \f$\gamma=\sum_i \beta_i\f$. |
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| 259 | */ |
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| 260 | class eDirich: public eEF |
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| 261 | { |
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| 262 | protected: |
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| 263 | //!sufficient statistics |
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| 264 | vec beta; |
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| 265 | public: |
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| 266 | //!\name Constructors |
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| 267 | //!@{ |
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| 268 | |
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| 269 | eDirich () : eEF ( ) {}; |
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| 270 | eDirich ( const eDirich &D0 ) : eEF () {set_parameters ( D0.beta );}; |
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| 271 | eDirich ( const vec &beta0 ) {set_parameters ( beta0 );}; |
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| 272 | void set_parameters ( const vec &beta0 ) |
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| 273 | { |
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| 274 | beta= beta0; |
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| 275 | dim = beta.length(); |
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| 276 | } |
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| 277 | //!@} |
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| 278 | |
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| 279 | vec sample() const {it_error ( "Not implemented" );return vec_1 ( 0.0 );}; |
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| 280 | vec mean() const {return beta/sum(beta);}; |
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| 281 | vec variance() const {double gamma =sum(beta); return elem_mult ( beta, ( beta+1 ) ) / ( gamma* ( gamma+1 ) );} |
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| 282 | //! In this instance, val is ... |
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| 283 | double evallog_nn ( const vec &val ) const |
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| 284 | { |
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| 285 | double tmp; tmp= ( beta-1 ) *log ( val ); |
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| 286 | // it_assert_debug ( std::isfinite ( tmp ),"Infinite value" ); |
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| 287 | return tmp; |
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| 288 | }; |
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| 289 | double lognc () const |
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| 290 | { |
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| 291 | double tmp; |
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| 292 | double gam=sum ( beta ); |
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| 293 | double lgb=0.0; |
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| 294 | for ( int i=0;i<beta.length();i++ ) {lgb+=lgamma ( beta ( i ) );} |
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| 295 | tmp= lgb-lgamma ( gam ); |
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| 296 | // it_assert_debug ( std::isfinite ( tmp ),"Infinite value" ); |
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| 297 | return tmp; |
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| 298 | }; |
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| 299 | //!access function |
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| 300 | vec& _beta() {return beta;} |
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| 301 | //!Set internal parameters |
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| 302 | }; |
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| 303 | |
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| 304 | //! \brief Estimator for Multinomial density |
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| 305 | class multiBM : public BMEF |
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| 306 | { |
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| 307 | protected: |
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| 308 | //! Conjugate prior and posterior |
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| 309 | eDirich est; |
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| 310 | //! Pointer inside est to sufficient statistics |
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| 311 | vec β |
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| 312 | public: |
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| 313 | //!Default constructor |
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| 314 | multiBM ( ) : BMEF ( ),est ( ),beta ( est._beta() ) |
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| 315 | { |
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| 316 | if ( beta.length() >0 ) {last_lognc=est.lognc();} |
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| 317 | else{last_lognc=0.0;} |
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| 318 | } |
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| 319 | //!Copy constructor |
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| 320 | multiBM ( const multiBM &B ) : BMEF ( B ),est ( B.est ),beta ( est._beta() ) {} |
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| 321 | //! Sets sufficient statistics to match that of givefrom mB0 |
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| 322 | void set_statistics ( const BM* mB0 ) {const multiBM* mB=dynamic_cast<const multiBM*> ( mB0 ); beta=mB->beta;} |
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| 323 | void bayes ( const vec &dt ) |
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| 324 | { |
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| 325 | if ( frg<1.0 ) {beta*=frg;last_lognc=est.lognc();} |
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| 326 | beta+=dt; |
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| 327 | if ( evalll ) {ll=est.lognc()-last_lognc;} |
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| 328 | } |
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| 329 | double logpred ( const vec &dt ) const |
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| 330 | { |
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| 331 | eDirich pred ( est ); |
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| 332 | vec &beta = pred._beta(); |
