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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13 | #ifndef MX_H |
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14 | #define MX_H |
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15 | |
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16 | #include "libBM.h" |
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17 | #include "libEF.h" |
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18 | //#include <std> |
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19 | |
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20 | namespace bdm { |
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21 | |
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22 | //this comes first because it is used inside emix! |
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23 | |
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24 | /*! \brief Class representing ratio of two densities |
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25 | which arise e.g. by applying the Bayes rule. |
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26 | It represents density in the form: |
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27 | \f[ |
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28 | f(rv|rvc) = \frac{f(rv,rvc)}{f(rvc)} |
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29 | \f] |
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30 | where \f$ f(rvc) = \int f(rv,rvc) d\ rv \f$. |
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31 | |
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32 | In particular this type of arise by conditioning of a mixture model. |
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33 | |
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34 | At present the only supported operation is evallogcond(). |
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35 | */ |
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36 | class mratio: public mpdf { |
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37 | protected: |
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38 | //! Nominator in the form of mpdf |
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39 | const epdf* nom; |
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40 | //!Denominator in the form of epdf |
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41 | epdf* den; |
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42 | //!flag for destructor |
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43 | bool destroynom; |
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44 | //!datalink between conditional and nom |
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45 | datalink_m2e dl; |
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46 | public: |
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47 | //!Default constructor. By default, the given epdf is not copied! |
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48 | //! It is assumed that this function will be used only temporarily. |
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49 | mratio ( const epdf* nom0, const RV &rv, bool copy=false ) :mpdf ( ), dl ( ) { |
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50 | // adjust rv and rvc |
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51 | rvc = nom0->_rv().subt ( rv ); |
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52 | dimc = rvc._dsize(); |
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53 | ep = new epdf; |
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54 | ep->set_parameters(rv._dsize()); |
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55 | ep->set_rv(rv); |
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56 | |
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57 | //prepare data structures |
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58 | if ( copy ) {it_error ( "todo" ); destroynom=true; } |
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59 | else { nom = nom0; destroynom = false; } |
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60 | it_assert_debug ( rvc.length() >0,"Makes no sense to use this object!" ); |
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61 | |
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62 | // build denominator |
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63 | den = nom->marginal ( rvc ); |
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64 | dl.set_connection(rv,rvc,nom0->_rv()); |
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65 | }; |
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66 | double evallogcond ( const vec &val, const vec &cond ) { |
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67 | double tmp; |
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68 | vec nom_val ( ep->dimension() + dimc ); |
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69 | dl.pushup_cond ( nom_val,val,cond ); |
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70 | tmp = exp ( nom->evallog ( nom_val ) - den->evallog ( cond ) ); |
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71 | it_assert_debug ( std::isfinite ( tmp ),"Infinite value" ); |
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72 | return tmp; |
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73 | } |
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74 | //! Object takes ownership of nom and will destroy it |
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75 | void ownnom() {destroynom=true;} |
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76 | //! Default destructor |
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77 | ~mratio() {delete den; if ( destroynom ) {delete nom;}} |
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78 | }; |
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79 | |
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80 | /*! |
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81 | * \brief Mixture of epdfs |
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82 | |
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83 | Density function: |
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84 | \f[ |
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85 | f(x) = \sum_{i=1}^{n} w_{i} f_i(x), \quad \sum_{i=1}^n w_i = 1. |
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86 | \f] |
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87 | where \f$f_i(x)\f$ is any density on random variable \f$x\f$, called \a component, |
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88 | |
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89 | */ |
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90 | class emix : public epdf { |
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91 | protected: |
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92 | //! weights of the components |
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93 | vec w; |
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94 | //! Component (epdfs) |
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95 | Array<epdf*> Coms; |
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96 | //!Flag if owning Coms |
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97 | bool destroyComs; |
