| 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 "../base/bdmbase.h" |
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| 18 | #include "../math/chmat.h" |
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| 19 | |
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| 20 | namespace bdm |
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| 21 | { |
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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 | { |
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| 39 | public: |
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| 40 | // eEF() :epdf() {}; |
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| 41 | //! default constructor |
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| 42 | eEF ( ) :epdf ( ) {}; |
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| 43 | //! logarithm of the normalizing constant, \f$\mathcal{I}\f$ |
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| 44 | virtual double lognc() const =0; |
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| 45 | //!TODO decide if it is really needed |
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| 46 | virtual void dupdate ( mat &v ) {it_error ( "Not implemented" );}; |
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| 47 | //!Evaluate normalized log-probability |
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| 48 | virtual double evallog_nn ( const vec &val ) const{it_error ( "Not implemented" );return 0.0;}; |
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| 49 | //!Evaluate normalized log-probability |
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| 50 | virtual double evallog ( const vec &val ) const { |
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| 51 | double tmp; |
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| 52 | tmp= evallog_nn ( val )-lognc(); |
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| 53 | // it_assert_debug ( std::isfinite ( tmp ),"Infinite value" ); |
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| 54 | return tmp;} |
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| 55 | //!Evaluate normalized log-probability for many samples |
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| 56 | virtual vec evallog ( const mat &Val ) const |
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| 57 | { |
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| 58 | vec x ( Val.cols() ); |
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| 59 | for ( int i=0;i<Val.cols();i++ ) {x ( i ) =evallog_nn ( Val.get_col ( i ) ) ;} |
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| 60 | return x-lognc(); |
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| 61 | } |
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| 62 | //!Power of the density, used e.g. to flatten the density |
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| 63 | virtual void pow ( double p ) {it_error ( "Not implemented" );}; |
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| 64 | }; |
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| 65 | |
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| 66 | /*! |
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| 67 | * \brief Exponential family model. |
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| 68 | |
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| 69 | * More?... |
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| 70 | */ |
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| 71 | |
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| 72 | class mEF : public mpdf |
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| 73 | { |
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| 74 | |
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| 75 | public: |
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| 76 | //! Default constructor |
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| 77 | mEF ( ) :mpdf ( ) {}; |
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| 78 | }; |
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| 79 | |
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| 80 | //! Estimator for Exponential family |
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| 81 | class BMEF : public BM |
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| 82 | { |
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| 83 | protected: |
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| 84 | //! forgetting factor |
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| 85 | double frg; |
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| 86 | //! cached value of lognc() in the previous step (used in evaluation of \c ll ) |
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| 87 | double last_lognc; |
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| 88 | public: |
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| 89 | //! Default constructor (=empty constructor) |
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| 90 | BMEF ( double frg0=1.0 ) :BM ( ), frg ( frg0 ) {} |
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| 91 | //! Copy constructor |
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| 92 | BMEF ( const BMEF &B ) :BM ( B ), frg ( B.frg ), last_lognc ( B.last_lognc ) {} |
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| 93 | //!get statistics from another model |
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| 94 | virtual void set_statistics ( const BMEF* BM0 ) {it_error ( "Not implemented" );}; |
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| 95 | //! Weighted update of sufficient statistics (Bayes rule) |
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| 96 | virtual void bayes ( const vec &data, const double w ) {}; |
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| 97 | //original Bayes |
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| 98 | void bayes ( const vec &dt ); |
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| 99 | //!Flatten the posterior according to the given BMEF (of the same type!) |
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| 100 | virtual void flatten ( const BMEF * B ) {it_error ( "Not implemented" );} |
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| 101 | //!Flatten the posterior as if to keep nu0 data |
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| 102 | // virtual void flatten ( double nu0 ) {it_error ( "Not implemented" );} |
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| 103 | |
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| 104 | BMEF* _copy_ () const {it_error ( "function _copy_ not implemented for this BM" ); return NULL;}; |
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| 105 | }; |
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| 106 | |
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| 107 | template<class sq_T> |
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| 108 | class mlnorm; |
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| 109 | |
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| 110 | /*! |
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| 111 | * \brief Gaussian density with positive definite (decomposed) covariance matrix. |
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| 112 | |
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| 113 | * More?... |
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| 114 | */ |
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| 115 | template<class sq_T> |
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| 116 | class enorm : public eEF |
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| 117 | { |
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| 118 | protected: |
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| 119 | //! mean value |
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| 120 | vec mu; |
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| 121 | //! Covariance matrix in decomposed form |
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| 122 | sq_T R; |
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| 123 | public: |
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| 124 | //!\name Constructors |
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| 125 | //!@{ |
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| 126 | |
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| 127 | enorm ( ) :eEF ( ), mu ( ),R ( ) {}; |
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| 128 | enorm ( const vec &mu,const sq_T &R ) {set_parameters ( mu,R );} |
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| 129 | void set_parameters ( const vec &mu,const sq_T &R ); |
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| 130 | void from_setting(const Setting &root); |
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| 131 | void validate() { |
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| 132 | it_assert(mu.length()==R.rows(),"parameters mismatch"); |
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| 133 | dim = mu.length(); |
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| 134 | } |
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| 135 | //!@} |
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| 136 | |
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| 137 | //! \name Mathematical operations |
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| 138 | //!@{ |
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| 139 | |
