[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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[182] | 41 | //!Denominator in the form of epdf |
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[192] | 42 | epdf* den; |
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| 43 | //!flag for destructor |
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| 44 | bool destroynom; |
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[193] | 45 | //!datalink between conditional and nom |
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| 46 | datalink_m2e dl; |
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[487] | 47 | //! dummy epdf that stores only rv and dim |
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| 48 | epdf iepdf; |
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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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[487] | 52 | mratio ( const epdf* nom0, const RV &rv, bool copy = false ) : mpdf ( ), dl ( ),iepdf() { |
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[286] | 53 | // adjust rv and rvc |
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| 54 | rvc = nom0->_rv().subt ( rv ); |
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| 55 | dimc = rvc._dsize(); |
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[487] | 56 | set_ep ( iepdf ); |
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| 57 | iepdf.set_parameters ( rv._dsize() ); |
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| 58 | iepdf.set_rv ( rv ); |
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[477] | 59 | |
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[286] | 60 | //prepare data structures |
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[477] | 61 | if ( copy ) { |
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| 62 | it_error ( "todo" ); |
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| 63 | destroynom = true; |
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| 64 | } else { |
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| 65 | nom = nom0; |
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| 66 | destroynom = false; |
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| 67 | } |
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| 68 | it_assert_debug ( rvc.length() > 0, "Makes no sense to use this object!" ); |
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| 69 | |
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[286] | 70 | // build denominator |
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[192] | 71 | den = nom->marginal ( rvc ); |
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[477] | 72 | dl.set_connection ( rv, rvc, nom0->_rv() ); |
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[192] | 73 | }; |
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[211] | 74 | double evallogcond ( const vec &val, const vec &cond ) { |
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[214] | 75 | double tmp; |
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[487] | 76 | vec nom_val ( dimension() + dimc ); |
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[477] | 77 | dl.pushup_cond ( nom_val, val, cond ); |
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[214] | 78 | tmp = exp ( nom->evallog ( nom_val ) - den->evallog ( cond ) ); |
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| 79 | return tmp; |
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[192] | 80 | } |
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[182] | 81 | //! Object takes ownership of nom and will destroy it |
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[477] | 82 | void ownnom() { |
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| 83 | destroynom = true; |
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| 84 | } |
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[182] | 85 | //! Default destructor |
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[477] | 86 | ~mratio() { |
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| 87 | delete den; |
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| 88 | if ( destroynom ) { |
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| 89 | delete nom; |
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| 90 | } |
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| 91 | } |
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[182] | 92 | }; |
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| 93 | |
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[107] | 94 | /*! |
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| 95 | * \brief Mixture of epdfs |
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| 96 | |
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| 97 | Density function: |
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| 98 | \f[ |
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| 99 | f(x) = \sum_{i=1}^{n} w_{i} f_i(x), \quad \sum_{i=1}^n w_i = 1. |
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| 100 | \f] |
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| 101 | where \f$f_i(x)\f$ is any density on random variable \f$x\f$, called \a component, |
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| 102 | |
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| 103 | */ |
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[145] | 104 | class emix : public epdf { |
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[162] | 105 | protected: |
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| 106 | //! weights of the components |
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| 107 | vec w; |
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| 108 | //! Component (epdfs) |
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| 109 | Array<epdf*> Coms; |
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[178] | 110 | //!Flag if owning Coms |
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| 111 | bool destroyComs; |
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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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[477] | 117 | void set_parameters ( const vec &w, const Array<epdf*> &Coms, bool copy = false ); |
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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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[182] | 166 | emix* marginal ( const RV &rv ) const; |
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| 167 | mratio* condition ( const RV &rv ) const; //why not mratio!! |
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| 168 | |
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[107] | 169 | //Access methods |
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[162] | 170 | //! returns a pointer to the internal mean value. Use with Care! |
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[477] | 171 | vec& _w() { |
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| 172 | return w; |
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| 173 | } |
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| 174 | virtual ~emix() { |
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| 175 | if ( destroyComs ) { |