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| 333 | |
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| 334 | double lll; |
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| 335 | if ( frg<1.0 ) |
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| 336 | {beta*=frg;lll=pred.lognc();} |
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| 337 | else |
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| 338 | if ( evalll ) {lll=last_lognc;} |
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| 339 | else{lll=pred.lognc();} |
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| 340 | |
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| 341 | beta+=dt; |
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| 342 | return pred.lognc()-lll; |
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| 343 | } |
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| 344 | void flatten ( const BMEF* B ) |
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| 345 | { |
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| 346 | const multiBM* E=dynamic_cast<const multiBM*> ( B ); |
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| 347 | // sum(beta) should be equal to sum(B.beta) |
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| 348 | const vec &Eb=E->beta;//const_cast<multiBM*> ( E )->_beta(); |
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| 349 | beta*= ( sum ( Eb ) /sum ( beta ) ); |
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| 350 | if ( evalll ) {last_lognc=est.lognc();} |
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| 351 | } |
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| 352 | const epdf& posterior() const {return est;}; |
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| 353 | const eDirich* _e() const {return &est;}; |
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| 354 | void set_parameters ( const vec &beta0 ) |
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| 355 | { |
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| 356 | est.set_parameters ( beta0 ); |
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| 357 | if ( evalll ) {last_lognc=est.lognc();} |
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| 358 | } |
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| 359 | }; |
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| 360 | |
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| 361 | /*! |
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| 362 | \brief Gamma posterior density |
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| 363 | |
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| 364 | Multivariate Gamma density as product of independent univariate densities. |
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| 365 | \f[ |
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| 366 | f(x|\alpha,\beta) = \prod f(x_i|\alpha_i,\beta_i) |
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| 367 | \f] |
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| 368 | */ |
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| 369 | |
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| 370 | class egamma : public eEF |
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| 371 | { |
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| 372 | protected: |
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| 373 | //! Vector \f$\alpha\f$ |
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| 374 | vec alpha; |
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| 375 | //! Vector \f$\beta\f$ |
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| 376 | vec beta; |
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| 377 | public : |
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| 378 | //! \name Constructors |
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| 379 | //!@{ |
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| 380 | egamma ( ) :eEF ( ), alpha ( 0 ), beta ( 0 ) {}; |
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| 381 | egamma ( const vec &a, const vec &b ) {set_parameters ( a, b );}; |
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| 382 | void set_parameters ( const vec &a, const vec &b ) {alpha=a,beta=b;dim = alpha.length();}; |
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| 383 | //!@} |
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| 384 | |
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| 385 | vec sample() const; |
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| 386 | //! TODO: is it used anywhere? |
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| 387 | // mat sample ( int N ) const; |
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| 388 | double evallog ( const vec &val ) const; |
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| 389 | double lognc () const; |
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| 390 | //! Returns poiter to alpha and beta. Potentially dengerous: use with care! |
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| 391 | vec& _alpha() {return alpha;} |
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| 392 | vec& _beta() {return beta;} |
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| 393 | vec mean() const {return elem_div ( alpha,beta );} |
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| 394 | vec variance() const {return elem_div ( alpha,elem_mult ( beta,beta ) ); } |
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| 395 | |
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| 396 | //! Load from structure with elements: |
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| 397 | //! \code |
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| 398 | //! { alpha = [...]; // vector of alpha |
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| 399 | //! beta = [...]; // vector of beta |
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| 400 | //! rv = {class="RV",...} // description |
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| 401 | //! } |
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| 402 | //! \endcode |
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| 403 | //!@} |
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| 404 | void from_setting(const Setting &set){ |
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| 405 | epdf::from_setting(set); // reads rv |
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| 406 | UI::get(alpha,set,"alpha", UI::compulsory); |