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| 140 | //! dupdate in exponential form (not really handy) |
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| 141 | void dupdate ( mat &v,double nu=1.0 ); |
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| 142 | |
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| 143 | vec sample() const; |
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| 144 | mat sample ( int N ) const; |
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| 145 | double evallog_nn ( const vec &val ) const; |
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| 146 | double lognc () const; |
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| 147 | vec mean() const {return mu;} |
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| 148 | vec variance() const {return diag ( R.to_mat() );} |
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| 149 | // mlnorm<sq_T>* condition ( const RV &rvn ) const ; <=========== fails to cmpile. Why? |
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| 150 | mpdf* condition ( const RV &rvn ) const ; |
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| 151 | enorm<sq_T>* marginal ( const RV &rv ) const; |
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| 152 | // epdf* marginal ( const RV &rv ) const; |
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| 153 | //!@} |
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| 154 | |
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| 155 | //! \name Access to attributes |
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| 156 | //!@{ |
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| 157 | |
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| 158 | vec& _mu() {return mu;} |
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| 159 | void set_mu ( const vec mu0 ) { mu=mu0;} |
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| 160 | sq_T& _R() {return R;} |
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| 161 | const sq_T& _R() const {return R;} |
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| 162 | //!@} |
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| 163 | |
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| 164 | }; |
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| 165 | UIREGISTER(enorm<chmat>); |
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| 166 | UIREGISTER(enorm<ldmat>); |
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| 167 | UIREGISTER(enorm<fsqmat>); |
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| 168 | |
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| 169 | |
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| 170 | /*! |
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| 171 | * \brief Gauss-inverse-Wishart density stored in LD form |
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| 172 | |
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| 173 | * For \f$p\f$-variate densities, given rv.count() should be \f$p\times\f$ V.rows(). |
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| 174 | * |
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| 175 | */ |
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| 176 | class egiw : public eEF |
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| 177 | { |
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| 178 | protected: |
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| 179 | //! Extended information matrix of sufficient statistics |
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| 180 | ldmat V; |
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| 181 | //! Number of data records (degrees of freedom) of sufficient statistics |
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| 182 | double nu; |
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| 183 | //! Dimension of the output |
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| 184 | int dimx; |
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| 185 | //! Dimension of the regressor |
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| 186 | int nPsi; |
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| 187 | public: |
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| 188 | //!\name Constructors |
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| 189 | //!@{ |
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| 190 | egiw() :eEF() {}; |
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| 191 | egiw ( int dimx0, ldmat V0, double nu0=-1.0 ) :eEF() {set_parameters ( dimx0,V0, nu0 );}; |
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| 192 | |
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| 193 | void set_parameters ( int dimx0, ldmat V0, double nu0=-1.0 ) |
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| 194 | { |
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| 195 | dimx=dimx0; |
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| 196 | nPsi = V0.rows()-dimx; |
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| 197 | dim = dimx* ( dimx+nPsi ); // size(R) + size(Theta) |
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| 198 | |
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| 199 | V=V0; |
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| 200 | if ( nu0<0 ) |
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| 201 | { |
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| 202 | nu = 0.1 +nPsi +2*dimx +2; // +2 assures finite expected value of R |
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| 203 | // terms before that are sufficient for finite normalization |
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| 204 | } |
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| 205 | else |
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| 206 | { |
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| 207 | nu=nu0; |
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| 208 | } |
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| 209 | } |
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| 210 | //!@} |
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| 211 | |
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| 212 | vec sample() const; |
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| 213 | vec mean() const; |
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| 214 | vec variance() const; |
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| 215 | |
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| 216 | //! LS estimate of \f$\theta\f$ |
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| 217 | vec est_theta() const; |
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| 218 | |
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| 219 | //! Covariance of the LS estimate |
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| 220 | ldmat est_theta_cov() const; |
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| 221 | |
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| 222 | void mean_mat ( mat &M, mat&R ) const; |
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| 223 | //! 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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| 224 | double evallog_nn ( const vec &val ) const; |
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| 225 | double lognc () const; |
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| 226 | void pow ( double p ) {V*=p;nu*=p;}; |
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| 227 | |
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| 228 | //! \name Access attributes |
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| 229 | //!@{ |
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| 230 | |
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| 231 | ldmat& _V() {return V;} |
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| 232 | const ldmat& _V() const {return V;} |
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| 233 | double& _nu() {return nu;} |
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| 234 | const double& _nu() const {return nu;} |
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| 235 | void from_setting(const Setting &set){ |
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| 236 | set.lookupValue("nu",nu); |
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| 237 | set.lookupValue("dimx",dimx); |
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| 238 | mat V; |
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| 239 | UI::get(V,set,"V"); |
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| 240 | set_parameters(dimx, V, nu); |
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| 241 | RV* rv=UI::build<RV>(set,"rv"); |
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| 242 | set_rv(*rv); |
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| 243 | delete rv; |
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| 244 | } |
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| 245 | //!@} |
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| 246 | }; |
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| 247 | UIREGISTER(egiw); |
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| 248 | |
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| 249 | /*! \brief Dirichlet posterior density |
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| 250 | |
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| 251 | Continuous Dirichlet density of \f$n\f$-dimensional variable \f$x\f$ |
