[8] | 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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[262] | 16 | |
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[461] | 17 | #include "../shared_ptr.h" |
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[384] | 18 | #include "../base/bdmbase.h" |
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[262] | 19 | #include "../math/chmat.h" |
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[8] | 20 | |
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[294] | 21 | namespace bdm |
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| 22 | { |
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[8] | 23 | |
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[32] | 24 | |
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| 25 | //! Global Uniform_RNG |
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[488] | 26 | extern Uniform_RNG UniRNG; |
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[33] | 27 | //! Global Normal_RNG |
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[488] | 28 | extern Normal_RNG NorRNG; |
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[33] | 29 | //! Global Gamma_RNG |
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[488] | 30 | extern Gamma_RNG GamRNG; |
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[32] | 31 | |
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[488] | 32 | /*! |
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| 33 | * \brief General conjugate exponential family posterior density. |
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[8] | 34 | |
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[488] | 35 | * More?... |
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| 36 | */ |
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[28] | 37 | |
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[488] | 38 | class eEF : public epdf |
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| 39 | { |
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| 40 | public: |
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[32] | 41 | // eEF() :epdf() {}; |
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[488] | 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 | } |
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| 57 | //!Evaluate normalized log-probability for many samples |
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| 58 | virtual vec evallog_m (const mat &Val) const { |
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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 | //!Evaluate normalized log-probability for many samples |
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| 64 | virtual vec evallog_m (const Array<vec> &Val) const { |
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| 65 | vec x (Val.length()); |
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| 66 | for (int i = 0;i < Val.length();i++) {x (i) = evallog_nn (Val (i)) ;} |
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| 67 | return x -lognc(); |
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| 68 | } |
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| 69 | //!Power of the density, used e.g. to flatten the density |
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| 70 | virtual void pow (double p) {it_error ("Not implemented");}; |
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| 71 | }; |
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[8] | 72 | |
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[33] | 73 | |
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[170] | 74 | //! Estimator for Exponential family |
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[488] | 75 | class BMEF : public BM |
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| 76 | { |
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| 77 | protected: |
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| 78 | //! forgetting factor |
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| 79 | double frg; |
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| 80 | //! cached value of lognc() in the previous step (used in evaluation of \c ll ) |
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| 81 | double last_lognc; |
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| 82 | public: |
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| 83 | //! Default constructor (=empty constructor) |
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| 84 | BMEF (double frg0 = 1.0) : BM (), frg (frg0) {} |
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| 85 | //! Copy constructor |
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| 86 | BMEF (const BMEF &B) : BM (B), frg (B.frg), last_lognc (B.last_lognc) {} |
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| 87 | //!get statistics from another model |
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| 88 | virtual void set_statistics (const BMEF* BM0) {it_error ("Not implemented");}; |
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| 89 | //! Weighted update of sufficient statistics (Bayes rule) |
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| 90 | virtual void bayes (const vec &data, const double w) {}; |
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| 91 | //original Bayes |
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| 92 | void bayes (const vec &dt); |
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| 93 | //!Flatten the posterior according to the given BMEF (of the same type!) |
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| 94 | virtual void flatten (const BMEF * B) {it_error ("Not implemented");} |
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| 95 | //!Flatten the posterior as if to keep nu0 data |
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[197] | 96 | // virtual void flatten ( double nu0 ) {it_error ( "Not implemented" );} |
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[198] | 97 | |
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[488] | 98 | BMEF* _copy_ () const {it_error ("function _copy_ not implemented for this BM"); return NULL;}; |
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| 99 | }; |
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[170] | 100 | |
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[488] | 101 | template<class sq_T, template <typename> class TEpdf > |
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| 102 | class mlnorm; |
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[178] | 103 | |
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[488] | 104 | /*! |
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| 105 | * \brief Gaussian density with positive definite (decomposed) covariance matrix. |
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[8] | 106 | |
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[488] | 107 | * More?... |
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| 108 | */ |
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| 109 | template<class sq_T> |
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| 110 | class enorm : public eEF |
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| 111 | { |
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| 112 | protected: |
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| 113 | //! mean value |
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| 114 | vec mu; |
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| 115 | //! Covariance matrix in decomposed form |
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| 116 | sq_T R; |
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| 117 | public: |
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| 118 | //!\name Constructors |
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| 119 | //!@{ |
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[270] | 120 | |
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[488] | 121 | enorm () : eEF (), mu (), R () {}; |
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| 122 | enorm (const vec &mu, const sq_T &R) {set_parameters (mu, R);} |
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| 123 | void set_parameters (const vec &mu, const sq_T &R); |
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| 124 | void from_setting (const Setting &root); |
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| 125 | void validate() { |
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| 126 | it_assert (mu.length() == R.rows(), "parameters mismatch"); |
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| 127 | dim = mu.length(); |
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| 128 | } |
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| 129 | //!@} |
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[270] | 130 | |
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[488] | 131 | //! \name Mathematical operations |