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98 | public: |
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99 | //!Default constructor |
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100 | emix ( ) : epdf ( ) {}; |
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101 | //! Set weights \c w and components \c Coms |
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102 | //!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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103 | void set_parameters ( const vec &w, const Array<epdf*> &Coms, bool copy=false ); |
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104 | |
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105 | vec sample() const; |
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106 | vec mean() const { |
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107 | int i; vec mu = zeros ( dim ); |
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108 | for ( i = 0;i < w.length();i++ ) {mu += w ( i ) * Coms ( i )->mean(); } |
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109 | return mu; |
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110 | } |
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111 | vec variance() const { |
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112 | //non-central moment |
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113 | vec mom2 = zeros ( dim ); |
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114 | for ( int i = 0;i < w.length();i++ ) {mom2 += w ( i ) * (Coms(i)->variance() + pow ( Coms ( i )->mean(),2 )); } |
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115 | //central moment |
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116 | return mom2-pow ( mean(),2 ); |
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117 | } |
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118 | double evallog ( const vec &val ) const { |
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119 | int i; |
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120 | double sum = 0.0; |
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121 | for ( i = 0;i < w.length();i++ ) {sum += w ( i ) * exp ( Coms ( i )->evallog ( val ) );} |
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122 | if ( sum==0.0 ) {sum=std::numeric_limits<double>::epsilon();} |
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123 | double tmp=log ( sum ); |
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124 | it_assert_debug ( std::isfinite ( tmp ),"Infinite" ); |
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125 | return tmp; |
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126 | }; |
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127 | vec evallog_m ( const mat &Val ) const { |
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128 | vec x=zeros ( Val.cols() ); |
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129 | for ( int i = 0; i < w.length(); i++ ) { |
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130 | x+= w ( i ) *exp ( Coms ( i )->evallog_m ( Val ) ); |
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131 | } |
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132 | return log ( x ); |
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133 | }; |
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134 | //! Auxiliary function that returns pdflog for each component |
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135 | mat evallog_M ( const mat &Val ) const { |
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136 | mat X ( w.length(), Val.cols() ); |
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137 | for ( int i = 0; i < w.length(); i++ ) { |
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138 | X.set_row ( i, w ( i ) *exp ( Coms ( i )->evallog_m ( Val ) ) ); |
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139 | } |
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140 | return X; |
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141 | }; |
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142 | |
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143 | emix* marginal ( const RV &rv ) const; |
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144 | mratio* condition ( const RV &rv ) const; //why not mratio!! |
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145 | |
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146 | //Access methods |
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147 | //! returns a pointer to the internal mean value. Use with Care! |
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148 | vec& _w() {return w;} |
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149 | virtual ~emix() {if ( destroyComs ) {for ( int i=0;i<Coms.length();i++ ) {delete Coms ( i );}}} |
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150 | //! Auxiliary function for taking ownership of the Coms() |
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151 | void ownComs() {destroyComs=true;} |
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152 | |
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153 | //!access function |
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154 | epdf* _Coms ( int i ) {return Coms ( i );} |
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155 | void set_rv(const RV &rv){ |
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156 | epdf::set_rv(rv); |
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157 | for(int i=0;i<Coms.length();i++){Coms(i)->set_rv(rv);} |
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158 | } |
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159 | }; |
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160 | |
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161 | /*! \brief Chain rule decomposition of epdf |
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162 | |
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163 | Probability density in the form of Chain-rule decomposition: |
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164 | \[ |
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165 | f(x_1,x_2,x_3) = f(x_1|x_2,x_3)f(x_2,x_3)f(x_3) |
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166 | \] |
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167 | Note that |
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168 | */ |
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169 | class mprod: public compositepdf, public mpdf { |
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170 | protected: |
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171 | //! pointers to epdfs - shortcut to mpdfs().posterior() |
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172 | Array<epdf*> epdfs; |
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173 | //! Data link for each mpdfs |
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174 | Array<datalink_m2m*> dls; |
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175 | //! dummy ep |
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176 | epdf dummy; |
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177 | public: |
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178 | /*!\brief Constructor from list of mFacs, |
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179 | */ |
