[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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| 37 | class mratio: public mpdf { |
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[192] | 38 | protected: |
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[182] | 39 | //! Nominator in the form of mpdf |
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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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[487] | 49 | //! dummy epdf that stores only rv and dim |
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| 50 | epdf iepdf; |
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[192] | 51 | public: |
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| 52 | //!Default constructor. By default, the given epdf is not copied! |
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[182] | 53 | //! It is assumed that this function will be used only temporarily. |
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[487] | 54 | mratio ( const epdf* nom0, const RV &rv, bool copy = false ) : mpdf ( ), dl ( ),iepdf() { |
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[286] | 55 | // adjust rv and rvc |
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| 56 | rvc = nom0->_rv().subt ( rv ); |
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| 57 | dimc = rvc._dsize(); |
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[487] | 58 | set_ep ( iepdf ); |
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| 59 | iepdf.set_parameters ( rv._dsize() ); |
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| 60 | iepdf.set_rv ( rv ); |
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[477] | 61 | |
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[286] | 62 | //prepare data structures |
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[477] | 63 | if ( copy ) { |
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| 64 | it_error ( "todo" ); |
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| 65 | destroynom = true; |
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| 66 | } else { |
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| 67 | nom = nom0; |
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| 68 | destroynom = false; |
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| 69 | } |
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| 70 | it_assert_debug ( rvc.length() > 0, "Makes no sense to use this object!" ); |
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| 71 | |
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[286] | 72 | // build denominator |
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[192] | 73 | den = nom->marginal ( rvc ); |
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[477] | 74 | dl.set_connection ( rv, rvc, nom0->_rv() ); |
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[192] | 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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[182] | 83 | //! Object takes ownership of nom and will destroy it |
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[477] | 84 | void ownnom() { |
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| 85 | destroynom = true; |
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| 86 | } |
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[182] | 87 | //! Default destructor |
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[477] | 88 | ~mratio() { |
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| 89 | if ( destroynom ) { |
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| 90 | delete nom; |
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| 91 | } |
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| 92 | } |
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[182] | 93 | }; |
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| 94 | |
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[107] | 95 | /*! |
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| 96 | * \brief Mixture of epdfs |
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| 97 | |
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| 98 | Density function: |
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| 99 | \f[ |
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| 100 | f(x) = \sum_{i=1}^{n} w_{i} f_i(x), \quad \sum_{i=1}^n w_i = 1. |
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| 101 | \f] |
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| 102 | where \f$f_i(x)\f$ is any density on random variable \f$x\f$, called \a component, |
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| 103 | |
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| 104 | */ |
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[145] | 105 | class emix : public epdf { |
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[162] | 106 | protected: |
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| 107 | //! weights of the components |
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| 108 | vec w; |
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| 109 | //! Component (epdfs) |
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[504] | 110 | Array<shared_ptr<epdf> > Coms; |
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| 111 | |
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[162] | 112 | public: |
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| 113 | //!Default constructor |
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[286] | 114 | emix ( ) : epdf ( ) {}; |
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[182] | 115 | //! Set weights \c w and components \c Coms |
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[224] | 116 | //!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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[504] | 117 | void set_parameters ( const vec &w, const Array<shared_ptr<epdf> > &Coms ); |
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[107] | 118 | |
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[162] | 119 | vec sample() const; |
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| 120 | vec mean() const { |
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[477] | 121 | int i; |
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| 122 | vec mu = zeros ( dim ); |
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| 123 | for ( i = 0; i < w.length(); i++ ) { |
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| 124 | mu += w ( i ) * Coms ( i )->mean(); |
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| 125 | } |
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[162] | 126 | return mu; |
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| 127 | } |
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[229] | 128 | vec variance() const { |
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| 129 | //non-central moment |
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[286] | 130 | vec mom2 = zeros ( dim ); |
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[477] | 131 | for ( int i = 0; i < w.length(); i++ ) { |
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| 132 | mom2 += w ( i ) * ( Coms ( i )->variance() + pow ( Coms ( i )->mean(), 2 ) ); |
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| 133 | } |
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[229] | 134 | //central moment |
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[477] | 135 | return mom2 - pow ( mean(), 2 ); |
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[229] | 136 | } |
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[211] | 137 | double evallog ( const vec &val ) const { |