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| 132 | //!@{ |
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[270] | 133 | |
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[488] | 134 | //! dupdate in exponential form (not really handy) |
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| 135 | void dupdate (mat &v, double nu = 1.0); |
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[28] | 136 | |
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[488] | 137 | vec sample() const; |
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[450] | 138 | |
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[488] | 139 | double evallog_nn (const vec &val) const; |
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| 140 | double lognc () const; |
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| 141 | vec mean() const {return mu;} |
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| 142 | vec variance() const {return diag (R.to_mat());} |
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[299] | 143 | // mlnorm<sq_T>* condition ( const RV &rvn ) const ; <=========== fails to cmpile. Why? |
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[488] | 144 | mpdf* condition (const RV &rvn) const ; |
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| 145 | enorm<sq_T>* marginal (const RV &rv) const; |
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[299] | 146 | // epdf* marginal ( const RV &rv ) const; |
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[488] | 147 | //!@} |
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[270] | 148 | |
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[488] | 149 | //! \name Access to attributes |
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| 150 | //!@{ |
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[270] | 151 | |
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[488] | 152 | vec& _mu() {return mu;} |
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| 153 | void set_mu (const vec mu0) { mu = mu0;} |
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| 154 | sq_T& _R() {return R;} |
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| 155 | const sq_T& _R() const {return R;} |
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| 156 | //!@} |
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[28] | 157 | |
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[488] | 158 | }; |
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| 159 | UIREGISTER (enorm<chmat>); |
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| 160 | UIREGISTER (enorm<ldmat>); |
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| 161 | UIREGISTER (enorm<fsqmat>); |
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[8] | 162 | |
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[388] | 163 | |
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[488] | 164 | /*! |
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| 165 | * \brief Gauss-inverse-Wishart density stored in LD form |
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[96] | 166 | |
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[488] | 167 | * For \f$p\f$-variate densities, given rv.count() should be \f$p\times\f$ V.rows(). |
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| 168 | * |
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| 169 | */ |
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| 170 | class egiw : public eEF |
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| 171 | { |
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| 172 | protected: |
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| 173 | //! Extended information matrix of sufficient statistics |
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| 174 | ldmat V; |
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| 175 | //! Number of data records (degrees of freedom) of sufficient statistics |
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| 176 | double nu; |
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| 177 | //! Dimension of the output |
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| 178 | int dimx; |
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| 179 | //! Dimension of the regressor |
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| 180 | int nPsi; |
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| 181 | public: |
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| 182 | //!\name Constructors |
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| 183 | //!@{ |
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| 184 | egiw() : eEF() {}; |
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| 185 | egiw (int dimx0, ldmat V0, double nu0 = -1.0) : eEF() {set_parameters (dimx0, V0, nu0);}; |
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[270] | 186 | |
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[488] | 187 | void set_parameters (int dimx0, ldmat V0, double nu0 = -1.0) { |
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| 188 | dimx = dimx0; |
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| 189 | nPsi = V0.rows() - dimx; |
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| 190 | dim = dimx * (dimx + nPsi); // size(R) + size(Theta) |
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[270] | 191 | |
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[488] | 192 | V = V0; |
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| 193 | if (nu0 < 0) { |
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| 194 | nu = 0.1 + nPsi + 2 * dimx + 2; // +2 assures finite expected value of R |
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| 195 | // terms before that are sufficient for finite normalization |
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| 196 | } else { |
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| 197 | nu = nu0; |
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[294] | 198 | } |
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[488] | 199 | } |
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| 200 | //!@} |
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[96] | 201 | |
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[488] | 202 | vec sample() const; |
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| 203 | vec mean() const; |
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| 204 | vec variance() const; |
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[330] | 205 | |
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[488] | 206 | //! LS estimate of \f$\theta\f$ |
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| 207 | vec est_theta() const; |
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[330] | 208 | |
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[488] | 209 | //! Covariance of the LS estimate |
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| 210 | ldmat est_theta_cov() const; |
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[330] | 211 | |
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[488] | 212 | void mean_mat (mat &M, mat&R) const; |
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| 213 | //! 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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| 214 | double evallog_nn (const vec &val) const; |
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| 215 | double lognc () const; |
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| 216 | void pow (double p) {V *= p;nu *= p;}; |
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[96] | 217 | |
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[488] | 218 | //! \name Access attributes |
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| 219 | //!@{ |
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[270] | 220 | |
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[488] | 221 | ldmat& _V() {return V;} |
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| 222 | const ldmat& _V() const {return V;} |
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| 223 | double& _nu() {return nu;} |
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| 224 | const double& _nu() const {return nu;} |
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| 225 | void from_setting (const Setting &set) { |
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| 226 | UI::get (nu, set, "nu", UI::compulsory); |
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| 227 | UI::get (dimx, set, "dimx", UI::compulsory); |
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| 228 | mat V; |
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| 229 | UI::get (V, set, "V", UI::compulsory); |
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| 230 | set_parameters (dimx, V, nu); |
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| 231 | RV* rv = UI::build<RV> (set, "rv", UI::compulsory); |
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| 232 | set_rv (*rv); |