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180 | mprod ( Array<mpdf*> mFacs ) : compositepdf ( mFacs ), mpdf (), epdfs ( n ), dls ( n ) { |
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181 | ep=&dummy; |
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182 | RV rv=getrv ( true ); |
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183 | set_rv ( rv );dummy.set_parameters ( rv._dsize() ); |
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184 | setrvc ( ep->_rv(),rvc ); |
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185 | // rv and rvc established = > we can link them with mpdfs |
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186 | for ( int i = 0;i < n;i++ ) { |
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187 | dls ( i ) = new datalink_m2m; |
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188 | dls(i)->set_connection( mpdfs ( i )->_rv(), mpdfs ( i )->_rvc(), _rv(), _rvc() ); |
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189 | } |
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190 | |
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191 | for ( int i=0;i<n;i++ ) { |
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192 | epdfs ( i ) =& ( mpdfs ( i )->_epdf() ); |
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193 | } |
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194 | }; |
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195 | |
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196 | double evallogcond ( const vec &val, const vec &cond ) { |
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197 | int i; |
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198 | double res = 0.0; |
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199 | for ( i = n - 1;i >= 0;i-- ) { |
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200 | /* if ( mpdfs(i)->_rvc().count() >0) { |
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201 | mpdfs ( i )->condition ( dls ( i )->get_cond ( val,cond ) ); |
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202 | } |
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203 | // add logarithms |
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204 | res += epdfs ( i )->evallog ( dls ( i )->pushdown ( val ) );*/ |
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205 | res += mpdfs ( i )->evallogcond ( |
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206 | dls ( i )->pushdown ( val ), |
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207 | dls ( i )->get_cond ( val, cond ) |
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208 | ); |
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209 | } |
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210 | return res; |
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211 | } |
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212 | //TODO smarter... |
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213 | vec samplecond ( const vec &cond ) { |
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214 | //! Ugly hack to help to discover if mpfs are not in proper order. Correct solution = check that explicitely. |
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215 | vec smp= std::numeric_limits<double>::infinity() * ones ( ep->dimension() ); |
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216 | vec smpi; |
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217 | // Hard assumption here!!! We are going backwards, to assure that samples that are needed from smp are already generated! |
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218 | for ( int i = ( n - 1 );i >= 0;i-- ) { |
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219 | if ( mpdfs ( i )->dimensionc() ) { |
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220 | mpdfs ( i )->condition ( dls ( i )->get_cond ( smp ,cond ) ); // smp is val here!! |
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221 | } |
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222 | smpi = epdfs ( i )->sample(); |
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223 | // copy contribution of this pdf into smp |
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224 | dls ( i )->pushup ( smp, smpi ); |
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225 | // add ith likelihood contribution |
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226 | } |
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227 | return smp; |
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228 | } |
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229 | mat samplecond ( const vec &cond, int N ) { |
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230 | mat Smp ( dimension(),N ); |
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231 | for ( int i=0;i<N;i++ ) {Smp.set_col ( i,samplecond ( cond ) );} |
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232 | return Smp; |
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233 | } |
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234 | |
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235 | ~mprod() {}; |
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236 | }; |
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237 | |
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238 | //! Product of independent epdfs. For dependent pdfs, use mprod. |
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239 | class eprod: public epdf { |
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240 | protected: |
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241 | //! Components (epdfs) |
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242 | Array<const epdf*> epdfs; |
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243 | //! Array of indeces |
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244 | Array<datalink*> dls; |
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245 | public: |
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246 | eprod () : epdfs ( 0 ),dls ( 0 ) {}; |
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247 | void set_parameters ( const Array<const epdf*> &epdfs0, bool named=true ) { |
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248 | epdfs=epdfs0;//.set_length ( epdfs0.length() ); |
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249 | dls.set_length ( epdfs.length() ); |
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250 | |
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251 | bool independent=true; |
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252 | if ( named ) { |
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253 | for ( int i=0;i<epdfs.length();i++ ) { |
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254 | independent=rv.add ( epdfs ( i )->_rv() ); |
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255 | it_assert_debug ( independent==true, "eprod:: given components are not independent." ); |
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256 | } |
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257 | dim=rv._dsize(); |
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258 | } |
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259 | else { |
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260 | dim =0; for ( int i=0;i<epdfs.length();i++ ) { |