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| 252 | \f[ |
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| 253 | 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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| 254 | \f] |
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| 255 | where \f$\gamma=\sum_i \beta_i\f$. |
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| 256 | */ |
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| 257 | class eDirich: public eEF |
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| 258 | { |
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| 259 | protected: |
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| 260 | //!sufficient statistics |
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| 261 | vec beta; |
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| 262 | public: |
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| 263 | //!\name Constructors |
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| 264 | //!@{ |
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| 265 | |
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| 266 | eDirich () : eEF ( ) {}; |
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| 267 | eDirich ( const eDirich &D0 ) : eEF () {set_parameters ( D0.beta );}; |
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| 268 | eDirich ( const vec &beta0 ) {set_parameters ( beta0 );}; |
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| 269 | void set_parameters ( const vec &beta0 ) |
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| 270 | { |
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| 271 | beta= beta0; |
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| 272 | dim = beta.length(); |
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| 273 | } |
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| 274 | //!@} |
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| 275 | |
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| 276 | vec sample() const {it_error ( "Not implemented" );return vec_1 ( 0.0 );}; |
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| 277 | vec mean() const {return beta/sum(beta);}; |
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| 278 | vec variance() const {double gamma =sum(beta); return elem_mult ( beta, ( beta+1 ) ) / ( gamma* ( gamma+1 ) );} |
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| 279 | //! In this instance, val is ... |
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| 280 | double evallog_nn ( const vec &val ) const |
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| 281 | { |
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| 282 | double tmp; tmp= ( beta-1 ) *log ( val ); |
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| 283 | // it_assert_debug ( std::isfinite ( tmp ),"Infinite value" ); |
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| 284 | return tmp; |
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| 285 | }; |
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| 286 | double lognc () const |
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| 287 | { |
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| 288 | double tmp; |
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| 289 | double gam=sum ( beta ); |
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| 290 | double lgb=0.0; |
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| 291 | for ( int i=0;i<beta.length();i++ ) {lgb+=lgamma ( beta ( i ) );} |
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| 292 | tmp= lgb-lgamma ( gam ); |
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| 293 | // it_assert_debug ( std::isfinite ( tmp ),"Infinite value" ); |
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| 294 | return tmp; |
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| 295 | }; |
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| 296 | //!access function |
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| 297 | vec& _beta() {return beta;} |
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| 298 | //!Set internal parameters |
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| 299 | }; |
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| 300 | |
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| 301 | //! \brief Estimator for Multinomial density |
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| 302 | class multiBM : public BMEF |
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| 303 | { |
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| 304 | protected: |
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| 305 | //! Conjugate prior and posterior |
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| 306 | eDirich est; |
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| 307 | //! Pointer inside est to sufficient statistics |
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| 308 | vec β |
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| 309 | public: |
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| 310 | //!Default constructor |
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| 311 | multiBM ( ) : BMEF ( ),est ( ),beta ( est._beta() ) |
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| 312 | { |
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| 313 | if ( beta.length() >0 ) {last_lognc=est.lognc();} |
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| 314 | else{last_lognc=0.0;} |
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| 315 | } |
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| 316 | //!Copy constructor |
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| 317 | multiBM ( const multiBM &B ) : BMEF ( B ),est ( B.est ),beta ( est._beta() ) {} |
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| 318 | //! Sets sufficient statistics to match that of givefrom mB0 |
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| 319 | void set_statistics ( const BM* mB0 ) {const multiBM* mB=dynamic_cast<const multiBM*> ( mB0 ); beta=mB->beta;} |
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| 320 | void bayes ( const vec &dt ) |
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| 321 | { |
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| 322 | if ( frg<1.0 ) {beta*=frg;last_lognc=est.lognc();} |
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| 323 | beta+=dt; |
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| 324 | if ( evalll ) {ll=est.lognc()-last_lognc;} |
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| 325 | } |
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| 326 | double logpred ( const vec &dt ) const |
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| 327 | { |
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| 328 | eDirich pred ( est ); |
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| 329 | vec &beta = pred._beta(); |
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| 330 | |
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| 331 | double lll; |
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| 332 | if ( frg<1.0 ) |
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| 333 | {beta*=frg;lll=pred.lognc();} |
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| 334 | else |
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| 335 | if ( evalll ) {lll=last_lognc;} |
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| 336 | else{lll=pred.lognc();} |
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| 337 | |
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| 338 | beta+=dt; |
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| 339 | return pred.lognc()-lll; |
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| 340 | } |
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| 341 | void flatten ( const BMEF* B ) |
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| 342 | { |
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| 343 | const multiBM* E=dynamic_cast<const multiBM*> ( B ); |
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| 344 | // sum(beta) should be equal to sum(B.beta) |
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| 345 | const vec &Eb=E->beta;//const_cast<multiBM*> ( E )->_beta(); |
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| 346 | beta*= ( sum ( Eb ) /sum ( beta ) ); |
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| 347 | if ( evalll ) {last_lognc=est.lognc();} |
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| 348 | } |
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| 349 | const epdf& posterior() const {return est;}; |
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| 350 | const eDirich* _e() const {return &est;}; |
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| 351 | void set_parameters ( const vec &beta0 ) |
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| 352 | { |
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| 353 | est.set_parameters ( beta0 ); |
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| 354 | if ( evalll ) {last_lognc=est.lognc();} |
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| 355 | } |
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| 356 | }; |
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| 357 | |
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| 358 | /*! |
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| 359 | \brief Gamma posterior density |