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| 233 | delete rv; |
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| 234 | } |
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| 235 | //!@} |
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| 236 | }; |
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| 237 | UIREGISTER (egiw); |
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[96] | 238 | |
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[488] | 239 | /*! \brief Dirichlet posterior density |
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[173] | 240 | |
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[488] | 241 | Continuous Dirichlet density of \f$n\f$-dimensional variable \f$x\f$ |
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| 242 | \f[ |
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| 243 | 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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| 244 | \f] |
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| 245 | where \f$\gamma=\sum_i \beta_i\f$. |
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| 246 | */ |
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| 247 | class eDirich: public eEF |
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| 248 | { |
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| 249 | protected: |
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| 250 | //!sufficient statistics |
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| 251 | vec beta; |
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| 252 | public: |
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| 253 | //!\name Constructors |
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| 254 | //!@{ |
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[270] | 255 | |
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[488] | 256 | eDirich () : eEF () {}; |
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| 257 | eDirich (const eDirich &D0) : eEF () {set_parameters (D0.beta);}; |
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| 258 | eDirich (const vec &beta0) {set_parameters (beta0);}; |
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| 259 | void set_parameters (const vec &beta0) { |
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| 260 | beta = beta0; |
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| 261 | dim = beta.length(); |
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| 262 | } |
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| 263 | //!@} |
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[270] | 264 | |
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[488] | 265 | vec sample() const {it_error ("Not implemented");return vec_1 (0.0);}; |
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| 266 | vec mean() const {return beta / sum (beta);}; |
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| 267 | vec variance() const {double gamma = sum (beta); return elem_mult (beta, (beta + 1)) / (gamma* (gamma + 1));} |
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| 268 | //! In this instance, val is ... |
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| 269 | double evallog_nn (const vec &val) const { |
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| 270 | double tmp; tmp = (beta - 1) * log (val); |
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[404] | 271 | // it_assert_debug ( std::isfinite ( tmp ),"Infinite value" ); |
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[488] | 272 | return tmp; |
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| 273 | }; |
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| 274 | double lognc () const { |
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| 275 | double tmp; |
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| 276 | double gam = sum (beta); |
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| 277 | double lgb = 0.0; |
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| 278 | for (int i = 0;i < beta.length();i++) {lgb += lgamma (beta (i));} |
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| 279 | tmp = lgb - lgamma (gam); |
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[404] | 280 | // it_assert_debug ( std::isfinite ( tmp ),"Infinite value" ); |
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[488] | 281 | return tmp; |
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| 282 | }; |
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| 283 | //!access function |
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| 284 | vec& _beta() {return beta;} |
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| 285 | //!Set internal parameters |
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| 286 | }; |
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[96] | 287 | |
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[181] | 288 | //! \brief Estimator for Multinomial density |
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[488] | 289 | class multiBM : public BMEF |
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| 290 | { |
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| 291 | protected: |
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| 292 | //! Conjugate prior and posterior |
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| 293 | eDirich est; |
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| 294 | //! Pointer inside est to sufficient statistics |
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| 295 | vec β |
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| 296 | public: |
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| 297 | //!Default constructor |
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| 298 | multiBM () : BMEF (), est (), beta (est._beta()) { |
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| 299 | if (beta.length() > 0) {last_lognc = est.lognc();} |
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| 300 | else{last_lognc = 0.0;} |
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| 301 | } |
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| 302 | //!Copy constructor |
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| 303 | multiBM (const multiBM &B) : BMEF (B), est (B.est), beta (est._beta()) {} |
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| 304 | //! Sets sufficient statistics to match that of givefrom mB0 |
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| 305 | void set_statistics (const BM* mB0) {const multiBM* mB = dynamic_cast<const multiBM*> (mB0); beta = mB->beta;} |
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| 306 | void bayes (const vec &dt) { |
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| 307 | if (frg < 1.0) {beta *= frg;last_lognc = est.lognc();} |
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| 308 | beta += dt; |
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| 309 | if (evalll) {ll = est.lognc() - last_lognc;} |
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| 310 | } |
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| 311 | double logpred (const vec &dt) const { |
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| 312 | eDirich pred (est); |
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| 313 | vec &beta = pred._beta(); |
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[176] | 314 | |
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[488] | 315 | double lll; |
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| 316 | if (frg < 1.0) |
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| 317 | {beta *= frg;lll = pred.lognc();} |
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| 318 | else |
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| 319 | if (evalll) {lll = last_lognc;} |
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| 320 | else{lll = pred.lognc();} |
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[170] | 321 | |
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[488] | 322 | beta += dt; |
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| 323 | return pred.lognc() - lll; |
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| 324 | } |
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| 325 | void flatten (const BMEF* B) { |
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| 326 | const multiBM* E = dynamic_cast<const multiBM*> (B); |
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| 327 | // sum(beta) should be equal to sum(B.beta) |
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| 328 | const vec &Eb = E->beta;//const_cast<multiBM*> ( E )->_beta(); |
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| 329 | beta *= (sum (Eb) / sum (beta)); |
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| 330 | if (evalll) {last_lognc = est.lognc();} |
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| 331 | } |
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| 332 | const epdf& posterior() const {return est;}; |