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| 407 | UI::get(beta,set,"beta", UI::compulsory); |
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| 408 | validate(); |
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| 409 | } |
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| 410 | void validate(){ |
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| 411 | it_assert(alpha.length() ==beta.length(), "parameters do not match"); |
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| 412 | dim =alpha.length(); |
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| 413 | } |
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| 414 | }; |
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| 415 | UIREGISTER(egamma); |
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| 416 | /*! |
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| 417 | \brief Inverse-Gamma posterior density |
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| 418 | |
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| 419 | Multivariate inverse-Gamma density as product of independent univariate densities. |
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| 420 | \f[ |
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| 421 | f(x|\alpha,\beta) = \prod f(x_i|\alpha_i,\beta_i) |
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| 422 | \f] |
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| 423 | |
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| 424 | Vector \f$\beta\f$ has different meaning (in fact it is 1/beta as used in definition of iG) |
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| 425 | |
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| 426 | Inverse Gamma can be converted to Gamma using \f[ |
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| 427 | x\sim iG(a,b) => 1/x\sim G(a,1/b) |
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| 428 | \f] |
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| 429 | This relation is used in sampling. |
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| 430 | */ |
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| 431 | |
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| 432 | class eigamma : public egamma |
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| 433 | { |
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| 434 | protected: |
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| 435 | public : |
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| 436 | //! \name Constructors |
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| 437 | //! All constructors are inherited |
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| 438 | //!@{ |
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| 439 | //!@} |
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| 440 | |
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| 441 | vec sample() const {return 1.0/egamma::sample();}; |
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| 442 | //! Returns poiter to alpha and beta. Potentially dangerous: use with care! |
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| 443 | vec mean() const {return elem_div ( beta,alpha-1 );} |
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| 444 | vec variance() const {vec mea=mean(); return elem_div ( elem_mult ( mea,mea ),alpha-2 );} |
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| 445 | }; |
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| 446 | /* |
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| 447 | //! Weighted mixture of epdfs with external owned components. |
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| 448 | class emix : public epdf { |
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| 449 | protected: |
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| 450 | int n; |
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| 451 | vec &w; |
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| 452 | Array<epdf*> Coms; |
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| 453 | public: |
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| 454 | //! Default constructor |
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| 455 | emix ( const RV &rv, vec &w0): epdf(rv), n(w0.length()), w(w0), Coms(n) {}; |
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| 456 | void set_parameters( int &i, double wi, epdf* ep){w(i)=wi;Coms(i)=ep;} |
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| 457 | vec mean(){vec pom; for(int i=0;i<n;i++){pom+=Coms(i)->mean()*w(i);} return pom;}; |
|---|
| 458 | vec sample() {it_error ( "Not implemented" );return 0;} |
|---|
| 459 | }; |
|---|
| 460 | */ |
|---|
| 461 | |
|---|
| 462 | //! Uniform distributed density on a rectangular support |
|---|
| 463 | |
|---|
| 464 | class euni: public epdf |
|---|
| 465 | { |
|---|
| 466 | protected: |
|---|
| 467 | //! lower bound on support |
|---|
| 468 | vec low; |
|---|
| 469 | //! upper bound on support |
|---|
| 470 | vec high; |
|---|
| 471 | //! internal |
|---|
| 472 | vec distance; |
|---|
| 473 | //! normalizing coefficients |
|---|
| 474 | double nk; |
|---|
| 475 | //! cache of log( \c nk ) |
|---|
| 476 | double lnk; |
|---|
| 477 | public: |
|---|
| 478 | //! \name Constructors |
|---|
| 479 | //!@{ |
|---|
| 480 | euni ( ) :epdf ( ) {} |
|---|
| 481 | euni ( const vec &low0, const vec &high0 ) {set_parameters ( low0,high0 );} |
|---|
| 482 | void set_parameters ( const vec &low0, const vec &high0 ) |
|---|
| 483 | { |
|---|
| 484 | distance = high0-low0; |
|---|
| 485 | it_assert_debug ( min ( distance ) >0.0,"bad support" ); |
|---|
| 486 | low = low0; |
|---|
| 487 | high = high0; |
|---|
| 488 | nk = prod ( 1.0/distance ); |
|---|
| 489 | lnk = log ( nk ); |
|---|
| 490 | dim = low.length(); |
|---|
| 491 | } |
|---|
| 492 | //!@} |
|---|
| 493 | |
|---|
| 494 | double eval ( const vec &val ) const {return nk;} |
|---|
| 495 | double evallog ( const vec &val ) const { |
|---|
| 496 | if (any(val<low) && any(val>high)) {return inf;} |
|---|
| 497 | else return lnk; |
|---|
| 498 | } |
|---|
| 499 | vec sample() const |
|---|
| 500 | { |
|---|
| 501 | vec smp ( dim ); |
|---|
| 502 | #pragma omp critical |
|---|
| 503 | UniRNG.sample_vector ( dim ,smp ); |
|---|
| 504 | return low+elem_mult ( distance,smp ); |
|---|
| 505 | } |
|---|
| 506 | //! set values of \c low and \c high |
|---|
| 507 | vec mean() const {return ( high-low ) /2.0;} |
|---|
| 508 | vec variance() const {return ( pow ( high,2 ) +pow ( low,2 ) +elem_mult ( high,low ) ) /3.0;} |
|---|
| 509 | //! Load from structure with elements: |