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| 360 | |
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| 361 | Multivariate Gamma density as product of independent univariate densities. |
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| 362 | \f[ |
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| 363 | f(x|\alpha,\beta) = \prod f(x_i|\alpha_i,\beta_i) |
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| 364 | \f] |
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| 365 | */ |
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| 366 | |
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| 367 | class egamma : public eEF |
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| 368 | { |
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| 369 | protected: |
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| 370 | //! Vector \f$\alpha\f$ |
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| 371 | vec alpha; |
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| 372 | //! Vector \f$\beta\f$ |
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| 373 | vec beta; |
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| 374 | public : |
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| 375 | //! \name Constructors |
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| 376 | //!@{ |
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| 377 | egamma ( ) :eEF ( ), alpha ( 0 ), beta ( 0 ) {}; |
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| 378 | egamma ( const vec &a, const vec &b ) {set_parameters ( a, b );}; |
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| 379 | void set_parameters ( const vec &a, const vec &b ) {alpha=a,beta=b;dim = alpha.length();}; |
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| 380 | //!@} |
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| 381 | |
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| 382 | vec sample() const; |
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| 383 | //! TODO: is it used anywhere? |
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| 384 | // mat sample ( int N ) const; |
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| 385 | double evallog ( const vec &val ) const; |
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| 386 | double lognc () const; |
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| 387 | //! Returns poiter to alpha and beta. Potentially dengerous: use with care! |
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| 388 | vec& _alpha() {return alpha;} |
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| 389 | vec& _beta() {return beta;} |
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| 390 | vec mean() const {return elem_div ( alpha,beta );} |
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| 391 | vec variance() const {return elem_div ( alpha,elem_mult ( beta,beta ) ); } |
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| 392 | |
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| 393 | //! Load from structure with elements: |
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| 394 | //! \code |
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| 395 | //! { alpha = [...]; // vector of alpha |
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| 396 | //! beta = [...]; // vector of beta |
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| 397 | //! rv = {class="RV",...} // description |
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| 398 | //! } |
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| 399 | //! \endcode |
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| 400 | //!@} |
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| 401 | void from_setting(const Setting &set){ |
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| 402 | epdf::from_setting(set); // reads rv |
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| 403 | UI::get(alpha,set,"alpha"); |
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| 404 | UI::get(beta,set,"beta"); |
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| 405 | validate(); |
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| 406 | } |
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| 407 | void validate(){ |
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| 408 | it_assert(alpha.length() ==beta.length(), "parameters do not match"); |
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| 409 | dim =alpha.length(); |
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| 410 | } |
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| 411 | }; |
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| 412 | UIREGISTER(egamma); |
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| 413 | /*! |
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| 414 | \brief Inverse-Gamma posterior density |
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| 415 | |
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| 416 | Multivariate inverse-Gamma density as product of independent univariate densities. |
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| 417 | \f[ |
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| 418 | f(x|\alpha,\beta) = \prod f(x_i|\alpha_i,\beta_i) |
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| 419 | \f] |
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| 420 | |
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| 421 | Vector \f$\beta\f$ has different meaning (in fact it is 1/beta as used in definition of iG) |
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| 422 | |
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| 423 | Inverse Gamma can be converted to Gamma using \f[ |
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| 424 | x\sim iG(a,b) => 1/x\sim G(a,1/b) |
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| 425 | \f] |
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| 426 | This relation is used in sampling. |
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| 427 | */ |
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| 428 | |
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| 429 | class eigamma : public egamma |
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| 430 | { |
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| 431 | protected: |
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| 432 | public : |
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| 433 | //! \name Constructors |
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| 434 | //! All constructors are inherited |
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| 435 | //!@{ |
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| 436 | //!@} |
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| 437 | |
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| 438 | vec sample() const {return 1.0/egamma::sample();}; |
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| 439 | //! Returns poiter to alpha and beta. Potentially dangerous: use with care! |
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| 440 | vec mean() const {return elem_div ( beta,alpha-1 );} |
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| 441 | vec variance() const {vec mea=mean(); return elem_div ( elem_mult ( mea,mea ),alpha-2 );} |
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| 442 | }; |
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| 443 | /* |
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| 444 | //! Weighted mixture of epdfs with external owned components. |
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| 445 | class emix : public epdf { |
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| 446 | protected: |
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| 447 | int n; |
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| 448 | vec &w; |
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| 449 | Array<epdf*> Coms; |
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| 450 | public: |
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| 451 | //! Default constructor |
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| 452 | emix ( const RV &rv, vec &w0): epdf(rv), n(w0.length()), w(w0), Coms(n) {}; |
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| 453 | void set_parameters( int &i, double wi, epdf* ep){w(i)=wi;Coms(i)=ep;} |
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| 454 | vec mean(){vec pom; for(int i=0;i<n;i++){pom+=Coms(i)->mean()*w(i);} return pom;}; |
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| 455 | vec sample() {it_error ( "Not implemented" );return 0;} |
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| 456 | }; |
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| 457 | */ |
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| 458 | |
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| 459 | //! Uniform distributed density on a rectangular support |
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| 460 | |
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| 461 | class euni: public epdf |
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| 462 | { |
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| 463 | protected: |
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| 464 | //! lower bound on support |
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| 465 | vec low; |
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| 466 | //! upper bound on support |
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| 467 | vec high; |