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| 333 | const eDirich* _e() const {return &est;}; |
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| 334 | void set_parameters (const vec &beta0) { |
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| 335 | est.set_parameters (beta0); |
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| 336 | if (evalll) {last_lognc = est.lognc();} |
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| 337 | } |
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| 338 | }; |
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[170] | 339 | |
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[488] | 340 | /*! |
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| 341 | \brief Gamma posterior density |
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[32] | 342 | |
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[488] | 343 | Multivariate Gamma density as product of independent univariate densities. |
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| 344 | \f[ |
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| 345 | f(x|\alpha,\beta) = \prod f(x_i|\alpha_i,\beta_i) |
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| 346 | \f] |
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| 347 | */ |
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[32] | 348 | |
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[488] | 349 | class egamma : public eEF |
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| 350 | { |
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| 351 | protected: |
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| 352 | //! Vector \f$\alpha\f$ |
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| 353 | vec alpha; |
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| 354 | //! Vector \f$\beta\f$ |
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| 355 | vec beta; |
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| 356 | public : |
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| 357 | //! \name Constructors |
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| 358 | //!@{ |
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| 359 | egamma () : eEF (), alpha (0), beta (0) {}; |
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| 360 | egamma (const vec &a, const vec &b) {set_parameters (a, b);}; |
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| 361 | void set_parameters (const vec &a, const vec &b) {alpha = a, beta = b;dim = alpha.length();}; |
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| 362 | //!@} |
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[270] | 363 | |
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[488] | 364 | vec sample() const; |
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| 365 | //! TODO: is it used anywhere? |
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[102] | 366 | // mat sample ( int N ) const; |
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[488] | 367 | double evallog (const vec &val) const; |
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| 368 | double lognc () const; |
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| 369 | //! Returns poiter to alpha and beta. Potentially dengerous: use with care! |
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| 370 | vec& _alpha() {return alpha;} |
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| 371 | vec& _beta() {return beta;} |
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| 372 | vec mean() const {return elem_div (alpha, beta);} |
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| 373 | vec variance() const {return elem_div (alpha, elem_mult (beta, beta)); } |
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[225] | 374 | |
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[488] | 375 | //! Load from structure with elements: |
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| 376 | //! \code |
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| 377 | //! { alpha = [...]; // vector of alpha |
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| 378 | //! beta = [...]; // vector of beta |
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| 379 | //! rv = {class="RV",...} // description |
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| 380 | //! } |
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| 381 | //! \endcode |
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| 382 | //!@} |
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| 383 | void from_setting (const Setting &set) { |
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| 384 | epdf::from_setting (set); // reads rv |
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| 385 | UI::get (alpha, set, "alpha", UI::compulsory); |
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| 386 | UI::get (beta, set, "beta", UI::compulsory); |
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| 387 | validate(); |
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| 388 | } |
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| 389 | void validate() { |
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| 390 | it_assert (alpha.length() == beta.length(), "parameters do not match"); |
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| 391 | dim = alpha.length(); |
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| 392 | } |
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| 393 | }; |
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| 394 | UIREGISTER (egamma); |
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| 395 | /*! |
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| 396 | \brief Inverse-Gamma posterior density |
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[225] | 397 | |
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[488] | 398 | Multivariate inverse-Gamma density as product of independent univariate densities. |
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| 399 | \f[ |
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| 400 | f(x|\alpha,\beta) = \prod f(x_i|\alpha_i,\beta_i) |
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| 401 | \f] |
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[283] | 402 | |
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[488] | 403 | Vector \f$\beta\f$ has different meaning (in fact it is 1/beta as used in definition of iG) |
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[225] | 404 | |
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[488] | 405 | Inverse Gamma can be converted to Gamma using \f[ |
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| 406 | x\sim iG(a,b) => 1/x\sim G(a,1/b) |
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| 407 | \f] |
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| 408 | This relation is used in sampling. |
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| 409 | */ |
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[270] | 410 | |
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[488] | 411 | class eigamma : public egamma |
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| 412 | { |
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[294] | 413 | protected: |
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[488] | 414 | public : |
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| 415 | //! \name Constructors |
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| 416 | //! All constructors are inherited |
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| 417 | //!@{ |
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| 418 | //!@} |
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[32] | 419 | |
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[488] | 420 | vec sample() const {return 1.0 / egamma::sample();}; |
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| 421 | //! Returns poiter to alpha and beta. Potentially dangerous: use with care! |
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| 422 | vec mean() const {return elem_div (beta, alpha - 1);} |
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| 423 | vec variance() const {vec mea = mean(); return elem_div (elem_mult (mea, mea), alpha - 2);} |
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| 424 | }; |
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| 425 | /* |
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| 426 | //! Weighted mixture of epdfs with external owned components. |
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| 427 | class emix : public epdf { |
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| 428 | protected: |
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| 429 | int n; |
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| 430 | vec &w; |
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| 431 | Array<epdf*> Coms; |
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| 432 | public: |