|---|
| 510 | //! \code |
|---|
| 511 | //! { high = [...]; // vector of upper bounds |
|---|
| 512 | //! low = [...]; // vector of lower bounds |
|---|
| 513 | //! rv = {class="RV",...} // description of RV |
|---|
| 514 | //! } |
|---|
| 515 | //! \endcode |
|---|
| 516 | //!@} |
|---|
| 517 | void from_setting(const Setting &set){ |
|---|
| 518 | epdf::from_setting(set); // reads rv and rvc |
|---|
| 519 | |
|---|
| 520 | UI::get(high,set,"high", UI::compulsory); |
|---|
| 521 | UI::get(low,set,"low", UI::compulsory); |
|---|
| 522 | } |
|---|
| 523 | }; |
|---|
| 524 | |
|---|
| 525 | |
|---|
| 526 | /*! |
|---|
| 527 | \brief Normal distributed linear function with linear function of mean value; |
|---|
| 528 | |
|---|
| 529 | Mean value \f$mu=A*rvc+mu_0\f$. |
|---|
| 530 | */ |
|---|
| 531 | template<class sq_T> |
|---|
| 532 | class mlnorm : public mEF |
|---|
| 533 | { |
|---|
| 534 | protected: |
|---|
| 535 | //! Internal epdf that arise by conditioning on \c rvc |
|---|
| 536 | shared_ptr<enorm<sq_T> > iepdf; |
|---|
| 537 | mat A; |
|---|
| 538 | vec mu_const; |
|---|
| 539 | vec& _mu; //cached epdf.mu; |
|---|
| 540 | public: |
|---|
| 541 | //! \name Constructors |
|---|
| 542 | //!@{ |
|---|
| 543 | mlnorm():iepdf(new enorm<sq_T>()), _mu(iepdf->_mu()) { set_ep(iepdf); }; |
|---|
| 544 | mlnorm (const mat &A, const vec &mu0, const sq_T &R ) :iepdf(new enorm<sq_T>()), _mu(iepdf->_mu()) |
|---|
| 545 | { |
|---|
| 546 | set_ep(iepdf); set_parameters ( A,mu0,R ); |
|---|
| 547 | } |
|---|
| 548 | |
|---|
| 549 | //! Set \c A and \c R |
|---|
| 550 | void set_parameters ( const mat &A, const vec &mu0, const sq_T &R ); |
|---|
| 551 | //!@} |
|---|
| 552 | //! Set value of \c rvc . Result of this operation is stored in \c epdf use function \c _ep to access it. |
|---|
| 553 | void condition ( const vec &cond ); |
|---|
| 554 | |
|---|
| 555 | //!access function |
|---|
| 556 | vec& _mu_const() {return mu_const;} |
|---|
| 557 | //!access function |
|---|
| 558 | mat& _A() {return A;} |
|---|
| 559 | //!access function |
|---|
| 560 | mat _R() { return iepdf->_R().to_mat(); } |
|---|
| 561 | |
|---|
| 562 | template<class sq_M> |
|---|
| 563 | friend std::ostream &operator<< ( std::ostream &os, mlnorm<sq_M> &ml ); |
|---|
| 564 | |
|---|
| 565 | void from_setting(const Setting &set){ |
|---|
| 566 | mpdf::from_setting(set); |
|---|
| 567 | |
|---|
| 568 | UI::get(A,set,"A", UI::compulsory); |
|---|
| 569 | UI::get(mu_const,set,"const", UI::compulsory); |
|---|
| 570 | mat R0; |
|---|
| 571 | UI::get(R0,set,"R", UI::compulsory); |
|---|
| 572 | set_parameters(A,mu_const,R0); |
|---|
| 573 | }; |
|---|
| 574 | }; |
|---|
| 575 | UIREGISTER(mlnorm<ldmat>); |
|---|
| 576 | UIREGISTER(mlnorm<fsqmat>); |
|---|
| 577 | UIREGISTER(mlnorm<chmat>); |
|---|
| 578 | |
|---|
| 579 | //! Mpdf with general function for mean value |
|---|
| 580 | template<class sq_T> |
|---|
| 581 | class mgnorm : public mEF |
|---|
| 582 | { |
|---|
| 583 | protected: |
|---|
| 584 | //! Internal epdf that arise by conditioning on \c rvc |
|---|
| 585 | shared_ptr<enorm<sq_T> > iepdf; |
|---|
| 586 | vec μ |
|---|
| 587 | fnc* g; |
|---|
| 588 | public: |
|---|
| 589 | //!default constructor |
|---|
| 590 | mgnorm():iepdf(new enorm<sq_T>()), mu(iepdf->_mu()) { set_ep(iepdf); } |
|---|
| 591 | //!set mean function |
|---|
| 592 | void set_parameters ( fnc* g0, const sq_T &R0 ) {g=g0; iepdf->set_parameters ( zeros ( g->dimension() ), R0 );} |
|---|
| 593 | void condition ( const vec &cond ) {mu=g->eval ( cond );}; |
|---|
| 594 | |
|---|
| 595 | |
|---|
| 596 | /*! UI for mgnorm |
|---|
| 597 | |
|---|
| 598 | The mgnorm is constructed from a structure with fields: |
|---|
| 599 | \code |
|---|
| 600 | system = { |
|---|
| 601 | type = "mgnorm"; |
|---|
| 602 | // function for mean value evolution |
|---|
| 603 | g = {type="fnc"; ... } |
|---|
| 604 | |
|---|
| 605 | // variance |
|---|
| 606 | R = [1, 0, |
|---|
| 607 | 0, 1]; |
|---|
| 608 | // --OR -- |
|---|
| 609 | dR = [1, 1]; |
|---|
| 610 | |
|---|
| 611 | // == OPTIONAL == |
|---|
| 612 | |
|---|
| 613 | // description of y variables |
|---|
| 614 | y = {type="rv"; names=["y", "u"];}; |
|---|
| 615 | // description of u variable |
|---|
| 616 | u = {type="rv"; names=[];} |
|---|
| 617 | }; |
|---|
| 618 | \endcode |
|---|
| 619 | |
|---|
| 620 | Result if |
|---|
| 621 | */ |
|---|
| 622 | |
|---|
| 623 | void from_setting( const Setting &set ) |
|---|
| 624 | { |
|---|
| 625 | fnc* g = UI::build<fnc>( set, "g", UI::compulsory ); |
|---|
| 626 | |
|---|
| 627 | mat R; |
|---|
| 628 | vec dR; |
|---|
| 629 | if ( UI::get( dR, set, "dR" ) ) |
|---|
| 630 | R=diag(dR); |
|---|
| 631 | else |
|---|
| 632 | UI::get( R, set, "R", UI::compulsory); |
|---|
| 633 | |
|---|
| 634 | set_parameters(g,R); |
|---|
| 635 | } |
|---|
| 636 | }; |
|---|
| 637 | |
|---|
| 638 | UIREGISTER(mgnorm<chmat>); |
|---|
| 639 | |
|---|
| 640 | |
|---|
| 641 | /*! (Approximate) Student t density with linear function of mean value |
|---|
| 642 | |
|---|
| 643 | The internal epdf of this class is of the type of a Gaussian (enorm). |
|---|
| 644 | However, each conditioning is trying to assure the best possible approximation by taking into account the zeta function. See [] for reference. |
|---|
| 645 | |
|---|
| 646 | Perhaps a moment-matching technique? |
|---|
| 647 | */ |
|---|
| 648 | class mlstudent : public mlnorm<ldmat> |
|---|
| 649 | { |
|---|
| 650 | protected: |
|---|
| 651 | ldmat Lambda; |
|---|
| 652 | ldmat &_R; |
|---|
| 653 | ldmat Re; |
|---|
| 654 | public: |
|---|
| 655 | mlstudent ( ) :mlnorm<ldmat> (), |
|---|
| 656 | Lambda (), _R ( iepdf->_R() ) {} |
|---|
| 657 | void set_parameters ( const mat &A0, const vec &mu0, const ldmat &R0, const ldmat& Lambda0 ) |
|---|
| 658 | { |
|---|
| 659 | it_assert_debug ( A0.rows() ==mu0.length(),"" ); |
|---|
| 660 | it_assert_debug ( R0.rows() ==A0.rows(),"" ); |
|---|
| 661 | |
|---|
| 662 | iepdf->set_parameters ( mu0,Lambda ); // |
|---|
| 663 | A = A0; |
|---|
| 664 | mu_const = mu0; |
|---|
| 665 | Re=R0; |
|---|
| 666 | Lambda = Lambda0; |
|---|
| 667 | } |
|---|
| 668 | void condition ( const vec &cond ) |
|---|
| 669 | { |
|---|
| 670 | _mu = A*cond + mu_const; |
|---|
| 671 | double zeta; |
|---|
| 672 | //ugly hack! |
|---|
| 673 | if ( ( cond.length() +1 ) ==Lambda.rows() ) |
|---|
| 674 | { |
|---|
| 675 | zeta = Lambda.invqform ( concat ( cond, vec_1 ( 1.0 ) ) ); |
|---|
| 676 | } |
|---|
| 677 | else |
|---|
| 678 | { |
|---|
| 679 | zeta = Lambda.invqform ( cond ); |
|---|
| 680 | } |
|---|
