[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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[737] | 21 | namespace bdm { |
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[8] | 22 | |
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[32] | 23 | |
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| 24 | //! Global Uniform_RNG |
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[488] | 25 | extern Uniform_RNG UniRNG; |
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[33] | 26 | //! Global Normal_RNG |
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[488] | 27 | extern Normal_RNG NorRNG; |
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[33] | 28 | //! Global Gamma_RNG |
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[488] | 29 | extern Gamma_RNG GamRNG; |
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[32] | 30 | |
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[1383] | 31 | |
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[488] | 32 | /*! |
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[1063] | 33 | * \brief Abstract class of 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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[737] | 37 | class eEF : public epdf { |
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| 38 | public: |
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[1066] | 39 | // eEF() :epdf() {}; |
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[1064] | 40 | //! default constructor |
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| 41 | eEF () : epdf () {}; |
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| 42 | //! logarithm of the normalizing constant, \f$\mathcal{I}\f$ |
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| 43 | virtual double lognc() const = 0; |
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[565] | 44 | |
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[1064] | 45 | //!Evaluate normalized log-probability |
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| 46 | virtual double evallog_nn ( const vec &val ) const NOT_IMPLEMENTED(0); |
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[565] | 47 | |
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[1064] | 48 | //!Evaluate normalized log-probability |
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| 49 | virtual double evallog ( const vec &val ) const { |
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| 50 | double tmp; |
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| 51 | tmp = evallog_nn ( val ) - lognc(); |
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| 52 | return tmp; |
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| 53 | } |
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| 54 | //!Evaluate normalized log-probability for many samples |
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| 55 | virtual vec evallog_mat ( const mat &Val ) const { |
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| 56 | vec x ( Val.cols() ); |
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| 57 | for ( int i = 0; i < Val.cols(); i++ ) { |
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| 58 | x ( i ) = evallog_nn ( Val.get_col ( i ) ) ; |
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| 59 | } |
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| 60 | return x - lognc(); |
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| 61 | } |
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| 62 | //!Evaluate normalized log-probability for many samples |
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| 63 | virtual vec evallog_mat ( const Array<vec> &Val ) const { |
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| 64 | vec x ( Val.length() ); |
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| 65 | for ( int i = 0; i < Val.length(); i++ ) { |
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| 66 | x ( i ) = evallog_nn ( Val ( i ) ) ; |
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| 67 | } |
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| 68 | return x - lognc(); |
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| 69 | } |
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[565] | 70 | |
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[1064] | 71 | //!Power of the density, used e.g. to flatten the density |
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| 72 | virtual void pow ( double p ) NOT_IMPLEMENTED_VOID; |
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[488] | 73 | }; |
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[8] | 74 | |
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[33] | 75 | |
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[170] | 76 | //! Estimator for Exponential family |
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[737] | 77 | class BMEF : public BM { |
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| 78 | public: |
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[1064] | 79 | //! forgetting factor |
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| 80 | double frg; |
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| 81 | protected: |
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| 82 | //! cached value of lognc() in the previous step (used in evaluation of \c ll ) |
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| 83 | double last_lognc; |
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| 84 | //! factor k = [0..1] for scheduling of forgetting factor: \f$ frg_t = (1-k) * frg_{t-1} + k \f$, default 0 |
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| 85 | double frg_sched_factor; |
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| 86 | public: |
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| 87 | //! Default constructor (=empty constructor) |
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| 88 | BMEF ( double frg0 = 1.0 ) : BM (), frg ( frg0 ), last_lognc(0.0),frg_sched_factor(0.0) {} |
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| 89 | //! Copy constructor |
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| 90 | BMEF ( const BMEF &B ) : BM ( B ), frg ( B.frg ), last_lognc ( B.last_lognc ),frg_sched_factor(B.frg_sched_factor) {} |
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| 91 | //!get statistics from another model |
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| 92 | virtual void set_statistics ( const BMEF* BM0 ) NOT_IMPLEMENTED_VOID; |
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[565] | 93 | |
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[1064] | 94 | //! Weighted update of sufficient statistics (Bayes rule) |
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| 95 | virtual void bayes_weighted ( const vec &data, const vec &cond = empty_vec, const double w = 1.0 ) { |
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| 96 | if (frg_sched_factor>0) { |
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| 97 | frg = frg*(1-frg_sched_factor)+frg_sched_factor; |
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| 98 | } |
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| 99 | }; |
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| 100 | //original Bayes |
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| 101 | void bayes ( const vec &yt, const vec &cond = empty_vec ); |
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[565] | 102 | |
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[1064] | 103 | //!Flatten the posterior according to the given BMEF (of the same type!) |
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| 104 | virtual void flatten ( const BMEF * B, double weight=1.0 ) NOT_IMPLEMENTED_VOID;; |
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[198] | 105 | |
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[746] | 106 | |
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[1064] | 107 | void to_setting ( Setting &set ) const |
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| 108 | { |
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| 109 | BM::to_setting( set ); |
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| 110 | UI::save(frg, set, "frg"); |
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| 111 | UI::save( frg_sched_factor, set, "frg_sched_factor" ); |
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| 112 | } |
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[907] | 113 | |
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[1077] | 114 | /*! Create object from the following structure |
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| 115 | |
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| 116 | \code |
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| 117 | class = 'BMEF'; |
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| 118 | --- optional fields --- |
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| 119 | frg = []; % forgetting factor |
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| 120 | frg_sched_factor = []; % factor for scheduling of forgetting factor: a number from [0..1] |
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| 121 | --- inherited fields --- |
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| 122 | bdm::BM::from_setting |
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| 123 | \endcode |
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| 124 | If the optional fields are not given, they will be filled as follows: |
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| 125 | \code |
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| 126 | frg = 1; % default forgetting factor |
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| 127 | frg_sched_factor = 0; |
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| 128 | \endcode |
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| 129 | */ |
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[1064] | 130 | void from_setting( const Setting &set) { |
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| 131 | BM::from_setting(set); |
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| 132 | if ( !UI::get ( frg, set, "frg" ) ) |
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| 133 | frg = 1.0; |
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[1169] | 134 | if ( !UI::get ( frg_sched_factor, set, "frg_sched_factor" ) ) |
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[1077] | 135 | frg_sched_factor = 0.0; |
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[1064] | 136 | } |
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[850] | 137 | |
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[1064] | 138 | void validate() { |
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| 139 | BM::validate(); |
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| 140 | } |
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[850] | 141 | |
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[488] | 142 | }; |
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[170] | 143 | |
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[1068] | 144 | /*! \brief Dirac delta density with predefined transformation |
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[797] | 145 | |
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| 146 | Density of the type:\f[ f(x_t | y_t) = \delta (x_t - g(y_t)) \f] |
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| 147 | where \f$ x_t \f$ is the \c rv, \f$ y_t \f$ is the \c rvc and g is a deterministic transformation of class fn. |
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| 148 | */ |
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[1064] | 149 | class mgdirac: public pdf { |
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| 150 | protected: |
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| 151 | shared_ptr<fnc> g; |
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| 152 | public: |
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| 153 | vec samplecond(const vec &cond) { |
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| 154 | bdm_assert_debug(cond.length()==g->dimensionc(),"given cond in not compatible with g"); |
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| 155 | vec tmp = g->eval(cond); |
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| 156 | return tmp; |
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| 157 | } |
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| 158 | double evallogcond ( const vec &yt, const vec &cond ) { |
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| 159 | return std::numeric_limits< double >::max(); |
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| 160 | } |
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[1068] | 161 | |
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| 162 | /*! Create object from the following structure |
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| 163 | |
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| 164 | \code |
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| 165 | class = 'mgdirac'; |
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| 166 | g = function bdm::fnc; % any offspring of fnc, bdm::fnc::from_setting |
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| 167 | --- inherited fields --- |
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| 168 | bdm::pdf::from_setting |
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| 169 | \endcode |
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| 170 | */ |
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[1064] | 171 | void from_setting(const Setting& set); |
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| 172 | void to_setting(Setting &set) const; |
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| 173 | void validate(); |