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[162] | 138 | int i; |
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| 139 | double sum = 0.0; |
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[477] | 140 | for ( i = 0; i < w.length(); i++ ) { |
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| 141 | sum += w ( i ) * exp ( Coms ( i )->evallog ( val ) ); |
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| 142 | } |
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| 143 | if ( sum == 0.0 ) { |
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| 144 | sum = std::numeric_limits<double>::epsilon(); |
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| 145 | } |
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| 146 | double tmp = log ( sum ); |
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| 147 | it_assert_debug ( std::isfinite ( tmp ), "Infinite" ); |
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[214] | 148 | return tmp; |
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[162] | 149 | }; |
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[211] | 150 | vec evallog_m ( const mat &Val ) const { |
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[477] | 151 | vec x = zeros ( Val.cols() ); |
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[192] | 152 | for ( int i = 0; i < w.length(); i++ ) { |
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[477] | 153 | x += w ( i ) * exp ( Coms ( i )->evallog_m ( Val ) ); |
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[182] | 154 | } |
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[192] | 155 | return log ( x ); |
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[182] | 156 | }; |
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[214] | 157 | //! Auxiliary function that returns pdflog for each component |
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[211] | 158 | mat evallog_M ( const mat &Val ) const { |
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[192] | 159 | mat X ( w.length(), Val.cols() ); |
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| 160 | for ( int i = 0; i < w.length(); i++ ) { |
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[211] | 161 | X.set_row ( i, w ( i ) *exp ( Coms ( i )->evallog_m ( Val ) ) ); |
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[189] | 162 | } |
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| 163 | return X; |
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| 164 | }; |
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[107] | 165 | |
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[504] | 166 | shared_ptr<epdf> marginal ( const RV &rv ) const; |
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| 167 | void marginal ( const RV &rv, emix &target ) const; |
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| 168 | shared_ptr<mpdf> condition ( const RV &rv ) const; |
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[182] | 169 | |
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[107] | 170 | //Access methods |
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[162] | 171 | //! returns a pointer to the internal mean value. Use with Care! |
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[477] | 172 | vec& _w() { |
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| 173 | return w; |
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| 174 | } |
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[204] | 175 | |
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[193] | 176 | //!access function |
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[504] | 177 | shared_ptr<epdf> _Coms ( int i ) { |
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[477] | 178 | return Coms ( i ); |
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[286] | 179 | } |
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[504] | 180 | |
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[477] | 181 | void set_rv ( const RV &rv ) { |
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| 182 | epdf::set_rv ( rv ); |
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| 183 | for ( int i = 0; i < Coms.length(); i++ ) { |
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| 184 | Coms ( i )->set_rv ( rv ); |
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| 185 | } |
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| 186 | } |
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[107] | 187 | }; |
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| 188 | |
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[333] | 189 | |
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| 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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[333] | 209 | |
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| 210 | //!return expected value |
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| 211 | vec mean() const; |
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| 212 | |
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| 213 | //!return a sample from the density |
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| 214 | vec sample() const; |
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| 215 | |
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| 216 | //!return the expected variance |
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[477] | 217 | vec variance() const; |
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[333] | 218 | |
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| 219 | // TODO!!! Defined to follow ANSI and/or for future development |
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| 220 | void mean_mat ( mat &M, mat&R ) const {}; |
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[477] | 221 | double evallog_nn ( const vec &val ) const { |
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| 222 | return 0; |
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| 223 | }; |
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| 224 | double lognc () const { |
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| 225 | return 0; |
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[504] | 226 | } |
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[333] | 227 | |
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[504] | 228 | shared_ptr<epdf> marginal ( const RV &rv ) const; |
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| 229 | void marginal ( const RV &rv, emix &target ) const; |
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| 230 | |
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[333] | 231 | //Access methods |
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| 232 | //! returns a pointer to the internal mean value. Use with Care! |
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[477] | 233 | vec& _w() { |
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| 234 | return w; |
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| 235 | } |
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| 236 | virtual ~egiwmix() { |
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| 237 | if ( destroyComs ) { |
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| 238 | for ( int i = 0; i < Coms.length(); i++ ) { |
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| 239 | delete Coms ( i ); |
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| 240 | } |
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| 241 | } |
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| 242 | } |
