[107] | 1 | /*! |
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| 2 | \file |
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| 3 | \brief Probability distributions for Mixtures of pdfs |
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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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[394] | 13 | #ifndef EMIX_H |
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| 14 | #define EMIX_H |
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[107] | 15 | |
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[477] | 16 | #define LOG2 0.69314718055995 |
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[333] | 17 | |
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[461] | 18 | #include "../shared_ptr.h" |
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[384] | 19 | #include "exp_family.h" |
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[107] | 20 | |
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[286] | 21 | namespace bdm { |
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[107] | 22 | |
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[182] | 23 | //this comes first because it is used inside emix! |
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| 24 | |
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| 25 | /*! \brief Class representing ratio of two densities |
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| 26 | which arise e.g. by applying the Bayes rule. |
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| 27 | It represents density in the form: |
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| 28 | \f[ |
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| 29 | f(rv|rvc) = \frac{f(rv,rvc)}{f(rvc)} |
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| 30 | \f] |
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| 31 | where \f$ f(rvc) = \int f(rv,rvc) d\ rv \f$. |
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| 32 | |
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| 33 | In particular this type of arise by conditioning of a mixture model. |
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| 34 | |
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[211] | 35 | At present the only supported operation is evallogcond(). |
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[182] | 36 | */ |
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[693] | 37 | class mratio: public pdf { |
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[192] | 38 | protected: |
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[693] | 39 | //! Nominator in the form of pdf |
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[192] | 40 | const epdf* nom; |
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[504] | 41 | |
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[182] | 42 | //!Denominator in the form of epdf |
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[504] | 43 | shared_ptr<epdf> den; |
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| 44 | |
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[192] | 45 | //!flag for destructor |
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| 46 | bool destroynom; |
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[193] | 47 | //!datalink between conditional and nom |
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| 48 | datalink_m2e dl; |
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[192] | 49 | public: |
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| 50 | //!Default constructor. By default, the given epdf is not copied! |
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[182] | 51 | //! It is assumed that this function will be used only temporarily. |
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[693] | 52 | mratio ( const epdf* nom0, const RV &rv, bool copy = false ) : pdf ( ), dl ( ) { |
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[286] | 53 | // adjust rv and rvc |
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[675] | 54 | |
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[766] | 55 | set_rv ( rv ); |
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[675] | 56 | dim = rv._dsize(); |
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| 57 | |
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[286] | 58 | rvc = nom0->_rv().subt ( rv ); |
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| 59 | dimc = rvc._dsize(); |
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[737] | 60 | |
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[286] | 61 | //prepare data structures |
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[477] | 62 | if ( copy ) { |
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[565] | 63 | bdm_error ( "todo" ); |
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| 64 | // destroynom = true; |
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[477] | 65 | } else { |
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| 66 | nom = nom0; |
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| 67 | destroynom = false; |
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| 68 | } |
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[565] | 69 | bdm_assert_debug ( rvc.length() > 0, "Makes no sense to use this object!" ); |
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[477] | 70 | |
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[286] | 71 | // build denominator |
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[192] | 72 | den = nom->marginal ( rvc ); |
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[477] | 73 | dl.set_connection ( rv, rvc, nom0->_rv() ); |
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[192] | 74 | }; |
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[675] | 75 | |
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[211] | 76 | double evallogcond ( const vec &val, const vec &cond ) { |
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[214] | 77 | double tmp; |
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[487] | 78 | vec nom_val ( dimension() + dimc ); |
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[477] | 79 | dl.pushup_cond ( nom_val, val, cond ); |
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[214] | 80 | tmp = exp ( nom->evallog ( nom_val ) - den->evallog ( cond ) ); |
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| 81 | return tmp; |
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[192] | 82 | } |
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[766] | 83 | |
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| 84 | //! Returns a sample from the density conditioned on \c cond, \f$x \sim epdf(rv|cond)\f$. \param cond is numeric value of \c rv |
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| 85 | virtual vec samplecond ( const vec &cond ) NOT_IMPLEMENTED(0); |
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| 86 | |
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[182] | 87 | //! Object takes ownership of nom and will destroy it |
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[477] | 88 | void ownnom() { |
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| 89 | destroynom = true; |
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| 90 | } |
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[182] | 91 | //! Default destructor |
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[477] | 92 | ~mratio() { |
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| 93 | if ( destroynom ) { |
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| 94 | delete nom; |