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| 468 | //! internal |
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| 469 | vec distance; |
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| 470 | //! normalizing coefficients |
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| 471 | double nk; |
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| 472 | //! cache of log( \c nk ) |
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| 473 | double lnk; |
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| 474 | public: |
|---|
| 475 | //! \name Constructors |
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| 476 | //!@{ |
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| 477 | euni ( ) :epdf ( ) {} |
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| 478 | euni ( const vec &low0, const vec &high0 ) {set_parameters ( low0,high0 );} |
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| 479 | void set_parameters ( const vec &low0, const vec &high0 ) |
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| 480 | { |
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| 481 | distance = high0-low0; |
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| 482 | it_assert_debug ( min ( distance ) >0.0,"bad support" ); |
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| 483 | low = low0; |
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| 484 | high = high0; |
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| 485 | nk = prod ( 1.0/distance ); |
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| 486 | lnk = log ( nk ); |
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| 487 | dim = low.length(); |
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| 488 | } |
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| 489 | //!@} |
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| 490 | |
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| 491 | double eval ( const vec &val ) const {return nk;} |
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| 492 | double evallog ( const vec &val ) const { |
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| 493 | if (any(val<low) && any(val>high)) {return inf;} |
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| 494 | else return lnk; |
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| 495 | } |
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| 496 | vec sample() const |
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| 497 | { |
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| 498 | vec smp ( dim ); |
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| 499 | #pragma omp critical |
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| 500 | UniRNG.sample_vector ( dim ,smp ); |
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| 501 | return low+elem_mult ( distance,smp ); |
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| 502 | } |
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| 503 | //! set values of \c low and \c high |
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| 504 | vec mean() const {return ( high-low ) /2.0;} |
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| 505 | vec variance() const {return ( pow ( high,2 ) +pow ( low,2 ) +elem_mult ( high,low ) ) /3.0;} |
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| 506 | //! Load from structure with elements: |
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| 507 | //! \code |
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| 508 | //! { high = [...]; // vector of upper bounds |
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| 509 | //! low = [...]; // vector of lower bounds |
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| 510 | //! rv = {class="RV",...} // description of RV |
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| 511 | //! } |
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| 512 | //! \endcode |
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| 513 | //!@} |
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| 514 | void from_setting(const Setting &set){ |
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| 515 | epdf::from_setting(set); // reads rv and rvc |
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| 516 | UI::get(high,set,"high"); |
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| 517 | UI::get(low,set,"low"); |
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| 518 | } |
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| 519 | }; |
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| 520 | |
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| 521 | |
|---|
| 522 | /*! |
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| 523 | \brief Normal distributed linear function with linear function of mean value; |
|---|
| 524 | |
|---|
| 525 | Mean value \f$mu=A*rvc+mu_0\f$. |
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| 526 | */ |
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| 527 | template<class sq_T> |
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| 528 | class mlnorm : public mEF |
|---|
| 529 | { |
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| 530 | protected: |
|---|
| 531 | //! Internal epdf that arise by conditioning on \c rvc |
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| 532 | enorm<sq_T> epdf; |
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| 533 | mat A; |
|---|
| 534 | vec mu_const; |
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| 535 | vec& _mu; //cached epdf.mu; |
|---|
| 536 | public: |
|---|
| 537 | //! \name Constructors |
|---|
| 538 | //!@{ |
|---|
| 539 | mlnorm ( ) :mEF (),epdf ( ),A ( ),_mu ( epdf._mu() ) {ep =&epdf; }; |
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| 540 | mlnorm ( const mat &A, const vec &mu0, const sq_T &R ) :epdf ( ),_mu ( epdf._mu() ) |
|---|
| 541 | { |
|---|
| 542 | ep =&epdf; set_parameters ( A,mu0,R ); |
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| 543 | }; |
|---|
| 544 | //! Set \c A and \c R |
|---|
| 545 | void set_parameters ( const mat &A, const vec &mu0, const sq_T &R ); |
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| 546 | //!@} |
|---|
| 547 | //! Set value of \c rvc . Result of this operation is stored in \c epdf use function \c _ep to access it. |
|---|
| 548 | void condition ( const vec &cond ); |
|---|
| 549 | |
|---|
| 550 | //!access function |
|---|
| 551 | vec& _mu_const() {return mu_const;} |
|---|
| 552 | //!access function |
|---|
| 553 | mat& _A() {return A;} |
|---|
| 554 | //!access function |
|---|
| 555 | mat _R() {return epdf._R().to_mat();} |
|---|
| 556 | |
|---|
| 557 | template<class sq_M> |
|---|
| 558 | friend std::ostream &operator<< ( std::ostream &os, mlnorm<sq_M> &ml ); |
|---|
| 559 | |
|---|
| 560 | void from_setting(const Setting &set){ |
|---|
| 561 | mpdf::from_setting(set); |
|---|
| 562 | UI::get(A,set,"A"); |
|---|
| 563 | UI::get(mu_const,set,"const"); |
|---|
| 564 | mat R0; |
|---|
| 565 | UI::get(R0,set,"R"); |
|---|
| 566 | set_parameters(A,mu_const,R0); |
|---|
| 567 | }; |
|---|
| 568 | }; |
|---|
| 569 | UIREGISTER(mlnorm<ldmat>); |
|---|
| 570 | UIREGISTER(mlnorm<fsqmat>); |
|---|
| 571 | UIREGISTER(mlnorm<chmat>); |
|---|
| 572 | |
|---|
| 573 | //! Mpdf with general function for mean value |
|---|
| 574 | template<class sq_T> |
|---|
| 575 | class mgnorm : public mEF |
|---|
| 576 | { |
|---|
| 577 | protected: |
|---|
| 578 | //! Internal epdf that arise by conditioning on \c rvc |
|---|
| 579 | enorm<sq_T> epdf; |
|---|
| 580 | vec μ |
|---|
| 581 | fnc* g; |
|---|
| 582 | public: |
|---|
| 583 | //!default constructor |
|---|
| 584 | mgnorm() :mu ( epdf._mu() ) {ep=&epdf;} |
|---|
| 585 | //!set mean function |
|---|
| 586 | void set_parameters ( fnc* g0, const sq_T &R0 ) {g=g0; epdf.set_parameters ( zeros ( g->dimension() ), R0 );} |
|---|
| 587 | void condition ( const vec &cond ) {mu=g->eval ( cond );}; |
|---|
| 588 | |
|---|
| 589 | |
|---|
| 590 | /*! UI for mgnorm |
|---|
| 591 | |
|---|
| 592 | The mgnorm is constructed from a structure with fields: |
|---|
| 593 | \code |
|---|
| 594 | system = { |
|---|
| 595 | type = "mgnorm"; |
|---|
| 596 | // function for mean value evolution |
|---|
| 597 | g = {type="fnc"; ... } |
|---|
| 598 | |
|---|
| 599 | // variance |
|---|
| 600 | R = [1, 0, |
|---|
| 601 | 0, 1]; |
|---|
| 602 | // --OR -- |
|---|
| 603 | dR = [1, 1]; |
|---|
| 604 | |
|---|
| 605 | // == OPTIONAL == |
|---|
| 606 | |
|---|
| 607 | // description of y variables |
|---|
| 608 | y = {type="rv"; names=["y", "u"];}; |
|---|
| 609 | // description of u variable |
|---|
| 610 | u = {type="rv"; names=[];} |
|---|
| 611 | }; |
|---|
| 612 | \endcode |
|---|
| 613 | |
|---|
| 614 | Result if |
|---|
| 615 | */ |
|---|
| 616 | |
|---|
| 617 | void from_setting( const Setting &set ) |
|---|
| 618 | { |
|---|
| 619 | fnc* g = UI::build<fnc>( set, "g" ); |
|---|
| 620 | |
|---|
| 621 | mat R; |
|---|
| 622 | if ( set.exists( "dR" ) ) |
|---|
| 623 | { |
|---|
| 624 | vec dR; |
|---|
| 625 | UI::get( dR, set, "dR" ); |
|---|
| 626 | R=diag(dR); |
|---|
| 627 | } |
|---|
| 628 | else |
|---|
| 629 | UI::get( R, set, "R"); |
|---|
| 630 | |
|---|
| 631 | set_parameters(g,R); |
|---|
| 632 | } |
|---|
| 633 | |
|---|
| 634 | /*void mgnorm::to_setting( Setting &set ) const |
|---|
| 635 | { |
|---|
| 636 | Transport::to_setting( set ); |
|---|
| 637 | |
|---|
| 638 | Setting &kilometers_setting = set.add("kilometers", Setting::TypeInt ); |
|---|