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[797] | 174 | }; |
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| 175 | UIREGISTER(mgdirac); |
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| 176 | |
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| 177 | |
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[504] | 178 | template<class sq_T, template <typename> class TEpdf> |
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[488] | 179 | class mlnorm; |
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[178] | 180 | |
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[488] | 181 | /*! |
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| 182 | * \brief Gaussian density with positive definite (decomposed) covariance matrix. |
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[8] | 183 | |
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[488] | 184 | * More?... |
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| 185 | */ |
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| 186 | template<class sq_T> |
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[737] | 187 | class enorm : public eEF { |
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| 188 | protected: |
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[1064] | 189 | //! mean value |
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| 190 | vec mu; |
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| 191 | //! Covariance matrix in decomposed form |
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| 192 | sq_T R; |
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[737] | 193 | public: |
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[1064] | 194 | //!\name Constructors |
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| 195 | //!@{ |
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[270] | 196 | |
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[1064] | 197 | enorm () : eEF (), mu (), R () {}; |
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| 198 | enorm ( const vec &mu, const sq_T &R ) { |
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| 199 | set_parameters ( mu, R ); |
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| 200 | } |
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| 201 | void set_parameters ( const vec &mu, const sq_T &R ); |
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| 202 | /*! Create Normal density |
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| 203 | \f[ f(rv) = N(\mu, R) \f] |
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| 204 | from structure |
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| 205 | \code |
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| 206 | class = 'enorm<ldmat>', (OR) 'enorm<chmat>', (OR) 'enorm<fsqmat>'; |
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| 207 | mu = []; // mean value |
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| 208 | R = []; // variance, square matrix of appropriate dimension |
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| 209 | \endcode |
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| 210 | */ |
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| 211 | void from_setting ( const Setting &root ); |
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| 212 | void to_setting ( Setting &root ) const ; |
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[270] | 213 | |
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[1064] | 214 | void validate(); |
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| 215 | //!@} |
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[270] | 216 | |
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[1064] | 217 | //! \name Mathematical operations |
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| 218 | //!@{ |
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[28] | 219 | |
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[1064] | 220 | //! dupdate in exponential form (not really handy) |
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| 221 | void dupdate ( mat &v, double nu = 1.0 ); |
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[450] | 222 | |
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[1064] | 223 | //! evaluate bhattacharya distance |
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| 224 | double bhattacharyya(const enorm<sq_T> &e2) { |
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| 225 | bdm_assert(dim == e2.dimension(), "enorms of differnt dimensions"); |
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| 226 | sq_T P=R; |
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| 227 | P.add(e2._R()); |
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[504] | 228 | |
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[1064] | 229 | double tmp = 0.125*P.invqform(mu - e2._mu()) + 0.5*(P.logdet() - 0.5*(R.logdet() + e2._R().logdet())); |
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| 230 | return tmp; |
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| 231 | } |
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[504] | 232 | |
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[1064] | 233 | vec sample() const; |
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[270] | 234 | |
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[1064] | 235 | double evallog_nn ( const vec &val ) const; |
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| 236 | double lognc () const; |
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| 237 | vec mean() const { |
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| 238 | return mu; |
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| 239 | } |
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| 240 | vec variance() const { |
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| 241 | return diag ( R.to_mat() ); |
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| 242 | } |
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| 243 | mat covariance() const { |
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| 244 | return R.to_mat(); |
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| 245 | } |
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[1066] | 246 | // mlnorm<sq_T>* condition ( const RV &rvn ) const ; <=========== fails to cmpile. Why? |
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[1064] | 247 | shared_ptr<pdf> condition ( const RV &rvn ) const; |
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[270] | 248 | |
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[1064] | 249 | // target not typed to mlnorm<sq_T, enorm<sq_T> > & |
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| 250 | // because that doesn't compile (perhaps because we |
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| 251 | // haven't finished defining enorm yet), but the type |
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| 252 | // is required |
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| 253 | void condition ( const RV &rvn, pdf &target ) const; |
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[28] | 254 | |
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[1064] | 255 | shared_ptr<epdf> marginal ( const RV &rvn ) const; |
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| 256 | void marginal ( const RV &rvn, enorm<sq_T> &target ) const; |
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| 257 | //!@} |
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| 258 | |
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| 259 | //! \name Access to attributes |
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| 260 | //!@{ |
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| 261 | |
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| 262 | vec& _mu() { |
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| 263 | return mu; |
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| 264 | } |
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| 265 | const vec& _mu() const { |
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| 266 | return mu; |
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| 267 | } |
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| 268 | void set_mu ( const vec mu0 ) { |
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| 269 | mu = mu0; |
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| 270 | } |
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| 271 | sq_T& _R() { |
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| 272 | return R; |
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| 273 | } |
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| 274 | const sq_T& _R() const { |
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| 275 | return R; |
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| 276 | } |
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| 277 | //!@} |
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| 278 | |
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[488] | 279 | }; |
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[737] | 280 | UIREGISTER2 ( enorm, chmat ); |
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[529] | 281 | SHAREDPTR2 ( enorm, chmat ); |
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[737] | 282 | UIREGISTER2 ( enorm, ldmat ); |
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[529] | 283 | SHAREDPTR2 ( enorm, ldmat ); |
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[737] | 284 | UIREGISTER2 ( enorm, fsqmat ); |
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[529] | 285 | SHAREDPTR2 ( enorm, fsqmat ); |
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[8] | 286 | |
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[1064] | 287 | //! \class bdm::egauss |
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[948] | 288 | //!\brief Gaussian (Normal) distribution. Same as enorm<fsqmat>. |
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[887] | 289 | typedef enorm<ldmat> egauss; |
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| 290 | UIREGISTER(egauss); |
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| 291 | |
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| 292 | |
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[802] | 293 | //forward declaration |
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| 294 | class mstudent; |
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[388] | 295 | |
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[802] | 296 | /*! distribution of multivariate Student t density |
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| 297 | |
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[1064] | 298 | Based on article by Genest and Zidek, |
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[802] | 299 | */ |
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| 300 | template<class sq_T> |
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[1064] | 301 | class estudent : public eEF { |
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| 302 | protected: |
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| 303 | //! mena value |
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| 304 | vec mu; |
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| 305 | //! matrix H |
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| 306 | sq_T H; |
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| 307 | //! degrees of freedom |
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| 308 | double delta; |
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| 309 | public: |
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| 310 | double evallog_nn(const vec &val) const { |
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| 311 | double tmp = -0.5*H.logdet() - 0.5*(delta + dim) * log(1+ H.invqform(val - mu)/delta); |
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| 312 | return tmp; |
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| 313 | } |
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| 314 | double lognc() const { |
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| 315 | //log(pi) = 1.14472988584940 |
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| 316 | double tmp = -lgamma(0.5*(delta+dim))+lgamma(0.5*delta) + 0.5*dim*(log(delta) + 1.14472988584940); |
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| 317 | return tmp; |
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| 318 | } |
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| 319 | void marginal (const RV &rvm, estudent<sq_T> &marg) const { |
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| 320 | ivec ind = rvm.findself_ids(rv); // indices of rvm in rv |
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| 321 | marg._mu() = mu(ind); |
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| 322 | marg._H() = sq_T(H,ind); |
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| 323 | marg._delta() = delta; |
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| 324 | marg.validate(); |
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| 325 | } |
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| 326 | shared_ptr<epdf> marginal(const RV &rvm) const { |
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| 327 | shared_ptr<estudent<sq_T> > tmp = new estudent<sq_T>; |
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| 328 | marginal(rvm, *tmp); |
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| 329 | return tmp; |
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| 330 | } |
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[1175] | 331 | vec sample() const { |
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| 332 | enorm<sq_T> en; |
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| 333 | en._mu()=mu; |
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| 334 | en._R()=H; |