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| 176 | for ( int i = 0; i < Coms.length(); i++ ) { |
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| 177 | delete Coms ( i ); |
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| 178 | } |
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| 179 | } |
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| 180 | } |
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[178] | 181 | //! Auxiliary function for taking ownership of the Coms() |
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[477] | 182 | void ownComs() { |
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| 183 | destroyComs = true; |
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| 184 | } |
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[204] | 185 | |
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[193] | 186 | //!access function |
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[477] | 187 | epdf* _Coms ( int i ) { |
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| 188 | return Coms ( i ); |
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[286] | 189 | } |
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[477] | 190 | void set_rv ( const RV &rv ) { |
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| 191 | epdf::set_rv ( rv ); |
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| 192 | for ( int i = 0; i < Coms.length(); i++ ) { |
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| 193 | Coms ( i )->set_rv ( rv ); |
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| 194 | } |
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| 195 | } |
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[107] | 196 | }; |
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| 197 | |
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[333] | 198 | |
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| 199 | /*! |
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| 200 | * \brief Mixture of egiws |
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| 201 | |
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| 202 | */ |
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| 203 | class egiwmix : public egiw { |
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| 204 | protected: |
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| 205 | //! weights of the components |
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| 206 | vec w; |
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| 207 | //! Component (epdfs) |
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| 208 | Array<egiw*> Coms; |
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| 209 | //!Flag if owning Coms |
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| 210 | bool destroyComs; |
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| 211 | public: |
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| 212 | //!Default constructor |
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| 213 | egiwmix ( ) : egiw ( ) {}; |
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| 214 | |
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| 215 | //! Set weights \c w and components \c Coms |
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| 216 | //!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] | 217 | void set_parameters ( const vec &w, const Array<egiw*> &Coms, bool copy = false ); |
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[333] | 218 | |
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| 219 | //!return expected value |
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| 220 | vec mean() const; |
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| 221 | |
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| 222 | //!return a sample from the density |
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| 223 | vec sample() const; |
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| 224 | |
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| 225 | //!return the expected variance |
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[477] | 226 | vec variance() const; |
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[333] | 227 | |
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| 228 | // TODO!!! Defined to follow ANSI and/or for future development |
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| 229 | void mean_mat ( mat &M, mat&R ) const {}; |
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[477] | 230 | double evallog_nn ( const vec &val ) const { |
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| 231 | return 0; |
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| 232 | }; |
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| 233 | double lognc () const { |
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| 234 | return 0; |
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| 235 | }; |
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[333] | 236 | emix* marginal ( const RV &rv ) const; |
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| 237 | |
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| 238 | //Access methods |
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| 239 | //! returns a pointer to the internal mean value. Use with Care! |
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[477] | 240 | vec& _w() { |
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| 241 | return w; |
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| 242 | } |
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| 243 | virtual ~egiwmix() { |
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| 244 | if ( destroyComs ) { |
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| 245 | for ( int i = 0; i < Coms.length(); i++ ) { |
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| 246 | delete Coms ( i ); |
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| 247 | } |
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| 248 | } |
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| 249 | } |
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[333] | 250 | //! Auxiliary function for taking ownership of the Coms() |
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[477] | 251 | void ownComs() { |
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| 252 | destroyComs = true; |
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| 253 | } |
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[333] | 254 | |
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| 255 | //!access function |
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[477] | 256 | egiw* _Coms ( int i ) { |
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| 257 | return Coms ( i ); |
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| 258 | } |
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[333] | 259 | |
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[477] | 260 | void set_rv ( const RV &rv ) { |
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| 261 | egiw::set_rv ( rv ); |
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| 262 | for ( int i = 0; i < Coms.length(); i++ ) { |
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| 263 | Coms ( i )->set_rv ( rv ); |
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| 264 | } |
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[333] | 265 | } |