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| 95 | } |
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| 96 | } |
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[550] | 97 | |
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[766] | 98 | |
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| 99 | |
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| 100 | |
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[550] | 101 | private: |
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| 102 | // not implemented |
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| 103 | mratio ( const mratio & ); |
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[737] | 104 | mratio &operator= ( const mratio & ); |
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[182] | 105 | }; |
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| 106 | |
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[107] | 107 | /*! |
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| 108 | * \brief Mixture of epdfs |
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| 109 | |
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| 110 | Density function: |
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| 111 | \f[ |
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| 112 | f(x) = \sum_{i=1}^{n} w_{i} f_i(x), \quad \sum_{i=1}^n w_i = 1. |
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| 113 | \f] |
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| 114 | where \f$f_i(x)\f$ is any density on random variable \f$x\f$, called \a component, |
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| 115 | |
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| 116 | */ |
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[145] | 117 | class emix : public epdf { |
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[162] | 118 | protected: |
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| 119 | //! weights of the components |
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| 120 | vec w; |
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[559] | 121 | |
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[162] | 122 | //! Component (epdfs) |
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[504] | 123 | Array<shared_ptr<epdf> > Coms; |
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| 124 | |
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[162] | 125 | public: |
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[559] | 126 | //! Default constructor |
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| 127 | emix ( ) : epdf ( ) { } |
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| 128 | |
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[750] | 129 | virtual void validate (); |
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[107] | 130 | |
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[162] | 131 | vec sample() const; |
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[715] | 132 | |
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[739] | 133 | vec mean() const; |
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[715] | 134 | |
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[739] | 135 | vec variance() const; |
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| 136 | |
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| 137 | double evallog ( const vec &val ) const; |
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| 138 | |
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| 139 | vec evallog_mat ( const mat &Val ) const; |
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| 140 | |
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[214] | 141 | //! Auxiliary function that returns pdflog for each component |
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[739] | 142 | mat evallog_coms ( const mat &Val ) const; |
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[107] | 143 | |
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[504] | 144 | shared_ptr<epdf> marginal ( const RV &rv ) const; |
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[536] | 145 | //! Update already existing marginal density \c target |
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[504] | 146 | void marginal ( const RV &rv, emix &target ) const; |
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[693] | 147 | shared_ptr<pdf> condition ( const RV &rv ) const; |
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[182] | 148 | |
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[766] | 149 | //Access methods |
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| 150 | //! returns a reference to the internal weights. Use with Care! |
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[477] | 151 | vec& _w() { |
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| 152 | return w; |
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| 153 | } |
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[204] | 154 | |
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[766] | 155 | /*! |
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| 156 | \brief returns a reference to the internal array of components. Use with Care! Set components \c Coms |
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| 157 | |
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| 158 | Shared pointers in Coms are kept inside this instance and |
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| 159 | shouldn't be modified after being passed to this method. |
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| 160 | */ |
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[775] | 161 | Array<shared_ptr<epdf> >& _Coms ( ) { |
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[766] | 162 | return Coms; |
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| 163 | } |
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| 164 | |
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| 165 | //! returns a reference to the internal components specified by index i. Use with Care! |
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[504] | 166 | shared_ptr<epdf> _Coms ( int i ) { |
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[477] | 167 | return Coms ( i ); |
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[286] | 168 | } |
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[504] | 169 | |
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[477] | 170 | void set_rv ( const RV &rv ) { |
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| 171 | epdf::set_rv ( rv ); |
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| 172 | for ( int i = 0; i < Coms.length(); i++ ) { |
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| 173 | Coms ( i )->set_rv ( rv ); |
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| 174 | } |
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| 175 | } |
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[713] | 176 | |
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| 177 | //! Load from structure with elements: |
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| 178 | //! \code |
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| 179 | //! { class='emix'; |
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| 180 | //! pdfs = (..., ...); // list of pdfs in the mixture |
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| 181 | //! weights = ( 0.5, 0.5 ); // weights of pdfs in the mixture |
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| 182 | //! } |
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| 183 | //! \endcode |