| 639 | kilometers_setting = kilometers; |
|---|
| 640 | |
|---|
| 641 | UI::save( passengers, set, "passengers" ); |
|---|
| 642 | }*/ |
|---|
| 643 | |
|---|
| 644 | }; |
|---|
| 645 | |
|---|
| 646 | UIREGISTER(mgnorm<chmat>); |
|---|
| 647 | |
|---|
| 648 | |
|---|
| 649 | /*! (Approximate) Student t density with linear function of mean value |
|---|
| 650 | |
|---|
| 651 | The internal epdf of this class is of the type of a Gaussian (enorm). |
|---|
| 652 | However, each conditioning is trying to assure the best possible approximation by taking into account the zeta function. See [] for reference. |
|---|
| 653 | |
|---|
| 654 | Perhaps a moment-matching technique? |
|---|
| 655 | */ |
|---|
| 656 | class mlstudent : public mlnorm<ldmat> |
|---|
| 657 | { |
|---|
| 658 | protected: |
|---|
| 659 | ldmat Lambda; |
|---|
| 660 | ldmat &_R; |
|---|
| 661 | ldmat Re; |
|---|
| 662 | public: |
|---|
| 663 | mlstudent ( ) :mlnorm<ldmat> (), |
|---|
| 664 | Lambda (), _R ( epdf._R() ) {} |
|---|
| 665 | void set_parameters ( const mat &A0, const vec &mu0, const ldmat &R0, const ldmat& Lambda0 ) |
|---|
| 666 | { |
|---|
| 667 | it_assert_debug ( A0.rows() ==mu0.length(),"" ); |
|---|
| 668 | it_assert_debug ( R0.rows() ==A0.rows(),"" ); |
|---|
| 669 | |
|---|
| 670 | epdf.set_parameters ( mu0,Lambda ); // |
|---|
| 671 | A = A0; |
|---|
| 672 | mu_const = mu0; |
|---|
| 673 | Re=R0; |
|---|
| 674 | Lambda = Lambda0; |
|---|
| 675 | } |
|---|
| 676 | void condition ( const vec &cond ) |
|---|
| 677 | { |
|---|
| 678 | _mu = A*cond + mu_const; |
|---|
| 679 | double zeta; |
|---|
| 680 | //ugly hack! |
|---|
| 681 | if ( ( cond.length() +1 ) ==Lambda.rows() ) |
|---|
| 682 | { |
|---|
| 683 | zeta = Lambda.invqform ( concat ( cond, vec_1 ( 1.0 ) ) ); |
|---|
| 684 | } |
|---|
| 685 | else |
|---|
| 686 | { |
|---|
| 687 | zeta = Lambda.invqform ( cond ); |
|---|
| 688 | } |
|---|
| 689 | _R = Re; |
|---|
| 690 | _R*= ( 1+zeta );// / ( nu ); << nu is in Re!!!!!! |
|---|
| 691 | }; |
|---|
| 692 | |
|---|
| 693 | }; |
|---|
| 694 | /*! |
|---|
| 695 | \brief Gamma random walk |
|---|
| 696 | |
|---|
| 697 | Mean value, \f$\mu\f$, of this density is given by \c rvc . |
|---|
| 698 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
|---|
| 699 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
|---|
| 700 | |
|---|
| 701 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
|---|
| 702 | */ |
|---|
| 703 | class mgamma : public mEF |
|---|
| 704 | { |
|---|
| 705 | protected: |
|---|
| 706 | //! Internal epdf that arise by conditioning on \c rvc |
|---|
| 707 | egamma epdf; |
|---|
| 708 | //! Constant \f$k\f$ |
|---|
| 709 | double k; |
|---|
| 710 | //! cache of epdf.beta |
|---|
| 711 | vec &_beta; |
|---|
| 712 | |
|---|
| 713 | public: |
|---|
| 714 | //! Constructor |
|---|
| 715 | mgamma ( ) : mEF ( ), epdf (), _beta ( epdf._beta() ) {ep=&epdf;}; |
|---|
| 716 | //! Set value of \c k |
|---|
| 717 | void set_parameters ( double k, const vec &beta0 ); |
|---|
| 718 | void condition ( const vec &val ) {_beta=k/val;}; |
|---|
| 719 | //! Load from structure with elements: |
|---|
| 720 | //! \code |
|---|
| 721 | //! { alpha = [...]; // vector of alpha |
|---|
| 722 | //! k = 1.1; // multiplicative constant k |
|---|
| 723 | //! rv = {class="RV",...} // description of RV |
|---|
| 724 | //! rvc = {class="RV",...} // description of RV in condition |
|---|
| 725 | //! } |
|---|
| 726 | //! \endcode |
|---|
| 727 | //!@} |
|---|
| 728 | void from_setting(const Setting &set){ |
|---|
| 729 | mpdf::from_setting(set); // reads rv and rvc |
|---|
| 730 | vec betatmp; // ugly but necessary |
|---|
| 731 | UI::get(betatmp,set,"beta"); |
|---|
| 732 | set.lookupValue("k",k); |
|---|
| 733 | set_parameters(k,betatmp); |
|---|
| 734 | } |
|---|
| 735 | }; |
|---|
| 736 | UIREGISTER(mgamma); |
|---|
| 737 | |
|---|
| 738 | /*! |
|---|
| 739 | \brief Inverse-Gamma random walk |
|---|
| 740 | |
|---|
| 741 | Mean value, \f$ \mu \f$, of this density is given by \c rvc . |
|---|
| 742 | Standard deviation of the random walk is proportional to one \f$ k \f$-th the mean. |
|---|
| 743 | This is achieved by setting \f$ \alpha=\mu/k^2+2 \f$ and \f$ \beta=\mu(\alpha-1)\f$. |
|---|
| 744 | |
|---|
| 745 | The standard deviation of the walk is then: \f$ \mu/\sqrt(k)\f$. |
|---|
| 746 | */ |
|---|
| 747 | class migamma : public mEF |
|---|
| 748 | { |
|---|
| 749 | protected: |
|---|
| 750 | //! Internal epdf that arise by conditioning on \c rvc |
|---|
| 751 | eigamma epdf; |
|---|
| 752 | //! Constant \f$k\f$ |
|---|
| 753 | double k; |
|---|
| 754 | //! cache of epdf.alpha |
|---|
| 755 | vec &_alpha; |
|---|
| 756 | //! cache of epdf.beta |
|---|
| 757 | vec &_beta; |
|---|
| 758 | |
|---|
| 759 | public: |
|---|
| 760 | //! \name Constructors |
|---|
| 761 | //!@{ |
|---|
| 762 | migamma ( ) : mEF (), epdf ( ), _alpha ( epdf._alpha() ), _beta ( epdf._beta() ) {ep=&epdf;}; |
|---|
| 763 | migamma ( const migamma &m ) : mEF (), epdf ( m.epdf ), _alpha ( epdf._alpha() ), _beta ( epdf._beta() ) {ep=&epdf;}; |
|---|
| 764 | //!@} |
|---|
| 765 | |
|---|
| 766 | //! Set value of \c k |
|---|
| 767 | void set_parameters ( int len, double k0 ) |
|---|
| 768 | { |
|---|
| 769 | k=k0; |
|---|
| 770 | epdf.set_parameters ( ( 1.0/ ( k*k ) +2.0 ) *ones ( len ) /*alpha*/, ones ( len ) /*beta*/ ); |
|---|
| 771 | dimc = dimension(); |
|---|
| 772 | }; |
|---|
| 773 | void condition ( const vec &val ) |
|---|
| 774 | { |
|---|
| 775 | _beta=elem_mult ( val, ( _alpha-1.0 ) ); |
|---|
| 776 | }; |
|---|
| 777 | }; |
|---|
| 778 | |
|---|
| 779 | |
|---|
| 780 | /*! |
|---|
| 781 | \brief Gamma random walk around a fixed point |
|---|
| 782 | |
|---|
| 783 | 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 |
|---|
| 784 | \f[ \mu = \mu_{t-1} ^{l} p^{1-l}\f] |
|---|
| 785 | |
|---|
| 786 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
|---|
| 787 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
|---|
| 788 | |
|---|
| 789 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
|---|
| 790 | */ |
|---|
| 791 | class mgamma_fix : public mgamma |
|---|
| 792 | { |
|---|
| 793 | protected: |
|---|
| 794 | //! parameter l |
|---|
| 795 | double l; |
|---|
| 796 | //! reference vector |
|---|
| 797 | vec refl; |
|---|
| 798 | public: |
|---|
| 799 | //! Constructor |
|---|
| 800 | mgamma_fix ( ) : mgamma ( ),refl () {}; |
|---|
| 801 | //! Set value of \c k |
|---|
| 802 | void set_parameters ( double k0 , vec ref0, double l0 ) |
|---|
| 803 | { |
|---|
| 804 | mgamma::set_parameters ( k0, ref0 ); |
|---|
| 805 | refl=pow ( ref0,1.0-l0 );l=l0; |
|---|
| 806 | dimc=dimension(); |
|---|
| 807 | }; |
|---|
| 808 | |
|---|
| 809 | void condition ( const vec &val ) {vec mean=elem_mult ( refl,pow ( val,l ) ); _beta=k/mean;}; |
|---|
| 810 | }; |
|---|
| 811 | |
|---|
| 812 | |
|---|
| 813 | /*! |
|---|
| 814 | \brief Inverse-Gamma random walk around a fixed point |
|---|
| 815 | |
|---|
| 816 | 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 |
|---|
| 817 | \f[ \mu = \mu_{t-1} ^{l} p^{1-l}\f] |
|---|
| 818 | |
|---|
| 819 | ==== Check == vv = |
|---|
| 820 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
|---|
| 821 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
|---|
| 822 | |
|---|
| 823 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
|---|
| 824 | */ |
|---|
| 825 | class migamma_ref : public migamma |
|---|
| 826 | { |
|---|
| 827 | protected: |
|---|
| 828 | //! parameter l |
|---|
| 829 | double l; |
|---|
| 830 | //! reference vector |
|---|
| 831 | vec refl; |
|---|
| 832 | public: |
|---|
| 833 | //! Constructor |
|---|
| 834 | migamma_ref ( ) : migamma (),refl ( ) {}; |
|---|
| 835 | //! Set value of \c k |
|---|
| 836 | void set_parameters ( double k0 , vec ref0, double l0 ) |
|---|
| 837 | { |
|---|
| 838 | migamma::set_parameters ( ref0.length(), k0 ); |
|---|
| 839 | refl=pow ( ref0,1.0-l0 ); |
|---|
| 840 | l=l0; |
|---|
| 841 | dimc = dimension(); |
|---|
| 842 | }; |
|---|
| 843 | |
|---|
| 844 | void condition ( const vec &val ) |
|---|
| 845 | { |
|---|
| 846 | vec mean=elem_mult ( refl,pow ( val,l ) ); |
|---|
| 847 | migamma::condition ( mean ); |
|---|
| 848 | }; |
|---|
| 849 | |
|---|
| 850 | /*! UI for migamma_ref |
|---|
| 851 | |
|---|
| 852 | The migamma_ref is constructed from a structure with fields: |
|---|
| 853 | \code |
|---|
| 854 | system = { |
|---|
| 855 | type = "migamma_ref"; |
|---|
| 856 | ref = [1e-5; 1e-5; 1e-2 1e-3]; // reference vector |
|---|
| 857 | l = 0.999; // constant l |
|---|
| 858 | k = 0.1; // constant k |
|---|
| 859 | |
|---|
| 860 | // == OPTIONAL == |
|---|
| 861 | // description of y variables |
|---|
| 862 | y = {type="rv"; names=["y", "u"];}; |
|---|
| 863 | // description of u variable |
|---|
| 864 | u = {type="rv"; names=[];} |
|---|
| 865 | }; |
|---|
| 866 | \endcode |
|---|
| 867 | |
|---|
| 868 | Result if |
|---|
| 869 | */ |
|---|
| 870 | void from_setting( const Setting &set ); |
|---|
| 871 | |
|---|
| 872 | // TODO dodelat void to_setting( Setting &set ) const; |
|---|
| 873 | }; |
|---|
| 874 | |
|---|
| 875 | |
|---|
| 876 | UIREGISTER(migamma_ref); |
|---|
| 877 | |
|---|
| 878 | /*! Log-Normal probability density |
|---|
| 879 | only allow diagonal covariances! |
|---|
| 880 | |
|---|
| 881 | Density of the form \f$ \log(x)\sim \mathcal{N}(\mu,\sigma^2) \f$ , i.e. |
|---|
| 882 | \f[ |
|---|
| 883 | x \sim \frac{1}{x\sigma\sqrt{2\pi}}\exp{-\frac{1}{2\sigma^2}(\log(x)-\mu)} |
|---|
| 884 | \f] |
|---|
| 885 | |