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| 335 | en._R()*=delta/(delta-2); |
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| 336 | en.validate(); |
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| 337 | return en.sample(); |
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| 338 | } |
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[1064] | 339 | |
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| 340 | vec mean() const { |
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| 341 | return mu; |
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| 342 | } |
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| 343 | mat covariance() const { |
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| 344 | return delta/(delta-2)*H.to_mat(); |
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| 345 | } |
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| 346 | vec variance() const { |
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| 347 | return diag(covariance()); |
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| 348 | } |
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| 349 | //! \name access |
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| 350 | //! @{ |
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| 351 | //! access function |
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| 352 | vec& _mu() { |
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| 353 | return mu; |
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| 354 | } |
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| 355 | //! access function |
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| 356 | sq_T& _H() { |
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| 357 | return H; |
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| 358 | } |
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| 359 | //! access function |
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| 360 | double& _delta() { |
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| 361 | return delta; |
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| 362 | } |
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| 363 | //!@} |
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| 364 | //! todo |
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| 365 | void from_setting(const Setting &set) { |
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| 366 | epdf::from_setting(set); |
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| 367 | mat H0; |
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| 368 | UI::get(H0,set, "H"); |
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| 369 | H= H0; // conversion!! |
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| 370 | UI::get(delta,set,"delta"); |
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| 371 | UI::get(mu,set,"mu"); |
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| 372 | } |
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| 373 | void to_setting(Setting &set) const { |
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| 374 | epdf::to_setting(set); |
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| 375 | UI::save(H.to_mat(), set, "H"); |
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| 376 | UI::save(delta, set, "delta"); |
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| 377 | UI::save(mu, set, "mu"); |
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| 378 | } |
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| 379 | void validate() { |
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| 380 | eEF::validate(); |
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| 381 | dim = H.rows(); |
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| 382 | } |
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[802] | 383 | }; |
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| 384 | UIREGISTER2(estudent,fsqmat); |
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| 385 | UIREGISTER2(estudent,ldmat); |
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| 386 | UIREGISTER2(estudent,chmat); |
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| 387 | |
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[1196] | 388 | // template < class sq_T, template <typename> class TEpdf = estudent > |
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| 389 | // class mstudent : public pdf_internal< TEpdf<sq_T> > { |
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| 390 | // protected: |
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| 391 | // //! Internal epdf that arise by conditioning on \c rvc |
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| 392 | // mat A; |
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| 393 | // //! Constant additive term |
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| 394 | // vec mu_const; |
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| 395 | // |
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| 396 | // public: |
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| 397 | // void condition( const vec &cond ) { |
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| 398 | // iepdf._mu()=A*val*mu_const; |
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| 399 | // } |
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| 400 | // |
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| 401 | // }; |
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| 402 | |
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[488] | 403 | /*! |
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| 404 | * \brief Gauss-inverse-Wishart density stored in LD form |
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[96] | 405 | |
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[1189] | 406 | * For \f$p\f$-variate densities, |
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| 407 | * |
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| 408 | * \f$ M,R \sim GiW( V_t, \nu_t) \propto |R|^{0.5\nu}\exp(-1/2 tr(R^{-1}[I,M] V_t [I;M'])) \f$ |
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[488] | 409 | * |
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[1189] | 410 | * Factorizes as: |
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| 411 | * \f$ M|R \sim N( \hat{M}, R \otimes Vz^{-1}) \propto |R|^{-0.5dim(psi)}\exp(-1/2 tr((M-\hat{M})R^{-1}(M-\hat{M})Vz) \f$ |
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| 412 | * \f$ R \sim iW( \Lambda,\delta) \propto |R|^{-0.5(\nu - dim(psi))} |\Lambda|^{}\exp(-1/2 tr(R^{-1}\Lambda) \f$ |
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| 413 | * where in standard notation \f$ |R|^{-0.5(\delta + p +1)}\f$, i.e. |
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| 414 | * \f$ \delta = \nu-dim(psi) -p-1 \f$ |
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[488] | 415 | */ |
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[737] | 416 | class egiw : public eEF { |
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[1064] | 417 | //! \var log_level_enums logvartheta |
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| 418 | //! Log variance of the theta part |
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[870] | 419 | |
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[1064] | 420 | LOG_LEVEL(egiw,logvartheta); |
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[907] | 421 | |
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[737] | 422 | protected: |
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[1064] | 423 | //! Extended information matrix of sufficient statistics |
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| 424 | ldmat V; |
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| 425 | //! Number of data records (degrees of freedom) of sufficient statistics |
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| 426 | double nu; |
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| 427 | //! Dimension of the output |
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| 428 | int dimx; |
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| 429 | //! Dimension of the regressor |
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| 430 | int nPsi; |
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[737] | 431 | public: |
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[1064] | 432 | //!\name Constructors |
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| 433 | //!@{ |
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| 434 | egiw() : eEF(),dimx(0) {}; |
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| 435 | egiw ( int dimx0, ldmat V0, double nu0 = -1.0 ) : eEF(),dimx(0) { |
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| 436 | set_parameters ( dimx0, V0, nu0 ); |
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| 437 | validate(); |
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| 438 | }; |
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[270] | 439 | |
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[1064] | 440 | void set_parameters ( int dimx0, ldmat V0, double nu0 = -1.0 ); |
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| 441 | //!@} |
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[96] | 442 | |
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[1064] | 443 | vec sample() const; |
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| 444 | mat sample_mat ( int n ) const; |
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| 445 | vec mean() const; |
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| 446 | vec variance() const; |
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| 447 | //mat covariance() const; |
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| 448 | void sample_mat ( mat &Mi, chmat &Ri ) const; |
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[330] | 449 | |
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[1064] | 450 | void factorize ( mat &M, ldmat &Vz, ldmat &Lam ) const; |
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[1189] | 451 | //! LS estimate of \f$\theta\f$ |
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[1064] | 452 | vec est_theta() const; |
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[330] | 453 | |
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[1064] | 454 | //! Covariance of the LS estimate |
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| 455 | ldmat est_theta_cov() const; |
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[96] | 456 | |
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[1064] | 457 | //! expected values of the linear coefficient and the covariance matrix are written to \c M and \c R , respectively |
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| 458 | void mean_mat ( mat &M, mat&R ) const; |
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| 459 | //! 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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| 460 | double evallog_nn ( const vec &val ) const; |
---|
| 461 | double lognc () const; |
---|
| 462 | void pow ( double p ) { |
---|
| 463 | V *= p; |
---|
| 464 | nu *= p; |
---|
| 465 | }; |
---|
[270] | 466 | |
---|
[1064] | 467 | //! marginal density (only student for now) |
---|
| 468 | shared_ptr<epdf> marginal(const RV &rvm) const { |
---|
| 469 | bdm_assert(dimx==1, "Not supported"); |
---|
| 470 | //TODO - this is too trivial!!! |
---|
| 471 | ivec ind = rvm.findself_ids(rv); |
---|
| 472 | if (min(ind)==0) { //assume it si |
---|
| 473 | shared_ptr<estudent<ldmat> > tmp = new estudent<ldmat>; |
---|
| 474 | mat M; |
---|
| 475 | ldmat Vz; |
---|
| 476 | ldmat Lam; |
---|
| 477 | factorize(M,Vz,Lam); |
---|
[737] | 478 | |
---|
[1064] | 479 | tmp->_mu() = M.get_col(0); |
---|
| 480 | ldmat H; |
---|
| 481 | Vz.inv(H); |
---|
| 482 | H *=Lam._D()(0)/nu; |
---|
| 483 | tmp->_H() = H; |
---|
| 484 | tmp->_delta() = nu; |
---|
| 485 | tmp->validate(); |
---|
| 486 | return tmp; |
---|
| 487 | } |
---|
| 488 | return NULL; |
---|
| 489 | } |
---|
| 490 | //! \name Access attributes |
---|
| 491 | //!@{ |
---|
[737] | 492 | |
---|
[1064] | 493 | ldmat& _V() { |
---|
| 494 | return V; |
---|
| 495 | } |
---|
| 496 | const ldmat& _V() const { |
---|
| 497 | return V; |
---|
| 498 | } |
---|
| 499 | double& _nu() { |
---|
| 500 | return nu; |
---|
| 501 | } |
---|
| 502 | const double& _nu() const { |
---|
| 503 | return nu; |
---|
| 504 | } |
---|
| 505 | const int & _dimx() const { |
---|
| 506 | return dimx; |
---|
| 507 | } |
---|
[889] | 508 | |
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[1066] | 509 | /*! Create object from the following structure |
---|
[1064] | 510 | \code |
---|
[1066] | 511 | |
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[1064] | 512 | class = 'egiw'; |
---|
[1066] | 513 | dimx = [...]; % dimension of the wishart part |
---|
| 514 | V.L = [...]; % L part of matrix V |
---|
| 515 | V.D = [...]; % D part of matrix V |
---|
[1079] | 516 | -or- fV = [...]; % full matrix V |
---|
[1066] | 517 | -or- dV = [...]; % vector of diagonal of V (when V not given) |
---|
| 518 | |
---|
| 519 | rv = RV({'names',...},[sizes,...],[times,...]); % description of RV |
---|
| 520 | rvc = RV({'names',...},[sizes,...],[times,...]); % description of RV in condition |
---|
| 521 | |
---|
| 522 | --- optional fields --- |
---|
| 523 | nu = []; % scalar \nu ((almost) degrees of freedom) |
---|
| 524 | --- inherited fields --- |
---|
| 525 | bdm::eEF::from_setting |
---|
[1064] | 526 | \endcode |
---|
[737] | 527 | |
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[1066] | 528 | fulfilling formula \f[ f(rv) = GiW(V,\nu) \f] |
---|
| 529 | |
---|
| 530 | If \nu is not given, it will be computed to obtain proper pdf. |
---|
| 531 | |
---|
[1064] | 532 | \sa log_level_enums |
---|
| 533 | */ |
---|