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| 433 | //! Default constructor |
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| 434 | emix ( const RV &rv, vec &w0): epdf(rv), n(w0.length()), w(w0), Coms(n) {}; |
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| 435 | void set_parameters( int &i, double wi, epdf* ep){w(i)=wi;Coms(i)=ep;} |
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| 436 | vec mean(){vec pom; for(int i=0;i<n;i++){pom+=Coms(i)->mean()*w(i);} return pom;}; |
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| 437 | vec sample() {it_error ( "Not implemented" );return 0;} |
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| 438 | }; |
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| 439 | */ |
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| 440 | |
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[32] | 441 | //! Uniform distributed density on a rectangular support |
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| 442 | |
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[488] | 443 | class euni: public epdf |
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| 444 | { |
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| 445 | protected: |
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[32] | 446 | //! lower bound on support |
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[488] | 447 | vec low; |
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[32] | 448 | //! upper bound on support |
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[488] | 449 | vec high; |
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[32] | 450 | //! internal |
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[488] | 451 | vec distance; |
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[32] | 452 | //! normalizing coefficients |
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[488] | 453 | double nk; |
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[33] | 454 | //! cache of log( \c nk ) |
---|
[488] | 455 | double lnk; |
---|
| 456 | public: |
---|
| 457 | //! \name Constructors |
---|
| 458 | //!@{ |
---|
| 459 | euni () : epdf () {} |
---|
| 460 | euni (const vec &low0, const vec &high0) {set_parameters (low0, high0);} |
---|
| 461 | void set_parameters (const vec &low0, const vec &high0) { |
---|
| 462 | distance = high0 - low0; |
---|
| 463 | it_assert_debug (min (distance) > 0.0, "bad support"); |
---|
| 464 | low = low0; |
---|
| 465 | high = high0; |
---|
| 466 | nk = prod (1.0 / distance); |
---|
| 467 | lnk = log (nk); |
---|
| 468 | dim = low.length(); |
---|
| 469 | } |
---|
| 470 | //!@} |
---|
[270] | 471 | |
---|
[488] | 472 | double eval (const vec &val) const {return nk;} |
---|
| 473 | double evallog (const vec &val) const { |
---|
| 474 | if (any (val < low) && any (val > high)) {return inf;} |
---|
| 475 | else return lnk; |
---|
| 476 | } |
---|
| 477 | vec sample() const { |
---|
| 478 | vec smp (dim); |
---|
[270] | 479 | #pragma omp critical |
---|
[488] | 480 | UniRNG.sample_vector (dim , smp); |
---|
| 481 | return low + elem_mult (distance, smp); |
---|
| 482 | } |
---|
| 483 | //! set values of \c low and \c high |
---|
| 484 | vec mean() const {return (high -low) / 2.0;} |
---|
| 485 | vec variance() const {return (pow (high, 2) + pow (low, 2) + elem_mult (high, low)) / 3.0;} |
---|
| 486 | //! Load from structure with elements: |
---|
| 487 | //! \code |
---|
| 488 | //! { high = [...]; // vector of upper bounds |
---|
| 489 | //! low = [...]; // vector of lower bounds |
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| 490 | //! rv = {class="RV",...} // description of RV |
---|
| 491 | //! } |
---|
| 492 | //! \endcode |
---|
| 493 | //!@} |
---|
| 494 | void from_setting (const Setting &set) { |
---|
| 495 | epdf::from_setting (set); // reads rv and rvc |
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[471] | 496 | |
---|
[488] | 497 | UI::get (high, set, "high", UI::compulsory); |
---|
| 498 | UI::get (low, set, "low", UI::compulsory); |
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| 499 | } |
---|
| 500 | }; |
---|
[32] | 501 | |
---|
| 502 | |
---|
[488] | 503 | /*! |
---|
| 504 | \brief Normal distributed linear function with linear function of mean value; |
---|
[32] | 505 | |
---|
[488] | 506 | Mean value \f$mu=A*rvc+mu_0\f$. |
---|
| 507 | */ |
---|
| 508 | template < class sq_T, template <typename> class TEpdf = enorm > |
---|
| 509 | class mlnorm : public mpdf_internal< TEpdf<sq_T> > |
---|
| 510 | { |
---|
| 511 | protected: |
---|
| 512 | //! Internal epdf that arise by conditioning on \c rvc |
---|
| 513 | mat A; |
---|
| 514 | vec mu_const; |
---|
[487] | 515 | // vec& _mu; //cached epdf.mu; !!!!!! WHY NOT? |
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[488] | 516 | public: |
---|
| 517 | //! \name Constructors |
---|
| 518 | //!@{ |
---|
| 519 | mlnorm() : mpdf_internal< TEpdf<sq_T> >() {}; |
---|
| 520 | mlnorm (const mat &A, const vec &mu0, const sq_T &R) : mpdf_internal< TEpdf<sq_T> >() { |
---|
| 521 | set_parameters (A, mu0, R); |
---|
| 522 | } |
---|
[461] | 523 | |
---|
[488] | 524 | //! Set \c A and \c R |
---|
| 525 | void set_parameters (const mat &A0, const vec &mu0, const sq_T &R0) { |
---|
| 526 | it_assert_debug (A0.rows() == mu0.length(), ""); |
---|
| 527 | it_assert_debug (A0.rows() == R0.rows(), ""); |
---|
[487] | 528 | |
---|
[488] | 529 | this->iepdf.set_parameters (zeros (A0.rows()), R0); |
---|
| 530 | A = A0; |
---|
| 531 | mu_const = mu0; |
---|
| 532 | this->dimc = A0.cols(); |
---|
| 533 | } |
---|
| 534 | //!@} |
---|
| 535 | //! Set value of \c rvc . Result of this operation is stored in \c epdf use function \c _ep to access it. |
---|
| 536 | void condition (const vec &cond) { |
---|
| 537 | this->iepdf._mu() = A * cond + mu_const; |
---|
[487] | 538 | //R is already assigned; |
---|
[488] | 539 | } |
---|
[198] | 540 | |
---|
[488] | 541 | //!access function |
---|
| 542 | vec& _mu_const() {return mu_const;} |
---|
| 543 | //!access function |
---|
| 544 | mat& _A() {return A;} |
---|
| 545 | //!access function |
---|
| 546 | mat _R() { return this->iepdf._R().to_mat(); } |
---|
[471] | 547 | |
---|
[488] | 548 | template<typename sq_M> |
---|
| 549 | friend std::ostream &operator<< (std::ostream &os, mlnorm<sq_M, enorm> &ml); |
---|
[8] | 550 | |
---|
[488] | 551 | void from_setting (const Setting &set) { |
---|
| 552 | mpdf::from_setting (set); |
---|
| 553 | |
---|
| 554 | UI::get (A, set, "A", UI::compulsory); |
---|
| 555 | UI::get (mu_const, set, "const", UI::compulsory); |
---|
| 556 | mat R0; |
---|
| 557 | UI::get (R0, set, "R", UI::compulsory); |
---|
| 558 | set_parameters (A, mu_const, R0); |
---|
| 559 | }; |
---|
| 560 | }; |
---|
| 561 | UIREGISTER (mlnorm<ldmat>); |
---|
| 562 | UIREGISTER (mlnorm<fsqmat>); |
---|
| 563 | UIREGISTER (mlnorm<chmat>); |
---|
| 564 | |
---|
[280] | 565 | //! Mpdf with general function for mean value |
---|
[488] | 566 | template<class sq_T> |
---|
| 567 | class mgnorm : public mpdf_internal< enorm< sq_T > > |
---|
| 568 | { |
---|
| 569 | protected: |
---|
[487] | 570 | // vec μ WHY NOT? |
---|
[488] | 571 | fnc* g; |
---|
| 572 | public: |
---|
| 573 | //!default constructor |
---|
| 574 | mgnorm() : mpdf_internal<enorm<sq_T> >() { } |
---|
| 575 | //!set mean function |
---|
| 576 | inline void set_parameters (fnc* g0, const sq_T &R0); |
---|
| 577 | inline void condition (const vec &cond); |
---|
[357] | 578 | |
---|
| 579 | |
---|
[488] | 580 | /*! UI for mgnorm |
---|
[357] | 581 | |
---|
[488] | 582 | The mgnorm is constructed from a structure with fields: |
---|
| 583 | \code |
---|
| 584 | system = { |
---|
| 585 | type = "mgnorm"; |
---|
| 586 | // function for mean value evolution |
---|
| 587 | g = {type="fnc"; ... } |
---|
[357] | 588 | |
---|
[488] | 589 | // variance |
---|
| 590 | R = [1, 0, |
---|
| 591 | 0, 1]; |
---|
| 592 | // --OR -- |
---|
| 593 | dR = [1, 1]; |
---|
[357] | 594 | |
---|
[488] | 595 | // == OPTIONAL == |
---|
[357] | 596 | |
---|
[488] | 597 | // description of y variables |
---|
| 598 | y = {type="rv"; names=["y", "u"];}; |
---|
| 599 | // description of u variable |
---|
| 600 | u = {type="rv"; names=[];} |
---|
| 601 | }; |
---|
| 602 | \endcode |
---|
[357] | 603 | |
---|
[488] | 604 | Result if |
---|
| 605 | */ |
---|
[357] | 606 | |
---|
[488] | 607 | void from_setting (const Setting &set) { |
---|
| 608 | fnc* g = UI::build<fnc> (set, "g", UI::compulsory); |
---|
[357] | 609 | |
---|
[488] | 610 | mat R; |
---|
| 611 | vec dR; |
---|
| 612 | if (UI::get (dR, set, "dR")) |
---|
| 613 | R = diag (dR); |
---|
| 614 | else |
---|
| 615 | UI::get (R, set, "R", UI::compulsory); |
---|
[280] | 616 | |
---|
[488] | 617 | set_parameters (g, R); |
---|
| 618 | } |
---|
| 619 | }; |
---|
[357] | 620 | |
---|
[488] | 621 | UIREGISTER (mgnorm<chmat>); |
---|
[357] | 622 | |
---|
[262] | 623 | |
---|
[488] | 624 | /*! (Approximate) Student t density with linear function of mean value |
---|
[262] | 625 | |
---|