| 681 | _R = Re; |
|---|
| 682 | _R*= ( 1+zeta );// / ( nu ); << nu is in Re!!!!!! |
|---|
| 683 | }; |
|---|
| 684 | |
|---|
| 685 | }; |
|---|
| 686 | /*! |
|---|
| 687 | \brief Gamma random walk |
|---|
| 688 | |
|---|
| 689 | Mean value, \f$\mu\f$, of this density is given by \c rvc . |
|---|
| 690 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
|---|
| 691 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
|---|
| 692 | |
|---|
| 693 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
|---|
| 694 | */ |
|---|
| 695 | class mgamma : public mEF |
|---|
| 696 | { |
|---|
| 697 | protected: |
|---|
| 698 | //! Internal epdf that arise by conditioning on \c rvc |
|---|
| 699 | shared_ptr<egamma> iepdf; |
|---|
| 700 | |
|---|
| 701 | //! Constant \f$k\f$ |
|---|
| 702 | double k; |
|---|
| 703 | |
|---|
| 704 | //! cache of iepdf.beta |
|---|
| 705 | vec &_beta; |
|---|
| 706 | |
|---|
| 707 | public: |
|---|
| 708 | //! Constructor |
|---|
| 709 | mgamma():iepdf(new egamma()), k(0), |
|---|
| 710 | _beta(iepdf->_beta()) { |
|---|
| 711 | set_ep(iepdf); |
|---|
| 712 | } |
|---|
| 713 | |
|---|
| 714 | //! Set value of \c k |
|---|
| 715 | void set_parameters(double k, const vec &beta0); |
|---|
| 716 | |
|---|
| 717 | void condition ( const vec &val ) {_beta=k/val;}; |
|---|
| 718 | //! Load from structure with elements: |
|---|
| 719 | //! \code |
|---|
| 720 | //! { alpha = [...]; // vector of alpha |
|---|
| 721 | //! k = 1.1; // multiplicative constant k |
|---|
| 722 | //! rv = {class="RV",...} // description of RV |
|---|
| 723 | //! rvc = {class="RV",...} // description of RV in condition |
|---|
| 724 | //! } |
|---|
| 725 | //! \endcode |
|---|
| 726 | //!@} |
|---|
| 727 | void from_setting(const Setting &set){ |
|---|
| 728 | mpdf::from_setting(set); // reads rv and rvc |
|---|
| 729 | vec betatmp; // ugly but necessary |
|---|
| 730 | UI::get(betatmp,set,"beta", UI::compulsory); |
|---|
| 731 | UI::get(k,set,"k", UI::compulsory); |
|---|
| 732 | set_parameters(k,betatmp); |
|---|
| 733 | } |
|---|
| 734 | }; |
|---|
| 735 | UIREGISTER(mgamma); |
|---|
| 736 | |
|---|
| 737 | /*! |
|---|
| 738 | \brief Inverse-Gamma random walk |
|---|
| 739 | |
|---|
| 740 | Mean value, \f$ \mu \f$, of this density is given by \c rvc . |
|---|
| 741 | Standard deviation of the random walk is proportional to one \f$ k \f$-th the mean. |
|---|
| 742 | This is achieved by setting \f$ \alpha=\mu/k^2+2 \f$ and \f$ \beta=\mu(\alpha-1)\f$. |
|---|
| 743 | |
|---|
| 744 | The standard deviation of the walk is then: \f$ \mu/\sqrt(k)\f$. |
|---|
| 745 | */ |
|---|
| 746 | class migamma : public mEF |
|---|
| 747 | { |
|---|
| 748 | protected: |
|---|
| 749 | //! Internal epdf that arise by conditioning on \c rvc |
|---|
| 750 | shared_ptr<eigamma> iepdf; |
|---|
| 751 | |
|---|
| 752 | //! Constant \f$k\f$ |
|---|
| 753 | double k; |
|---|
| 754 | |
|---|
| 755 | //! cache of iepdf.alpha |
|---|
| 756 | vec &_alpha; |
|---|
| 757 | |
|---|
| 758 | //! cache of iepdf.beta |
|---|
| 759 | vec &_beta; |
|---|
| 760 | |
|---|
| 761 | public: |
|---|
| 762 | //! \name Constructors |
|---|
| 763 | //!@{ |
|---|
| 764 | migamma():iepdf(new eigamma()), |
|---|
| 765 | k(0), |
|---|
| 766 | _alpha(iepdf->_alpha()), |
|---|
| 767 | _beta(iepdf->_beta()) { |
|---|
| 768 | set_ep(iepdf); |
|---|
| 769 | } |
|---|
| 770 | |
|---|
| 771 | migamma(const migamma &m):iepdf(m.iepdf), |
|---|
| 772 | k(0), |
|---|
| 773 | _alpha(iepdf->_alpha()), |
|---|
| 774 | _beta(iepdf->_beta()) { |
|---|
| 775 | set_ep(iepdf); |
|---|
| 776 | } |
|---|
| 777 | //!@} |
|---|
| 778 | |
|---|
| 779 | //! Set value of \c k |
|---|
| 780 | void set_parameters ( int len, double k0 ) |
|---|
| 781 | { |
|---|
| 782 | k=k0; |
|---|
| 783 | iepdf->set_parameters ( ( 1.0/ ( k*k ) +2.0 ) *ones ( len ) /*alpha*/, ones ( len ) /*beta*/ ); |
|---|
| 784 | dimc = dimension(); |
|---|
| 785 | }; |
|---|
| 786 | void condition ( const vec &val ) |
|---|
| 787 | { |
|---|
| 788 | _beta=elem_mult ( val, ( _alpha-1.0 ) ); |
|---|
| 789 | }; |
|---|
| 790 | }; |
|---|
| 791 | |
|---|
| 792 | |
|---|
| 793 | /*! |
|---|
| 794 | \brief Gamma random walk around a fixed point |
|---|
| 795 | |
|---|
| 796 | 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 |
|---|
| 797 | \f[ \mu = \mu_{t-1} ^{l} p^{1-l}\f] |
|---|
| 798 | |
|---|
| 799 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
|---|
| 800 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
|---|
| 801 | |
|---|
| 802 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
|---|
| 803 | */ |
|---|
| 804 | class mgamma_fix : public mgamma |
|---|
| 805 | { |
|---|
| 806 | protected: |
|---|
| 807 | //! parameter l |
|---|
| 808 | double l; |
|---|
| 809 | //! reference vector |
|---|
| 810 | vec refl; |
|---|
| 811 | public: |
|---|
| 812 | //! Constructor |
|---|
| 813 | mgamma_fix ( ) : mgamma ( ),refl () {}; |
|---|
| 814 | //! Set value of \c k |
|---|
| 815 | void set_parameters ( double k0 , vec ref0, double l0 ) |
|---|
| 816 | { |
|---|
| 817 | mgamma::set_parameters ( k0, ref0 ); |
|---|
| 818 | refl=pow ( ref0,1.0-l0 );l=l0; |
|---|
| 819 | dimc=dimension(); |
|---|
| 820 | }; |
|---|
| 821 | |
|---|
| 822 | void condition ( const vec &val ) {vec mean=elem_mult ( refl,pow ( val,l ) ); _beta=k/mean;}; |
|---|
| 823 | }; |
|---|
| 824 | |
|---|
| 825 | |
|---|
| 826 | /*! |
|---|
| 827 | \brief Inverse-Gamma random walk around a fixed point |
|---|
| 828 | |
|---|
| 829 | 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 |
|---|
| 830 | \f[ \mu = \mu_{t-1} ^{l} p^{1-l}\f] |
|---|
| 831 | |
|---|
| 832 | ==== Check == vv = |
|---|
| 833 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
|---|
| 834 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
|---|
| 835 | |
|---|
| 836 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
|---|
| 837 | */ |
|---|
| 838 | class migamma_ref : public migamma |
|---|
| 839 | { |
|---|
| 840 | protected: |
|---|
| 841 | //! parameter l |
|---|
| 842 | double l; |
|---|
| 843 | //! reference vector |
|---|
| 844 | vec refl; |
|---|
| 845 | public: |
|---|
| 846 | //! Constructor |
|---|
| 847 | migamma_ref ( ) : migamma (),refl ( ) {}; |
|---|
| 848 | //! Set value of \c k |
|---|
| 849 | void set_parameters ( double k0 , vec ref0, double l0 ) |
|---|
| 850 | { |
|---|
| 851 | migamma::set_parameters ( ref0.length(), k0 ); |
|---|
| 852 | refl=pow ( ref0,1.0-l0 ); |
|---|
| 853 | l=l0; |
|---|
| 854 | dimc = dimension(); |
|---|
| 855 | }; |
|---|
| 856 | |
|---|
| 857 | void condition ( const vec &val ) |
|---|
| 858 | { |
|---|