| 534 | void from_setting ( const Setting &set ); |
---|
| 535 | //! see egiw::from_setting |
---|
| 536 | void to_setting ( Setting& set ) const; |
---|
| 537 | void validate(); |
---|
| 538 | void log_register ( bdm::logger& L, const string& prefix ); |
---|
| 539 | |
---|
| 540 | void log_write() const; |
---|
| 541 | //!@} |
---|
[488] | 542 | }; |
---|
[529] | 543 | UIREGISTER ( egiw ); |
---|
| 544 | SHAREDPTR ( egiw ); |
---|
[96] | 545 | |
---|
[1121] | 546 | //! \brief Gauss-Wishart with recursion on moments |
---|
| 547 | //! Using precision as parameter |
---|
| 548 | //! following notation of [Karny Andrysek 2009], precision |
---|
| 549 | template<class sq_T> |
---|
| 550 | class egw_ls: public eEF{ |
---|
| 551 | public: |
---|
| 552 | vec theta; |
---|
| 553 | sq_T P; |
---|
| 554 | double omega; |
---|
| 555 | double nu; |
---|
| 556 | |
---|
| 557 | vec mean() const{ |
---|
| 558 | return concat(theta, omega); |
---|
| 559 | } |
---|
| 560 | mat covariance() const { |
---|
| 561 | sq_T tmp=P; |
---|
| 562 | tmp*=nu/((nu-2)*omega); |
---|
| 563 | return tmp.to_mat();//<======= error - missing omega |
---|
| 564 | } |
---|
| 565 | vec variance() const { |
---|
| 566 | return diag(covariance());//<======= error - missing omega |
---|
| 567 | } |
---|
| 568 | vec sample() const NOT_IMPLEMENTED(vec(0)); |
---|
| 569 | double lognc() const {return 0.0;} //TODO |
---|
| 570 | }; |
---|
| 571 | |
---|
[488] | 572 | /*! \brief Dirichlet posterior density |
---|
[173] | 573 | |
---|
[488] | 574 | Continuous Dirichlet density of \f$n\f$-dimensional variable \f$x\f$ |
---|
| 575 | \f[ |
---|
| 576 | f(x|\beta) = \frac{\Gamma[\gamma]}{\prod_{i=1}^{n}\Gamma(\beta_i)} \prod_{i=1}^{n}x_i^{\beta_i-1} |
---|
| 577 | \f] |
---|
| 578 | where \f$\gamma=\sum_i \beta_i\f$. |
---|
| 579 | */ |
---|
[737] | 580 | class eDirich: public eEF { |
---|
| 581 | protected: |
---|
[1064] | 582 | //!sufficient statistics |
---|
| 583 | vec beta; |
---|
[737] | 584 | public: |
---|
[1064] | 585 | //!\name Constructors |
---|
| 586 | //!@{ |
---|
[270] | 587 | |
---|
[1064] | 588 | eDirich () : eEF () {}; |
---|
| 589 | eDirich ( const eDirich &D0 ) : eEF () { |
---|
| 590 | set_parameters ( D0.beta ); |
---|
| 591 | validate(); |
---|
| 592 | }; |
---|
| 593 | eDirich ( const vec &beta0 ) { |
---|
| 594 | set_parameters ( beta0 ); |
---|
| 595 | validate(); |
---|
| 596 | }; |
---|
| 597 | void set_parameters ( const vec &beta0 ) { |
---|
| 598 | beta = beta0; |
---|
| 599 | dim = beta.length(); |
---|
| 600 | } |
---|
| 601 | //!@} |
---|
[270] | 602 | |
---|
[1064] | 603 | //! using sampling procedure from wikipedia |
---|
| 604 | vec sample() const { |
---|
| 605 | vec y ( beta.length() ); |
---|
| 606 | for ( int i = 0; i < beta.length(); i++ ) { |
---|
| 607 | GamRNG.setup ( beta ( i ), 1 ); |
---|
[737] | 608 | #pragma omp critical |
---|
[1064] | 609 | y ( i ) = GamRNG(); |
---|
| 610 | } |
---|
| 611 | return y / sum ( y ); |
---|
| 612 | } |
---|
[565] | 613 | |
---|
[1064] | 614 | vec mean() const { |
---|
| 615 | return beta / sum ( beta ); |
---|
| 616 | }; |
---|
| 617 | vec variance() const { |
---|
| 618 | double gamma = sum ( beta ); |
---|
| 619 | return elem_mult ( beta, ( gamma - beta ) ) / ( gamma*gamma* ( gamma + 1 ) ); |
---|
| 620 | } |
---|
| 621 | //! In this instance, val is ... |
---|
| 622 | double evallog_nn ( const vec &val ) const { |
---|
| 623 | double tmp; |
---|
| 624 | tmp = ( beta - 1 ) * log ( val ); |
---|
| 625 | return tmp; |
---|
| 626 | } |
---|
[565] | 627 | |
---|
[1064] | 628 | double lognc () const { |
---|
| 629 | double tmp; |
---|
| 630 | double gam = sum ( beta ); |
---|
| 631 | double lgb = 0.0; |
---|
| 632 | for ( int i = 0; i < beta.length(); i++ ) { |
---|
| 633 | lgb += lgamma ( beta ( i ) ); |
---|
| 634 | } |
---|
| 635 | tmp = lgb - lgamma ( gam ); |
---|
| 636 | return tmp; |
---|
| 637 | } |
---|
[565] | 638 | |
---|
[1064] | 639 | //!access function |
---|
| 640 | vec& _beta() { |
---|
| 641 | return beta; |
---|
| 642 | } |
---|
[1063] | 643 | |
---|
[1064] | 644 | /*! Create object from the following structure |
---|
| 645 | \code |
---|
| 646 | class = 'eDirich'; |
---|
| 647 | beta = [...]; % vector parameter beta |
---|
| 648 | --- inherited fields --- |
---|
| 649 | bdm::eEF::from_setting |
---|
| 650 | \endcode |
---|
| 651 | */ |
---|
| 652 | void from_setting ( const Setting &set ); |
---|
[1063] | 653 | |
---|
[1064] | 654 | void validate(); |
---|
[1063] | 655 | |
---|
[1064] | 656 | void to_setting ( Setting &set ) const; |
---|
[488] | 657 | }; |
---|
[737] | 658 | UIREGISTER ( eDirich ); |
---|
[96] | 659 | |
---|
[1063] | 660 | /*! \brief Product of Beta distributions |
---|
[1033] | 661 | |
---|
| 662 | Continuous Dirichlet density of \f$n\f$-dimensional variable \f$x\f$ |
---|
| 663 | \f[ |
---|
[1064] | 664 | f(x|\alpha,\beta) = \frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)\Gamma(\beta)}\, x^{\alpha-1}(1-x)^{\beta-1} |
---|
[1033] | 665 | \f] |
---|
| 666 | is a simplification of Dirichlet to univariate case. |
---|
| 667 | */ |
---|
| 668 | class eBeta: public eEF { |
---|
[1064] | 669 | public: |
---|
| 670 | //!sufficient statistics |
---|
| 671 | vec alpha; |
---|
| 672 | //!sufficient statistics |
---|
| 673 | vec beta; |
---|
| 674 | public: |
---|
| 675 | //!\name Constructors |
---|
| 676 | //!@{ |
---|
[1063] | 677 | |
---|
[1064] | 678 | eBeta () : eEF () {}; |
---|
| 679 | eBeta ( const eBeta &B0 ) : eEF (), alpha(B0.alpha),beta(B0.beta) { |
---|
| 680 | validate(); |
---|
| 681 | }; |
---|
| 682 | //!@} |
---|
[1063] | 683 | |
---|
[1064] | 684 | //! using sampling procedure from wikipedia |
---|
| 685 | vec sample() const { |
---|
| 686 | vec y ( beta.length() ); // all vectors |
---|
| 687 | for ( int i = 0; i < beta.length(); i++ ) { |
---|
| 688 | GamRNG.setup ( alpha ( i ), 1 ); |
---|
| 689 | #pragma omp critical |
---|
| 690 | double Ga = GamRNG(); |
---|
[1063] | 691 | |
---|
[1064] | 692 | GamRNG.setup ( beta ( i ), 1 ); |
---|
| 693 | #pragma omp critical |
---|
| 694 | double Gb = GamRNG(); |
---|
| 695 | |
---|
| 696 | y ( i ) = Ga/(Ga+Gb); |
---|
| 697 | } |
---|
| 698 | return y; |
---|
| 699 | } |
---|
| 700 | |
---|
| 701 | vec mean() const { |
---|
| 702 | return elem_div(alpha, alpha + beta); // dot-division |
---|
| 703 | }; |
---|
| 704 | vec variance() const { |
---|
| 705 | vec apb=alpha+beta; |
---|
| 706 | return elem_div (elem_mult ( alpha, beta) , |
---|
| 707 | elem_mult ( elem_mult(apb,apb), apb+1 ) ); |
---|
| 708 | } |
---|
| 709 | //! In this instance, val is ... |
---|
| 710 | double evallog_nn ( const vec &val ) const { |
---|
| 711 | double tmp; |
---|
| 712 | tmp = ( alpha - 1 ) * log ( val ) + (beta-1)*log(1-val); |
---|
| 713 | return tmp; |
---|
| 714 | } |
---|
| 715 | |
---|
| 716 | double lognc () const { |
---|
| 717 | double lgb = 0.0; |
---|
| 718 | for ( int i = 0; i < beta.length(); i++ ) { |
---|
| 719 | lgb += -lgamma ( alpha(i)+beta(i) ) + lgamma(alpha(i)) + lgamma(beta(i)); |
---|
| 720 | } |
---|
| 721 | return lgb; |
---|
| 722 | } |
---|
| 723 | |
---|
| 724 | /*! Create object from the following structure |
---|
| 725 | |
---|
| 726 | \code |
---|
| 727 | class = 'eBeta'; |
---|
| 728 | alpha = [...]; % vector parameter alpha |
---|
| 729 | beta = [...]; % vector parameter beta of the same length as alpha |
---|
| 730 | \endcode |
---|
| 731 | |
---|
| 732 | Class does not call bdm::eEF::from_setting |
---|
| 733 | */ |
---|
| 734 | void from_setting ( const Setting &set ) { |
---|
| 735 | UI::get(alpha, set, "alpha", UI::compulsory); |
---|
| 736 | UI::get(beta, set, "beta", UI::compulsory); |
---|
| 737 | } |
---|
| 738 | |
---|
| 739 | void validate() { |
---|
| 740 | bdm_assert(alpha.length()==beta.length(), "eBeta:: alpha and beta length do not match"); |
---|
| 741 | dim = alpha.length(); |
---|
| 742 | } |
---|
| 743 | |
---|
| 744 | void to_setting ( Setting &set ) const { |
---|
| 745 | UI::save(alpha, set, "alpha"); |
---|
| 746 | UI::save(beta, set, "beta"); |
---|
| 747 | } |
---|
[1033] | 748 | }; |
---|
| 749 | UIREGISTER ( eBeta ); |
---|
| 750 | |
---|
[1068] | 751 | /*! \brief Random Walk on Dirichlet |
---|
| 752 | |
---|
[737] | 753 | Using simple assignment |
---|
[637] | 754 | \f[ \beta = rvc / k + \beta_c \f] |
---|
| 755 | hence, mean value = rvc, variance = (k+1)*mean*mean; |
---|
[737] | 756 | |
---|
[637] | 757 | The greater k is, the greater is the variance of the random walk; |
---|
[737] | 758 | |
---|
[637] | 759 | \f$ \beta_c \f$ is used as regularizing element to avoid corner cases, i.e. when one element of rvc is zero. |
---|
| 760 | By default is it set to 0.1; |
---|
| 761 | */ |
---|
[693] | 762 | class mDirich: public pdf_internal<eDirich> { |
---|
[737] | 763 | protected: |
---|
[1064] | 764 | //! constant \f$ k \f$ of the random walk |
---|
| 765 | double k; |
---|
| 766 | //! cache of beta_i |
---|
| 767 | vec &_beta; |
---|
| 768 | //! stabilizing coefficient \f$ \beta_c \f$ |
---|
| 769 | vec betac; |
---|
[737] | 770 | public: |
---|
[1064] | 771 | mDirich() : pdf_internal<eDirich>(), _beta ( iepdf._beta() ) {}; |
---|
| 772 | void condition ( const vec &val ) { |
---|
| 773 | _beta = val / k + betac; |
---|
| 774 | }; |
---|
[1068] | 775 | |
---|
| 776 | /*! Create object from the following structure |
---|
[1064] | 777 | \code |
---|
| 778 | class = 'mDirich'; |
---|
[1068] | 779 | k = 1; % multiplicative constant k |
---|
[1064] | 780 | --- optional --- |
---|
[1068] | 781 | beta0 = [...]; % initial values of beta |
---|
| 782 | betac = [...]; % initial values of beta stabilizing coefficients |
---|
| 783 | --- inherited fields --- |
---|
| 784 | bdm::pdf::from_setting |
---|
[1064] | 785 | \endcode |
---|
[1068] | 786 | fulfilling form \f[ f(rv|rvc) = Di(rvc*k) \f] |
---|
| 787 | |
---|
| 788 | If the optional fields are not given, they will be filled as follows: |
---|
| 789 | \code |
---|
| 790 | beta0 = [1,1,1,...]; |
---|
| 791 | betac = 0.1 * [1,1,1,...]; |
---|
| 792 | \endcode |
---|
[1064] | 793 | */ |
---|
| 794 | void from_setting ( const Setting &set ); |
---|
[1066] | 795 | void to_setting (Setting &set) const; |
---|
[1064] | 796 | void validate(); |
---|
[637] | 797 | }; |
---|
[737] | 798 | UIREGISTER ( mDirich ); |
---|
[637] | 799 | |
---|
[1033] | 800 | /*! \brief Random Walk with vector Beta distribution |
---|
[1068] | 801 | |
---|
[1033] | 802 | Using simple assignment |
---|
[1064] | 803 | \f{eqnarray*} |
---|
[1063] | 804 | \alpha & = & rvc / k + \beta_c \\ |
---|
| 805 | \beta & = &(1-rvc) / k + \beta_c \\ |
---|
| 806 | \f} |
---|
[1033] | 807 | for each element of alpha and beta, mean value = rvc, variance = (k+1)*mean*mean; |
---|
[977] | 808 | |
---|
[1033] | 809 | The greater \f$ k \f$ is, the greater is the variance of the random walk; |
---|
| 810 | |
---|
| 811 | \f$ \beta_c \f$ is used as regularizing element to avoid corner cases, i.e. when one element of rvc is zero. |
---|
| 812 | By default is it set to 0.1; |
---|
| 813 | */ |
---|
[1064] | 814 | class mBeta: public pdf_internal<eBeta> { |
---|
| 815 | //! vector of constants \f$ k \f$ of the random walk |
---|
| 816 | vec k; |
---|
| 817 | //! stabilizing coefficient \f$ \beta_c \f$ |
---|
| 818 | vec betac; |
---|
[1033] | 819 | |
---|
[1064] | 820 | public: |
---|
| 821 | void condition ( const vec &val ) { |
---|
| 822 | this->iepdf.alpha = elem_div(val , k) + betac; |
---|
| 823 | this->iepdf.beta = elem_div (1-val , k) + betac; |
---|
| 824 | }; |
---|
[1063] | 825 | |
---|
[1068] | 826 | /*! Create object from the following structure |
---|
[1064] | 827 | \code |
---|
| 828 | class = 'mBeta'; |
---|
[1068] | 829 | k = [...]; % vector of multiplicative constants k |
---|
| 830 | --- optional fields --- |
---|
| 831 | beta = [...]; % initial values of beta |
---|
| 832 | betac = [...]; % initial values of beta stabilizing constants |
---|
| 833 | --- inherited fields --- |
---|
| 834 | bdm::pdf::from_setting |
---|
[1064] | 835 | \endcode |
---|
[1068] | 836 | fulfilling form \f[ f(rv|rvc) = \prod Beta(rvc,k) \f] |
---|
| 837 | |
---|
| 838 | If the optional fields are not given, they will be filled as follows: |
---|
| 839 | \code |
---|
| 840 | beta = [1,1,1,...]; |
---|
| 841 | betac = 0.1 * [1,1,1,...]; |
---|
| 842 | \endcode |
---|
| 843 | |
---|
[1064] | 844 | */ |
---|
| 845 | void from_setting ( const Setting &set ); |
---|
[1063] | 846 | |
---|
[1064] | 847 | void to_setting (Setting &set) const; |
---|
| 848 | |
---|
| 849 | void validate() { |
---|
| 850 | pdf_internal<eBeta>::validate(); |
---|
| 851 | bdm_assert(betac.length()==dimension(),"Incomaptible betac"); |
---|
| 852 | bdm_assert(k.length()==dimension(),"Incomaptible k"); |
---|
| 853 | dimc = iepdf.dimension(); |
---|
| 854 | } |
---|
| 855 | //! |
---|
[1033] | 856 | }; |
---|
| 857 | UIREGISTER(mBeta); |
---|
| 858 | |
---|
[181] | 859 | //! \brief Estimator for Multinomial density |
---|
[737] | 860 | class multiBM : public BMEF { |
---|
| 861 | protected: |
---|
[1064] | 862 | //! Conjugate prior and posterior |
---|
| 863 | eDirich est; |
---|
| 864 | //! Pointer inside est to sufficient statistics |
---|
| 865 | vec β |
---|
[737] | 866 | public: |
---|
[1064] | 867 | //!Default constructor |
---|
| 868 | multiBM () : BMEF (), est (), beta ( est._beta() ) { |
---|
| 869 | if ( beta.length() > 0 ) { |
---|
| 870 | last_lognc = est.lognc(); |
---|
| 871 | } else { |
---|
| 872 | last_lognc = 0.0; |
---|
| 873 | } |
---|
| 874 | } |
---|
| 875 | //!Copy constructor |
---|
| 876 | multiBM ( const multiBM &B ) : BMEF ( B ), est ( B.est ), beta ( est._beta() ) {} |
---|
| 877 | //! Sets sufficient statistics to match that of givefrom mB0 |
---|
| 878 | void set_statistics ( const BM* mB0 ) { |
---|
| 879 | const multiBM* mB = dynamic_cast<const multiBM*> ( mB0 ); |
---|
| 880 | beta = mB->beta; |
---|
| 881 | } |
---|