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| 266 | |
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| 267 | //! Approximation of a GiW mix by a single GiW pdf |
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| 268 | egiw* approx(); |
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| 269 | }; |
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| 270 | |
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[115] | 271 | /*! \brief Chain rule decomposition of epdf |
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| 272 | |
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[145] | 273 | Probability density in the form of Chain-rule decomposition: |
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| 274 | \[ |
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| 275 | f(x_1,x_2,x_3) = f(x_1|x_2,x_3)f(x_2,x_3)f(x_3) |
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| 276 | \] |
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| 277 | Note that |
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[115] | 278 | */ |
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[175] | 279 | class mprod: public compositepdf, public mpdf { |
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[162] | 280 | protected: |
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[192] | 281 | //! Data link for each mpdfs |
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| 282 | Array<datalink_m2m*> dls; |
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[461] | 283 | |
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[487] | 284 | //! dummy epdf used only as storage for RV and dim |
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| 285 | epdf iepdf; |
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[461] | 286 | |
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[162] | 287 | public: |
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[168] | 288 | /*!\brief Constructor from list of mFacs, |
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[165] | 289 | */ |
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[487] | 290 | mprod() : iepdf( ) { } |
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[477] | 291 | mprod ( Array<mpdf*> mFacs ) : |
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[487] | 292 | iepdf ( ) { |
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[477] | 293 | set_elements ( mFacs ); |
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[461] | 294 | } |
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| 295 | |
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[477] | 296 | void set_elements ( Array<mpdf*> mFacs , bool own = false ) { |
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| 297 | |
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| 298 | compositepdf::set_elements ( mFacs, own ); |
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| 299 | dls.set_size ( mFacs.length() ); |
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| 300 | |
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[487] | 301 | set_ep ( iepdf); |
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[477] | 302 | RV rv = getrv ( true ); |
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[395] | 303 | set_rv ( rv ); |
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[487] | 304 | iepdf.set_parameters ( rv._dsize() ); |
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| 305 | setrvc (_rv(), rvc ); |
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[192] | 306 | // rv and rvc established = > we can link them with mpdfs |
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[477] | 307 | for ( int i = 0; i < mpdfs.length(); i++ ) { |
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[286] | 308 | dls ( i ) = new datalink_m2m; |
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[477] | 309 | dls ( i )->set_connection ( mpdfs ( i )->_rv(), mpdfs ( i )->_rvc(), _rv(), _rvc() ); |
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[181] | 310 | } |
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| 311 | |
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[175] | 312 | }; |
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[124] | 313 | |
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[211] | 314 | double evallogcond ( const vec &val, const vec &cond ) { |
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[162] | 315 | int i; |
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[270] | 316 | double res = 0.0; |
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[477] | 317 | for ( i = mpdfs.length() - 1; i >= 0; i-- ) { |
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[193] | 318 | /* if ( mpdfs(i)->_rvc().count() >0) { |
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| 319 | mpdfs ( i )->condition ( dls ( i )->get_cond ( val,cond ) ); |
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| 320 | } |
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| 321 | // add logarithms |
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[270] | 322 | res += epdfs ( i )->evallog ( dls ( i )->pushdown ( val ) );*/ |
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| 323 | res += mpdfs ( i )->evallogcond ( |
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| 324 | dls ( i )->pushdown ( val ), |
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[204] | 325 | dls ( i )->get_cond ( val, cond ) |
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| 326 | ); |
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[145] | 327 | } |
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[193] | 328 | return res; |
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[162] | 329 | } |
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[477] | 330 | vec evallogcond_m ( const mat &Dt, const vec &cond ) { |
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| 331 | vec tmp ( Dt.cols() ); |
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| 332 | for ( int i = 0; i < Dt.cols(); i++ ) { |
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| 333 | tmp ( i ) = evallogcond ( Dt.get_col ( i ), cond ); |
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[395] | 334 | } |
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| 335 | return tmp; |
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| 336 | }; |
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[477] | 337 | vec evallogcond_m ( const Array<vec> &Dt, const vec &cond ) { |
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| 338 | vec tmp ( Dt.length() ); |
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| 339 | for ( int i = 0; i < Dt.length(); i++ ) { |
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| 340 | tmp ( i ) = evallogcond ( Dt ( i ), cond ); |
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[395] | 341 | } |
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[477] | 342 | return tmp; |
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[395] | 343 | }; |
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| 344 | |
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| 345 | |
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[270] | 346 | //TODO smarter... |
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| 347 | vec samplecond ( const vec &cond ) { |