[488] | 626 | The internal epdf of this class is of the type of a Gaussian (enorm). |
---|
| 627 | However, each conditioning is trying to assure the best possible approximation by taking into account the zeta function. See [] for reference. |
---|
[270] | 628 | |
---|
[488] | 629 | Perhaps a moment-matching technique? |
---|
| 630 | */ |
---|
| 631 | class mlstudent : public mlnorm<ldmat, enorm> |
---|
| 632 | { |
---|
| 633 | protected: |
---|
| 634 | ldmat Lambda; |
---|
| 635 | ldmat &_R; |
---|
| 636 | ldmat Re; |
---|
| 637 | public: |
---|
| 638 | mlstudent () : mlnorm<ldmat, enorm> (), |
---|
| 639 | Lambda (), _R (iepdf._R()) {} |
---|
| 640 | void set_parameters (const mat &A0, const vec &mu0, const ldmat &R0, const ldmat& Lambda0) { |
---|
| 641 | it_assert_debug (A0.rows() == mu0.length(), ""); |
---|
| 642 | it_assert_debug (R0.rows() == A0.rows(), ""); |
---|
| 643 | |
---|
| 644 | iepdf.set_parameters (mu0, Lambda); // |
---|
| 645 | A = A0; |
---|
| 646 | mu_const = mu0; |
---|
| 647 | Re = R0; |
---|
| 648 | Lambda = Lambda0; |
---|
| 649 | } |
---|
| 650 | void condition (const vec &cond) { |
---|
| 651 | iepdf._mu() = A * cond + mu_const; |
---|
| 652 | double zeta; |
---|
| 653 | //ugly hack! |
---|
| 654 | if ( (cond.length() + 1) == Lambda.rows()) { |
---|
| 655 | zeta = Lambda.invqform (concat (cond, vec_1 (1.0))); |
---|
| 656 | } else { |
---|
| 657 | zeta = Lambda.invqform (cond); |
---|
[294] | 658 | } |
---|
[488] | 659 | _R = Re; |
---|
| 660 | _R *= (1 + zeta);// / ( nu ); << nu is in Re!!!!!! |
---|
| 661 | }; |
---|
[294] | 662 | |
---|
[488] | 663 | }; |
---|
| 664 | /*! |
---|
| 665 | \brief Gamma random walk |
---|
[198] | 666 | |
---|
[488] | 667 | Mean value, \f$\mu\f$, of this density is given by \c rvc . |
---|
| 668 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
---|
| 669 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
---|
[32] | 670 | |
---|
[488] | 671 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
---|
| 672 | */ |
---|
| 673 | class mgamma : public mpdf_internal<egamma> |
---|
| 674 | { |
---|
| 675 | protected: |
---|
[461] | 676 | |
---|
[488] | 677 | //! Constant \f$k\f$ |
---|
| 678 | double k; |
---|
[461] | 679 | |
---|
[488] | 680 | //! cache of iepdf.beta |
---|
| 681 | vec &_beta; |
---|
[32] | 682 | |
---|
[488] | 683 | public: |
---|
| 684 | //! Constructor |
---|
| 685 | mgamma() : mpdf_internal<egamma>(), k (0), |
---|
| 686 | _beta (iepdf._beta()) { |
---|
| 687 | } |
---|
[461] | 688 | |
---|
[488] | 689 | //! Set value of \c k |
---|
| 690 | void set_parameters (double k, const vec &beta0); |
---|
[461] | 691 | |
---|
[488] | 692 | void condition (const vec &val) {_beta = k / val;}; |
---|
| 693 | //! Load from structure with elements: |
---|
| 694 | //! \code |
---|
| 695 | //! { alpha = [...]; // vector of alpha |
---|
| 696 | //! k = 1.1; // multiplicative constant k |
---|
| 697 | //! rv = {class="RV",...} // description of RV |
---|
| 698 | //! rvc = {class="RV",...} // description of RV in condition |
---|
| 699 | //! } |
---|
| 700 | //! \endcode |
---|
| 701 | //!@} |
---|
| 702 | void from_setting (const Setting &set) { |
---|
| 703 | mpdf::from_setting (set); // reads rv and rvc |
---|
| 704 | vec betatmp; // ugly but necessary |
---|
| 705 | UI::get (betatmp, set, "beta", UI::compulsory); |
---|
| 706 | UI::get (k, set, "k", UI::compulsory); |
---|
| 707 | set_parameters (k, betatmp); |
---|
| 708 | } |
---|
| 709 | }; |
---|
| 710 | UIREGISTER (mgamma); |
---|
[32] | 711 | |
---|
[488] | 712 | /*! |
---|
| 713 | \brief Inverse-Gamma random walk |
---|
[225] | 714 | |
---|
[488] | 715 | Mean value, \f$ \mu \f$, of this density is given by \c rvc . |
---|
| 716 | Standard deviation of the random walk is proportional to one \f$ k \f$-th the mean. |
---|
| 717 | This is achieved by setting \f$ \alpha=\mu/k^2+2 \f$ and \f$ \beta=\mu(\alpha-1)\f$. |
---|
[461] | 718 | |
---|
[488] | 719 | The standard deviation of the walk is then: \f$ \mu/\sqrt(k)\f$. |
---|
| 720 | */ |
---|
| 721 | class migamma : public mpdf_internal<eigamma> |
---|
| 722 | { |
---|
| 723 | protected: |
---|
| 724 | //! Constant \f$k\f$ |
---|
| 725 | double k; |
---|
[461] | 726 | |
---|
[488] | 727 | //! cache of iepdf.alpha |
---|
| 728 | vec &_alpha; |
---|
[225] | 729 | |
---|
[488] | 730 | //! cache of iepdf.beta |
---|
| 731 | vec &_beta; |
---|
[461] | 732 | |
---|
[488] | 733 | public: |
---|
| 734 | //! \name Constructors |
---|
| 735 | //!@{ |
---|
| 736 | migamma() : mpdf_internal<eigamma>(), |
---|
| 737 | k (0), |
---|
| 738 | _alpha (iepdf._alpha()), |
---|
| 739 | _beta (iepdf._beta()) { |
---|
| 740 | } |
---|
[225] | 741 | |
---|
[488] | 742 | migamma (const migamma &m) : mpdf_internal<eigamma>(), |
---|
| 743 | k (0), |
---|
| 744 | _alpha (iepdf._alpha()), |
---|
| 745 | _beta (iepdf._beta()) { |
---|
| 746 | } |
---|
| 747 | //!@} |
---|
[225] | 748 | |
---|
[488] | 749 | //! Set value of \c k |
---|
| 750 | void set_parameters (int len, double k0) { |
---|
| 751 | k = k0; |
---|
| 752 | iepdf.set_parameters ( (1.0 / (k*k) + 2.0) *ones (len) /*alpha*/, ones (len) /*beta*/); |
---|
| 753 | dimc = dimension(); |
---|
| 754 | }; |
---|
| 755 | void condition (const vec &val) { |
---|
| 756 | _beta = elem_mult (val, (_alpha - 1.0)); |
---|
| 757 | }; |
---|
| 758 | }; |
---|
[357] | 759 | |
---|
[60] | 760 | |
---|
[488] | 761 | /*! |
---|
| 762 | \brief Gamma random walk around a fixed point |
---|
[60] | 763 | |
---|
[488] | 764 | 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 |
---|
| 765 | \f[ \mu = \mu_{t-1} ^{l} p^{1-l}\f] |
---|
[60] | 766 | |
---|
[488] | 767 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
---|
| 768 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
---|
[294] | 769 | |
---|
[488] | 770 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
---|
| 771 | */ |
---|
| 772 | class mgamma_fix : public mgamma |
---|
| 773 | { |
---|
| 774 | protected: |
---|
| 775 | //! parameter l |
---|
| 776 | double l; |
---|
| 777 | //! reference vector |
---|
| 778 | vec refl; |
---|
| 779 | public: |
---|
| 780 | //! Constructor |
---|
| 781 | mgamma_fix () : mgamma (), refl () {}; |
---|
| 782 | //! Set value of \c k |
---|
| 783 | void set_parameters (double k0 , vec ref0, double l0) { |
---|
| 784 | mgamma::set_parameters (k0, ref0); |
---|
| 785 | refl = pow (ref0, 1.0 - l0);l = l0; |
---|
| 786 | dimc = dimension(); |
---|
| 787 | }; |
---|
[60] | 788 | |
---|
[488] | 789 | void condition (const vec &val) {vec mean = elem_mult (refl, pow (val, l)); _beta = k / mean;}; |
---|
| 790 | }; |
---|
[60] | 791 | |
---|
[225] | 792 | |
---|
[488] | 793 | /*! |
---|
| 794 | \brief Inverse-Gamma random walk around a fixed point |
---|
[225] | 795 | |
---|
[488] | 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] |
---|
[225] | 798 | |
---|
[488] | 799 | ==== Check == vv = |
---|
| 800 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
---|
| 801 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
---|
[225] | 802 | |
---|
[488] | 803 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
---|
| 804 | */ |
---|
| 805 | class migamma_ref : public migamma |
---|
| 806 | { |
---|
| 807 | protected: |
---|
| 808 | //! parameter l |
---|
| 809 | double l; |
---|
| 810 | //! reference vector |
---|
| 811 | vec refl; |
---|
| 812 | public: |
---|
| 813 | //! Constructor |
---|
| 814 | migamma_ref () : migamma (), refl () {}; |
---|
| 815 | //! Set value of \c k |
---|
| 816 | void set_parameters (double k0 , vec ref0, double l0) { |
---|
| 817 | migamma::set_parameters (ref0.length(), k0); |
---|
| 818 | refl = pow (ref0, 1.0 - l0); |
---|
| 819 | l = l0; |
---|
| 820 | dimc = dimension(); |
---|
| 821 | }; |
---|
[357] | 822 | |
---|
[488] | 823 | void condition (const vec &val) { |
---|
| 824 | vec mean = elem_mult (refl, pow (val, l)); |
---|
| 825 | migamma::condition (mean); |
---|
| 826 | }; |
---|
[357] | 827 | |
---|
[488] | 828 | /*! UI for migamma_ref |
---|
[357] | 829 | |
---|
[488] | 830 | The migamma_ref is constructed from a structure with fields: |
---|
| 831 | \code |
---|
| 832 | system = { |
---|
| 833 | type = "migamma_ref"; |
---|
| 834 | ref = [1e-5; 1e-5; 1e-2 1e-3]; // reference vector |
---|
| 835 | l = 0.999; // constant l |
---|
| 836 | k = 0.1; // constant k |
---|
| 837 | |
---|
| 838 | // == OPTIONAL == |
---|
| 839 | // description of y variables |
---|
| 840 | y = {type="rv"; names=["y", "u"];}; |
---|
| 841 | // description of u variable |
---|
| 842 | u = {type="rv"; names=[];} |
---|
| 843 | }; |
---|
| 844 | \endcode |
---|
[357] | 845 | |
---|
[488] | 846 | Result if |
---|
| 847 | */ |
---|
| 848 | void from_setting (const Setting &set); |
---|
[225] | 849 | |
---|
[488] | 850 | // TODO dodelat void to_setting( Setting &set ) const; |
---|
| 851 | }; |
---|
[357] | 852 | |
---|
| 853 | |
---|
[488] | 854 | UIREGISTER (migamma_ref); |
---|
[294] | 855 | |
---|
[488] | 856 | /*! Log-Normal probability density |
---|