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| 184 | //!@} |
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[766] | 185 | void from_setting ( const Setting &set ); |
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[107] | 186 | }; |
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[737] | 187 | SHAREDPTR ( emix ); |
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[713] | 188 | UIREGISTER ( emix ); |
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[107] | 189 | |
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[333] | 190 | /*! |
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| 191 | * \brief Mixture of egiws |
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| 192 | |
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| 193 | */ |
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| 194 | class egiwmix : public egiw { |
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| 195 | protected: |
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| 196 | //! weights of the components |
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| 197 | vec w; |
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| 198 | //! Component (epdfs) |
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| 199 | Array<egiw*> Coms; |
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| 200 | //!Flag if owning Coms |
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| 201 | bool destroyComs; |
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| 202 | public: |
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| 203 | //!Default constructor |
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| 204 | egiwmix ( ) : egiw ( ) {}; |
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| 205 | |
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| 206 | //! Set weights \c w and components \c Coms |
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| 207 | //!By default Coms are copied inside. Parameter \c copy can be set to false if Coms live externally. Use method ownComs() if Coms should be destroyed by the destructor. |
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[477] | 208 | void set_parameters ( const vec &w, const Array<egiw*> &Coms, bool copy = false ); |
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[878] | 209 | |
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[333] | 210 | //!return expected value |
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[878] | 211 | void validate(); |
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| 212 | |
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[333] | 213 | vec mean() const; |
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| 214 | |
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| 215 | //!return a sample from the density |
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| 216 | vec sample() const; |
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| 217 | |
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| 218 | //!return the expected variance |
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[477] | 219 | vec variance() const; |
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[333] | 220 | |
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| 221 | // TODO!!! Defined to follow ANSI and/or for future development |
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| 222 | void mean_mat ( mat &M, mat&R ) const {}; |
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[477] | 223 | double evallog_nn ( const vec &val ) const { |
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| 224 | return 0; |
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| 225 | }; |
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| 226 | double lognc () const { |
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| 227 | return 0; |
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[504] | 228 | } |
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[333] | 229 | |
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[504] | 230 | shared_ptr<epdf> marginal ( const RV &rv ) const; |
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[660] | 231 | //! marginal density update |
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[504] | 232 | void marginal ( const RV &rv, emix &target ) const; |
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| 233 | |
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[333] | 234 | //Access methods |
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| 235 | //! returns a pointer to the internal mean value. Use with Care! |
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[477] | 236 | vec& _w() { |
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| 237 | return w; |
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| 238 | } |
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| 239 | virtual ~egiwmix() { |
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| 240 | if ( destroyComs ) { |
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| 241 | for ( int i = 0; i < Coms.length(); i++ ) { |
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| 242 | delete Coms ( i ); |
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| 243 | } |
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| 244 | } |
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| 245 | } |
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[333] | 246 | //! Auxiliary function for taking ownership of the Coms() |
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[477] | 247 | void ownComs() { |
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| 248 | destroyComs = true; |
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| 249 | } |
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[333] | 250 | |
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| 251 | //!access function |
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[477] | 252 | egiw* _Coms ( int i ) { |
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| 253 | return Coms ( i ); |
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| 254 | } |
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[333] | 255 | |
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[477] | 256 | void set_rv ( const RV &rv ) { |
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| 257 | egiw::set_rv ( rv ); |
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| 258 | for ( int i = 0; i < Coms.length(); i++ ) { |
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| 259 | Coms ( i )->set_rv ( rv ); |
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| 260 | } |
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[333] | 261 | } |
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| 262 | |
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| 263 | //! Approximation of a GiW mix by a single GiW pdf |
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| 264 | egiw* approx(); |
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| 265 | }; |
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| 266 | |
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[115] | 267 | /*! \brief Chain rule decomposition of epdf |
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| 268 | |
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[145] | 269 | Probability density in the form of Chain-rule decomposition: |
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| 270 | \[ |
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| 271 | f(x_1,x_2,x_3) = f(x_1|x_2,x_3)f(x_2,x_3)f(x_3) |
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| 272 | \] |