| 859 | vec mean=elem_mult ( refl,pow ( val,l ) ); |
|---|
| 860 | migamma::condition ( mean ); |
|---|
| 861 | }; |
|---|
| 862 | |
|---|
| 863 | /*! UI for migamma_ref |
|---|
| 864 | |
|---|
| 865 | The migamma_ref is constructed from a structure with fields: |
|---|
| 866 | \code |
|---|
| 867 | system = { |
|---|
| 868 | type = "migamma_ref"; |
|---|
| 869 | ref = [1e-5; 1e-5; 1e-2 1e-3]; // reference vector |
|---|
| 870 | l = 0.999; // constant l |
|---|
| 871 | k = 0.1; // constant k |
|---|
| 872 | |
|---|
| 873 | // == OPTIONAL == |
|---|
| 874 | // description of y variables |
|---|
| 875 | y = {type="rv"; names=["y", "u"];}; |
|---|
| 876 | // description of u variable |
|---|
| 877 | u = {type="rv"; names=[];} |
|---|
| 878 | }; |
|---|
| 879 | \endcode |
|---|
| 880 | |
|---|
| 881 | Result if |
|---|
| 882 | */ |
|---|
| 883 | void from_setting( const Setting &set ); |
|---|
| 884 | |
|---|
| 885 | // TODO dodelat void to_setting( Setting &set ) const; |
|---|
| 886 | }; |
|---|
| 887 | |
|---|
| 888 | |
|---|
| 889 | UIREGISTER(migamma_ref); |
|---|
| 890 | |
|---|
| 891 | /*! Log-Normal probability density |
|---|
| 892 | only allow diagonal covariances! |
|---|
| 893 | |
|---|
| 894 | Density of the form \f$ \log(x)\sim \mathcal{N}(\mu,\sigma^2) \f$ , i.e. |
|---|
| 895 | \f[ |
|---|
| 896 | x \sim \frac{1}{x\sigma\sqrt{2\pi}}\exp{-\frac{1}{2\sigma^2}(\log(x)-\mu)} |
|---|
| 897 | \f] |
|---|
| 898 | |
|---|
| 899 | */ |
|---|
| 900 | class elognorm: public enorm<ldmat> |
|---|
| 901 | { |
|---|
| 902 | public: |
|---|
| 903 | vec sample() const {return exp ( enorm<ldmat>::sample() );}; |
|---|
| 904 | vec mean() const {vec var=enorm<ldmat>::variance();return exp ( mu - 0.5*var );}; |
|---|
| 905 | |
|---|
| 906 | }; |
|---|
| 907 | |
|---|
| 908 | /*! |
|---|
| 909 | \brief Log-Normal random walk |
|---|
| 910 | |
|---|
| 911 | Mean value, \f$\mu\f$, is... |
|---|
| 912 | |
|---|
| 913 | ==== Check == vv = |
|---|
| 914 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
|---|
| 915 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
|---|
| 916 | |
|---|
| 917 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
|---|
| 918 | */ |
|---|
| 919 | class mlognorm : public mpdf |
|---|
| 920 | { |
|---|
| 921 | protected: |
|---|
| 922 | shared_ptr<elognorm> eno; |
|---|
| 923 | |
|---|
| 924 | //! parameter 1/2*sigma^2 |
|---|
| 925 | double sig2; |
|---|
| 926 | |
|---|
| 927 | //! access |
|---|
| 928 | vec μ |
|---|
| 929 | public: |
|---|
| 930 | //! Constructor |
|---|
| 931 | mlognorm():eno(new elognorm()), |
|---|
| 932 | sig2(0), |
|---|
| 933 | mu(eno->_mu()) { |
|---|
| 934 | set_ep(eno); |
|---|
| 935 | } |
|---|
| 936 | |
|---|
| 937 | //! Set value of \c k |
|---|
| 938 | void set_parameters ( int size, double k ) |
|---|
| 939 | { |
|---|
| 940 | sig2 = 0.5*log ( k*k+1 ); |
|---|
| 941 | eno->set_parameters ( zeros ( size ),2*sig2*eye ( size ) ); |
|---|
| 942 | |
|---|
| 943 | dimc = size; |
|---|
| 944 | }; |
|---|
| 945 | |
|---|
| 946 | void condition ( const vec &val ) |
|---|
| 947 | { |
|---|
| 948 | mu=log ( val )-sig2;//elem_mult ( refl,pow ( val,l ) ); |
|---|
| 949 | }; |
|---|
| 950 | |
|---|
| 951 | /*! UI for mlognorm |
|---|
| 952 | |
|---|
| 953 | The mlognorm is constructed from a structure with fields: |
|---|
| 954 | \code |
|---|
| 955 | system = { |
|---|
| 956 | type = "mlognorm"; |
|---|
| 957 | k = 0.1; // constant k |
|---|
| 958 | mu0 = [1., 1.]; |
|---|
| 959 | |
|---|
| 960 | // == OPTIONAL == |
|---|
| 961 | // description of y variables |
|---|
| 962 | y = {type="rv"; names=["y", "u"];}; |
|---|
| 963 | // description of u variable |
|---|
| 964 | u = {type="rv"; names=[];} |
|---|
| 965 | }; |
|---|
| 966 | \endcode |
|---|
| 967 | |
|---|
| 968 | */ |
|---|
| 969 | void from_setting( const Setting &set ); |
|---|
| 970 | |
|---|
| 971 | // TODO dodelat void to_setting( Setting &set ) const; |
|---|
| 972 | |
|---|
| 973 | }; |
|---|
| 974 | |
|---|
| 975 | UIREGISTER(mlognorm); |
|---|
| 976 | |
|---|
| 977 | /*! inverse Wishart density defined on Choleski decomposition |
|---|
| 978 | |
|---|
| 979 | */ |
|---|
| 980 | class eWishartCh : public epdf |
|---|
| 981 | { |
|---|
| 982 | protected: |
|---|
| 983 | //! Upper-Triagle of Choleski decomposition of \f$ \Psi \f$ |
|---|
| 984 | chmat Y; |
|---|
| 985 | //! dimension of matrix \f$ \Psi \f$ |
|---|
| 986 | int p; |
|---|
| 987 | //! degrees of freedom \f$ \nu \f$ |
|---|
| 988 | double delta; |
|---|
| 989 | public: |
|---|
| 990 | void set_parameters ( const mat &Y0, const double delta0 ) {Y=chmat ( Y0 );delta=delta0; p=Y.rows(); dim = p*p; } |
|---|
| 991 | mat sample_mat() const |
|---|
| 992 | { |
|---|
| 993 | mat X=zeros ( p,p ); |
|---|
| 994 | |
|---|
| 995 | //sample diagonal |
|---|
| 996 | for ( int i=0;i<p;i++ ) |
|---|
| 997 | { |
|---|
| 998 | GamRNG.setup ( 0.5* ( delta-i ) , 0.5 ); // no +1 !! index if from 0 |
|---|
| 999 | #pragma omp critical |
|---|
| 1000 | X ( i,i ) =sqrt ( GamRNG() ); |
|---|
| 1001 | } |
|---|
| 1002 | //do the rest |
|---|
| 1003 | for ( int i=0;i<p;i++ ) |
|---|
| 1004 | { |
|---|
| 1005 | for ( int j=i+1;j<p;j++ ) |
|---|
| 1006 | { |
|---|
| 1007 | #pragma omp critical |
|---|
| 1008 | X ( i,j ) =NorRNG.sample(); |
|---|
| 1009 | } |
|---|
| 1010 | } |
|---|
| 1011 | return X*Y._Ch();// return upper triangular part of the decomposition |
|---|
| 1012 | } |
|---|
| 1013 | vec sample () const |
|---|
| 1014 | { |
|---|
| 1015 | return vec ( sample_mat()._data(),p*p ); |
|---|
| 1016 | } |
|---|
| 1017 | //! fast access function y0 will be copied into Y.Ch. |
|---|
| 1018 | void setY ( const mat &Ch0 ) {copy_vector ( dim,Ch0._data(), Y._Ch()._data() );} |
|---|
| 1019 | //! fast access function y0 will be copied into Y.Ch. |
|---|
| 1020 | void _setY ( const vec &ch0 ) {copy_vector ( dim, ch0._data(), Y._Ch()._data() ); } |
|---|
| 1021 | //! access function |
|---|
| 1022 | const chmat& getY()const {return Y;} |
|---|
| 1023 | }; |
|---|
| 1024 | |
|---|
| 1025 | class eiWishartCh: public epdf |
|---|
| 1026 | { |
|---|
| 1027 | protected: |
|---|
| 1028 | eWishartCh W; |
|---|
| 1029 | int p; |
|---|
| 1030 | double delta; |
|---|
| 1031 | public: |
|---|
| 1032 | void set_parameters ( const mat &Y0, const double delta0) { |
|---|
| 1033 | delta = delta0; |
|---|
| 1034 | W.set_parameters ( inv ( Y0 ),delta0 ); |
|---|
| 1035 | dim = W.dimension(); p=Y0.rows(); |
|---|
| 1036 | } |
|---|
| 1037 | vec sample() const {mat iCh; iCh=inv ( W.sample_mat() ); return vec ( iCh._data(),dim );} |
|---|
| 1038 | void _setY ( const vec &y0 ) |
