1 | /*! |
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2 | \file |
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3 | \brief Bayesian Models (bm) that use Bayes rule to learn from observations |
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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 | /*! |
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14 | \defgroup core Core BDM classes |
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15 | @{ |
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16 | */ |
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17 | #ifndef BM_H |
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18 | #define BM_H |
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19 | |
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20 | #include <itpp/itbase.h> |
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21 | #include "../itpp_ext.h" |
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22 | //#include <std> |
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23 | |
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24 | namespace bdm{ |
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25 | using namespace itpp; |
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26 | |
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27 | //! Root class of BDM objects |
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28 | class bdmroot{ |
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29 | virtual void print(){} |
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30 | }; |
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31 | |
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32 | //! Structure of RV (used internally), i.e. expanded RVs |
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33 | class str { |
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34 | public: |
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35 | //! vector id ids (non-unique!) |
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36 | ivec ids; |
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37 | //! vector of times |
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38 | ivec times; |
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39 | //!Default constructor |
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40 | str ( ivec ids0, ivec times0 ) :ids ( ids0 ),times ( times0 ) { |
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41 | it_assert_debug ( times0.length() ==ids0.length(),"Incompatible input" ); |
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42 | }; |
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43 | }; |
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44 | |
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45 | /*! |
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46 | * \brief Class representing variables, most often random variables |
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47 | |
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48 | * More?... |
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49 | */ |
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50 | |
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51 | class RV :public bdmroot{ |
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52 | protected: |
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53 | //! size = sum of sizes |
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54 | int tsize; |
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55 | //! len = number of individual rvs |
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56 | int len; |
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57 | //! Vector of unique IDs |
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58 | ivec ids; |
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59 | //! Vector of sizes |
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60 | ivec sizes; |
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61 | //! Vector of shifts from current time |
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62 | ivec times; |
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63 | //! Array of names |
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64 | Array<std::string> names; |
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65 | |
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66 | private: |
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67 | //! auxiliary function used in constructor |
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68 | void init ( ivec in_ids, Array<std::string> in_names, ivec in_sizes, ivec in_times ); |
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69 | public: |
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70 | //! Full constructor |
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71 | RV ( Array<std::string> in_names, ivec in_sizes, ivec in_times ); |
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72 | //! Constructor with times=0 |
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73 | RV ( Array<std::string> in_names, ivec in_sizes ); |
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74 | //! Constructor with sizes=1, times=0 |
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75 | RV ( Array<std::string> in_names ); |
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76 | //! Constructor of empty RV |
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77 | RV (); |
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78 | |
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79 | //! Printing output e.g. for debugging. |
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80 | friend std::ostream &operator<< ( std::ostream &os, const RV &rv ); |
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81 | |
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82 | //! Return number of scalars in the RV. |
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83 | int count() const {return tsize;} ; |
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84 | //! Return length (number of entries) of the RV. |
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85 | int length() const {return len;} ; |
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86 | |
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87 | //TODO why not inline and later?? |
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88 | |
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89 | //! Find indexes of self in another rv, \return ivec of the same size as self. |
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90 | ivec findself ( const RV &rv2 ) const; |
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91 | //! Compare if \c rv2 is identical to this \c RV |
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92 | bool equal ( const RV &rv2 ) const; |
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93 | //! Add (concat) another variable to the current one, \return true if all rv2 were added, false if rv2 is in conflict |
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94 | bool add ( const RV &rv2 ); |
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95 | //! Subtract another variable from the current one |
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96 | RV subt ( const RV &rv2 ) const; |
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97 | //! Select only variables at indeces ind |