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| 273 | Note that |
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[115] | 274 | */ |
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[693] | 275 | class mprod: public pdf { |
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[507] | 276 | private: |
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[693] | 277 | Array<shared_ptr<pdf> > pdfs; |
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[507] | 278 | |
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[693] | 279 | //! Data link for each pdfs |
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[546] | 280 | Array<shared_ptr<datalink_m2m> > dls; |
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[461] | 281 | |
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[162] | 282 | public: |
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[507] | 283 | //! \brief Default constructor |
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| 284 | mprod() { } |
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| 285 | |
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| 286 | /*!\brief Constructor from list of mFacs |
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[165] | 287 | */ |
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[693] | 288 | mprod ( const Array<shared_ptr<pdf> > &mFacs ) { |
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[477] | 289 | set_elements ( mFacs ); |
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[461] | 290 | } |
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[693] | 291 | //! Set internal \c pdfs from given values |
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[737] | 292 | void set_elements ( const Array<shared_ptr<pdf> > &mFacs ); |
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[477] | 293 | |
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[739] | 294 | double evallogcond ( const vec &val, const vec &cond ); |
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[395] | 295 | |
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[739] | 296 | vec evallogcond_mat ( const mat &Dt, const vec &cond ); |
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[395] | 297 | |
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[739] | 298 | vec evallogcond_mat ( const Array<vec> &Dt, const vec &cond ); |
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| 299 | |
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[270] | 300 | //TODO smarter... |
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| 301 | vec samplecond ( const vec &cond ) { |
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[477] | 302 | //! Ugly hack to help to discover if mpfs are not in proper order. Correct solution = check that explicitely. |
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[487] | 303 | vec smp = std::numeric_limits<double>::infinity() * ones ( dimension() ); |
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[165] | 304 | vec smpi; |
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[192] | 305 | // Hard assumption here!!! We are going backwards, to assure that samples that are needed from smp are already generated! |
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[693] | 306 | for ( int i = ( pdfs.length() - 1 ); i >= 0; i-- ) { |
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| 307 | // generate contribution of this pdf |
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[737] | 308 | smpi = pdfs ( i )->samplecond ( dls ( i )->get_cond ( smp , cond ) ); |
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[162] | 309 | // copy contribution of this pdf into smp |
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[270] | 310 | dls ( i )->pushup ( smp, smpi ); |
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[145] | 311 | } |
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[162] | 312 | return smp; |
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| 313 | } |
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| 314 | |
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[395] | 315 | //! Load from structure with elements: |
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| 316 | //! \code |
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| 317 | //! { class='mprod'; |
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[693] | 318 | //! pdfs = (..., ...); // list of pdfs in the order of chain rule |
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[395] | 319 | //! } |
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| 320 | //! \endcode |
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| 321 | //!@} |
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[477] | 322 | void from_setting ( const Setting &set ) { |
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[766] | 323 | Array<shared_ptr<pdf> > temp_array; |
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| 324 | UI::get ( temp_array, set, "pdfs", UI::compulsory ); |
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| 325 | set_elements ( temp_array ); |
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[395] | 326 | } |
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[107] | 327 | }; |
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[477] | 328 | UIREGISTER ( mprod ); |
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[529] | 329 | SHAREDPTR ( mprod ); |
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[107] | 330 | |
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[168] | 331 | //! Product of independent epdfs. For dependent pdfs, use mprod. |
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| 332 | class eprod: public epdf { |
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| 333 | protected: |
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| 334 | //! Components (epdfs) |
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[170] | 335 | Array<const epdf*> epdfs; |
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[168] | 336 | //! Array of indeces |
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[270] | 337 | Array<datalink*> dls; |
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[168] | 338 | public: |
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[536] | 339 | //! Default constructor |
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[477] | 340 | eprod () : epdfs ( 0 ), dls ( 0 ) {}; |
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[737] | 341 | //! Set internal |
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[477] | 342 | void set_parameters ( const Array<const epdf*> &epdfs0, bool named = true ) { |
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| 343 | epdfs = epdfs0;//.set_length ( epdfs0.length() ); |
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[286] | 344 | dls.set_length ( epdfs.length() ); |
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[477] | 345 | bool independent = true; |
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[286] | 346 | if ( named ) { |
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[477] | 347 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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| 348 | independent = rv.add ( epdfs ( i )->_rv() ); |
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[565] | 349 | bdm_assert_debug ( independent, "eprod:: given components are not independent." ); |
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[286] | 350 | } |
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[477] | 351 | dim = rv._dsize(); |
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[878] | 352 | |