| 882 | void bayes ( const vec &yt, const vec &cond = empty_vec ); |
---|
[176] | 883 | |
---|
[1064] | 884 | double logpred ( const vec &yt ) const; |
---|
[170] | 885 | |
---|
[1064] | 886 | void flatten ( const BMEF* B , double weight); |
---|
[739] | 887 | |
---|
[1064] | 888 | //! return correctly typed posterior (covariant return) |
---|
| 889 | const eDirich& posterior() const { |
---|
| 890 | return est; |
---|
| 891 | }; |
---|
| 892 | //! constructor function |
---|
| 893 | void set_parameters ( const vec &beta0 ) { |
---|
| 894 | est.set_parameters ( beta0 ); |
---|
| 895 | est.validate(); |
---|
| 896 | if ( evalll ) { |
---|
| 897 | last_lognc = est.lognc(); |
---|
| 898 | } |
---|
| 899 | } |
---|
[746] | 900 | |
---|
[1064] | 901 | void to_setting ( Setting &set ) const { |
---|
| 902 | BMEF::to_setting ( set ); |
---|
| 903 | UI::save( &est, set, "prior" ); |
---|
| 904 | } |
---|
[1077] | 905 | |
---|
| 906 | /*! Create object from the following structure |
---|
| 907 | |
---|
| 908 | \code |
---|
| 909 | class = 'MultiBM'; |
---|
| 910 | prior = configuration of bdm::eDirich; % any offspring of eDirich, bdm::eDirich::from_setting |
---|
| 911 | --- inherited fields --- |
---|
| 912 | bdm::BMEF::from_setting |
---|
| 913 | \endcode |
---|
| 914 | */ |
---|
[1064] | 915 | void from_setting (const Setting &set ) { |
---|
| 916 | BMEF::from_setting ( set ); |
---|
| 917 | UI::get( est, set, "prior" ); |
---|
| 918 | } |
---|
[488] | 919 | }; |
---|
[746] | 920 | UIREGISTER( multiBM ); |
---|
[170] | 921 | |
---|
[488] | 922 | /*! |
---|
| 923 | \brief Gamma posterior density |
---|
[32] | 924 | |
---|
[488] | 925 | Multivariate Gamma density as product of independent univariate densities. |
---|
| 926 | \f[ |
---|
| 927 | f(x|\alpha,\beta) = \prod f(x_i|\alpha_i,\beta_i) |
---|
| 928 | \f] |
---|
| 929 | */ |
---|
[32] | 930 | |
---|
[737] | 931 | class egamma : public eEF { |
---|
| 932 | protected: |
---|
[1064] | 933 | //! Vector \f$\alpha\f$ |
---|
| 934 | vec alpha; |
---|
| 935 | //! Vector \f$\beta\f$ |
---|
| 936 | vec beta; |
---|
[737] | 937 | public : |
---|
[1064] | 938 | //! \name Constructors |
---|
| 939 | //!@{ |
---|
| 940 | egamma () : eEF (), alpha ( 0 ), beta ( 0 ) {}; |
---|
| 941 | egamma ( const vec &a, const vec &b ) { |
---|
| 942 | set_parameters ( a, b ); |
---|
| 943 | validate(); |
---|
| 944 | }; |
---|
| 945 | void set_parameters ( const vec &a, const vec &b ) { |
---|
| 946 | alpha = a, beta = b; |
---|
| 947 | }; |
---|
| 948 | //!@} |
---|
[270] | 949 | |
---|
[1064] | 950 | vec sample() const; |
---|
[1083] | 951 | double evallog_nn ( const vec &val ) const; |
---|
| 952 | double lognc () const; |
---|
[1064] | 953 | //! Returns pointer to internal alpha. Potentially dengerous: use with care! |
---|
| 954 | vec& _alpha() { |
---|
| 955 | return alpha; |
---|
| 956 | } |
---|
| 957 | //! Returns pointer to internal beta. Potentially dengerous: use with care! |
---|
| 958 | vec& _beta() { |
---|
| 959 | return beta; |
---|
| 960 | } |
---|
| 961 | vec mean() const { |
---|
| 962 | return elem_div ( alpha, beta ); |
---|
| 963 | } |
---|
| 964 | vec variance() const { |
---|
| 965 | return elem_div ( alpha, elem_mult ( beta, beta ) ); |
---|
| 966 | } |
---|
[225] | 967 | |
---|
[1064] | 968 | /*! Create object from the following structure |
---|
[1063] | 969 | |
---|
[1064] | 970 | \code |
---|
| 971 | class = 'egamma'; |
---|
[1066] | 972 | alpha = [...]; % vector alpha |
---|
| 973 | beta = [...]; % vector beta |
---|
[1064] | 974 | --- inherited fields --- |
---|
| 975 | bdm::eEF::from_setting |
---|
| 976 | \endcode |
---|
| 977 | fulfilling formula \f[ f(rv|rvc) = \Gamma(\alpha, \beta) \f] |
---|
| 978 | */ |
---|
| 979 | void from_setting ( const Setting &set ); |
---|
[1063] | 980 | |
---|
[1064] | 981 | void to_setting ( Setting &set ) const; |
---|
| 982 | void validate(); |
---|
[488] | 983 | }; |
---|
[737] | 984 | UIREGISTER ( egamma ); |
---|
[529] | 985 | SHAREDPTR ( egamma ); |
---|
| 986 | |
---|
[488] | 987 | /*! |
---|
| 988 | \brief Inverse-Gamma posterior density |
---|
[225] | 989 | |
---|
[488] | 990 | Multivariate inverse-Gamma density as product of independent univariate densities. |
---|
| 991 | \f[ |
---|
| 992 | f(x|\alpha,\beta) = \prod f(x_i|\alpha_i,\beta_i) |
---|
| 993 | \f] |
---|
[283] | 994 | |
---|
[488] | 995 | Vector \f$\beta\f$ has different meaning (in fact it is 1/beta as used in definition of iG) |
---|
[225] | 996 | |
---|
[488] | 997 | Inverse Gamma can be converted to Gamma using \f[ |
---|
| 998 | x\sim iG(a,b) => 1/x\sim G(a,1/b) |
---|
| 999 | \f] |
---|
| 1000 | This relation is used in sampling. |
---|
| 1001 | */ |
---|
[270] | 1002 | |
---|
[737] | 1003 | class eigamma : public egamma { |
---|
| 1004 | protected: |
---|
| 1005 | public : |
---|
[1064] | 1006 | //! \name Constructors |
---|
| 1007 | //! All constructors are inherited |
---|
| 1008 | //!@{ |
---|
| 1009 | //!@} |
---|
[32] | 1010 | |
---|
[1064] | 1011 | vec sample() const { |
---|
| 1012 | return 1.0 / egamma::sample(); |
---|
| 1013 | }; |
---|
| 1014 | //! Returns poiter to alpha and beta. Potentially dangerous: use with care! |
---|
| 1015 | vec mean() const { |
---|
| 1016 | return elem_div ( beta, alpha - 1 ); |
---|
| 1017 | } |
---|
| 1018 | vec variance() const { |
---|
| 1019 | vec mea = mean(); |
---|
| 1020 | return elem_div ( elem_mult ( mea, mea ), alpha - 2 ); |
---|
| 1021 | } |
---|
[488] | 1022 | }; |
---|
| 1023 | /* |
---|
| 1024 | //! Weighted mixture of epdfs with external owned components. |
---|
| 1025 | class emix : public epdf { |
---|
| 1026 | protected: |
---|
[1066] | 1027 | int n; |
---|
| 1028 | vec &w; |
---|
| 1029 | Array<epdf*> Coms; |
---|
[488] | 1030 | public: |
---|
| 1031 | //! Default constructor |
---|
[1066] | 1032 | emix ( const RV &rv, vec &w0): epdf(rv), n(w0.length()), w(w0), Coms(n) {}; |
---|
| 1033 | void set_parameters( int &i, double wi, epdf* ep){w(i)=wi;Coms(i)=ep;} |
---|
| 1034 | vec mean(){vec pom; for(int i=0;i<n;i++){pom+=Coms(i)->mean()*w(i);} return pom;}; |
---|
[488] | 1035 | }; |
---|
| 1036 | */ |
---|
| 1037 | |
---|
[1068] | 1038 | //! \brief Uniform distributed density on a rectangular support |
---|
[737] | 1039 | class euni: public epdf { |
---|
| 1040 | protected: |
---|
[32] | 1041 | //! lower bound on support |
---|
[1064] | 1042 | vec low; |
---|
[32] | 1043 | //! upper bound on support |
---|
[1064] | 1044 | vec high; |
---|
[32] | 1045 | //! internal |
---|
[1064] | 1046 | vec distance; |
---|
[32] | 1047 | //! normalizing coefficients |
---|
[1064] | 1048 | double nk; |
---|
[33] | 1049 | //! cache of log( \c nk ) |
---|
[1064] | 1050 | double lnk; |
---|
[737] | 1051 | public: |
---|
[1064] | 1052 | //! \name Constructors |
---|
| 1053 | //!@{ |
---|
| 1054 | euni () : epdf () {} |
---|
| 1055 | euni ( const vec &low0, const vec &high0 ) { |
---|
| 1056 | set_parameters ( low0, high0 ); |
---|
| 1057 | } |
---|
| 1058 | void set_parameters ( const vec &low0, const vec &high0 ) { |
---|
| 1059 | distance = high0 - low0; |
---|
| 1060 | low = low0; |
---|
| 1061 | high = high0; |
---|
| 1062 | nk = prod ( 1.0 / distance ); |
---|
| 1063 | lnk = log ( nk ); |
---|
| 1064 | } |
---|
| 1065 | //!@} |
---|
[270] | 1066 | |
---|
[1064] | 1067 | double evallog ( const vec &val ) const { |
---|
| 1068 | if ( any ( val < low ) && any ( val > high ) ) { |
---|
| 1069 | return -inf; |
---|
| 1070 | } else return lnk; |
---|
| 1071 | } |
---|
| 1072 | vec sample() const { |
---|
| 1073 | vec smp ( dim ); |
---|
[270] | 1074 | #pragma omp critical |
---|
[1064] | 1075 | UniRNG.sample_vector ( dim , smp ); |
---|
| 1076 | return low + elem_mult ( distance, smp ); |
---|
| 1077 | } |
---|
| 1078 | //! set values of \c low and \c high |
---|
| 1079 | vec mean() const { |
---|
| 1080 | return ( high - low ) / 2.0; |
---|
| 1081 | } |
---|
| 1082 | vec variance() const { |
---|
| 1083 | return ( pow ( high, 2 ) + pow ( low, 2 ) + elem_mult ( high, low ) ) / 3.0; |
---|
| 1084 | } |
---|
[1068] | 1085 | |
---|
| 1086 | |
---|
| 1087 | /*! Create object from the following structure |
---|
[1064] | 1088 | \code |
---|
[1068] | 1089 | |
---|
[1064] | 1090 | class = 'euni' |
---|
[1068] | 1091 | high = [...]; % vector of upper bounds |
---|
| 1092 | low = [...]; % vector of lower bounds |
---|
| 1093 | rv = RV({'names',...},[sizes,...],[times,...]); % description of RV |
---|
| 1094 | --- inherited fields --- |
---|
| 1095 | bdm::epdf::from_setting |
---|
[1064] | 1096 | \endcode |
---|
[1068] | 1097 | |
---|
| 1098 | fulfilling form \f[ f(rv) = U(low,high) \f] |
---|
[1064] | 1099 | */ |
---|
| 1100 | void from_setting ( const Setting &set ); |
---|
[1066] | 1101 | void to_setting (Setting &set) const; |
---|
[1064] | 1102 | void validate(); |
---|
[488] | 1103 | }; |
---|
[737] | 1104 | UIREGISTER ( euni ); |
---|
[32] | 1105 | |
---|
[665] | 1106 | //! Uniform density with conditional mean value |
---|
[737] | 1107 | class mguni : public pdf_internal<euni> { |
---|
[1064] | 1108 | //! function of the mean value |
---|
| 1109 | shared_ptr<fnc> mean; |
---|
| 1110 | //! distance from mean to both sides |
---|
| 1111 | vec delta; |
---|
[737] | 1112 | public: |
---|
[1064] | 1113 | void condition ( const vec &cond ) { |
---|
| 1114 | vec mea = mean->eval ( cond ); |
---|
| 1115 | iepdf.set_parameters ( mea - delta, mea + delta ); |
---|
| 1116 | } |
---|
[1068] | 1117 | |
---|
| 1118 | /*! Create object from the following structure |
---|
| 1119 | \code |
---|
| 1120 | class = 'mguni'; |
---|
| 1121 | mean = function bdm::fnc; % any offspring of fnc, bdm::fnc::from_setting |
---|
| 1122 | delta = [...]; % distance from mean to both sides |
---|
| 1123 | --- inherited fields --- |
---|
| 1124 | bdm::pdf::from_setting |
---|
| 1125 | \endcode |
---|
| 1126 | */ |
---|
[1064] | 1127 | void from_setting ( const Setting &set ) { |
---|
| 1128 | pdf::from_setting ( set ); //reads rv and rvc |
---|
| 1129 | UI::get ( delta, set, "delta", UI::compulsory ); |
---|
| 1130 | mean = UI::build<fnc> ( set, "mean", UI::compulsory ); |
---|
| 1131 | iepdf.set_parameters ( -delta, delta ); |
---|
| 1132 | } |
---|
[1066] | 1133 | void to_setting (Setting &set) const { |
---|
[1064] | 1134 | pdf::to_setting ( set ); |
---|
| 1135 | UI::save( iepdf.mean(), set, "delta"); |
---|
| 1136 | UI::save(mean, set, "mean"); |
---|
| 1137 | } |
---|
| 1138 | void validate() { |
---|
| 1139 | pdf_internal<euni>::validate(); |
---|
| 1140 | dimc = mean->dimensionc(); |
---|
[878] | 1141 | |
---|
[1064] | 1142 | } |
---|
| 1143 | |
---|
[665] | 1144 | }; |
---|
[737] | 1145 | UIREGISTER ( mguni ); |
---|
[488] | 1146 | /*! |
---|
| 1147 | \brief Normal distributed linear function with linear function of mean value; |
---|
[32] | 1148 | |
---|
[536] | 1149 | Mean value \f$ \mu=A*\mbox{rvc}+\mu_0 \f$. |
---|
[488] | 1150 | */ |
---|
| 1151 | template < class sq_T, template <typename> class TEpdf = enorm > |
---|
[737] | 1152 | class mlnorm : public pdf_internal< TEpdf<sq_T> > { |
---|
| 1153 | protected: |
---|
[1196] | 1154 | //! Internal epdf that arise by conditioning on \c rvc |
---|
| 1155 | mat A; |
---|
| 1156 | //! Constant additive term |
---|
| 1157 | vec mu_const; |
---|
| 1158 | // vec& _mu; //cached epdf.mu; !!!!!! WHY NOT? |
---|
[737] | 1159 | public: |
---|
[1064] | 1160 | //! \name Constructors |
---|
| 1161 | //!@{ |
---|
| 1162 | mlnorm() : pdf_internal< TEpdf<sq_T> >() {}; |
---|
| 1163 | mlnorm ( const mat &A, const vec &mu0, const sq_T &R ) : pdf_internal< TEpdf<sq_T> >() { |
---|
| 1164 | set_parameters ( A, mu0, R ); |
---|
| 1165 | validate(); |
---|
| 1166 | } |
---|
[461] | 1167 | |
---|
[1064] | 1168 | //! Set \c A and \c R |
---|
| 1169 | void set_parameters ( const mat &A0, const vec &mu0, const sq_T &R0 ) { |
---|
| 1170 | this->iepdf.set_parameters ( zeros ( A0.rows() ), R0 ); |
---|
| 1171 | A = A0; |
---|
| 1172 | mu_const = mu0; |
---|
| 1173 | } |
---|
[878] | 1174 | |
---|
[1064] | 1175 | //!@} |
---|
| 1176 | //! Set value of \c rvc . Result of this operation is stored in \c epdf use function \c _ep to access it. |
---|
| 1177 | void condition ( const vec &cond ) { |
---|
| 1178 | this->iepdf._mu() = A * cond + mu_const; |
---|
[487] | 1179 | //R is already assigned; |
---|
[1064] | 1180 | } |
---|
[198] | 1181 | |
---|
[1064] | 1182 | //!access function |
---|
| 1183 | const vec& _mu_const() const { |
---|
| 1184 | return mu_const; |
---|
| 1185 | } |
---|
| 1186 | //!access function |
---|
| 1187 | const mat& _A() const { |
---|
| 1188 | return A; |
---|
| 1189 | } |
---|
| 1190 | //!access function |
---|
| 1191 | mat _R() const { |
---|
| 1192 | return this->iepdf._R().to_mat(); |
---|
| 1193 | } |
---|
| 1194 | //!access function |
---|
| 1195 | sq_T __R() const { |
---|
| 1196 | return this->iepdf._R(); |
---|
| 1197 | } |
---|
[8] | 1198 | |
---|
[1064] | 1199 | //! Debug stream |
---|
| 1200 | template<typename sq_M> |
---|
| 1201 | friend std::ostream &operator<< ( std::ostream &os, mlnorm<sq_M, enorm> &ml ); |
---|
[488] | 1202 | |
---|
[1064] | 1203 | /*! Create Normal density with linear function of mean value |
---|
| 1204 | \f[ f(rv|rvc) = N(A*rvc+const, R) \f] |
---|
| 1205 | from structure |
---|
| 1206 | \code |
---|
| 1207 | class = 'mlnorm<ldmat>', (OR) 'mlnorm<chmat>', (OR) 'mlnorm<fsqmat>'; |
---|
| 1208 | A = []; // matrix or vector of appropriate dimension |
---|
| 1209 | R = []; // square matrix of appropriate dimension |
---|
| 1210 | --- optional --- |
---|
| 1211 | const = zeros(A.rows); // vector of constant term |
---|
| 1212 | \endcode |
---|
| 1213 | */ |
---|
| 1214 | void from_setting ( const Setting &set ) { |
---|
| 1215 | pdf::from_setting ( set ); |
---|
[737] | 1216 | |
---|
[1064] | 1217 | UI::get ( A, set, "A", UI::compulsory ); |
---|
| 1218 | UI::get ( mu_const, set, "const", UI::optional); |
---|
| 1219 | mat R0; |
---|