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98 | RV subselect ( const ivec &ind ) const; |
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99 | //! Select only variables at indeces ind |
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100 | RV operator() ( const ivec &ind ) const; |
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101 | //! Shift \c time shifted by delta. |
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102 | void t ( int delta ); |
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103 | //! generate \c str from rv, by expanding sizes |
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104 | str tostr() const; |
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105 | //! when this rv is a part of bigger rv, this function returns indeces of self in the data vector of the bigger crv. |
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106 | //! Then, data can be copied via: data_of_this = cdata(ind); |
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107 | ivec dataind ( const RV &crv ) const; |
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108 | //! generate mutual indeces when copying data betwenn self and crv. |
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109 | //! Data are copied via: data_of_this(selfi) = data_of_rv2(rv2i) |
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110 | void dataind ( const RV &rv2, ivec &selfi, ivec &rv2i ) const; |
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111 | |
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112 | //!access function |
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113 | Array<std::string>& _names() {return names;}; |
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114 | |
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115 | //!access function |
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116 | int id ( int at ) {return ids ( at );}; |
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117 | //!access function |
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118 | int size ( int at ) {return sizes ( at );}; |
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119 | //!access function |
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120 | int time ( int at ) {return times ( at );}; |
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121 | //!access function |
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122 | std::string name ( int at ) {return names ( at );}; |
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123 | |
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124 | //!access function |
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125 | void set_id ( int at, int id0 ) {ids ( at ) =id0;}; |
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126 | //!access function |
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127 | void set_size ( int at, int size0 ) {sizes ( at ) =size0; tsize=sum ( sizes );}; |
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128 | //!access function |
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129 | void set_time ( int at, int time0 ) {times ( at ) =time0;}; |
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130 | |
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131 | //!Assign unused ids to this rv |
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132 | void newids(); |
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133 | }; |
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134 | |
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135 | //! Concat two random variables |
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136 | RV concat ( const RV &rv1, const RV &rv2 ); |
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137 | |
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138 | //!Default empty RV that can be used as default argument |
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139 | extern RV RV0; |
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140 | |
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141 | //! Class representing function \f$f(x)\f$ of variable \f$x\f$ represented by \c rv |
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142 | |
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143 | class fnc :public bdmroot{ |
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144 | protected: |
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145 | //! Length of the output vector |
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146 | int dimy; |
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147 | public: |
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148 | //!default constructor |
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149 | fnc ( int dy ) :dimy ( dy ) {}; |
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150 | //! function evaluates numerical value of \f$f(x)\f$ at \f$x=\f$ \c cond |
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151 | virtual vec eval ( const vec &cond ) { |
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152 | return vec ( 0 ); |
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153 | }; |
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154 | |
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155 | //! function substitutes given value into an appropriate position |
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156 | virtual void condition(const vec &val){}; |
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157 | |
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158 | //! access function |
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159 | int _dimy() const{return dimy;} |
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160 | |
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161 | //! Destructor for future use; |
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162 | virtual ~fnc() {}; |
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163 | }; |
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164 | |
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165 | class mpdf; |
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166 | |
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167 | //! Probability density function with numerical statistics, e.g. posterior density. |
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168 | |
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169 | class epdf :public bdmroot { |
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170 | protected: |
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171 | //! Identified of the random variable |
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172 | RV rv; |
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173 | public: |
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174 | //!default constructor |
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175 | epdf() :rv ( ) {}; |
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176 | |
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177 | //!default constructor |
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178 | epdf ( const RV &rv0 ) :rv ( rv0 ) {}; |
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179 | |
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180 | // //! Returns the required moment of the epdf |
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181 | // virtual vec moment ( const int order = 1 ); |