|---|
| 1039 | { |
|---|
| 1040 | mat Ch ( p,p ); |
|---|
| 1041 | mat iCh ( p,p ); |
|---|
| 1042 | copy_vector ( dim, y0._data(), Ch._data() ); |
|---|
| 1043 | |
|---|
| 1044 | iCh=inv ( Ch ); |
|---|
| 1045 | W.setY ( iCh ); |
|---|
| 1046 | } |
|---|
| 1047 | virtual double evallog ( const vec &val ) const { |
|---|
| 1048 | chmat X(p); |
|---|
| 1049 | const chmat& Y=W.getY(); |
|---|
| 1050 | |
|---|
| 1051 | copy_vector(p*p,val._data(),X._Ch()._data()); |
|---|
| 1052 | chmat iX(p);X.inv(iX); |
|---|
| 1053 | // compute |
|---|
| 1054 | // \frac{ |\Psi|^{m/2}|X|^{-(m+p+1)/2}e^{-tr(\Psi X^{-1})/2} }{ 2^{mp/2}\Gamma_p(m/2)}, |
|---|
| 1055 | mat M=Y.to_mat()*iX.to_mat(); |
|---|
| 1056 | |
|---|
| 1057 | double log1 = 0.5*p*(2*Y.logdet())-0.5*(delta+p+1)*(2*X.logdet())-0.5*trace(M); |
|---|
| 1058 | //Fixme! Multivariate gamma omitted!! it is ok for sampling, but not otherwise!! |
|---|
| 1059 | |
|---|
| 1060 | /* if (0) { |
|---|
| 1061 | mat XX=X.to_mat(); |
|---|
| 1062 | mat YY=Y.to_mat(); |
|---|
| 1063 | |
|---|
| 1064 | double log2 = 0.5*p*log(det(YY))-0.5*(delta+p+1)*log(det(XX))-0.5*trace(YY*inv(XX)); |
|---|
| 1065 | cout << log1 << "," << log2 << endl; |
|---|
| 1066 | }*/ |
|---|
| 1067 | return log1; |
|---|
| 1068 | }; |
|---|
| 1069 | |
|---|
| 1070 | }; |
|---|
| 1071 | |
|---|
| 1072 | class rwiWishartCh : public mpdf |
|---|
| 1073 | { |
|---|
| 1074 | protected: |
|---|
| 1075 | shared_ptr<eiWishartCh> eiW; |
|---|
| 1076 | //!square root of \f$ \nu-p-1 \f$ - needed for computation of \f$ \Psi \f$ from conditions |
|---|
| 1077 | double sqd; |
|---|
| 1078 | //reference point for diagonal |
|---|
| 1079 | vec refl; |
|---|
| 1080 | double l; |
|---|
| 1081 | int p; |
|---|
| 1082 | |
|---|
| 1083 | public: |
|---|
| 1084 | rwiWishartCh():eiW(new eiWishartCh()), |
|---|
| 1085 | sqd(0), l(0), p(0) { |
|---|
| 1086 | set_ep(eiW); |
|---|
| 1087 | } |
|---|
| 1088 | |
|---|
| 1089 | void set_parameters ( int p0, double k, vec ref0, double l0 ) |
|---|
| 1090 | { |
|---|
| 1091 | p=p0; |
|---|
| 1092 | double delta = 2/(k*k)+p+3; |
|---|
| 1093 | sqd=sqrt ( delta-p-1 ); |
|---|
| 1094 | l=l0; |
|---|
| 1095 | refl=pow(ref0,1-l); |
|---|
| 1096 | |
|---|
| 1097 | eiW->set_parameters ( eye ( p ),delta ); |
|---|
| 1098 | dimc=eiW->dimension(); |
|---|
| 1099 | } |
|---|
| 1100 | void condition ( const vec &c ) { |
|---|
| 1101 | vec z=c; |
|---|
| 1102 | int ri=0; |
|---|
| 1103 | for(int i=0;i<p*p;i+=(p+1)){//trace diagonal element |
|---|
| 1104 | z(i) = pow(z(i),l)*refl(ri); |
|---|
| 1105 | ri++; |
|---|
| 1106 | } |
|---|
| 1107 | |
|---|
| 1108 | eiW->_setY ( sqd*z ); |
|---|
| 1109 | } |
|---|
| 1110 | }; |
|---|
| 1111 | |
|---|
| 1112 | //! Switch between various resampling methods. |
|---|
| 1113 | enum RESAMPLING_METHOD { MULTINOMIAL = 0, STRATIFIED = 1, SYSTEMATIC = 3 }; |
|---|
| 1114 | /*! |
|---|
| 1115 | \brief Weighted empirical density |
|---|
| 1116 | |
|---|
| 1117 | Used e.g. in particle filters. |
|---|
| 1118 | */ |
|---|
| 1119 | class eEmp: public epdf |
|---|
| 1120 | { |
|---|
| 1121 | protected : |
|---|
| 1122 | //! Number of particles |
|---|
| 1123 | int n; |
|---|
| 1124 | //! Sample weights \f$w\f$ |
|---|
| 1125 | vec w; |
|---|
| 1126 | //! Samples \f$x^{(i)}, i=1..n\f$ |
|---|
| 1127 | Array<vec> samples; |
|---|
| 1128 | public: |
|---|
| 1129 | //! \name Constructors |
|---|
| 1130 | //!@{ |
|---|
| 1131 | eEmp ( ) :epdf ( ),w ( ),samples ( ) {}; |
|---|
| 1132 | //! copy constructor |
|---|
| 1133 | eEmp ( const eEmp &e ) : epdf ( e ), w ( e.w ), samples ( e.samples ) {}; |
|---|
| 1134 | //!@} |
|---|
| 1135 | |
|---|
| 1136 | //! Set samples and weights |
|---|
| 1137 | void set_statistics ( const vec &w0, const epdf* pdf0 ); |
|---|
| 1138 | //! Set samples and weights |
|---|
| 1139 | void set_statistics ( const epdf* pdf0 , int n ) {set_statistics ( ones ( n ) /n,pdf0 );}; |
|---|
| 1140 | //! Set sample |
|---|
| 1141 | void set_samples ( const epdf* pdf0 ); |
|---|
| 1142 | //! Set sample |
|---|
| 1143 | void set_parameters ( int n0, bool copy=true ) {n=n0; w.set_size ( n0,copy );samples.set_size ( n0,copy );}; |
|---|
| 1144 | //! Potentially dangerous, use with care. |
|---|
| 1145 | vec& _w() {return w;}; |
|---|
| 1146 | //! Potentially dangerous, use with care. |
|---|
| 1147 | const vec& _w() const {return w;}; |
|---|
| 1148 | //! access function |
|---|
| 1149 | Array<vec>& _samples() {return samples;}; |
|---|
| 1150 | //! access function |
|---|
| 1151 | const Array<vec>& _samples() const {return samples;}; |
|---|
| 1152 | //! 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. |
|---|
| 1153 | ivec resample ( RESAMPLING_METHOD method=SYSTEMATIC ); |
|---|
| 1154 | //! inherited operation : NOT implemneted |
|---|
| 1155 | vec sample() const {it_error ( "Not implemented" );return 0;} |
|---|
| 1156 | //! inherited operation : NOT implemneted |
|---|
| 1157 | double evallog ( const vec &val ) const {it_error ( "Not implemented" );return 0.0;} |
|---|
| 1158 | vec mean() const |
|---|
| 1159 | { |
|---|
| 1160 | vec pom=zeros ( dim ); |
|---|
| 1161 | for ( int i=0;i<n;i++ ) {pom+=samples ( i ) *w ( i );} |
|---|
| 1162 | return pom; |
|---|
| 1163 | } |
|---|
| 1164 | vec variance() const |
|---|
| 1165 | { |
|---|
| 1166 | vec pom=zeros ( dim ); |
|---|
| 1167 | for ( int i=0;i<n;i++ ) {pom+=pow ( samples ( i ),2 ) *w ( i );} |
|---|
| 1168 | return pom-pow ( mean(),2 ); |
|---|
| 1169 | } |
|---|
| 1170 | //! For this class, qbounds are minimum and maximum value of the population! |
|---|
| 1171 | void qbounds ( vec &lb, vec &ub, double perc=0.95 ) const |
|---|
| 1172 | { |
|---|
| 1173 | // lb in inf so than it will be pushed below; |
|---|
| 1174 | lb.set_size ( dim ); |
|---|
| 1175 | ub.set_size ( dim ); |
|---|
| 1176 | lb = std::numeric_limits<double>::infinity(); |
|---|
| 1177 | ub = -std::numeric_limits<double>::infinity(); |
|---|
| 1178 | int j; |
|---|
| 1179 | for ( int i=0;i<n;i++ ) |
|---|
| 1180 | { |
|---|
| 1181 | for ( j=0;j<dim; j++ ) |
|---|
| 1182 | { |
|---|
| 1183 | if ( samples ( i ) ( j ) <lb ( j ) ) {lb ( j ) =samples ( i ) ( j );} |
|---|
| 1184 | if ( samples ( i ) ( j ) >ub ( j ) ) {ub ( j ) =samples ( i ) ( j );} |
|---|
| 1185 | } |
|---|
| 1186 | } |
|---|
| 1187 | } |
|---|
| 1188 | }; |
|---|
| 1189 | |
|---|
| 1190 | |
|---|
| 1191 | //////////////////////// |
|---|
| 1192 | |
|---|
| 1193 | template<class sq_T> |
|---|
| 1194 | void enorm<sq_T>::set_parameters ( const vec &mu0, const sq_T &R0 ) |
|---|
| 1195 | { |
|---|
| 1196 | //Fixme test dimensions of mu0 and R0; |