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[477] | 348 | //! Ugly hack to help to discover if mpfs are not in proper order. Correct solution = check that explicitely. |
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[487] | 349 | vec smp = std::numeric_limits<double>::infinity() * ones ( dimension() ); |
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[165] | 350 | vec smpi; |
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[192] | 351 | // Hard assumption here!!! We are going backwards, to assure that samples that are needed from smp are already generated! |
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[477] | 352 | for ( int i = ( mpdfs.length() - 1 ); i >= 0; i-- ) { |
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[487] | 353 | // generate contribution of this mpdf |
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| 354 | smpi = mpdfs(i)->samplecond(dls ( i )->get_cond ( smp , cond )); |
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[162] | 355 | // copy contribution of this pdf into smp |
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[270] | 356 | dls ( i )->pushup ( smp, smpi ); |
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[145] | 357 | } |
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[162] | 358 | return smp; |
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| 359 | } |
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[270] | 360 | mat samplecond ( const vec &cond, int N ) { |
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[477] | 361 | mat Smp ( dimension(), N ); |
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| 362 | for ( int i = 0; i < N; i++ ) { |
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| 363 | Smp.set_col ( i, samplecond ( cond ) ); |
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| 364 | } |
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[162] | 365 | return Smp; |
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| 366 | } |
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| 367 | |
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| 368 | ~mprod() {}; |
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[395] | 369 | //! Load from structure with elements: |
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| 370 | //! \code |
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| 371 | //! { class='mprod'; |
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| 372 | //! mpdfs = (..., ...); // list of mpdfs in the order of chain rule |
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| 373 | //! } |
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| 374 | //! \endcode |
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| 375 | //!@} |
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[477] | 376 | void from_setting ( const Setting &set ) { |
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[395] | 377 | Array<mpdf*> Atmp; //temporary Array |
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[477] | 378 | UI::get ( Atmp, set, "mpdfs", UI::compulsory ); |
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| 379 | set_elements ( Atmp, true ); |
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[395] | 380 | } |
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[477] | 381 | |
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[107] | 382 | }; |
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[477] | 383 | UIREGISTER ( mprod ); |
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[107] | 384 | |
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[168] | 385 | //! Product of independent epdfs. For dependent pdfs, use mprod. |
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| 386 | class eprod: public epdf { |
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| 387 | protected: |
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| 388 | //! Components (epdfs) |
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[170] | 389 | Array<const epdf*> epdfs; |
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[168] | 390 | //! Array of indeces |
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[270] | 391 | Array<datalink*> dls; |
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[168] | 392 | public: |
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[477] | 393 | eprod () : epdfs ( 0 ), dls ( 0 ) {}; |
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| 394 | void set_parameters ( const Array<const epdf*> &epdfs0, bool named = true ) { |
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| 395 | epdfs = epdfs0;//.set_length ( epdfs0.length() ); |
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[286] | 396 | dls.set_length ( epdfs.length() ); |
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| 397 | |
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[477] | 398 | bool independent = true; |
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[286] | 399 | if ( named ) { |
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[477] | 400 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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| 401 | independent = rv.add ( epdfs ( i )->_rv() ); |
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| 402 | it_assert_debug ( independent == true, "eprod:: given components are not independent." ); |
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[286] | 403 | } |
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[477] | 404 | dim = rv._dsize(); |
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| 405 | } else { |
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| 406 | dim = 0; |
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| 407 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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| 408 | dim += epdfs ( i )->dimension(); |
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[286] | 409 | } |
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[204] | 410 | } |
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[286] | 411 | // |
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[477] | 412 | int cumdim = 0; |
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| 413 | int dimi = 0; |
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[286] | 414 | int i; |
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[477] | 415 | for ( i = 0; i < epdfs.length(); i++ ) { |
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[286] | 416 | dls ( i ) = new datalink; |
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[477] | 417 | if ( named ) { |
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| 418 | dls ( i )->set_connection ( epdfs ( i )->_rv() , rv ); |
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| 419 | } else { |
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[286] | 420 | dimi = epdfs ( i )->dimension(); |
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[477] | 421 | dls ( i )->set_connection ( dimi, dim, linspace ( cumdim, cumdim + dimi - 1 ) ); |
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| 422 | cumdim += dimi; |
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[286] | 423 | } |
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| 424 | } |
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[168] | 425 | } |