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182 | |
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183 | //! Returns a sample, \f$x\f$ from density \f$epdf(rv)\f$ |
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184 | virtual vec sample () const =0; |
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185 | //! Returns N samples from density \f$epdf(rv)\f$ |
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186 | virtual mat sample_m ( int N ) const; |
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187 | |
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188 | //! Compute log-probability of argument \c val |
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189 | virtual double evallog ( const vec &val ) const =0; |
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190 | |
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191 | //! Compute log-probability of multiple values argument \c val |
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192 | virtual vec evallog_m ( const mat &Val ) const { |
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193 | vec x ( Val.cols() ); |
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194 | for ( int i=0;i<Val.cols();i++ ) {x ( i ) =evallog ( Val.get_col ( i ) ) ;} |
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195 | return x; |
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196 | } |
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197 | //! Return conditional density on the given RV, the remaining rvs will be in conditioning |
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198 | virtual mpdf* condition ( const RV &rv ) const {it_warning ( "Not implemented" ); return NULL;} |
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199 | //! Return marginal density on the given RV, the remainig rvs are intergrated out |
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200 | virtual epdf* marginal ( const RV &rv ) const {it_warning ( "Not implemented" ); return NULL;} |
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201 | |
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202 | //! return expected value |
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203 | virtual vec mean() const =0; |
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204 | |
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205 | //! return expected variance (not covariance!) |
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206 | virtual vec variance() const = 0; |
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207 | |
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208 | //! Destructor for future use; |
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209 | virtual ~epdf() {}; |
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210 | //! access function, possibly dangerous! |
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211 | const RV& _rv() const {return rv;} |
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212 | //! modifier function - useful when copying epdfs |
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213 | void _renewrv ( const RV &in_rv ) {rv=in_rv;} |
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214 | //! |
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215 | }; |
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216 | |
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217 | |
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218 | //! Conditional probability density, e.g. modeling some dependencies. |
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219 | //TODO Samplecond can be generalized |
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220 | |
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221 | class mpdf : public bdmroot{ |
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222 | protected: |
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223 | //! modeled random variable |
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224 | RV rv; |
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225 | //! random variable in condition |
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226 | RV rvc; |
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227 | //! pointer to internal epdf |
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228 | epdf* ep; |
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229 | public: |
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230 | |
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231 | //! Returns a sample from the density conditioned on \c cond, \f$x \sim epdf(rv|cond)\f$. \param cond is numeric value of \c rv \param ll is a return value of log-likelihood of the sample. |
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232 | virtual vec samplecond ( const vec &cond, double &ll ) { |
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233 | this->condition ( cond ); |
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234 | vec temp= ep->sample(); |
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235 | ll=ep->evallog ( temp );return temp; |
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236 | }; |
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237 | //! Returns \param N samples from the density conditioned on \c cond, \f$x \sim epdf(rv|cond)\f$. \param cond is numeric value of \c rv \param ll is a return value of log-likelihood of the sample. |
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238 | virtual mat samplecond_m ( const vec &cond, vec &ll, int N ) { |
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239 | this->condition ( cond ); |
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240 | mat temp ( rv.count(),N ); vec smp ( rv.count() ); |
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241 | for ( int i=0;i<N;i++ ) {smp=ep->sample() ;temp.set_col ( i, smp );ll ( i ) =ep->evallog ( smp );} |
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242 | return temp; |
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243 | }; |
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244 | //! Update \c ep so that it represents this mpdf conditioned on \c rvc = cond |
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245 | virtual void condition ( const vec &cond ) {it_error ( "Not implemented" );}; |
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246 | |
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247 | //! Shortcut for conditioning and evaluation of the internal epdf. In some cases, this operation can be implemented efficiently. |
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248 | virtual double evallogcond ( const vec &dt, const vec &cond ) {double tmp; this->condition ( cond );tmp = ep->evallog ( dt ); it_assert_debug(std::isfinite(tmp),"Infinite value"); return tmp; |
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249 | }; |
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250 | |
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251 | //! Matrix version of evallogcond |
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252 | virtual vec evallogcond_m ( const mat &Dt, const vec &cond ) {this->condition ( cond );return ep->evallog_m ( Dt );}; |
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253 | |
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254 | //! Destructor for future use; |
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255 | virtual ~mpdf() {}; |