| 1220 | UI::get ( R0, set, "R", UI::compulsory ); |
---|
| 1221 | set_parameters ( A, mu_const, R0 ); |
---|
| 1222 | } |
---|
[956] | 1223 | |
---|
[1064] | 1224 | void to_setting (Setting &set) const { |
---|
| 1225 | pdf::to_setting(set); |
---|
| 1226 | UI::save ( A, set, "A"); |
---|
| 1227 | UI::save ( mu_const, set, "const"); |
---|
| 1228 | UI::save ( _R(), set, "R"); |
---|
| 1229 | } |
---|
[956] | 1230 | |
---|
[1064] | 1231 | void validate() { |
---|
| 1232 | pdf_internal<TEpdf<sq_T> >::validate(); |
---|
| 1233 | if (mu_const.length()==0) { // default in from_setting |
---|
| 1234 | mu_const=zeros(A.rows()); |
---|
| 1235 | } |
---|
| 1236 | bdm_assert ( A.rows() == mu_const.length(), "mlnorm: A vs. mu mismatch" ); |
---|
| 1237 | bdm_assert ( A.rows() == _R().rows(), "mlnorm: A vs. R mismatch" ); |
---|
| 1238 | this->dimc = A.cols(); |
---|
[737] | 1239 | |
---|
[1064] | 1240 | } |
---|
[488] | 1241 | }; |
---|
[737] | 1242 | UIREGISTER2 ( mlnorm, ldmat ); |
---|
[529] | 1243 | SHAREDPTR2 ( mlnorm, ldmat ); |
---|
[737] | 1244 | UIREGISTER2 ( mlnorm, fsqmat ); |
---|
[529] | 1245 | SHAREDPTR2 ( mlnorm, fsqmat ); |
---|
[737] | 1246 | UIREGISTER2 ( mlnorm, chmat ); |
---|
[529] | 1247 | SHAREDPTR2 ( mlnorm, chmat ); |
---|
[488] | 1248 | |
---|
[1064] | 1249 | //! \class mlgauss |
---|
[948] | 1250 | //!\brief Normal distribution with linear function of mean value. Same as mlnorm<fsqmat>. |
---|
| 1251 | typedef mlnorm<fsqmat> mlgauss; |
---|
| 1252 | UIREGISTER(mlgauss); |
---|
| 1253 | |
---|
[693] | 1254 | //! pdf with general function for mean value |
---|
[488] | 1255 | template<class sq_T> |
---|
[737] | 1256 | class mgnorm : public pdf_internal< enorm< sq_T > > { |
---|
| 1257 | private: |
---|
[1066] | 1258 | // vec μ WHY NOT? |
---|
[1064] | 1259 | shared_ptr<fnc> g; |
---|
[527] | 1260 | |
---|
[737] | 1261 | public: |
---|
[1064] | 1262 | //!default constructor |
---|
| 1263 | mgnorm() : pdf_internal<enorm<sq_T> >() { } |
---|
| 1264 | //!set mean function |
---|
| 1265 | inline void set_parameters ( const shared_ptr<fnc> &g0, const sq_T &R0 ); |
---|
| 1266 | inline void condition ( const vec &cond ); |
---|
[357] | 1267 | |
---|
| 1268 | |
---|
[1064] | 1269 | /*! Create Normal density with given function of mean value |
---|
| 1270 | \f[ f(rv|rvc) = N( g(rvc), R) \f] |
---|
| 1271 | from structure |
---|
| 1272 | \code |
---|
| 1273 | class = 'mgnorm'; |
---|
| 1274 | g.class = 'fnc'; // function for mean value evolution |
---|
| 1275 | g._fields_of_fnc = ...; |
---|
[357] | 1276 | |
---|
[1064] | 1277 | R = [1, 0; // covariance matrix |
---|
[1066] | 1278 | 0, 1]; |
---|
| 1279 | --OR -- |
---|
[1064] | 1280 | dR = [1, 1]; // diagonal of cavariance matrix |
---|
[357] | 1281 | |
---|
[1064] | 1282 | rv = RV({'name'}) // description of RV |
---|
| 1283 | rvc = RV({'name'}) // description of RV in condition |
---|
| 1284 | \endcode |
---|
| 1285 | */ |
---|
[357] | 1286 | |
---|
[956] | 1287 | |
---|
[1064] | 1288 | void from_setting ( const Setting &set ) { |
---|
| 1289 | pdf::from_setting ( set ); |
---|
| 1290 | shared_ptr<fnc> g = UI::build<fnc> ( set, "g", UI::compulsory ); |
---|
[357] | 1291 | |
---|
[1064] | 1292 | mat R; |
---|
| 1293 | vec dR; |
---|
| 1294 | if ( UI::get ( dR, set, "dR" ) ) |
---|
| 1295 | R = diag ( dR ); |
---|
| 1296 | else |
---|
| 1297 | UI::get ( R, set, "R", UI::compulsory ); |
---|
[280] | 1298 | |
---|
[1064] | 1299 | set_parameters ( g, R ); |
---|
| 1300 | //validate(); |
---|
| 1301 | } |
---|
[956] | 1302 | |
---|
| 1303 | |
---|
[1064] | 1304 | void to_setting (Setting &set) const { |
---|
| 1305 | UI::save( g,set, "g"); |
---|
| 1306 | UI::save(this->iepdf._R().to_mat(),set, "R"); |
---|
[956] | 1307 | |
---|
[1064] | 1308 | } |
---|
[956] | 1309 | |
---|
| 1310 | |
---|
[1064] | 1311 | |
---|
| 1312 | void validate() { |
---|
| 1313 | this->iepdf.validate(); |
---|
| 1314 | bdm_assert ( g->dimension() == this->iepdf.dimension(), "incompatible function" ); |
---|
| 1315 | this->dim = g->dimension(); |
---|
| 1316 | this->dimc = g->dimensionc(); |
---|
| 1317 | this->iepdf.validate(); |
---|
| 1318 | } |
---|
| 1319 | |
---|
[488] | 1320 | }; |
---|
[357] | 1321 | |
---|
[737] | 1322 | UIREGISTER2 ( mgnorm, chmat ); |
---|
[944] | 1323 | UIREGISTER2 ( mgnorm, ldmat ); |
---|
[529] | 1324 | SHAREDPTR2 ( mgnorm, chmat ); |
---|
[357] | 1325 | |
---|
[262] | 1326 | |
---|
[1068] | 1327 | /*! \brief (Approximate) Student t density with linear function of mean value |
---|
[262] | 1328 | |
---|
[488] | 1329 | The internal epdf of this class is of the type of a Gaussian (enorm). |
---|
| 1330 | However, each conditioning is trying to assure the best possible approximation by taking into account the zeta function. See [] for reference. |
---|
[270] | 1331 | |
---|
[488] | 1332 | Perhaps a moment-matching technique? |
---|
| 1333 | */ |
---|
[737] | 1334 | class mlstudent : public mlnorm<ldmat, enorm> { |
---|
| 1335 | protected: |
---|
[1064] | 1336 | //! Variable \f$ \Lambda \f$ from theory |
---|
| 1337 | ldmat Lambda; |
---|
| 1338 | //! Reference to variable \f$ R \f$ |
---|
| 1339 | ldmat &_R; |
---|
| 1340 | //! Variable \f$ R_e \f$ |
---|
| 1341 | ldmat Re; |
---|
[737] | 1342 | public: |
---|
[1064] | 1343 | mlstudent () : mlnorm<ldmat, enorm> (), |
---|
[1066] | 1344 | Lambda (), _R ( iepdf._R() ) {} |
---|
[1064] | 1345 | //! constructor function |
---|
| 1346 | void set_parameters ( const mat &A0, const vec &mu0, const ldmat &R0, const ldmat& Lambda0 ) { |
---|
| 1347 | iepdf.set_parameters ( mu0, R0 );// was Lambda, why? |
---|
| 1348 | A = A0; |
---|
| 1349 | mu_const = mu0; |
---|
| 1350 | Re = R0; |
---|
| 1351 | Lambda = Lambda0; |
---|
| 1352 | } |
---|
[294] | 1353 | |
---|
[1064] | 1354 | void condition ( const vec &cond ); |
---|
[739] | 1355 | |
---|
[1064] | 1356 | void validate() { |
---|
| 1357 | mlnorm<ldmat, enorm>::validate(); |
---|
| 1358 | bdm_assert ( A.rows() == mu_const.length(), "mlstudent: A vs. mu mismatch" ); |
---|
| 1359 | bdm_assert ( _R.rows() == A.rows(), "mlstudent: A vs. R mismatch" ); |
---|
[737] | 1360 | |
---|
[1064] | 1361 | } |
---|
[488] | 1362 | }; |
---|
[811] | 1363 | |
---|
[488] | 1364 | /*! |
---|
| 1365 | \brief Gamma random walk |
---|
[198] | 1366 | |
---|
[488] | 1367 | Mean value, \f$\mu\f$, of this density is given by \c rvc . |
---|
| 1368 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
---|
| 1369 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
---|
[32] | 1370 | |
---|
[488] | 1371 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
---|
| 1372 | */ |
---|
[737] | 1373 | class mgamma : public pdf_internal<egamma> { |
---|
| 1374 | protected: |
---|
[461] | 1375 | |
---|
[1064] | 1376 | //! Constant \f$k\f$ |
---|
| 1377 | double k; |
---|
[461] | 1378 | |
---|
[1064] | 1379 | //! cache of iepdf.beta |
---|
| 1380 | vec &_beta; |
---|
[32] | 1381 | |
---|
[737] | 1382 | public: |
---|
[1064] | 1383 | //! Constructor |
---|
| 1384 | mgamma() : pdf_internal<egamma>(), k ( 0 ), |
---|
| 1385 | _beta ( iepdf._beta() ) { |
---|
| 1386 | } |
---|
[461] | 1387 | |
---|
[1064] | 1388 | //! Set value of \c k |
---|
| 1389 | void set_parameters ( double k, const vec &beta0 ); |
---|
[461] | 1390 | |
---|
[1064] | 1391 | void condition ( const vec &val ) { |
---|
| 1392 | _beta = k / val; |
---|
| 1393 | }; |
---|
[1068] | 1394 | |
---|
| 1395 | /*! Create object from the following structure |
---|
[1064] | 1396 | \code |
---|
[1068] | 1397 | class = 'mgamma'; |
---|
| 1398 | beta = [...]; % vector of initial beta |
---|
| 1399 | k = x; % multiplicative scalar constant k |
---|
| 1400 | --- inherited fields --- |
---|
| 1401 | bdm::pdf::from_setting |
---|
| 1402 | \endcode |
---|
| 1403 | fulfilling form \f[ f(rv|rvc) = \Gamma(k, k/rvc) \f] |
---|
[1064] | 1404 | */ |
---|
| 1405 | void from_setting ( const Setting &set ); |
---|
[1066] | 1406 | void to_setting (Setting &set) const; |
---|
[1064] | 1407 | void validate(); |
---|
[488] | 1408 | }; |
---|
[737] | 1409 | UIREGISTER ( mgamma ); |
---|
| 1410 | SHAREDPTR ( mgamma ); |
---|
[32] | 1411 | |
---|
[488] | 1412 | /*! |
---|
| 1413 | \brief Inverse-Gamma random walk |
---|
[225] | 1414 | |
---|
[488] | 1415 | Mean value, \f$ \mu \f$, of this density is given by \c rvc . |
---|
| 1416 | Standard deviation of the random walk is proportional to one \f$ k \f$-th the mean. |
---|
| 1417 | This is achieved by setting \f$ \alpha=\mu/k^2+2 \f$ and \f$ \beta=\mu(\alpha-1)\f$. |
---|
[461] | 1418 | |
---|
[488] | 1419 | The standard deviation of the walk is then: \f$ \mu/\sqrt(k)\f$. |
---|
| 1420 | */ |
---|
[737] | 1421 | class migamma : public pdf_internal<eigamma> { |
---|
| 1422 | protected: |
---|
[1064] | 1423 | //! Constant \f$k\f$ |
---|
| 1424 | double k; |
---|
[461] | 1425 | |
---|
[1064] | 1426 | //! cache of iepdf.alpha |
---|
| 1427 | vec &_alpha; |
---|
[225] | 1428 | |
---|
[1064] | 1429 | //! cache of iepdf.beta |
---|
| 1430 | vec &_beta; |
---|
[461] | 1431 | |
---|
[737] | 1432 | public: |
---|
[1064] | 1433 | //! \name Constructors |
---|
| 1434 | //!@{ |
---|
| 1435 | migamma() : pdf_internal<eigamma>(), |
---|
| 1436 | k ( 0 ), |
---|
| 1437 | _alpha ( iepdf._alpha() ), |
---|
| 1438 | _beta ( iepdf._beta() ) { |
---|
| 1439 | } |
---|
[225] | 1440 | |
---|
[1064] | 1441 | migamma ( const migamma &m ) : pdf_internal<eigamma>(), |
---|
| 1442 | k ( 0 ), |
---|
| 1443 | _alpha ( iepdf._alpha() ), |
---|
| 1444 | _beta ( iepdf._beta() ) { |
---|
| 1445 | } |
---|
| 1446 | //!@} |
---|
[225] | 1447 | |
---|
[1064] | 1448 | //! Set value of \c k |
---|
| 1449 | void set_parameters ( int len, double k0 ) { |
---|
| 1450 | k = k0; |
---|
| 1451 | iepdf.set_parameters ( ( 1.0 / ( k*k ) + 2.0 ) *ones ( len ) /*alpha*/, ones ( len ) /*beta*/ ); |
---|
| 1452 | }; |
---|
[878] | 1453 | |
---|
[1066] | 1454 | void validate () { |
---|
[1064] | 1455 | pdf_internal<eigamma>::validate(); |
---|
| 1456 | dimc = dimension(); |
---|
| 1457 | }; |
---|
[878] | 1458 | |
---|
[1064] | 1459 | void condition ( const vec &val ) { |
---|
| 1460 | _beta = elem_mult ( val, ( _alpha - 1.0 ) ); |
---|
| 1461 | }; |
---|
[488] | 1462 | }; |
---|
[357] | 1463 | |
---|
[488] | 1464 | /*! |
---|
| 1465 | \brief Gamma random walk around a fixed point |
---|
[60] | 1466 | |
---|
[488] | 1467 | 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 |
---|
| 1468 | \f[ \mu = \mu_{t-1} ^{l} p^{1-l}\f] |
---|
[60] | 1469 | |
---|
[488] | 1470 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
---|
| 1471 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
---|
[294] | 1472 | |
---|
[488] | 1473 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
---|
| 1474 | */ |
---|
[737] | 1475 | class mgamma_fix : public mgamma { |
---|
| 1476 | protected: |
---|
[1064] | 1477 | //! parameter l |
---|
| 1478 | double l; |
---|
| 1479 | //! reference vector |
---|
| 1480 | vec refl; |
---|
[737] | 1481 | public: |
---|
[1064] | 1482 | //! Constructor |
---|
| 1483 | mgamma_fix () : mgamma (), refl () {}; |
---|
| 1484 | //! Set value of \c k |
---|
| 1485 | void set_parameters ( double k0 , vec ref0, double l0 ) { |
---|
| 1486 | mgamma::set_parameters ( k0, ref0 ); |
---|
| 1487 | refl = pow ( ref0, 1.0 - l0 ); |
---|
| 1488 | l = l0; |
---|
| 1489 | }; |
---|
[878] | 1490 | |
---|
[1068] | 1491 | void validate () { |
---|
[1064] | 1492 | mgamma::validate(); |
---|
| 1493 | dimc = dimension(); |
---|
| 1494 | }; |
---|
[60] | 1495 | |
---|
[1064] | 1496 | void condition ( const vec &val ) { |
---|
| 1497 | vec mean = elem_mult ( refl, pow ( val, l ) ); |
---|
| 1498 | _beta = k / mean; |
---|
| 1499 | }; |
---|
[488] | 1500 | }; |
---|
[60] | 1501 | |
---|
[225] | 1502 | |
---|
[488] | 1503 | /*! |
---|
| 1504 | \brief Inverse-Gamma random walk around a fixed point |
---|
[225] | 1505 | |
---|
[488] | 1506 | 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 |
---|
| 1507 | \f[ \mu = \mu_{t-1} ^{l} p^{1-l}\f] |
---|
[225] | 1508 | |
---|
[488] | 1509 | ==== Check == vv = |
---|
| 1510 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
---|
| 1511 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
---|
[225] | 1512 | |
---|
[488] | 1513 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
---|
| 1514 | */ |
---|
[737] | 1515 | class migamma_ref : public migamma { |
---|
| 1516 | protected: |
---|
[1064] | 1517 | //! parameter l |
---|
| 1518 | double l; |
---|
| 1519 | //! reference vector |
---|
| 1520 | vec refl; |
---|
[737] | 1521 | public: |
---|
[1064] | 1522 | //! Constructor |
---|
| 1523 | migamma_ref () : migamma (), refl () {}; |
---|
[878] | 1524 | |
---|
[1064] | 1525 | //! Set value of \c k |
---|
| 1526 | void set_parameters ( double k0 , vec ref0, double l0 ) { |
---|
| 1527 | migamma::set_parameters ( ref0.length(), k0 ); |
---|
| 1528 | refl = pow ( ref0, 1.0 - l0 ); |
---|
| 1529 | l = l0; |
---|
| 1530 | }; |
---|
[357] | 1531 | |
---|
[1064] | 1532 | void validate() { |
---|
| 1533 | migamma::validate(); |
---|
| 1534 | dimc = dimension(); |
---|
| 1535 | }; |
---|
[357] | 1536 | |
---|
[1064] | 1537 | void condition ( const vec &val ) { |
---|
| 1538 | vec mean = elem_mult ( refl, pow ( val, l ) ); |
---|
| 1539 | migamma::condition ( mean ); |
---|
| 1540 | }; |
---|
[957] | 1541 | |
---|
[1068] | 1542 | /*! Create object from the following structure |
---|
[1064] | 1543 | \code |
---|
| 1544 | class = 'migamma_ref'; |
---|
[1068] | 1545 | ref = [...]; % reference vector |
---|
| 1546 | l = []; % constant scalar l |
---|
| 1547 | k = []; % constant scalar k |
---|
| 1548 | --- inherited fields --- |
---|
| 1549 | bdm::migamma::from_setting |
---|
[1064] | 1550 | \endcode |
---|
[1068] | 1551 | fulfilling form \f[ f(rv|rvc) = i\Gamma(k, k/(rvc^l \circ ref^{(1-l)}) \f] |
---|
[1064] | 1552 | */ |
---|
| 1553 | void from_setting ( const Setting &set ); |
---|
| 1554 | |
---|