|---|
| 886 | */ |
|---|
| 887 | class elognorm: public enorm<ldmat> |
|---|
| 888 | { |
|---|
| 889 | public: |
|---|
| 890 | vec sample() const {return exp ( enorm<ldmat>::sample() );}; |
|---|
| 891 | vec mean() const {vec var=enorm<ldmat>::variance();return exp ( mu - 0.5*var );}; |
|---|
| 892 | |
|---|
| 893 | }; |
|---|
| 894 | |
|---|
| 895 | /*! |
|---|
| 896 | \brief Log-Normal random walk |
|---|
| 897 | |
|---|
| 898 | Mean value, \f$\mu\f$, is... |
|---|
| 899 | |
|---|
| 900 | ==== Check == vv = |
|---|
| 901 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
|---|
| 902 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
|---|
| 903 | |
|---|
| 904 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
|---|
| 905 | */ |
|---|
| 906 | class mlognorm : public mpdf |
|---|
| 907 | { |
|---|
| 908 | protected: |
|---|
| 909 | elognorm eno; |
|---|
| 910 | //! parameter 1/2*sigma^2 |
|---|
| 911 | double sig2; |
|---|
| 912 | //! access |
|---|
| 913 | vec μ |
|---|
| 914 | public: |
|---|
| 915 | //! Constructor |
|---|
| 916 | mlognorm ( ) : eno (), mu ( eno._mu() ) {ep=&eno;}; |
|---|
| 917 | //! Set value of \c k |
|---|
| 918 | void set_parameters ( int size, double k ) |
|---|
| 919 | { |
|---|
| 920 | sig2 = 0.5*log ( k*k+1 ); |
|---|
| 921 | eno.set_parameters ( zeros ( size ),2*sig2*eye ( size ) ); |
|---|
| 922 | |
|---|
| 923 | dimc = size; |
|---|
| 924 | }; |
|---|
| 925 | |
|---|
| 926 | void condition ( const vec &val ) |
|---|
| 927 | { |
|---|
| 928 | mu=log ( val )-sig2;//elem_mult ( refl,pow ( val,l ) ); |
|---|
| 929 | }; |
|---|
| 930 | |
|---|
| 931 | /*! UI for mlognorm |
|---|
| 932 | |
|---|
| 933 | The mlognorm is constructed from a structure with fields: |
|---|
| 934 | \code |
|---|
| 935 | system = { |
|---|
| 936 | type = "mlognorm"; |
|---|
| 937 | k = 0.1; // constant k |
|---|
| 938 | mu0 = [1., 1.]; |
|---|
| 939 | |
|---|
| 940 | // == OPTIONAL == |
|---|
| 941 | // description of y variables |
|---|
| 942 | y = {type="rv"; names=["y", "u"];}; |
|---|
| 943 | // description of u variable |
|---|
| 944 | u = {type="rv"; names=[];} |
|---|
| 945 | }; |
|---|
| 946 | \endcode |
|---|
| 947 | |
|---|
| 948 | */ |
|---|
| 949 | void from_setting( const Setting &set ); |
|---|
| 950 | |
|---|
| 951 | // TODO dodelat void to_setting( Setting &set ) const; |
|---|
| 952 | |
|---|
| 953 | }; |
|---|
| 954 | |
|---|
| 955 | UIREGISTER(mlognorm); |
|---|
| 956 | |
|---|
| 957 | /*! inverse Wishart density defined on Choleski decomposition |
|---|
| 958 | |
|---|
| 959 | */ |
|---|
| 960 | class eWishartCh : public epdf |
|---|
| 961 | { |
|---|
| 962 | protected: |
|---|
| 963 | //! Upper-Triagle of Choleski decomposition of \f$ \Psi \f$ |
|---|
| 964 | chmat Y; |
|---|
| 965 | //! dimension of matrix \f$ \Psi \f$ |
|---|
| 966 | int p; |
|---|
| 967 | //! degrees of freedom \f$ \nu \f$ |
|---|
| 968 | double delta; |
|---|
| 969 | public: |
|---|
| 970 | void set_parameters ( const mat &Y0, const double delta0 ) {Y=chmat ( Y0 );delta=delta0; p=Y.rows(); dim = p*p; } |
|---|
| 971 | mat sample_mat() const |
|---|
| 972 | { |
|---|
| 973 | mat X=zeros ( p,p ); |
|---|
| 974 | |
|---|
| 975 | //sample diagonal |
|---|
| 976 | for ( int i=0;i<p;i++ ) |
|---|
| 977 | { |
|---|
| 978 | GamRNG.setup ( 0.5* ( delta-i ) , 0.5 ); // no +1 !! index if from 0 |
|---|
| 979 | #pragma omp critical |
|---|
| 980 | X ( i,i ) =sqrt ( GamRNG() ); |
|---|
| 981 | } |
|---|
| 982 | //do the rest |
|---|
| 983 | for ( int i=0;i<p;i++ ) |
|---|
| 984 | { |
|---|
| 985 | for ( int j=i+1;j<p;j++ ) |
|---|
| 986 | { |
|---|
| 987 | #pragma omp critical |
|---|
| 988 | X ( i,j ) =NorRNG.sample(); |
|---|
| 989 | } |
|---|
| 990 | } |
|---|
| 991 | return X*Y._Ch();// return upper triangular part of the decomposition |
|---|
| 992 | } |
|---|
| 993 | vec sample () const |
|---|
| 994 | { |
|---|
| 995 | return vec ( sample_mat()._data(),p*p ); |
|---|
| 996 | } |
|---|
| 997 | //! fast access function y0 will be copied into Y.Ch. |
|---|
| 998 | void setY ( const mat &Ch0 ) {copy_vector ( dim,Ch0._data(), Y._Ch()._data() );} |
|---|
| 999 | //! fast access function y0 will be copied into Y.Ch. |
|---|
| 1000 | void _setY ( const vec &ch0 ) {copy_vector ( dim, ch0._data(), Y._Ch()._data() ); } |
|---|
| 1001 | //! access function |
|---|
| 1002 | const chmat& getY()const {return Y;} |
|---|
| 1003 | }; |
|---|
| 1004 | |
|---|
| 1005 | class eiWishartCh: public epdf |
|---|
| 1006 | { |
|---|
| 1007 | protected: |
|---|
| 1008 | eWishartCh W; |
|---|
| 1009 | int p; |
|---|
| 1010 | double delta; |
|---|
| 1011 | public: |
|---|
| 1012 | void set_parameters ( const mat &Y0, const double delta0) { |
|---|
| 1013 | delta = delta0; |
|---|
| 1014 | W.set_parameters ( inv ( Y0 ),delta0 ); |
|---|
| 1015 | dim = W.dimension(); p=Y0.rows(); |
|---|
| 1016 | } |
|---|
| 1017 | vec sample() const {mat iCh; iCh=inv ( W.sample_mat() ); return vec ( iCh._data(),dim );} |
|---|
| 1018 | void _setY ( const vec &y0 ) |
|---|
| 1019 | { |
|---|
| 1020 | mat Ch ( p,p ); |
|---|
| 1021 | mat iCh ( p,p ); |
|---|
| 1022 | copy_vector ( dim, y0._data(), Ch._data() ); |
|---|
| 1023 | |
|---|
| 1024 | iCh=inv ( Ch ); |
|---|
| 1025 | W.setY ( iCh ); |
|---|
| 1026 | } |
|---|
| 1027 | virtual double evallog ( const vec &val ) const { |
|---|
| 1028 | chmat X(p); |
|---|
| 1029 | const chmat& Y=W.getY(); |
|---|
| 1030 | |
|---|
| 1031 | copy_vector(p*p,val._data(),X._Ch()._data()); |
|---|
| 1032 | chmat iX(p);X.inv(iX); |
|---|
| 1033 | // compute |
|---|
| 1034 | // \frac{ |\Psi|^{m/2}|X|^{-(m+p+1)/2}e^{-tr(\Psi X^{-1})/2} }{ 2^{mp/2}\Gamma_p(m/2)}, |
|---|
| 1035 | mat M=Y.to_mat()*iX.to_mat(); |
|---|
| 1036 | |
|---|
| 1037 | double log1 = 0.5*p*(2*Y.logdet())-0.5*(delta+p+1)*(2*X.logdet())-0.5*trace(M); |
|---|
| 1038 | //Fixme! Multivariate gamma omitted!! it is ok for sampling, but not otherwise!! |
|---|
| 1039 | |
|---|
| 1040 | /* if (0) { |
|---|
| 1041 | mat XX=X.to_mat(); |
|---|
| 1042 | mat YY=Y.to_mat(); |
|---|
| 1043 | |
|---|
| 1044 | double log2 = 0.5*p*log(det(YY))-0.5*(delta+p+1)*log(det(XX))-0.5*trace(YY*inv(XX)); |
|---|
| 1045 | cout << log1 << "," << log2 << endl; |
|---|
| 1046 | }*/ |
|---|
| 1047 | return log1; |
|---|
| 1048 | }; |
|---|
| 1049 | |
|---|
| 1050 | }; |
|---|
| 1051 | |
|---|
| 1052 | class rwiWishartCh : public mpdf |
|---|
| 1053 | { |
|---|
| 1054 | protected: |
|---|
| 1055 | eiWishartCh eiW; |
|---|
| 1056 | //!square root of \f$ \nu-p-1 \f$ - needed for computation of \f$ \Psi \f$ from conditions |
|---|
| 1057 | double sqd; |
|---|
| 1058 | //reference point for diagonal |
|---|
| 1059 | vec refl; |
|---|
| 1060 | double l; |
|---|
| 1061 | int p; |
|---|
| 1062 | public: |
|---|
| 1063 | void set_parameters ( int p0, double k, vec ref0, double l0 ) |
|---|
| 1064 | { |
|---|
| 1065 | p=p0; |
|---|
| 1066 | double delta = 2/(k*k)+p+3; |
|---|
| 1067 | sqd=sqrt ( delta-p-1 ); |
|---|
| 1068 | l=l0; |
|---|
| 1069 | refl=pow(ref0,1-l); |
|---|
| 1070 | |
|---|
| 1071 | eiW.set_parameters ( eye ( p ),delta ); |
|---|
| 1072 | ep=&eiW; |
|---|
| 1073 | dimc=eiW.dimension(); |
|---|
| 1074 | } |
|---|
| 1075 | void condition ( const vec &c ) { |
|---|
| 1076 | vec z=c; |
|---|
| 1077 | int ri=0; |
|---|
| 1078 | for(int i=0;i<p*p;i+=(p+1)){//trace diagonal element |
|---|
| 1079 | z(i) = pow(z(i),l)*refl(ri); |
|---|
| 1080 | ri++; |
|---|
| 1081 | } |
|---|
| 1082 | |
|---|
| 1083 | eiW._setY ( sqd*z ); |
|---|
| 1084 | } |
|---|
| 1085 | }; |
|---|
| 1086 | |
|---|
| 1087 | //! Switch between various resampling methods. |
|---|
| 1088 | enum RESAMPLING_METHOD { MULTINOMIAL = 0, STRATIFIED = 1, SYSTEMATIC = 3 }; |
|---|
| 1089 | /*! |
|---|
| 1090 | \brief Weighted empirical density |
|---|
| 1091 | |
|---|
| 1092 | Used e.g. in particle filters. |
|---|
| 1093 | */ |
|---|
| 1094 | class eEmp: public epdf |
|---|
| 1095 | { |
|---|
| 1096 | protected : |
|---|
| 1097 | //! Number of particles |
|---|
| 1098 | int n; |
|---|
| 1099 | //! Sample weights \f$w\f$ |
|---|
| 1100 | vec w; |
|---|
| 1101 | //! Samples \f$x^{(i)}, i=1..n\f$ |
|---|
| 1102 | Array<vec> samples; |
|---|
| 1103 | public: |
|---|
| 1104 | //! \name Constructors |
|---|
| 1105 | //!@{ |
|---|
| 1106 | eEmp ( ) :epdf ( ),w ( ),samples ( ) {}; |
|---|
| 1107 | //! copy constructor |
|---|
| 1108 | eEmp ( const eEmp &e ) : epdf ( e ), w ( e.w ), samples ( e.samples ) {}; |
|---|
| 1109 | //!@} |
|---|
| 1110 | |
|---|
| 1111 | //! Set samples and weights |
|---|
| 1112 | void set_statistics ( const vec &w0, const epdf* pdf0 ); |
|---|
| 1113 | //! Set samples and weights |
|---|
| 1114 | void set_statistics ( const epdf* pdf0 , int n ) {set_statistics ( ones ( n ) /n,pdf0 );}; |
|---|
| 1115 | //! Set sample |
|---|
| 1116 | void set_samples ( const epdf* pdf0 ); |
|---|
| 1117 | //! Set sample |
|---|
| 1118 | void set_parameters ( int n0, bool copy=true ) {n=n0; w.set_size ( n0,copy );samples.set_size ( n0,copy );}; |
|---|
| 1119 | //! Potentially dangerous, use with care. |
|---|
| 1120 | vec& _w() {return w;}; |
|---|
| 1121 | //! Potentially dangerous, use with care. |
|---|
| 1122 | const vec& _w() const {return w;}; |
|---|
| 1123 | //! access function |
|---|
| 1124 | Array<vec>& _samples() {return samples;}; |
|---|
| 1125 | //! access function |
|---|
| 1126 | const Array<vec>& _samples() const {return samples;}; |
|---|
| 1127 | //! 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. |
|---|
| 1128 | ivec resample ( RESAMPLING_METHOD method=SYSTEMATIC ); |