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[477] | 353 | } else { |
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| 354 | dim = 0; |
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| 355 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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| 356 | dim += epdfs ( i )->dimension(); |
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[286] | 357 | } |
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[204] | 358 | } |
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[286] | 359 | // |
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[477] | 360 | int cumdim = 0; |
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| 361 | int dimi = 0; |
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[286] | 362 | int i; |
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[477] | 363 | for ( i = 0; i < epdfs.length(); i++ ) { |
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[286] | 364 | dls ( i ) = new datalink; |
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[477] | 365 | if ( named ) { |
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| 366 | dls ( i )->set_connection ( epdfs ( i )->_rv() , rv ); |
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| 367 | } else { |
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[286] | 368 | dimi = epdfs ( i )->dimension(); |
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[477] | 369 | dls ( i )->set_connection ( dimi, dim, linspace ( cumdim, cumdim + dimi - 1 ) ); |
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| 370 | cumdim += dimi; |
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[286] | 371 | } |
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| 372 | } |
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[878] | 373 | |
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[168] | 374 | } |
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| 375 | |
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[878] | 376 | |
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[739] | 377 | vec mean() const; |
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| 378 | |
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| 379 | vec variance() const; |
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| 380 | |
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| 381 | vec sample() const; |
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| 382 | |
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| 383 | double evallog ( const vec &val ) const; |
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| 384 | |
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[170] | 385 | //!access function |
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[477] | 386 | const epdf* operator () ( int i ) const { |
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[565] | 387 | bdm_assert_debug ( i < epdfs.length(), "wrong index" ); |
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[477] | 388 | return epdfs ( i ); |
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| 389 | } |
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[204] | 390 | |
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[193] | 391 | //!Destructor |
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[477] | 392 | ~eprod() { |
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| 393 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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| 394 | delete dls ( i ); |
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| 395 | } |
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| 396 | } |
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[168] | 397 | }; |
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| 398 | |
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| 399 | |
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[693] | 400 | /*! \brief Mixture of pdfs with constant weights, all pdfs are of equal RV and RVC |
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[124] | 401 | |
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| 402 | */ |
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[693] | 403 | class mmix : public pdf { |
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[488] | 404 | protected: |
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[693] | 405 | //! Component (pdfs) |
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| 406 | Array<shared_ptr<pdf> > Coms; |
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[488] | 407 | //!weights of the components |
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| 408 | vec w; |
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| 409 | public: |
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| 410 | //!Default constructor |
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[878] | 411 | mmix() : Coms ( 0 ) { }; |
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[461] | 412 | |
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[878] | 413 | |
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| 414 | |
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| 415 | |
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| 416 | |
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| 417 | |
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[737] | 418 | double evallogcond ( const vec &dt, const vec &cond ) { |
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| 419 | double ll = 0.0; |
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| 420 | for ( int i = 0; i < Coms.length(); i++ ) { |
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| 421 | ll += Coms ( i )->evallogcond ( dt, cond ); |
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[488] | 422 | } |
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| 423 | return ll; |
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| 424 | } |
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| 425 | |
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[737] | 426 | vec samplecond ( const vec &cond ); |
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[488] | 427 | |
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[711] | 428 | //! Load from structure with elements: |
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| 429 | //! \code |
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| 430 | //! { class='mmix'; |
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| 431 | //! pdfs = (..., ...); // list of pdfs in the mixture |
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| 432 | //! weights = ( 0.5, 0.5 ); // weights of pdfs in the mixture |
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| 433 | //! } |
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| 434 | //! \endcode |
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| 435 | //!@} |
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[766] | 436 | void from_setting ( const Setting &set ); |
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[711] | 437 | |
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[766] | 438 | virtual void validate(); |
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[488] | 439 | }; |
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[737] | 440 | SHAREDPTR ( mmix ); |
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[711] | 441 | UIREGISTER ( mmix ); |
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[488] | 442 | |
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[254] | 443 | } |
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[107] | 444 | #endif //MX_H |
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