| 1555 | void to_setting (Setting &set) const; |
---|
[488] | 1556 | }; |
---|
[357] | 1557 | |
---|
| 1558 | |
---|
[737] | 1559 | UIREGISTER ( migamma_ref ); |
---|
| 1560 | SHAREDPTR ( migamma_ref ); |
---|
[294] | 1561 | |
---|
[1068] | 1562 | /*! \brief Log-Normal probability density - it allows only diagonal covariances! |
---|
[294] | 1563 | |
---|
[488] | 1564 | Density of the form \f$ \log(x)\sim \mathcal{N}(\mu,\sigma^2) \f$ , i.e. |
---|
| 1565 | \f[ |
---|
| 1566 | x \sim \frac{1}{x\sigma\sqrt{2\pi}}\exp{-\frac{1}{2\sigma^2}(\log(x)-\mu)} |
---|
| 1567 | \f] |
---|
[294] | 1568 | |
---|
[621] | 1569 | Function from_setting loads mu and R in the same way as it does for enorm<>! |
---|
[488] | 1570 | */ |
---|
[737] | 1571 | class elognorm: public enorm<ldmat> { |
---|
| 1572 | public: |
---|
[1064] | 1573 | vec sample() const { |
---|
| 1574 | return exp ( enorm<ldmat>::sample() ); |
---|
| 1575 | }; |
---|
| 1576 | vec mean() const { |
---|
| 1577 | vec var = enorm<ldmat>::variance(); |
---|
| 1578 | return exp ( mu - 0.5*var ); |
---|
| 1579 | }; |
---|
[285] | 1580 | |
---|
[488] | 1581 | }; |
---|
[285] | 1582 | |
---|
[488] | 1583 | /*! |
---|
| 1584 | \brief Log-Normal random walk |
---|
[285] | 1585 | |
---|
[488] | 1586 | Mean value, \f$\mu\f$, is... |
---|
[285] | 1587 | |
---|
[488] | 1588 | */ |
---|
[737] | 1589 | class mlognorm : public pdf_internal<elognorm> { |
---|
| 1590 | protected: |
---|
[1064] | 1591 | //! parameter 1/2*sigma^2 |
---|
| 1592 | double sig2; |
---|
[461] | 1593 | |
---|
[1064] | 1594 | //! access |
---|
| 1595 | vec μ |
---|
[737] | 1596 | public: |
---|
[1064] | 1597 | //! Constructor |
---|
| 1598 | mlognorm() : pdf_internal<elognorm>(), |
---|
| 1599 | sig2 ( 0 ), |
---|
| 1600 | mu ( iepdf._mu() ) { |
---|
| 1601 | } |
---|
[285] | 1602 | |
---|
[1064] | 1603 | //! Set value of \c k |
---|
| 1604 | void set_parameters ( int size, double k ) { |
---|
| 1605 | sig2 = 0.5 * log ( k * k + 1 ); |
---|
| 1606 | iepdf.set_parameters ( zeros ( size ), 2*sig2*eye ( size ) ); |
---|
| 1607 | }; |
---|
[357] | 1608 | |
---|
[1064] | 1609 | void validate() { |
---|
| 1610 | pdf_internal<elognorm>::validate(); |
---|
| 1611 | dimc = iepdf.dimension(); |
---|
| 1612 | } |
---|
[357] | 1613 | |
---|
[1064] | 1614 | void condition ( const vec &val ) { |
---|
| 1615 | mu = log ( val ) - sig2;//elem_mult ( refl,pow ( val,l ) ); |
---|
| 1616 | }; |
---|
| 1617 | |
---|
[1068] | 1618 | /*! Create object from the following structure |
---|
[1064] | 1619 | \code |
---|
| 1620 | class = 'mlognorm'; |
---|
[1068] | 1621 | k = []; % "variance" k |
---|
| 1622 | mu0 = []; % initial value of mean |
---|
| 1623 | --- inherited fields --- |
---|
| 1624 | bdm::pdf_internal<elognorm>::from_setting |
---|
[1064] | 1625 | \endcode |
---|
[1068] | 1626 | fulfilling form \f[ f(rv|rvc) = log\mathcal{N}( \log(rvc)-0.5\log(k^2+1), k I) \f] |
---|
[1064] | 1627 | */ |
---|
| 1628 | void from_setting ( const Setting &set ); |
---|
| 1629 | |
---|
| 1630 | void to_setting (Setting &set) const; |
---|
[488] | 1631 | }; |
---|
[294] | 1632 | |
---|
[737] | 1633 | UIREGISTER ( mlognorm ); |
---|
| 1634 | SHAREDPTR ( mlognorm ); |
---|
[294] | 1635 | |
---|
[1068] | 1636 | /*! \brief Inverse Wishart density defined on Choleski decomposition |
---|
[1189] | 1637 | * |
---|
| 1638 | * here \f$\Omega \sim |\Sigma|^{-0.5(\delta}|\Omega|^{0.5(\delta -p -1)} \exp(-1/2 tr(\Omega\Sigma^{-1}))\$f |
---|
[488] | 1639 | */ |
---|
[737] | 1640 | class eWishartCh : public epdf { |
---|
| 1641 | protected: |
---|
[1064] | 1642 | //! Upper-Triagle of Choleski decomposition of \f$ \Psi \f$ |
---|
[1189] | 1643 | chmat Sigma; |
---|
[1064] | 1644 | //! dimension of matrix \f$ \Psi \f$ |
---|
| 1645 | int p; |
---|
| 1646 | //! degrees of freedom \f$ \nu \f$ |
---|
| 1647 | double delta; |
---|
[737] | 1648 | public: |
---|
[1064] | 1649 | //! Set internal structures |
---|
| 1650 | void set_parameters ( const mat &Y0, const double delta0 ) { |
---|
[1189] | 1651 | Sigma = chmat ( Y0 ); |
---|
[1064] | 1652 | delta = delta0; |
---|
[1189] | 1653 | p = Sigma.rows(); |
---|
[1064] | 1654 | } |
---|
| 1655 | //! Set internal structures |
---|
| 1656 | void set_parameters ( const chmat &Y0, const double delta0 ) { |
---|
[1189] | 1657 | Sigma = Y0; |
---|
[1064] | 1658 | delta = delta0; |
---|
[1189] | 1659 | p = Sigma.rows(); |
---|
[1064] | 1660 | } |
---|
[878] | 1661 | |
---|
[1064] | 1662 | virtual void validate () { |
---|
| 1663 | epdf::validate(); |
---|
| 1664 | dim = p * p; |
---|
| 1665 | } |
---|
[488] | 1666 | |
---|
[1189] | 1667 | //! Sample matrix argument - lower |
---|
| 1668 | //! Using Bartlet decomposition: W=L A A^T L^T where A is lower triag and L is choleski factor of Sigma. |
---|
| 1669 | chmat sample_mat() const { |
---|
| 1670 | mat A_T = zeros ( p, p ); // A transpose |
---|
[1064] | 1671 | |
---|
| 1672 | //sample diagonal |
---|
| 1673 | for ( int i = 0; i < p; i++ ) { |
---|
| 1674 | GamRNG.setup ( 0.5* ( delta - i ) , 0.5 ); // no +1 !! index if from 0 |
---|
[294] | 1675 | #pragma omp critical |
---|
[1189] | 1676 | A_T ( i, i ) = sqrt ( GamRNG() ); |
---|
[1064] | 1677 | } |
---|
| 1678 | //do the rest |
---|
| 1679 | for ( int i = 0; i < p; i++ ) { |
---|
| 1680 | for ( int j = i + 1; j < p; j++ ) { |
---|
[294] | 1681 | #pragma omp critical |
---|
[1189] | 1682 | A_T ( i, j ) = NorRNG.sample(); |
---|
[1064] | 1683 | } |
---|
| 1684 | } |
---|
[1189] | 1685 | chmat tmp; |
---|
| 1686 | tmp._Ch()=A_T*Sigma._Ch(); |
---|
| 1687 | return tmp;// return upper triangular part of the decomposition |
---|
[1064] | 1688 | } |
---|
[766] | 1689 | |
---|
[1064] | 1690 | vec sample () const { |
---|
[1189] | 1691 | return vec ( sample_mat().to_mat()._data(), p*p ); |
---|
[1064] | 1692 | } |
---|
[766] | 1693 | |
---|
[1064] | 1694 | virtual vec mean() const NOT_IMPLEMENTED(0); |
---|
[766] | 1695 | |
---|
[1064] | 1696 | //! return expected variance (not covariance!) |
---|
| 1697 | virtual vec variance() const NOT_IMPLEMENTED(0); |
---|
[766] | 1698 | |
---|
[1064] | 1699 | virtual double evallog ( const vec &val ) const NOT_IMPLEMENTED(0); |
---|
[766] | 1700 | |
---|
[1064] | 1701 | //! fast access function y0 will be copied into Y.Ch. |
---|
| 1702 | void setY ( const mat &Ch0 ) { |
---|
[1189] | 1703 | copy_vector ( dim, Ch0._data(), Sigma._Ch()._data() ); |
---|
[1064] | 1704 | } |
---|
[766] | 1705 | |
---|
[1064] | 1706 | //! fast access function y0 will be copied into Y.Ch. |
---|
| 1707 | void _setY ( const vec &ch0 ) { |
---|
[1189] | 1708 | copy_vector ( dim, ch0._data(), Sigma._Ch()._data() ); |
---|
[1064] | 1709 | } |
---|
[766] | 1710 | |
---|
[1064] | 1711 | //! access function |
---|
| 1712 | const chmat& getY() const { |
---|
[1189] | 1713 | return Sigma; |
---|
[1064] | 1714 | } |
---|
[488] | 1715 | }; |
---|
[294] | 1716 | |
---|
[536] | 1717 | //! Inverse Wishart on Choleski decomposition |
---|
| 1718 | /*! Being computed by conversion from `standard' Wishart |
---|
| 1719 | */ |
---|
[737] | 1720 | class eiWishartCh: public epdf { |
---|
| 1721 | protected: |
---|
[1064] | 1722 | //! Internal instance of Wishart density |
---|
| 1723 | eWishartCh W; |
---|
| 1724 | //! size of Ch |
---|
| 1725 | int p; |
---|
| 1726 | //! parameter delta |
---|
| 1727 | double delta; |
---|
[737] | 1728 | public: |
---|
[1064] | 1729 | //! constructor function |
---|
| 1730 | void set_parameters ( const mat &Y0, const double delta0 ) { |
---|
| 1731 | delta = delta0; |
---|
| 1732 | W.set_parameters ( inv ( Y0 ), delta0 ); |
---|
| 1733 | p = Y0.rows(); |
---|
| 1734 | } |
---|
[488] | 1735 | |
---|
[1066] | 1736 | virtual void validate () { |
---|
[1064] | 1737 | epdf::validate(); |
---|
| 1738 | W.validate(); |
---|
| 1739 | dim = W.dimension(); |
---|
| 1740 | } |
---|
[766] | 1741 | |
---|
[488] | 1742 | |
---|
[1064] | 1743 | vec sample() const { |
---|
| 1744 | mat iCh; |
---|
[1189] | 1745 | iCh = inv ( W.sample_mat()._Ch() ); |
---|
[1064] | 1746 | return vec ( iCh._data(), dim ); |
---|
| 1747 | } |
---|
| 1748 | //! access function |
---|
| 1749 | void _setY ( const vec &y0 ) { |
---|
| 1750 | mat Ch ( p, p ); |
---|
| 1751 | mat iCh ( p, p ); |
---|
| 1752 | copy_vector ( dim, y0._data(), Ch._data() ); |
---|
| 1753 | |
---|
| 1754 | iCh = inv ( Ch ); |
---|
| 1755 | W.setY ( iCh ); |
---|
| 1756 | } |
---|
| 1757 | |
---|
| 1758 | virtual double evallog ( const vec &val ) const { |
---|
| 1759 | chmat X ( p ); |
---|
| 1760 | const chmat& Y = W.getY(); |
---|
| 1761 | |
---|
| 1762 | copy_vector ( p*p, val._data(), X._Ch()._data() ); |
---|
| 1763 | chmat iX ( p ); |
---|
| 1764 | X.inv ( iX ); |
---|
| 1765 | // compute |
---|
[1066] | 1766 | // \frac{ |\Psi|^{m/2}|X|^{-(m+p+1)/2}e^{-tr(\Psi X^{-1})/2} }{ 2^{mp/2}\Gamma_p(m/2)}, |
---|
[1064] | 1767 | mat M = Y.to_mat() * iX.to_mat(); |
---|
[285] | 1768 | |
---|
[1064] | 1769 | double log1 = 0.5 * p * ( 2 * Y.logdet() ) - 0.5 * ( delta + p + 1 ) * ( 2 * X.logdet() ) - 0.5 * trace ( M ); |
---|
| 1770 | //Fixme! Multivariate gamma omitted!! it is ok for sampling, but not otherwise!! |
---|
[461] | 1771 | |
---|
[1066] | 1772 | /* if (0) { |
---|
| 1773 | mat XX=X.to_mat(); |
---|
| 1774 | mat YY=Y.to_mat(); |
---|
[461] | 1775 | |
---|
[1066] | 1776 | double log2 = 0.5*p*log(det(YY))-0.5*(delta+p+1)*log(det(XX))-0.5*trace(YY*inv(XX)); |
---|
| 1777 | cout << log1 << "," << log2 << endl; |
---|
| 1778 | }*/ |
---|
[1064] | 1779 | return log1; |
---|
| 1780 | }; |
---|
[285] | 1781 | |
---|
[1064] | 1782 | virtual vec mean() const NOT_IMPLEMENTED(0); |
---|
[766] | 1783 | |
---|
[1064] | 1784 | //! return expected variance (not covariance!) |
---|
| 1785 | virtual vec variance() const NOT_IMPLEMENTED(0); |
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[488] | 1786 | }; |
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| 1787 | |
---|
[536] | 1788 | //! Random Walk on inverse Wishart |
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[737] | 1789 | class rwiWishartCh : public pdf_internal<eiWishartCh> { |
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| 1790 | protected: |
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[1064] | 1791 | //!square root of \f$ \nu-p-1 \f$ - needed for computation of \f$ \Psi \f$ from conditions |
---|
| 1792 | double sqd; |
---|
| 1793 | //!reference point for diagonal |
---|
| 1794 | vec refl; |
---|
| 1795 | //! power of the reference |
---|
| 1796 | double l; |
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| 1797 | //! dimension |
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| 1798 | int p; |
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[488] | 1799 | |
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[737] | 1800 | public: |
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[1064] | 1801 | rwiWishartCh() : sqd ( 0 ), l ( 0 ), p ( 0 ) {} |
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| 1802 | //! constructor function |
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| 1803 | void set_parameters ( int p0, double k, vec ref0, double l0 ) { |
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| 1804 | p = p0; |
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| 1805 | double delta = 2 / ( k * k ) + p + 3; |
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| 1806 | sqd = sqrt ( delta - p - 1 ); |
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| 1807 | l = l0; |
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| 1808 | refl = pow ( ref0, 1 - l ); |
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| 1809 | iepdf.set_parameters ( eye ( p ), delta ); |
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| 1810 | }; |
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[285] | 1811 | |
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[1064] | 1812 | void validate() { |
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| 1813 | pdf_internal<eiWishartCh>::validate(); |
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| 1814 | dimc = iepdf.dimension(); |
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| 1815 | } |
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| 1816 | |
---|
| 1817 | void condition ( const vec &c ) { |
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| 1818 | vec z = c; |
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| 1819 | int ri = 0; |
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| 1820 | for ( int i = 0; i < p*p; i += ( p + 1 ) ) {//trace diagonal element |
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| 1821 | z ( i ) = pow ( z ( i ), l ) * refl ( ri ); |
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| 1822 | ri++; |
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| 1823 | } |
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| 1824 | |
---|
| 1825 | iepdf._setY ( sqd*z ); |
---|
| 1826 | } |
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[488] | 1827 | }; |
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| 1828 | |
---|
[32] | 1829 | //! Switch between various resampling methods. |
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[488] | 1830 | enum RESAMPLING_METHOD { MULTINOMIAL = 0, STRATIFIED = 1, SYSTEMATIC = 3 }; |
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[887] | 1831 | |
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[1064] | 1832 | //! Shortcut for multinomial.sample(int n). Various simplifications are allowed see RESAMPLING_METHOD |
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[887] | 1833 | void resample(const vec &w, ivec &ind, RESAMPLING_METHOD=SYSTEMATIC); |
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| 1834 | |
---|
[1063] | 1835 | /*! \brief Weighted empirical density |
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[32] | 1836 | |
---|
[488] | 1837 | Used e.g. in particle filters. |
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| 1838 | */ |