| 857 | only allow diagonal covariances! |
---|
[294] | 858 | |
---|
[488] | 859 | Density of the form \f$ \log(x)\sim \mathcal{N}(\mu,\sigma^2) \f$ , i.e. |
---|
| 860 | \f[ |
---|
| 861 | x \sim \frac{1}{x\sigma\sqrt{2\pi}}\exp{-\frac{1}{2\sigma^2}(\log(x)-\mu)} |
---|
| 862 | \f] |
---|
[294] | 863 | |
---|
[488] | 864 | */ |
---|
| 865 | class elognorm: public enorm<ldmat> |
---|
| 866 | { |
---|
| 867 | public: |
---|
| 868 | vec sample() const {return exp (enorm<ldmat>::sample());}; |
---|
| 869 | vec mean() const {vec var = enorm<ldmat>::variance();return exp (mu - 0.5*var);}; |
---|
[285] | 870 | |
---|
[488] | 871 | }; |
---|
[285] | 872 | |
---|
[488] | 873 | /*! |
---|
| 874 | \brief Log-Normal random walk |
---|
[285] | 875 | |
---|
[488] | 876 | Mean value, \f$\mu\f$, is... |
---|
[285] | 877 | |
---|
[488] | 878 | ==== Check == vv = |
---|
| 879 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
---|
| 880 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
---|
[461] | 881 | |
---|
[488] | 882 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
---|
| 883 | */ |
---|
| 884 | class mlognorm : public mpdf_internal<elognorm> |
---|
| 885 | { |
---|
| 886 | protected: |
---|
| 887 | //! parameter 1/2*sigma^2 |
---|
| 888 | double sig2; |
---|
[461] | 889 | |
---|
[488] | 890 | //! access |
---|
| 891 | vec μ |
---|
| 892 | public: |
---|
| 893 | //! Constructor |
---|
| 894 | mlognorm() : mpdf_internal<elognorm>(), |
---|
| 895 | sig2 (0), |
---|
| 896 | mu (iepdf._mu()) { |
---|
| 897 | } |
---|
[285] | 898 | |
---|
[488] | 899 | //! Set value of \c k |
---|
| 900 | void set_parameters (int size, double k) { |
---|
| 901 | sig2 = 0.5 * log (k * k + 1); |
---|
| 902 | iepdf.set_parameters (zeros (size), 2*sig2*eye (size)); |
---|
[285] | 903 | |
---|
[488] | 904 | dimc = size; |
---|
| 905 | }; |
---|
[357] | 906 | |
---|
[488] | 907 | void condition (const vec &val) { |
---|
| 908 | mu = log (val) - sig2;//elem_mult ( refl,pow ( val,l ) ); |
---|
| 909 | }; |
---|
[357] | 910 | |
---|
[488] | 911 | /*! UI for mlognorm |
---|
[357] | 912 | |
---|
[488] | 913 | The mlognorm is constructed from a structure with fields: |
---|
| 914 | \code |
---|
| 915 | system = { |
---|
| 916 | type = "mlognorm"; |
---|
| 917 | k = 0.1; // constant k |
---|
| 918 | mu0 = [1., 1.]; |
---|
| 919 | |
---|
| 920 | // == OPTIONAL == |
---|
| 921 | // description of y variables |
---|
| 922 | y = {type="rv"; names=["y", "u"];}; |
---|
| 923 | // description of u variable |
---|
| 924 | u = {type="rv"; names=[];} |
---|
| 925 | }; |
---|
| 926 | \endcode |
---|
[357] | 927 | |
---|
[488] | 928 | */ |
---|
| 929 | void from_setting (const Setting &set); |
---|
[357] | 930 | |
---|
[488] | 931 | // TODO dodelat void to_setting( Setting &set ) const; |
---|
[285] | 932 | |
---|
[488] | 933 | }; |
---|
[294] | 934 | |
---|
[488] | 935 | UIREGISTER (mlognorm); |
---|
[294] | 936 | |
---|
[488] | 937 | /*! inverse Wishart density defined on Choleski decomposition |
---|
| 938 | |
---|
| 939 | */ |
---|
| 940 | class eWishartCh : public epdf |
---|
| 941 | { |
---|
| 942 | protected: |
---|
| 943 | //! Upper-Triagle of Choleski decomposition of \f$ \Psi \f$ |
---|
| 944 | chmat Y; |
---|
| 945 | //! dimension of matrix \f$ \Psi \f$ |
---|
| 946 | int p; |
---|
| 947 | //! degrees of freedom \f$ \nu \f$ |
---|
| 948 | double delta; |
---|
| 949 | public: |
---|
| 950 | void set_parameters (const mat &Y0, const double delta0) {Y = chmat (Y0);delta = delta0; p = Y.rows(); dim = p * p; } |
---|
| 951 | mat sample_mat() const { |
---|
| 952 | mat X = zeros (p, p); |
---|
| 953 | |
---|
| 954 | //sample diagonal |
---|
| 955 | for (int i = 0;i < p;i++) { |
---|
| 956 | GamRNG.setup (0.5* (delta - i) , 0.5); // no +1 !! index if from 0 |
---|
[294] | 957 | #pragma omp critical |
---|
[488] | 958 | X (i, i) = sqrt (GamRNG()); |
---|
| 959 | } |
---|
| 960 | //do the rest |
---|
| 961 | for (int i = 0;i < p;i++) { |
---|
| 962 | for (int j = i + 1;j < p;j++) { |
---|
[294] | 963 | #pragma omp critical |
---|
[488] | 964 | X (i, j) = NorRNG.sample(); |
---|
[294] | 965 | } |
---|
| 966 | } |
---|
[488] | 967 | return X*Y._Ch();// return upper triangular part of the decomposition |
---|
| 968 | } |
---|
| 969 | vec sample () const { |
---|
| 970 | return vec (sample_mat()._data(), p*p); |
---|
| 971 | } |
---|
| 972 | //! fast access function y0 will be copied into Y.Ch. |
---|
| 973 | void setY (const mat &Ch0) {copy_vector (dim, Ch0._data(), Y._Ch()._data());} |
---|
| 974 | //! fast access function y0 will be copied into Y.Ch. |
---|
| 975 | void _setY (const vec &ch0) {copy_vector (dim, ch0._data(), Y._Ch()._data()); } |
---|
| 976 | //! access function |
---|
| 977 | const chmat& getY() const {return Y;} |
---|
| 978 | }; |
---|
[294] | 979 | |
---|
[488] | 980 | class eiWishartCh: public epdf |
---|
| 981 | { |
---|
| 982 | protected: |
---|
| 983 | eWishartCh W; |
---|
| 984 | int p; |
---|
| 985 | double delta; |
---|
| 986 | public: |
---|
| 987 | void set_parameters (const mat &Y0, const double delta0) { |
---|
| 988 | delta = delta0; |
---|
| 989 | W.set_parameters (inv (Y0), delta0); |
---|
| 990 | dim = W.dimension(); p = Y0.rows(); |
---|
| 991 | } |
---|
| 992 | vec sample() const {mat iCh; iCh = inv (W.sample_mat()); return vec (iCh._data(), dim);} |
---|
| 993 | void _setY (const vec &y0) { |
---|
| 994 | mat Ch (p, p); |
---|
| 995 | mat iCh (p, p); |
---|
| 996 | copy_vector (dim, y0._data(), Ch._data()); |
---|
| 997 | |
---|
| 998 | iCh = inv (Ch); |
---|
| 999 | W.setY (iCh); |
---|
| 1000 | } |
---|
| 1001 | virtual double evallog (const vec &val) const { |
---|
| 1002 | chmat X (p); |
---|
| 1003 | const chmat& Y = W.getY(); |
---|
| 1004 | |
---|
| 1005 | copy_vector (p*p, val._data(), X._Ch()._data()); |
---|
| 1006 | chmat iX (p);X.inv (iX); |
---|
| 1007 | // compute |
---|
[294] | 1008 | // \frac{ |\Psi|^{m/2}|X|^{-(m+p+1)/2}e^{-tr(\Psi X^{-1})/2} }{ 2^{mp/2}\Gamma_p(m/2)}, |
---|
[488] | 1009 | mat M = Y.to_mat() * iX.to_mat(); |
---|
[285] | 1010 | |
---|
[488] | 1011 | double log1 = 0.5 * p * (2 * Y.logdet()) - 0.5 * (delta + p + 1) * (2 * X.logdet()) - 0.5 * trace (M); |
---|
| 1012 | //Fixme! Multivariate gamma omitted!! it is ok for sampling, but not otherwise!! |
---|
[461] | 1013 | |
---|
[488] | 1014 | /* if (0) { |
---|
| 1015 | mat XX=X.to_mat(); |
---|
| 1016 | mat YY=Y.to_mat(); |
---|
[461] | 1017 | |
---|
[488] | 1018 | double log2 = 0.5*p*log(det(YY))-0.5*(delta+p+1)*log(det(XX))-0.5*trace(YY*inv(XX)); |
---|
| 1019 | cout << log1 << "," << log2 << endl; |
---|
| 1020 | }*/ |
---|
| 1021 | return log1; |
---|
| 1022 | }; |
---|
[285] | 1023 | |
---|
[488] | 1024 | }; |
---|
| 1025 | |
---|
| 1026 | class rwiWishartCh : public mpdf |
---|
| 1027 | { |
---|
| 1028 | protected: |
---|
| 1029 | eiWishartCh eiW; |
---|
| 1030 | //!square root of \f$ \nu-p-1 \f$ - needed for computation of \f$ \Psi \f$ from conditions |
---|
| 1031 | double sqd; |
---|
| 1032 | //reference point for diagonal |
---|
| 1033 | vec refl; |
---|
| 1034 | double l; |
---|
| 1035 | int p; |
---|
| 1036 | |
---|
| 1037 | public: |
---|
| 1038 | rwiWishartCh() : eiW(), |
---|
| 1039 | sqd (0), l (0), p (0) { |
---|
| 1040 | set_ep (eiW); |
---|
| 1041 | } |
---|
| 1042 | |
---|
| 1043 | void set_parameters (int p0, double k, vec ref0, double l0) { |
---|
| 1044 | p = p0; |
---|
| 1045 | double delta = 2 / (k * k) + p + 3; |
---|
| 1046 | sqd = sqrt (delta - p - 1); |
---|
| 1047 | l = l0; |
---|
| 1048 | refl = pow (ref0, 1 - l); |
---|
| 1049 | |
---|
| 1050 | eiW.set_parameters (eye (p), delta); |
---|
| 1051 | dimc = eiW.dimension(); |
---|
| 1052 | } |
---|
| 1053 | void condition (const vec &c) { |
---|
| 1054 | vec z = c; |
---|
| 1055 | int ri = 0; |
---|
| 1056 | for (int i = 0;i < p*p;i += (p + 1)) {//trace diagonal element |
---|
| 1057 | z (i) = pow (z (i), l) * refl (ri); |
---|
| 1058 | ri++; |
---|
[294] | 1059 | } |
---|
[285] | 1060 | |
---|
[488] | 1061 | eiW._setY (sqd*z); |
---|
| 1062 | } |
---|
| 1063 | }; |
---|
| 1064 | |
---|
[32] | 1065 | //! Switch between various resampling methods. |
---|
[488] | 1066 | enum RESAMPLING_METHOD { MULTINOMIAL = 0, STRATIFIED = 1, SYSTEMATIC = 3 }; |
---|
| 1067 | /*! |
---|
| 1068 | \brief Weighted empirical density |
---|
[32] | 1069 | |
---|
[488] | 1070 | Used e.g. in particle filters. |
---|
| 1071 | */ |
---|
| 1072 | class eEmp: public epdf |
---|
| 1073 | { |
---|
| 1074 | protected : |
---|
| 1075 | //! Number of particles |
---|
| 1076 | int n; |
---|
| 1077 | //! Sample weights \f$w\f$ |
---|
| 1078 | vec w; |
---|
| 1079 | //! Samples \f$x^{(i)}, i=1..n\f$ |
---|
| 1080 | Array<vec> samples; |
---|
| 1081 | public: |
---|
| 1082 | //! \name Constructors |
---|
| 1083 | //!@{ |
---|
| 1084 | eEmp () : epdf (), w (), samples () {}; |
---|
| 1085 | //! copy constructor |
---|
| 1086 | eEmp (const eEmp &e) : epdf (e), w (e.w), samples (e.samples) {}; |
---|
| 1087 | //!@} |
---|
[280] | 1088 | |
---|