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[333] | 243 | //! Auxiliary function for taking ownership of the Coms() |
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[477] | 244 | void ownComs() { |
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| 245 | destroyComs = true; |
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| 246 | } |
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[333] | 247 | |
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| 248 | //!access function |
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[477] | 249 | egiw* _Coms ( int i ) { |
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| 250 | return Coms ( i ); |
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| 251 | } |
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[333] | 252 | |
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[477] | 253 | void set_rv ( const RV &rv ) { |
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| 254 | egiw::set_rv ( rv ); |
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| 255 | for ( int i = 0; i < Coms.length(); i++ ) { |
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| 256 | Coms ( i )->set_rv ( rv ); |
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| 257 | } |
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[333] | 258 | } |
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| 259 | |
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| 260 | //! Approximation of a GiW mix by a single GiW pdf |
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| 261 | egiw* approx(); |
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| 262 | }; |
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| 263 | |
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[115] | 264 | /*! \brief Chain rule decomposition of epdf |
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| 265 | |
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[145] | 266 | Probability density in the form of Chain-rule decomposition: |
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| 267 | \[ |
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| 268 | f(x_1,x_2,x_3) = f(x_1|x_2,x_3)f(x_2,x_3)f(x_3) |
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| 269 | \] |
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| 270 | Note that |
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[115] | 271 | */ |
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[507] | 272 | class mprod: public mpdf { |
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| 273 | private: |
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| 274 | Array<shared_ptr<mpdf> > mpdfs; |
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| 275 | |
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[162] | 276 | protected: |
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[192] | 277 | //! Data link for each mpdfs |
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| 278 | Array<datalink_m2m*> dls; |
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[461] | 279 | |
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[487] | 280 | //! dummy epdf used only as storage for RV and dim |
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| 281 | epdf iepdf; |
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[461] | 282 | |
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[162] | 283 | public: |
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[507] | 284 | //! \brief Default constructor |
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| 285 | mprod() { } |
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| 286 | |
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| 287 | /*!\brief Constructor from list of mFacs |
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[165] | 288 | */ |
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[507] | 289 | mprod ( const Array<shared_ptr<mpdf> > &mFacs ) { |
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[477] | 290 | set_elements ( mFacs ); |
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[461] | 291 | } |
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| 292 | |
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[507] | 293 | void set_elements (const Array<shared_ptr<mpdf> > &mFacs ); |
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[477] | 294 | |
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[211] | 295 | double evallogcond ( const vec &val, const vec &cond ) { |
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[162] | 296 | int i; |
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[270] | 297 | double res = 0.0; |
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[477] | 298 | for ( i = mpdfs.length() - 1; i >= 0; i-- ) { |
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[193] | 299 | /* if ( mpdfs(i)->_rvc().count() >0) { |
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| 300 | mpdfs ( i )->condition ( dls ( i )->get_cond ( val,cond ) ); |
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| 301 | } |
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| 302 | // add logarithms |
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[270] | 303 | res += epdfs ( i )->evallog ( dls ( i )->pushdown ( val ) );*/ |
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| 304 | res += mpdfs ( i )->evallogcond ( |
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| 305 | dls ( i )->pushdown ( val ), |
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[204] | 306 | dls ( i )->get_cond ( val, cond ) |
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| 307 | ); |
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[145] | 308 | } |
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[193] | 309 | return res; |
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[162] | 310 | } |
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[477] | 311 | vec evallogcond_m ( const mat &Dt, const vec &cond ) { |
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| 312 | vec tmp ( Dt.cols() ); |
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| 313 | for ( int i = 0; i < Dt.cols(); i++ ) { |
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| 314 | tmp ( i ) = evallogcond ( Dt.get_col ( i ), cond ); |
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[395] | 315 | } |
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| 316 | return tmp; |
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| 317 | }; |
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[477] | 318 | vec evallogcond_m ( const Array<vec> &Dt, const vec &cond ) { |
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| 319 | vec tmp ( Dt.length() ); |
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| 320 | for ( int i = 0; i < Dt.length(); i++ ) { |
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| 321 | tmp ( i ) = evallogcond ( Dt ( i ), cond ); |
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[395] | 322 | } |
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[477] | 323 | return tmp; |
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[395] | 324 | }; |
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| 325 | |
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| 326 | |
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[270] | 327 | //TODO smarter... |
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| 328 | vec samplecond ( const vec &cond ) { |
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[477] | 329 | //! Ugly hack to help to discover if mpfs are not in proper order. Correct solution = check that explicitely. |
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[487] | 330 | vec smp = std::numeric_limits<double>::infinity() * ones ( dimension() ); |