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[737] | 1839 | class eEmp: public epdf { |
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| 1840 | protected : |
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[1064] | 1841 | //! Number of particles |
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| 1842 | int n; |
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| 1843 | //! Sample weights \f$w\f$ |
---|
| 1844 | vec w; |
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| 1845 | //! Samples \f$x^{(i)}, i=1..n\f$ |
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| 1846 | Array<vec> samples; |
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[737] | 1847 | public: |
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[1064] | 1848 | //! \name Constructors |
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| 1849 | //!@{ |
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| 1850 | eEmp () : epdf (), w (), samples () {}; |
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| 1851 | //! copy constructor |
---|
| 1852 | eEmp ( const eEmp &e ) : epdf ( e ), w ( e.w ), samples ( e.samples ) {}; |
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| 1853 | //!@} |
---|
[280] | 1854 | |
---|
[1064] | 1855 | //! Set samples and weights |
---|
| 1856 | void set_statistics ( const vec &w0, const epdf &pdf0 ); |
---|
| 1857 | //! Set samples and weights |
---|
| 1858 | void set_statistics ( const epdf &pdf0 , int n ) { |
---|
| 1859 | set_statistics ( ones ( n ) / n, pdf0 ); |
---|
| 1860 | }; |
---|
| 1861 | //! Set sample |
---|
| 1862 | void set_samples ( const epdf* pdf0 ); |
---|
| 1863 | //! Set sample |
---|
| 1864 | void set_parameters ( int n0, bool copy = true ) { |
---|
| 1865 | n = n0; |
---|
| 1866 | w.set_size ( n0, copy ); |
---|
| 1867 | samples.set_size ( n0, copy ); |
---|
| 1868 | }; |
---|
| 1869 | //! Set samples |
---|
| 1870 | void set_parameters ( const Array<vec> &Av ) { |
---|
| 1871 | n = Av.size(); |
---|
| 1872 | w = 1 / n * ones ( n ); |
---|
| 1873 | samples = Av; |
---|
| 1874 | }; |
---|
[1066] | 1875 | virtual void validate (); |
---|
[1064] | 1876 | //! Potentially dangerous, use with care. |
---|
| 1877 | vec& _w() { |
---|
| 1878 | return w; |
---|
| 1879 | }; |
---|
| 1880 | //! Potentially dangerous, use with care. |
---|
| 1881 | const vec& _w() const { |
---|
| 1882 | return w; |
---|
| 1883 | }; |
---|
| 1884 | //! access function |
---|
| 1885 | Array<vec>& _samples() { |
---|
| 1886 | return samples; |
---|
| 1887 | }; |
---|
| 1888 | //! access function |
---|
| 1889 | const vec& _sample ( int i ) const { |
---|
| 1890 | return samples ( i ); |
---|
| 1891 | }; |
---|
| 1892 | //! access function |
---|
| 1893 | const Array<vec>& _samples() const { |
---|
| 1894 | return samples; |
---|
| 1895 | }; |
---|
| 1896 | //! 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. |
---|
| 1897 | void resample ( RESAMPLING_METHOD method = SYSTEMATIC ); |
---|
[565] | 1898 | |
---|
[1064] | 1899 | //! inherited operation : NOT implemented |
---|
| 1900 | vec sample() const NOT_IMPLEMENTED(0); |
---|
[565] | 1901 | |
---|
[1064] | 1902 | //! inherited operation : NOT implemented |
---|
| 1903 | double evallog ( const vec &val ) const NOT_IMPLEMENTED(0); |
---|
[737] | 1904 | |
---|
[1064] | 1905 | vec mean() const { |
---|
| 1906 | vec pom = zeros ( dim ); |
---|
| 1907 | for ( int i = 0; i < n; i++ ) { |
---|
| 1908 | pom += samples ( i ) * w ( i ); |
---|
| 1909 | } |
---|
| 1910 | return pom; |
---|
| 1911 | } |
---|
| 1912 | vec variance() const { |
---|
| 1913 | vec pom = zeros ( dim ); |
---|
| 1914 | for ( int i = 0; i < n; i++ ) { |
---|
| 1915 | pom += pow ( samples ( i ), 2 ) * w ( i ); |
---|
| 1916 | } |
---|
| 1917 | return pom - pow ( mean(), 2 ); |
---|
| 1918 | } |
---|
| 1919 | //! For this class, qbounds are minimum and maximum value of the population! |
---|
| 1920 | void qbounds ( vec &lb, vec &ub, double perc = 0.95 ) const; |
---|
[760] | 1921 | |
---|
[1064] | 1922 | void to_setting ( Setting &set ) const; |
---|
[1063] | 1923 | |
---|
[1064] | 1924 | /*! Create object from the following structure |
---|
| 1925 | |
---|
| 1926 | \code |
---|
| 1927 | class = 'eEmp'; |
---|
[1066] | 1928 | samples = [...]; % array of samples |
---|
| 1929 | w = [...]; % weights of samples stored in vector |
---|
[1064] | 1930 | --- inherited fields --- |
---|
| 1931 | bdm::epdf::from_setting |
---|
| 1932 | \endcode |
---|
| 1933 | */ |
---|
| 1934 | void from_setting ( const Setting &set ); |
---|
[488] | 1935 | }; |
---|
[760] | 1936 | UIREGISTER(eEmp); |
---|
[32] | 1937 | |
---|
| 1938 | |
---|
[8] | 1939 | //////////////////////// |
---|
| 1940 | |
---|
[488] | 1941 | template<class sq_T> |
---|
[737] | 1942 | void enorm<sq_T>::set_parameters ( const vec &mu0, const sq_T &R0 ) { |
---|
[28] | 1943 | //Fixme test dimensions of mu0 and R0; |
---|
[1064] | 1944 | mu = mu0; |
---|
| 1945 | R = R0; |
---|
| 1946 | validate(); |
---|
[488] | 1947 | }; |
---|
[8] | 1948 | |
---|
[488] | 1949 | template<class sq_T> |
---|
[737] | 1950 | void enorm<sq_T>::from_setting ( const Setting &set ) { |
---|
[1064] | 1951 | epdf::from_setting ( set ); //reads rv |
---|
[384] | 1952 | |
---|
[1064] | 1953 | UI::get ( mu, set, "mu", UI::compulsory ); |
---|
| 1954 | mat Rtmp;// necessary for conversion |
---|
| 1955 | UI::get ( Rtmp, set, "R", UI::compulsory ); |
---|
| 1956 | R = Rtmp; // conversion |
---|
[488] | 1957 | } |
---|
[8] | 1958 | |
---|
[488] | 1959 | template<class sq_T> |
---|
[956] | 1960 | void enorm<sq_T>::validate() { |
---|
[1064] | 1961 | eEF::validate(); |
---|
| 1962 | bdm_assert ( mu.length() == R.rows(), "mu and R parameters do not match" ); |
---|
| 1963 | dim = mu.length(); |
---|
| 1964 | } |
---|
[956] | 1965 | |
---|
| 1966 | template<class sq_T> |
---|
[773] | 1967 | void enorm<sq_T>::to_setting ( Setting &set ) const { |
---|
[1064] | 1968 | epdf::to_setting ( set ); //reads rv |
---|
| 1969 | UI::save ( mu, set, "mu"); |
---|
| 1970 | UI::save ( R.to_mat(), set, "R"); |
---|
[773] | 1971 | } |
---|
| 1972 | |
---|
[956] | 1973 | |
---|
| 1974 | |
---|
[773] | 1975 | template<class sq_T> |
---|
[737] | 1976 | void enorm<sq_T>::dupdate ( mat &v, double nu ) { |
---|
[1064] | 1977 | // |
---|
[488] | 1978 | }; |
---|
| 1979 | |
---|
[178] | 1980 | // template<class sq_T> |
---|
| 1981 | // void enorm<sq_T>::tupdate ( double phi, mat &vbar, double nubar ) { |
---|
[1066] | 1982 | // // |
---|
[178] | 1983 | // }; |
---|
[8] | 1984 | |
---|
[488] | 1985 | template<class sq_T> |
---|
[737] | 1986 | vec enorm<sq_T>::sample() const { |
---|
[1064] | 1987 | vec x ( dim ); |
---|
[270] | 1988 | #pragma omp critical |
---|
[1064] | 1989 | NorRNG.sample_vector ( dim, x ); |
---|
| 1990 | vec smp = R.sqrt_mult ( x ); |
---|
[12] | 1991 | |
---|
[1064] | 1992 | smp += mu; |
---|
| 1993 | return smp; |
---|
[488] | 1994 | }; |
---|
[8] | 1995 | |
---|
[214] | 1996 | // template<class sq_T> |
---|
| 1997 | // double enorm<sq_T>::eval ( const vec &val ) const { |
---|
[1066] | 1998 | // double pdfl,e; |
---|
| 1999 | // pdfl = evallog ( val ); |
---|
| 2000 | // e = exp ( pdfl ); |
---|
| 2001 | // return e; |
---|
[214] | 2002 | // }; |
---|
[8] | 2003 | |
---|
[488] | 2004 | template<class sq_T> |
---|
[737] | 2005 | double enorm<sq_T>::evallog_nn ( const vec &val ) const { |
---|
[1064] | 2006 | // 1.83787706640935 = log(2pi) |
---|
| 2007 | double tmp = -0.5 * ( R.invqform ( mu - val ) );// - lognc(); |
---|
| 2008 | return tmp; |
---|
[488] | 2009 | }; |
---|
[28] | 2010 | |
---|
[488] | 2011 | template<class sq_T> |
---|
[737] | 2012 | inline double enorm<sq_T>::lognc () const { |
---|
[1064] | 2013 | // 1.83787706640935 = log(2pi) |
---|
| 2014 | double tmp = 0.5 * ( R.cols() * 1.83787706640935 + R.logdet() ); |
---|
| 2015 | return tmp; |
---|
[488] | 2016 | }; |
---|
[28] | 2017 | |
---|
[8] | 2018 | |
---|
[192] | 2019 | // template<class sq_T> |
---|
| 2020 | // vec mlnorm<sq_T>::samplecond (const vec &cond, double &lik ) { |
---|
[1066] | 2021 | // this->condition ( cond ); |
---|
| 2022 | // vec smp = epdf.sample(); |
---|
| 2023 | // lik = epdf.eval ( smp ); |
---|
| 2024 | // return smp; |
---|
[192] | 2025 | // } |
---|
[8] | 2026 | |
---|
[192] | 2027 | // template<class sq_T> |
---|
| 2028 | // mat mlnorm<sq_T>::samplecond (const vec &cond, vec &lik, int n ) { |
---|
[1066] | 2029 | // int i; |
---|
| 2030 | // int dim = rv.count(); |
---|
| 2031 | // mat Smp ( dim,n ); |
---|
| 2032 | // vec smp ( dim ); |
---|
| 2033 | // this->condition ( cond ); |
---|
[198] | 2034 | // |
---|
[1066] | 2035 | // for ( i=0; i<n; i++ ) { |
---|
| 2036 | // smp = epdf.sample(); |
---|
| 2037 | // lik ( i ) = epdf.eval ( smp ); |
---|
| 2038 | // Smp.set_col ( i ,smp ); |
---|
| 2039 | // } |
---|
[198] | 2040 | // |
---|
[1066] | 2041 | // return Smp; |
---|
[192] | 2042 | // } |
---|
[28] | 2043 | |
---|
[8] | 2044 | |
---|
[488] | 2045 | template<class sq_T> |
---|
[737] | 2046 | shared_ptr<epdf> enorm<sq_T>::marginal ( const RV &rvn ) const { |
---|
[1064] | 2047 | enorm<sq_T> *tmp = new enorm<sq_T> (); |
---|
| 2048 | shared_ptr<epdf> narrow ( tmp ); |
---|
| 2049 | marginal ( rvn, *tmp ); |
---|
| 2050 | return narrow; |
---|
[504] | 2051 | } |
---|
| 2052 | |
---|
| 2053 | template<class sq_T> |
---|
[737] | 2054 | void enorm<sq_T>::marginal ( const RV &rvn, enorm<sq_T> &target ) const { |
---|
[1064] | 2055 | bdm_assert ( isnamed(), "rv description is not assigned" ); |
---|
| 2056 | ivec irvn = rvn.dataind ( rv ); |
---|
[178] | 2057 | |
---|
[1064] | 2058 | sq_T Rn ( R, irvn ); // select rows and columns of R |
---|
[280] | 2059 | |
---|
[1064] | 2060 | target.set_rv ( rvn ); |
---|
| 2061 | target.set_parameters ( mu ( irvn ), Rn ); |
---|
[488] | 2062 | } |
---|
[178] | 2063 | |
---|
[488] | 2064 | template<class sq_T> |
---|
[737] | 2065 | shared_ptr<pdf> enorm<sq_T>::condition ( const RV &rvn ) const { |
---|
[1064] | 2066 | mlnorm<sq_T> *tmp = new mlnorm<sq_T> (); |
---|
| 2067 | shared_ptr<pdf> narrow ( tmp ); |
---|
| 2068 | condition ( rvn, *tmp ); |
---|
| 2069 | return narrow; |
---|
[504] | 2070 | } |
---|
[178] | 2071 | |
---|
[504] | 2072 | template<class sq_T> |
---|
[737] | 2073 | void enorm<sq_T>::condition ( const RV &rvn, pdf &target ) const { |
---|
[1064] | 2074 | typedef mlnorm<sq_T> TMlnorm; |
---|
[504] | 2075 | |
---|
[1064] | 2076 | bdm_assert ( isnamed(), "rvs are not assigned" ); |
---|
| 2077 | TMlnorm &uptarget = dynamic_cast<TMlnorm &> ( target ); |
---|
[270] | 2078 | |
---|
[1064] | 2079 | RV rvc = rv.subt ( rvn ); |
---|
| 2080 | bdm_assert ( ( rvc._dsize() + rvn._dsize() == rv._dsize() ), "wrong rvn" ); |
---|
| 2081 | //Permutation vector of the new R |
---|
| 2082 | ivec irvn = rvn.dataind ( rv ); |
---|
| 2083 | ivec irvc = rvc.dataind ( rv ); |
---|
| 2084 | ivec perm = concat ( irvn , irvc ); |
---|
| 2085 | sq_T Rn ( R, perm ); |
---|
[178] | 2086 | |
---|
[1064] | 2087 | //fixme - could this be done in general for all sq_T? |
---|
| 2088 | mat S = Rn.to_mat(); |
---|
| 2089 | //fixme |
---|
| 2090 | int n = rvn._dsize() - 1; |
---|
| 2091 | int end = R.rows() - 1; |
---|
| 2092 | mat S11 = S.get ( 0, n, 0, n ); |
---|
| 2093 | mat S12 = S.get ( 0, n , rvn._dsize(), end ); |
---|
| 2094 | mat S22 = S.get ( rvn._dsize(), end, rvn._dsize(), end ); |
---|
[178] | 2095 | |
---|
[1064] | 2096 | vec mu1 = mu ( irvn ); |
---|
| 2097 | vec mu2 = mu ( irvc ); |
---|
| 2098 | mat A = S12 * inv ( S22 ); |
---|
| 2099 | sq_T R_n ( S11 - A *S12.T() ); |
---|
[178] | 2100 | |
---|
[1064] | 2101 | uptarget.set_rv ( rvn ); |
---|
| 2102 | uptarget.set_rvc ( rvc ); |
---|
| 2103 | uptarget.set_parameters ( A, mu1 - A*mu2, R_n ); |
---|
| 2104 | uptarget.validate(); |
---|
[488] | 2105 | } |
---|
[178] | 2106 | |
---|
[1063] | 2107 | /*! \brief Dirac delta function distribution */ |
---|
[1064] | 2108 | class dirac: public epdf { |
---|
| 2109 | public: |
---|
| 2110 | vec point; |
---|
| 2111 | public: |
---|
| 2112 | double evallog (const vec &dt) const { |
---|
| 2113 | return -inf; |
---|
| 2114 | } |
---|
| 2115 | vec mean () const { |
---|
| 2116 | return point; |
---|
| 2117 | } |
---|
| 2118 | vec variance () const { |
---|
| 2119 | return zeros(point.length()); |
---|
| 2120 | } |
---|
| 2121 | void qbounds ( vec &lb, vec &ub, double percentage = 0.95 ) const { |
---|
| 2122 | lb = point; |
---|
| 2123 | ub = point; |
---|
| 2124 | } |
---|
| 2125 | //! access |
---|
| 2126 | const vec& _point() { |
---|
| 2127 | return point; |
---|
| 2128 | } |
---|
| 2129 | void set_point(const vec& p) { |
---|
| 2130 | point =p; |
---|
| 2131 | dim=p.length(); |
---|
| 2132 | } |
---|
| 2133 | vec sample() const { |
---|
| 2134 | return point; |
---|
| 2135 | } |
---|
| 2136 | }; |
---|
[887] | 2137 | |
---|
[1063] | 2138 | |
---|
| 2139 | /////////// |
---|
| 2140 | |
---|
[488] | 2141 | template<class sq_T> |
---|
[737] | 2142 | void mgnorm<sq_T >::set_parameters ( const shared_ptr<fnc> &g0, const sq_T &R0 ) { |
---|
[1064] | 2143 | g = g0; |
---|
| 2144 | this->iepdf.set_parameters ( zeros ( g->dimension() ), R0 ); |
---|
[527] | 2145 | } |
---|
| 2146 | |
---|
[488] | 2147 | template<class sq_T> |
---|
[737] | 2148 | void mgnorm<sq_T >::condition ( const vec &cond ) { |
---|
[1064] | 2149 | this->iepdf._mu() = g->eval ( cond ); |
---|
[737] | 2150 | }; |
---|
[28] | 2151 | |
---|
[1077] | 2152 | //! odo unify this stuff with to_string() |
---|
[488] | 2153 | template<class sq_T> |
---|
[737] | 2154 | std::ostream &operator<< ( std::ostream &os, mlnorm<sq_T> &ml ) { |
---|
[1064] | 2155 | os << "A:" << ml.A << endl; |
---|
| 2156 | os << "mu:" << ml.mu_const << endl; |
---|
| 2157 | os << "R:" << ml._R() << endl; |
---|
| 2158 | return os; |
---|
[488] | 2159 | }; |
---|
[28] | 2160 | |
---|
[254] | 2161 | } |
---|
[8] | 2162 | #endif //EF_H |
---|