|---|
| 1197 | mu = mu0; |
|---|
| 1198 | R = R0; |
|---|
| 1199 | validate(); |
|---|
| 1200 | }; |
|---|
| 1201 | |
|---|
| 1202 | template<class sq_T> |
|---|
| 1203 | void enorm<sq_T>::from_setting(const Setting &set){ |
|---|
| 1204 | epdf::from_setting(set); //reads rv |
|---|
| 1205 | |
|---|
| 1206 | UI::get(mu,set,"mu", UI::compulsory); |
|---|
| 1207 | mat Rtmp;// necessary for conversion |
|---|
| 1208 | UI::get(Rtmp,set,"R", UI::compulsory); |
|---|
| 1209 | R=Rtmp; // conversion |
|---|
| 1210 | validate(); |
|---|
| 1211 | } |
|---|
| 1212 | |
|---|
| 1213 | template<class sq_T> |
|---|
| 1214 | void enorm<sq_T>::dupdate ( mat &v, double nu ) |
|---|
| 1215 | { |
|---|
| 1216 | // |
|---|
| 1217 | }; |
|---|
| 1218 | |
|---|
| 1219 | // template<class sq_T> |
|---|
| 1220 | // void enorm<sq_T>::tupdate ( double phi, mat &vbar, double nubar ) { |
|---|
| 1221 | // // |
|---|
| 1222 | // }; |
|---|
| 1223 | |
|---|
| 1224 | template<class sq_T> |
|---|
| 1225 | vec enorm<sq_T>::sample() const |
|---|
| 1226 | { |
|---|
| 1227 | vec x ( dim ); |
|---|
| 1228 | #pragma omp critical |
|---|
| 1229 | NorRNG.sample_vector ( dim,x ); |
|---|
| 1230 | vec smp = R.sqrt_mult ( x ); |
|---|
| 1231 | |
|---|
| 1232 | smp += mu; |
|---|
| 1233 | return smp; |
|---|
| 1234 | }; |
|---|
| 1235 | |
|---|
| 1236 | // template<class sq_T> |
|---|
| 1237 | // double enorm<sq_T>::eval ( const vec &val ) const { |
|---|
| 1238 | // double pdfl,e; |
|---|
| 1239 | // pdfl = evallog ( val ); |
|---|
| 1240 | // e = exp ( pdfl ); |
|---|
| 1241 | // return e; |
|---|
| 1242 | // }; |
|---|
| 1243 | |
|---|
| 1244 | template<class sq_T> |
|---|
| 1245 | double enorm<sq_T>::evallog_nn ( const vec &val ) const |
|---|
| 1246 | { |
|---|
| 1247 | // 1.83787706640935 = log(2pi) |
|---|
| 1248 | double tmp=-0.5* ( R.invqform ( mu-val ) );// - lognc(); |
|---|
| 1249 | return tmp; |
|---|
| 1250 | }; |
|---|
| 1251 | |
|---|
| 1252 | template<class sq_T> |
|---|
| 1253 | inline double enorm<sq_T>::lognc () const |
|---|
| 1254 | { |
|---|
| 1255 | // 1.83787706640935 = log(2pi) |
|---|
| 1256 | double tmp=0.5* ( R.cols() * 1.83787706640935 +R.logdet() ); |
|---|
| 1257 | return tmp; |
|---|
| 1258 | }; |
|---|
| 1259 | |
|---|
| 1260 | template<class sq_T> |
|---|
| 1261 | void mlnorm<sq_T>::set_parameters ( const mat &A0, const vec &mu0, const sq_T &R0 ) |
|---|
| 1262 | { |
|---|
| 1263 | it_assert_debug ( A0.rows() ==mu0.length(),"" ); |
|---|
| 1264 | it_assert_debug ( A0.rows() ==R0.rows(),"" ); |
|---|
| 1265 | |
|---|
| 1266 | iepdf->set_parameters(zeros(A0.rows()), R0); |
|---|
| 1267 | A = A0; |
|---|
| 1268 | mu_const = mu0; |
|---|
| 1269 | dimc = A0.cols(); |
|---|
| 1270 | } |
|---|
| 1271 | |
|---|
| 1272 | // template<class sq_T> |
|---|
| 1273 | // vec mlnorm<sq_T>::samplecond (const vec &cond, double &lik ) { |
|---|
| 1274 | // this->condition ( cond ); |
|---|
| 1275 | // vec smp = epdf.sample(); |
|---|
| 1276 | // lik = epdf.eval ( smp ); |
|---|
| 1277 | // return smp; |
|---|
| 1278 | // } |
|---|
| 1279 | |
|---|
| 1280 | // template<class sq_T> |
|---|
| 1281 | // mat mlnorm<sq_T>::samplecond (const vec &cond, vec &lik, int n ) { |
|---|
| 1282 | // int i; |
|---|
| 1283 | // int dim = rv.count(); |
|---|
| 1284 | // mat Smp ( dim,n ); |
|---|
| 1285 | // vec smp ( dim ); |
|---|
| 1286 | // this->condition ( cond ); |
|---|
| 1287 | // |
|---|
| 1288 | // for ( i=0; i<n; i++ ) { |
|---|
| 1289 | // smp = epdf.sample(); |
|---|
| 1290 | // lik ( i ) = epdf.eval ( smp ); |
|---|
| 1291 | // Smp.set_col ( i ,smp ); |
|---|
| 1292 | // } |
|---|
| 1293 | // |
|---|
| 1294 | // return Smp; |
|---|
| 1295 | // } |
|---|
| 1296 | |
|---|
| 1297 | template<class sq_T> |
|---|
| 1298 | void mlnorm<sq_T>::condition ( const vec &cond ) |
|---|
| 1299 | { |
|---|
| 1300 | _mu = A*cond + mu_const; |
|---|
| 1301 | //R is already assigned; |
|---|
| 1302 | } |
|---|
| 1303 | |
|---|
| 1304 | template<class sq_T> |
|---|
| 1305 | enorm<sq_T>* enorm<sq_T>::marginal ( const RV &rvn ) const |
|---|
| 1306 | { |
|---|
| 1307 | it_assert_debug ( isnamed(), "rv description is not assigned" ); |
|---|
| 1308 | ivec irvn = rvn.dataind ( rv ); |
|---|
| 1309 | |
|---|
| 1310 | sq_T Rn ( R,irvn ); //select rows and columns of R |
|---|
| 1311 | |
|---|
| 1312 | enorm<sq_T>* tmp = new enorm<sq_T>; |
|---|
| 1313 | tmp->set_rv ( rvn ); |
|---|
| 1314 | tmp->set_parameters ( mu ( irvn ), Rn ); |
|---|
| 1315 | return tmp; |
|---|
| 1316 | } |
|---|
| 1317 | |
|---|
| 1318 | template<class sq_T> |
|---|
| 1319 | mpdf* enorm<sq_T>::condition ( const RV &rvn ) const |
|---|
| 1320 | { |
|---|
| 1321 | |
|---|
| 1322 | it_assert_debug ( isnamed(),"rvs are not assigned" ); |
|---|
| 1323 | |
|---|
| 1324 | RV rvc = rv.subt ( rvn ); |
|---|
| 1325 | it_assert_debug ( ( rvc._dsize() +rvn._dsize() ==rv._dsize() ),"wrong rvn" ); |
|---|
| 1326 | //Permutation vector of the new R |
|---|
| 1327 | ivec irvn = rvn.dataind ( rv ); |
|---|
| 1328 | ivec irvc = rvc.dataind ( rv ); |
|---|
| 1329 | ivec perm=concat ( irvn , irvc ); |
|---|
| 1330 | sq_T Rn ( R,perm ); |
|---|
| 1331 | |
|---|
| 1332 | //fixme - could this be done in general for all sq_T? |
|---|
| 1333 | mat S=Rn.to_mat(); |
|---|
| 1334 | //fixme |
|---|
| 1335 | int n=rvn._dsize()-1; |
|---|
| 1336 | int end=R.rows()-1; |
|---|
| 1337 | mat S11 = S.get ( 0,n, 0, n ); |
|---|
| 1338 | mat S12 = S.get ( 0, n , rvn._dsize(), end ); |
|---|
| 1339 | mat S22 = S.get ( rvn._dsize(), end, rvn._dsize(), end ); |
|---|
| 1340 | |
|---|
| 1341 | vec mu1 = mu ( irvn ); |
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| 1342 | vec mu2 = mu ( irvc ); |
|---|
| 1343 | mat A=S12*inv ( S22 ); |
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| 1344 | sq_T R_n ( S11 - A *S12.T() ); |
|---|
| 1345 | |
|---|
| 1346 | mlnorm<sq_T>* tmp=new mlnorm<sq_T> ( ); |
|---|
| 1347 | tmp->set_rv ( rvn ); tmp->set_rvc ( rvc ); |
|---|
| 1348 | tmp->set_parameters ( A,mu1-A*mu2,R_n ); |
|---|
| 1349 | return tmp; |
|---|
| 1350 | } |
|---|
| 1351 | |
|---|
| 1352 | /////////// |
|---|
| 1353 | |
|---|
| 1354 | template<class sq_T> |
|---|
| 1355 | std::ostream &operator<< ( std::ostream &os, mlnorm<sq_T> &ml ) |
|---|
| 1356 | { |
|---|
| 1357 | os << "A:"<< ml.A<<endl; |
|---|
| 1358 | os << "mu:"<< ml.mu_const<<endl; |
|---|
| 1359 | os << "R:" << ml.iepdf->_R().to_mat() <<endl; |
|---|
| 1360 | return os; |
|---|
| 1361 | }; |
|---|
| 1362 | |
|---|
| 1363 | } |
|---|
| 1364 | #endif //EF_H |
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