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261 | dim+=epdfs ( i )->dimension(); |
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262 | } |
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263 | } |
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264 | // |
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265 | int cumdim=0; |
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266 | int dimi=0; |
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267 | int i; |
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268 | for ( i=0;i<epdfs.length();i++ ) { |
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269 | dls ( i ) = new datalink; |
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270 | if ( named ) {dls ( i )->set_connection ( epdfs ( i )->_rv() , rv );} |
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271 | else { |
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272 | dimi = epdfs ( i )->dimension(); |
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273 | dls ( i )->set_connection ( dimi, dim, linspace ( cumdim,cumdim+dimi-1 ) ); |
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274 | cumdim+=dimi; |
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275 | } |
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276 | } |
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277 | } |
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278 | |
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279 | vec mean() const { |
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280 | vec tmp ( dim ); |
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281 | for ( int i=0;i<epdfs.length();i++ ) { |
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282 | vec pom = epdfs ( i )->mean(); |
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283 | dls ( i )->pushup ( tmp, pom ); |
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284 | } |
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285 | return tmp; |
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286 | } |
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287 | vec variance() const { |
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288 | vec tmp ( dim ); //second moment |
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289 | for ( int i=0;i<epdfs.length();i++ ) { |
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290 | vec pom = epdfs ( i )->mean(); |
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291 | dls ( i )->pushup ( tmp, pow ( pom,2 ) ); |
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292 | } |
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293 | return tmp-pow ( mean(),2 ); |
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294 | } |
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295 | vec sample() const { |
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296 | vec tmp ( dim ); |
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297 | for ( int i=0;i<epdfs.length();i++ ) { |
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298 | vec pom = epdfs ( i )->sample(); |
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299 | dls ( i )->pushup ( tmp, pom ); |
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300 | } |
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301 | return tmp; |
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302 | } |
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303 | double evallog ( const vec &val ) const { |
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304 | double tmp=0; |
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305 | for ( int i=0;i<epdfs.length();i++ ) { |
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306 | tmp+=epdfs ( i )->evallog ( dls ( i )->pushdown ( val ) ); |
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307 | } |
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308 | it_assert_debug ( std::isfinite ( tmp ),"Infinite" ); |
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309 | return tmp; |
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310 | } |
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311 | //!access function |
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312 | const epdf* operator () ( int i ) const {it_assert_debug ( i<epdfs.length(),"wrong index" );return epdfs ( i );} |
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313 | |
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314 | //!Destructor |
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315 | ~eprod() {for ( int i=0;i<epdfs.length();i++ ) {delete dls ( i );}} |
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316 | }; |
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317 | |
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318 | |
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319 | /*! \brief Mixture of mpdfs with constant weights, all mpdfs are of equal type |
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320 | |
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321 | */ |
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322 | class mmix : public mpdf { |
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323 | protected: |
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324 | //! Component (epdfs) |
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325 | Array<mpdf*> Coms; |
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326 | //!Internal epdf |
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327 | emix Epdf; |
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328 | public: |
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329 | //!Default constructor |
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330 | mmix ( ) : mpdf ( ), Epdf () {ep = &Epdf;}; |
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331 | //! Set weights \c w and components \c R |
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332 | void set_parameters ( const vec &w, const Array<mpdf*> &Coms ) { |
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333 | Array<epdf*> Eps ( Coms.length() ); |
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334 | |
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335 | for ( int i = 0;i < Coms.length();i++ ) { |
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336 | Eps ( i ) = & ( Coms ( i )->_epdf() ); |
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337 | } |
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338 | Epdf.set_parameters ( w, Eps ); |
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339 | }; |
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340 | |
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341 | void condition ( const vec &cond ) { |
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342 | for ( int i = 0;i < Coms.length();i++ ) {Coms ( i )->condition ( cond );} |
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343 | }; |
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344 | }; |
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345 | |
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346 | } |
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347 | #endif //MX_H |
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