|---|
| 1129 | //! inherited operation : NOT implemneted |
|---|
| 1130 | vec sample() const {it_error ( "Not implemented" );return 0;} |
|---|
| 1131 | //! inherited operation : NOT implemneted |
|---|
| 1132 | double evallog ( const vec &val ) const {it_error ( "Not implemented" );return 0.0;} |
|---|
| 1133 | vec mean() const |
|---|
| 1134 | { |
|---|
| 1135 | vec pom=zeros ( dim ); |
|---|
| 1136 | for ( int i=0;i<n;i++ ) {pom+=samples ( i ) *w ( i );} |
|---|
| 1137 | return pom; |
|---|
| 1138 | } |
|---|
| 1139 | vec variance() const |
|---|
| 1140 | { |
|---|
| 1141 | vec pom=zeros ( dim ); |
|---|
| 1142 | for ( int i=0;i<n;i++ ) {pom+=pow ( samples ( i ),2 ) *w ( i );} |
|---|
| 1143 | return pom-pow ( mean(),2 ); |
|---|
| 1144 | } |
|---|
| 1145 | //! For this class, qbounds are minimum and maximum value of the population! |
|---|
| 1146 | void qbounds ( vec &lb, vec &ub, double perc=0.95 ) const |
|---|
| 1147 | { |
|---|
| 1148 | // lb in inf so than it will be pushed below; |
|---|
| 1149 | lb.set_size ( dim ); |
|---|
| 1150 | ub.set_size ( dim ); |
|---|
| 1151 | lb = std::numeric_limits<double>::infinity(); |
|---|
| 1152 | ub = -std::numeric_limits<double>::infinity(); |
|---|
| 1153 | int j; |
|---|
| 1154 | for ( int i=0;i<n;i++ ) |
|---|
| 1155 | { |
|---|
| 1156 | for ( j=0;j<dim; j++ ) |
|---|
| 1157 | { |
|---|
| 1158 | if ( samples ( i ) ( j ) <lb ( j ) ) {lb ( j ) =samples ( i ) ( j );} |
|---|
| 1159 | if ( samples ( i ) ( j ) >ub ( j ) ) {ub ( j ) =samples ( i ) ( j );} |
|---|
| 1160 | } |
|---|
| 1161 | } |
|---|
| 1162 | } |
|---|
| 1163 | }; |
|---|
| 1164 | |
|---|
| 1165 | |
|---|
| 1166 | //////////////////////// |
|---|
| 1167 | |
|---|
| 1168 | template<class sq_T> |
|---|
| 1169 | void enorm<sq_T>::set_parameters ( const vec &mu0, const sq_T &R0 ) |
|---|
| 1170 | { |
|---|
| 1171 | //Fixme test dimensions of mu0 and R0; |
|---|
| 1172 | mu = mu0; |
|---|
| 1173 | R = R0; |
|---|
| 1174 | validate(); |
|---|
| 1175 | }; |
|---|
| 1176 | |
|---|
| 1177 | template<class sq_T> |
|---|
| 1178 | void enorm<sq_T>::from_setting(const Setting &set){ |
|---|
| 1179 | epdf::from_setting(set); //reads rv |
|---|
| 1180 | |
|---|
| 1181 | UI::get(mu,set,"mu"); |
|---|
| 1182 | mat Rtmp;// necessary for conversion |
|---|
| 1183 | UI::get(Rtmp,set,"R"); |
|---|
| 1184 | R=Rtmp; // conversion |
|---|
| 1185 | validate(); |
|---|
| 1186 | } |
|---|
| 1187 | |
|---|
| 1188 | template<class sq_T> |
|---|
| 1189 | void enorm<sq_T>::dupdate ( mat &v, double nu ) |
|---|
| 1190 | { |
|---|
| 1191 | // |
|---|
| 1192 | }; |
|---|
| 1193 | |
|---|
| 1194 | // template<class sq_T> |
|---|
| 1195 | // void enorm<sq_T>::tupdate ( double phi, mat &vbar, double nubar ) { |
|---|
| 1196 | // // |
|---|
| 1197 | // }; |
|---|
| 1198 | |
|---|
| 1199 | template<class sq_T> |
|---|
| 1200 | vec enorm<sq_T>::sample() const |
|---|
| 1201 | { |
|---|
| 1202 | vec x ( dim ); |
|---|
| 1203 | #pragma omp critical |
|---|
| 1204 | NorRNG.sample_vector ( dim,x ); |
|---|
| 1205 | vec smp = R.sqrt_mult ( x ); |
|---|
| 1206 | |
|---|
| 1207 | smp += mu; |
|---|
| 1208 | return smp; |
|---|
| 1209 | }; |
|---|
| 1210 | |
|---|
| 1211 | template<class sq_T> |
|---|
| 1212 | mat enorm<sq_T>::sample ( int N ) const |
|---|
| 1213 | { |
|---|
| 1214 | mat X ( dim,N ); |
|---|
| 1215 | vec x ( dim ); |
|---|
| 1216 | vec pom; |
|---|
| 1217 | int i; |
|---|
| 1218 | |
|---|
| 1219 | for ( i=0;i<N;i++ ) |
|---|
| 1220 | { |
|---|
| 1221 | #pragma omp critical |
|---|
| 1222 | NorRNG.sample_vector ( dim,x ); |
|---|
| 1223 | pom = R.sqrt_mult ( x ); |
|---|
| 1224 | pom +=mu; |
|---|
| 1225 | X.set_col ( i, pom ); |
|---|
| 1226 | } |
|---|
| 1227 | |
|---|
| 1228 | return X; |
|---|
| 1229 | }; |
|---|
| 1230 | |
|---|
| 1231 | // template<class sq_T> |
|---|
| 1232 | // double enorm<sq_T>::eval ( const vec &val ) const { |
|---|
| 1233 | // double pdfl,e; |
|---|
| 1234 | // pdfl = evallog ( val ); |
|---|
| 1235 | // e = exp ( pdfl ); |
|---|
| 1236 | // return e; |
|---|
| 1237 | // }; |
|---|
| 1238 | |
|---|
| 1239 | template<class sq_T> |
|---|
| 1240 | double enorm<sq_T>::evallog_nn ( const vec &val ) const |
|---|
| 1241 | { |
|---|
| 1242 | // 1.83787706640935 = log(2pi) |
|---|
| 1243 | double tmp=-0.5* ( R.invqform ( mu-val ) );// - lognc(); |
|---|
| 1244 | return tmp; |
|---|
| 1245 | }; |
|---|
| 1246 | |
|---|
| 1247 | template<class sq_T> |
|---|
| 1248 | inline double enorm<sq_T>::lognc () const |
|---|
| 1249 | { |
|---|
| 1250 | // 1.83787706640935 = log(2pi) |
|---|
| 1251 | double tmp=0.5* ( R.cols() * 1.83787706640935 +R.logdet() ); |
|---|
| 1252 | return tmp; |
|---|
| 1253 | }; |
|---|
| 1254 | |
|---|
| 1255 | template<class sq_T> |
|---|
| 1256 | void mlnorm<sq_T>::set_parameters ( const mat &A0, const vec &mu0, const sq_T &R0 ) |
|---|
| 1257 | { |
|---|
| 1258 | it_assert_debug ( A0.rows() ==mu0.length(),"" ); |
|---|
| 1259 | it_assert_debug ( A0.rows() ==R0.rows(),"" ); |
|---|
| 1260 | |
|---|
| 1261 | epdf.set_parameters ( zeros ( A0.rows() ),R0 ); |
|---|
| 1262 | A = A0; |
|---|
| 1263 | mu_const = mu0; |
|---|
| 1264 | dimc=A0.cols(); |
|---|
| 1265 | } |
|---|
| 1266 | |
|---|
| 1267 | // template<class sq_T> |
|---|
| 1268 | // vec mlnorm<sq_T>::samplecond (const vec &cond, double &lik ) { |
|---|
| 1269 | // this->condition ( cond ); |
|---|
| 1270 | // vec smp = epdf.sample(); |
|---|
| 1271 | // lik = epdf.eval ( smp ); |
|---|
| 1272 | // return smp; |
|---|
| 1273 | // } |
|---|
| 1274 | |
|---|
| 1275 | // template<class sq_T> |
|---|
| 1276 | // mat mlnorm<sq_T>::samplecond (const vec &cond, vec &lik, int n ) { |
|---|
| 1277 | // int i; |
|---|
| 1278 | // int dim = rv.count(); |
|---|
| 1279 | // mat Smp ( dim,n ); |
|---|
| 1280 | // vec smp ( dim ); |
|---|
| 1281 | // this->condition ( cond ); |
|---|
| 1282 | // |
|---|
| 1283 | // for ( i=0; i<n; i++ ) { |
|---|
| 1284 | // smp = epdf.sample(); |
|---|
| 1285 | // lik ( i ) = epdf.eval ( smp ); |
|---|
| 1286 | // Smp.set_col ( i ,smp ); |
|---|
| 1287 | // } |
|---|
| 1288 | // |
|---|
| 1289 | // return Smp; |
|---|
| 1290 | // } |
|---|
| 1291 | |
|---|
| 1292 | template<class sq_T> |
|---|
| 1293 | void mlnorm<sq_T>::condition ( const vec &cond ) |
|---|
| 1294 | { |
|---|
| 1295 | _mu = A*cond + mu_const; |
|---|
| 1296 | //R is already assigned; |
|---|
| 1297 | } |
|---|
| 1298 | |
|---|
| 1299 | template<class sq_T> |
|---|
| 1300 | enorm<sq_T>* enorm<sq_T>::marginal ( const RV &rvn ) const |
|---|
| 1301 | { |
|---|
| 1302 | it_assert_debug ( isnamed(), "rv description is not assigned" ); |
|---|
| 1303 | ivec irvn = rvn.dataind ( rv ); |
|---|
| 1304 | |
|---|
| 1305 | sq_T Rn ( R,irvn ); //select rows and columns of R |
|---|
| 1306 | |
|---|
| 1307 | enorm<sq_T>* tmp = new enorm<sq_T>; |
|---|
| 1308 | tmp->set_rv ( rvn ); |
|---|
| 1309 | tmp->set_parameters ( mu ( irvn ), Rn ); |
|---|
| 1310 | return tmp; |
|---|
| 1311 | } |
|---|
| 1312 | |
|---|
| 1313 | template<class sq_T> |
|---|
| 1314 | mpdf* enorm<sq_T>::condition ( const RV &rvn ) const |
|---|
| 1315 | { |
|---|
| 1316 | |
|---|
| 1317 | it_assert_debug ( isnamed(),"rvs are not assigned" ); |
|---|
| 1318 | |
|---|
| 1319 | RV rvc = rv.subt ( rvn ); |
|---|
| 1320 | it_assert_debug ( ( rvc._dsize() +rvn._dsize() ==rv._dsize() ),"wrong rvn" ); |
|---|
| 1321 | //Permutation vector of the new R |
|---|
| 1322 | ivec irvn = rvn.dataind ( rv ); |
|---|
| 1323 | ivec irvc = rvc.dataind ( rv ); |
|---|
| 1324 | ivec perm=concat ( irvn , irvc ); |
|---|
| 1325 | sq_T Rn ( R,perm ); |
|---|
| 1326 | |
|---|
| 1327 | //fixme - could this be done in general for all sq_T? |
|---|
| 1328 | mat S=Rn.to_mat(); |
|---|
| 1329 | //fixme |
|---|
| 1330 | int n=rvn._dsize()-1; |
|---|
| 1331 | int end=R.rows()-1; |
|---|
| 1332 | mat S11 = S.get ( 0,n, 0, n ); |
|---|
| 1333 | mat S12 = S.get ( 0, n , rvn._dsize(), end ); |
|---|
| 1334 | mat S22 = S.get ( rvn._dsize(), end, rvn._dsize(), end ); |
|---|
| 1335 | |
|---|
| 1336 | vec mu1 = mu ( irvn ); |
|---|
| 1337 | vec mu2 = mu ( irvc ); |
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| 1338 | mat A=S12*inv ( S22 ); |
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| 1339 | sq_T R_n ( S11 - A *S12.T() ); |
|---|
| 1340 | |
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| 1341 | mlnorm<sq_T>* tmp=new mlnorm<sq_T> ( ); |
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| 1342 | tmp->set_rv ( rvn ); tmp->set_rvc ( rvc ); |
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| 1343 | tmp->set_parameters ( A,mu1-A*mu2,R_n ); |
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| 1344 | return tmp; |
|---|
| 1345 | } |
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| 1346 | |
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| 1347 | /////////// |
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| 1348 | |
|---|
| 1349 | template<class sq_T> |
|---|
| 1350 | std::ostream &operator<< ( std::ostream &os, mlnorm<sq_T> &ml ) |
|---|
| 1351 | { |
|---|
| 1352 | os << "A:"<< ml.A<<endl; |
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| 1353 | os << "mu:"<< ml.mu_const<<endl; |
|---|
| 1354 | os << "R:" << ml.epdf._R().to_mat() <<endl; |
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| 1355 | return os; |
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| 1356 | }; |
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| 1357 | |
|---|
| 1358 | } |
|---|
| 1359 | #endif //EF_H |
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