[488] | 1089 | //! Set samples and weights |
---|
| 1090 | void set_statistics (const vec &w0, const epdf &pdf0); |
---|
| 1091 | //! Set samples and weights |
---|
| 1092 | void set_statistics (const epdf &pdf0 , int n) {set_statistics (ones (n) / n, pdf0);}; |
---|
| 1093 | //! Set sample |
---|
| 1094 | void set_samples (const epdf* pdf0); |
---|
| 1095 | //! Set sample |
---|
| 1096 | void set_parameters (int n0, bool copy = true) {n = n0; w.set_size (n0, copy);samples.set_size (n0, copy);}; |
---|
| 1097 | //! Potentially dangerous, use with care. |
---|
| 1098 | vec& _w() {return w;}; |
---|
| 1099 | //! Potentially dangerous, use with care. |
---|
| 1100 | const vec& _w() const {return w;}; |
---|
| 1101 | //! access function |
---|
| 1102 | Array<vec>& _samples() {return samples;}; |
---|
| 1103 | //! access function |
---|
| 1104 | const Array<vec>& _samples() const {return samples;}; |
---|
| 1105 | //! 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. |
---|
| 1106 | ivec resample (RESAMPLING_METHOD method = SYSTEMATIC); |
---|
| 1107 | //! inherited operation : NOT implemneted |
---|
| 1108 | vec sample() const {it_error ("Not implemented");return 0;} |
---|
| 1109 | //! inherited operation : NOT implemneted |
---|
| 1110 | double evallog (const vec &val) const {it_error ("Not implemented");return 0.0;} |
---|
| 1111 | vec mean() const { |
---|
| 1112 | vec pom = zeros (dim); |
---|
| 1113 | for (int i = 0;i < n;i++) {pom += samples (i) * w (i);} |
---|
| 1114 | return pom; |
---|
| 1115 | } |
---|
| 1116 | vec variance() const { |
---|
| 1117 | vec pom = zeros (dim); |
---|
| 1118 | for (int i = 0;i < n;i++) {pom += pow (samples (i), 2) * w (i);} |
---|
| 1119 | return pom -pow (mean(), 2); |
---|
| 1120 | } |
---|
| 1121 | //! For this class, qbounds are minimum and maximum value of the population! |
---|
| 1122 | void qbounds (vec &lb, vec &ub, double perc = 0.95) const { |
---|
| 1123 | // lb in inf so than it will be pushed below; |
---|
| 1124 | lb.set_size (dim); |
---|
| 1125 | ub.set_size (dim); |
---|
| 1126 | lb = std::numeric_limits<double>::infinity(); |
---|
| 1127 | ub = -std::numeric_limits<double>::infinity(); |
---|
| 1128 | int j; |
---|
| 1129 | for (int i = 0;i < n;i++) { |
---|
| 1130 | for (j = 0;j < dim; j++) { |
---|
| 1131 | if (samples (i) (j) < lb (j)) {lb (j) = samples (i) (j);} |
---|
| 1132 | if (samples (i) (j) > ub (j)) {ub (j) = samples (i) (j);} |
---|
[294] | 1133 | } |
---|
| 1134 | } |
---|
[488] | 1135 | } |
---|
| 1136 | }; |
---|
[32] | 1137 | |
---|
| 1138 | |
---|
[8] | 1139 | //////////////////////// |
---|
| 1140 | |
---|
[488] | 1141 | template<class sq_T> |
---|
| 1142 | void enorm<sq_T>::set_parameters (const vec &mu0, const sq_T &R0) |
---|
| 1143 | { |
---|
[28] | 1144 | //Fixme test dimensions of mu0 and R0; |
---|
[488] | 1145 | mu = mu0; |
---|
| 1146 | R = R0; |
---|
| 1147 | validate(); |
---|
| 1148 | }; |
---|
[8] | 1149 | |
---|
[488] | 1150 | template<class sq_T> |
---|
| 1151 | void enorm<sq_T>::from_setting (const Setting &set) |
---|
| 1152 | { |
---|
| 1153 | epdf::from_setting (set); //reads rv |
---|
[384] | 1154 | |
---|
[488] | 1155 | UI::get (mu, set, "mu", UI::compulsory); |
---|
| 1156 | mat Rtmp;// necessary for conversion |
---|
| 1157 | UI::get (Rtmp, set, "R", UI::compulsory); |
---|
| 1158 | R = Rtmp; // conversion |
---|
| 1159 | validate(); |
---|
| 1160 | } |
---|
[8] | 1161 | |
---|
[488] | 1162 | template<class sq_T> |
---|
| 1163 | void enorm<sq_T>::dupdate (mat &v, double nu) |
---|
| 1164 | { |
---|
| 1165 | // |
---|
| 1166 | }; |
---|
| 1167 | |
---|
[178] | 1168 | // template<class sq_T> |
---|
| 1169 | // void enorm<sq_T>::tupdate ( double phi, mat &vbar, double nubar ) { |
---|
| 1170 | // // |
---|
| 1171 | // }; |
---|
[8] | 1172 | |
---|
[488] | 1173 | template<class sq_T> |
---|
| 1174 | vec enorm<sq_T>::sample() const |
---|
| 1175 | { |
---|
| 1176 | vec x (dim); |
---|
[270] | 1177 | #pragma omp critical |
---|
[488] | 1178 | NorRNG.sample_vector (dim, x); |
---|
| 1179 | vec smp = R.sqrt_mult (x); |
---|
[12] | 1180 | |
---|
[488] | 1181 | smp += mu; |
---|
| 1182 | return smp; |
---|
| 1183 | }; |
---|
[8] | 1184 | |
---|
[214] | 1185 | // template<class sq_T> |
---|
| 1186 | // double enorm<sq_T>::eval ( const vec &val ) const { |
---|
| 1187 | // double pdfl,e; |
---|
| 1188 | // pdfl = evallog ( val ); |
---|
| 1189 | // e = exp ( pdfl ); |
---|
| 1190 | // return e; |
---|
| 1191 | // }; |
---|
[8] | 1192 | |
---|
[488] | 1193 | template<class sq_T> |
---|
| 1194 | double enorm<sq_T>::evallog_nn (const vec &val) const |
---|
| 1195 | { |
---|
| 1196 | // 1.83787706640935 = log(2pi) |
---|
| 1197 | double tmp = -0.5 * (R.invqform (mu - val));// - lognc(); |
---|
| 1198 | return tmp; |
---|
| 1199 | }; |
---|
[28] | 1200 | |
---|
[488] | 1201 | template<class sq_T> |
---|
| 1202 | inline double enorm<sq_T>::lognc () const |
---|
| 1203 | { |
---|
| 1204 | // 1.83787706640935 = log(2pi) |
---|
| 1205 | double tmp = 0.5 * (R.cols() * 1.83787706640935 + R.logdet()); |
---|
| 1206 | return tmp; |
---|
| 1207 | }; |
---|
[28] | 1208 | |
---|
[8] | 1209 | |
---|
[192] | 1210 | // template<class sq_T> |
---|
| 1211 | // vec mlnorm<sq_T>::samplecond (const vec &cond, double &lik ) { |
---|
| 1212 | // this->condition ( cond ); |
---|
| 1213 | // vec smp = epdf.sample(); |
---|
| 1214 | // lik = epdf.eval ( smp ); |
---|
| 1215 | // return smp; |
---|
| 1216 | // } |
---|
[8] | 1217 | |
---|
[192] | 1218 | // template<class sq_T> |
---|
| 1219 | // mat mlnorm<sq_T>::samplecond (const vec &cond, vec &lik, int n ) { |
---|
| 1220 | // int i; |
---|
| 1221 | // int dim = rv.count(); |
---|
| 1222 | // mat Smp ( dim,n ); |
---|
| 1223 | // vec smp ( dim ); |
---|
| 1224 | // this->condition ( cond ); |
---|
[198] | 1225 | // |
---|
[192] | 1226 | // for ( i=0; i<n; i++ ) { |
---|
| 1227 | // smp = epdf.sample(); |
---|
| 1228 | // lik ( i ) = epdf.eval ( smp ); |
---|
| 1229 | // Smp.set_col ( i ,smp ); |
---|
| 1230 | // } |
---|
[198] | 1231 | // |
---|
[192] | 1232 | // return Smp; |
---|
| 1233 | // } |
---|
[28] | 1234 | |
---|
[8] | 1235 | |
---|
[488] | 1236 | template<class sq_T> |
---|
| 1237 | enorm<sq_T>* enorm<sq_T>::marginal (const RV &rvn) const |
---|
| 1238 | { |
---|
| 1239 | it_assert_debug (isnamed(), "rv description is not assigned"); |
---|
| 1240 | ivec irvn = rvn.dataind (rv); |
---|
[178] | 1241 | |
---|
[488] | 1242 | sq_T Rn (R, irvn); //select rows and columns of R |
---|
[280] | 1243 | |
---|
[488] | 1244 | enorm<sq_T>* tmp = new enorm<sq_T>; |
---|
| 1245 | tmp->set_rv (rvn); |
---|
| 1246 | tmp->set_parameters (mu (irvn), Rn); |
---|
| 1247 | return tmp; |
---|
| 1248 | } |
---|
[178] | 1249 | |
---|
[488] | 1250 | template<class sq_T> |
---|
| 1251 | mpdf* enorm<sq_T>::condition (const RV &rvn) const |
---|
| 1252 | { |
---|
[178] | 1253 | |
---|
[488] | 1254 | it_assert_debug (isnamed(), "rvs are not assigned"); |
---|
[270] | 1255 | |
---|
[488] | 1256 | RV rvc = rv.subt (rvn); |
---|
| 1257 | it_assert_debug ( (rvc._dsize() + rvn._dsize() == rv._dsize()), "wrong rvn"); |
---|
| 1258 | //Permutation vector of the new R |
---|
| 1259 | ivec irvn = rvn.dataind (rv); |
---|
| 1260 | ivec irvc = rvc.dataind (rv); |
---|
| 1261 | ivec perm = concat (irvn , irvc); |
---|
| 1262 | sq_T Rn (R, perm); |
---|
[178] | 1263 | |
---|
[488] | 1264 | //fixme - could this be done in general for all sq_T? |
---|
| 1265 | mat S = Rn.to_mat(); |
---|
| 1266 | //fixme |
---|
| 1267 | int n = rvn._dsize() - 1; |
---|
| 1268 | int end = R.rows() - 1; |
---|
| 1269 | mat S11 = S.get (0, n, 0, n); |
---|
| 1270 | mat S12 = S.get (0, n , rvn._dsize(), end); |
---|
| 1271 | mat S22 = S.get (rvn._dsize(), end, rvn._dsize(), end); |
---|
[178] | 1272 | |
---|
[488] | 1273 | vec mu1 = mu (irvn); |
---|
| 1274 | vec mu2 = mu (irvc); |
---|
| 1275 | mat A = S12 * inv (S22); |
---|
| 1276 | sq_T R_n (S11 - A *S12.T()); |
---|
[178] | 1277 | |
---|
[488] | 1278 | mlnorm<sq_T>* tmp = new mlnorm<sq_T> (); |
---|
| 1279 | tmp->set_rv (rvn); tmp->set_rvc (rvc); |
---|
| 1280 | tmp->set_parameters (A, mu1 - A*mu2, R_n); |
---|
| 1281 | return tmp; |
---|
| 1282 | } |
---|
[178] | 1283 | |
---|
[488] | 1284 | //// |
---|
| 1285 | /////// |
---|
| 1286 | template<class sq_T> |
---|
| 1287 | void mgnorm<sq_T >::set_parameters (fnc* g0, const sq_T &R0) {g = g0; this->iepdf.set_parameters (zeros (g->dimension()), R0);} |
---|
| 1288 | template<class sq_T> |
---|
| 1289 | void mgnorm<sq_T >::condition (const vec &cond) {this->iepdf._mu() = g->eval (cond);}; |
---|
[28] | 1290 | |
---|
[488] | 1291 | template<class sq_T> |
---|
| 1292 | std::ostream &operator<< (std::ostream &os, mlnorm<sq_T> &ml) |
---|
| 1293 | { |
---|
| 1294 | os << "A:" << ml.A << endl; |
---|
| 1295 | os << "mu:" << ml.mu_const << endl; |
---|
| 1296 | os << "R:" << ml._R() << endl; |
---|
| 1297 | return os; |
---|
| 1298 | }; |
---|
[28] | 1299 | |
---|
[254] | 1300 | } |
---|
[8] | 1301 | #endif //EF_H |
---|