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256 | |
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257 | //! Default constructor |
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258 | mpdf ( const RV &rv0, const RV &rvc0 ) :rv ( rv0 ),rvc ( rvc0 ) {}; |
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259 | //! access function |
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260 | RV _rvc() const {return rvc;} |
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261 | //! access function |
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262 | RV _rv() const {return rv;} |
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263 | //!access function |
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264 | epdf& _epdf() {return *ep;} |
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265 | //!access function |
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266 | epdf* _e() {return ep;} |
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267 | }; |
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268 | |
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269 | //!DataLink is a connection between an epdf and its superordinate epdf (Up) |
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270 | //! It is assumed that my val is fully present in "Up" |
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271 | class datalink_e2e { |
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272 | protected: |
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273 | //! Remember how long val should be |
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274 | int valsize; |
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275 | //! Remember how long val of "Up" should be |
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276 | int valupsize; |
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277 | //! val-to-val link, indeces of the upper val |
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278 | ivec v2v_up; |
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279 | public: |
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280 | //! Constructor |
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281 | datalink_e2e ( const RV &rv, const RV &rv_up ) : |
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282 | valsize ( rv.count() ), valupsize ( rv_up.count() ), v2v_up ( rv.dataind ( rv_up ) ) { |
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283 | it_assert_debug ( v2v_up.length() ==valsize,"rv is not fully in rv_up" ); |
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284 | } |
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285 | //! Get val for myself from val of "Up" |
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286 | vec get_val ( const vec &val_up ) {it_assert_debug ( valupsize==val_up.length(),"Wrong val_up" ); return get_vec ( val_up,v2v_up );} |
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287 | //! Fill val of "Up" by my pieces |
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288 | void fill_val ( vec &val_up, const vec &val ) { |
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289 | it_assert_debug ( valsize==val.length(),"Wrong val" ); |
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290 | it_assert_debug ( valupsize==val_up.length(),"Wrong val_up" ); |
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291 | set_subvector ( val_up, v2v_up, val ); |
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292 | } |
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293 | }; |
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294 | |
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295 | //! data link between |
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296 | class datalink_m2e: public datalink_e2e { |
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297 | protected: |
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298 | //! Remember how long cond should be |
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299 | int condsize; |
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300 | //!upper_val-to-local_cond link, indeces of the upper val |
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301 | ivec v2c_up; |
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302 | //!upper_val-to-local_cond link, ideces of the local cond |
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303 | ivec v2c_lo; |
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304 | |
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305 | public: |
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306 | //! Constructor |
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307 | datalink_m2e ( const RV &rv, const RV &rvc, const RV &rv_up ) : |
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308 | datalink_e2e ( rv,rv_up ), condsize ( rvc.count() ) { |
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309 | //establish v2c connection |
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310 | rvc.dataind ( rv_up, v2c_lo, v2c_up ); |
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311 | } |
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312 | //!Construct condition |
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313 | vec get_cond ( const vec &val_up ) { |
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314 | vec tmp ( condsize ); |
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315 | set_subvector ( tmp,v2c_lo,val_up ( v2c_up ) ); |
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316 | return tmp; |
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317 | } |
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318 | void fill_val_cond ( vec &val_up, const vec &val, const vec &cond ) { |
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319 | it_assert_debug ( valsize==val.length(),"Wrong val" ); |
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320 | it_assert_debug ( valupsize==val_up.length(),"Wrong val_up" ); |
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321 | set_subvector ( val_up, v2v_up, val ); |
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322 | set_subvector ( val_up, v2c_up, cond ); |
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323 | } |
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324 | }; |
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325 | //!DataLink is a connection between mpdf and its superordinate (Up) |
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326 | //! This class links |
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327 | class datalink_m2m: public datalink_m2e { |
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328 | protected: |
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329 | //!cond-to-cond link, indeces of the upper cond |
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330 | ivec c2c_up; |
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331 | //!cond-to-cond link, indeces of the local cond |
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332 | ivec c2c_lo; |
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333 | public: |
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334 | //! Constructor |
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335 | datalink_m2m ( const RV &rv, const RV &rvc, const RV &rv_up, const RV &rvc_up ) : |
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336 | datalink_m2e ( rv, rvc, rv_up) { |