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[165] | 331 | vec smpi; |
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[192] | 332 | // Hard assumption here!!! We are going backwards, to assure that samples that are needed from smp are already generated! |
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[477] | 333 | for ( int i = ( mpdfs.length() - 1 ); i >= 0; i-- ) { |
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[487] | 334 | // generate contribution of this mpdf |
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| 335 | smpi = mpdfs(i)->samplecond(dls ( i )->get_cond ( smp , cond )); |
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[162] | 336 | // copy contribution of this pdf into smp |
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[270] | 337 | dls ( i )->pushup ( smp, smpi ); |
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[145] | 338 | } |
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[162] | 339 | return smp; |
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| 340 | } |
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[270] | 341 | mat samplecond ( const vec &cond, int N ) { |
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[477] | 342 | mat Smp ( dimension(), N ); |
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| 343 | for ( int i = 0; i < N; i++ ) { |
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| 344 | Smp.set_col ( i, samplecond ( cond ) ); |
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| 345 | } |
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[162] | 346 | return Smp; |
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| 347 | } |
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| 348 | |
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[395] | 349 | //! Load from structure with elements: |
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| 350 | //! \code |
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| 351 | //! { class='mprod'; |
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| 352 | //! mpdfs = (..., ...); // list of mpdfs in the order of chain rule |
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| 353 | //! } |
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| 354 | //! \endcode |
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| 355 | //!@} |
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[477] | 356 | void from_setting ( const Setting &set ) { |
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[507] | 357 | Array<mpdf*> atmp; //temporary Array |
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| 358 | UI::get ( atmp, set, "mpdfs", UI::compulsory ); |
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| 359 | |
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| 360 | Array<shared_ptr<mpdf> > btmp ( atmp.length() ); |
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| 361 | for (int i = 0; i < atmp.length(); ++i) { |
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| 362 | btmp ( i ) = shared_ptr<mpdf> ( atmp ( i ) ); |
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| 363 | } |
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| 364 | |
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| 365 | set_elements ( btmp ); |
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[395] | 366 | } |
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[477] | 367 | |
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[107] | 368 | }; |
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[477] | 369 | UIREGISTER ( mprod ); |
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[107] | 370 | |
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[168] | 371 | //! Product of independent epdfs. For dependent pdfs, use mprod. |
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| 372 | class eprod: public epdf { |
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| 373 | protected: |
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| 374 | //! Components (epdfs) |
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[170] | 375 | Array<const epdf*> epdfs; |
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[168] | 376 | //! Array of indeces |
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[270] | 377 | Array<datalink*> dls; |
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[168] | 378 | public: |
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[477] | 379 | eprod () : epdfs ( 0 ), dls ( 0 ) {}; |
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| 380 | void set_parameters ( const Array<const epdf*> &epdfs0, bool named = true ) { |
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| 381 | epdfs = epdfs0;//.set_length ( epdfs0.length() ); |
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[286] | 382 | dls.set_length ( epdfs.length() ); |
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| 383 | |
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[477] | 384 | bool independent = true; |
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[286] | 385 | if ( named ) { |
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[477] | 386 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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| 387 | independent = rv.add ( epdfs ( i )->_rv() ); |
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| 388 | it_assert_debug ( independent == true, "eprod:: given components are not independent." ); |
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[286] | 389 | } |
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[477] | 390 | dim = rv._dsize(); |
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| 391 | } else { |
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| 392 | dim = 0; |
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| 393 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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| 394 | dim += epdfs ( i )->dimension(); |
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[286] | 395 | } |
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[204] | 396 | } |
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[286] | 397 | // |
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[477] | 398 | int cumdim = 0; |
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| 399 | int dimi = 0; |
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[286] | 400 | int i; |
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[477] | 401 | for ( i = 0; i < epdfs.length(); i++ ) { |
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[286] | 402 | dls ( i ) = new datalink; |
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[477] | 403 | if ( named ) { |
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| 404 | dls ( i )->set_connection ( epdfs ( i )->_rv() , rv ); |
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| 405 | } else { |
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[286] | 406 | dimi = epdfs ( i )->dimension(); |
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[477] | 407 | dls ( i )->set_connection ( dimi, dim, linspace ( cumdim, cumdim + dimi - 1 ) ); |
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| 408 | cumdim += dimi; |
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[286] | 409 | } |
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| 410 | } |
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[168] | 411 | } |
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| 412 | |
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| 413 | vec mean() const { |