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| 426 | |
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| 427 | vec mean() const { |
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[270] | 428 | vec tmp ( dim ); |
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[477] | 429 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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[168] | 430 | vec pom = epdfs ( i )->mean(); |
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[270] | 431 | dls ( i )->pushup ( tmp, pom ); |
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[168] | 432 | } |
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| 433 | return tmp; |
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| 434 | } |
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[229] | 435 | vec variance() const { |
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[270] | 436 | vec tmp ( dim ); //second moment |
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[477] | 437 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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[229] | 438 | vec pom = epdfs ( i )->mean(); |
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[477] | 439 | dls ( i )->pushup ( tmp, pow ( pom, 2 ) ); |
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[229] | 440 | } |
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[477] | 441 | return tmp - pow ( mean(), 2 ); |
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[229] | 442 | } |
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[168] | 443 | vec sample() const { |
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[270] | 444 | vec tmp ( dim ); |
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[477] | 445 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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[168] | 446 | vec pom = epdfs ( i )->sample(); |
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[270] | 447 | dls ( i )->pushup ( tmp, pom ); |
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[168] | 448 | } |
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| 449 | return tmp; |
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| 450 | } |
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[211] | 451 | double evallog ( const vec &val ) const { |
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[477] | 452 | double tmp = 0; |
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| 453 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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| 454 | tmp += epdfs ( i )->evallog ( dls ( i )->pushdown ( val ) ); |
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[168] | 455 | } |
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[477] | 456 | it_assert_debug ( std::isfinite ( tmp ), "Infinite" ); |
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[168] | 457 | return tmp; |
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| 458 | } |
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[170] | 459 | //!access function |
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[477] | 460 | const epdf* operator () ( int i ) const { |
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| 461 | it_assert_debug ( i < epdfs.length(), "wrong index" ); |
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| 462 | return epdfs ( i ); |
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| 463 | } |
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[204] | 464 | |
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[193] | 465 | //!Destructor |
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[477] | 466 | ~eprod() { |
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| 467 | for ( int i = 0; i < epdfs.length(); i++ ) { |
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| 468 | delete dls ( i ); |
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| 469 | } |
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| 470 | } |
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[168] | 471 | }; |
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| 472 | |
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| 473 | |
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[145] | 474 | /*! \brief Mixture of mpdfs with constant weights, all mpdfs are of equal type |
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[124] | 475 | |
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| 476 | */ |
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[487] | 477 | // class mmix : public mpdf { |
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| 478 | // protected: |
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| 479 | // //! Component (epdfs) |
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| 480 | // Array<mpdf*> Coms; |
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| 481 | // |
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| 482 | // //!Internal epdf |
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| 483 | // emix iepdf; |
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| 484 | // |
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| 485 | // public: |
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| 486 | // //!Default constructor |
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| 487 | // mmix() : iepdf ( ) { |
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| 488 | // set_ep ( iepdf ); |
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| 489 | // } |
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| 490 | // |
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| 491 | // //! Set weights \c w and components \c R |
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| 492 | // void set_parameters ( const vec &w, const Array<mpdf*> &Coms ) { |
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| 493 | // Array<epdf*> Eps ( Coms.length() ); |
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| 494 | // |
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| 495 | // for ( int i = 0; i < Coms.length(); i++ ) { |
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| 496 | // Eps ( i ) = Coms ( i )->e(); |
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| 497 | // } |
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| 498 | // |
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| 499 | // iepdf->set_parameters ( w, Eps ); |
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| 500 | // } |
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| 501 | // |
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| 502 | // void condition ( const vec &cond ) { |
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| 503 | // for ( int i = 0; i < Coms.length(); i++ ) { |
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| 504 | // Coms ( i )->condition ( cond ); |
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| 505 | // } |
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| 506 | // }; |
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| 507 | // }; |
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[461] | 508 | |
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[254] | 509 | } |
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[107] | 510 | #endif //MX_H |
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