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337 | //establish c2c connection |
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338 | rvc.dataind ( rvc_up, c2c_lo, c2c_up ); |
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339 | it_assert_debug(c2c_lo.length()+v2c_lo.length()==condsize, "cond is not fully given"); |
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340 | } |
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341 | //! Get cond for myself from val and cond of "Up" |
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342 | vec get_cond ( const vec &val_up, const vec &cond_up ) { |
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343 | vec tmp ( condsize ); |
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344 | set_subvector ( tmp,v2c_lo,val_up ( v2c_up ) ); |
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345 | set_subvector ( tmp,c2c_lo,cond_up ( c2c_up ) ); |
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346 | return tmp; |
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347 | } |
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348 | //! Fill |
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349 | |
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350 | }; |
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351 | |
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352 | /*! \brief Unconditional mpdf, allows using epdf in the role of mpdf. |
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353 | |
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354 | */ |
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355 | class mepdf : public mpdf { |
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356 | public: |
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357 | //!Default constructor |
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358 | mepdf (const epdf* em ) :mpdf ( em->_rv(),RV() ) {ep=const_cast<epdf*>(em);}; |
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359 | void condition ( const vec &cond ) {} |
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360 | }; |
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361 | |
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362 | //!\brief Abstract composition of pdfs, will be used for specific classes |
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363 | //!this abstract class is common to epdf and mpdf |
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364 | class compositepdf { |
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365 | protected: |
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366 | //!Number of mpdfs in the composite |
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367 | int n; |
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368 | //! Elements of composition |
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369 | Array<mpdf*> mpdfs; |
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370 | public: |
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371 | compositepdf ( Array<mpdf*> A0 ) : n ( A0.length() ), mpdfs ( A0 ) {}; |
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372 | //! find common rv, flag \param checkoverlap modifies whether overlaps are acceptable |
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373 | RV getrv ( bool checkoverlap=false ); |
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374 | //! common rvc of all mpdfs is written to rvc |
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375 | void setrvc ( const RV &rv, RV &rvc ); |
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376 | }; |
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377 | |
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378 | /*! \brief Abstract class for discrete-time sources of data. |
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379 | |
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380 | The class abstracts operations of: (i) data aquisition, (ii) data-preprocessing, (iii) scaling of data, and (iv) data resampling from the task of estimation and control. |
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381 | Moreover, for controlled systems, it is able to receive the desired control action and perform it in the next step. (Or as soon as possible). |
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382 | |
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383 | */ |
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384 | |
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385 | class DS : public bdmroot{ |
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386 | protected: |
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387 | //!Observed variables, returned by \c getdata(). |
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388 | RV Drv; |
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389 | //!Action variables, accepted by \c write(). |
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390 | RV Urv; // |
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391 | public: |
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392 | DS():Drv(RV0),Urv(RV0) {}; |
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393 | //! Returns full vector of observed data |
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394 | void getdata ( vec &dt ); |
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395 | //! Returns data records at indeces. |
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396 | void getdata ( vec &dt, ivec &indeces ); |
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397 | //! Accepts action variable and schedule it for application. |
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398 | void write ( vec &ut ); |
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399 | //! Accepts action variables at specific indeces |
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400 | void write ( vec &ut, ivec &indeces ); |
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401 | /*! \brief Method that assigns random variables to the datasource. |
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402 | Typically, the datasource will be constructed without knowledge of random variables. This method will associate existing variables with RVs. |
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403 | |
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404 | (Inherited from m3k, may be deprecated soon). |
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405 | */ |
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406 | void linkrvs ( RV &drv, RV &urv ); |
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407 | |
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408 | //! Moves from \f$t\f$ to \f$t+1\f$, i.e. perfroms the actions and reads response of the system. |
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409 | void step(); |
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410 | |
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411 | }; |
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412 | |
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413 | /*! \brief Bayesian Model of the world, i.e. all uncertainty is modeled by probabilities. |
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414 | |
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415 | */ |
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416 | |