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[270] | 414 | vec tmp ( dim ); |
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[477] | 415 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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[168] | 416 | vec pom = epdfs ( i )->mean(); |
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[270] | 417 | dls ( i )->pushup ( tmp, pom ); |
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[168] | 418 | } |
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| 419 | return tmp; |
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| 420 | } |
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[229] | 421 | vec variance() const { |
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[270] | 422 | vec tmp ( dim ); //second moment |
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[477] | 423 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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[229] | 424 | vec pom = epdfs ( i )->mean(); |
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[477] | 425 | dls ( i )->pushup ( tmp, pow ( pom, 2 ) ); |
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[229] | 426 | } |
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[477] | 427 | return tmp - pow ( mean(), 2 ); |
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[229] | 428 | } |
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[168] | 429 | vec sample() const { |
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[270] | 430 | vec tmp ( dim ); |
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[477] | 431 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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[168] | 432 | vec pom = epdfs ( i )->sample(); |
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[270] | 433 | dls ( i )->pushup ( tmp, pom ); |
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[168] | 434 | } |
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| 435 | return tmp; |
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| 436 | } |
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[211] | 437 | double evallog ( const vec &val ) const { |
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[477] | 438 | double tmp = 0; |
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| 439 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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| 440 | tmp += epdfs ( i )->evallog ( dls ( i )->pushdown ( val ) ); |
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[168] | 441 | } |
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[477] | 442 | it_assert_debug ( std::isfinite ( tmp ), "Infinite" ); |
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[168] | 443 | return tmp; |
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| 444 | } |
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[170] | 445 | //!access function |
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[477] | 446 | const epdf* operator () ( int i ) const { |
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| 447 | it_assert_debug ( i < epdfs.length(), "wrong index" ); |
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| 448 | return epdfs ( i ); |
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| 449 | } |
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[204] | 450 | |
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[193] | 451 | //!Destructor |
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[477] | 452 | ~eprod() { |
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| 453 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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| 454 | delete dls ( i ); |
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| 455 | } |
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| 456 | } |
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[168] | 457 | }; |
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| 458 | |
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| 459 | |
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[488] | 460 | /*! \brief Mixture of mpdfs with constant weights, all mpdfs are of equal RV and RVC |
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[124] | 461 | |
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| 462 | */ |
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[488] | 463 | class mmix : public mpdf { |
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| 464 | protected: |
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| 465 | //! Component (mpdfs) |
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| 466 | Array<shared_ptr<mpdf> > Coms; |
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| 467 | //!weights of the components |
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| 468 | vec w; |
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| 469 | //! dummy epdfs |
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| 470 | epdf dummy_epdf; |
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| 471 | public: |
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| 472 | //!Default constructor |
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| 473 | mmix() : Coms(0), dummy_epdf() { set_ep(dummy_epdf); } |
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[461] | 474 | |
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[488] | 475 | //! Set weights \c w and components \c R |
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| 476 | void set_parameters ( const vec &w0, const Array<shared_ptr<mpdf> > &Coms0 ) { |
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| 477 | //!\TODO check if all components are OK |
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| 478 | Coms = Coms0; |
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| 479 | w=w0; |
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[503] | 480 | |
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[513] | 481 | if (Coms0.length()>0){ |
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| 482 | set_rv(Coms(0)->_rv()); |
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[515] | 483 | dummy_epdf.set_parameters(Coms(0)->_rv()._dsize()); |
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[513] | 484 | set_rvc(Coms(0)->_rvc()); |
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| 485 | dimc = rvc._dsize(); |
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| 486 | } |
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[488] | 487 | } |
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| 488 | double evallogcond (const vec &dt, const vec &cond) { |
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| 489 | double ll=0.0; |
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| 490 | for (int i=0;i<Coms.length();i++){ |
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| 491 | ll+=Coms(i)->evallogcond(dt,cond); |
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| 492 | } |
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| 493 | return ll; |
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| 494 | } |
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| 495 | |
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| 496 | vec samplecond (const vec &cond); |
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| 497 | |
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| 498 | }; |
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| 499 | |
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[254] | 500 | } |
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[107] | 501 | #endif //MX_H |
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