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417 | class BM :public bdmroot{ |
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418 | protected: |
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419 | //!Random variable of the posterior |
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420 | RV rv; |
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421 | //!Logarithm of marginalized data likelihood. |
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422 | double ll; |
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423 | //! If true, the filter will compute likelihood of the data record and store it in \c ll . Set to false if you want to save computational time. |
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424 | bool evalll; |
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425 | public: |
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426 | |
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427 | //!Default constructor |
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428 | BM ( const RV &rv0, double ll0=0,bool evalll0=true ) :rv ( rv0 ), ll ( ll0 ),evalll ( evalll0 ) {//Fixme: test rv |
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429 | }; |
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430 | //!Copy constructor |
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431 | BM ( const BM &B ) : rv ( B.rv ), ll ( B.ll ), evalll ( B.evalll ) {} |
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432 | |
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433 | /*! \brief Incremental Bayes rule |
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434 | @param dt vector of input data |
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435 | */ |
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436 | virtual void bayes ( const vec &dt ) = 0; |
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437 | //! Batch Bayes rule (columns of Dt are observations) |
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438 | virtual void bayesB ( const mat &Dt ); |
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439 | //! Returns a reference to the epdf representing posterior density on parameters. |
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440 | virtual const epdf& _epdf() const =0; |
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441 | |
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442 | //! Returns a pointer to the epdf representing posterior density on parameters. Use with care! |
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443 | virtual const epdf* _e() const =0; |
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444 | |
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445 | //! Evaluates predictive log-likelihood of the given data record |
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446 | //! I.e. marginal likelihood of the data with the posterior integrated out. |
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447 | virtual double logpred ( const vec &dt ) const{it_error ( "Not implemented" );return 0.0;} |
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448 | //! Matrix version of logpred |
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449 | vec logpred_m ( const mat &dt ) const{vec tmp ( dt.cols() );for ( int i=0;i<dt.cols();i++ ) {tmp ( i ) =logpred ( dt.get_col ( i ) );}return tmp;} |
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450 | |
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451 | //!Constructs a predictive density (marginal density on data) |
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452 | virtual epdf* predictor ( const RV &rv ) const {it_error ( "Not implemented" );return NULL;}; |
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453 | |
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454 | //! Destructor for future use; |
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455 | virtual ~BM() {}; |
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456 | //!access function |
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457 | const RV& _rv() const {return rv;} |
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458 | //!access function |
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459 | double _ll() const {return ll;} |
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460 | //!access function |
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461 | void set_evalll ( bool evl0 ) {evalll=evl0;} |
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462 | |
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463 | //! Copy function required in vectors, Arrays of BM etc. Have to be DELETED manually! |
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464 | //! Prototype: BM* _copy_(){BM Tmp*=new Tmp(this*); return Tmp; } |
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465 | virtual BM* _copy_ ( bool changerv=false ) {it_error ( "function _copy_ not implemented for this BM" ); return NULL;}; |
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466 | }; |
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467 | |
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468 | /*! |
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469 | \brief Conditional Bayesian Filter |
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470 | |
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471 | Evaluates conditional filtering density \f$f(rv|rvc,data)\f$ for a given \c rvc which is specified in each step by calling function \c condition. |
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472 | |
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473 | This is an interface class used to assure that certain BM has operation \c condition . |
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474 | |
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475 | */ |
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476 | |
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477 | class BMcond :public bdmroot{ |
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478 | protected: |
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479 | //! Identificator of the conditioning variable |
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480 | RV rvc; |
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481 | public: |
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482 | //! Substitute \c val for \c rvc. |
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483 | virtual void condition ( const vec &val ) =0; |
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484 | //! Default constructor |
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485 | BMcond ( RV &rv0 ) :rvc ( rv0 ) {}; |
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486 | //! Destructor for future use |
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487 | virtual ~BMcond() {}; |
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488 | //! access function |
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489 | const RV& _rvc() const {return rvc;} |
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490 | }; |
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491 | |
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492 | }; //namespace |
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493 | /*! @} */ |
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494 | #endif // BM_H |
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